Collision Frequency and Relative Velocity in Enzyme-Substrate Interactions

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Discussion Overview

The discussion revolves around the collision frequency and relative velocity in enzyme-substrate interactions, particularly focusing on the implications of immobilizing a substrate versus having it mobile. Participants explore theoretical aspects of collision probability, factors influencing interactions, and the dynamics of molecular movement in solution.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions whether immobilizing a substrate increases the likelihood of collisions with mobile enzymes, suggesting that concentration and temperature may play significant roles.
  • Another participant argues that having both the enzyme and substrate mobile would likely result in more collisions than if either were immobilized.
  • A participant explains collision probability in terms of spatial occupation, using an analogy of two individuals trying to meet, where one remains fixed, suggesting that a fixed substrate may increase the likelihood of collision with a mobile enzyme.
  • One participant reflects on the idea that if all particles are moving, there could be an equal chance of moving away from each other, complicating the initial assumption about collision likelihood.
  • Another participant introduces the concepts of collisional frequency and density, proposing that a fixed substrate might lead to a higher frequency of collisions based on kinetic energy considerations and spatial constraints.
  • A later reply suggests looking into physical chemistry texts for concepts related to relative velocity, indicating that a higher relative velocity could correlate with increased collision frequency.

Areas of Agreement / Disagreement

Participants express differing views on the impact of immobilization on collision frequency, with no consensus reached. Some argue for the benefits of mobility while others highlight the potential advantages of a fixed substrate.

Contextual Notes

Participants note that the discussion is influenced by various factors such as concentration, temperature, and the assumptions regarding molecular movement. There are also references to theoretical models that may not fully account for real-world complexities.

Who May Find This Useful

This discussion may be of interest to those studying enzyme kinetics, molecular biology, or physical chemistry, particularly in the context of reaction dynamics and collision theory.

Hootenanny
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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 :smile:
 
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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.
 
DocToxyn said:
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. :smile:
 
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.
 
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.
 
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.
 
Thanks for the replies people :smile:
 
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 [tex]c_{rel}[/tex] relative velocity concepts in relation to this. If one agent is fixed and the other is at a velocity [tex]v[/tex], if I'm understanding the concept correctly, and then we consider one which has all molecules at a velocity [tex]v[/tex] (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.
 

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