Molecular motor-based models of random intermittent search in dendrites
A key component in the cellular mechanisms underlying learning and memory involves the distribution and delivery of mRNA to synaptic sites in dendrites. A minimal three-state random intermittent search model of motor-driven mRNA transport is developed to explore the question of why motor-driven mRNA are observed moving bidirectionally. The model is analyzed by computing the probability an mRNA is delivered to a synaptic target and the average delivery time (MFPT). It is found that if the branched geometry of the dendrite is ignored, a purely unidirectional transport strategy will result in the smallest MFPT at any given delivery probability. The branched geometry of the dendrite is then incorporated into the model, and it is shown that a phase transition exists for a critical delivery probability where bidirectional strategies improve the corresponding MFPT. To further explore the impact of motor-driven transport behavior on mRNA delivery, the three-state model is extended to include a detailed, biophysical model of a multimotor complex coordinated through a tug-of-war. The model is analyzed to explore how various measurable, physical quantities, such as adenosine triphosphate, can be tuned to optimize cargo delivery.