Optimality of Spatially Inhomogeneous Search Strategies

Abstract

We consider random search processes alternating stochastically between diffusion and ballistic motion, in which the distribution function of ballistic motion directions varies from point to point in space. The specific space dependence of the directional distribution together with the switching rates between the two modes of motion establishes a spatially inhomogeneous search strategy. We show that the mean first passage times for several standard search problems-narrow escape, reaction partner finding, reaction escape-can be minimized with a directional distribution that is reminiscent of the spatial organization of the cytoskeleton filaments of cells with a centrosome: radial ballistic transport from the center to the periphery and back, and ballistic transport in random directions within a concentric shell of thickness Δ_{opt} along the domain boundary. The results suggest that living cells realize efficient search strategies for various intracellular transport problems economically through a spatial cytoskeleton organization that involves radial microtubules in the central region and only a narrow actin cortex rather than a cell body filled with randomly oriented actin filaments.

Spatial Cytoskeleton Organization Supports Targeted Intracellular Transport

“…Here we study in addition the reaction and the reaction-escape problem in inhomogeneous environments. Our results are in agreement with recent findings for inhomogeneous search strategies with intermittent diffusion in the limit of a vanishing diffusion coefficient (49,50). In contrast to (49,50), we systematically study the impact of pausing states on the efficiency of intracellular transport task.…”

“…In particular, we check for the impact of an inhomogeneous cytoskeleton organization and two different reaction modes. In the context of intermittent search strategies, it is typically assumed that detection is only possible in the phase of slow displacement (28,49,50), i.e., in the waiting state. Although some experimental data suggest a connection between mobility of particles and likelihood of reactions (51,52), it remains elusive whether this assumption is valid for all chemical reactions that take place inside living cells.…”

Spatial cytoskeleton organization supports targeted intracellular transport

“…Our results indicate that cells with a centrosome are able to realize efficient intracellular search strategies by intermittent transport on a cytoskeleton with specific spatial structure (see also [33,34] for similar findings in a model with intermittent diffusion). In comparison to the homogeneous pendant, an inhomogeneous cytoskeleton organi-zation which displays only a thin actin cortex generally leads to a considerable gain in search efficiency for diverse intracellular transport tasks.…”

“…In essence, the specific spatial organization of the cytoskeleton represents, in conjunction with motorassisted transport, an intermittent search strategy, which is probably optimized for specific frequently occurring transport tasks, but less well suited for others. Despite recent achievements in inhomogeneous intermittent search strategies [33][34][35], it is still obscure how much the efficiency of diverse transport tasks is effected by the interplay between spatially inhomogeneous cytoskeleton organization, motor performance and detection mode, in particular in comparison to homogeneous search strategies.…”

The narrow escape problem in a circular domain with radial piecewise constant diffusivity

“…Thus in the model considered in Refs. [8,9], it is the enforced re-injection of the searcher into the outer shell that is crucial for the optimization effect. It leads to an increased probability to find the particle in the outer shell, which is where the target is: the narrow escape region.…”