We study the effect of spatial structure, genetic drift, mutation, and selective pressure on the evolutionary dynamics in a simplified model of asexual organisms colonizing a new territory. Under an appropriate coarse-graining, the evolutionary dynamics is related to the directed percolation processes that arise in voter models, the Domany-Kinzel (DK) model, contact process, etc. We explore the differences between linear (flat front) expansions and the much less familiar radial (curved front) range expansions. For the radial expansion, we develop a generalized, off-lattice DK model that minimizes otherwise persistent lattice artifacts. With both simulations and analytical techniques, we study the survival probability of advantageous mutants, the spatial correlations between domains of neutral strains, and the dynamics of populations with deleterious mutations. "Inflation" at the frontier leads to striking differences between radial and linear expansions. For a colony with initial radius R0 expanding at velocity v, significant genetic demixing, caused by local genetic drift, only occurs up to a finite time t * = R0/v, after which portions of the colony become causally disconnected due to the inflating perimeter of the expanding front. As a result, the effect of a selective advantage is amplified relative to genetic drift, increasing the survival probability of advantageous mutants. Inflation also modifies the underlying directed percolation transition, introducing novel scaling functions and modifications similar to a finite size effect. Finally, we consider radial range expansions with deflating perimeters, as might arise from colonization initiated along the shores of an island.

No abstract

Chirality, ubiquitous in complex biological systems, can be controlled and quantified in synthetic materials such as cholesteric liquid crystal (CLC) systems. In this work, we study spherical shells of CLC under weak anchoring conditions. We induce anchoring transitions at the inner and outer boundaries using two independent methods: by changing the surfactant concentration or by raising the temperature close to the clearing point. The shell confinement leads to new states and associated surface structures: a state where large stripes on the shell can be filled with smaller, perpendicular substripes, and a focal conic domain (FCD) state, where thin stripes wrap into at least two, topologically required, double spirals. Focusing on the latter state, we use a Landau-de Gennes model of the CLC to simulate its detailed configurations as a function of anchoring strength. By abruptly changing the topological constraints on the shell, we are able to study the interconversion between director defects and pitch defects, a phenomenon usually restricted by the complexity of the cholesteric phase. This work extends the knowledge of cholesteric patterns, structures that not only have potential for use as intricate, self-assembly blueprints but are also pervasive in biological systems.

Cellular nutrient consumption is influenced by both the nutrient uptake kinetics of an individual cell and the cells’ spatial arrangement. Large cell clusters or colonies have inhibited growth at the cluster's center due to the shielding of nutrients by the cells closer to the surface. We develop an effective medium theory that predicts a thickness ℓ of the outer shell of cells in the cluster that receives enough nutrient to grow. The cells are treated as partially absorbing identical spherical nutrient sinks, and we identify a dimensionless parameter ν that characterizes the absorption strength of each cell. The parameter ν can vary over many orders of magnitude between different cell types, ranging from bacteria and yeast to human tissue. The thickness ℓ decreases with increasing ν, increasing cell volume fraction ϕ, and decreasing ambient nutrient concentration ψ∞. The theoretical results are compared with numerical simulations and experiments. In the latter studies, colonies of budding yeast, Saccharomyces cerevisiae, are grown on glucose media and imaged under a confocal microscope. We measure the growth inside the colonies via a fluorescent protein reporter and compare the experimental and theoretical results for the thickness ℓ.

Athermal disordered systems can exhibit a remarkable response to an applied oscillatory shear: after a relatively few shearing cycles, the system falls into a configuration that had already been visited in a previous cycle. After this point the system repeats its dynamics periodically despite undergoing many particle rearrangements during each cycle. We study the behavior of orbits as we approach the jamming point in simulations of jammed particles subject to oscillatory shear at fixed pressure and zero temperature. As the pressure is lowered, we find that it becomes more common for the system to find periodic states where it takes multiple cycles before returning to a previously visited state. Thus, there is a proliferation of longer periods as the jamming point is approached.Keywords: cyclic shearing, reversibility, memory, absorbing-state phase transition, jammingOscillatory sheared athermal particle packings or suspensions can fall into periodic "absorbing states" [1] in which the system returns to a configuration previously visited during the shearing process at the same point in the cycle. Once it returns to that configuration, the dynamics repeats itself indefinitely. At low densities in the absorbing state, the particles follow the flow without ever making contact with one another so that the system moves back and forth along a flat direction in the energy landscape [2][3][4], and particles return to their original positions after a single shear cycle: T = 1. As the strain amplitude γ t increases beyond some value γ * t , particles can no longer avoid each other and the system undergoes a dynamical "absorbing state" transition from the absorbing phase to a phase in which the system continually visits new configurations. Models [3,[5][6][7][8] have linked this transition to variants of directed percolation [8][9][10], which represents a broad class of non-equilibrium phase transitions [1].Athermal glasses such as Lennard-Jones glasses, by contrast, have an extensive entropy of energy minima that are not flat [11][12][13]. At very small strain amplitudes, they exhibit elastic behavior in which they explore different configurations within the same energy minimum. As γ t increases so that the system can explore more than one minimum, one might expect the system to meander indefinitely around a hopelessly intricate energy landscape as the system is driven in an oscillatory fashion. Yet, remarkably, these systems can fall into absorbing states-they can find their way back to previously visited energy minima even as they undergo multiple particle rearrangements. Thus these systems explore many such minima [14-17] over and over again. Finally, when γ t is increased to γ * t , the system undergoes an absorbing state transition to a phase in which the system never returns to previously visited minima.In this paper we investigate the fate of absorbing states in packings of jammed spheres that can be tuned to the jamming transition, where the system loses rigidity [18,19]. Far above this transition, absorbing states...