How molecular interactions are modeled

[Q_Goest]

This animation is amazing! It shows molecular interactions between DNA and other molecules.
http://uk.youtube.com/watch?v=4PKjF7OumYo&feature=related

How do you think they were able to get the information to create this animation? The molecular interactions could be mathematically modeled I suppose, or perhaps the animation relies on some experimental testing. I’d guess it’s a bit of both, but I’d be interested to hear if anyone has an idea how it might have been done.

 

[Ygggdrasil]

Most of the interactions are known based on x-ray crystalographic studies of the structures of various protein/DNA complexes. Throughout the years, researchers have captured these complexes in various intermediate states allowing people like Drew Barry to imagine the motions of these proteins. However, a lot of the dynamics of these processes (e.g. the actual motions that the proteins make during catalysis) remain unknown and are an active area of research. Some of these processes have been modeled computationally using molecular dynamics, but these simulations generally can simulate only a few nanoseconds worth of time, so we lack the computational ability to examine the motions of most proteins during their catalysis.

But yes, the animations are great and they highlight just how amazing enzymes are.

 

[Q_Goest]

Thanks Ygggdrasil,
Never heard of http://www.google.com/search?hl=en&q=x-ray+crystallography+", but I did look it up. So if these molecules were examined using x-ray crystallography, would the molecules need to be removed from the cell? If not, if still in the cell, would the cell still be alive, do you know? Thanks again for the responce.

 

[Ygggdrasil]

Yes, to solve the structure of a biomolecule using x-ray crystallography, researchers must remove the molecule from the cell. In general, people will engineer bacteria to produce a lot of their protein of interest and then purify their protein from a large culture of the engineered bacteria. Although the protein is not in its native environment, most proteins will retain their characteristic shape upon crystallization. Of course, there are examples in the literature where crystallized proteins adopt folds or conformations that are purely artifacts of crystallization, but most researchers will test whether their structure represents a functionally relevant form of the protein by performing some biochemistry/cell biology to examine the protein in a cellular environment.

The only good way of imaging live cells is currently light microscopy (specifically, fluorescence microscopy). However, the resolution limit of light microscopy (~200nm) is not sufficient to look at the details of molecular interactions (proteins are ~1-10nm in diameter) or molecular structure (features as small as 0.1nm).

 

[Charion]

The only good way of imaging live cells is currently light microscopy (specifically, fluorescence microscopy). However, the resolution limit of light microscopy (~200nm) is not sufficient to look at the details of molecular interactions (proteins are ~1-10nm in diameter) or molecular structure (features as small as 0.1nm).

Well, and atomic force microscopy (resolution of around 1 nm). However here you are limited to visualizing surfaces.

 

[Andy Resnick]

I'll just point out that x-ray crystallographic methods (and many other methods such as cryo-EM) only work for *soluable* proteins. Membrane proteins (receptors, channels, etc) cannot be used with x-ray crystallography. There has been some NMR work with membrane proteins, but solving the structure is extremely difficult. In addition, many proteins have disordered domains in addition to ordered domains. Finally, many proteins undergo modification (prenylation, phosphoylation, glycolation, etc) to alter their function. In summary, determination of the structure of a protein is highly non-trivial.

Understanding even if two proteins associate with each other is tricky and requires several different methods to ensure the results are artifact-free. Those computer animations are great and impressive, but also contain a lot of creative licence-specifically, the dynamics.

 

[Q_Goest]

Thanks for the responce folks. I guess what I'm hearing is that the method used is primarily empirical with potentially some minor amount of analytical analysis.

The entire flik represents a long series of interactions which from what I'm hearing, isn't something that has been 'seen' (x-ray crystallography doesn't take video, does it?) Doesn't x-ray crystallography only capture a single or very small number of interactions? The film would then have to piece together the information created by these individual experiments to create the model portrayed.

 

[Ygggdrasil]

X-ray crystallography does work on membrane proteins. My former lab did membrane protein crystallography. Membrane proteins are much, much harder to crystallize than soluble proteins, but it is still doable. Several examples of famous membrane proteins that have been crystallized are the potassium channel (for which Rod MacKinnon won the 2003 Nobel prize in chemistry), aquaporins (Peter Agre, also a recpient of the 2003 Nobel prize in chemistry), and GPCRs (bacteriorhodopsin and more recently, the beta-adrenergic receptor). Most crystallographic studies of membrane proteins, however, have focused on the soluble portions of the receptors, for example, examining the extracellular ligand binding domain of a single-pass receptor isolated from the transmembrane domain. Also, EM methods also work for membrane proteins (electron crystallography), which has been very successful in elucidating the structure of nicotinic acetylcholine receptors, along with other membrane protein. But, Andy's point is valid; protein structure determination is not easy.

Crystallography cannot take video. By its nature, crystallography can only look at static pictures. One can try to piece together static images of proteins in different intermediate states (e.g. by trapping the protein in an intermediate state using a chemical inhibitor), but crystallographic techniques cannot show one how the transitions between these intermediate states occurs. Such studies, however, are not trivial and it can take decades to piece together the relevant intermediates along an important catalytic or regulatory step.

Furthermore, as Q_Goest mentioned, crystallography can only capture a small number of interactions. For example, in the movie on transcription, no one has ever solved the structure of the entire replication complex (furthermore, the structures of some of the components, lack high resolution structures). So, yes, the movie pieces together decades worth of structural and biochemical information to summarize our understanding of molecular biology. No one method could give us all the information contained in the movie. Biologists need to use a variety of tools, some of which can analyze a large amount of proteins performing a certain task but lack spatial and temporal resolution (traditional biochemistry), others which give high spatial resolution give only static pictures (crystallography), and newer methods which can give insights into dynamics but rely on results from the two previous methods (single molecule methods).

 

[Q_Goest]

Thanks again. Now that I understand the basics of the modeling technique, I wonder how reasonable it is and to what degree does our understanding suffer due to the classical mechanical scale analogies used.

We often substitute analogies for reality (ex: the solar system for atoms) knowing such metaphors are only an aid to understanding. In the case of this movie, it starts with DNA being “fibers” and “threads” and talks about “machines” spinning “like a jet engine”. There’s a “blue molecule” racing along the DNA (4:00 minutes in), unzipping and copying the strand, sucking in yellow molecules through an “intake hole”. This RNA strand then leaves the nucleus to have a “molecular factory” (ribosome) lock onto it and we find yet another assembly line that cranks out proteins.

If you watch, there are molecules on flight paths that appear less than haphazard. I’m assuming these flight paths are guided primarily by electrical interactions between the molecules, though I have no idea if that’s a reasonable interpretation of this model.

All these dynamics are of course, molecular (ie: quantum) level. However, the movie uses classical scale metaphors to aid in understanding. That’s all well and good, and I can’t knock WEHI (movie’s creator) for this. The end result is exceptional as an aid to understanding the molecular interactions at play.

The real question I have is, how does the model portrayed (ie: using classical mechanical metaphors) compare to reality? What fundamental differences might there be between the reality of quantum mechanical interactions and the classical scale metaphors that could adversely affect our understanding of these reactions? Are these metaphors perfectly acceptable such that we don’t loose any understanding? Or is this model so imperfect that our understanding of the various processes suffers?

 

[Ygggdrasil]

That's a really great question. Proteins are large enough that quantum effects can generally be ignored. However, the movie does simplify the physics of really nano-scale systems in a few ways. Although the movie tries to show this with some of the random wriggling of the molecules, Brownian motion and diffusion are the main forces that bring interacting molecules together. All these interactions are occurring in cells that have a fairly high concentration of electrolytes. Under these conditions, electrostatic forces are pretty well shielded, so electrostatics have effects at only relatively short distances (the Bjerrum length is probably less than a nanometer).

Another thing that the movie does not show well is how crowded the cell really is. The cell is very densely packed with proteins which is in stark contrast to the picture of these relatively isolated enzymes that the movie shows.

The movie also shows the enzymes moving along at relatively constant rates whereas in reality, each step occurs stochastically (e.g. they need to wait until diffusion brings a substrate to the enzyme). This fact has been verified experimentally with a number of biological enzymes.

Finally, at the length scales pictured here and in a relatively viscous fluid, mechanics works very differently. Since we are fairly large and move through a very nonviscous fluid (air), we tend to focus on the effects of intertia and ignore friction and viscosity. However, these molecules and even organisms as large as bacteria live in a low Reynolds number world where the situation is reversed; at low Reynolds number, viscosity and diffusion dominate and inertia can safely be ignored. An interesting discussion of just how different mechanics is in this type of environment, look up the classic biophysics paper entitled "Life at Low Reynolds Number" by E.M. Purcell (doi: 10.1119/1.10903). Another striking example of the counterintuitive laws governing low Reynolds number mechanics can be found at post 832 of thechemblog.com, which shows that you can actually mix and unmix fluids at low Reynolds number. (unfortunately, physics forum will not allow me to post links yet so you'll have to look these up for yourself).

 

[Gokul43201]

Welcome to PF yggdrasil. There's a 15 post minimum for posting links (to keep spammers out). Hope you stick around here!

 

[Q_Goest]

Yes, where’s my manners? Welcome to the board!

Your links:
http://jilawww.colorado.edu/perkinsgroup/Purcell_life_at_low_reynolds_number.pdf"
http://www.thechemblog.com/?p=832"

You make some excellent points, especially the cell being crowded and diffusion bringing molecules together which seems to be a main point Purcell is making. The paradigm that quantum mechanical interactions are unnecessary for understanding these molecular interactions I’m assuming is widely accepted. Or is it?

http://www.pnas.org/cgi/reprint/97/1/32.pdf"argues for organizing principals at the mesoscopic scale and cites protein folding as an example. McFadden argues that quantum mechanics plays a key role in the origin and evolution of life. A number of arguments come to mind that leave me wondering whether the paradigm of quantum mechanical interactions being unnecessary is really valid. Just what those interactions might be, I’m not sure.

I wonder, what are the issues around the classical versus quantum mechanical models of these molecular interactions?

 

[Mike H]

Some points in no particular order...

1.) For something like protein folding, what are the main determinants of the thermodynamics of that process? Typically (and to be very simplistic about it), one has hydrophobic interactions, hydrogen bonding, and electrostatics all competing against conformational entropy. Using molecular dynamics is a pretty sensible route given that these are the major players at work here.

2.) Having said that, it's pretty much the reality for all of these MD force fields to use the results of quantum mechanical calculations of small molecule model compounds Imagine trying to quantum mechanically simulate translation with all of those atoms with our current computational capabilities. Gives me a headache just thinking about it. But with high-quality calculations of individual base pairs or small stretches of nucleic acid that are fed into a force field (or whatever your fancy), it becomes a far more tenable situation.

3.) Of course, for things like actual chemistry (bonds breaking, bonds forming), a quantum mechanical treatment is necessary. Here is where things like combined quantum mechanical/molecular mechanical methods are useful, where the active site is modeled quantum mechanically, while the rest of the system is modeled classically.

I would say you need both, depending on what you're looking at in particular. Sometimes one can see, very clearly, that simple classical or semi-classical notions and thermodynamics will be adequate. Other times, especially where one is doing actual chemistry, quantum mechanics are essential.

 

[Q_Goest]

Yep... that makes a lot of sense. Thanks Mike.

 

[Ygggdrasil]

Quantum mechanics certainly underlies many of the processes in biology. After all, cells are made of molecules and are just chemical systems, so they should obey all of the principles governing chemical systems. For example, molecular interactions are governed by the law of mass action. This law (at least for large ensembles) defines an equilibrium constant that governs the strength of intermolecular interactions, such as the interactions between proteins. As you may know, equilibrium constants can be calculated from partition functions - which are based in quantum mechanics. So, quantum mechanics does play a fundamental role in understanding molecular interactions in biology. However, I agree with Mike; it is very difficult to get meaningful results from an application of quantum mechanics to large, complex biological systems. In practice, treating the systems classically when possible can give meaningful results that are close enough to reality.

Also, just a small point, while molecular dynamics simulations are certainly useful for studying protein folding, the long timescale required for the folding of even a small protein are hard to achieve in an MD experiment. The most protein folding simulations apply Monte-Carlo methods to search for the free energy minimum of the polypeptide chain, which in most cases corresponds to the native fold of the protein. While these MC methods do not provide good insights into the kinetics of the process, they have helped to contribute some insight into folding pathways and transition states in the folding process.

Following up on Mike's point #3, a great example of the utility of combining quantum mechanical and molecular mechanical methods comes from two recently published protein engineering studies from the Baker Lab (doi:10.1126/science.1152692, 10.1038/nature06879). Here, they computationally designed two enzymes with catalytic functions not described in any other enzyme. To design the active sites of these enzymes, they employed quantum mechanical calculations, but to design the rest of the enzyme, they used classical molecular mechanical calculations. The fact that these researchers needed quantum chemical calculations to design the active site really emphasizes Mike's point that quantum mechanics becomes essential when doing actual chemistry.

 

[Mike H]

Two other points that may be of interest...

Quantum mechanical treatments for computer simulations also becomes important when you're dealing with metals, especially transition metals. One of the underappreciated facts in biology and biochemistry (in my observations, at least) is that there are a number of proteins and enzymes that use metals as cofactors in one form or another.

Also, when we talk about treating a system or some part of a system quantum mechanically, there are a number of methods actually used by theorists to do the QM modeling. It can range from relatively straightforward semi-empirical methods to density functional theory methods to the Hartree-Fock scheme to others. Even here, there is a lot of discussion about the best way to go about implementing it (preferred functionals for DFT studies, what kinds of basis sets to use, and so on). I've noticed that this point sometimes flies underneath the radar of a number of people - it's not as if there's only one way to implement quantum mechanical calculations. I'm not sure how much play these realities get outside of the computational chemistry/biochemistry/biophysics field.

 

[maverick_starstrider]

These simulations always look so fake to me (as a computational physicist). Since everything involved in this 'simulation' is just a molecule then the over all behaviour we observe will be an EMERGENT phenomena from sheer random motion with short and long range interactions This video is so ordered as everything beautifully coils in unison with no random variation and such. Not to mention all the molecules appear to be little balls. I'd guess that this is 90% CGI art based on a rough experimental guess about how this kind of stuff happens.

 

[maverick_starstrider]

I mean those DNA polymerase just motor on over to the DNA and attach itself. I'm not a biologist (although I dabbled in undergrad) but would not the attaching of a polymerase to an origin occur from a fortuitious random collision at the right angle as they just bounce around aimlessly?

 

[maverick_starstrider]

Look at something like this:

http://uk.youtube.com/watch?v=gmjLXrMaFTg&feature=related

Which is just water freezing. The structuring is something that EMERGES from randomness. The water molecules don't just mozy on over to another one an attach themselves and then they head off together on an adventure to find a third one and then a fourth... It's order from seeming chaos

 

[Andy Resnick]

My problem with all of these MD simulations is that they simply mirror whatever assumptions were put into them-they are not predictive in any sense of the word. With sufficient tweaking, any desired behavior or property can be generated.

That in itself isn't a problem, since the problems that can be modeled are sufficiently complex to resist analytic expression. The problem is when "results" of a MD simulation are used as evidence of "understanding" an unsolved problem when in fact, no understanding at all has been generated: can anyone tell the effect of perturbing the MD system? Or must yet more simulations be run (with yet more useless papers generated)?

 

[maverick_starstrider]

Well, the work I do which is in computation quantum many-body stuff, it is absolutely predictive. You know what the short and long-range interactions of the individual constituents are (from quantum mechanics) and you just model many of these particles and then you can investigate how emergent phenomena form (a phenomena where a system displays a certain property which its individual components do not have but 'emerges' from the collective behaviour of the individual constituents). For example, in the video I posted where you see symmetry breaking (a phase transition to a more ordered phase) occur.

 

[Mike H]

These simulations always look so fake to me (as a computational physicist). Since everything involved in this 'simulation' is just a molecule then the over all behaviour we observe will be an EMERGENT phenomena from sheer random motion with short and long range interactions This video is so ordered as everything beautifully coils in unison with no random variation and such. Not to mention all the molecules appear to be little balls. I'd guess that this is 90% CGI art based on a rough experimental guess about how this kind of stuff happens.

That's because the YouTube video in the original post is an animation of multiple biological processes and not a simulation. An actual MD simulation of a protein/biological macromolecular assembly looks more like the YouTube video you posted of water freezing. You wait and see if, for instance, a loop suggested in regulating the activity of the protein being studied in the MD simulation does in fact adopt multiple conformations when a ligand is bound.

Perhaps the point could have been made more explicit that the discussion of different simulation/computational/theoretical techniques is not *truly* reflected in the original animation, but I figured we all knew that.

Replication actually involves a whole boatload of proteins, but I can't remember them all, so it's not just a lonely polymerase. There are some variations between prokaryotic and eukaryotic organisms, which doesn't help my memory. The actual kinetics of assembling that complex are not necessarily accurate, but once assembled, the replication machinery does work at a nice pace as implied (something like 300 nucleotides per minute in bacteria, slower in eukaryotes as I recall).