Chaos: An Interdisciplinary Journal of Nonlinear Science

The awake brain is known to display asynchronous (AS) states during periods of attention and arousal, but the responsiveness properties of such states remain unclear. Here, we investigate this question using computational models of spiking networks of excitatory and inhibitory neurons, mimicking recurrently-connected networks in layer 2/3 of the cerebral cortex. The networks can generate a continuum of AS states, but with different responsiveness characteristics. By using a mean-field model to infer the dynamic properties of the system, we find that there are two families of AS states, which we call "underdamped" (UD) and "overdamped" (OD). Responsiveness is maximised at the transition between OD and UD states, which identifies a "working point" that may present advantageous computational properties.

Growing interest to describe the electrical behavior of glial cells, mainly astrocytes, in intact brain tissue poses more and more challenges to commonly accepted belief they only respond in a linear manner in uptake of the excess of extracellular potassium and maintenance of their network equipotentiality. Their highly conductive mutual interconnections via gap junction (GJ) connections introduce yet another class of nonlinear elements. As more studies report nonlinearities in membrane voltage Vm dependence of both, the membrane and junctional conductances, the need to formulate minimal dynamical models of their transient behavior is getting more acute. Since ODE models of coupled cells, even in simplest 1-d arrays, require simplified descriptions and small set of parameters, rare quantitative studies on glia makes the task even more difficult. This study attempts to qualify a self-coupled cell, or a glial cell coupled to fixed voltage as useful system for detecting the nature of instabilities and transitions coming from coupling. In a novel biophysical model of coupled astrocyte, we introduce nonlinear kinetics of deactivation for large junctional voltages for the first time. We found that N-shaped nonlinearities and corresponding fold structure in the vector field of isolated cell serves as a baseline on top of which coupling nonlinearities enrich the bifurcation picture. Numerical simulations of 1-d array of coupled astrocytes show that coupling increases the propensity of astrocytic Vm to bistability and front propagation. We believe that presented illustrations of possible effects of coupling nonlinearities will motivate neurobiologists to further explore their impact in disease. Significance statementTransient changes in membrane voltage of glial cells may produce significant transient voltage difference between directly coupled cells. Nonlinear steady-state conductance of their interconnection elements, the gap junctions, introduce nonlinear current profiles which are very difficult to measure and quantitate using the available methods due to marked permeability of the junctions and leakiness of glial membrane in general. We propose a minimal model of glial membrane extended with a self-coupled feedback loop, which under realistic simplifying assumptions could serve for qualitative analysis of the impact of coupling, on the stability of resting membrane voltage. Neuronal cells of the brain and spinal cord cannot exist and function without supportive and neuromodulatory functions of the diverse population of glial cells. This applies to virtually all physiological processes on cell level - from cell development, metabolic support, membrane signaling, slow molecular signal transduction, ion homeostasis, neurovascular coupling, myelination, to mention only a few, manifest neuro-glial interaction. Even though all glial cell types are interconnected, the most abundant ones, the astrocytes are massively interconnected by gap junctions to form ordered networks. Electrically, astrocytic networks display membrane voltage equipotentiality, which is considered system-wide resting state for given neuro-glial circuit or unit. With molecular and cellular substrates of glial connectivity being slowly elucidated, network science and dynamical modeling are slowly "invading" that area with many important issues left open. In this study using classical dynamical systems approaches we give indications how nonlinear intercellular coupling between astrocytes affects physiological resting state and its instabilities compared to isolated, uncoupled cell. We strongly believe the suggested minimal model could fill the gap in ODE modeling of neuro-glial circuits, within broadest scope of hypothesis-driven research in cell-level neuroscience.

Adolescence is an important developmental period during which there are diverse changes in the brain and behavior. Goal-directed behaviors and the component processes underlying those behaviors improve during adolescence, including working memory, response inhibition, and reinforcement learning. At the same time there is substantial pruning of excitatory connections in prefrontal cortex and ongoing myelination of axons. However, psychiatric disorders also become increasingly prevalent in late adolescence and early adulthood. In this study, we develop computational models that suggest a hypothesis for how the ongoing changes in the brain can give rise to the increased prevalence of psychiatric disorders. We show that both myelination and pruning during adolescence lead to attractor landscapes in which strongly encoded memories, driven by three-factor learning rules that modulate Hebbian plasticity, come to dominate the landscape of brain activity, at the expense of weakly encoded memories. Pruning and myelination lead to large, strong attractors which, if they are related to aversive emotions, can drive intrusive thoughts and compulsions in obsessive compulsive disorder, rumination in depression, and aversive memories in post-traumatic stress disorder. The link between pruning, myelination and the emergence of dominant attractors for emotionally salient memories is well supported by the models. The way these effects map onto forebrain circuits requires more work.

The routing of information across the brains structural network is central to its wide range of functional capabilities. However, the mechanisms underlying information routing in complex brain networks, particularly between regions that do not share a direct anatomical connection, remain poorly understood. Neural mass models (NMMs), a computational modelling framework capable of capturing complex neural dynamics across scales, can potentially be used to study the dynamical and network bases of these vital polysynaptic routing processes. In this study, we investigate polysynaptic signalling in three widely used NMMs, obeying Ornstein-Uhlenbeck, Stuart-Landau, and Jansen-Rit dynamics, by tracking the propagation of a discrete, focal, high-amplitude perturbation across the underlying network. We find that polysynaptic propagation emerges in all tested NMMs when configured within dynamical regimes that effectively enhance the persistence of perturbations. We also find distinct parameter domains that maximise signal propagation to directly connected regions and to those separated from the source by at least two hops. Finally, we benchmark in silico stimulus propagation in the brain network against an empirical dataset of direct electrical stimulation trials, to explore the relative capabilities of the NMMs in capturing signal propagation to connected versus unconnected regions. This analysis highlights the significance of dynamical repertoire in capturing stimulus propagation outcomes. Overall, this study provides insights into how dynamical and network features shape signal propagation over complex brain networks.

In previous studies by the author on binocular vision with the asymmetric eye (AE), which models a healthy human eye with misaligned optical components, the results were primarily presented in the Rodrigues vector (RV) framework and supported by simulations and 3D visualizations in GeoGebras dynamic geometry environment. In this paper, the novel geometric kinematics of the human eye, that is, the eye with misaligned optics, and simplified assumptions about the eye rotations (the eyes translational movements are disregarded), are developed within the framework of rigid-body rotations. The originality of the analysis lies in a precise geometric decomposition of a full rotation of the eyes posture into a torsion-free rotation (the geodesic part) and a torsional rotation (the non-geodesic extension of the geodesic part). This decomposition is extended to the corresponding decomposition of the angular velocity. A novel derivation of the eyes angular velocity from the RV formulation of the eye kinematics is proposed.

Scientific models are widely used across the natural sciences as an interface between scientific theories and empirical data [1]. Such models play a key role, for example, in the study of human and animal learning, where they express algorithmic hypotheses and relate them to psychology and neuroscience data [2, 3]. These models are traditionally handcrafted by expert researchers based on existing theory or new insights. Such handcrafted models, however, are now known to fall short of capturing the full richness of behavior, even in their narrow domains [4-7]. An alternative data-driven approach has emerged, seeking to discover new insights by fitting and interpreting flexible models [8-11]. However, these tools require substantial human effort to derive insight from data, and it has been unclear how to discover new ideas from data efficiently. Here, we present DataDIVER, a general approach for automatically discovering computational models from data, and demonstrate that these models surface novel mechanistic insights into human and animal learning. Our approach delivers models that take the form of short computer programs, which are optimized both to fit data well and to be simple. These programs explicitly connect with existing theoretical frameworks and are readily understandable by human scientists. They can also be used to make novel predictions, some of which we show are borne out in re-analysis of existing data. General-purpose tools for surfacing new ideas from data, especially in combination with the large datasets that are increasingly available in many fields, stand to dramatically accelerate scientific discovery.

Metabolic networks are typically viewed as homeostatic systems that stabilize flux, energy charge, redox balance, and metabolite availability under perturbation. However, it remains unclear whether the same feedback architectures that support metabolic robustness can also generate learning-like, experience-dependent adaptation. Here, we develop a coarse-grained dynamical model of mammalian energy metabolism to test whether prior perturbation can improve future metabolic responses. The model represents core glucose, glutamine, fatty acid, and oxidative phosphorylation pathways as coupled ordinary differential equations with Michaelis-Menten-type fluxes, product-inhibition feedback, adaptive enzyme-capacity regulation, and explicit ATP costs for enzyme adjustment. Rather than aiming to reproduce quantitative fluxes for a specific cell type, the framework is designed to expose how metabolic feedback, regulatory cost, repeated perturbation, and environmental variability interact. We use this model to ask whether adaptive enzyme regulation enables improved recovery after repeated challenges, whether such effects depend on energetic control costs, and whether environmental variability broadens or constrains the set of reachable adaptive states. This approach provides a tractable way to investigate how homeostatic metabolic regulation may give rise to experience-dependent metabolic plasticity.

Building on a complex between a tubulin protofilament (PF) and a fragment of the Tau protein containing residues 169 to 367, we investigate the dynamics of the disordered elements of the system, namely the tubulin C-terminal tails (CTTs) and the Tau protein, using classical all-atom molecular dynamics simulations. Our results show that CTTs adopt a hook-like dynamic pattern on the bare PF while remaining highly mobile. The binding of Tau on the PF surface alters the dynamics of the I-CTTs in a sequence-dependent manner. While the repeat domains of Tau are mostly maintained on the PF by weak and strong binding patches with the tubulin cores, the Proline-Rich Region (PRR) relies on the wrapping phenomenon of I-CTTs to fuzzily stabilize its interaction with the PF. Our study thus provides a deep dive into the dynamic interplay between the Tau protein and the CTTs of microtubules, the latter being characterized extensively using a variety of disorder-adapted metrics. TOC Graphic O_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=111 SRC="FIGDIR/small/721901v1_ufig1.gif" ALT="Figure 1"> View larger version (25K): org.highwire.dtl.DTLVardef@b3f985org.highwire.dtl.DTLVardef@1c2bf70org.highwire.dtl.DTLVardef@a66b95org.highwire.dtl.DTLVardef@1e138e0_HPS_FORMAT_FIGEXP M_FIG C_FIG

This work focuses on the global and partial identification problem for fractional differential equations. We provide a general numerical procedure based on global and local optimization algorithms with two refinements for biological systems that ensure solution positivity and homogeneous parameter units. The method is applied to a new fractional model of Dengue outbreak called the Fractional Homogeneous Nishiura (FHN) model, calibrated using data of newly infected people in Cape Verde. We show that our identification method yields a better fit between data and model solutions than previous approaches and that our FHN model captures the dynamics of Dengue more closely than existing systems.

Cerebellar neural circuit dynamics rely on a rich repertoire of synaptic and excitability mechanisms, which are thought to determine network computation in physiological and pathological conditions. In this work, we develop and validate a biologically-grounded spiking neural network of the cerebellar cortex, embedding key mechanisms of cellular excitability and synaptic transmission, and assess their impact on signal processing. Neuronal input-output functions, short-term synaptic plasticity, receptor-specific kinetics, and NMDA channel voltage-dependent gating were calibrated against detailed multicompartmental models through automatic tuning procedures. Incorporating these realistic biological properties allowed the network model to simulate key features observed in recordings from acute cerebellar slices. The neuronal discharge and local field potentials elicited by mossy fiber stimulation faithfully reproduced the natural patterns with millisecond precision. Then, selective receptor switch-off revealed the contribution of NMDA, GABA, and AMPA receptors to the frequency-dependent input-output function of the granular layer and Purkinje cells, linking previous empirical findings to specific synaptic mechanisms. This model combines high computational performance with biological realism and offers a computationally efficient framework to investigate neurophysiological phenomena and the neural correlates of behavior in large-scale long-lasting simulations, such as those needed to address the neural underpinnings of learning and of cerebellar pathologies.

Temporal gradient sensing is a fundamental capability observed across diverse natural biological systems, contributing to the coordination of their functions. Harnessing this ability is also of significant interest in synthetic biology, particularly for sensing and control applications. In this work, we focus on a biomolecular topology that exemplifies a broader class of signal-differentiating architectures, while introducing a structural variant of it. We examine their behavior under both nominal and non-ideal conditions, accounting for stochastic noise arising from different sources. Our investigation includes scenarios where these topologies operate independently, as well as when embedded within minimal regulatory architectures based on negative as well as positive feedback. We analyze the stability of the resulting macroscopic dynamics--a prerequisite for practical deployment--and quantify stochastic fluctuations in system output, providing comparisons with the corresponding input/unregulated process. Importantly, our results demonstrate that signal differentiation can be effectively implemented in a biomolecular setting without incurring deleterious noise amplification--a major concern in the utilization of derivative action across disciplines.

Cells communicate via extracellular ligands, such as hormones, which bind to plasma membrane receptors and trigger intracellular signaling cascades. G Protein-Coupled Receptors (GPCRs) exemplify this mechanism by initiating signaling both at the cell surface and, from intracellular compartments such as endosomes. The kinetics and spatial localization of these signals are critical determinants of cellular responses, yet receptor trafficking-including internalization, endosomal sorting, and recycling-remains a pivotal but often overlooked component of theoretical GPCR models. In this study, we present a mathematical framework that integrates receptor trafficking and signaling compartmentalization into generic GPCR dynamic models. Using a compartmentalized approach based on systems of ordinary differential equations (Chemical Reaction Networks), we analyze how receptor internalization and recycling modulate ligand-induced responses. Our results show that the balance between plasma membrane and endosomal signaling can significantly enhance or diminish ligand efficacy. Calibrated with high-throughput kinetic data, our model offers a refined tool for ligand pharmacological characterization and advances the understanding of GPCR signaling spatial organization.

Improving long-term memory in artificial neural networks remains an open challenge. To address this, we developed a novel brain-inspired framework for memory prioritization based on the principle of emotional valence. Our framework includes: (i) a valence-weighted cross-entropy loss that scales the learning signal by the valence magnitude, analogous to neuromodulation; (ii) an amygdala-inspired module that learns high-dimensional valence embeddings; and (iii) a hippocampus-inspired module that integrates valence embeddings into the attention mechanism to modulate information retrieval. We demonstrated the generalization of our framework across spatial, episodic, and language-based memory tasks, consistently improving memory prioritization and long-term retention of high-salience information. In addition to improving long-term memory, we also showed that our framework can help mitigate the "lost-in-the-middle" problem in language modeling. More generally, this research provides further evidence of the potential of brain-inspired algorithms to advance the field of machine learning.

Counterfactual Explanation (CE) algorithms have been successfully applied to uncover the main factors driving computational diagnostic and prognostic predictions on tabular medical data. Recently, a new Network Medicine paradigm has been introduced for patient diagnosis and prognosis using Patient Similarity Networks (PSNs), i.e. graphs where patients are represented as nodes and their clinical and biomolecular similarities as edges. In this context, graph-based algorithms, including Graph Neural Networks (GNNs), can provide predictions using not only individual patient features but also their relations within a network of clinically and biomolecularly similar individuals. In this work, we propose the first CE algorithm tailored to explain diagnostic and prognostic predictions within PSNs. Alongside a contrastive GNN backbone, we introduce a versatile, model-agnostic counterfactual search method compatible with any underlying classifier. Preliminary results on synthetic data and on a cohort of patients affected by the Alzheimers disease show that our algorithm is competitive both with seminal tabular based CE algorithms and GNNExplainer, a well-established method for explaining graph-based classification tasks.

Glioblastoma multiforme (GBM) is characterised by profound genomic heterogeneity and heavy-tailed gene-expression distributions that challenge conventional machine-learning methods. We introduce the Tsallis-Gated Autoencoder (Tsallis-GAE), a physics-informed architecture that replaces classical softmax attention with a learnable Tsallis q-softmax followed by mean-field smoothing iterations, motivated by recent work on curved statistical manifolds and dense associative networks. Trained on the full TCGA-GBM RNA-seq cohort (391 samples, top 2,000 high-variance genes) under a rigorous 80/20 hold-out protocol, the Tsallis-GAE achieves a mean AUC-ROC of 0.977 {+/-} 0.002 across five independent seeds, compared to 0.906 {+/-} 0.003 for a matched-capacity Vanilla autoencoder trained under the identical protocol. The matched-capacity Vanilla autoencoder is statistically indistinguishable from a LocalOutlierFactor baseline (AUC 0.906 vs 0.906), confirming that the +0.07 AUC gain over the Vanilla AE stems from the gated attention architecture rather than from the use of a neural network per se. A fixed-q Softmax-AE ablation (q {equiv}1 by construction) achieves AUC 0.976 {+/-}0.001, only +0.001 below the Tsallis-GAE (DeLong p = 0.44); the physically meaningful contribution of the learnable q is its spontaneous convergence to the non-extensive regime described below. The three attention blocks each carry an independent learnable entropic index q; across 5 seeds x3 blocks = 15 measurements, q converges spontaneously to 1.554{+/-} 0.019, strictly bounded away from the Boltzmann-Gibbs limit q = 1 and in the moderate non-extensivity regime characteristic of complex biological systems. Cross-detector validation against OneClassSVM and LocalOutlier-Factor pseudo-labels yields Tsallis-GAE AUCs of 0.998 and 0.992 respectively, indicating that the learned representation captures anomaly structure intrinsic to the data rather than the decision boundary of any single labeling heuristic. We declare that DeLongs paired test on the present test-set size (n = 79) does not certify the +0.07 AUC gap as formally significant (p{approx} 0.26); a 5-fold cross-validation over the full cohort, which would supply the needed statistical power, is left to future work. The source code is available upon reasonable request to the corresponding author.

The learning dynamics of biological brains and artificial neural networks are of interest to both neuroscience and machine learning. A key difference between them is that neural networks are often trained from a randomly initialized state whereas each brain is the product of generations of evolutionary optimization, yielding innate structures that enable few-shot learning and inbuilt reflexes. Artificial neural networks, by contrast, require non-ethological quantities of training data to attain comparable performance. To investigate the effect of evolutionary optimization on the learning dynamics of neural networks, we combined algorithms simulating natural selection and online learning to produce a method for evolutionarily conditioning artificial neural networks, and applied it to both reinforcement and supervised learning contexts. We found the evolutionary conditioning algorithm, by itself, performs comparably to an unoptimized baseline. However, evolutionarily conditioned networks show signs of unique and latent learning dynamics, and can be rapidly fine-tuned to optimal performance. These results suggest evolution constitutes an inductive bias that tunes neural systems to enable rapid learning.

How is it possible to double the lifespan of an organism already close to death? Many biological theories of aging fail to explain this phenomenon. At the Physics of Aging workshop, we presented and discussed late-life lifespan extension in Caenorhabditis elegans to illustrate how a simple stochastic dynamical systems model can account for dramatic geriatric interventions. We build on a Langevin-type instability framework in which aging is a manifestation of dynamical instability-a scenario where stochastic fluctuations amplify over time, driving the system toward a failure thresh-old at which death occurs as a first-passage event. The instability rate (equivalently, the inverse of the mortality-rate doubling time) quantifies the speed of this divergence: a larger means faster exponential growth of z, a steeper Gompertz slope, and a shorter lifespan. The failure threshold zmax{approx} /g, where g is the strength of nonlinear feedback, marks the point beyond which the system diverges irreversibly--physiologically, the saturation of metabolic and regulatory capacity. Within this dynamical-systems framework, auxin-induced degradation of the insulin/IGF-1 receptor DAF-2 in very old animals is naturally interpreted as a late shift in stability parameters that nearly doubles remaining lifespan without resetting accumulated structural damage. This interpretation reconciles the persistence of many senescent pathologies with restored proteostasis and stress resilience, and it shows that targeting the dynamical instability of the regulatory network-rather than reversing damage--can strongly reshape survival trajectories in unstable animals. More broadly, our work exemplifies how physics-inspired low-dimensional stochastic models can capture key features of aging, and we hope it will inspire more collaborations between biologists and physicists to work on late-life interventions.

Individuals adapt their behavior in response to infectious disease epidemics. Understanding the determinants of behavior, particularly the impact of infections themselves, can help model the feedback loop between disease and behavior in epidemic models. We combined the Imperial College London YouGov COVID-19 behavior survey with hospitalization data and the Oxford COVID-19 government response tracker stringency index to identify the key predictors of three health behaviors--social distancing, masking, and personal protective measures (e.g. handwashing)-- during an early phase of the COVID-19 pandemic in six different countries. We compared two machine learning algorithms--logistic regression with stepwise Akaike Information Criterion and extreme gradient boosting (XGBoost). Top predictors of health behavior were perceived disease severity, hospitalizations, willingness to isolate, and intervention effectiveness, across the six countries. Logistic regression and XGBoost had comparable performance. Machine learning algorithms trained on real-world data could be used to predict individual behavior uptake in agent-based network models.

Sex-related differences in the aging of the human brain were studied using large array of experimental data. The open archive CamCan was used as a source of data: the magnetic encephalograms, co-registered with magnetic resonance images of the head, were obtained for each of 434 subjects (ages 18-87 years, mean age 54.7 {+/-}18.4): 217 females (ages 18-87 years, mean age 54.5 {+/-}18.4) and 217 males (ages 18-84 years, mean age 54.8 {+/-}18.3). Recordings were split in 10-year age cohorts, each cohort consisted of equal number of men and women to calculate average intersex characteristics correctly. By massively solving the inverse problem, functional tomograms were calculated - the spatial distribution of elementary spectral components. Physiological noise was eliminated by joint analysis of MEG-based functional tomogram and magnetic resonance image for each subject. Then multichannel spectra were transformed into time series of the power of elementary current dipoles. Summary electric powers were calculated in six conventional frequency bands (1-4 Hz - delta; 4-8 Hz - theta; 8-13 Hz - alpha; 13-21 Hz - beta1; 21-30 Hz - beta2; 30-48 Hz - gamma), and sex differences in age-related changes were examined. It was found that in the youngest age cohort (18-29 years) the summary electrical power of the brain for males is 1.5 times greater than such power for females. For adults (30-69 years), male and female powers are approximately equal, while in older cohorts (70-87 years), male total brain power is greater. Age dependencies in various frequency bands are generally different for men and women, excluding higher frequencies 21-48 Hz. Basic conclusion can be made that after intersex averaging total electric power of the human brain is invariant through the lifespan from 18 to 87 years. The proposed method of joint MEG and MRI analysis can be used for further study of the sex-related details of brain sources in their connection with age changes.

The phenomenon of splitting was originally observed in hamsters which, after prolonged exposure to constant light, exhibit two rest/wake cycles within a subjective day. Splitting is a consequence of the left and right suprachiasmatic nuclei (SCN) falling out of synchrony. While it is known that split activity is characterized by an antiphase relationship between the left and right SCN and between the core and shell within each hemisphere, the role of the commissural projections that connect the right and left SCN is not known. In the present study, we investigate the impact of the inter-hemispheric connections on the split and unsplit dynamics of a computational model of the bilateral SCN. Our model has 4 nodes corresponding to each right and left core and shell. We simulated our bilateral model under different lighting conditions and measured its period and the phase relationships among the 4 nodes. To further characterize the dynamics of the system, we performed a bifurcation analysis. We found that the bilateral model automatically splits unless entrained by bright light/dark cycles, or unless it has excitatory inter-hemispheric connections. This suggests that excitatory cross-connections may be important for freerunning behavior. We found that constant light of varying intensities transitions the model between split and unsplit activity only in very limited conditions, but the strength and polarity of the contralateral connections play a much greater role in this dynamical transition. These findings suggest that splitting may involve plasticity of the inter-hemispheric connections of the SCN.