Abstract
The location of distinct sites is mandatory for many cellular processes.
In the subcompartments of the cell nucleus, only very small numbers
of diffusing macromolecules and specific target sites of some types
may be present. In this case, we are faced with the Brownian movement
of individual macromolecules and their "random search" for single/few
specific target sites, rather than bulk-averaged diffusion and multiple
sites. In this article, I consider the location of a distant central
target site, e.g. a globular protein, by individual macromolecules
executing unbiased (i.e. drift-free) random walks in a spherical
compartment. For this walk-and-capture model, the closed-form analytic
solution of the first passage time probability density function (p.d.f.)
has been obtained as well as the first and second moment. In the
limit of a large ratio of the radii of the spherical diffusion space
and central target, well-known relations for the variance and the
first two moments for the exponential p.d.f. were found to hold with
high accuracy. These calculations reinforce earlier numerical results
and Monte Carlo simulations. A major implication derivable from the
model is that non-directed random movement is an effective means
for locating single sites in submicron-sized compartments, even when
the diffusion coefficients are comparatively small and the diffusing
species are present in one copy only. These theoretical conclusions
are underscored numerically for effective diffusion constants ranging
from 0.5 to 10.0 microm(2) s(-1), which have been reported for a
couple of nuclear proteins in their physiological environment. Spherical
compartments of submicron size are, for example, the Cajal bodies
(size: 0.1-1.0 microm), which are present in 1-5 copies in the cell
nucleus. Within a small Cajal body of radius 0.1 microm a single
diffusing protein molecule (with D=0.5 microm(2) s(-1)) would encounter
a medium-sized protein of radius 2.5 nm within 1 s with a probability
near certainty (p=0.98).
- 12634045
- animals,
- biological,
- car,
- cell
- diffusion,
- fractions,
- lo
- macromolecular
- method,
- models,
- monte
- motion,
- nuclear
- nucleus,
- proteins,
- subcellular
- substances,
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