APh161: Physical Biology of the CellHomework 2Due Date: Tuesday, January 23, 2007“To arrive at the truth it is necessary, at least once in life, to rid oneselfof all the opinions one has received, and to construct anew, and from thefundamentals, all the system’s of one’s knowledge.” – R. DescartesA. Reading and RefereeingThis week you will be asked to do quite a bit of reading and to write refereereports. Please take this seriously.(a) Read the article on the website that we are planning on submittingto the American Journal Physics entitled “A First Exposure to StatisticalMechanics for Life Scientists”. Write a referee report in which you give gen-eral comments on how this article might be improved. In addition, make alist of specific comments. Make sure to comment on your views of the extentto which this article would serve as an introduction to statistical mechanicsfor first-time statistical mechanicians. Also, comment on how well the articlemotivates the need for statistical mechanics in biology.(b) To develop your skills in using the two-state formalism introduced inthe paper, consider a protein that can exist in two states (active and inac-tive) and also, can exist in a phosphorylated or unphosphorylated state. Theact of phosphorylation tunes the relative probability of active and inactivestates. Make a states and weights diagram for the four possible states ofthe protein molecule and use two different two-state variables to characterizeeach of the states.(c) Read chap. 2 of “Physical Biology of the Cell” and write a refereereport in the spirit of the referee report that we have posted on the website.1. Viruses and the Size of Things(a) Estimate the number of protein units that make up a viral capsid forinfluenza virus. In addition, estimate the number of lipid molecules associ-1ated with one of these viruses. The lipid molecules surround the protein coatin lipid bilayer form. Make sure you show a picture of the virus and givea rough description of what the structure is like - where is the nucleic acid,what is the shape, etc.. Also, describe the genome of this virus and computethe total length of the nucleic acid molecules if they were strung togetherone after the other.(b) Use fig. 1 of the paper by Briggs et al. on HIV that is posted onthe course website to measure the dimensions of the immature HIV virion.Based on what you know about the makeup of the virion, estimate the num-ber of lipids and the number of Gag proteins in the immature virion. Then,consider the mature virion and using fig. 2 of the second paper by Briggset al. estimate the number of proteins in the ic e-cream-cone- shaped capsid.How does your estimate for the number of proteins in the capsid compare toyour estimate for the number of Gag proteins?2. A Feeling for the Number s: The Rates of ThingsIn the previous homework, we worked hard to get a sense for the physicalsizes of various biological entities. Another interesting angle on all of this isto try and get a feel for the rates at which things happen. Following in thetradition of the previous problems, here you will try to make some estimatesof the rates of some processes. Much of what you will do in this problem Ihave already done partially in class - your job is to make it your own now.(a) Consider the division of an E. coli cell. Think of such a cell duringrapid growth phase where the cell is dividing roughly once every 20 minutes.Make estimates of the number of water molecules being taken on board persecond during this phase, the number of lipid molecules that are being addedonto the surface membranes, the number of proteins being synthesized persecond and how many ribosomes are needed to do so. Also, estimate thenumber of carbon atoms it takes to make a bacterium and use that estimateto make a lower bound estimate on the rate of sugar uptake by a growingbacterium.(b) In this case, think about the motility of the bacterium Listeria mono-cytogenes and a typical eukaryotic cell. In the case of Listeria, the motion of2the bacterium is mediated by the formation of actin comet tails which dependin turn upon the linear polymerization of actin filaments. The formation ofthe actin comet results in a speed for the bacterium of something around0.1 µm/sec. In the eukaryotic setting, the cell extends arms called filopodiawhich permit it to crawl, again by virtue of actin polymerization. For Lis-teria, use the measured rate of motion of the bacterium to estimate the rateof actin polymerization both in microns/sec and monomers/sec. Make sureyou draw a picture of the process and explain your rationale. Now, take thatestimate for the rate of actin polymerization and estimate the rate at whicha filopodium extends on a eukaryotic cell. Anything you can do to comparethese estimates with measurements would be useful - one excellent source isCell Movements by Dennis Bray.(c) Look at fig. 6-9 of Essential Cell Biology and assuming that this isa representative sample of the replication process, estimate the number ofDNA polymerase molecules in a eukaryotic cell like this one from the fly.Note that the fly DNA is about 1.8 × 108nucleotide pairs in size. Estimatethe fraction of the total fly DNA shown in the micrograph. There are eightforks in the micrograph, numbered 1-8. Estimate the lengths of the DNAstrands between replication forks 4 and 5 where we count the forks from leftto right. If a replication fork moves at a speed of 100 nucleotides/s, how longwill it take for forks 4 and 5 to collide. Also, given the mean spacing of thebubbles, estimate how long it will take to replicate the entire fly
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