Random walks in biological systems: Nonergodic subdiffusion from transient interactions with heterogeneous partners

2019 edition

Christos Charalambous

In this work, motivated by experimental results on the diffusion properties of the DC-SIGN receptor, we propose a model where spatiotemporal disorder explains the arising of an anomalous nonergodic motion. Spatiotemporal disorder has been recently associated to the occurrence of anomalous nonergodic diffusion of molecular components in biological systems, but the underlying microscopic mechanism is unclear. We introduce a model in which a particle performs continuous Brownian motion with changes of diffusion coefficients induced by transient molecular interactions with diffusive binding partners. In spite of the exponential distribution of waiting times, the model shows subdiffusion and nonergodicity similar to a continuous time random walk (CTRW).
In our model, the Brownian motion of a random walker is temporarily modified upon interactions with a set of random walkers called hunters: as a consequence of the interaction, the motion of the walker is altered by a factor randomly drawn from a distribution with a power law tail. A particular case of this general scenario is provided by a distribution obtained considering that the diffusivity is the sum of several squared Gaussian random variables arising out of many microscopic degrees of freedom. We consider a case in which interactions slow down the diffusion of the prey. The model describes a diffusing molecule which, upon interaction with another molecule, undergoes a change of diffusivity for the time the interaction takes place. An example of this effect is provided by the formation of transient dimers and oligomers among chemically identical molecules, as well as by interactions occurring among different molecular species. Our model is general enough such that it can describe scenarios that include a variety of interactions between a multiplicity of cellular components (e.g. proteins, lipids, vesicles, or organelles).
A novelty of our model, compared to a CTRW, is that, the walker always performs Brownian motion although with different diffusivities. A crucial aspect of this model is that we explicitly introduce a physical mechanism (i.e., transient interactions) causing the change of diffusivity. Moreover, even though the prey experiences the disorder only for a limited amount of time (i.e., upon interaction), this is sufficient to generate anomalous diffusion and non-ergodicity even in the dilute limit. The occurrence of such interactions can be experimentally verified, e.g. using multicolor single particle tracking experiments. In addition, the model allows one to estimate microscopic parameters of the system under investigation. This sets a great advantage over models with diffusion coefficient varying in space or time. Furthermore, the dependence of these properties, subdiffusivity and nonergodicity, on the density of binding partners is analyzed and discussed. Our work provides an experimentally-testable microscopic model to investigate the nature of nonergodicity in disordered media.