The protein cyclophilin is a monomer with a diffusion constant of 1.2 x 10–8 cm2•sec–1 in water at 25°C. Cyclophilin binds HIV capsid and the complex has a diffusion constant of 7 x 10–9 cm2•sec–1. What is the difference in the typical (r. m.s.) distance that cyclophilin alone will travel versus the cyclophilin-capsid complex in 10 seconds? Please answer in cm.

RMS distance = 0.0002 cm.

Explanation: Diffusion (D) is the random movement of molecules or small particles caused by thermal energy.

Diffusion constant is a property of interaction between solute and solution. It is the magnitude of molar moving thorugh a surface per unit concentration  gradient. Depends on size and shape of the molecule and viscosity of solvent and its unit, in SI, is meter per second.

The relationship between diffusion and mean square displacement is given by:

x is the mean square displacement;

q is a constant dependent on dimensionality(for 1 dimension, q = 2; for 2 dimensions, q = 4; and for 3 dimensions, q = 6);

D is diffusion constant;

t is time;

Calculating RMS distance for cyclophilin alone and as protein is in 3 dimensions, q = 6:

RMS for cyclophilin-capsid complex, also in 3 dimensions:

The difference between alone and complex:

RMSd =

RMSd =

The difference in the typical (rms) distance between the travel of cyclophilin alone and cyclophilin-capsid complex in 10s is 0.0002cm.