Population-level heterogeneity as a reflection of mixed strategy: A computational perspective on the Crabtree effect.

Is population-level heterogeneity a reflection of distinct subpopulations, exhibiting different metabolic functions, or dynamic metabolism of individuals within the population? This fascinating question has remained a subject of great interest in studying metabolic specialization in microorganisms. The Crabtree effect - i.e., the ability of some microorganisms to switch from respiration to fermentation in the presence of oxygen - is an appropriate case study to address the aforementioned question. Game-theoretical approaches have been routinely used to examine and explain the way a microorganism, such as yeast, would switch between the two ATP-producing pathways, i.e., respiration and fermentation. Here we attempt to explain the switch between respiration and fermentation in yeast by constructing a simple metabolic switch. We then utilize an individual-based model, in which each individual is equipped with all the relevant chemical reactions, to see how cells equipped with such metabolic switch would behave in different conditions. We further investigate our proposed metabolic switch using the game-theoretical approach. Based on this model, we postulate that the population-level metabolic heterogeneity in microorganisms can simply arise from individuals utilizing a mixed strategy.

Noise-driven cell differentiation and the emergence of spatiotemporal patterns.

The emergence of phenotypic diversity in a population of cells and their arrangement in space and time is one of the most fascinating features of living systems. In fact, understanding multicellularity is unthinkable without explaining the proximate and the ultimate causes of cell differentiation in time and space. Simpler forms of cell differentiation can be found in unicellular organisms, such as bacterial biofilm, where reversible cell differentiation results in phenotypically diverse populations. In this manuscript, we attempt to start with the simple case of reversible nongenetic phenotypic to construct a model of differentiation and pattern formation. Our model, which we refer to as noise-driven differentiation (NDD) model, is an attempt to consider the prevalence of noise in biological systems, alongside what is known about genetic switches and signaling, to create a simple model which generates spatiotemporal patterns from bottom-up. Our simulations indicate that the presence of noise in cells can lead to reversible differentiation and the addition of signaling can create spatiotemporal pattern.

From indication to decision: A hierarchical approach to model the chemotactic behavior of Escherichia coli.

Reducing the complex behavior of living entities to its underlying physical and chemical processes is a formidable task in biology. Complex behaviors can be characterized as decision making: the ability to process the incoming information via an intracellular network and act upon this information to choose appropriate strategies. Motility is one such behavior that has been the focus many modeling efforts in the past. Our aim is to reduce the chemotactic behavior in Escherichia coli to its molecular constituents in order to paint a comprehensive and end-to-end picture of this intricate behavior. We utilize a hierarchical approach, consisting of three layers, to achieve this goal: at the first level, chemical reactions involved in chemotaxis are simulated. In the second level, the chemical reactions give rise to the mechanical movement of six independent flagella. At the last layer, the two lower layers are combined to allow a digital bacterium to receive information from its environment and swim through it with verve. Our results are in concert with the experimental studies concerning the motility of E.coli cells. In addition, we show that our detailed model of chemotaxis is reducible to a non-homogeneous Markov process.

Aging underdamped scaled Brownian motion: Ensemble- and time-averaged particle displacements, nonergodicity, and the failure of the overdamping approximation.

We investigate both analytically and by computer simulations the ensemble- and time-averaged, nonergodic, and aging properties of massive particles diffusing in a medium with a time dependent diffusivity. We call this stochastic diffusion process the (aging) underdamped scaled Brownian motion (UDSBM). We demonstrate how the mean squared displacement (MSD) and the time-averaged MSD of UDSBM are affected by the inertial term in the Langevin equation, both at short, intermediate, and even long diffusion times. In particular, we quantify the ballistic regime for the MSD and the time-averaged MSD as well as the spread of individual time-averaged MSD trajectories. One of the main effects we observe is that, both for the MSD and the time-averaged MSD, for superdiffusive UDSBM the ballistic regime is much shorter than for ordinary Brownian motion. In contrast, for subdiffusive UDSBM, the ballistic region extends to much longer diffusion times. Therefore, particular care needs to be taken under what conditions the overdamped limit indeed provides a correct description, even in the long time limit. We also analyze to what extent ergodicity in the Boltzmann-Khinchin sense in this nonstationary system is broken, both for subdiffusive and superdiffusive UDSBM. Finally, the limiting case of ultraslow UDSBM is considered, with a mixed logarithmic and power-law dependence of the ensemble- and time-averaged MSDs of the particles. In the limit of strong aging, remarkably, the ordinary UDSBM and the ultraslow UDSBM behave similarly in the short time ballistic limit. The approaches developed here open ways for considering other stochastic processes under physically important conditions when a finite particle mass and aging in the system cannot be neglected.

Underdamped scaled Brownian motion: (non-)existence of the overdamped limit in anomalous diffusion.

It is quite generally assumed that the overdamped Langevin equation provides a quantitative description of the dynamics of a classical Brownian particle in the long time limit. We establish and investigate a paradigm anomalous diffusion process governed by an underdamped Langevin equation with an explicit time dependence of the system temperature and thus the diffusion and damping coefficients. We show that for this underdamped scaled Brownian motion (UDSBM) the overdamped limit fails to describe the long time behaviour of the system and may practically even not exist at all for a certain range of the parameter values. Thus persistent inertial effects play a non-negligible role even at significantly long times. From this study a general questions on the applicability of the overdamped limit to describe the long time motion of an anomalously diffusing particle arises, with profound consequences for the relevance of overdamped anomalous diffusion models. We elucidate our results in view of analytical and simulations results for the anomalous diffusion of particles in free cooling granular gases.

Fractional Dynamics of Network Growth Constrained by Aging Node Interactions.

In many social complex systems, in which agents are linked by non-linear interactions, the history of events strongly influences the whole network dynamics. However, a class of "commonly accepted beliefs" seems rarely studied. In this paper, we examine how the growth process of a (social) network is influenced by past circumstances. In order to tackle this cause, we simply modify the well known preferential attachment mechanism by imposing a time dependent kernel function in the network evolution equation. This approach leads to a fractional order Barabási-Albert (BA) differential equation, generalizing the BA model. Our results show that, with passing time, an aging process is observed for the network dynamics. The aging process leads to a decay for the node degree values, thereby creating an opposing process to the preferential attachment mechanism. On one hand, based on the preferential attachment mechanism, nodes with a high degree are more likely to absorb links; but, on the other hand, a node's age has a reduced chance for new connections. This competitive scenario allows an increased chance for younger members to become a hub. Simulations of such a network growth with aging constraint confirm the results found from solving the fractional BA equation. We also report, as an exemplary application, an investigation of the collaboration network between Hollywood movie actors. It is undubiously shown that a decay in the dynamics of their collaboration rate is found, even including a sex difference. Such findings suggest a widely universal application of the so generalized BA model.

Aging scaled Brownian motion.

Scaled Brownian motion (SBM) is widely used to model anomalous diffusion of passive tracers in complex and biological systems. It is a highly nonstationary process governed by the Langevin equation for Brownian motion, however, with a power-law time dependence of the noise strength. Here we study the aging properties of SBM for both unconfined and confined motion. Specifically, we derive the ensemble and time averaged mean squared displacements and analyze their behavior in the regimes of weak, intermediate, and strong aging. A very rich behavior is revealed for confined aging SBM depending on different aging times and whether the process is sub- or superdiffusive. We demonstrate that the information on the aging factorizes with respect to the lag time and exhibits a functional form that is identical to the aging behavior of scale-free continuous time random walk processes. While SBM exhibits a disparity between ensemble and time averaged observables and is thus weakly nonergodic, strong aging is shown to effect a convergence of the ensemble and time averaged mean squared displacement. Finally, we derive the density of first passage times in the semi-infinite domain that features a crossover defined by the aging time.