  Experiments have found that diffusion in metabolically active cells is much
faster than in dormant cells, especially for large particles. However, the
mechanism of this size-dependent diffusion enhancement in living cells is still
unclear. In this work, we approximate the net effect of metabolic processes as
a white-noise active force and simulate a model system of bacterial cytoplasm
with a highly polydisperse particle size distribution. We find that diffusion
enhancement in active cells relative to dormant cells can be more substantial
for large particles. Our simulations agree quantitatively with the experimental
data of Escherichia coli, suggesting an autocorrelation function of the active
force proportional to the cube of particle radius. We demonstrate that such a
white-noise active force is equivalent to an active force of about 0.57 pN with
random orientation. Our work unveils an emergent simplicity of random processes
inside living cells.
