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Register a new userDifferentiating swarming models by mimicking a frustrated anti-Ferromagnet
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Self propelled particle (SPP) models are often compared with animal swarms. However, the collective behaviour observed in experiments usually leaves considerable unconstrained freedom in the structure of these models. To tackle this degeneracy, and better distinguish between candidate models, we study swarms of SPPs circulating in channels (like spins) where we permit information to pass through windows between neighbouring channels. Co-alignment between particles then couples the channels (antiferromagnetically) so that they tend to counter-rotate. We study channels arranged to mimic a geometrically frustrated antiferromagnet and show how the effects of this frustration allow us to better distinguish between SPP models. Similar experiments could therefore improve our understanding of collective motion in animals. Finally we discuss how the spin analogy can be exploited to construct universal logic gates and therefore swarming systems that can function as Turing machines.
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Regulatory T cells (Tregs) play a crucial role in mediating immune response. Yet an algorithmic understanding of the role of Tregs in adaptive immunity remains lacking. Here, we present a biophysically realistic model of Treg mediated self-tolerance in which Tregs bind to self-antigens and locally inhibit the proliferation of nearby activated T cells. By exploiting a duality between ecological dynamics and constrained optimization, we show that Tregs tile the potential antigen space while simultaneously minimizing the overlap between Treg activation profiles. We find that for sufficiently high Treg diversity, Treg mediated self-tolerance is robust to fluctuations in self-antigen concentrations but lowering the Treg diversity results in a sharp transition -- related to the Gardner transition in perceptrons -- to a regime where changes in self-antigen concentrations can result in an auto-immune response. We propose a novel experimental test of this transition in immune-deficient mice and discuss potential implications for autoimmune diseases.
Social hierarchy is central to decision-making in the coordinated movement of many swarming species. Here we propose a hierarchical swarm model in the spirit of the Vicsek model of self-propelled particles. We show that, as the hierarchy becomes important, the swarming transition changes from the weak first-order transition observed for egalitarian populations, to a stronger first-order transition for intermediately strong hierarchies, and finally the discontinuity reduces till vanish, where the order-disorder transition appears to be absent in the extremely despotic societies. Associated to this we observe that the spatial structure of the swarm, as measured by the correlation between the density and velocity fields, is strongly mediated by the hierarchy. A two-group model and vectorial noise are also studied for verification. Our results point out the particular relevance of the hierarchical structures to swarming transitions when doing specific case studies.
We propose an improved prediction method of the tertiary structures of $alpha$-helical membrane proteins based on the replica-exchange method by taking into account helix deformations. Our method allows wide applications because transmembrane helices of native membrane proteins are often distorted. In order to test the effectiveness of the present method, we applied it to the structure predictions of glycophorin A and phospholamban. The results were in accord with experiments.
Biopolymer self-assembly pathways are central to biological activity, but are complicated by the ability of the monomeric subunits of biopolymers to adopt different conformational states. As a result, biopolymer nucleation often involves a two-step mechanism where the monomers first condense to form a metastable intermediate, and this then converts to a stable polymer by conformational rearrangement of its constituent monomers. While existing mathematical models neglect the dynamics by which intermediates convert to stable polymers, experiments and simulations show that these dynamics frequently occur on comparable timescales to condensation of intermediates and growth of mature polymers, and thus cannot be ignored. Moreover, nucleation intermediates are responsible for cell toxicity in pathologies such as Alzheimers, Parkinsons, and prion diseases. Due to the relationship between conformation and biological function, the slow conversion dynamics of these species will strongly affect their toxicity. In this study, we present a modified Oosawa model which explicitly accounts for simultaneous assembly and conversion. To describe the conversion dynamics, we propose an experimentally motivated initiation-propagation (IP) mechanism in which the stable phase arises locally within the intermediate, and then spreads through additional conversion events induced by nearest-neighbor interactions, analogous to one-dimensional Glauber dynamics. Our mathematical analysis shows that the competing timescales of assembly and conversion result in a nonequilibrium critical point, separating a regime where intermediates are kinetically unstable from one where conformationally mixed intermediates can accumulate. Our work provides the first general model of two-step biopolymer nucleation, which can be used to quantitatively predict the concentration and composition of biologically crucial intermediates.
One of the causes of high fidelity of copying in biological systems is kinetic discrimination. In this mechanism larger dissipation and copying velocity result in improved copying accuracy. We consider a model of a polymerase which simultaneously copies a single stranded RNA and opens a single- to double-stranded junction serving as an obstacle. The presence of the obstacle slows down the motor, resulting in a change of its fidelity, which can be used to gain information about the motor and junction dynamics. We find that the motors fidelity does not depend on details of the motor-junction interaction, such as whether the interaction is passive or active. Analysis of the copying fidelity can still be used as a tool for investigating the junction kinetics.
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