The Hitchhiker model for Laplace diffusion processes in the cell environment

Aggregation and fragmentation of single molecules in the cell environment lead to a spectrum of diffusivities and to statistical laws of movement very different from typical Brownian motion. Current models of intracellular transport do not explain at a microscopical level the emergence of theses deviations. Employing a many body approach, which we call the Hitchhiker model, we elucidate how the widely observed exponential tails in the particle spreading, i.e. the Laplace distribution and the modulations of the diffusivities, are controlled by size fluctuations of single molecules. By means of numerical simulations Laplace distributions are obtained whether we track one molecule or many molecules in parallel. However, we show that the diffusivity varies significantly depending on which tracking protocol is applied. Using a renewal process in the space of sizes, we quantify to what extent the average diffusivity in the single molecule technique is decreased compared with the ensemble average.