Collision Frequency and Relative Velocity in Enzyme-Substrate Interactions

[Hootenanny]

My question is "If I have an immobilised substrate (protein molecule), is it more likely that when in a solution with enzymes(which are free to move) that a collision will occur than if the substrate was mobile.

Any input would be appreciated

 

[DocToxyn]

First off, I would think this is going to be highly dependent on concentration, temperature, etc. But regardless, my guess is that you would get more interactions/collisions if both the protein and the enzyme are mobile that if either one was immobilized.

 

[Hootenanny]

First off, I would think this is going to be highly dependent on concentration, temperature, etc. But regardless, my guess is that you would get more interactions/collisions if both the protein and the enzyme are mobile that if either one was immobilized.

Thank-you for your reply.

 

[Bystander]

You are interested in collision probability; the probability that A and B occupy the same small volume of space at the same time. This is equal to the product of the probabilities of A occupying the space and of B occupying the space. If probability of A is fixed at 1, and the coordinates of the space are fixed, the probability is simply that of B. If A is mobile, the probability is the sum of the probability products over all volume increments available that A and B simultaneously occupy the same volume.

What I remember (don't take it to the bank) is that "fixed A" is "found" more often by B. Two drunks agree to meet at the "Dew Drop Inn" at eight (A fixed) and look for each other if the other doesn't show up by 8:05 (A and B mobile) --- the drunk who stays put an extra five minutes has a much higher probability of meeting his "friend" than the drunk who concludes the other must be drunk and has to be hunted.

 

[DocToxyn]

You know that sounds better than my initial assumption. Upon thinking about it, if all particles are moving, there is just as much (perhaps more?) of a chance that they are moving away from each other as there is that they are moving towards each other. Thanks Bystander.

 

[GCT]

This may simply be a case of collisional frequency and collisional density, I'll need to refer to my text. At this point, I'm leaning more towards the frequency of collisions being higher, if we were to consider two molecules in a box and elastic collisions, both of them with kinetic energies then with one of them being fixed, perhaps the mean free path would be greater, since you have a constrained region; kind of similar to where two trains approach each other as opposed to one of them being required to pass another at a fixed point. That is they will move away from the other at combined speeds and approach at combined speeds as well, the combined effect of the two would decrease the time between the collisions I would imagine.

But it may depend on the proportion of molecules one considers fixed and the ones that possesses kinetic energy.

The drunk example is very interesting and I think Bystander has made a good point, but it may involve some novel factors.

 

[Hootenanny]

Thanks for the replies people

 

[GCT]

You might want to take a peek in a P. Chemistry Text, Atkins is nice, towards the end of the text. Search for the term $$c_{rel}$$ relative velocity concepts in relation to this. If one agent is fixed and the other is at a velocity $$v$$, if I'm understanding the concept correctly, and then we consider one which has all molecules at a velocity $$v$$ (not really realistic considering the Boltzmann distribution) the relative velocity would be higher with the situation where the molecule is not fixed.

My thought is that with a higher c rel, you would have a higher collision frequency and you can should find the explicit equation which describes their relationships.