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Homework2

# Homework2 - Homework#2 Due Monday October 2 2006 1 For each...

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Homework #2 Due Monday, October 2, 2006. 1. For each of the following particles calculate the three-dimensional root-mean-squared (r.m.s.) displacement (in units of μm) that occurs in a one second time period. Assume that the particles are immersed in cytoplasm at body (a.k.a. physiological) temperature (37 o C), which has a viscosity of ~0.008 kg/m s. First, use the Stokes-Einstein equation for spherical particles to estimate the diffusion coefficient in m 2 /s and in μm 2 /s. Particle Spherical Diameter* Sodium ion 1 nm Glucose 2 nm Immunoglobulin G (IgG) 6 nm HIV retrovirus 100 nm Bacterium 2000 nm Animal cell 10,000 nm Human 1 m *IgG and some viruses and cells are not spherical. Corrections for nonspherical particles are given in Howard. To estimate the extent of diffusive movement of particles inside cells, we need to know the viscosity of the cytoplasm. Experimental studies have yielded estimates of viscosity that are 8-fold more viscous than water at the same temperature, at least for particles that are ~50 nm in diameter or less. For each of the particles above (except those with a diameter greater than 50 nm), recalculate the 3-d r.m.s. displacement in 100 seconds assuming the estimated viscosity of cytoplasm at physiological temperature. Under these conditions, which of the particles have a 3-d r.m.s. displacement that exceeds the dimensions of an animal cell (i.e. 10 μm)? Using the equation for 1-d r.m.s. displacement as a function of time, estimate the time (in units of years) for a virus to travel from a neuron’s axon terminus to its cell body, assuming a distance of 1 m. Most axons are actually much shorter than 1 m. Assuming a length of 0.1 mm, how long will the transport take? A swimmer is feeling lazy as swims in Lake Nokomis (viscosity~0.001 kg/m s), and decides to let diffusion take him to shore. How long would it take him to diffuse to shore, assuming he starts 200 m off-shore in the middle of the lake.

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Homework2 - Homework#2 Due Monday October 2 2006 1 For each...

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