state variables

[biplabbose@gmail.com]

Hi every one
In classical thermodynamics the four state variables are P, V, T and
composition. These are quite obvious for a system of Gases. However
what are the state variables for any non-gas system. For example, in
cases interaction between proteins or between protein and DNA.
With regards
Biplab

[Igor Khavkine]

biplabbose@gmail.com wrote:
> Hi every one
> In classical thermodynamics the four state variables are P, V, T and
> composition. These are quite obvious for a system of Gases. However
> what are the state variables for any non-gas system. For example, in
> cases interaction between proteins or between protein and DNA.

In general, the thermodynamic variables correspond to the possible ways
extracting or performing mechanical (or chemical) work on the system,
plus either entropy or temperature. The latter must always be included
to account for energy transfered through other than macroscopic
mechanical work or change in the number of particles.

The variables that you listed for the gas are familiar ones, but not
really independent. P and V cannot both be specified at the same time,
since they are thermodynamically conjugate (one corresponds to the work
needed to change the other by a given amount). To completely describe
the thermodynamic state, one needs to specify S, V, and N. Other sets
of state variables can be obtained by replacing any of the three by the
corresponding thermodynamic conjugate, respectively T, p, or mu.

As I said before, each of these variables corresponds to a means of
transfering energy from or to the system. The volume V corresponds to
mechanical compression or expansion of the gas. N corresponds to the
chemical energy of the system which can be changed by changing the
number of particles. And S corresponds to heat transfer, i.e. energy
that cannot be accessed by any other means.

For example, for an elastic solid, there is more than one way for it to
expand or to be compressed. So its volume alone is not an adequate
measure of how mechanical work can be performed on it. That's why one
introduces the elastic displacement tensor and the stress tensor which
is conjugate to it. Other examples include the polarization of
dielectrics which is conjugate to the electric field and magnetization
which is conjugate to the magnetic field.

Coming back to the example you seem to be interested in, a mixture of
interacting (reacting?) proteins and DNA. Since you have different
species of molecules which may undergo chemical reactions, you must
include their respective concentrations as state variables. Other than
that, as long as you can approximate the mixture as a homogeneous fluid
which is neither polarizable nor magnetizable (or equivalently with no
external electric or magnetic fields), your options for other state
variables are basically cut down to the same as the ideal gas.

What may be special about these organic molecules is that they have
extended shapes and their individual rotations may carry some overall
angular momentum, which will couple to the rate of rotation of the
fluid. But I don't think you'll see anything like this.

One more generalization you can introduce in the thermodynamics of
continua is the notion of local equilibrium. Any given fluid or solid
element of the system may be in equilibrium, while neighboring ones are
not. Strictly speaking, in this case the system is not in equilibrium,
but it can be assumed to be quasistatic if the global equilibration
time is much larger than the time scale you are interested in. So the
thermodynamic formalism will still apply. The only change necessary
will be the introduction of position dependence in all the state
variables.

Hope this helps.

Igor

[Igor Khavkine]

biplabbose@gmail.com wrote:
> Hi every one
> In classical thermodynamics the four state variables are P, V, T and
> composition. These are quite obvious for a system of Gases. However
> what are the state variables for any non-gas system. For example, in
> cases interaction between proteins or between protein and DNA.

In general, the thermodynamic variables correspond to the possible ways
extracting or performing mechanical (or chemical) work on the system,
plus either entropy or temperature. The latter must always be included
to account for energy transfered through other than macroscopic
mechanical work or change in the number of particles.

The variables that you listed for the gas are familiar ones, but not
really independent. P and V cannot both be specified at the same time,
since they are thermodynamically conjugate (one corresponds to the work
needed to change the other by a given amount). To completely describe
the thermodynamic state, one needs to specify S, V, and N. Other sets
of state variables can be obtained by replacing any of the three by the
corresponding thermodynamic conjugate, respectively T, p, or mu.

As I said before, each of these variables corresponds to a means of
transfering energy from or to the system. The volume V corresponds to
mechanical compression or expansion of the gas. N corresponds to the
chemical energy of the system which can be changed by changing the
number of particles. And S corresponds to heat transfer, i.e. energy
that cannot be accessed by any other means.

For example, for an elastic solid, there is more than one way for it to
expand or to be compressed. So its volume alone is not an adequate
measure of how mechanical work can be performed on it. That's why one
introduces the elastic displacement tensor and the stress tensor which
is conjugate to it. Other examples include the polarization of
dielectrics which is conjugate to the electric field and magnetization
which is conjugate to the magnetic field.

Coming back to the example you seem to be interested in, a mixture of
interacting (reacting?) proteins and DNA. Since you have different
species of molecules which may undergo chemical reactions, you must
include their respective concentrations as state variables. Other than
that, as long as you can approximate the mixture as a homogeneous fluid
which is neither polarizable nor magnetizable (or equivalently with no
external electric or magnetic fields), your options for other state
variables are basically cut down to the same as the ideal gas.

What may be special about these organic molecules is that they have
extended shapes and their individual rotations may carry some overall
angular momentum, which will couple to the rate of rotation of the
fluid. But I don't think you'll see anything like this.

One more generalization you can introduce in the thermodynamics of
continua is the notion of local equilibrium. Any given fluid or solid
element of the system may be in equilibrium, while neighboring ones are
not. Strictly speaking, in this case the system is not in equilibrium,
but it can be assumed to be quasistatic if the global equilibration
time is much larger than the time scale you are interested in. So the
thermodynamic formalism will still apply. The only change necessary
will be the introduction of position dependence in all the state
variables.

Hope this helps.

Igor

[Igor Khavkine]

biplabbose@gmail.com wrote:
> Hi every one
> In classical thermodynamics the four state variables are P, V, T and
> composition. These are quite obvious for a system of Gases. However
> what are the state variables for any non-gas system. For example, in
> cases interaction between proteins or between protein and DNA.

In general, the thermodynamic variables correspond to the possible ways
extracting or performing mechanical (or chemical) work on the system,
plus either entropy or temperature. The latter must always be included
to account for energy transfered through other than macroscopic
mechanical work or change in the number of particles.

The variables that you listed for the gas are familiar ones, but not
really independent. P and V cannot both be specified at the same time,
since they are thermodynamically conjugate (one corresponds to the work
needed to change the other by a given amount). To completely describe
the thermodynamic state, one needs to specify S, V, and N. Other sets
of state variables can be obtained by replacing any of the three by the
corresponding thermodynamic conjugate, respectively T, p, or mu.

As I said before, each of these variables corresponds to a means of
transfering energy from or to the system. The volume V corresponds to
mechanical compression or expansion of the gas. N corresponds to the
chemical energy of the system which can be changed by changing the
number of particles. And S corresponds to heat transfer, i.e. energy
that cannot be accessed by any other means.

For example, for an elastic solid, there is more than one way for it to
expand or to be compressed. So its volume alone is not an adequate
measure of how mechanical work can be performed on it. That's why one
introduces the elastic displacement tensor and the stress tensor which
is conjugate to it. Other examples include the polarization of
dielectrics which is conjugate to the electric field and magnetization
which is conjugate to the magnetic field.

Coming back to the example you seem to be interested in, a mixture of
interacting (reacting?) proteins and DNA. Since you have different
species of molecules which may undergo chemical reactions, you must
include their respective concentrations as state variables. Other than
that, as long as you can approximate the mixture as a homogeneous fluid
which is neither polarizable nor magnetizable (or equivalently with no
external electric or magnetic fields), your options for other state
variables are basically cut down to the same as the ideal gas.

What may be special about these organic molecules is that they have
extended shapes and their individual rotations may carry some overall
angular momentum, which will couple to the rate of rotation of the
fluid. But I don't think you'll see anything like this.

One more generalization you can introduce in the thermodynamics of
continua is the notion of local equilibrium. Any given fluid or solid
element of the system may be in equilibrium, while neighboring ones are
not. Strictly speaking, in this case the system is not in equilibrium,
but it can be assumed to be quasistatic if the global equilibration
time is much larger than the time scale you are interested in. So the
thermodynamic formalism will still apply. The only change necessary
will be the introduction of position dependence in all the state
variables.

Hope this helps.

Igor

[Igor Khavkine]

biplabbose@gmail.com wrote:
> Hi every one
> In classical thermodynamics the four state variables are P, V, T and
> composition. These are quite obvious for a system of Gases. However
> what are the state variables for any non-gas system. For example, in
> cases interaction between proteins or between protein and DNA.

In general, the thermodynamic variables correspond to the possible ways
extracting or performing mechanical (or chemical) work on the system,
plus either entropy or temperature. The latter must always be included
to account for energy transfered through other than macroscopic
mechanical work or change in the number of particles.

The variables that you listed for the gas are familiar ones, but not
really independent. P and V cannot both be specified at the same time,
since they are thermodynamically conjugate (one corresponds to the work
needed to change the other by a given amount). To completely describe
the thermodynamic state, one needs to specify S, V, and N. Other sets
of state variables can be obtained by replacing any of the three by the
corresponding thermodynamic conjugate, respectively T, p, or mu.

As I said before, each of these variables corresponds to a means of
transfering energy from or to the system. The volume V corresponds to
mechanical compression or expansion of the gas. N corresponds to the
chemical energy of the system which can be changed by changing the
number of particles. And S corresponds to heat transfer, i.e. energy
that cannot be accessed by any other means.

For example, for an elastic solid, there is more than one way for it to
expand or to be compressed. So its volume alone is not an adequate
measure of how mechanical work can be performed on it. That's why one
introduces the elastic displacement tensor and the stress tensor which
is conjugate to it. Other examples include the polarization of
dielectrics which is conjugate to the electric field and magnetization
which is conjugate to the magnetic field.

Coming back to the example you seem to be interested in, a mixture of
interacting (reacting?) proteins and DNA. Since you have different
species of molecules which may undergo chemical reactions, you must
include their respective concentrations as state variables. Other than
that, as long as you can approximate the mixture as a homogeneous fluid
which is neither polarizable nor magnetizable (or equivalently with no
external electric or magnetic fields), your options for other state
variables are basically cut down to the same as the ideal gas.

What may be special about these organic molecules is that they have
extended shapes and their individual rotations may carry some overall
angular momentum, which will couple to the rate of rotation of the
fluid. But I don't think you'll see anything like this.

One more generalization you can introduce in the thermodynamics of
continua is the notion of local equilibrium. Any given fluid or solid
element of the system may be in equilibrium, while neighboring ones are
not. Strictly speaking, in this case the system is not in equilibrium,
but it can be assumed to be quasistatic if the global equilibration
time is much larger than the time scale you are interested in. So the
thermodynamic formalism will still apply. The only change necessary
will be the introduction of position dependence in all the state
variables.

Hope this helps.

Igor

[Igor Khavkine]

biplabbose@gmail.com wrote:
> Hi every one
> In classical thermodynamics the four state variables are P, V, T and
> composition. These are quite obvious for a system of Gases. However
> what are the state variables for any non-gas system. For example, in
> cases interaction between proteins or between protein and DNA.

In general, the thermodynamic variables correspond to the possible ways
extracting or performing mechanical (or chemical) work on the system,
plus either entropy or temperature. The latter must always be included
to account for energy transfered through other than macroscopic
mechanical work or change in the number of particles.

The variables that you listed for the gas are familiar ones, but not
really independent. P and V cannot both be specified at the same time,
since they are thermodynamically conjugate (one corresponds to the work
needed to change the other by a given amount). To completely describe
the thermodynamic state, one needs to specify S, V, and N. Other sets
of state variables can be obtained by replacing any of the three by the
corresponding thermodynamic conjugate, respectively T, p, or mu.

As I said before, each of these variables corresponds to a means of
transfering energy from or to the system. The volume V corresponds to
mechanical compression or expansion of the gas. N corresponds to the
chemical energy of the system which can be changed by changing the
number of particles. And S corresponds to heat transfer, i.e. energy
that cannot be accessed by any other means.

For example, for an elastic solid, there is more than one way for it to
expand or to be compressed. So its volume alone is not an adequate
measure of how mechanical work can be performed on it. That's why one
introduces the elastic displacement tensor and the stress tensor which
is conjugate to it. Other examples include the polarization of
dielectrics which is conjugate to the electric field and magnetization
which is conjugate to the magnetic field.

Coming back to the example you seem to be interested in, a mixture of
interacting (reacting?) proteins and DNA. Since you have different
species of molecules which may undergo chemical reactions, you must
include their respective concentrations as state variables. Other than
that, as long as you can approximate the mixture as a homogeneous fluid
which is neither polarizable nor magnetizable (or equivalently with no
external electric or magnetic fields), your options for other state
variables are basically cut down to the same as the ideal gas.

What may be special about these organic molecules is that they have
extended shapes and their individual rotations may carry some overall
angular momentum, which will couple to the rate of rotation of the
fluid. But I don't think you'll see anything like this.

One more generalization you can introduce in the thermodynamics of
continua is the notion of local equilibrium. Any given fluid or solid
element of the system may be in equilibrium, while neighboring ones are
not. Strictly speaking, in this case the system is not in equilibrium,
but it can be assumed to be quasistatic if the global equilibration
time is much larger than the time scale you are interested in. So the
thermodynamic formalism will still apply. The only change necessary
will be the introduction of position dependence in all the state
variables.

Hope this helps.

Igor

[Igor Khavkine]

biplabbose@gmail.com wrote:
> Hi every one
> In classical thermodynamics the four state variables are P, V, T and
> composition. These are quite obvious for a system of Gases. However
> what are the state variables for any non-gas system. For example, in
> cases interaction between proteins or between protein and DNA.

In general, the thermodynamic variables correspond to the possible ways
extracting or performing mechanical (or chemical) work on the system,
plus either entropy or temperature. The latter must always be included
to account for energy transfered through other than macroscopic
mechanical work or change in the number of particles.

The variables that you listed for the gas are familiar ones, but not
really independent. P and V cannot both be specified at the same time,
since they are thermodynamically conjugate (one corresponds to the work
needed to change the other by a given amount). To completely describe
the thermodynamic state, one needs to specify S, V, and N. Other sets
of state variables can be obtained by replacing any of the three by the
corresponding thermodynamic conjugate, respectively T, p, or mu.

As I said before, each of these variables corresponds to a means of
transfering energy from or to the system. The volume V corresponds to
mechanical compression or expansion of the gas. N corresponds to the
chemical energy of the system which can be changed by changing the
number of particles. And S corresponds to heat transfer, i.e. energy
that cannot be accessed by any other means.

For example, for an elastic solid, there is more than one way for it to
expand or to be compressed. So its volume alone is not an adequate
measure of how mechanical work can be performed on it. That's why one
introduces the elastic displacement tensor and the stress tensor which
is conjugate to it. Other examples include the polarization of
dielectrics which is conjugate to the electric field and magnetization
which is conjugate to the magnetic field.

Coming back to the example you seem to be interested in, a mixture of
interacting (reacting?) proteins and DNA. Since you have different
species of molecules which may undergo chemical reactions, you must
include their respective concentrations as state variables. Other than
that, as long as you can approximate the mixture as a homogeneous fluid
which is neither polarizable nor magnetizable (or equivalently with no
external electric or magnetic fields), your options for other state
variables are basically cut down to the same as the ideal gas.

What may be special about these organic molecules is that they have
extended shapes and their individual rotations may carry some overall
angular momentum, which will couple to the rate of rotation of the
fluid. But I don't think you'll see anything like this.

One more generalization you can introduce in the thermodynamics of
continua is the notion of local equilibrium. Any given fluid or solid
element of the system may be in equilibrium, while neighboring ones are
not. Strictly speaking, in this case the system is not in equilibrium,
but it can be assumed to be quasistatic if the global equilibration
time is much larger than the time scale you are interested in. So the
thermodynamic formalism will still apply. The only change necessary
will be the introduction of position dependence in all the state
variables.

Hope this helps.

Igor

[Igor Khavkine]

biplabbose@gmail.com wrote:
> Hi every one
> In classical thermodynamics the four state variables are P, V, T and
> composition. These are quite obvious for a system of Gases. However
> what are the state variables for any non-gas system. For example, in
> cases interaction between proteins or between protein and DNA.

In general, the thermodynamic variables correspond to the possible ways
extracting or performing mechanical (or chemical) work on the system,
plus either entropy or temperature. The latter must always be included
to account for energy transfered through other than macroscopic
mechanical work or change in the number of particles.

The variables that you listed for the gas are familiar ones, but not
really independent. P and V cannot both be specified at the same time,
since they are thermodynamically conjugate (one corresponds to the work
needed to change the other by a given amount). To completely describe
the thermodynamic state, one needs to specify S, V, and N. Other sets
of state variables can be obtained by replacing any of the three by the
corresponding thermodynamic conjugate, respectively T, p, or mu.

As I said before, each of these variables corresponds to a means of
transfering energy from or to the system. The volume V corresponds to
mechanical compression or expansion of the gas. N corresponds to the
chemical energy of the system which can be changed by changing the
number of particles. And S corresponds to heat transfer, i.e. energy
that cannot be accessed by any other means.

For example, for an elastic solid, there is more than one way for it to
expand or to be compressed. So its volume alone is not an adequate
measure of how mechanical work can be performed on it. That's why one
introduces the elastic displacement tensor and the stress tensor which
is conjugate to it. Other examples include the polarization of
dielectrics which is conjugate to the electric field and magnetization
which is conjugate to the magnetic field.

Coming back to the example you seem to be interested in, a mixture of
interacting (reacting?) proteins and DNA. Since you have different
species of molecules which may undergo chemical reactions, you must
include their respective concentrations as state variables. Other than
that, as long as you can approximate the mixture as a homogeneous fluid
which is neither polarizable nor magnetizable (or equivalently with no
external electric or magnetic fields), your options for other state
variables are basically cut down to the same as the ideal gas.

What may be special about these organic molecules is that they have
extended shapes and their individual rotations may carry some overall
angular momentum, which will couple to the rate of rotation of the
fluid. But I don't think you'll see anything like this.

One more generalization you can introduce in the thermodynamics of
continua is the notion of local equilibrium. Any given fluid or solid
element of the system may be in equilibrium, while neighboring ones are
not. Strictly speaking, in this case the system is not in equilibrium,
but it can be assumed to be quasistatic if the global equilibration
time is much larger than the time scale you are interested in. So the
thermodynamic formalism will still apply. The only change necessary
will be the introduction of position dependence in all the state
variables.

Hope this helps.

Igor

[Igor Khavkine]

biplabbose@gmail.com wrote:
> Hi every one
> In classical thermodynamics the four state variables are P, V, T and
> composition. These are quite obvious for a system of Gases. However
> what are the state variables for any non-gas system. For example, in
> cases interaction between proteins or between protein and DNA.

In general, the thermodynamic variables correspond to the possible ways
extracting or performing mechanical (or chemical) work on the system,
plus either entropy or temperature. The latter must always be included
to account for energy transfered through other than macroscopic
mechanical work or change in the number of particles.

The variables that you listed for the gas are familiar ones, but not
really independent. P and V cannot both be specified at the same time,
since they are thermodynamically conjugate (one corresponds to the work
needed to change the other by a given amount). To completely describe
the thermodynamic state, one needs to specify S, V, and N. Other sets
of state variables can be obtained by replacing any of the three by the
corresponding thermodynamic conjugate, respectively T, p, or mu.

As I said before, each of these variables corresponds to a means of
transfering energy from or to the system. The volume V corresponds to
mechanical compression or expansion of the gas. N corresponds to the
chemical energy of the system which can be changed by changing the
number of particles. And S corresponds to heat transfer, i.e. energy
that cannot be accessed by any other means.

For example, for an elastic solid, there is more than one way for it to
expand or to be compressed. So its volume alone is not an adequate
measure of how mechanical work can be performed on it. That's why one
introduces the elastic displacement tensor and the stress tensor which
is conjugate to it. Other examples include the polarization of
dielectrics which is conjugate to the electric field and magnetization
which is conjugate to the magnetic field.

Coming back to the example you seem to be interested in, a mixture of
interacting (reacting?) proteins and DNA. Since you have different
species of molecules which may undergo chemical reactions, you must
include their respective concentrations as state variables. Other than
that, as long as you can approximate the mixture as a homogeneous fluid
which is neither polarizable nor magnetizable (or equivalently with no
external electric or magnetic fields), your options for other state
variables are basically cut down to the same as the ideal gas.

What may be special about these organic molecules is that they have
extended shapes and their individual rotations may carry some overall
angular momentum, which will couple to the rate of rotation of the
fluid. But I don't think you'll see anything like this.

One more generalization you can introduce in the thermodynamics of
continua is the notion of local equilibrium. Any given fluid or solid
element of the system may be in equilibrium, while neighboring ones are
not. Strictly speaking, in this case the system is not in equilibrium,
but it can be assumed to be quasistatic if the global equilibration
time is much larger than the time scale you are interested in. So the
thermodynamic formalism will still apply. The only change necessary
will be the introduction of position dependence in all the state
variables.

Hope this helps.

Igor

[Igor Khavkine]

biplabbose@gmail.com wrote:
> Hi every one
> In classical thermodynamics the four state variables are P, V, T and
> composition. These are quite obvious for a system of Gases. However
> what are the state variables for any non-gas system. For example, in
> cases interaction between proteins or between protein and DNA.

In general, the thermodynamic variables correspond to the possible ways
extracting or performing mechanical (or chemical) work on the system,
plus either entropy or temperature. The latter must always be included
to account for energy transfered through other than macroscopic
mechanical work or change in the number of particles.

The variables that you listed for the gas are familiar ones, but not
really independent. P and V cannot both be specified at the same time,
since they are thermodynamically conjugate (one corresponds to the work
needed to change the other by a given amount). To completely describe
the thermodynamic state, one needs to specify S, V, and N. Other sets
of state variables can be obtained by replacing any of the three by the
corresponding thermodynamic conjugate, respectively T, p, or mu.

As I said before, each of these variables corresponds to a means of
transfering energy from or to the system. The volume V corresponds to
mechanical compression or expansion of the gas. N corresponds to the
chemical energy of the system which can be changed by changing the
number of particles. And S corresponds to heat transfer, i.e. energy
that cannot be accessed by any other means.

For example, for an elastic solid, there is more than one way for it to
expand or to be compressed. So its volume alone is not an adequate
measure of how mechanical work can be performed on it. That's why one
introduces the elastic displacement tensor and the stress tensor which
is conjugate to it. Other examples include the polarization of
dielectrics which is conjugate to the electric field and magnetization
which is conjugate to the magnetic field.

Coming back to the example you seem to be interested in, a mixture of
interacting (reacting?) proteins and DNA. Since you have different
species of molecules which may undergo chemical reactions, you must
include their respective concentrations as state variables. Other than
that, as long as you can approximate the mixture as a homogeneous fluid
which is neither polarizable nor magnetizable (or equivalently with no
external electric or magnetic fields), your options for other state
variables are basically cut down to the same as the ideal gas.

What may be special about these organic molecules is that they have
extended shapes and their individual rotations may carry some overall
angular momentum, which will couple to the rate of rotation of the
fluid. But I don't think you'll see anything like this.

One more generalization you can introduce in the thermodynamics of
continua is the notion of local equilibrium. Any given fluid or solid
element of the system may be in equilibrium, while neighboring ones are
not. Strictly speaking, in this case the system is not in equilibrium,
but it can be assumed to be quasistatic if the global equilibration
time is much larger than the time scale you are interested in. So the
thermodynamic formalism will still apply. The only change necessary
will be the introduction of position dependence in all the state
variables.

Hope this helps.

Igor

[Collet Olivier - PERMANENT]

biplabbose@gmail.com wrote:

> Hi every one
> In classical thermodynamics the four state variables are P, V, T and
> composition. These are quite obvious for a system of Gases. However
> what are the state variables for any non-gas system. For example, in
> cases interaction between proteins or between protein and DNA.
> With regards
> Biplab

In thermodynamics, the four state variables are P, V, T and the entropy S
(!)

[Collet Olivier - PERMANENT]

biplabbose@gmail.com wrote:

> Hi every one
> In classical thermodynamics the four state variables are P, V, T and
> composition. These are quite obvious for a system of Gases. However
> what are the state variables for any non-gas system. For example, in
> cases interaction between proteins or between protein and DNA.
> With regards
> Biplab

In thermodynamics, the four state variables are P, V, T and the entropy S
(!)

[Collet Olivier - PERMANENT]

biplabbose@gmail.com wrote:

> Hi every one
> In classical thermodynamics the four state variables are P, V, T and
> composition. These are quite obvious for a system of Gases. However
> what are the state variables for any non-gas system. For example, in
> cases interaction between proteins or between protein and DNA.
> With regards
> Biplab

In thermodynamics, the four state variables are P, V, T and the entropy S
(!)

[Collet Olivier - PERMANENT]

biplabbose@gmail.com wrote:

> Hi every one
> In classical thermodynamics the four state variables are P, V, T and
> composition. These are quite obvious for a system of Gases. However
> what are the state variables for any non-gas system. For example, in
> cases interaction between proteins or between protein and DNA.
> With regards
> Biplab

In thermodynamics, the four state variables are P, V, T and the entropy S
(!)

[Collet Olivier - PERMANENT]

biplabbose@gmail.com wrote:

> Hi every one
> In classical thermodynamics the four state variables are P, V, T and
> composition. These are quite obvious for a system of Gases. However
> what are the state variables for any non-gas system. For example, in
> cases interaction between proteins or between protein and DNA.
> With regards
> Biplab

In thermodynamics, the four state variables are P, V, T and the entropy S
(!)

[Collet Olivier - PERMANENT]

biplabbose@gmail.com wrote:

> Hi every one
> In classical thermodynamics the four state variables are P, V, T and
> composition. These are quite obvious for a system of Gases. However
> what are the state variables for any non-gas system. For example, in
> cases interaction between proteins or between protein and DNA.
> With regards
> Biplab

In thermodynamics, the four state variables are P, V, T and the entropy S
(!)

[Collet Olivier - PERMANENT]

biplabbose@gmail.com wrote:

> Hi every one
> In classical thermodynamics the four state variables are P, V, T and
> composition. These are quite obvious for a system of Gases. However
> what are the state variables for any non-gas system. For example, in
> cases interaction between proteins or between protein and DNA.
> With regards
> Biplab

In thermodynamics, the four state variables are P, V, T and the entropy S
(!)

[Collet Olivier - PERMANENT]

biplabbose@gmail.com wrote:

> Hi every one
> In classical thermodynamics the four state variables are P, V, T and
> composition. These are quite obvious for a system of Gases. However
> what are the state variables for any non-gas system. For example, in
> cases interaction between proteins or between protein and DNA.
> With regards
> Biplab

In thermodynamics, the four state variables are P, V, T and the entropy S
(!)

[Collet Olivier - PERMANENT]

biplabbose@gmail.com wrote:

> Hi every one
> In classical thermodynamics the four state variables are P, V, T and
> composition. These are quite obvious for a system of Gases. However
> what are the state variables for any non-gas system. For example, in
> cases interaction between proteins or between protein and DNA.
> With regards
> Biplab

In thermodynamics, the four state variables are P, V, T and the entropy S
(!)

[Arnold Neumaier]

Igor Khavkine wrote:

> Coming back to the example you seem to be interested in, a mixture of
> interacting (reacting?) proteins and DNA. Since you have different
> species of molecules which may undergo chemical reactions, you must
> include their respective concentrations as state variables. Other than
> that, as long as you can approximate the mixture as a homogeneous fluid
> which is neither polarizable nor magnetizable (or equivalently with no
> external electric or magnetic fields), your options for other state
> variables are basically cut down to the same as the ideal gas.
>
> What may be special about these organic molecules is that they have
> extended shapes and their individual rotations may carry some overall
> angular momentum, which will couple to the rate of rotation of the
> fluid. But I don't think you'll see anything like this.

Of course one does. The shape and relative orientation of two colliding
molecules determines how likely it is that they react; so a
thermodynamic model must include this information. The thermodynamics of
proteins is quite complex because proteins are flexible molecules, so
many degrees of freedoms are needed for an adequate description.
Moreover, shape deformations are slow but not extremely slow,
so that proteins are usually only in local equilibrium, not in
true equilibrium. At least before they are boilt. In particular,
living matter depends on local equilibrium.


Arnold Neumaier

[Arnold Neumaier]

Igor Khavkine wrote:

> Coming back to the example you seem to be interested in, a mixture of
> interacting (reacting?) proteins and DNA. Since you have different
> species of molecules which may undergo chemical reactions, you must
> include their respective concentrations as state variables. Other than
> that, as long as you can approximate the mixture as a homogeneous fluid
> which is neither polarizable nor magnetizable (or equivalently with no
> external electric or magnetic fields), your options for other state
> variables are basically cut down to the same as the ideal gas.
>
> What may be special about these organic molecules is that they have
> extended shapes and their individual rotations may carry some overall
> angular momentum, which will couple to the rate of rotation of the
> fluid. But I don't think you'll see anything like this.

Of course one does. The shape and relative orientation of two colliding
molecules determines how likely it is that they react; so a
thermodynamic model must include this information. The thermodynamics of
proteins is quite complex because proteins are flexible molecules, so
many degrees of freedoms are needed for an adequate description.
Moreover, shape deformations are slow but not extremely slow,
so that proteins are usually only in local equilibrium, not in
true equilibrium. At least before they are boilt. In particular,
living matter depends on local equilibrium.


Arnold Neumaier

[Arnold Neumaier]

Igor Khavkine wrote:

> Coming back to the example you seem to be interested in, a mixture of
> interacting (reacting?) proteins and DNA. Since you have different
> species of molecules which may undergo chemical reactions, you must
> include their respective concentrations as state variables. Other than
> that, as long as you can approximate the mixture as a homogeneous fluid
> which is neither polarizable nor magnetizable (or equivalently with no
> external electric or magnetic fields), your options for other state
> variables are basically cut down to the same as the ideal gas.
>
> What may be special about these organic molecules is that they have
> extended shapes and their individual rotations may carry some overall
> angular momentum, which will couple to the rate of rotation of the
> fluid. But I don't think you'll see anything like this.

Of course one does. The shape and relative orientation of two colliding
molecules determines how likely it is that they react; so a
thermodynamic model must include this information. The thermodynamics of
proteins is quite complex because proteins are flexible molecules, so
many degrees of freedoms are needed for an adequate description.
Moreover, shape deformations are slow but not extremely slow,
so that proteins are usually only in local equilibrium, not in
true equilibrium. At least before they are boilt. In particular,
living matter depends on local equilibrium.


Arnold Neumaier

[Arnold Neumaier]

Igor Khavkine wrote:

> Coming back to the example you seem to be interested in, a mixture of
> interacting (reacting?) proteins and DNA. Since you have different
> species of molecules which may undergo chemical reactions, you must
> include their respective concentrations as state variables. Other than
> that, as long as you can approximate the mixture as a homogeneous fluid
> which is neither polarizable nor magnetizable (or equivalently with no
> external electric or magnetic fields), your options for other state
> variables are basically cut down to the same as the ideal gas.
>
> What may be special about these organic molecules is that they have
> extended shapes and their individual rotations may carry some overall
> angular momentum, which will couple to the rate of rotation of the
> fluid. But I don't think you'll see anything like this.

Of course one does. The shape and relative orientation of two colliding
molecules determines how likely it is that they react; so a
thermodynamic model must include this information. The thermodynamics of
proteins is quite complex because proteins are flexible molecules, so
many degrees of freedoms are needed for an adequate description.
Moreover, shape deformations are slow but not extremely slow,
so that proteins are usually only in local equilibrium, not in
true equilibrium. At least before they are boilt. In particular,
living matter depends on local equilibrium.


Arnold Neumaier

[Arnold Neumaier]

Igor Khavkine wrote:

> Coming back to the example you seem to be interested in, a mixture of
> interacting (reacting?) proteins and DNA. Since you have different
> species of molecules which may undergo chemical reactions, you must
> include their respective concentrations as state variables. Other than
> that, as long as you can approximate the mixture as a homogeneous fluid
> which is neither polarizable nor magnetizable (or equivalently with no
> external electric or magnetic fields), your options for other state
> variables are basically cut down to the same as the ideal gas.
>
> What may be special about these organic molecules is that they have
> extended shapes and their individual rotations may carry some overall
> angular momentum, which will couple to the rate of rotation of the
> fluid. But I don't think you'll see anything like this.

Of course one does. The shape and relative orientation of two colliding
molecules determines how likely it is that they react; so a
thermodynamic model must include this information. The thermodynamics of
proteins is quite complex because proteins are flexible molecules, so
many degrees of freedoms are needed for an adequate description.
Moreover, shape deformations are slow but not extremely slow,
so that proteins are usually only in local equilibrium, not in
true equilibrium. At least before they are boilt. In particular,
living matter depends on local equilibrium.


Arnold Neumaier

[Arnold Neumaier]

Igor Khavkine wrote:

> Coming back to the example you seem to be interested in, a mixture of
> interacting (reacting?) proteins and DNA. Since you have different
> species of molecules which may undergo chemical reactions, you must
> include their respective concentrations as state variables. Other than
> that, as long as you can approximate the mixture as a homogeneous fluid
> which is neither polarizable nor magnetizable (or equivalently with no
> external electric or magnetic fields), your options for other state
> variables are basically cut down to the same as the ideal gas.
>
> What may be special about these organic molecules is that they have
> extended shapes and their individual rotations may carry some overall
> angular momentum, which will couple to the rate of rotation of the
> fluid. But I don't think you'll see anything like this.

Of course one does. The shape and relative orientation of two colliding
molecules determines how likely it is that they react; so a
thermodynamic model must include this information. The thermodynamics of
proteins is quite complex because proteins are flexible molecules, so
many degrees of freedoms are needed for an adequate description.
Moreover, shape deformations are slow but not extremely slow,
so that proteins are usually only in local equilibrium, not in
true equilibrium. At least before they are boilt. In particular,
living matter depends on local equilibrium.


Arnold Neumaier

[Arnold Neumaier]

Igor Khavkine wrote:

> Coming back to the example you seem to be interested in, a mixture of
> interacting (reacting?) proteins and DNA. Since you have different
> species of molecules which may undergo chemical reactions, you must
> include their respective concentrations as state variables. Other than
> that, as long as you can approximate the mixture as a homogeneous fluid
> which is neither polarizable nor magnetizable (or equivalently with no
> external electric or magnetic fields), your options for other state
> variables are basically cut down to the same as the ideal gas.
>
> What may be special about these organic molecules is that they have
> extended shapes and their individual rotations may carry some overall
> angular momentum, which will couple to the rate of rotation of the
> fluid. But I don't think you'll see anything like this.

Of course one does. The shape and relative orientation of two colliding
molecules determines how likely it is that they react; so a
thermodynamic model must include this information. The thermodynamics of
proteins is quite complex because proteins are flexible molecules, so
many degrees of freedoms are needed for an adequate description.
Moreover, shape deformations are slow but not extremely slow,
so that proteins are usually only in local equilibrium, not in
true equilibrium. At least before they are boilt. In particular,
living matter depends on local equilibrium.


Arnold Neumaier

[Arnold Neumaier]

Igor Khavkine wrote:

> Coming back to the example you seem to be interested in, a mixture of
> interacting (reacting?) proteins and DNA. Since you have different
> species of molecules which may undergo chemical reactions, you must
> include their respective concentrations as state variables. Other than
> that, as long as you can approximate the mixture as a homogeneous fluid
> which is neither polarizable nor magnetizable (or equivalently with no
> external electric or magnetic fields), your options for other state
> variables are basically cut down to the same as the ideal gas.
>
> What may be special about these organic molecules is that they have
> extended shapes and their individual rotations may carry some overall
> angular momentum, which will couple to the rate of rotation of the
> fluid. But I don't think you'll see anything like this.

Of course one does. The shape and relative orientation of two colliding
molecules determines how likely it is that they react; so a
thermodynamic model must include this information. The thermodynamics of
proteins is quite complex because proteins are flexible molecules, so
many degrees of freedoms are needed for an adequate description.
Moreover, shape deformations are slow but not extremely slow,
so that proteins are usually only in local equilibrium, not in
true equilibrium. At least before they are boilt. In particular,
living matter depends on local equilibrium.


Arnold Neumaier

[Arnold Neumaier]

Igor Khavkine wrote:

> Coming back to the example you seem to be interested in, a mixture of
> interacting (reacting?) proteins and DNA. Since you have different
> species of molecules which may undergo chemical reactions, you must
> include their respective concentrations as state variables. Other than
> that, as long as you can approximate the mixture as a homogeneous fluid
> which is neither polarizable nor magnetizable (or equivalently with no
> external electric or magnetic fields), your options for other state
> variables are basically cut down to the same as the ideal gas.
>
> What may be special about these organic molecules is that they have
> extended shapes and their individual rotations may carry some overall
> angular momentum, which will couple to the rate of rotation of the
> fluid. But I don't think you'll see anything like this.

Of course one does. The shape and relative orientation of two colliding
molecules determines how likely it is that they react; so a
thermodynamic model must include this information. The thermodynamics of
proteins is quite complex because proteins are flexible molecules, so
many degrees of freedoms are needed for an adequate description.
Moreover, shape deformations are slow but not extremely slow,
so that proteins are usually only in local equilibrium, not in
true equilibrium. At least before they are boilt. In particular,
living matter depends on local equilibrium.


Arnold Neumaier

[Igor Khavkine]

Arnold Neumaier wrote:
> Igor Khavkine wrote:
>
> > Coming back to the example you seem to be interested in, a mixture of
> > interacting (reacting?) proteins and DNA. Since you have different
> > species of molecules which may undergo chemical reactions, you must
> > include their respective concentrations as state variables. Other than
> > that, as long as you can approximate the mixture as a homogeneous fluid
> > which is neither polarizable nor magnetizable (or equivalently with no
> > external electric or magnetic fields), your options for other state
> > variables are basically cut down to the same as the ideal gas.
> >
> > What may be special about these organic molecules is that they have
> > extended shapes and their individual rotations may carry some overall
> > angular momentum, which will couple to the rate of rotation of the
> > fluid. But I don't think you'll see anything like this.
>
> Of course one does. The shape and relative orientation of two colliding
> molecules determines how likely it is that they react; so a
> thermodynamic model must include this information. The thermodynamics of
> proteins is quite complex because proteins are flexible molecules, so
> many degrees of freedoms are needed for an adequate description.
> Moreover, shape deformations are slow but not extremely slow,
> so that proteins are usually only in local equilibrium, not in
> true equilibrium. At least before they are boilt. In particular,
> living matter depends on local equilibrium.

I was thinking of the system of proteins macroscopically as a
homogeneous/isotropic fluid. As you point out, that's probably wrong.

Out of curiosity, what kind of system does one usually have in mind
when talking about proteins? Single proteins? A macroscopically large
system of protein molecules, like some sort of fluid? Or a certain
concentration of protein molecules dissolved in another substance, such
as water for example? Each of these possibilities, I think, would
warrant a different thermodynamic description.

As you can tell by now, I don't know much about proteins. But I do know
a little bit about liquid crystals which are also composed of extended,
rod-like molecules. In the nematic phase, where the molecules align
along a particular axis, one must introduce another state variable
beside the usual ones of a fluid. The new variable is the orientation
of the alignment axis. Presumabely, something similar can be introduced
for proteins. But I'm not sure, specifically, what other kinds of state
variables can be introduced to take the extended nature of the
molecules into account.

Igor

[Igor Khavkine]

Arnold Neumaier wrote:
> Igor Khavkine wrote:
>
> > Coming back to the example you seem to be interested in, a mixture of
> > interacting (reacting?) proteins and DNA. Since you have different
> > species of molecules which may undergo chemical reactions, you must
> > include their respective concentrations as state variables. Other than
> > that, as long as you can approximate the mixture as a homogeneous fluid
> > which is neither polarizable nor magnetizable (or equivalently with no
> > external electric or magnetic fields), your options for other state
> > variables are basically cut down to the same as the ideal gas.
> >
> > What may be special about these organic molecules is that they have
> > extended shapes and their individual rotations may carry some overall
> > angular momentum, which will couple to the rate of rotation of the
> > fluid. But I don't think you'll see anything like this.
>
> Of course one does. The shape and relative orientation of two colliding
> molecules determines how likely it is that they react; so a
> thermodynamic model must include this information. The thermodynamics of
> proteins is quite complex because proteins are flexible molecules, so
> many degrees of freedoms are needed for an adequate description.
> Moreover, shape deformations are slow but not extremely slow,
> so that proteins are usually only in local equilibrium, not in
> true equilibrium. At least before they are boilt. In particular,
> living matter depends on local equilibrium.

I was thinking of the system of proteins macroscopically as a
homogeneous/isotropic fluid. As you point out, that's probably wrong.

Out of curiosity, what kind of system does one usually have in mind
when talking about proteins? Single proteins? A macroscopically large
system of protein molecules, like some sort of fluid? Or a certain
concentration of protein molecules dissolved in another substance, such
as water for example? Each of these possibilities, I think, would
warrant a different thermodynamic description.

As you can tell by now, I don't know much about proteins. But I do know
a little bit about liquid crystals which are also composed of extended,
rod-like molecules. In the nematic phase, where the molecules align
along a particular axis, one must introduce another state variable
beside the usual ones of a fluid. The new variable is the orientation
of the alignment axis. Presumabely, something similar can be introduced
for proteins. But I'm not sure, specifically, what other kinds of state
variables can be introduced to take the extended nature of the
molecules into account.

Igor

[Igor Khavkine]

Arnold Neumaier wrote:
> Igor Khavkine wrote:
>
> > Coming back to the example you seem to be interested in, a mixture of
> > interacting (reacting?) proteins and DNA. Since you have different
> > species of molecules which may undergo chemical reactions, you must
> > include their respective concentrations as state variables. Other than
> > that, as long as you can approximate the mixture as a homogeneous fluid
> > which is neither polarizable nor magnetizable (or equivalently with no
> > external electric or magnetic fields), your options for other state
> > variables are basically cut down to the same as the ideal gas.
> >
> > What may be special about these organic molecules is that they have
> > extended shapes and their individual rotations may carry some overall
> > angular momentum, which will couple to the rate of rotation of the
> > fluid. But I don't think you'll see anything like this.
>
> Of course one does. The shape and relative orientation of two colliding
> molecules determines how likely it is that they react; so a
> thermodynamic model must include this information. The thermodynamics of
> proteins is quite complex because proteins are flexible molecules, so
> many degrees of freedoms are needed for an adequate description.
> Moreover, shape deformations are slow but not extremely slow,
> so that proteins are usually only in local equilibrium, not in
> true equilibrium. At least before they are boilt. In particular,
> living matter depends on local equilibrium.

I was thinking of the system of proteins macroscopically as a
homogeneous/isotropic fluid. As you point out, that's probably wrong.

Out of curiosity, what kind of system does one usually have in mind
when talking about proteins? Single proteins? A macroscopically large
system of protein molecules, like some sort of fluid? Or a certain
concentration of protein molecules dissolved in another substance, such
as water for example? Each of these possibilities, I think, would
warrant a different thermodynamic description.

As you can tell by now, I don't know much about proteins. But I do know
a little bit about liquid crystals which are also composed of extended,
rod-like molecules. In the nematic phase, where the molecules align
along a particular axis, one must introduce another state variable
beside the usual ones of a fluid. The new variable is the orientation
of the alignment axis. Presumabely, something similar can be introduced
for proteins. But I'm not sure, specifically, what other kinds of state
variables can be introduced to take the extended nature of the
molecules into account.

Igor

[Igor Khavkine]

Arnold Neumaier wrote:
> Igor Khavkine wrote:
>
> > Coming back to the example you seem to be interested in, a mixture of
> > interacting (reacting?) proteins and DNA. Since you have different
> > species of molecules which may undergo chemical reactions, you must
> > include their respective concentrations as state variables. Other than
> > that, as long as you can approximate the mixture as a homogeneous fluid
> > which is neither polarizable nor magnetizable (or equivalently with no
> > external electric or magnetic fields), your options for other state
> > variables are basically cut down to the same as the ideal gas.
> >
> > What may be special about these organic molecules is that they have
> > extended shapes and their individual rotations may carry some overall
> > angular momentum, which will couple to the rate of rotation of the
> > fluid. But I don't think you'll see anything like this.
>
> Of course one does. The shape and relative orientation of two colliding
> molecules determines how likely it is that they react; so a
> thermodynamic model must include this information. The thermodynamics of
> proteins is quite complex because proteins are flexible molecules, so
> many degrees of freedoms are needed for an adequate description.
> Moreover, shape deformations are slow but not extremely slow,
> so that proteins are usually only in local equilibrium, not in
> true equilibrium. At least before they are boilt. In particular,
> living matter depends on local equilibrium.

I was thinking of the system of proteins macroscopically as a
homogeneous/isotropic fluid. As you point out, that's probably wrong.

Out of curiosity, what kind of system does one usually have in mind
when talking about proteins? Single proteins? A macroscopically large
system of protein molecules, like some sort of fluid? Or a certain
concentration of protein molecules dissolved in another substance, such
as water for example? Each of these possibilities, I think, would
warrant a different thermodynamic description.

As you can tell by now, I don't know much about proteins. But I do know
a little bit about liquid crystals which are also composed of extended,
rod-like molecules. In the nematic phase, where the molecules align
along a particular axis, one must introduce another state variable
beside the usual ones of a fluid. The new variable is the orientation
of the alignment axis. Presumabely, something similar can be introduced
for proteins. But I'm not sure, specifically, what other kinds of state
variables can be introduced to take the extended nature of the
molecules into account.

Igor

[Igor Khavkine]

Arnold Neumaier wrote:
> Igor Khavkine wrote:
>
> > Coming back to the example you seem to be interested in, a mixture of
> > interacting (reacting?) proteins and DNA. Since you have different
> > species of molecules which may undergo chemical reactions, you must
> > include their respective concentrations as state variables. Other than
> > that, as long as you can approximate the mixture as a homogeneous fluid
> > which is neither polarizable nor magnetizable (or equivalently with no
> > external electric or magnetic fields), your options for other state
> > variables are basically cut down to the same as the ideal gas.
> >
> > What may be special about these organic molecules is that they have
> > extended shapes and their individual rotations may carry some overall
> > angular momentum, which will couple to the rate of rotation of the
> > fluid. But I don't think you'll see anything like this.
>
> Of course one does. The shape and relative orientation of two colliding
> molecules determines how likely it is that they react; so a
> thermodynamic model must include this information. The thermodynamics of
> proteins is quite complex because proteins are flexible molecules, so
> many degrees of freedoms are needed for an adequate description.
> Moreover, shape deformations are slow but not extremely slow,
> so that proteins are usually only in local equilibrium, not in
> true equilibrium. At least before they are boilt. In particular,
> living matter depends on local equilibrium.

I was thinking of the system of proteins macroscopically as a
homogeneous/isotropic fluid. As you point out, that's probably wrong.

Out of curiosity, what kind of system does one usually have in mind
when talking about proteins? Single proteins? A macroscopically large
system of protein molecules, like some sort of fluid? Or a certain
concentration of protein molecules dissolved in another substance, such
as water for example? Each of these possibilities, I think, would
warrant a different thermodynamic description.

As you can tell by now, I don't know much about proteins. But I do know
a little bit about liquid crystals which are also composed of extended,
rod-like molecules. In the nematic phase, where the molecules align
along a particular axis, one must introduce another state variable
beside the usual ones of a fluid. The new variable is the orientation
of the alignment axis. Presumabely, something similar can be introduced
for proteins. But I'm not sure, specifically, what other kinds of state
variables can be introduced to take the extended nature of the
molecules into account.

Igor

[Igor Khavkine]

Arnold Neumaier wrote:
> Igor Khavkine wrote:
>
> > Coming back to the example you seem to be interested in, a mixture of
> > interacting (reacting?) proteins and DNA. Since you have different
> > species of molecules which may undergo chemical reactions, you must
> > include their respective concentrations as state variables. Other than
> > that, as long as you can approximate the mixture as a homogeneous fluid
> > which is neither polarizable nor magnetizable (or equivalently with no
> > external electric or magnetic fields), your options for other state
> > variables are basically cut down to the same as the ideal gas.
> >
> > What may be special about these organic molecules is that they have
> > extended shapes and their individual rotations may carry some overall
> > angular momentum, which will couple to the rate of rotation of the
> > fluid. But I don't think you'll see anything like this.
>
> Of course one does. The shape and relative orientation of two colliding
> molecules determines how likely it is that they react; so a
> thermodynamic model must include this information. The thermodynamics of
> proteins is quite complex because proteins are flexible molecules, so
> many degrees of freedoms are needed for an adequate description.
> Moreover, shape deformations are slow but not extremely slow,
> so that proteins are usually only in local equilibrium, not in
> true equilibrium. At least before they are boilt. In particular,
> living matter depends on local equilibrium.

I was thinking of the system of proteins macroscopically as a
homogeneous/isotropic fluid. As you point out, that's probably wrong.

Out of curiosity, what kind of system does one usually have in mind
when talking about proteins? Single proteins? A macroscopically large
system of protein molecules, like some sort of fluid? Or a certain
concentration of protein molecules dissolved in another substance, such
as water for example? Each of these possibilities, I think, would
warrant a different thermodynamic description.

As you can tell by now, I don't know much about proteins. But I do know
a little bit about liquid crystals which are also composed of extended,
rod-like molecules. In the nematic phase, where the molecules align
along a particular axis, one must introduce another state variable
beside the usual ones of a fluid. The new variable is the orientation
of the alignment axis. Presumabely, something similar can be introduced
for proteins. But I'm not sure, specifically, what other kinds of state
variables can be introduced to take the extended nature of the
molecules into account.

Igor

[Igor Khavkine]

Arnold Neumaier wrote:
> Igor Khavkine wrote:
>
> > Coming back to the example you seem to be interested in, a mixture of
> > interacting (reacting?) proteins and DNA. Since you have different
> > species of molecules which may undergo chemical reactions, you must
> > include their respective concentrations as state variables. Other than
> > that, as long as you can approximate the mixture as a homogeneous fluid
> > which is neither polarizable nor magnetizable (or equivalently with no
> > external electric or magnetic fields), your options for other state
> > variables are basically cut down to the same as the ideal gas.
> >
> > What may be special about these organic molecules is that they have
> > extended shapes and their individual rotations may carry some overall
> > angular momentum, which will couple to the rate of rotation of the
> > fluid. But I don't think you'll see anything like this.
>
> Of course one does. The shape and relative orientation of two colliding
> molecules determines how likely it is that they react; so a
> thermodynamic model must include this information. The thermodynamics of
> proteins is quite complex because proteins are flexible molecules, so
> many degrees of freedoms are needed for an adequate description.
> Moreover, shape deformations are slow but not extremely slow,
> so that proteins are usually only in local equilibrium, not in
> true equilibrium. At least before they are boilt. In particular,
> living matter depends on local equilibrium.

I was thinking of the system of proteins macroscopically as a
homogeneous/isotropic fluid. As you point out, that's probably wrong.

Out of curiosity, what kind of system does one usually have in mind
when talking about proteins? Single proteins? A macroscopically large
system of protein molecules, like some sort of fluid? Or a certain
concentration of protein molecules dissolved in another substance, such
as water for example? Each of these possibilities, I think, would
warrant a different thermodynamic description.

As you can tell by now, I don't know much about proteins. But I do know
a little bit about liquid crystals which are also composed of extended,
rod-like molecules. In the nematic phase, where the molecules align
along a particular axis, one must introduce another state variable
beside the usual ones of a fluid. The new variable is the orientation
of the alignment axis. Presumabely, something similar can be introduced
for proteins. But I'm not sure, specifically, what other kinds of state
variables can be introduced to take the extended nature of the
molecules into account.

Igor

[Igor Khavkine]

Arnold Neumaier wrote:
> Igor Khavkine wrote:
>
> > Coming back to the example you seem to be interested in, a mixture of
> > interacting (reacting?) proteins and DNA. Since you have different
> > species of molecules which may undergo chemical reactions, you must
> > include their respective concentrations as state variables. Other than
> > that, as long as you can approximate the mixture as a homogeneous fluid
> > which is neither polarizable nor magnetizable (or equivalently with no
> > external electric or magnetic fields), your options for other state
> > variables are basically cut down to the same as the ideal gas.
> >
> > What may be special about these organic molecules is that they have
> > extended shapes and their individual rotations may carry some overall
> > angular momentum, which will couple to the rate of rotation of the
> > fluid. But I don't think you'll see anything like this.
>
> Of course one does. The shape and relative orientation of two colliding
> molecules determines how likely it is that they react; so a
> thermodynamic model must include this information. The thermodynamics of
> proteins is quite complex because proteins are flexible molecules, so
> many degrees of freedoms are needed for an adequate description.
> Moreover, shape deformations are slow but not extremely slow,
> so that proteins are usually only in local equilibrium, not in
> true equilibrium. At least before they are boilt. In particular,
> living matter depends on local equilibrium.

I was thinking of the system of proteins macroscopically as a
homogeneous/isotropic fluid. As you point out, that's probably wrong.

Out of curiosity, what kind of system does one usually have in mind
when talking about proteins? Single proteins? A macroscopically large
system of protein molecules, like some sort of fluid? Or a certain
concentration of protein molecules dissolved in another substance, such
as water for example? Each of these possibilities, I think, would
warrant a different thermodynamic description.

As you can tell by now, I don't know much about proteins. But I do know
a little bit about liquid crystals which are also composed of extended,
rod-like molecules. In the nematic phase, where the molecules align
along a particular axis, one must introduce another state variable
beside the usual ones of a fluid. The new variable is the orientation
of the alignment axis. Presumabely, something similar can be introduced
for proteins. But I'm not sure, specifically, what other kinds of state
variables can be introduced to take the extended nature of the
molecules into account.

Igor

[Igor Khavkine]

Arnold Neumaier wrote:
> Igor Khavkine wrote:
>
> > Coming back to the example you seem to be interested in, a mixture of
> > interacting (reacting?) proteins and DNA. Since you have different
> > species of molecules which may undergo chemical reactions, you must
> > include their respective concentrations as state variables. Other than
> > that, as long as you can approximate the mixture as a homogeneous fluid
> > which is neither polarizable nor magnetizable (or equivalently with no
> > external electric or magnetic fields), your options for other state
> > variables are basically cut down to the same as the ideal gas.
> >
> > What may be special about these organic molecules is that they have
> > extended shapes and their individual rotations may carry some overall
> > angular momentum, which will couple to the rate of rotation of the
> > fluid. But I don't think you'll see anything like this.
>
> Of course one does. The shape and relative orientation of two colliding
> molecules determines how likely it is that they react; so a
> thermodynamic model must include this information. The thermodynamics of
> proteins is quite complex because proteins are flexible molecules, so
> many degrees of freedoms are needed for an adequate description.
> Moreover, shape deformations are slow but not extremely slow,
> so that proteins are usually only in local equilibrium, not in
> true equilibrium. At least before they are boilt. In particular,
> living matter depends on local equilibrium.

I was thinking of the system of proteins macroscopically as a
homogeneous/isotropic fluid. As you point out, that's probably wrong.

Out of curiosity, what kind of system does one usually have in mind
when talking about proteins? Single proteins? A macroscopically large
system of protein molecules, like some sort of fluid? Or a certain
concentration of protein molecules dissolved in another substance, such
as water for example? Each of these possibilities, I think, would
warrant a different thermodynamic description.

As you can tell by now, I don't know much about proteins. But I do know
a little bit about liquid crystals which are also composed of extended,
rod-like molecules. In the nematic phase, where the molecules align
along a particular axis, one must introduce another state variable
beside the usual ones of a fluid. The new variable is the orientation
of the alignment axis. Presumabely, something similar can be introduced
for proteins. But I'm not sure, specifically, what other kinds of state
variables can be introduced to take the extended nature of the
molecules into account.

Igor

[Arnold Neumaier]

Igor Khavkine wrote:
> Arnold Neumaier wrote:
>
>>Igor Khavkine wrote:
>>
>>
>>>Coming back to the example you seem to be interested in, a mixture of
>>>interacting (reacting?) proteins and DNA. Since you have different
>>>species of molecules which may undergo chemical reactions, you must
>>>include their respective concentrations as state variables. Other than
>>>that, as long as you can approximate the mixture as a homogeneous fluid
>>>which is neither polarizable nor magnetizable (or equivalently with no
>>>external electric or magnetic fields), your options for other state
>>>variables are basically cut down to the same as the ideal gas.
>>>
>>>What may be special about these organic molecules is that they have
>>>extended shapes and their individual rotations may carry some overall
>>>angular momentum, which will couple to the rate of rotation of the
>>>fluid. But I don't think you'll see anything like this.
>>
>>Of course one does. The shape and relative orientation of two colliding
>>molecules determines how likely it is that they react; so a
>>thermodynamic model must include this information. The thermodynamics of
>>proteins is quite complex because proteins are flexible molecules, so
>>many degrees of freedoms are needed for an adequate description.
>>Moreover, shape deformations are slow but not extremely slow,
>>so that proteins are usually only in local equilibrium, not in
>>true equilibrium. At least before they are boilt. In particular,
>>living matter depends on local equilibrium.
>
>
> I was thinking of the system of proteins macroscopically as a
> homogeneous/isotropic fluid. As you point out, that's probably wrong.
>
> Out of curiosity, what kind of system does one usually have in mind
> when talking about proteins? Single proteins? A macroscopically large
> system of protein molecules, like some sort of fluid? Or a certain
> concentration of protein molecules dissolved in another substance, such
> as water for example? Each of these possibilities, I think, would
> warrant a different thermodynamic description.
>
> As you can tell by now, I don't know much about proteins.

For single protein molecules, see, e.g., my survey
Molecular modeling of proteins and mathematical prediction of
protein structure,
SIAM Rev. 39 (1997), 407-460.
http://www.mat.univie.ac.at/~neum/papers.html#protein
They are usually not modelled in terms of thermodynamics but by
molecular modeling, with some thermodynamic add on to account for finite
temperature.

My description above was for proteins in solution, considered as a
fluid. Only on this level is local equilibrium appropriate. But on this
level, one cannot use the model of an isotropic fluid, which leads to
Newtonian behavior. Macromolecules are strongly non-Newtonian.

For the thermodynamics of complex fluids, see

Beris and Edwards
Thermodynamics of flowing systems with internal microstructure
New York 1994

Hans C. Oettinger
Beyond Equilibrium Thermodynamics
Wiley 2005


> But I do know
> a little bit about liquid crystals which are also composed of extended,
> rod-like molecules. In the nematic phase, where the molecules align
> along a particular axis, one must introduce another state variable
> beside the usual ones of a fluid. The new variable is the orientation
> of the alignment axis. Presumabely, something similar can be introduced
> for proteins.

Indeed. Liquid crystals are among the simplest complex fluids.
Proteins are much more complex.


> But I'm not sure, specifically, what other kinds of state
> variables can be introduced to take the extended nature of the
> molecules into account.

Basically, a sufficiently large set of torsion angles accounting for
nonrigidity, together with a (usually fixed) set of bond distances
and bond angles.


Arnold Neumaier

[Arnold Neumaier]

Igor Khavkine wrote:
> Arnold Neumaier wrote:
>
>>Igor Khavkine wrote:
>>
>>
>>>Coming back to the example you seem to be interested in, a mixture of
>>>interacting (reacting?) proteins and DNA. Since you have different
>>>species of molecules which may undergo chemical reactions, you must
>>>include their respective concentrations as state variables. Other than
>>>that, as long as you can approximate the mixture as a homogeneous fluid
>>>which is neither polarizable nor magnetizable (or equivalently with no
>>>external electric or magnetic fields), your options for other state
>>>variables are basically cut down to the same as the ideal gas.
>>>
>>>What may be special about these organic molecules is that they have
>>>extended shapes and their individual rotations may carry some overall
>>>angular momentum, which will couple to the rate of rotation of the
>>>fluid. But I don't think you'll see anything like this.
>>
>>Of course one does. The shape and relative orientation of two colliding
>>molecules determines how likely it is that they react; so a
>>thermodynamic model must include this information. The thermodynamics of
>>proteins is quite complex because proteins are flexible molecules, so
>>many degrees of freedoms are needed for an adequate description.
>>Moreover, shape deformations are slow but not extremely slow,
>>so that proteins are usually only in local equilibrium, not in
>>true equilibrium. At least before they are boilt. In particular,
>>living matter depends on local equilibrium.
>
>
> I was thinking of the system of proteins macroscopically as a
> homogeneous/isotropic fluid. As you point out, that's probably wrong.
>
> Out of curiosity, what kind of system does one usually have in mind
> when talking about proteins? Single proteins? A macroscopically large
> system of protein molecules, like some sort of fluid? Or a certain
> concentration of protein molecules dissolved in another substance, such
> as water for example? Each of these possibilities, I think, would
> warrant a different thermodynamic description.
>
> As you can tell by now, I don't know much about proteins.

For single protein molecules, see, e.g., my survey
Molecular modeling of proteins and mathematical prediction of
protein structure,
SIAM Rev. 39 (1997), 407-460.
http://www.mat.univie.ac.at/~neum/papers.html#protein
They are usually not modelled in terms of thermodynamics but by
molecular modeling, with some thermodynamic add on to account for finite
temperature.

My description above was for proteins in solution, considered as a
fluid. Only on this level is local equilibrium appropriate. But on this
level, one cannot use the model of an isotropic fluid, which leads to
Newtonian behavior. Macromolecules are strongly non-Newtonian.

For the thermodynamics of complex fluids, see

Beris and Edwards
Thermodynamics of flowing systems with internal microstructure
New York 1994

Hans C. Oettinger
Beyond Equilibrium Thermodynamics
Wiley 2005


> But I do know
> a little bit about liquid crystals which are also composed of extended,
> rod-like molecules. In the nematic phase, where the molecules align
> along a particular axis, one must introduce another state variable
> beside the usual ones of a fluid. The new variable is the orientation
> of the alignment axis. Presumabely, something similar can be introduced
> for proteins.

Indeed. Liquid crystals are among the simplest complex fluids.
Proteins are much more complex.


> But I'm not sure, specifically, what other kinds of state
> variables can be introduced to take the extended nature of the
> molecules into account.

Basically, a sufficiently large set of torsion angles accounting for
nonrigidity, together with a (usually fixed) set of bond distances
and bond angles.


Arnold Neumaier

[Arnold Neumaier]

Igor Khavkine wrote:
> Arnold Neumaier wrote:
>
>>Igor Khavkine wrote:
>>
>>
>>>Coming back to the example you seem to be interested in, a mixture of
>>>interacting (reacting?) proteins and DNA. Since you have different
>>>species of molecules which may undergo chemical reactions, you must
>>>include their respective concentrations as state variables. Other than
>>>that, as long as you can approximate the mixture as a homogeneous fluid
>>>which is neither polarizable nor magnetizable (or equivalently with no
>>>external electric or magnetic fields), your options for other state
>>>variables are basically cut down to the same as the ideal gas.
>>>
>>>What may be special about these organic molecules is that they have
>>>extended shapes and their individual rotations may carry some overall
>>>angular momentum, which will couple to the rate of rotation of the
>>>fluid. But I don't think you'll see anything like this.
>>
>>Of course one does. The shape and relative orientation of two colliding
>>molecules determines how likely it is that they react; so a
>>thermodynamic model must include this information. The thermodynamics of
>>proteins is quite complex because proteins are flexible molecules, so
>>many degrees of freedoms are needed for an adequate description.
>>Moreover, shape deformations are slow but not extremely slow,
>>so that proteins are usually only in local equilibrium, not in
>>true equilibrium. At least before they are boilt. In particular,
>>living matter depends on local equilibrium.
>
>
> I was thinking of the system of proteins macroscopically as a
> homogeneous/isotropic fluid. As you point out, that's probably wrong.
>
> Out of curiosity, what kind of system does one usually have in mind
> when talking about proteins? Single proteins? A macroscopically large
> system of protein molecules, like some sort of fluid? Or a certain
> concentration of protein molecules dissolved in another substance, such
> as water for example? Each of these possibilities, I think, would
> warrant a different thermodynamic description.
>
> As you can tell by now, I don't know much about proteins.

For single protein molecules, see, e.g., my survey
Molecular modeling of proteins and mathematical prediction of
protein structure,
SIAM Rev. 39 (1997), 407-460.
http://www.mat.univie.ac.at/~neum/papers.html#protein
They are usually not modelled in terms of thermodynamics but by
molecular modeling, with some thermodynamic add on to account for finite
temperature.

My description above was for proteins in solution, considered as a
fluid. Only on this level is local equilibrium appropriate. But on this
level, one cannot use the model of an isotropic fluid, which leads to
Newtonian behavior. Macromolecules are strongly non-Newtonian.

For the thermodynamics of complex fluids, see

Beris and Edwards
Thermodynamics of flowing systems with internal microstructure
New York 1994

Hans C. Oettinger
Beyond Equilibrium Thermodynamics
Wiley 2005


> But I do know
> a little bit about liquid crystals which are also composed of extended,
> rod-like molecules. In the nematic phase, where the molecules align
> along a particular axis, one must introduce another state variable
> beside the usual ones of a fluid. The new variable is the orientation
> of the alignment axis. Presumabely, something similar can be introduced
> for proteins.

Indeed. Liquid crystals are among the simplest complex fluids.
Proteins are much more complex.


> But I'm not sure, specifically, what other kinds of state
> variables can be introduced to take the extended nature of the
> molecules into account.

Basically, a sufficiently large set of torsion angles accounting for
nonrigidity, together with a (usually fixed) set of bond distances
and bond angles.


Arnold Neumaier

[Arnold Neumaier]

Igor Khavkine wrote:
> Arnold Neumaier wrote:
>
>>Igor Khavkine wrote:
>>
>>
>>>Coming back to the example you seem to be interested in, a mixture of
>>>interacting (reacting?) proteins and DNA. Since you have different
>>>species of molecules which may undergo chemical reactions, you must
>>>include their respective concentrations as state variables. Other than
>>>that, as long as you can approximate the mixture as a homogeneous fluid
>>>which is neither polarizable nor magnetizable (or equivalently with no
>>>external electric or magnetic fields), your options for other state
>>>variables are basically cut down to the same as the ideal gas.
>>>
>>>What may be special about these organic molecules is that they have
>>>extended shapes and their individual rotations may carry some overall
>>>angular momentum, which will couple to the rate of rotation of the
>>>fluid. But I don't think you'll see anything like this.
>>
>>Of course one does. The shape and relative orientation of two colliding
>>molecules determines how likely it is that they react; so a
>>thermodynamic model must include this information. The thermodynamics of
>>proteins is quite complex because proteins are flexible molecules, so
>>many degrees of freedoms are needed for an adequate description.
>>Moreover, shape deformations are slow but not extremely slow,
>>so that proteins are usually only in local equilibrium, not in
>>true equilibrium. At least before they are boilt. In particular,
>>living matter depends on local equilibrium.
>
>
> I was thinking of the system of proteins macroscopically as a
> homogeneous/isotropic fluid. As you point out, that's probably wrong.
>
> Out of curiosity, what kind of system does one usually have in mind
> when talking about proteins? Single proteins? A macroscopically large
> system of protein molecules, like some sort of fluid? Or a certain
> concentration of protein molecules dissolved in another substance, such
> as water for example? Each of these possibilities, I think, would
> warrant a different thermodynamic description.
>
> As you can tell by now, I don't know much about proteins.

For single protein molecules, see, e.g., my survey
Molecular modeling of proteins and mathematical prediction of
protein structure,
SIAM Rev. 39 (1997), 407-460.
http://www.mat.univie.ac.at/~neum/papers.html#protein
They are usually not modelled in terms of thermodynamics but by
molecular modeling, with some thermodynamic add on to account for finite
temperature.

My description above was for proteins in solution, considered as a
fluid. Only on this level is local equilibrium appropriate. But on this
level, one cannot use the model of an isotropic fluid, which leads to
Newtonian behavior. Macromolecules are strongly non-Newtonian.

For the thermodynamics of complex fluids, see

Beris and Edwards
Thermodynamics of flowing systems with internal microstructure
New York 1994

Hans C. Oettinger
Beyond Equilibrium Thermodynamics
Wiley 2005


> But I do know
> a little bit about liquid crystals which are also composed of extended,
> rod-like molecules. In the nematic phase, where the molecules align
> along a particular axis, one must introduce another state variable
> beside the usual ones of a fluid. The new variable is the orientation
> of the alignment axis. Presumabely, something similar can be introduced
> for proteins.

Indeed. Liquid crystals are among the simplest complex fluids.
Proteins are much more complex.


> But I'm not sure, specifically, what other kinds of state
> variables can be introduced to take the extended nature of the
> molecules into account.

Basically, a sufficiently large set of torsion angles accounting for
nonrigidity, together with a (usually fixed) set of bond distances
and bond angles.


Arnold Neumaier

[Arnold Neumaier]

Igor Khavkine wrote:
> Arnold Neumaier wrote:
>
>>Igor Khavkine wrote:
>>
>>
>>>Coming back to the example you seem to be interested in, a mixture of
>>>interacting (reacting?) proteins and DNA. Since you have different
>>>species of molecules which may undergo chemical reactions, you must
>>>include their respective concentrations as state variables. Other than
>>>that, as long as you can approximate the mixture as a homogeneous fluid
>>>which is neither polarizable nor magnetizable (or equivalently with no
>>>external electric or magnetic fields), your options for other state
>>>variables are basically cut down to the same as the ideal gas.
>>>
>>>What may be special about these organic molecules is that they have
>>>extended shapes and their individual rotations may carry some overall
>>>angular momentum, which will couple to the rate of rotation of the
>>>fluid. But I don't think you'll see anything like this.
>>
>>Of course one does. The shape and relative orientation of two colliding
>>molecules determines how likely it is that they react; so a
>>thermodynamic model must include this information. The thermodynamics of
>>proteins is quite complex because proteins are flexible molecules, so
>>many degrees of freedoms are needed for an adequate description.
>>Moreover, shape deformations are slow but not extremely slow,
>>so that proteins are usually only in local equilibrium, not in
>>true equilibrium. At least before they are boilt. In particular,
>>living matter depends on local equilibrium.
>
>
> I was thinking of the system of proteins macroscopically as a
> homogeneous/isotropic fluid. As you point out, that's probably wrong.
>
> Out of curiosity, what kind of system does one usually have in mind
> when talking about proteins? Single proteins? A macroscopically large
> system of protein molecules, like some sort of fluid? Or a certain
> concentration of protein molecules dissolved in another substance, such
> as water for example? Each of these possibilities, I think, would
> warrant a different thermodynamic description.
>
> As you can tell by now, I don't know much about proteins.

For single protein molecules, see, e.g., my survey
Molecular modeling of proteins and mathematical prediction of
protein structure,
SIAM Rev. 39 (1997), 407-460.
http://www.mat.univie.ac.at/~neum/papers.html#protein
They are usually not modelled in terms of thermodynamics but by
molecular modeling, with some thermodynamic add on to account for finite
temperature.

My description above was for proteins in solution, considered as a
fluid. Only on this level is local equilibrium appropriate. But on this
level, one cannot use the model of an isotropic fluid, which leads to
Newtonian behavior. Macromolecules are strongly non-Newtonian.

For the thermodynamics of complex fluids, see

Beris and Edwards
Thermodynamics of flowing systems with internal microstructure
New York 1994

Hans C. Oettinger
Beyond Equilibrium Thermodynamics
Wiley 2005


> But I do know
> a little bit about liquid crystals which are also composed of extended,
> rod-like molecules. In the nematic phase, where the molecules align
> along a particular axis, one must introduce another state variable
> beside the usual ones of a fluid. The new variable is the orientation
> of the alignment axis. Presumabely, something similar can be introduced
> for proteins.

Indeed. Liquid crystals are among the simplest complex fluids.
Proteins are much more complex.


> But I'm not sure, specifically, what other kinds of state
> variables can be introduced to take the extended nature of the
> molecules into account.

Basically, a sufficiently large set of torsion angles accounting for
nonrigidity, together with a (usually fixed) set of bond distances
and bond angles.


Arnold Neumaier

[Arnold Neumaier]

Igor Khavkine wrote:
> Arnold Neumaier wrote:
>
>>Igor Khavkine wrote:
>>
>>
>>>Coming back to the example you seem to be interested in, a mixture of
>>>interacting (reacting?) proteins and DNA. Since you have different
>>>species of molecules which may undergo chemical reactions, you must
>>>include their respective concentrations as state variables. Other than
>>>that, as long as you can approximate the mixture as a homogeneous fluid
>>>which is neither polarizable nor magnetizable (or equivalently with no
>>>external electric or magnetic fields), your options for other state
>>>variables are basically cut down to the same as the ideal gas.
>>>
>>>What may be special about these organic molecules is that they have
>>>extended shapes and their individual rotations may carry some overall
>>>angular momentum, which will couple to the rate of rotation of the
>>>fluid. But I don't think you'll see anything like this.
>>
>>Of course one does. The shape and relative orientation of two colliding
>>molecules determines how likely it is that they react; so a
>>thermodynamic model must include this information. The thermodynamics of
>>proteins is quite complex because proteins are flexible molecules, so
>>many degrees of freedoms are needed for an adequate description.
>>Moreover, shape deformations are slow but not extremely slow,
>>so that proteins are usually only in local equilibrium, not in
>>true equilibrium. At least before they are boilt. In particular,
>>living matter depends on local equilibrium.
>
>
> I was thinking of the system of proteins macroscopically as a
> homogeneous/isotropic fluid. As you point out, that's probably wrong.
>
> Out of curiosity, what kind of system does one usually have in mind
> when talking about proteins? Single proteins? A macroscopically large
> system of protein molecules, like some sort of fluid? Or a certain
> concentration of protein molecules dissolved in another substance, such
> as water for example? Each of these possibilities, I think, would
> warrant a different thermodynamic description.
>
> As you can tell by now, I don't know much about proteins.

For single protein molecules, see, e.g., my survey
Molecular modeling of proteins and mathematical prediction of
protein structure,
SIAM Rev. 39 (1997), 407-460.
http://www.mat.univie.ac.at/~neum/papers.html#protein
They are usually not modelled in terms of thermodynamics but by
molecular modeling, with some thermodynamic add on to account for finite
temperature.

My description above was for proteins in solution, considered as a
fluid. Only on this level is local equilibrium appropriate. But on this
level, one cannot use the model of an isotropic fluid, which leads to
Newtonian behavior. Macromolecules are strongly non-Newtonian.

For the thermodynamics of complex fluids, see

Beris and Edwards
Thermodynamics of flowing systems with internal microstructure
New York 1994

Hans C. Oettinger
Beyond Equilibrium Thermodynamics
Wiley 2005


> But I do know
> a little bit about liquid crystals which are also composed of extended,
> rod-like molecules. In the nematic phase, where the molecules align
> along a particular axis, one must introduce another state variable
> beside the usual ones of a fluid. The new variable is the orientation
> of the alignment axis. Presumabely, something similar can be introduced
> for proteins.

Indeed. Liquid crystals are among the simplest complex fluids.
Proteins are much more complex.


> But I'm not sure, specifically, what other kinds of state
> variables can be introduced to take the extended nature of the
> molecules into account.

Basically, a sufficiently large set of torsion angles accounting for
nonrigidity, together with a (usually fixed) set of bond distances
and bond angles.


Arnold Neumaier

[Arnold Neumaier]

Igor Khavkine wrote:
> Arnold Neumaier wrote:
>
>>Igor Khavkine wrote:
>>
>>
>>>Coming back to the example you seem to be interested in, a mixture of
>>>interacting (reacting?) proteins and DNA. Since you have different
>>>species of molecules which may undergo chemical reactions, you must
>>>include their respective concentrations as state variables. Other than
>>>that, as long as you can approximate the mixture as a homogeneous fluid
>>>which is neither polarizable nor magnetizable (or equivalently with no
>>>external electric or magnetic fields), your options for other state
>>>variables are basically cut down to the same as the ideal gas.
>>>
>>>What may be special about these organic molecules is that they have
>>>extended shapes and their individual rotations may carry some overall
>>>angular momentum, which will couple to the rate of rotation of the
>>>fluid. But I don't think you'll see anything like this.
>>
>>Of course one does. The shape and relative orientation of two colliding
>>molecules determines how likely it is that they react; so a
>>thermodynamic model must include this information. The thermodynamics of
>>proteins is quite complex because proteins are flexible molecules, so
>>many degrees of freedoms are needed for an adequate description.
>>Moreover, shape deformations are slow but not extremely slow,
>>so that proteins are usually only in local equilibrium, not in
>>true equilibrium. At least before they are boilt. In particular,
>>living matter depends on local equilibrium.
>
>
> I was thinking of the system of proteins macroscopically as a
> homogeneous/isotropic fluid. As you point out, that's probably wrong.
>
> Out of curiosity, what kind of system does one usually have in mind
> when talking about proteins? Single proteins? A macroscopically large
> system of protein molecules, like some sort of fluid? Or a certain
> concentration of protein molecules dissolved in another substance, such
> as water for example? Each of these possibilities, I think, would
> warrant a different thermodynamic description.
>
> As you can tell by now, I don't know much about proteins.

For single protein molecules, see, e.g., my survey
Molecular modeling of proteins and mathematical prediction of
protein structure,
SIAM Rev. 39 (1997), 407-460.
http://www.mat.univie.ac.at/~neum/papers.html#protein
They are usually not modelled in terms of thermodynamics but by
molecular modeling, with some thermodynamic add on to account for finite
temperature.

My description above was for proteins in solution, considered as a
fluid. Only on this level is local equilibrium appropriate. But on this
level, one cannot use the model of an isotropic fluid, which leads to
Newtonian behavior. Macromolecules are strongly non-Newtonian.

For the thermodynamics of complex fluids, see

Beris and Edwards
Thermodynamics of flowing systems with internal microstructure
New York 1994

Hans C. Oettinger
Beyond Equilibrium Thermodynamics
Wiley 2005


> But I do know
> a little bit about liquid crystals which are also composed of extended,
> rod-like molecules. In the nematic phase, where the molecules align
> along a particular axis, one must introduce another state variable
> beside the usual ones of a fluid. The new variable is the orientation
> of the alignment axis. Presumabely, something similar can be introduced
> for proteins.

Indeed. Liquid crystals are among the simplest complex fluids.
Proteins are much more complex.


> But I'm not sure, specifically, what other kinds of state
> variables can be introduced to take the extended nature of the
> molecules into account.

Basically, a sufficiently large set of torsion angles accounting for
nonrigidity, together with a (usually fixed) set of bond distances
and bond angles.


Arnold Neumaier

[Arnold Neumaier]

Igor Khavkine wrote:
> Arnold Neumaier wrote:
>
>>Igor Khavkine wrote:
>>
>>
>>>Coming back to the example you seem to be interested in, a mixture of
>>>interacting (reacting?) proteins and DNA. Since you have different
>>>species of molecules which may undergo chemical reactions, you must
>>>include their respective concentrations as state variables. Other than
>>>that, as long as you can approximate the mixture as a homogeneous fluid
>>>which is neither polarizable nor magnetizable (or equivalently with no
>>>external electric or magnetic fields), your options for other state
>>>variables are basically cut down to the same as the ideal gas.
>>>
>>>What may be special about these organic molecules is that they have
>>>extended shapes and their individual rotations may carry some overall
>>>angular momentum, which will couple to the rate of rotation of the
>>>fluid. But I don't think you'll see anything like this.
>>
>>Of course one does. The shape and relative orientation of two colliding
>>molecules determines how likely it is that they react; so a
>>thermodynamic model must include this information. The thermodynamics of
>>proteins is quite complex because proteins are flexible molecules, so
>>many degrees of freedoms are needed for an adequate description.
>>Moreover, shape deformations are slow but not extremely slow,
>>so that proteins are usually only in local equilibrium, not in
>>true equilibrium. At least before they are boilt. In particular,
>>living matter depends on local equilibrium.
>
>
> I was thinking of the system of proteins macroscopically as a
> homogeneous/isotropic fluid. As you point out, that's probably wrong.
>
> Out of curiosity, what kind of system does one usually have in mind
> when talking about proteins? Single proteins? A macroscopically large
> system of protein molecules, like some sort of fluid? Or a certain
> concentration of protein molecules dissolved in another substance, such
> as water for example? Each of these possibilities, I think, would
> warrant a different thermodynamic description.
>
> As you can tell by now, I don't know much about proteins.

For single protein molecules, see, e.g., my survey
Molecular modeling of proteins and mathematical prediction of
protein structure,
SIAM Rev. 39 (1997), 407-460.
http://www.mat.univie.ac.at/~neum/papers.html#protein
They are usually not modelled in terms of thermodynamics but by
molecular modeling, with some thermodynamic add on to account for finite
temperature.

My description above was for proteins in solution, considered as a
fluid. Only on this level is local equilibrium appropriate. But on this
level, one cannot use the model of an isotropic fluid, which leads to
Newtonian behavior. Macromolecules are strongly non-Newtonian.

For the thermodynamics of complex fluids, see

Beris and Edwards
Thermodynamics of flowing systems with internal microstructure
New York 1994

Hans C. Oettinger
Beyond Equilibrium Thermodynamics
Wiley 2005


> But I do know
> a little bit about liquid crystals which are also composed of extended,
> rod-like molecules. In the nematic phase, where the molecules align
> along a particular axis, one must introduce another state variable
> beside the usual ones of a fluid. The new variable is the orientation
> of the alignment axis. Presumabely, something similar can be introduced
> for proteins.

Indeed. Liquid crystals are among the simplest complex fluids.
Proteins are much more complex.


> But I'm not sure, specifically, what other kinds of state
> variables can be introduced to take the extended nature of the
> molecules into account.

Basically, a sufficiently large set of torsion angles accounting for
nonrigidity, together with a (usually fixed) set of bond distances
and bond angles.


Arnold Neumaier

[Arnold Neumaier]

Igor Khavkine wrote:
> Arnold Neumaier wrote:
>
>>Igor Khavkine wrote:
>>
>>
>>>Coming back to the example you seem to be interested in, a mixture of
>>>interacting (reacting?) proteins and DNA. Since you have different
>>>species of molecules which may undergo chemical reactions, you must
>>>include their respective concentrations as state variables. Other than
>>>that, as long as you can approximate the mixture as a homogeneous fluid
>>>which is neither polarizable nor magnetizable (or equivalently with no
>>>external electric or magnetic fields), your options for other state
>>>variables are basically cut down to the same as the ideal gas.
>>>
>>>What may be special about these organic molecules is that they have
>>>extended shapes and their individual rotations may carry some overall
>>>angular momentum, which will couple to the rate of rotation of the
>>>fluid. But I don't think you'll see anything like this.
>>
>>Of course one does. The shape and relative orientation of two colliding
>>molecules determines how likely it is that they react; so a
>>thermodynamic model must include this information. The thermodynamics of
>>proteins is quite complex because proteins are flexible molecules, so
>>many degrees of freedoms are needed for an adequate description.
>>Moreover, shape deformations are slow but not extremely slow,
>>so that proteins are usually only in local equilibrium, not in
>>true equilibrium. At least before they are boilt. In particular,
>>living matter depends on local equilibrium.
>
>
> I was thinking of the system of proteins macroscopically as a
> homogeneous/isotropic fluid. As you point out, that's probably wrong.
>
> Out of curiosity, what kind of system does one usually have in mind
> when talking about proteins? Single proteins? A macroscopically large
> system of protein molecules, like some sort of fluid? Or a certain
> concentration of protein molecules dissolved in another substance, such
> as water for example? Each of these possibilities, I think, would
> warrant a different thermodynamic description.
>
> As you can tell by now, I don't know much about proteins.

For single protein molecules, see, e.g., my survey
Molecular modeling of proteins and mathematical prediction of
protein structure,
SIAM Rev. 39 (1997), 407-460.
http://www.mat.univie.ac.at/~neum/papers.html#protein
They are usually not modelled in terms of thermodynamics but by
molecular modeling, with some thermodynamic add on to account for finite
temperature.

My description above was for proteins in solution, considered as a
fluid. Only on this level is local equilibrium appropriate. But on this
level, one cannot use the model of an isotropic fluid, which leads to
Newtonian behavior. Macromolecules are strongly non-Newtonian.

For the thermodynamics of complex fluids, see

Beris and Edwards
Thermodynamics of flowing systems with internal microstructure
New York 1994

Hans C. Oettinger
Beyond Equilibrium Thermodynamics
Wiley 2005


> But I do know
> a little bit about liquid crystals which are also composed of extended,
> rod-like molecules. In the nematic phase, where the molecules align
> along a particular axis, one must introduce another state variable
> beside the usual ones of a fluid. The new variable is the orientation
> of the alignment axis. Presumabely, something similar can be introduced
> for proteins.

Indeed. Liquid crystals are among the simplest complex fluids.
Proteins are much more complex.


> But I'm not sure, specifically, what other kinds of state
> variables can be introduced to take the extended nature of the
> molecules into account.

Basically, a sufficiently large set of torsion angles accounting for
nonrigidity, together with a (usually fixed) set of bond distances
and bond angles.


Arnold Neumaier

[Munir]

When talking about proteins and their interactions, it's important to
mention on what scale you're aiming to model them. Individual proteins
are huge (thousands of daltons), have several different stereochemical
forms, and hence different electrical, polar, and bonding site
behaviours based upon their current configuration.

Some physical chemists make a study of looking at a single type of
protein at small scale and developing thermodynamic models for the
changes in shape from one conformation to the next.

At a higher level, molecular biology people are less interested in this
than the reaction rates of a population of said protein or, more often,
a soup of various proteins that represent part of a biochemical
pathway. For this type of model, the different conformations of a
protein might be modeled as different populations such that P1a
(protein 1 in configuration a) is tracked separately from P1b (protein
1 in configuration b), etc., with some probability over time of P1a
turning into P1B (or vice-versa) due to a configuration change, or
other control.

This all relates to computer modeling of the situation. I usually work
from the target to the mathematical model to the simulation. My first
question for you, in creating a thermodynamically valid approach, would
be to ask you at what level you want to simulate or mathematically
model this system.

I'm not sure if this helps at all. But if it does, great!

-Munir

P.S. Check out the ERATO simulator at Caltech if you need a good
database and simulation system without starting from scratch.

P.P.S. The above discussion of different state variables being
thermodynamically complementary to each other is informative. Thanks
for a good and useful thread.

[Munir]

When talking about proteins and their interactions, it's important to
mention on what scale you're aiming to model them. Individual proteins
are huge (thousands of daltons), have several different stereochemical
forms, and hence different electrical, polar, and bonding site
behaviours based upon their current configuration.

Some physical chemists make a study of looking at a single type of
protein at small scale and developing thermodynamic models for the
changes in shape from one conformation to the next.

At a higher level, molecular biology people are less interested in this
than the reaction rates of a population of said protein or, more often,
a soup of various proteins that represent part of a biochemical
pathway. For this type of model, the different conformations of a
protein might be modeled as different populations such that P1a
(protein 1 in configuration a) is tracked separately from P1b (protein
1 in configuration b), etc., with some probability over time of P1a
turning into P1B (or vice-versa) due to a configuration change, or
other control.

This all relates to computer modeling of the situation. I usually work
from the target to the mathematical model to the simulation. My first
question for you, in creating a thermodynamically valid approach, would
be to ask you at what level you want to simulate or mathematically
model this system.

I'm not sure if this helps at all. But if it does, great!

-Munir

P.S. Check out the ERATO simulator at Caltech if you need a good
database and simulation system without starting from scratch.

P.P.S. The above discussion of different state variables being
thermodynamically complementary to each other is informative. Thanks
for a good and useful thread.

[Munir]

When talking about proteins and their interactions, it's important to
mention on what scale you're aiming to model them. Individual proteins
are huge (thousands of daltons), have several different stereochemical
forms, and hence different electrical, polar, and bonding site
behaviours based upon their current configuration.

Some physical chemists make a study of looking at a single type of
protein at small scale and developing thermodynamic models for the
changes in shape from one conformation to the next.

At a higher level, molecular biology people are less interested in this
than the reaction rates of a population of said protein or, more often,
a soup of various proteins that represent part of a biochemical
pathway. For this type of model, the different conformations of a
protein might be modeled as different populations such that P1a
(protein 1 in configuration a) is tracked separately from P1b (protein
1 in configuration b), etc., with some probability over time of P1a
turning into P1B (or vice-versa) due to a configuration change, or
other control.

This all relates to computer modeling of the situation. I usually work
from the target to the mathematical model to the simulation. My first
question for you, in creating a thermodynamically valid approach, would
be to ask you at what level you want to simulate or mathematically
model this system.

I'm not sure if this helps at all. But if it does, great!

-Munir

P.S. Check out the ERATO simulator at Caltech if you need a good
database and simulation system without starting from scratch.

P.P.S. The above discussion of different state variables being
thermodynamically complementary to each other is informative. Thanks
for a good and useful thread.

[Munir]

When talking about proteins and their interactions, it's important to
mention on what scale you're aiming to model them. Individual proteins
are huge (thousands of daltons), have several different stereochemical
forms, and hence different electrical, polar, and bonding site
behaviours based upon their current configuration.

Some physical chemists make a study of looking at a single type of
protein at small scale and developing thermodynamic models for the
changes in shape from one conformation to the next.

At a higher level, molecular biology people are less interested in this
than the reaction rates of a population of said protein or, more often,
a soup of various proteins that represent part of a biochemical
pathway. For this type of model, the different conformations of a
protein might be modeled as different populations such that P1a
(protein 1 in configuration a) is tracked separately from P1b (protein
1 in configuration b), etc., with some probability over time of P1a
turning into P1B (or vice-versa) due to a configuration change, or
other control.

This all relates to computer modeling of the situation. I usually work
from the target to the mathematical model to the simulation. My first
question for you, in creating a thermodynamically valid approach, would
be to ask you at what level you want to simulate or mathematically
model this system.

I'm not sure if this helps at all. But if it does, great!

-Munir

P.S. Check out the ERATO simulator at Caltech if you need a good
database and simulation system without starting from scratch.

P.P.S. The above discussion of different state variables being
thermodynamically complementary to each other is informative. Thanks
for a good and useful thread.

[Munir]

When talking about proteins and their interactions, it's important to
mention on what scale you're aiming to model them. Individual proteins
are huge (thousands of daltons), have several different stereochemical
forms, and hence different electrical, polar, and bonding site
behaviours based upon their current configuration.

Some physical chemists make a study of looking at a single type of
protein at small scale and developing thermodynamic models for the
changes in shape from one conformation to the next.

At a higher level, molecular biology people are less interested in this
than the reaction rates of a population of said protein or, more often,
a soup of various proteins that represent part of a biochemical
pathway. For this type of model, the different conformations of a
protein might be modeled as different populations such that P1a
(protein 1 in configuration a) is tracked separately from P1b (protein
1 in configuration b), etc., with some probability over time of P1a
turning into P1B (or vice-versa) due to a configuration change, or
other control.

This all relates to computer modeling of the situation. I usually work
from the target to the mathematical model to the simulation. My first
question for you, in creating a thermodynamically valid approach, would
be to ask you at what level you want to simulate or mathematically
model this system.

I'm not sure if this helps at all. But if it does, great!

-Munir

P.S. Check out the ERATO simulator at Caltech if you need a good
database and simulation system without starting from scratch.

P.P.S. The above discussion of different state variables being
thermodynamically complementary to each other is informative. Thanks
for a good and useful thread.

[Munir]

When talking about proteins and their interactions, it's important to
mention on what scale you're aiming to model them. Individual proteins
are huge (thousands of daltons), have several different stereochemical
forms, and hence different electrical, polar, and bonding site
behaviours based upon their current configuration.

Some physical chemists make a study of looking at a single type of
protein at small scale and developing thermodynamic models for the
changes in shape from one conformation to the next.

At a higher level, molecular biology people are less interested in this
than the reaction rates of a population of said protein or, more often,
a soup of various proteins that represent part of a biochemical
pathway. For this type of model, the different conformations of a
protein might be modeled as different populations such that P1a
(protein 1 in configuration a) is tracked separately from P1b (protein
1 in configuration b), etc., with some probability over time of P1a
turning into P1B (or vice-versa) due to a configuration change, or
other control.

This all relates to computer modeling of the situation. I usually work
from the target to the mathematical model to the simulation. My first
question for you, in creating a thermodynamically valid approach, would
be to ask you at what level you want to simulate or mathematically
model this system.

I'm not sure if this helps at all. But if it does, great!

-Munir

P.S. Check out the ERATO simulator at Caltech if you need a good
database and simulation system without starting from scratch.

P.P.S. The above discussion of different state variables being
thermodynamically complementary to each other is informative. Thanks
for a good and useful thread.

[Munir]

When talking about proteins and their interactions, it's important to
mention on what scale you're aiming to model them. Individual proteins
are huge (thousands of daltons), have several different stereochemical
forms, and hence different electrical, polar, and bonding site
behaviours based upon their current configuration.

Some physical chemists make a study of looking at a single type of
protein at small scale and developing thermodynamic models for the
changes in shape from one conformation to the next.

At a higher level, molecular biology people are less interested in this
than the reaction rates of a population of said protein or, more often,
a soup of various proteins that represent part of a biochemical
pathway. For this type of model, the different conformations of a
protein might be modeled as different populations such that P1a
(protein 1 in configuration a) is tracked separately from P1b (protein
1 in configuration b), etc., with some probability over time of P1a
turning into P1B (or vice-versa) due to a configuration change, or
other control.

This all relates to computer modeling of the situation. I usually work
from the target to the mathematical model to the simulation. My first
question for you, in creating a thermodynamically valid approach, would
be to ask you at what level you want to simulate or mathematically
model this system.

I'm not sure if this helps at all. But if it does, great!

-Munir

P.S. Check out the ERATO simulator at Caltech if you need a good
database and simulation system without starting from scratch.

P.P.S. The above discussion of different state variables being
thermodynamically complementary to each other is informative. Thanks
for a good and useful thread.

[Munir]

When talking about proteins and their interactions, it's important to
mention on what scale you're aiming to model them. Individual proteins
are huge (thousands of daltons), have several different stereochemical
forms, and hence different electrical, polar, and bonding site
behaviours based upon their current configuration.

Some physical chemists make a study of looking at a single type of
protein at small scale and developing thermodynamic models for the
changes in shape from one conformation to the next.

At a higher level, molecular biology people are less interested in this
than the reaction rates of a population of said protein or, more often,
a soup of various proteins that represent part of a biochemical
pathway. For this type of model, the different conformations of a
protein might be modeled as different populations such that P1a
(protein 1 in configuration a) is tracked separately from P1b (protein
1 in configuration b), etc., with some probability over time of P1a
turning into P1B (or vice-versa) due to a configuration change, or
other control.

This all relates to computer modeling of the situation. I usually work
from the target to the mathematical model to the simulation. My first
question for you, in creating a thermodynamically valid approach, would
be to ask you at what level you want to simulate or mathematically
model this system.

I'm not sure if this helps at all. But if it does, great!

-Munir

P.S. Check out the ERATO simulator at Caltech if you need a good
database and simulation system without starting from scratch.

P.P.S. The above discussion of different state variables being
thermodynamically complementary to each other is informative. Thanks
for a good and useful thread.

[Munir]

When talking about proteins and their interactions, it's important to
mention on what scale you're aiming to model them. Individual proteins
are huge (thousands of daltons), have several different stereochemical
forms, and hence different electrical, polar, and bonding site
behaviours based upon their current configuration.

Some physical chemists make a study of looking at a single type of
protein at small scale and developing thermodynamic models for the
changes in shape from one conformation to the next.

At a higher level, molecular biology people are less interested in this
than the reaction rates of a population of said protein or, more often,
a soup of various proteins that represent part of a biochemical
pathway. For this type of model, the different conformations of a
protein might be modeled as different populations such that P1a
(protein 1 in configuration a) is tracked separately from P1b (protein
1 in configuration b), etc., with some probability over time of P1a
turning into P1B (or vice-versa) due to a configuration change, or
other control.

This all relates to computer modeling of the situation. I usually work
from the target to the mathematical model to the simulation. My first
question for you, in creating a thermodynamically valid approach, would
be to ask you at what level you want to simulate or mathematically
model this system.

I'm not sure if this helps at all. But if it does, great!

-Munir

P.S. Check out the ERATO simulator at Caltech if you need a good
database and simulation system without starting from scratch.

P.P.S. The above discussion of different state variables being
thermodynamically complementary to each other is informative. Thanks
for a good and useful thread.

[Ralph Hartley]

Arnold Neumaier wrote:
> My description above was for proteins in solution, considered as a
> fluid. Only on this level is local equilibrium appropriate. But on this
> level, one cannot use the model of an isotropic fluid, which leads to
> Newtonian behavior. Macromolecules are strongly non-Newtonian.

If you are thinking about physiological conditions, things are worse
still. Many proteins do not function in solution, but are embedded in
membranes with different conditions on each side (e.g. ion pumps), or
bound in complexes with hundreds of proteins and other molecules (e.g.
ribosomes, chromosomes), or both.

Also, the thermodynamic approximation may not be very good. Some
molecules must exist in exact numbers (chromosomes again, one extra or
one missing is bad news), and a *single* molecule of some proteins (e.g.
ricin) will kill a cell.

Ralph Hartley

[Ralph Hartley]

Arnold Neumaier wrote:
> My description above was for proteins in solution, considered as a
> fluid. Only on this level is local equilibrium appropriate. But on this
> level, one cannot use the model of an isotropic fluid, which leads to
> Newtonian behavior. Macromolecules are strongly non-Newtonian.

If you are thinking about physiological conditions, things are worse
still. Many proteins do not function in solution, but are embedded in
membranes with different conditions on each side (e.g. ion pumps), or
bound in complexes with hundreds of proteins and other molecules (e.g.
ribosomes, chromosomes), or both.

Also, the thermodynamic approximation may not be very good. Some
molecules must exist in exact numbers (chromosomes again, one extra or
one missing is bad news), and a *single* molecule of some proteins (e.g.
ricin) will kill a cell.

Ralph Hartley

[Ralph Hartley]

Arnold Neumaier wrote:
> My description above was for proteins in solution, considered as a
> fluid. Only on this level is local equilibrium appropriate. But on this
> level, one cannot use the model of an isotropic fluid, which leads to
> Newtonian behavior. Macromolecules are strongly non-Newtonian.

If you are thinking about physiological conditions, things are worse
still. Many proteins do not function in solution, but are embedded in
membranes with different conditions on each side (e.g. ion pumps), or
bound in complexes with hundreds of proteins and other molecules (e.g.
ribosomes, chromosomes), or both.

Also, the thermodynamic approximation may not be very good. Some
molecules must exist in exact numbers (chromosomes again, one extra or
one missing is bad news), and a *single* molecule of some proteins (e.g.
ricin) will kill a cell.

Ralph Hartley

[Ralph Hartley]

Arnold Neumaier wrote:
> My description above was for proteins in solution, considered as a
> fluid. Only on this level is local equilibrium appropriate. But on this
> level, one cannot use the model of an isotropic fluid, which leads to
> Newtonian behavior. Macromolecules are strongly non-Newtonian.

If you are thinking about physiological conditions, things are worse
still. Many proteins do not function in solution, but are embedded in
membranes with different conditions on each side (e.g. ion pumps), or
bound in complexes with hundreds of proteins and other molecules (e.g.
ribosomes, chromosomes), or both.

Also, the thermodynamic approximation may not be very good. Some
molecules must exist in exact numbers (chromosomes again, one extra or
one missing is bad news), and a *single* molecule of some proteins (e.g.
ricin) will kill a cell.

Ralph Hartley

[Ralph Hartley]

Arnold Neumaier wrote:
> My description above was for proteins in solution, considered as a
> fluid. Only on this level is local equilibrium appropriate. But on this
> level, one cannot use the model of an isotropic fluid, which leads to
> Newtonian behavior. Macromolecules are strongly non-Newtonian.

If you are thinking about physiological conditions, things are worse
still. Many proteins do not function in solution, but are embedded in
membranes with different conditions on each side (e.g. ion pumps), or
bound in complexes with hundreds of proteins and other molecules (e.g.
ribosomes, chromosomes), or both.

Also, the thermodynamic approximation may not be very good. Some
molecules must exist in exact numbers (chromosomes again, one extra or
one missing is bad news), and a *single* molecule of some proteins (e.g.
ricin) will kill a cell.

Ralph Hartley

[Ralph Hartley]

Arnold Neumaier wrote:
> My description above was for proteins in solution, considered as a
> fluid. Only on this level is local equilibrium appropriate. But on this
> level, one cannot use the model of an isotropic fluid, which leads to
> Newtonian behavior. Macromolecules are strongly non-Newtonian.

If you are thinking about physiological conditions, things are worse
still. Many proteins do not function in solution, but are embedded in
membranes with different conditions on each side (e.g. ion pumps), or
bound in complexes with hundreds of proteins and other molecules (e.g.
ribosomes, chromosomes), or both.

Also, the thermodynamic approximation may not be very good. Some
molecules must exist in exact numbers (chromosomes again, one extra or
one missing is bad news), and a *single* molecule of some proteins (e.g.
ricin) will kill a cell.

Ralph Hartley

[Ralph Hartley]

Arnold Neumaier wrote:
> My description above was for proteins in solution, considered as a
> fluid. Only on this level is local equilibrium appropriate. But on this
> level, one cannot use the model of an isotropic fluid, which leads to
> Newtonian behavior. Macromolecules are strongly non-Newtonian.

If you are thinking about physiological conditions, things are worse
still. Many proteins do not function in solution, but are embedded in
membranes with different conditions on each side (e.g. ion pumps), or
bound in complexes with hundreds of proteins and other molecules (e.g.
ribosomes, chromosomes), or both.

Also, the thermodynamic approximation may not be very good. Some
molecules must exist in exact numbers (chromosomes again, one extra or
one missing is bad news), and a *single* molecule of some proteins (e.g.
ricin) will kill a cell.

Ralph Hartley

[Ralph Hartley]

Arnold Neumaier wrote:
> My description above was for proteins in solution, considered as a
> fluid. Only on this level is local equilibrium appropriate. But on this
> level, one cannot use the model of an isotropic fluid, which leads to
> Newtonian behavior. Macromolecules are strongly non-Newtonian.

If you are thinking about physiological conditions, things are worse
still. Many proteins do not function in solution, but are embedded in
membranes with different conditions on each side (e.g. ion pumps), or
bound in complexes with hundreds of proteins and other molecules (e.g.
ribosomes, chromosomes), or both.

Also, the thermodynamic approximation may not be very good. Some
molecules must exist in exact numbers (chromosomes again, one extra or
one missing is bad news), and a *single* molecule of some proteins (e.g.
ricin) will kill a cell.

Ralph Hartley

[Ralph Hartley]

Arnold Neumaier wrote:
> My description above was for proteins in solution, considered as a
> fluid. Only on this level is local equilibrium appropriate. But on this
> level, one cannot use the model of an isotropic fluid, which leads to
> Newtonian behavior. Macromolecules are strongly non-Newtonian.

If you are thinking about physiological conditions, things are worse
still. Many proteins do not function in solution, but are embedded in
membranes with different conditions on each side (e.g. ion pumps), or
bound in complexes with hundreds of proteins and other molecules (e.g.
ribosomes, chromosomes), or both.

Also, the thermodynamic approximation may not be very good. Some
molecules must exist in exact numbers (chromosomes again, one extra or
one missing is bad news), and a *single* molecule of some proteins (e.g.
ricin) will kill a cell.

Ralph Hartley