Cell biology lecture 21

Kinetics

what determines rate of a reaction?

what does Maxwell Boltzmann distribution describe?

• distribution of molecule speeds in a gas or liquid​

• Particles in a box can collide with each other or the box​

• If we started them all with the same speed and let them equilibrate, collisions would transfer energy between particles and we get a distribution of speed​

Probability distribution plot

• Most molecules have similar speed​

• A few have very high speed​

• A few have very low speed​

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Distriibution plot with changes in mass or temp

MB and particle kinetic energy distribution

Why KE does not depend on particle mass?

What determines a rate of reaction?

Three major factors:​

1. Temperature

Higher T​

• Average kinetic energy increases​

• more molecules exceed activation energy​

2. (Enzymatic) catalysis​

Enzymes lower activation energy​

 More molecules exceed activation energy​

3. Concentration

As concentration increases​

• Same fraction of molecules have KE greater than activation energy​

• But more molecules in total ​

 more molecules enough KE to react

Rate of reaction reminder

Change in conc/time

Reaction orders 

• Consider reaction:​

A + B  C + D​

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• Rate of decrease of reactants given by:​

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rate = k[A]x[B]y​

• x, y are orders of reaction with respect to A, B respectively​

• Overall order of reaction is x+y​

• k (rate constant) is dependent on temp 

First order reactions

• A FIRST ORDER reaction is one in which a single atom or molecule determinesthe rate​

rate = k [A]​

• Eg radioactive decay:​

• In a first order reaction: if we double the amount of A, the rate doubles​

Second order reactions

• When two molecules collide to determine the rate, the reaction is SECOND ORDER​

• Consider reaction:​

A+A to B​

with rate = k[A]squared​

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• This reaction is second order w.r.t. A and overall​ second order

Or

• Bimolecular interaction:​

A + B to C​

with rate = k[A][B]​

• ​

• This reaction is first order w.r.t. A and B and second order overall​

how do we determine the order of a reaction?

Experimentally, determined by the slowest RATE LIMITING/DETERMINING step of a reaction

Order of reaction and rate limiting steps​

• So to get the reaction order we need to measure the rate​

• Because there may well be intermediate steps in a reaction​

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Famous biological example:​

• Michaelis-Menten enzyme kinetics​

• Rate limiting intermediate step​

Equilibrium and equilibrium constant Kc

why is Kc useful?

Kc process 

Why is Kc calculated without consideration of rate limiting steps and intermediates?

This is the equilibrium constant at equilibrium, so all the rates must balance (principle of detailed balance) so only the first and last states need to be considered. 

Kc example Q

Equilibrium constant biological example

How do systems at equilibrium respond to perturbation?​

• If we add more reactant A or B, the system readjusts back towards equilibrium by making more product C + D​

• If we add more product C or D, the system readjusts back towards equilibrium by making more product A + B​

• Example of Le Chatelier’s principle:

When a system at equilibrium is subjected to disturbance, the composition of the system adjusts to minimize the disturbance​

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Free energy and equilibrium links 

Free energy and equilibrium example *