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Register a new userWavelength selection of rippling patterns in myxobacteria
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Rippling patterns of myxobacteria appear in starving colonies before they aggregate to form fruiting bodies. These periodic traveling cell density waves arise from the coordination of individual cell reversals, resulting from an internal clock regulating them, and from contact signaling during bacterial collisions. Here we revisit a mathematical model of rippling in myxobacteria due to Igoshin et al. [Proc. Natl. Acad. Sci. USA {bf 98}, 14913 (2001) and Phys. Rev. E {bf 70}, 041911 (2004)]. Bacteria in this model are phase oscillators with an extra internal phase through which they are coupled to a mean-field of oppositely moving bacteria. Previously, patterns for this model were obtained only by numerical methods and it was not possible to find their wavenumber analytically. We derive an evolution equation for the reversal point density that selects the pattern wavenumber in the weak signaling limit, show the validity of the selection rule by solving numerically the model equations and describe other stable patterns in the strong signaling limit. The nonlocal mean-field coupling tends to decohere and confine patterns. Under appropriate circumstances, it can annihilate the patterns leaving a constant density state via a nonequilibrium phase transition reminiscent of destruction of synchronization in the Kuramoto model.
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We present a study on the selection of a variety of activity patterns among neurons that are connected in multiplex framework, with neurons on two layers with different functional couplings. With Hindmarsh-Rose model for the dynamics of single neurons, we analyze the possible patterns of dynamics in each layer separately, and report emergent patterns of activity like anti-phase oscillations in multi-clusters with phase regularities and enhanced amplitude and frequency with mixed mode oscillations when the connections are inhibitory. When they are multiplexed with neurons of one layer coupled with excitatory synaptic coupling and neurons of the other layer coupled with inhibitory synaptic coupling, we observe transfer or selection of interesting patterns of collective behaviour between the layers, inducing anti-phase oscillations and multi-cluster oscillations. While the revival of oscillations occurs in the layer with excitatory coupling, the transition from anti-phase to in-phase and vice versa is observed in the other layer with inhibitory synaptic coupling. We also discuss how the selection of these patterns can be controlled by tuning the intra-layer or inter-layer coupling strengths or increasing the range of non-local coupling. With one layer having electrical coupling while the other synaptic coupling of excitatory(inhibitory)type, we find in-phase(anti-phase) synchronized patterns of activity among neurons in both layers.
Wavelength selection in reaction--diffusion systems can be understood as a coarsening process that is interrupted by counteracting processes at certain wavelengths. We first show that coarsening in mass-conserving systems is driven by self-amplifying mass transport between neighboring high-density domains. We derive a general coarsening criterion and show that coarsening is generically uninterrupted in two-component systems that conserve mass. The theory is then generalized to study interrupted coarsening and anti-coarsening due to weakly-broken mass conservation, providing a general path to analyze wavelength selection in pattern formation far from equilibrium.
Life has most likely originated as a consequence of processes taking place in non-equilibrium conditions (textit{e.g.} in the proximity of deep-sea thermal vents) selecting states of matter that would have been otherwise unfavorable at equilibrium. Here we present a simple chemical network in which the selection of states is driven by the thermodynamic necessity of dissipating heat as rapidly as possible in the presence of a thermal gradient: states participating to faster reactions contribute the most to the dissipation rate, and are the most populated ones in non-equilibrium steady-state conditions. Building upon these results, we show that, as the complexity of the chemical network increases, the textit{velocity} of the reaction path leading to a given state determines its selection, giving rise to non-trivial localization phenomena in state space. A byproduct of our studies is that, in the presence of a temperature gradient, thermophoresis-like behavior inevitably appears depending on the transport properties of each individual state, thus hinting at a possible microscopic explanation of this intriguing yet still not fully understood phenomenon.
Understanding the thermodynamics of the duplication process is a fundamental step towards a comprehensive physical theory of biological systems. However, the immense complexity of real cells obscures the fundamental tensions between energy gradients and entropic contributions that underlie duplication. The study of synthetic, feasible systems reproducing part of the key ingredients of living entities but overcoming major sources of biological complexity is of great relevance to deepen the comprehension of the fundamental thermodynamic processes underlying life and its prevalence. In this paper an abstract -- yet realistic -- synthetic system made of small synthetic protocell aggregates is studied in detail. A fundamental relation between free energy and entropic gradients is derived for a general, non-equilibrium scenario, setting the thermodynamic conditions for the occurrence and prevalence of duplication phenomena. This relation sets explicitly how the energy gradients invested in creating and maintaining structural -- and eventually, functional -- elements of the system must always compensate the entropic gradients, whose contributions come from changes in the translational, configurational and macrostate entropies, as well as from dissipation due to irreversible transitions. Work/energy relations are also derived, defining lower bounds on the energy required for the duplication event to take place. A specific example including real ternary emulsions is provided in order to grasp the orders of magnitude involved in the problem. It is found that the minimal work invested over the system to trigger a duplication event is around $sim 10^{-13}{rm J}$. Without aiming to describe a truly biological process of duplication, this theoretical contribution seeks to explicitly define and identify the key actors that participate in it.
Biological sensory systems react to changes in their surroundings. They are characterized by fast response and slow adaptation to varying environmental cues. Insofar as sensory adaptive systems map environmental changes to changes of their internal degrees of freedom, they can be regarded as computational devices manipulating information. Landauer established that information is ultimately physical, and its manipulation subject to the entropic and energetic bounds of thermodynamics. Thus the fundamental costs of biological sensory adaptation can be elucidated by tracking how the information the system has about its environment is altered. These bounds are particularly relevant for small organisms, which unlike everyday computers operate at very low energies. In this paper, we establish a general framework for the thermodynamics of information processing in sensing. With it, we quantify how during sensory adaptation information about the past is erased, while information about the present is gathered. This process produces entropy larger than the amount of old information erased and has an energetic cost bounded by the amount of new information written to memory. We apply these principles to the E. colis chemotaxis pathway during binary ligand concentration changes. In this regime, we quantify the amount of information stored by each methyl group and show that receptors consume energy in the range of the information-theoretic minimum. Our work provides a basis for further inquiries into more complex phenomena, such as gradient sensing and frequency response.
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