We extend the theoretical framework used to study search processes with stochastic resetting to the case of partially absorbing targets. Instead of an absorption event occurring when the search particle reaches the boundary of a target, the particle can diffuse freely in and out of the target region and is absorbed at a rate κ when inside the target. In the context of cell biology, the target could represent a chemically reactive substrate within a cell or a region where a particle can be offloaded onto a nearby compartment. We apply this framework to a partially absorbing interval and to spherically symmetric targets in . In each case, we determine how the mean first passage time (MFPT) for absorption depends on κ, the resetting rate r, and the target geometry. For the given examples, we find that the MFPT is a monotonically decreasing function of κ, whereas it is a unimodal function of r with a unique minimum at an optimal resetting rate r opt. The variation of r opt with κ depends on the spatial dimension d, decreasing in sensitivity as d increases. For finite κ, r opt is a non-trivial function of the target size and distance between the target and the reset point. We also show how our results converge to those obtained previously for problems with totally absorbing targets and similar geometries when the absorption rate becomes infinite. Finally, we generalize the theory to take into account an extended chemical reaction scheme within a target.

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We extend the theoretical framework used to study search processes with stochastic resetting to the case of partially absorbing targets. Instead of an absorption event occurring when the search particle reaches the boundary of a target, the particle can diffuse freely in and out of the target region and is absorbed at a rate κ when inside the target. In the context of cell biology, the target could represent a chemically reactive substrate within a cell or a region where a particle can be offloaded onto a nearby compartment. We apply this framework to a partially absorbing interval and to spherically symmetric targets in R d . In each case, we determine how the mean first passage time (MFPT) for absorption depends on κ, the resetting rate r, and the target geometry. For the given examples, we find that the MFPT is a monotonically decreasing function of κ, whereas it is a unimodal function of r with a unique minimum at an optimal resetting rate ropt. The variation of ropt with κ depends on the spatial dimension d, decreasing in sensitivity as d increases. For finite κ, ropt is a non-trivial function of the target size and distance between the target and the reset point. We also show how our results converge to those obtained previously for problems with totally absorbing targets and similar geometries when the absorption rate becomes infinite. Finally, we generalize the theory to take into account an extended chemical reaction scheme within a target.

The lateral diffusion and trapping of neurotransmitter receptors within the postsynaptic membrane of a neuron plays a key role in determining synaptic strength and plasticity. Trapping is mediated by the reversible binding of receptors to scaffolding proteins (slots) within a synapse. In this paper we introduce a new method for analyzing the transient dynamics of synapses in a diffusion-trapping model of receptor trafficking. Given a population of spatially distributed synapses, each of which has a fixed number of slots, we calculate the rate of relaxation to the steady-state distribution of bound slots (synaptic weights) in terms of a set of local accumulation times. Assuming that the rates of exocytosis and endocytosis are sufficiently slow, we show that the steady-state synaptic weights are independent of each other (purely local). On the other hand, the local accumulation time of a given synapse depends on the number of slots and the spatial location of all the synapses, indicating a form of transient heterosynaptic plasticity. This suggests that local accumulation time measurements could provide useful information regarding the distribution of synaptic weights within a dendrite.