| Popis: |
Features inside the living cell are complex and crowded; in such complex environments diffusion processes can be said to exhibit three distinct behaviours: pure or Fickian diffusion, superdiffusion and subdiffusion. Furthermore, the behaviour of biochemical processes taking place in these environments does not follow classical theory. Because of these factors, the task of modelling dynamical proceses in complex environments becomes very challenging and demanding and has received considerable attention from other researchers seeking to construct a coherent model. Here, we are interested to study the phenomenon of subdiffusion, which occurs when there is molecular crowding. The Reaction Diffusion Partial Differential Equations (RDPDEs) approach has been used traditionally to study diffusion. However, these equations have limitations due to their unsuitability for a subdiffusive setting. However, I provide models based on Fractional Reaction Diffusion Partial Differential Equations (FRDPDEs), which are able to portray intracellular diffusion in crowded environments. In particular, we will consider a class of continuous spatial models to describe concentrations of molecular species in crowded environments. In order to investigate the variability of the crowdedness, we have used the anomalous diffusion parameter $\alpha$ to mimic immobile obstacles or barriers. We particularly use the notation $D_t^{1-\alpha} f(t)$ to represent a differential operator of noninteger order. When the power exponent is $\alpha=1$, this corresponds to pure diffusion and to subdiffusion when $0 |
