  We present a numerical simulation study of the dynamics of filopodial growth
in the presence of active transport by myosin X motors. We employ both a
microscopic agent-based model, which captures the stochasticity of the growth
process, and a continuum mean-field theory which neglects fluctuations. We show
that in the absence of motors, filopodia growth is overestimated by the
continuum mean-field theory. Thus fluctuations slow down the growth, especially
when the protrusions are driven by a small number (10 or less) of F-actin
fibres, and when the force opposing growth (coming from membrane elasticity) is
large enough. We also show that, with typical parameter values for eukaryotic
cells, motors are unlikely to provide an actin transport mechanism which
enhances filopodial size significantly, unless the G-actin concentration within
the filopodium greatly exceeds that of the cytosol bulk. We explain these
observations in terms of order-of-magnitude estimates of diffusion-induced and
advection-induced growth of a bundle of Brownian ratchets.
