A stochastic model for patterning of the cytoplasm by the saltatory movement

In various cases of importance for animal physiology and development, a specific distribution of cellular components is achieved through the active transport of these components along cytoskeletal fibres by molecular motors. The pattern-generating transport is stochastic; it is commonly referred to as the saltatory movement which means frequent, random change of direction of movement of individual transported particles. Inference of the distribution of the cellular components and kinetics of transitions between different patterns from parameters of the saltatory movement is the goal of the proposed theory. The theory is presented by developing a sample model for the redistribution of lipid droplets at early stages of Drosophila development, a process well studied at the quantitative level. The saltatory movement is modelled at the fundamental level as a stochastic velocity jump process. A diffusion (in the mathematical sense) model is derived from the fundamental velocity jump description as its simple and accurate approximation. This approximation reduces the number of parameters, simplifies the methods of their measurement and clarifies the relationship between the kinetics and the resulting pattern.