A perspective on SOAL, a stochastic model of neuronal outgrowth

Abstract

A functional nervous system requires neuronal connections to be made in a highly detailed and stereotypic manner. During development, neurons extend processes that can branch, travel in different directions, and form elaborate patterns. These patterns are essential for forming proper connections. Patterns of outgrowth are produced by complex molecular events that cause a fluid membrane to move. The collective impact of dynamic fluctuating events at the microscale cause the patterns of outgrowth observed at the macroscale. Patterning is genetically controlled, but the effects genes have on membrane movement and patterning are not well understood. To better understand how genes control outgrowth patterns, I propose a statistically-oriented asymmetric localization (SOAL) model. This model is based on the theory that receptor-mediated outgrowth activity is stochastically oriented and when the system is at equilibrium there is an equal probability of outgrowth being oriented in any direction. This concept allows a statistical mechanics approach that can correlate the microscale events of outgrowth to the observed macroscale patterns. Proof-of-concept experiments suggest this approach can be used to study the effect genes have on outgrowth patterns. The SOAL model also provides a new theoretical framework for conceptualizing guidance. According to the model, outgrowth activity becomes asymmetrically localized to the neuron's surface in a statistically dependent manner. Extracellular cues regulate the probability of outgrowth along the surface and the orientation of outgrowth fluctuates across the surface over time. This creates a directional bias that allows the growth cone to navigate in reference to the composition of extracellular cues.