Brownian yet non-Gaussian diffusion, characterised by a linear scaling in time of the mean squared displacement but a non-Gaussian displacement distribution is a phenomenon that has been observed in a variety of systems. In my talk, after a brief historical introduction to Brownian motion and the theory of diffusion, I will review experimental evidence and show how non-Gaussian statistics...
For two molecules to react they first have to meet. Yet, reaction times are rarely on par with the first passage times that govern such molecular encounters. A prime reason for this discrepancy is stochastic transitions between reactive and nonreactive molecular states, which results in effective gating of product formation and altered reaction kinetics. To better understand this phenomenon we...
We consider the possibility of socioeconomic collapse of the population caused by epidemics spreading. Using a simple model of negative feedback we study the dynamics of epidemic spreading in a group of agents with its mutual influence on some formal resource (economical, financial, etc). A coupling mechanism between spreading- and resource-subsystem is supposed to be governed by over-barrier...
The survival of natural populations may be greatly affected by environmental conditions that vary in space and time. We look at a population residing in two locations (patches) coupled by migration, in which the local conditions fluctuate in time. We report on two findings. First, we find that, unlike rare events in many other systems, here the histories leading to a rare extinction event are...
In embryo development, cells specialize into their future role by changing their gene expression levels in response to the concentrations of competing chemical signals, called morphogens. This paradigm is known as Wolpert’s French flag model. In the mathematical modelling of these phenomena, a profound role is played by the reaction-diffusion equations involving some form of activation term...
Spinal cord development is a complex process due to the interplay of signaling molecules over varying length and time scales. Despite the intrinsic stochasticity of signaling events, the resulting pattern of gene expression domains is remarkably precise and reproducible between individuals. How this patterning precision is achieved is still poorly understood. By investigating formation of...
The shape of many biomolecules is similar to the Coxeter-Boerdijk (CB) helix, made of tetrahedra placed next to each other in such a way that the tetrahedrons are adjacent to each other with their faces. The helix CB is the solution to the maximum packing task. In the collagen helix, every third amino acid is glycine (Gly), and the entire chain contains primarily proline (Pro). Half of the Pro...
