Hydrodynamic flow and concentration gradients in the gut enhance neutral bacterial diversity.

The gut microbiota features important genetic diversity, and the specific spatial features of the gut may shape evolution within this environment. We investigate the fixation probability of neutral bacterial mutants within a minimal model of the gut that includes hydrodynamic flow and resulting gradients of food and bacterial concentrations. We find that this fixation probability is substantially increased, compared with an equivalent well-mixed system, in the regime where the profiles of food and bacterial concentration are strongly spatially dependent. Fixation probability then becomes independent of total population size. We show that our results can be rationalized by introducing an active population, which consists of those bacteria that are actively consuming food and dividing. The active population size yields an effective population size for neutral mutant fixation probability in the gut.

Theoretical study of the impact of adaptation on cell-fate heterogeneity and fractional killing.

Fractional killing illustrates the cell propensity to display a heterogeneous fate response over a wide range of stimuli. The interplay between the nonlinear and stochastic dynamics of biochemical networks plays a fundamental role in shaping this probabilistic response and in reconciling requirements for heterogeneity and controllability of cell-fate decisions. The stress-induced fate choice between life and death depends on an early adaptation response which may contribute to fractional killing by amplifying small differences between cells. To test this hypothesis, we consider a stochastic modeling framework suited for comprehensive sensitivity analysis of dose response curve through the computation of a fractionality index. Combining bifurcation analysis and Langevin simulation, we show that adaptation dynamics enhances noise-induced cell-fate heterogeneity by shifting from a saddle-node to a saddle-collision transition scenario. The generality of this result is further assessed by a computational analysis of a detailed regulatory network model of apoptosis initiation and by a theoretical analysis of stochastic bifurcation mechanisms. Overall, the present study identifies a cooperative interplay between stochastic, adaptation and decision intracellular processes that could promote cell-fate heterogeneity in many contexts.

Scaling laws of cell-fate responses to transient stress.

Analysis and modelling of dose-survival curves of cells and tissues are often used to assess therapeutic efficacy or environmental risks, much less to infer the intracellular regulatory mechanisms of cellular stress response. However, systematic measurements of how cell survival depends on the time profile of stress, such as exposure duration, provide practical means to decipher the homeostatic dynamics of stress-response regulatory networks. In this paper, we propose a dynamical framework to theoretically address the relationship between cell fate response to a transient stress and the underlying regulatory feedback mechanisms. A simple network topology that couples a homeostatic negative feedback and a death-triggering positive feedback is shown to display four response regimes for which the iso-effect relationships between duration and intensity are captured by specific power laws. These distinct response regimes define several windows of stress duration for which lethality is not merely proportional to the product of intensity and duration, and, thus, for which cells are either more tolerant or more vulnerable to a given dose. Overall, this study highlights the differential roles of feedback strength, timescale and nonlinearity in promoting survivability to particular stress profiles, providing a valuable framework for a comparative analysis of diverse stress-specific regulatory networks.

Long-period clocks from short-period oscillators.

We analyze repulsively coupled Kuramoto oscillators, which are exposed to a distribution of natural frequencies. This source of disorder leads to closed orbits of repetitive temporary patterns of phase-locked motion, providing clocks on macroscopic time scales. The periods can be orders of magnitude longer than the periods of individual oscillators. By construction, the attractor space is quite rich. This may cause long transients until the deterministic trajectories find their stationary orbits. The smaller the width of the distribution about the common natural frequency, the longer are the emerging time scales on average. Among the long-period orbits, we find self-similar sequences of temporary phase-locked motion on different time scales. The ratio of time scales is determined by the ratio of widths of the distributions. The results illustrate a mechanism for how simple systems can provide rather flexible dynamics, with a variety of periods even without external entrainment.

Networks of coupled circuits: from a versatile toggle switch to collective coherent behavior.

We study the versatile performance of networks of coupled circuits. Each of these circuits is composed of a positive and a negative feedback loop in a motif that is frequently found in genetic and neural networks. When two of these circuits are coupled with mutual repression, the system can function as a toggle switch. The variety of its states can be controlled by two parameters as we demonstrate by a detailed bifurcation analysis. In the bistable regimes, switches between the coexisting attractors can be induced by noise. When we couple larger sets of these units, we numerically observe collective coherent modes of individual fixed-point and limit-cycle behavior. It is there that the monotonic change of a single bifurcation parameter allows one to control the onset and arrest of the synchronized oscillations. This mechanism may play a role in biological applications, in particular, in connection with the segmentation clock. While tuning the bifurcation parameter, also a variety of transient patterns emerges upon approaching the stationary states, in particular, a self-organized pacemaker in a completely uniformly equipped ensemble, so that the symmetry breaking happens dynamically.

Caveats in modeling a common motif in genetic circuits.

From a coarse-grained perspective, the motif of a self-activating species, activating a second species that acts as its own repressor, is widely found in biological systems, in particular in genetic systems with inherent oscillatory behavior. Here we consider a specific realization of this motif as a genetic circuit, termed the bistable frustrated unit, in which genes are described as directly producing proteins. Upon an improved resolution in time, we focus on the effect that inherent time scales on the underlying scale can have on the bifurcation patterns on a coarser scale. Time scales are set by the binding and unbinding rates of the transcription factors to the promoter regions of the genes. Depending on the ratio of these rates to the decay times of both proteins, the appropriate averaging procedure for obtaining a coarse-grained description changes and leads to sets of deterministic equations, which considerably differ in their bifurcation structure. In particular, the desired intermediate range of regular limit cycles fades away when the binding rates of genes are not fast as compared to the decay time of the proteins. Our analysis illustrates that the common topology of the widely found motif alone does not imply universal features in the dynamics.