Strong disorder leads to scale invariance in complex biological systems

Abstract

Despite the innate complexity of the cell, emergent scale-invariant behavior is observed in many biological systems. We investigate one example of this phenomenon: the dynamics of large complexes in the bacterial cytoplasm. The observed dynamics of these complexes is scale invariant in three measures of dynamics: mean-squared displacement (MSD), velocity autocorrelation function, and the step-size distribution. To investigate the physical mechanism for this emergent scale invariance, we explore minimal models in which mobility is modeled as diffusion on a rough free-energy landscape in one dimension. We discover that all three scale-invariant characteristics emerge generically in the strong disorder limit. (Strong disorder is defined by the divergence of the ensemble-averaged hop time between lattice sites.) In particular, we demonstrate how the scale invariance of the relative step-size distribution can be understood from the perspective of extreme-value theory in statistics (EVT). We show that the Gumbel scale parameter is simply related to the MSD scaling parameter. The EVT mechanism of scale invariance is expected to be generic to strongly disordered systems and therefore a powerful tool for the analysis of other systems in biology and beyond.

Brownian yet non-Gaussian diffusion in heterogeneous media: from superstatistics to homogenization

“…[1][2][3] and references therein. Similar effects are also seen in anomalous diffusion [4][5][6] which case however is not discussed in the present work.…”

“…3 displays the PDFs for equilibrated Ito case at different times. These exhibit the transition from exponential to a Gaussian distribution, showing a pronounced central peak at intermediate times, which is well known from the experimental realizations [1][2][3], as well as from other models [6,29].…”

Anomalous transport in the soft-sphere Lorentz model

“…Interestingly, our result is in contrast to what is seen in a periodic Lorentz gas, where softening the interactions drastically changes the nature of the transport. [66] As a further extension to our work, we expect that the combination of using soft interaction potentials with Brownian dynamics will lead to interesting new results, with particular relevance to biological systems, [7,[15][16][17][18][19][67][68][69][70][71][72][73][74] where soft interactions and Brownian motion are typical. As in the case of adding many interacting tracers to the Lorentz model, [75][76][77][78][79][80][81][82] the localization transition will become rounded.…”

Probability Thermodynamics and Probability Quantum Field

“…The Laplace distribution has fatter tails than the normal distribution. The Laplace distribution appears in for example neuronal growth [53], complex networks [54], and complex biological systems [55].…”