APh161: Physical Biology of the CellHomework 3Due Date: Tuesday, February 10, 2009“It is the highest bliss for the thinking person to have explored what canbe explored and quietly to worship what cannot.” – GoetheReading:Read chap. 5 of Physical Biology of the Cell (PBOC), especially section5.5.2. Also, read chap. 8 of PBoC.1. ATP synthesis.Estimate the daily ATP synthesis by ATP synthases in a human. To do thisestimate, imagine a typical human diet and hypothesize that roughly halfof the caloric input is converted into ATPs. What is the mean rate of ATPsynthesis per cell in the human body resulting from this estimate? If eachATP synthase synthesizes roughly 100 ATPs per second (see Alberts, MBoC,chap. 14), what does this imply about the number of such ATP synthasesper cell? Note: the entirety of this question is to give us a feeling for thenumbers and the actual numbers might be substantially different because ofcell type and physiology.2. Concentration Gradients, Free Energy and the Proton MotiveForce.In class, we discussed the role of transmembrane concentration gradients asan important source of biological free energy. In this problem you will explorethe significance of these concentration gradients in several different ways, ba-sically viewing the material in class from slightly different angles.(a) As a warm up exercise, deduce the chemical potential for an idealsolution by filling in all of the steps between eqn. 6.78 and 6.85 of PBoC.Make sure you explain briefly in words what is going on at each step andthat you are clear on how to get from 6.81 to 6.82.1(b) As mentioned several times in class, one of the consequences of theelectron transfer reactions in photosynthesis is that a concentration gradientof hydrogen ions is set up across the membrane. Using your result for thechemical potential, compute ∆µ across a pH difference of 1 across a mem-brane. Express your result in both eV and kBT units. More generally, findan expression for the entropic contribution to ∆µ as a function of ∆pH.(c) In fact, if we allow charged particles to move across a membrane acrosswhich there is an electrical potential difference, this too will contribute to thefree energy change. For a transmembrane potential difference of ∆V , workout the contribution to the free energy difference across the membrane. Atypical transmembrane potential is 100 mV. What is the energy associatedwith this transmembrane potential?(d) Assemble your results from parts (b) and (c) to work out the so-called“proton motive force” across the membrane (i.e. the total free energy dif-ference due to both concentration gradients and transmembrane potentialdifference). Write your result in terms of ∆V and ∆pH.3. Estimates on Genome Packing in Viruses and Prokaryotes.Write a brief (less than two pages including calculations) “Scientific American”-style essay on genome size (in bp) by referring to figures 1.13 and 8.6 of PBoCand the estimates on pgs. 291-292. What I want you to do is to explain howlarge the genome is in solution without the confining influences of the viralcapsid or the cell and once you have this physical size, translate it into acorresponding estimate of the genome length in basepairs. How compactedis the genome in the confines of the virus capsid or the cell? Words alone willnot suffice here. You need to do a simple estimate of the kind I do in class.You can use the formula for the radius of gyration as a function of number ofKuhn segments given by eqns. 8.32 or 8.33 in PBoC, but you need to explainto the reader what it means and why you are invoking it. You should havean estimate for the case of a bacterial virus (such as lambda phage) and forE. coli.24. Sturtevant Experiment.- Problem 4.4 of PBoC5. Random Walks and Polymers.- problem 8.4 of
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