You want to use retroviruses to deliver DNA to a type of cellsto promote certain phenotype. Before you start, you want toestimate the delivery efficiency. The cells are spread on a solidsupport and covered with an aqueous medium. The culture dish is 6cm in diameter and the medium is 6 mm deep. You add the virusparticle at the top of the medium. The virus has a half life of 8hours in solution. The diffusion coefficient of the virus is10-7 cm2/s.
(a) Estimate the fraction of virus particles that reach cellswithin their half life when the medium is stagnant. Hints: (1)using scaling analysis to find out the time scale for the virus todiffuse from top to bottom; (2) assume death of the virus followsthe kinetics of first order reactions.
(b) Comment on the efficiency of delivery. Suggest approach(es)to improve the delivery efficiency
