2 2 chemotaxis and receptor binding part 1 as

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2. Chemotaxis and Receptor Binding: Part 1. As described in class, bacterial chemotaxis is claimed to be the best studied signal transduction problem in biology. In this problem, we work through some of the statements and results in a few of the classic papers I presented in class. We develop a feeling for the numbers by examining direct quota- tions from the experimental papers that have really driven the field recently as well as a commentary on this work by Dennis Bray. Begin by reading both of these papers which are attached on the website. In their 2002 paper in PNAS entitled “Receptor sensitivity in bacterial chemotaxis”, Sourjik and Berg say: “The changes in receptor occupancy en- countered by bacteria swimming in spatial gradients (e.g., near the mouth of a capillary tube in the capillary assay) are very small. For example, in the tracking experiments, cells about 0.6 mm from the tip of a capillary tube (consider a pipette with a radius of 5.0 μ m) containing 1 mM aspar- tate moved in a gradient of steepness 0.02 μ M/ μ m at a mean concentration of about 8 μ M. A 10- μ m run straight up such a gradient would change the concentration from 8 to 8.2 μ M, i.e., by 2.5 %. Assuming K d values for as- partate of 7.1 μ M and 62 mM (see above), this step gives a fractional change in receptor occupancy of about 0.003”. RP to class: the two K d values correspond to the fact that two of the different chemotactic receptors (Tar and Tsr) will bind aspartate, but with quite different affinities. For your estimates, only consider the smaller K d since the larger one will be irrelevant at the concentrations of interest here. Your job is to carry out calculations that exploit the numbers given above and using what you know about the definitions of concentration, the size of E. coli cells and about the meaning of K d and simple binding curves (i.e.
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