An E. coli strain has a length of 10 micrometers under normal conditions. A drug molecule of average size spends an average of 2 microseconds between jumps, and it travels a distance of 10 nanometers at every jump. Calculate the diffusion coefficient and estimate the time it will take to reach the center of the cell if the main mode of transport for this drug is diffusion. The antibiotic molecule starts diffusion from the cell membrane. Hint: antibiotics move in three dimensions in bacteria.
1) Diffusion coefficient is ________ μm^2/msec.
(msec: millisecond; μm: micrometer)
2) The time required for the drug molecule to reach the center of the cell is _________ msec.
Additional info:
D = (x^2) / (a * t)
a will be 6 in this equation since it is 3D.