Brownian yet Non-Gaussian Diffusion: From Superstatistics to Subordination of Diffusing Diffusivities

Aleksei V. Chechkin, Flavio Seno, Ralf Metzler, and Igor M. Sokolov                      
Phys. Rev. X 7, 021002

Key Image

Any microscopic particle placed in a fluid will move about randomly. This effect, known as Brownian motion, is caused by collisions between the particle and the surrounding molecules. Two hallmarks of Brownian motion are that particles spread out linearly over time, and the probability of finding a particle at a certain position at a given time is mathematically described by a Gaussian function (a bell curve). However, in certain situations, such as individual nematodes (a type of roundworm) or microscopic beads on lipid tubes, this probability behaves quite differently—sometimes as an exponential function. At first, this phenomenon, now observed in a large range of systems, seems to violate a universal mathematical law known as the central limit theorem, which predicts that this probability should converge to a Gaussian function. Here, we establish a physical minimal model for such “Brownian yet non-Gaussian” diffusion.

Using analytical calculations and simulations, we show that both the linear spread of particles and an exponential probability distribution can be reconciled when the intensity of the random jiggling of the particles itself becomes a random function of time. We augment the standard Langevin equation—a differential equation that describes the Brownian motion of a particle—with a random noise strength. This “diffusing diffusivity” has an inherent correlation time that defines a crossover from the non-Gaussian probability seen on short time scales to a long-time Gaussian.

Our minimal model for the diffusing-diffusivity approach to Brownian yet non-Gaussian diffusion is very versatile, and we believe that it will help establish this approach as a new paradigm in the physics of stochastic processes.

Modeling quorum sensing trade-offs between bacterial cell density and system extension from open boundaries

Mattia Marenda, Marina Zanardo, Antonio Trovato, Flavio Seno and A. Squartini 
Scientific Reports 6, Article number: 39142 (2016)

Figure 1

Bacterial communities undergo collective behavioural switches upon producing and sensing diffusible signal molecules; a mechanism referred to as Quorum Sensing (QS). Exemplarily, biofilm organic matrices are built concertedly by bacteria in several environments. QS scope in bacterial ecology has been debated for over 20 years. Different perspectives counterpose the role of density reporter for populations to that of local environment diffusivity probe for individual cells. Here we devise a model system where tubes of different heights contain matrix-embedded producers and sensors. These tubes allow non-limiting signal diffusion from one open end, thereby showing that population spatial extension away from an open boundary can be a main critical factor in QS. Experimental data, successfully recapitulated by a comprehensive mathematical model, demonstrate how tube height can overtake the role of producer density in triggering sensor activation. The biotic degradation of the signal is found to play a major role and to be species-specific and entirely feedback-independent.

Linking in domain-swapped protein dimers

Marco Baiesi, Enzo Orlandini, Amntonio Trovato and Flavio Seno                   
Scientific Reports 6, Article number: 33872 (2016)

Figure 1

The presence of knots has been observed in a small fraction of single-domain proteins and related to their thermodynamic and kinetic properties. The exchanging of identical structural elements, typical of domain-swapped proteins, makes such dimers suitable candidates to validate the possibility that mutual entanglement between chains may play a similar role for protein complexes. We suggest that such entanglement is captured by the linking number. This represents, for two closed curves, the number of times that each curve winds around the other. We show that closing the curves is not necessary, as a novel parameter G′, termed Gaussian entanglement, is strongly correlated with the linking number. Based on 110 non redundant domain-swapped dimers, our analysis evidences a high fraction of chains with a significant intertwining, that is with |G′| > 1. We report that Nature promotes configurations with negative mutual entanglement and surprisingly, it seems to suppress intertwining in long protein dimers. Supported by numerical simulations of dimer dissociation, our results provide a novel topology-based classification of protein-swapped dimers together with some preliminary evidence of its impact on their physical and biological properties.