Understanding the hierarchical URLanization of living systems is one of the biggest conceptual challenges of the present century . A generically observed mechanism that drives URLanization is interaction among the individual elements---which may represent cells, bacteria, or even enzymes---via chemical signals. We use dynamical renormalization group approach to study a stochastic model for chemotactic particles in which we introduce polarization effects in chemotaxis. We find exact dynamic scaling exponents that represent superdiffusive behavior of the particles. The number fluctuations within sub-regions of the system show a hyperuniform structure or exhibit giant number fluctuations, depending on whether or not the noise is conserved. We expect our results to shed light on how molecular regulation of chemotactic circuits can determine large-scale behavior of cell colonies and tissues through emergent properties that result from a subtle interplay between nonequilibrium fluctuations and long-range interactions that are constrained by exact symmetries.
Understanding the hierarchical URLanization of living systems is a challenge that requires the development of a multiscale description of their constituents . A generically observed mechanism that drives URLanization is interaction among the individual elements---which may represent cells, bacteria, or even enzymes---via chemical signals. We develop a systematic coarse-graining scheme using which we can construct a general theoretical framework to study many-body effects in chemotactic populations. The framework unveils a polarization-induced coupling term, which originates from quorum effects and can compete with the chemotactic drift term. We use the dynamical renormalization group approach to study a stochastic model for chemotactic particles in which we introduce polarization effects in chemotaxis. We find exact dynamic scaling exponents that represent superdiffusive behavior of the particles. The number fluctuations within subregions of the system show a hyperuniform structure or exhibit giant number fluctuations, depending on whether or not the noise is conserved. We expect our results to shed light on how molecular regulation of chemotactic circuits can determine large-scale behavior of cell colonies and tissues through emergent properties that result from a subtle interplay between nonequilibrium fluctuations and long-range interactions that are constrained by exact symmetries.
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one of the biggest conceptual challenges of the present century
a challenge that requires the development of a multiscale description of their constituents
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use
develop a systematic coarse-graining scheme using which we can construct a general theoretical framework to study many-body effects in chemotactic populations. The framework unveils a polarization-induced coupling term, which originates from quorum effects and can compete with the chemotactic drift term. We use the
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sub-regions
subregions