Numerical analysis of homogeneous and inhomogeneous intermittent search strategies

Abstract

Random search processes for targets that are inhomogeneously distributed in a search domain require spatially inhomogeneous search strategies to find the target as fast as possible. Here, we compare systematically the efficiency of homogeneous and inhomogeneous strategies for intermittent search, which alternates stochastically between slow, diffusive motion in which the target can be detected and fast ballistic motion during which targets cannot be detected. We analyze the mean first-passage time of homogeneous and inhomogeneous strategies for three paradigmatic search problems: (1) the narrow escape problem, i.e., the searcher looks for a small area on the boundary of the search domain, (2) reaction kinetics, i.e., the detection of an immobile target in the interior of a search domain, and (3) the reaction-escape problem, i.e., the searcher first needs to find a mobile target before it can escape through a narrow area on the boundary. Using families of inhomogeneous strategies, partially motivated by the organization of the cytoskeleton in cells with a centrosome, we show that they are almost always more efficient than homogeneous strategies.

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.…”

Spatial Cytoskeleton Organization Supports Targeted Intracellular Transport

“…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.…”

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

“…Recently the narrow escape problem was studied in spatially inhomogeneous environments [8]. The type of spatial inhomogeneity was inspired by the spatial organization of the cytoskeleton of cells with a centrosome [9,23,24] along which ballistic transport is possible in addition to simple diffusion: a circular or spherical domain is divided into two concentric shells, the inner shell allowing only radial ballistic transport (and diffusion) and the outer shell of width ∆ allows multi-directional ballistic transport (and diffusion). In these studies it was shown that the MFPT for the narrow escape problem is optimizable with respect to the width of the outer shell.…”