Proteins within the model cytoplasm are represented as spheres, with different masses/sizes. They interact through effective potentials (attractive) containing aspecific interactions and also the effect of the solvent. These potentials further depend on the sizes of the interacting objects.
The solvent is implicit and so I use the Langevin equation with a proper friction for each protein because friction too depends on the size of the protein.
I see anomalous diffusion (above all for big proteins) and I so I was trying to understand the connection of my model with one of the model between CTRW or FLM. How can understand/prove formally what is this connection, if any?
Article The role of ergodicity in anomalous stochastic processes: An...
Unfortunately I have no clear idea of friction in a Langevin equation (LE). Is it like a memory kernel? The CTRW, to my understanding, is an Ornstein-Uhlenbeck process with a stochastically fluctuating intrinsic time. This results in intermittent, i.e., non-Gaussian and heavy-tailed increment PDFs of the CTRW. The application of CTRW to generate synthetic (intermittent) wind fields is discussed in the PhD thesis of D. Kleinhans. The CTRW can principally be transformed to a fractional LE in real time. There are several publications on fractional LE by R. Friedrich and T.D. Frank. On the application of LE to spherical movement of molecules there are publications by S.J. Lade, but Im am not sure wether this is closely connected to your application.
Fabio, what you see as anomalous diffusion may be due to any kind of confined diffusion. See for example the discussion of the model of walking confined diffusion in our article: http://pubs.rsc.org/en/content/articlelanding/2011/sm/c1sm05217a
When confinement causes nonlinear dependence of mean square displacement on time, the anomalousness is a transient between fast normal diffusion and slow normal diffusion. And the apparent anomalous exponent depends on the time range of measurement.