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Question 2: Polymer diffusion through membrane channel [25 pts] Left Reservoir Right Reservoir A membrane separates two reservoirs containing different concentrations of lambda-DNA, a medium-sized E.coli bacteriophage, dissolved in water. The permeability of this system is known to be p = 0.341 um/s. The left reservoir's DNA concentration is Cleft = 3 nM, whereas the right reservoir concentration is Cright = 1 nM. An opening in the membrane is large enough to allow the polymers to freely diffuse from one side to the other of the membrane. Since the reservoirs are very large, a quasi-steady state is reached and a constant DNA flux of from the left reservoir to the right. a) What is the flux through the membrane in um-2s-1 units? 0.411 um-2s-1 Reminder that 1 M = 12 = 1000 mod b) Lambda-DNA is well represented by an ideal random walk consisting of 970 segments of length 50 nm. What is its mean end-to-end distance and its radius of gyration? c) How thick is the membrane, i.e. the length of the channel? d) Given that DNA is negatively charged, what happens to the polymer flux if you apply an electric field pointing left or right to the system