Physics4S036S03-MolecularBiophysics.docVIP

Physics 4S03 / 6S03 - Molecular Biophysics – Assignment 2 Question 1. The figure below is taken from Fygensen et al (on the web site). It shows an experimentally measured phase diagram for microtubules as a function of temperature and concentration of tubulin. Seeds acting as nucleation sites are present in the experiment. In region I, almost no growth occurs. Hardly any of seeds are observed to have microtubules on them. In region II, growth occurs from the seeds only. A substantial fraction of seeds have microtubules growing. In region III, spontaneous nucleation of microtubules occurs in addition to growth from the seeds. The dotted line marks a transition from a region of bounded growth (finite length microtubules) to unbounded growth (microtubules keep increasing in length if the tubulin concentration is maintained constant). The following simple model explains some of these observations. Let M be the total concentration of seeds. Let Mn be the concentration of seeds with n units growing (one unit is one tubulin dimer). Therefore we know that . Assume that the rate of addition of each new unit to the microtubule is konC, where C is the concentration of units in solution. Assume that C is kept fixed, so that we do not need to consider the depletion of tubulin from solution as the microtubules grow. The rate of loss of each unit from the end of the chain is koff. We can therefore write (a) Write down equations to describe the rates of change of M1 and Mn (where n is any number greater than 1). Calculate the equilibrium values of M0, M1 and Mn in the region where the growth is bounded. Draw a diagram illustrating the distribution of lengths of microtubules at equilibrium. What is the mean number of units per microtubule? (10 marks) (b) Why does spontaneous nucleation of microtubules only occur at high C? Suggest what additional terms we might add to the rate equations if we wanted to include the possibility of spontaneous nucleation in the mo