Hints on problem set 1

Hi class-

If you're having a little bit of trouble getting started with PS1, here are a few hints for some of the more challenging problems.

On problems 6,7, and 9, you are using the Boltzmann population rules that we discussed in class. These may be new concepts for you, but these problems will help you grow comfortable in applying them. When you are working on these problems, you need to start by thinking about states: what are the possible states the system can have (e.g., folded or unfolded, bound or unbound, correct or incorrect nucleotide)?

• Write down a list of all states.
  
• Next, you need to assign a probability to each of the states, and that probability is given by the Boltzmann rule. You need to know the list of all of the states in order to normalize the probabilities, i.e., to ensure that they sum to one over all states.
  
• Keep the following in mind for the Boltzmann rule. If your state consists of multiple possible molecular configurations, you want to use a free energy in the Boltzmann exponential. If it consists of only one, you can use the internal energy.

On problem 8, you will be using concepts from your earlier chemistry courses that should be more than familiar to you. Keep in mind that the equilibrium constant for a reaction relates to the reaction free energy by:

K = exp( - DeltaG0/ R T )

We'll eventually derive this rule in class this week. You will need to know this relationship in order to solve problem 8. Also keep in mind for problem 8 that the total concentration of hemoglobin molecules is constant, [H] + [H(O2)] + [H(O2)2] + [H(O2)3] + [H(O2)4] = const = [H]0. What you are trying to find is f0 = [H]/[H]0, f1 = [H]/[H]1, and so on and so forth.

Cheers,
MSS