HW03

Due 11:59 PM, September 19, 2016

Submit as pdf to at https://cpcb-courses.herokuapp.com/.

  1. (15 points) Calculations with the MWC model of dimoglobin (based on PBOC2, Problem 7.4).
    1. Derive expressions for p0, p1, and p2, the probabilities of different states of occupancy for both the T and R states of the two-site MWC model in terms of the dimensionless concentration, c'= c*exp(-βεT), taking μ0=0. (Hint: these should depend only on the parameters ε and Δε= εR-εT. (see pp. 300-301 for notation).
    2. Plot p0, p1, and p2, the probabilities of different states of occupancy for both the T and R states taking ε= 2 kBT and Δε= 0, -2 kBT, and -4 kBT.
    3. Compute the Hill numbers for the total occupancy for the same set of parameters and explain your findings.
  2. (15 points + 5 possible extra credit) EGF-induced dimerization of EGFR. For this problem consider the model shown on page 9 of the Cooperative binding notes.
    1. Of the six binding parameters, how many are independent? Justify your answer by showing the thermodynamic cycles that constrain the parameters. Determine the minimal set of binding constants as a set of single site affinities and cooperativity factors.
    2. Derive an expression for the fraction of receptors in dimers in the absence of ligand. (Hint: Set up and solve a mass conservation equation for the total number of receptors to determine the concentration of free receptors. Then use this to determine the fraction of receptors in dimers.)
    3. Now consider the effect of ligand binding on dimerization. Show how to compute the fraction of receptors in dimers for any set of binding constants and use this capability to determine at least 4 qualitatively different behaviors. Make a full plot of the dimerization curve as a function of log(L/K), i.e., the log of the dimensionless ligand concentration. Report the parameters you used to obtain each behavior both in terms of the binding parameters and the free energy parameters as defined in the free energy function for the model given in the notes (p. 8). (Hint 1: Follow the same steps as in the previous part but don't try to derive a full final expression, but rather just give the expression for the fraction of dimers as a function of the parameters, the free ligand concentration, and the free receptor concentration you determined. Hint 2: Set Kd=0.1 and RT=1.) (5 point bonus if you can find a 5th behavior.)