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Register a new userDynamical Pattern Selection of Growing Cellular Mosaic in Fish Retina
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A Markovian lattice model for photoreceptor cells is introduced to describe the growth of mosaic patterns on fish retina. The radial stripe pattern observed in wild-type zebrafish is shown to be selected naturally during the retina growth, against the geometrically equivalent, circular stripe pattern. The mechanism of such dynamical pattern selection is clarified on the basis of both numerical simulations and theoretical analyses, which find that the successive emergence of local defects plays a critical role in the realization of the wild-type pattern.
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Actin networks in certain single-celled organisms exhibit a complex pattern-forming dynamics that starts with the appearance of static spots of actin on the cell cortex. Spots soon become mobile, executing persistent random walks, and eventually give rise to traveling waves of actin. Here we describe a possible physical mechanism for this distinctive set of dynamic transformations, by equipping an excitable reaction-diffusion model with a field describing the spatial orientation of its chief constituent (which we consider to be actin). The interplay of anisotropic actin growth and spatial inhibition drives a transformation at fixed parameter values from static spots to moving spots to waves.
Microbiological systems evolve to fulfill their tasks with maximal efficiency. The immune system is a remarkable example, where self-non self distinction is accomplished by means of molecular interaction between self proteins and antigens, triggering affinity-dependent systemic actions. Specificity of this binding and the infinitude of potential antigenic patterns call for novel mechanisms to generate antibody diversity. Inspired by this problem, we develop a genetic algorithm where agents evolve their strings in the presence of random antigenic strings and reproduce with affinity-dependent rates. We ask what is the best strategy to generate diversity if agents can rearrange their strings a finite number of times. We find that endowing each agent with an inheritable cellular automaton rule for performing rearrangements makes the system more efficient in pattern-matching than if transformations are totally random. In the former implementation, the population evolves to a stationary state where agents with different automata rules coexist.
By embedding inert tracer particles (TPs) in a growing multicellular spheroid the local stresses on the cancer cells (CCs) can be measured. In order for this technique to be effective the unknown effect of the dynamics of the TPs on the CCs has to be elucidated to ensure that the TPs do not greatly alter the local stresses on the CCs. We show, using theory and simulations, that the self-generated (active) forces arising from proliferation and apoptosis of the CCs drive the dynamics of the TPs far from equilibrium. On time scales less than the division times of the CCs, the TPs exhibit sub-diffusive dynamics (the mean square displacement, $Delta_{TP}(t) sim t^{beta_{TP}}$ with $beta_{TP}<1$), similar to glass-forming systems. Surprisingly, in the long-time limit, the motion of the TPs is hyper-diffusive ($Delta_{TP}(t) sim t^{alpha_{TP}}$ with $alpha_{TP}>2$) due to persistent directed motion for long times. In comparison, proliferation of the CCs randomizes their motion leading to superdiffusive behavior with $alpha_{CC}$ exceeding unity. Most importantly, $alpha_{CC}$ is not significantly affected by the TPs. Our predictions could be tested using textit{in vitro} imaging methods where the motion of the TPs and the CCs can be tracked.
Microbial metabolic networks perform the basic function of harvesting energy from nutrients to generate the work and free energy required for survival, growth and replication. The robust physiological outcomes they generate across vastly different organisms in spite of major environmental and genetic differences represent an especially remarkable trait. Most notably, it suggests that metabolic activity in bacteria may follow universal principles, the search for which is a long-standing issue. Most theoretical approaches to modeling metabolism assume that cells optimize specific evolutionarily-motivated objective functions (like their growth rate) under general physico-chemical or regulatory constraints. While conceptually and practically useful in many situations, the idea that certain objectives are optimized is hard to validate in data. Moreover, it is not clear how optimality can be reconciled with the degree of single-cell variability observed within microbial populations. To shed light on these issues, we propose here an inverse modeling framework that connects fitness to variability through the Maximum-Entropy guided inference of metabolic flux distributions from data. While no clear optimization emerges, we find that, as the medium gets richer, Escherichia coli populations slowly approach the theoretically optimal performance defined by minimal reduction of phenotypic variability at given mean growth rate. Inferred flux distributions provide multiple biological insights, including on metabolic reactions that are experimentally inaccessible. These results suggest that bacterial metabolism is crucially shaped by a population-level trade-off between fitness and cell-to-cell heterogeneity.
We study the force generation by a set of parallel actin filaments growing against an elastic membrane. The elastic membrane tries to stay flat and any deformation from this flat state, either caused by thermal fluctuations or due to protrusive polymerization force exerted by the filaments, costs energy. We study two lattice models to describe the membrane dynamics. In one case, the energy cost is assumed to be proportional to the absolute magnitude of the height gradient (gradient model) and in the other case it is proportional to the square of the height gradient (Gaussian model). For the gradient model we find that the membrane velocity is a non-monotonic function of the elastic constant $mu$, and reaches a peak at $mu=mu^ast$. For $mu < mu^ast$ the system fails to reach a steady state and the membrane energy keeps increasing with time. For the Gaussian model, the system always reaches a steady state and the membrane velocity decreases monotonically with the elastic constant $ u$ for all nonzero values of $ u$. Multiple filaments give rise to protrusions at different regions of the membrane and the elasticity of the membrane induces an effective attraction between the two protrusions in the Gaussian model which causes the protrusions to merge and a single wide protrusion is present in the system. In both the models, the relative time-scale between the membrane and filament dynamics plays an important role in deciding whether the shape of elasticity-velocity curve is concave or convex. Our numerical simulations agree reasonably well with our analytical calculations.
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