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## Activation Energy and Enzyme Catalysis

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### Activation Energy and Enzyme Catalysis

Hey,

I'm pretty new to the Biology game (I'm a community college student), but I have a pretty good basic understanding of general chemistry. Right now I'm trying to understand enzyme catalysis, and it turns out it's a pretty complicated and tough subject. Well, actually, chemical kinetics is pretty tough to understand to begin with.

I don't have a super strong understanding of kinetics and thermodynamics, so bear with me. I've checked out a book called Kinetics and Mechanism (by Moore and Pearson), but much of it is way over my head - my mathematical background being limited to Calc III and diff eq. I've also gone all over the internet looking for answers, but most of the information is either way to basic, or gives information without providing some kind of fundamental understanding. I've tried to put together a basic picture in my mind of how reactions take place, but the conflicting (to me) information out there is making this very hard.

Okay then, here is what I'm confused about (I'll explain what I think I know in parts - please correct me in any place where I'm mistaken)

1) Consider a bimolecular reaction. From what I've learned in general chemistry the rate of reaction depends on (using collision theory):

Rate = kl[A][C] = pfZ[A][C] (I had to use C instead of because of BOLD code)

where,
p = the steric factor (or the fraction of collisions properly oriented for reaction)

f = the fraction of collisions that exceed Arrhenius activation energy (Ea)

Z[A][C] = collision frequency, where Z is a constant

ALSO: f = exp(-Ea/RT) (Although, from what I understand this is an approximation)

I also understand that the steric factor cannot be predicted, but must be calculated after experimentation.

When this equation is taken as a whole, it means that reaction rate is equal to the (collision rate)(fraction of collisions that exceed Ea)(fraction of collisions with proper orientation)

2) [this is where my understanding gets really hazy]
The progress of a reaction can be graphed 2-dimensionally as a reaction coordinate vs potential energy. Everyone has seen these potential energy profiles. From what I understand, the profile for a reaction is derived in this way: The potential energy of a set of nuclei can be graphed as dependent variable on a hyperdimensional surface. The extra dimensions include different states of the nuclei (vibrational rotational etc.)and their positions with respect to each other. If all but 2 dimensions can be set as constant, then those 2 independent variables (usually representing internuclear distance?) can be graphed with respect to the dependent variable of potential energy. The low points on this surface represent reactants, products, or intermediates. The saddle points represent transition states. The lowest energy path (the gradient) from reactant to transition state to product is the potential energy profile, which is graphed against a reaction coordinate.

3) The top of a potential energy profile is the transition state. The difference between the potential energy of the activated complex and the reactants is the threshold energy, and is the barrier which must be surmounted to complete a reaction. This is done when the reactants have enough kinetic energy to convert into potential energy. The potential energy comes from electrostatic repulsions between the atoms' electrons.

4) Reaction rate depends on the height of this barrier, and the fraction of collisions (of reactants) with sufficient KE to surmount it. This fraction of collisions can be calculated (although I honestly have no idea how) using the maxwell-boltzmann distribution.

5) I'm not going to get into how an inorganic catalyst reduces activation energy, except to say that it provides an alternative reaction mechanism with a lower peak potential energy profile.

6) Enzymes are catalysts. I'm not going to go into how they bind to a substrate. They catalyze reactions in a number of different ways, and I'm pretty sure no one truly understands them yet. Supposedly, just like all catalysts, they increase the rate of a reaction by lowering activation energy.

7) One of the most basic ways in which an enzyme works is by providing a space for its reactants to come close together in the proper orientation.

8) The progress of a reaction can also be graphed against Gibbs free energy. When discussing enzymes, it seems most sources DO use a Gibbs energy profile, but it is never discussed how this relates to a potential energy profile.

Questions:
1) There seems to be a difference between threshold energy and Arrhenius activation energy, but I don't understand what it is. My Gen Chem book actually calls this potential energy difference Activation Energy (Ea) (it never even mentions threshold energy Eo).

2) When an enzyme brings together 2 reactants in the proper orientation, it seems to me as if it is increasing the effective concentration, and increasing the steric factor (p) from the rate equation at the top of this post. If it is changing these factors in the rate equation to affect reaction rate, how is this lowering Ea ? In other words, it seems like the enzyme is increasing rate without changing activation energy.

3) How does a potential energy profile relate to a Gibbs free energy profile? I don't understand how you could use this profile in reference to a single reaction. Does an individual molecule have an entropy assigned to it?

4) How does (Gibbs) free energy of activation relate to activation energy and threshold energy?

5) From what I understand, by using transition state theory, the rate constant can be calculated using Gibbs free energy of activation, temperature, and some constants. (k=kbT/h*exp(-delta G of activation/RT) How does this calculation ignore the effect of molecular orientation during a collision?

6) When an enzyme increases the effective concentration by bringing together 2 reactants, even when using the previous equation, the portion of the rate equation being affected is the concentration part. In other words, it seems that the enzyme is catalyzing the reaction by increasing concentration without affecting free energy of activation. Is this true? Is the statement that a catalyst operates by lowering activation energy not valid in this case?

Okay, that is all I can think of right now - Thanks to anyone who reads this, and hopefully some of you can help me out. If these questions can be answered maybe the whole picture will fall together for me.
roark
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