Homework #2
Due Monday, October 2, 2006.
1.
For each of the following particles calculate the threedimensional rootmeansquared (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 StokesEinstein 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 8fold 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 3d 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 3d r.m.s. displacement that exceeds
the dimensions of an animal cell (i.e. 10 μm)? Using the equation for 1d 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 offshore in the middle of the lake.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '10
 S
 Bacteria, Orders of magnitude, Adenosine triphosphate, NM

Click to edit the document details