How microscopic epistasis and clonal interference shape the fitness trajectory in a spin glass model of microbial long-term evolution.

The adaptive dynamics of evolving microbial populations takes place on a complex fitness landscape generated by epistatic interactions. The population generically consists of multiple competing strains, a phenomenon known as clonal interference. Microscopic epistasis and clonal interference are central aspects of evolution in microbes, but their combined effects on the functional form of the population's mean fitness are poorly understood. Here, we develop a computational method that resolves the full microscopic complexity of a simulated evolving population subject to a standard serial dilution protocol. Through extensive numerical experimentation, we find that stronger microscopic epistasis gives rise to fitness trajectories with slower growth independent of the number of competing strains, which we quantify with power-law fits and understand mechanistically via a random walk model that neglects dynamical correlations between genes. We show that increasing the level of clonal interference leads to fitness trajectories with faster growth (in functional form) without microscopic epistasis, but leaves the rate of growth invariant when epistasis is sufficiently strong, indicating that the role of clonal interference depends intimately on the underlying fitness landscape. The simulation package for this work may be found at https://github.com/nmboffi/spin_glass_evodyn.

The effect of weak clonal interference on average fitness trajectories in the presence of macroscopic epistasis.

Adaptation dynamics on fitness landscapes is often studied theoretically in the strong-selection, weak-mutation regime. However, in a large population, multiple beneficial mutants can emerge before any of them fixes in the population. Competition between mutants is known as clonal interference, and while it is known to slow down the rate of adaptation (when compared to the strong-selection, weak-mutation model with the same parameters), how it affects the shape of long-term fitness trajectories in the presence of epistasis is an open question. Here, by considering how changes in fixation probabilities arising from weak clonal interference affect the dynamics of adaptation on fitness-parameterized landscapes, we find that the change in the shape of fitness trajectory arises only through changes in the supply of beneficial mutations (or equivalently, the beneficial mutation rate). Furthermore, a depletion of beneficial mutations as a population climbs up the fitness landscape can speed up the rescaled fitness trajectory (where adaptation speed is measured relative to its value at the start of the experiment), while an enhancement of the beneficial mutation rate does the opposite of slowing it down. Our findings suggest that by carrying out evolution experiments in both regimes (with and without clonal interference), one could potentially distinguish the different sources of macroscopic epistasis (fitness effect of mutations vs change in fraction of beneficial mutations).

Programming cell growth into different cluster shapes using diffusible signals.

Advances in genetic engineering technologies have allowed the construction of artificial genetic circuits, which have been used to generate spatial patterns of differential gene expression. However, the question of how cells can be programmed, and how complex the rules need to be, to achieve a desired tissue morphology has received less attention. Here, we address these questions by developing a mathematical model to study how cells can collectively grow into clusters with different structural morphologies by secreting diffusible signals that can influence cellular growth rates. We formulate how growth regulators can be used to control the formation of cellular protrusions and how the range of achievable structures scales with the number of distinct signals. We show that a single growth inhibitor is insufficient for the formation of multiple protrusions but may be achieved with multiple growth inhibitors, and that other types of signals can regulate the shape of protrusion tips. These examples illustrate how our approach could potentially be used to guide the design of regulatory circuits for achieving a desired target structure.

Exploring the effect of network topology, mRNA and protein dynamics on gene regulatory network stability.

Homeostasis of protein concentrations in cells is crucial for their proper functioning, requiring steady-state concentrations to be stable to fluctuations. Since gene expression is regulated by proteins such as transcription factors (TFs), the full set of proteins within the cell constitutes a large system of interacting components, which can become unstable. We explore factors affecting stability by coupling the dynamics of mRNAs and proteins in a growing cell. We find that mRNA degradation rate does not affect stability, contrary to previous claims. However, global structural features of the network can dramatically enhance stability. Importantly, a network resembling a bipartite graph with a lower fraction of interactions that target TFs has a higher chance of being stable. Scrambling the E. coli transcription network, we find that the biological network is significantly more stable than its randomized counterpart, suggesting that stability constraints may have shaped network structure during the course of evolution.

Stochastic tunneling across fitness valleys can give rise to a logarithmic long-term fitness trajectory.

Adaptation, where a population evolves increasing fitness in a fixed environment, is typically thought of as a hill-climbing process on a fitness landscape. With a finite genome, such a process eventually leads the population to a fitness peak, at which point fitness can no longer increase through individual beneficial mutations. Instead, the ruggedness of typical landscapes due to epistasis between genes or DNA sites suggests that the accumulation of multiple mutations (via a process known as stochastic tunneling) can allow a population to continue increasing in fitness. However, it is not clear how such a phenomenon would affect long-term fitness evolution. By using a spin-glass type model for the fitness function that takes into account microscopic epistasis, we find that hopping between metastable states can mechanistically and robustly give rise to a slow, logarithmic average fitness trajectory.

Local growth rules can maintain metabolically efficient spatial structure throughout growth.

A ubiquitous feature of bacterial communities is the existence of spatial structures. These are often coupled to metabolism, whereby the spatial organization can improve chemical reaction efficiency. However, it is not clear whether or how a desired colony configuration, for example, one that optimizes some overall global objective, could be achieved by individual cells that do not have knowledge of their positions or of the states of all other cells. By using a model which consists of cells producing enzymes that catalyze coupled metabolic reactions, we show that simple, local rules can be sufficient for achieving a global, community-level goal. In particular, even though the optimal configuration varies with colony size, we demonstrate that cells regulating their relative enzyme levels based solely on local metabolite concentrations can maintain the desired overall spatial structure during colony growth. We also show that these rules can be very simple and hence easily implemented by cells. Our framework also predicts scenarios where additional signaling mechanisms may be required.

Near fundamental mode 1.1 kW Yb:YAG thin-disk laser.

We report on a Yb:YAG thin-disk laser with 1.1 kW output power and beam quality factor M²<1.4 using a simple stable resonator comprising just a single cavity mirror and a single thin disk, without the use of any aspherical elements or any adaptive optics. An optical-to-optical efficiency of 40% was obtained. The cavity was designed to give good beam quality and low misalignment sensitivity to maintain stable and robust laser operation throughout the changes in the thin-disk curvature. To the best of the authors' knowledge, this is the first time an output power beyond 1 kW has been achieved from a single thin-disk laser in near fundamental mode operation (M²<1.4).