1. Building on the \'state variable\' methods we developed last week, let\'s con

Question

1. Building on the 'state variable' methods we developed last week, let's consider a substrate (e.g. a 'big' molecule) that can bind up to two, identical small molecules in solution. The small molecules are at a concentration c with a reference concentration co, and each small molecule individually binds to the larger molecule with an energy 0. Assume a constant concentration ensemble a) Find the probability that one site on the larger molecule is bound b) Find the probability that both sites on the larger molecule are bound c) Find the occupation probability for a site - that is, the probability that if you look at any given site in equilibrium, it will be bound. d) Now assume that there is an additional binding energy that only applies when both sites are bound Find the probability that both sites are bound and simplify this result using the assumption that 0 e) Sketch the qualitative differences between the probabilities in (c) and (d) as a function of the concentration c

Explanation / Answer

State variable is one of the set of variables that are used to describe the mathematical state of a dynamical system.

a) assuming reference concentration is the (Co)

Pr=2C/Co

(b) C/2Co

(c) C/Co

(d) -

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