Summary Embryos of most metazoans undergo rapid and synchronous cell cycles following fertilization. While diffusion is too slow for synchronization of mitosis across large spatial scales, waves of Cdk1 activity represent a possible process of synchronization. However, the mechanisms regulating Cdk1 waves during embryonic development remain poorly understood. Using biosensors of Cdk1 and Chk1 activities, we dissect the regulation of Cdk1 waves in the Drosophila syncytial blastoderm. We show that Cdk1 waves are not controlled by the mitotic switch but by a double negative feedback between Cdk1 and Chk1. Using mathematical modeling and surgical ligations we demonstrate a fundamental distinction between S-phase Cdk1 waves, which propagate as active trigger waves in an excitable medium, and mitotic Cdk1 waves, which propagate as passive phase waves. Our findings show that in Drosophila embryos, Cdk1 positive feedback serves primarily to ensure the rapid onset of mitosis, while wave propagation is regulated by S-phase events.

Existing theoretical models of evolution focus on the relative fitness advantages of different mutants in a population while the dynamic behavior of the population size is mostly left unconsidered. We here present a generic stochastic model which combines the growth dynamics of the population and its internal evolution. Our model thereby accounts for the fact that both evolutionary and growth dynamics are based on individual reproduction events and hence are highly coupled and stochastic in nature. We exemplify our approach by studying the dilemma of cooperation in growing populations and show that genuinely stochastic events can ease the dilemma by leading to a transient but robust increase in cooperation.

Length regulation of microtubules (MTs) is essential for many cellular processes. Molecular motors like kinesin-8, which move along MTs and also act as depolymerases, are known as key players in MT dynamics. However, the regulatory mechanisms of length control remain elusive. Here, we investigate a stochastic model accounting for the interplay between polymerization kinetics and motor-induced depolymerization. We determine the dependence of MT length and variance on rate constants and motor concentration. Moreover, our analyses reveal how collective phenomena lead to a well-defined MT length.

Microbes providing public goods are widespread in nature despite running the risk of being exploited by free-riders. However, the precise ecological factors supporting cooperation are still puzzling. Following recent experiments, we consider the role of population growth and the repetitive fragmentation of populations into new colonies mimicking simple microbial life-cycles. Individual-based modeling reveals that demographic fluctuations, which lead to a large variance in the composition of colonies, promote cooperation. Biased by population dynamics these fluctuations result in two qualitatively distinct regimes of robust cooperation under repetitive fragmentation into groups. First, if the level of cooperation exceeds a threshold, cooperators will take over the whole population. Second, cooperators can also emerge from a single mutant leading to a robust coexistence between cooperators and free-riders. We find frequency and size of population bottlenecks, and growth dynamics to be the major ecological factors determining the regimes and thereby the evolutionary pathway towards cooperation.

The concept of fitness as a measure for a species’ success in natural selection is central to the theory of evolution. We here investigate how reproduction rates which are not constant but vary in response to environmental fluctuations, influence a species’ prosperity and thereby its fitness. Interestingly, we find that not only larger growth rates but also reduced sensitivities to environmental changes substantially increase the fitness. Thereby, depending on the noise level of the environment, it might be an evolutionary successful strategy to minimize this sensitivity rather than to optimize the reproduction speed. Also for neutral evolution, where species with exactly the same properties compete, variability in the growth rates plays a crucial role. The time for one species to fixate is strongly reduced in the presence of environmental noise. Hence, environmental fluctuations constitute a possible explanation for effective population sizes inferred from genetic data that often are much smaller than the census population size.

We study the interplay of population growth and evolutionary dynamics using a stochastic model based on birth and death events. In contrast to the common assumption of an independent population size, evolution can be strongly affected by population dynamics in general. Especially for fast reproducing microbes which are subject to selection, both types of dynamics are often closely intertwined. We illustrate this by considering different growth scenarios. Depending on whether microbes die or stop to reproduce (dormancy), qualitatively different behaviors emerge. For cooperating bacteria, a permanent increase of costly cooperation can occur. Even if not permanent, cooperation can still increase transiently due to demographic fluctuations. We validate our analysis via stochastic simulations and analytic calculations. In particular, we derive a condition for an increase in the level of cooperation.

The assembly and disassembly dynamics of microtubules (MTs) is tightly controlled by MT-associated proteins. Here, we investigate how plus-end-directed depolymerases of the kinesin-8 family regulate MT depolymerization dynamics. Using an individual-based model, we reproduce experimental findings. Moreover, crowding is identified as the key regulatory mechanism of depolymerization dynamics. Our analysis reveals two qualitatively distinct regimes. For motor densities above a particular threshold, a macroscopic traffic jam emerges at the plus-end and the MT dynamics become independent of the motor concentration. Below this threshold, microscopic traffic jams at the tip arise that cancel out the effect of the depolymerization kinetics such that the depolymerization speed is solely determined by the motor density. Because this density changes over the MT length, length-dependent regulation is possible. Remarkably, motor cooperativity affects only the end-residence time of depolymerases and not the depolymerization speed.

T lymphocytes’ ability to discriminate between structurally related antigens has been attributed to the unique signaling properties of the T cell receptor. However, recent studies have suggested that the output of this discrimination process is conditioned by environmental cues. Here we demonstrate how the IL-2 cytokine, collectively generated by strongly activated T cell clones, can induce weaker T cell clones to proliferate. We identify the PI3K pathway as being critical for integrating the antigen and cytokine responses and for controlling cell cycle entry. We build a hybrid stochastic/deterministic computational model that accounts for such signal-synergism and demonstrates quantitatively how T-cells tune their cell cycle entry according to environmental cytokine cues. Our findings indicate that antigen discrimination by T-cells is not solely an intrinsic cellular property but rather a product of integration of multiple cues, including local cues like antigen quality and quantity, to global ones like the extracellular concentration of inflammatory cytokines.