Chaos: An Interdisciplinary Journal of Nonlinear Science

Allergic conjunctivitis is an inflammation of the conjunctiva caused by allergen; it is common disorder affecting up to 40% of the population. In this work, we study seasonal allergic conjunctivitis (SAC), also called "hay fever eyes", which is caused by exposure to airborne pollens. We develop a mathematical model quantifying the ocular immune system response to the allergens. First, we present a simplified qualitative description of the immunopathogenesis of SAC. Then, we express each chosen immunopathological mechanism mathematically to construct a system of thirty-one ordinary differential equations. We compare summary statistics of the predicted observable immune signals to experimental measurements and find our model captures key qualitative features of SAC progression. We then compare our predicted time series of histamine concentration to symptom scores and find a strong correlation suggesting the model predicts relevant clinically trends. Next, we calibrate the model through multi-step process. We find the most influential parameters are the production and depletion rates of IL-4, and the production rates of IL-5 and IL-8. These cytokines are targeted in treatments for asthma, atopic dermatitis, and severe eosinophilic associated disorder and suggest potential therapeutic targets for SAC. Our calibrated model mimics most of the summary statistics of the experimentally observable immune signals with discrepancies for IL-5 and IL-13 indicating that additional immunopathological mechanisms could be important.

Interception of moving objects is a universal pattern of animal behavior with many industrial applications. Inspired by the behavior of the characid fish Brycon guatemalensis, which catches fruits falling onto the surface of a river, we study one-shot (i.e., open-loop) interceptions using both stochastic optimal control theory and reinforcement learning. In the first instance, an agent actuates a control (wait time before launch and heading angle) to meet its target, given a noisy estimate of the target initial state. In a minimal setting, where launch velocity and actuated control are constants, we show that the optimal wait time is attenuated by noise in both the target measurement and control actuation, as well as agent energy conservation. We then derive an upper bound for the heading angle variance which scales as the ratio of the non-vanishing optimal interception error to the initial planar separation. Complementing our control framework, our deep reinforcement learning approach shows that the neural network representing the fish first learns the value function for the interception, then learns how to aim, and finally learns the optimal wait time. Beyond the specific problem at hand, our results may also have applications to problems with little time for feedback or corrections such as perching, landing, and docking.

Emerging research on desynchronization reveals strong relations to memory formation and recollection with much of the evidence originating from studies of the hippocampus, a brain region central to memory processing. However, growing evidence emphasizing the role of desynchronization is accompanied by challenges, most notably the synchronization/desynchronization conundrum. The conundrum arises from an apparent contradiction between learning and Shannon's information theory: spike-timing-dependent plasticity (STDP) acquires information via synchronized populational activity whereas information theory suggests that information channel is encoded through higher variability. Both frameworks are well-founded. Learning is widely accepted as the mathematical abstraction of STDP while Shannon's information theory showcases its power ubiquitously across fields from communication systems to neuroscience. Here, we propose that learning and Shannon's information theory are not necessarily opposing principles. Rather, learning plays a critical role in the process of synchronization and desynchronization. To justify our claim, we conduct computational simulations based on a Hodgkin-Huxley neuronal model coupled with NMDA, AMPA, and GABA synapses with inputs of biologically realistic spiking data. Our results show that enabling STDP significantly influences synchronization and desynchronization dynamics. Specifically, we find that STDP and desynchronization form a regulatory loop, in which STDP regulates the level of synchrony, and synchrony regulates subsequent learning strength. Further study reveals STDP is capable of switching neurons from synchronization to desynchronization. This framework mitigates the synchronization/desynchronization conundrum by clarifying the relationship between desynchronization and learning, and offers a new perspective on how synchrony contributes to memory formation and recollection.

Obesity is a major health concern worldwide and is caused by an excessive fat accumulation in the body due to adipogenesis. Recent studies suggest that excessive stress or disruption of circadian rhythms can enhance adipogenic commitment and lead to obesity. Moreover, this adipogenic commitment occurs at a specific time of day, highlighting a correlation with the circadian rhythm. However, the dynamical nature of this kind of stress-induced adipogenic differentiation remains an unresolved puzzle. Herein, we proposed a mathematical model centred on the key transcription factor PPAR{gamma}, associated with adipogenic differentiation, and demonstrated that adipogenic commitment is a bistable, irreversible differentiation process in which slow positive feedback regulation of PPAR{gamma} primarily controls the differentiation commitment threshold. The model reproduced the experimental observations regarding the extent of adipogenesis induced by constant and pulsatile stress input signals and explained the correlation between adipogenic differentiation time and circadian phase. It further predicts how to control the adipogenic commitment even under stressful conditions. Overall, our study elucidates how stress signalling dynamically governs adipogenesis.

Japanese Encephalitis Virus (JEV) belongs to the Flavivirus family, and the RNA dependent RNA polymerase (RdRp) domain located at the C terminus of non structural protein 5 (NS5) regulates de novo viral genome synthesis. The conserved priming loop inserted in the thumb domain of RDRP initiates de novo genome synthesis. Interestingly, the reported replication process initiates with an interaction between NS5 (methyltransferase/RDRP) and NS3 (protease/helicase), and inhibiting this interaction directly correlates with the inhibition of viral replication. The function of the priming loop in the context of the NS5 NS3 interaction is not yet known. In this study, we studied the priming loop function in the NS5 NS3 interaction and viral replication. Using a structure based drug design approach, we screened the Maybridge compound library against the RdRp priming loop and identified 15 candidate compounds based on binding energy. Among them, DSHS00151 showed significant dose dependent inhibition of the NS5 NS3 interaction with an IC50 of 3.5 micromolar in the mammalian two hybrid assay, inhibited viral infectivity with an IC50 of 2.54 micromolar, and reduced viral RNA load with an IC50 of 2.9 micromolar, compared to CD10712. Molecular Dynamics (MD) simulations revealed that DSHS00151 exhibits stronger and more stable binding with the priming loop residues (790 to 812) compared to CD10712. The molecular mechanism suggested by the docking of the NS5 and NS3 proteins showed that the priming loop tends to rotate toward the NS3 protein to stabilize the complex, and compound binding restricts this loop rotation, thus compromising the stability of the NS5 and NS3 complex and affecting viral replication. Overall, our study validated the function of the NS5 priming loop as an allosteric site, and compounds binding to this allosteric site belong to the Non Nucleoside Reverse Transcriptase Inhibitors (NNRTI) class of inhibitors, which disrupt the NS5 and NS3 interaction and could be developed as novel anti JEV therapeutics.

Trigger waves are positive feedback-mediated traveling waves that propagate without slowing down or diminishing in amplitude, enabling biochemical coordination over distances where diffusion alone would be insufficient. Apoptosis can spread as trigger waves of caspase activity, as demonstrated in Xenopus eggs and egg extracts. We measured apoptotic wave speeds in extracts at two cell cycle states and found that waves propagated more slowly in M-phase arrested cytostatic factor (CSF) extracts than in interphase extracts (21 versus 27 m min-1). Luther's equation, v=2{surd}D{kappa}, predicts wave speed from the diffusion coefficient D and the positive-feedback doubling rate {kappa}. However, D and {kappa} were comparable between the two extracts and could not explain the speed difference. This discrepancy highlighted a key limitation of the classical equation: it does not account for an activation threshold in trigger wave initiation, and in fact the threshold required to trigger apoptosis was found to differ between cell cycle states. We therefore extended Luther's equation to include such a threshold, obtaining v{propto}{surd}(AD/Uc ), where A is the reaction rate and Uc is the activation threshold. Perturbing apoptotic sensitivity confirmed the predicted threshold-speed relationship. These findings establish the activation threshold as a key determinant of trigger wave speed and provide a broadly applicable scaling law for predicting the spread of switch-like biochemical signals.

Astrocytes actively regulate synaptic transmission and neuronal excitability, yet their role in orchestrating macroscopic cortical network regimes and slow-wave oscillations remains an active area of reasearch. This study investigates how bidirectional neuron astrocyte interactions shape emergent population dynamics using a computational network model of excitatory and inhibitory neurons coupled to an astrocyte. The results identify astrocytic feedback topology, rather than astrocytic coupling strength alone, as a key determinant of emergent cortical network dynamics. By systematically dissecting pathway-specific connectivity, it has been shown that the neuronal population driving astrocytic activation and the neuronal population receiving gliotransmission jointly determine whether the network occupies asynchronous irregular (AI), synchronous irregular (SI), synchronous regular(SR), asynchronous regular(AR) or quiescent regimes.Directing gliotransmission selectively onto excitatory neurons consistently promotes population synchrony regardless of the population influencing astrocytic dynamics, whereas selective modulation of inhibitory interneurons induces network quiescence via strong suppression. Under dual-target gliotransmission, network synchrony is dictated by the population driving astrocytic dynamics: excitatory-only drive promotes synchrony, while combined or inhibitory-specific drive preserves asynchronous states. Furthermore, the model reveals that astrocytic signaling kinetics provide an additional temporal control mechanism that regulates the frequency and persistence of self sustained up states.

The circadian clock allows living systems to anticipate environmental daily variations by scheduling cellular mechanisms according to the time of the day. The reciprocal interplay between metabolism and circadian clock is essential for energy homeostasis, and the disruption of metabolic clock inputs contributes to dysfunction of clocks in peripheral tissues. However, the molecular mechanisms through which the feeding/fasting cycle entrains peripheral clocks remain incompletely understood. Here, we investigate experimentally and theoretically the role of AMP-dependent kinase (AMPK), a key fasting sensor, in metabolic regulation of the circadian clock. Using a luciferase reporter driven by the Bmal1 promoter to monitor molecular clock activity in human U2OS cells, and thanks to a signal processing method based on the Hilbert transform to retrieve the instantaneous phase and period of circadian signals, we show that pharmacological activation of AMPK by AICAR significantly elevates Bmal1 promoter activity and markedly lengthens the clock period in a dose-dependent manner. Conversely, the clock period is shortened by the pharmacological inhibition by SR18292 of Peroxisome proliferator-activated receptor gamma coactivator 1-alpha (PGC-1-alpha). Importantly, the action of AICAR is abolished by FK866, a nicotinamide phosphoribosyltransferase (NAMPT) inhibitor, demonstrating that AMPK-dependent modulation of Bmal1 promoter activity requires NAD+ availability. These experimental results are recapitulated by numerical simulations of our previously published mathematical model, where PGC-1-alpha plays a key role in mediating AMPK activity to the clock. Moreover, the comparison of experimentally measured and theoretically predicted phase response curves, following AMPK activation at different circadian phases, provides an additional validation of the model. By integrating biological experiments with mathematical modeling, our results identify a key mechanism through which metabolic factors can entrain and regulate the circadian clock via NAD+-dependent AMPK-mediated regulation of Bmal1 promoter activity.

Non-exponential residence times give rise to history-dependent or memory effects in epidemic dynamics, yet their mathematical formulations remain fragmented. Here we develop a unified framework for a history-dependent SEIR model with general latent- and infectious-period distributions. We first establish the equivalence between the stage-age and renewal formulations and show that both admit a unified transition-flow representation. We then introduce the concept of a transition-flow multiplier, which provides a direct link between residence-time distributions and transition flows. When the multiplier is a weighted sum of shifted power functions, the model admits an exact representation in terms of Riemann-Liouville or tempered Riemann-Liouville fractional operators, providing a first-principles foundation for fractional epidemic models. Finally, using Euler-Lotka equations and stochastic-order arguments, we characterize how the latent- and infectious-period distributions shape epidemic growth and decay. A longer latent period slows both early growth and late decay, while, at fixed means, greater variability in the latent period accelerates early growth but slows late decay, whereas greater variability in the infectious period slows both.

We propose a minimal mathematical framework to describe the go-or-grow dynamics of tumor cells comprising two phenotypically distinct populations. One population is migratory and undergoes constant diffusion, while the other proliferates in an oxygen-dependent manner. The local oxygen concentration governs transitions between these phenotypes. We then ask whether the time scale of cyclic hypoxia, where oxygen is spatially homogeneous but fluctuates between normoxic and hypoxic levels over time, alters the dynamics of the reduced generalist model in the fast phenotype-switching regime compared with the full go-or-grow model. We observe that the reduced generalist phenotype model fails to capture the go-or-grow dynamics under rapid oxygen fluctuations. Our results predict that the tumor growth rate increases in the generalist-phenotype model under rapid oxygen fluctuations compared with tumors of the proposed go-or-grow model. We then explore whether oxygen consumption, which leads to spatial heterogeneity in oxygen concentration, plays a role in distinguishing the dynamics of the reduced model from the proposed go-or-grow model. We demonstrate that the tumor in the proposed go-or-grow model exhibits a higher growth rate than the tumor in the reduced generalist-phenotype model under a slow oxygen consumption rate.

Recurrent cortical circuits are hypothesized to perform Bayesian posterior sampling through their stochastic dynamics. Yet identifying which sampling algorithm a circuit intrinsically implements, as opposed to mapping manually designing algorithms onto circuits, requires rigorous theoretical analysis of the biological circuit dynamics, and remains a fundamental open challenge because of the analytical intractability of nonlinear recurrent dynamics. Here, we tackle this challenge through comprehensive theoretical analysis of analytically tractable nonlinear recurrent circuit dynamics used in neuroscience research-- the continuous attractor network (CAN). Surprisingly, we find that the circuit, without any non-Gaussian components in its connectivity or internal variability, intrinsically emerges heavy-tailed subspaces dynamics described as scale-mixture Langevin posterior sampling. The mechanism emerges from the circuits own nonlinear dynamics: divisive normalization renders the overall population activation Gamma-distributed which multiplicatively modulates the time constant of the Langevin sampling in the stimulus feature subspace. Eventually, this scale-mixture structure produces a heavy-tailed (Student-t) sampling step size distribution, significantly accelerating the sampling speed. Moreover, the scale-mixture Langevin sampling approaches a Levy-like regime in the weak input limit. Our results analytically identify an intrinsic circuit algorithm embedded in subspaces of nonlinear recurrent dynamics, and establish a minimal circuit mechanism for endogenous heavy-tail statistics without any explicit non-Gaussian components.

Moment-closure methods provide a widely used approach for approximating low-order statistics of stochastic biochemical reaction networks, but the resulting closed equations may exhibit physically meaningless dynamics. Here, we systematically investigate the stability of second-order moment-closure approximations for a bursty gene expression model with nonlinear protein degradation. We consider the Gaussian, log-normal, and negative-binomial closures. By analyzing the resulting dynamical systems, we show that the Gaussian closure fails the proposed stability criterion for all parameter values, whereas both the log-normal and negative-binomial closures possess a unique physically accessible fixed point and are stable if and only if kB(1 + 2B) [≥] 1, where B is the mean burst size and k is the dimensionless protein synthesis rate. Moreover, this condition is automatically satisfied when the steady-state mean protein copy number is at least one, suggesting that it is mild in biologically relevant regimes. Numerical comparisons over a broad parameter range further show that the negative-binomial closure is the most accurate, while the Gaussian closure is the least accurate. We further develop higher-order negative-binomial moment-closure schemes and demonstrate that increasing the closure order substantially improves predictive accuracy. These results highlight the importance of considering dynamical stability, in addition to numerical accuracy, when assessing moment-closure approximations.

Game theory in biology started as an attempt to model animal contests by making assumptions about the fitness costs individuals pay in aggressive interactions. Among the different approaches, a notable one is to construct mechanistic models, using assumptions about behaviours and cognitive processes. Reinforcement learning is an important cognitive process, and we use it here to model pairwise and coalitional contests. We study situations where territorial neighbours become so-called dear enemies. A defending individual can get help from a neighbour through a defender-neighbour coalition against a challenger attempting territory takeover. In our model, coalition members have an advantage in contests in terms of costs of aggression, with the challenger being exposed to aggression from both members and each member only receiving part of the aggression from the challenger. We find that notable costs of border conflicts between neighbours, together with substantial advantages for coalitions, favour intervention. Neighbours intervene when they can help weaker defenders, in this way avoiding costs of border renegotiation with a new and potentially stronger territory owner. We also introduce different forms of perceived costs into the model, which we show correspond to the range from pure mutual assessment to partial self-assessment.

We show that the p53-Mdm2 gene interaction can be understood as a form of antithetic feedback, but with mixed feedback loops. In particular, we show that this viewpoint sheds light on the emergence and robustness properties of p53's oscillatory behaviour, as observed experimentally.

Mixed-timescale signals are ubiquitous in natural stimuli and real-world applications, yet they remain challenging to process with recurrent neural networks. Reservoir computing offers an efficient framework for temporal processing, but extending its temporal range typically requires tuning neuronal timescales, which can compromise the representation of faster dynamics. Here, we propose an alternative approach in which synaptic plasticity provides an additional, slower timescale for computation. We introduce Hebbian plasticity into recurrent networks and show that its dynamics enable the reservoir to simultaneously process fast and slow components of mixed-timescale inputs: neuronal dynamics encode fast fluctuations, while synaptic dynamics support slower components. Remarkably, the resulting computational benefit extends over more than an order of magnitude beyond the intrinsic timescale of the plasticity. We show that this extended processing range arises from the dependence of the plasticity rule on postsynaptic activity, which effectively injects a filtered memory of past states into the network current. These results identify synaptic plasticity as a mechanism for extending the temporal processing capabilities of recurrent networks without altering neuronal timescales, and also suggest a potential computational role for plastic synapses in the processing of slowly varying stimuli in biological neuronal networks.

Decision-making requires accumulation of evidence over time, yet exactly how neural circuits implement this computation remains debated. Classical models posit that evidence accumulation is realized by ramping neural activity, whereas recent experimental findings suggest an alternative mechanism in which neural activity remains largely silent before abruptly transitioning into an active decision state. This mechanism leaves a fundamental question unanswered: how is evidence accumulated during the neural activity-silent period? To address this question, we trained excitatory-inhibitory recurrent neural networks (RNNs) with short-term synaptic plasticity (STP) on a reaction-time decision task. We found that after training, the networks learned to leverage STP to make decisions in an activity-silent manner. Choice-tuning analysis revealed a clear functional organization of the network, and connection-pruning analysis uncovered the coupling between choice-selective excitatory and inhibitory neural groups. Guided by the architecture of trained RNNs, we constructed a minimal neural circuit model, in which evidence accumulates in facilitated synaptic efficacy that progressively reshapes the circuit's phase portrait, eventually driving the network state across the stability boundary and triggering a rapid transition to a choice state. We further compared activity before a choice between the theoretical STP and Static models to examine the potential energy benefit of activity-silent decision-making. Together, our results suggest STP as a mechanism for evidence accumulation in activity-silent decision-making and offer insights into the design of energy-efficient artificial neural networks.

The basal ganglia (BG), thalamus and cortex form the BG-thalamo-cortical (BGTC) network, which is essential for voluntary movement and centrally involved in Parkinson's disease (PD). In both patients and animal models, BG neuronal activity exhibits exaggerated oscillatory synchronization in the beta frequencies (13-30 Hz). Theoretical studies have proposed multiple network mechanisms for the generation of these abnormal beta oscillations. However, key properties, such as frequency and power distribution across BG nuclei, vary substantially among patients and between animal models (rodents vs. non-human primates). This variability complicates direct comparisons between theoretical models and experimental data, and questions whether distinct neuronal mechanisms may underlie beta oscillations across species. In an experimentally constrained BGTC network model with species-specific parameters (synaptic, neuronal, and network properties), we evaluate the features of abnormal beta oscillatory activity generated by different mechanisms. The network's negative feedback loops serve as potential sources of spontaneous oscillations. Using rodent- or primate-constrained models, we compare the spectral properties of oscillatory activity across network populations for each loop and derive the expected phase relationships between populations to align predictions with existing rodent data and propose testable hypotheses for primates. We also demonstrate how oscillation frequency can be modulated when multiple generation mechanisms interact as coupled oscillators in the full network. Our results, combined with observed cross-species beta oscillations characteristics, suggest that abnormal beta oscillations likely arise from distinct mechanisms in rodents and primates.

Spiders arrest their fall by abseiling on dragline silk, varying silk release rate to avoid excessive strains that could break the thread. To understand how this is achieved, we develop a minimal dynamical model of abseiling and formulate a time-optimal control problem subject to physical limits on silk strain and dragline spinning rate. We find that the optimal trajectory includes an interval over which the strain is constant, resulting in uniform deceleration consistent with published experiments. To test the generality of this strategy, we then turn to a distinct extreme motor behavior seen in jumping spiders: using a dragline anchored at the takeoff site to correct their orientation while jumping at speeds exceeding 100 body lengths per second. We show that the same constant-strain strategy suffices to counteract the initial body rotation and ensure an upright landing without significant loss of range. Together, our theoretical framework suggests how strain regulation may serve as a strategy for controlling extreme movements such as abseiling seen in many spiders and may be specialized to tasks such as aerial braking and reorientation in jumping spiders.

Brain network organization emerges from ongoing network dynamics that continuously create, maintain, and reorganize connectivity patterns. At both the structural and functional levels, these dynamics shape network evolution throughout the lifespan. Here, we introduce a data-driven framework based on Stochastic Actor-Oriented Models (SAOMs), which model longitudinal network changes as a process of local edge formation and dissolution driven by local-connectivity factors. Applied to functional and structural brain networks from an aging cohort, the resulting models recovered a set of interacting mechanisms that collectively promote hub formation, short-range connectivity, and modular organization. These factors were derived through a novel data-driven factor-selection procedure rather than specified a priori, allowing network mechanisms underlying longitudinal change to be identified directly from observations. Functional networks exhibited substantially higher rates of change than structural networks, suggesting more frequent opportunities for network maintenance and reorganization. Structural networks additionally showed despecification in the hub-forming mechanisms with cognitive impairment. These results support a view of brain network organization as an actively maintained process emerging from ongoing local connectivity dynamics. More broadly, this framework provides a general approach for studying longitudinal network dynamics through the estimation of network-generating mechanisms over time.

Host immunity acquired through prior infections is a key factor shaping the spread of emerging variants. However, accounting for complete infection histories in mathematical models is challenging because the number of possible histories grows exponentially with the number of variants. Here, we present a flexible framework for modeling the co-circulation of multiple variants emerging at arbitrary times while incorporating cross-immunity and variant-specific characteristics. We introduce three tractable approximations: truncation, which retains only infection histories up to a given number of strains; one variant at a time, which is exact when variants circulation does not overlap; and two variants at a time, which is exact when at most two strains co-circulate. We systematically evaluate these approximations across a range of cross-immunity levels and inter-variant emergence delays. Truncation approximations perform best under short emergence delays and strong cross-immunity, whereas the other approaches outperform them at longer delays. When applied to SARS-CoV-2 variant dynamics, the second-order truncation and the two variants at a time approximation accurately capture incidence patterns, whereas the other approaches perform well only for specific subsets of variants. These results identify the parameter regimes in which simplifying assumptions remain valid, provide guidance for model selection, and highlight the key role of infection history in shaping epidemic trajectories.