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This paper reports the first finding of cupolets in a chaotic Hindmarsh-Rose neural model. Cupolets (chaotic, unstable, periodic, orbit-lets) are unstable periodic orbits that have been stabilized through a particular control scheme by applying a binary control sequence. We demonstrate different neural dynamics (periodic or chaotic) of the Hindmarsh-Rose model through a bifurcation diagram where the external input current, I, is the bifurcation parameter. We select a region in the chaotic parameter space and provide the results of numerical simulations. In this chosen parameter space, a control scheme is applied when the trajectory intersects with either of the two control planes. The type of the control is determined by a bit in a binary control sequence. The control is either a small microcontrol (0) or a large macrocontrol (1) that adjusts the future dynamics of the trajectory by a perturbation determined by the coding function r ( x ). We report the discovery of many cupolets with corresponding control sequences and comment on the differences with previously reported cupolets in the double scroll system. We provide some examples of the generated cupolets and conclude by discussing potential implications for biological neurons.
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Neurônios , Análise por ConglomeradosRESUMO
In chaotic entanglement, pairs of interacting classically-chaotic systems are induced into a state of mutual stabilization that can be maintained without external controls and that exhibits several properties consistent with quantum entanglement. In such a state, the chaotic behavior of each system is stabilized onto one of the system's many unstable periodic orbits (generally located densely on the associated attractor), and the ensuing periodicity of each system is sustained by the symbolic dynamics of its partner system, and vice versa. Notably, chaotic entanglement is an entropy-reversing event: the entropy of each member of an entangled pair decreases to zero when each system collapses onto a given period orbit. In this paper, we discuss the role that entropy plays in chaotic entanglement. We also describe the geometry that arises when pairs of entangled chaotic systems organize into coherent structures that range in complexity from simple tripartite lattices to more involved patterns. We conclude with a discussion of future research directions.
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Cupolets are a relatively new class of waveforms that represent highly accurate approximations to the unstable periodic orbits of chaotic systems, and large numbers can be efficiently generated via a control method where small kicks are applied along intersections with a control plane. Cupolets exhibit the interesting property that a given set of controls, periodically repeated, will drive the associated chaotic system onto a uniquely defined cupolet regardless of the system's initial state. We have previously demonstrated a method for efficiently steering from one cupolet to another using a graph-theoretic analysis of the connections between these orbits. In this paper, we discuss how connections between cupolets can be analyzed to show that complicated cupolets are often composed of combinations of simpler cupolets. Hence, it is possible to distinguish cupolets according to their reducibility: a cupolet is classified either as composite, if its orbit can be decomposed into the orbits of other cupolets or as fundamental, if no such decomposition is possible. In doing so, we demonstrate an algorithm that not only classifies each member of a large collection of cupolets as fundamental or composite, but that also determines a minimal set of fundamental cupolets that can exactly reconstruct the orbit of a given composite cupolet. Furthermore, this work introduces a new way to generate higher-order cupolets simply by adjoining fundamental cupolets via sequences of controlled transitions. This allows for large collections of cupolets to be collapsed onto subsets of fundamental cupolets without losing any dynamical information. We conclude by discussing potential future applications.
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This paper investigates the interaction between two coupled neurons at the terminal end of a long chain of neurons. Specifically, we examine a bidirectional, two-cell FitzHugh-Nagumo neural model capable of exhibiting chaotic dynamics. Analysis of this model shows how mutual stabilization of the chaotic dynamics can occur through sigmoidal synaptic learning. Initially, this paper begins with a bifurcation analysis of an adapted version of a previously studied FitzHugh-Nagumo model that indicates regions of periodic and chaotic behaviors. Through allowing the synaptic properties to change dynamically via neural learning, it is shown how the system can evolve from chaotic to stable periodic behavior. The driving factor between this transition is representative of a stimulus coming down a long neural pathway. The result that two chaotic neurons can mutually stabilize via a synaptic learning implies that this may be a mechanism whereby neurons can transition from a disordered, chaotic state to a stable, ordered periodic state that persists. This approach shows that even at the simplest level of two terminal neurons, chaotic behavior can become stable, sustained periodic behavior. This is achieved without the need for a large network of neurons.
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Potenciais de Ação/fisiologia , Neurônios/fisiologia , Transmissão Sináptica/fisiologia , Simulação por Computador , Humanos , Aprendizagem/fisiologia , Modelos Neurológicos , Modelos Teóricos , Rede Nervosa , Redes Neurais de ComputaçãoRESUMO
We examine the quantum-classical correspondence from a classical perspective by discussing the potential for chaotic systems to support behaviors normally associated with quantum mechanical systems. Our main analytical tool is a chaotic system's set of cupolets, which are highly-accurate stabilizations of its unstable periodic orbits. Our discussion is motivated by the bound or entangled states that we have recently detected between interacting chaotic systems, wherein pairs of cupolets are induced into a state of mutually-sustaining stabilization that can be maintained without external controls. This state is known as chaotic entanglement as it has been shown to exhibit several properties consistent with quantum entanglement. For instance, should the interaction be disturbed, the chaotic entanglement would then be broken. In this paper, we further describe chaotic entanglement and go on to address the capacity for chaotic systems to exhibit other characteristics that are conventionally associated with quantum mechanics, namely analogs to wave function collapse, various entropy definitions, the superposition of states, and the measurement problem. In doing so, we argue that these characteristics need not be regarded exclusively as quantum mechanical. We also discuss several characteristics of quantum systems that are not fully compatible with chaotic entanglement and that make quantum entanglement unique.
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We present an efficient control scheme that stabilizes the unstable periodic orbits of a chaotic system. The resulting orbits are known as cupolets and collectively provide an important skeleton for the dynamical system. Cupolets exhibit the interesting property that a given sequence of controls will uniquely identify a cupolet, regardless of the system's initial state. This makes it possible to transition between cupolets, and thus unstable periodic orbits, simply by switching control sequences. We demonstrate that although these transitions require minimal controls, they may also involve significant chaotic transients unless carefully controlled. As a result, we present an effective technique that relies on Dijkstra's shortest path algorithm from algebraic graph theory to minimize the transients and also to induce certainty into the control of nonlinear systems, effectively providing an efficient algorithm for the steering and targeting of chaotic systems.
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Direct oral anticoagulants (DOACs), which includes thrombin and factor Xa inhibitors, have emerged as the preferred therapeutics for thrombotic disorders, penetrating a market previously dominated by warfarin and heparin. This article describes the discovery and profiling of a novel series of N-acylpyrazoles, which act as selective, covalent, reversible, non-competitive inhibitors of thrombin. We describe in vitro stability issues associated with this chemotype and, importantly, demonstrate that N-acylpyrazoles successfully act in vivo as anticoagulants in basic thrombotic animal models. Crucially, this anticoagulant nature is unaccompanied by the higher bleeding risk profile that has become an undesirable characteristic of the DTIs and factor Xa inhibitors. We propose that the N-acylpyrazole chemotype shows intriguing promise as next-generation oral anticoagulants.
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Trombina , Trombose , Humanos , Inibidores do Fator Xa/farmacologia , Anticoagulantes/farmacologia , Anticoagulantes/uso terapêutico , Heparina , Varfarina/uso terapêutico , Trombose/tratamento farmacológico , Administração OralRESUMO
INTRODUCTION: High incidence of bleeding events remains a key risk for patients taking anticoagulants, especially those in need of long-term combination therapy with antiplatelet agents. As a consequence, patients may not receive clinically indicated combination antithrombotic therapy. Here, we report on VE-1902, a member of a novel class of precision oral anticoagulants (PROACs) that combines effective anticoagulation with reduced bleeding in preclinical testing. METHODS AND RESULTS: Acting through covalent, reversible active-site modification of thrombin similar to a previously described molecule [1], VE-1902 shows potency and selectivity for thrombin inhibition in human plasma comparable to clinically relevant direct thrombin inhibitors (DTI) such as argatroban and dabigatran (thrombin generation assay ETP EC50 = 1.3 µM compared to 0.36 µM and 0.31 µM for argatroban and dabigatran; >100-fold selectivity against related serine proteases). Unlike the current anticoagulants, VE-1902 does not significantly inhibit thrombin-mediated platelet activation in in vivo models of thrombosis. In the thrombin generation assay, the compound inhibits thrombin formation without significantly delaying the initiation phase of the clotting cascade. These features are possibly responsible for the observed reduced bleeding in tail bleeding and saphenous vein bleeding models. Consistent with this novel pharmacological profile, VE-1902 shows efficacious anticoagulation in several fibrin-driven animal models of thrombosis (arteriovenous shunt, venous stasis thrombosis, and thrombin-induced thromboembolism models), whereas it does not significantly prevent arterial occlusion in the platelet dependent FeCl3 model. CONCLUSIONS: By leaving platelet activation following vascular injury mostly unaffected, VE-1902, and the PROACs more generally, represent a new generation of precision anticoagulants with reduced bleeding risk.
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Antitrombinas , Trombose , Animais , Anticoagulantes/farmacologia , Anticoagulantes/uso terapêutico , Hemorragia/induzido quimicamente , Hemorragia/tratamento farmacológico , Humanos , Roedores , Trombina , Trombose/tratamento farmacológicoRESUMO
INTRODUCTION: In recent years, the traditional treatments for thrombotic diseases, heparin and warfarin, are increasingly being replaced by novel oral anticoagulants offering convenient dosing regimens, more predictable anticoagulant responses, and less frequent monitoring. However, these drugs can be contraindicated for some patients and, in particular, their bleeding liability remains high. METHODS: We have developed a new class of direct thrombin inhibitors (VE-DTIs) and have utilized kinetics, biochemical, and X-ray structural studies to characterize the mechanism of action and in vitro pharmacology of an exemplary compound from this class, Compound 1. RESULTS: We demonstrate that Compound 1, an exemplary VE-DTI, acts through reversible covalent inhibition. Compound 1 inhibits thrombin by transiently acylating the active site S195 with high potency and significant selectivity over other trypsin-like serine proteases. The compound inhibits the binding of a peptide substrate with both clot-bound and free thrombin with nanomolar potency. Compound 1 is a low micromolar inhibitor of thrombin activity against endogenous substrates such as fibrinogen and a nanomolar inhibitor of the activation of protein C and thrombin-activatable fibrinolysis inhibitor. In the thrombin generation assay, Compound 1 inhibits thrombin generation with low micromolar potency but does not increase the lag time for thrombin formation. In addition, Compound 1 showed weak inhibition of clotting in PT and aPTT assays consistent with its distinctive profile in the thrombin generation assay. CONCLUSION: Compound 1, while maintaining strong potency comparable to the current DTIs, has a distinct mechanism of action which produces a differentiating pharmacological profile. Acting through reversible covalent inhibition, these direct thrombin inhibitors could lead to new anticoagulants with better combined efficacy and bleeding profiles.
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Antitrombinas/química , Modelos Químicos , Trombina/química , Domínio Catalítico , Cristalografia por Raios X , HumanosRESUMO
A highly constrained pseudo-tetrapeptide (OC252-324) further defines a new allosteric binding site located near the center of fructose-1,6-bisphosphatase. In a crystal structure, pairs of inhibitory molecules bind to opposite faces of the enzyme tetramer. Each ligand molecule is in contact with three of four subunits of the tetramer, hydrogen bonding with the side chain of Asp187 and the backbone carbonyl of residue 71, and electrostatically interacting with the backbone carbonyl of residue 51. The ligated complex adopts a quaternary structure between the canonical R- and T-states of fructose-1,6-bisphosphatase, and yet a dynamic loop essential for catalysis (residues 52-72) is in a conformation identical to that of the T-state enzyme. Inhibition by the pseudo-tetrapeptide is cooperative (Hill coefficient of 2), synergistic with both AMP and fructose 2,6-bisphosphate, noncompetitive with respect to Mg2+, and uncompetitive with respect to fructose 1,6-bisphosphate. The ligand dramatically lowers the concentration at which substrate inhibition dominates the kinetics of fructose-1,6-bisphosphatase. Elevated substrate concentrations employed in kinetic screens may have facilitated the discovery of this uncompetitive inhibitor. Moreover, the inhibitor could mimic an unknown natural effector of fructose-1,6-bisphosphatase, as it interacts strongly with a conserved residue of undetermined functional significance.