Chaos: An Interdisciplinary Journal of Nonlinear Science

Imagine you walk in a plane. You move by making a step of a certain length per time interval in a chosen direction. Repeating this process by randomly sampling step length and turning angle defines a two-dimensional random walk in what we call comoving frame coordinates. This is precisely how Ross and Pearson proposed to model the movements of organisms more than a century ago. Decades later their concept was generalised by including persistence leading to a correlated random walk, which became a popular model in Movement Ecology. In contrast, Langevin equations describing cell migration and used in active matter theory are typically formulated by position and velocity in a fixed Cartesian frame. In this article, we explore the transformation of stochastic Langevin dynamics from the Cartesian into the comoving frame. We show that the Ornstein-Uhlenbeck process for the Cartesian velocity of a walker can be transformed exactly into a stochastic process that is defined self-consistently in the comoving frame, thereby profoundly generalising correlated random walk models. This approach yields a general conceptual framework how to transform stochastic processes from the Cartesian into the comoving frame. Our theory paves the way to derive, invent and explore novel stochastic processes in the comoving frame for modelling the movements of organisms. It can also be applied to design novel stochastic dynamics for autonomously moving robots and drones.

AO_SCPLOWBSTRACTC_SCPLOWWe study an extension of an environmentally mediated epidemiological model that incorporates direct human-to-human transmission. While the original formulation accounted for environmental exposure, it did not include direct transmission between individuals. Allowing both transmission routes to interact leads to significant qualitative changes in the system dynamics. The analysis reveals multiple dynamical regimes governed by environmental and combined threshold quantities. The stability of the disease-free equilibrium is controlled by an environmental threshold, whereas a combined reproduction number determines the onset of multistability. For certain parameter ranges, endemic equilibria coexist with the disease-free equilibrium, giving rise to backward-type bifurcation behavior and sensitivity to initial conditions. Moreover, the direct transmission rate acts as an organizing parameter by inducing the emergence of an environmental-free equilibrium when exceeding its classical threshold. These results highlight how environmentally coupled transmission mechanisms can generate rich dynamics in low-dimensional models.

A key component of intraneuronal communication is the modulation of postsynaptic firing frequencies by stochastic transmitter release from presynaptic neurons. The time interval between successive postsynaptic firings is called the inter-spike interval (ISI), and understanding its statistics is integral to neural information processing. We start with a model of an excitatory chemical synapse with postsynaptic neuron firing governed as per a classical integrate-and-fire model. Using a first-passage time framework, we derive exact analytical results for the ISI statistical moments, revealing parameter regimes driving precision in postsynaptic action potential timing. Next, we extended this analysis to include both an excitatory and an inhibitory presynaptic connection onto the same postsynaptic neuron. We consider both a fixed postsynaptic-firing threshold and a threshold that adapts based on the postsynaptic membrane potential history. Our analysis shows that the latter adaptive threshold can result in scenarios where increasing the inhibitory input frequency increases the postsynaptic firing frequency. Moreover, we characterize parameter regimes where ISI noise is hypo-exponential or hyperexponential based on its coefficient of variation being less than or higher than one, respectively.

We describe an approach for analyzing biological networks using rows of the Krylov subspace of the adjacency matrix. Specifically, we explore the scenario where the Krylov subspace matrix is computed via power iteration using a non-random and potentially non-uniform initial vector that captures a specific biological state or perturbation. In this case, the rows the Krylov subspace matrix (i.e., Krylov trajectories) carry important functional information about the network nodes in the biological context represented by the initial vector. We demonstrate the utility of this approach for community detection and perturbation analysis using the C. Elegans neural network.

Voltage perturbations to a repetitively firing Hodgkin-Huxley (HH) model of neuronal spiking in the bistable regime with coexisting limit cycle and stable steady node can either lead to the spikes phase resetting or collapse to the stable steady state. The latter describes a non-firing hyperpolarized quiescent state of the neuron despite the presence of constant external current. Using asymptotic phase response curve (PRC), the impact of voltage perturbations on a repetitively firing HH model is studied here while it is diffusively coupled to another HH model under identical external stimulation. It is observed that the pre-perturbation state of synchronization and the coupling strength critically determine the PRC response of the perturbed HH dynamics. Higher coupling strengths of perfectly in-phase (anti-phase) synchronized HH models shrink (expand) the combinatorial space of perturbation strengths and the oscillation phases causing collapse to the quiescent state. This indicates reduced (enlarged) basin of attraction, viz. the null space, associated with the steady state in the HH phase space. The findings bear important implications to the spiking dynamics of diverse interneurons, as well as special cases of pyramidal neurons, coupled through electrical synapses via. gap junctions, and suggest the role of gap junction plasticity in tuning vulnerability to quiescent state in the presence of biological noise and spikelets.

Biological systems rely on asynchronous and temporally overlapping dynamics, allowing for the concurrent activation of multiple processes. This principle is particularly evident in brain function, where cognitive tasks engage distributed, interacting regions rather than sequentially isolated ones. To investigate the mechanisms enabling such coordination, we study a modular spiking neural network composed of leaky integrate-and-fire neurons and governed by spike-timing-dependent plasticity (STDP). Our model stores modular spatiotemporal patterns both at the mesoscopic level (sequences of modules) and at the microscopic level (precise spike timings) and includes a parameter, , which regulates the degree of temporal overlap between modules activations. By tuning , the network transitions from sequential to overlapping regimes, ranging from synfire chain-like dynamics to fully co-activated modules. We investigate how the temporal structure influences the networks capacity to encode and selectively retrieve multiple dynamical patterns, while considering biological constraints such as the cost of long-range connectivity. Our results offer insight into how spatiotemporal coding and network organisation support robust, large-scale memory storage and replay.

Organisms must manage a trade-off between robustness and flexibility as they enact adaptive behaviors. One way organisms achieve this is by navigating a network of quasi-stable behavioral states. Evidence for such behavioral states has been observed in many organisms, and new methods for detecting these states have taken on a prominent research focus. Although dynamical models demonstrating behavioral switching have been developed significantly over the past few decades, theories of the similarities and differences among these models, necessary for advancing empirical modeling, have not yet been fully elaborated. Here, we consider behavioral switching in two different classes of dynamical models of the forward-reversal behavioral transition in C. elegans. We first show how fundamentally different models can give rise to similar phenomena under noisy conditions. We then analyze the deterministic aspects of these models to expand on their differences, clarifying the theoretical relationship between them. Finally, we demonstrate how sequence models can be further extended to incorporate dwell times for behavioral states. Our work contributes toward a broader theoretical understanding of behavioral switching in adaptive systems.

Protein expression within oncogenic or suppressive pathways is a hallmark indicator of oncogenesis. While traditional AI models in digital pathology attempt to predict singular proteins, there is a need to predict the downstream expression of proteins to indicate the propagation of signals. RNA expression provides novel information, but does not provide information about the downstream propagation of protein signals or whether those signals are functional. Using Reverse Phase Protein Array (RPPA) data with whole-slide images (WSIs) from the publicly available Cancer Genome Atlas Breast Adenocarcinoma dataset (TCGA-BRCA), we predict the expression of five key proteins identified from the apoptosis cascade, using DNA damage and repair (DDR) cascades as a biological control. Furthermore, we examine the performance of patch-level Vision Transformers (ViT) on the regression task, which was tested against the designed cellular-level ViT, CellRPPA. Our results demonstrate that patch-level vision transformers were unable to obtain statistically significant predictive results, achieving R-squared values {inverted exclamation} 0.1 for all folds. In addition, CellViT obtained R-squared values {inverted question} 0.1 in all five test folds. We also show that morphologically indicative cascades, such as the apoptosis cascade, provide significantly higher performance compared to the DDR cascade.

In this work, the impact of outliers on the performance of machine learning and deep learning models is investigated, specifically for the case of histopathological images of colorectal cancer stained with Haematoxylin and Eosin. The evaluation of the impact is done through the systematic comparison of one machine learning model (Random Forests) and one deep learning model (ResNet-18). Both models were trained with the popular NCT-CRC-HE-VAL-100K dataset and tested on the CRC-HE-VAL-7K companion set. Then, a curation process was performed by analysing the divergence of patches based on chromatic, textural and topological features of the training set and removing outliers to repeat the training with a cleaned dataset. The results showed that machine learning models, can benefit more from improvements in the quality of data, than deep learning models. Further, the results suggest that deep learning models are more robust to outliers as, through the training process, the architectures can learn features other than those previously mentioned.

Foraging is a central decision-making behavior performed by all animals, essential to garnishing enough energy for an organism to survive. Similarly, mating is crucial for evolutionary continuity and offspring production. Mate choice is one of the central tenets of sexual selection, driving major evolutionary processes, and can be regarded as a decision-making process between potential mating partners. Often researchers have used coarse-grained models to describe macroscopic phenomenology pertaining to mate choice without detailed quantitative mechanisms of how animals use individual and environmental signals to guide their mating decisions. In this letter, we show that mate choice can be cast as a foraging problem, and we present an analytically tractable optimal foraging-inspired mechanistic theory of decision-making underlying mate choice. We begin from the premise that deciding upon which partner with which to mate is at its core a stochastic decision-making process. Agents adopt a variety of decision strategies, tuned by decision thresholds for leaving or committing to a mate. We find that sensitive leaving thresholds are favored independently of signal availability in the population. By contrast, optimal thresholds for committing to a mate depend upon signal availability in the population, with signal-rich populations generally favoring less eager strategies compared to signal-poor populations.

Neural population activity typically evolves on low-dimensional manifolds and can be described as trajectories in attractor-like state spaces, including metastable switching among quasi-stable assembly states. Here we develop a unified definition of clustered neural networks with local excitatory-inhibitory balance in which enhanced within-cluster effective coupling can be realized by connection probability (structural clustering), synaptic efficacy (weight clustering), or any mixture of both. We introduce a single mixing parameter{kappa} [isin] [0, 1] that redistributes a defined clustering contrast between connection probabilities and synaptic efficacies while preserving the mean input of a balanced random network. Using mean-field theory and network simulations, we show that metastable dynamics are supported across the full{kappa} continuum. Shifting contrast between structural and weight clustering changes higher-order input structure, reshaping multistable regimes, neuronal correlations, and the balance between single- and multi-cluster episodes. Because real nervous systems jointly organize topology and synaptic strength, our approach provides a biologically realistic assembly definition and a basis for future models combining structural and functional plasticity. In practical terms,{kappa} offers a translation axis for neuromorphic and other constrained substrates, clarifying trade-offs between routing resources and synaptic weight resolution when implementing attractor-based computational primitives such as winner-take-all decisions and working-memory states for artificial agents.

The immune system was historically defined as a system that provides protection from pathogens. Numerous models have been developed to understand how immunity faces a complex world of microbes that includes pathogens and symbionts, as well as cells of our own self that may develop tumors. Based on the classical assumption that survival depends on internal homeostasis, we have developed a formal model of homeostasis for a host interacting with microbes and self. We propose that such a model must include two fundamental functions: a function that counters change (including tissue repair), and a function that counters the agent of change (such as "immunity" to microbes or self). We show that this elementary model is sufficient to generate symbiosis, and that symbiosis is an emergent property of the host-microbe relationship that does not require the microbe or the host to express "traits of symbiosis". We suggest that the conditions leading to symbiosis contribute to eukaryotic evolution and ontogeny. This model may be further applied to symbiotic interactions between organisms and non-microbial or non-cellular agents of change.

We present an approach to analysing cell homeostasis using a bond graph modelling approach that ensures that the conservation laws of physics (conservation of mass, charge, and energy, respectively) are satisfied for the interdependent biochemical, electrical, mechanical, and thermal energy storage mechanisms operating within the cell. We apply the bond graph approach to several cell membrane transport mechanisms and then consider how physics constrains intracellular electrolyte homeostasis for enterocytes (the epithelial absorptive cells of the gut). The model includes the electrogenic sodium-potassium ATPase pump (NKA), the glucose transporter (GLUT2), and an inwardly rectifying potassium channel, all in the basolateral membrane, and the electrogenic sodium-driven glucose transporter (SGLT1) in the apical membrane. Glycolysis converts the imported glucose to ATP to drive NKA. For specified levels of sodium, potassium, and glucose in the blood, the model demonstrates how enterocytes absorb sodium and glucose from the gut and transfer glucose to the blood while maintaining the membrane potential and homeostasis of intracellular sodium and potassium. The Gibbs free energy available from the ATP hydrolysis ensures that the cell operates as a sodium battery with a high external to internal ratio of sodium concentration in order to provide the energy for many other cellular transport processes. We show that the 3:2 stoichiometry of Na+/K+ exchange in NKA, coupled with 2:1 Na+/glucose cotransport in SGLT1, a 1:2:2 ratio between glucose consumption and ATP and water production in glycolysis, and K+ and glucose efflux through Kir and GLUT2, respectively, provides a balanced system that maintains homeostasis of intracellular Na+, K+, glucose, ATP and water, and homeostasis of the membrane potential, under varying levels of transport of glucose from the gut to the blood. We also show how the flux expressions for SLC transporters, ATPase pumps and ion channels can all be expressed in a consistent and thermodynamically valid way.

Memory consolidation is the process by which temporary, malleable memories are transformed into more stable, longer-lasting forms. On a coarse anatomical scale, consolidation redistributes memories in the brain, but it remains poorly understood how these changes manifest themselves on the finer, cellular scale of neuronal engrams and how they relate to the cognitive level. In this study, we developed a phenomenological model of engram dynamics under systems consolidation. The model describes consolidation as a brain-wide phenomenon, where memories deterministically follow a trajectory through a space of patterns distributed among brain regions. It captures a broad range of features of memory consolidation, including selective consolidation, semantization, and power-law forgetting. In the model, consolidation is accompanied by population-level changes in neuronal representations that resemble the widely observed phenomenon of representational drift. When only a subset of neurons is observed, the deterministic dynamics of the model can appear stochastic, and a readout of task features deteriorates over time even when a stable readout exists for the full system. Our model offers a dynamical systems perspective on memory consolidation as a distributed process, moving beyond the classic region-centered view, and provides a functional interpretation of drift as a means of redistributing engrams for improved memory retention.

A methodology for computationally unstructuring proteins is described and the results of its application to a variety of proteins analyzed and discussed. Some proteins prove more susceptible than others, and fold topology plays a part in this. Alpha helical structure is found to be generally somewhat robust, and, perhaps unsurprisingly, unstructuring often begins at exposed chain termini. Phosphofructokinase-1 and phosphofructokinase-2, which have similar sizes but different fold topologies, are found to differ markedly in their unstructuring behaviour.

Resource sharing is a fundamental form of social exchange underlying the formation and maintenance of social bonds in humans and other species. While reciprocity has long been proposed as a key mechanism in group interactions, the dynamic processes underlying resource allocation remain poorly understood. In this study, we employed computational modeling to investigate the temporal dynamics of resource sharing in a novel group decision-making task across three experiments. We found that, beyond the well-documented reciprocity, participants exhibited consistent alternating behavior, characterized by the switching between potential recipients. This alternation was not driven by fairness concerns but reflected a strategic balance between maintaining stable partnerships and exploring alternatives. Crucially, a reinforcement learning model incorporating Theory of Mind (ToM) consistently outperformed all alternative models. These findings highlight the critical role of ToM in social decision-making and suggest that mentalizing others intentions may be essential for effective resource sharing and social bond formation.

Biocircuits often realize their functions only within specific parameter regimes, yet identifying those regimes and quantifying how difficult they are to satisfy remain challenging. Powered by the recently developed Reaction Order Polyhedra (ROP) framework enabling a holistic analysis of the behavior in biomolecular networks, we are now able to analyze these questions in a systematic way. In this work, we use ROP to derive the conditions under which Hill-like behaviors and adaptation in enzymatic negative feedback biocircuits can emerge. We also introduce the Realizability Index (R-index), i.e. the volume fraction of valid parameter regions, to quantify how hard it is for a biocircuit to achieve a desired function. We envision ROP theory and the R-index as important components of a new validity-aware conceptual language for studying and designing functional biocircuits.

Cellular adaptation is inherently nonstationary processes with complex stochastic dynamics1-5. Despite remarkable progress in quantitative biology6-11, a quantitative understanding of the cell adaptation dynamics in terms of the underlying cellular network remains elusive. Here, we present the next-generation chemical dynamics model and theory for cellular networks, providing an effective, quantitative description of the adaptive gene expression dynamics in living cells responding to external stimuli. Unlike conventional kinetics, chemical dynamics of cellular network modules are characterized by their reaction-time distributions, rather than by rate coefficients12. For a general model of cell signal transduction and adaptive gene expression, we derive exact analytical expressions for the time-dependent mean and variance of protein numbers produced in response to external stimuli, validated by accurate stochastic simulations. These results provide a unified, quantitative explanation of the stochastic responses of diverse E. coli genes to antibiotic stress and transcriptional induction. Our analysis reveals existence of a general quadratic relationship between the mean and variance of activation times across diverse genes. The gene activation process influences transient dynamics of downstream protein levels, but not their steady-state levels. In contrast, post-translational maturation process affects both transient dynamics and steady-state variability of mature protein levels. This finding indicates that the gene expression variability measured by fluorescent reporter proteins depends on the maturation time of the reporters. This work suggests a new direction for the development of digital twins of living cells.

Common knowledge states that the spontaneous somatic evolution of a normal tissue may lead to a tumor. Once the tumor is formed, it naturally evolves towards a state of higher malignancy. On the other hand, perfect gene expression markers for normal tissue and tumor--the so-called N-genes and T-genes--were recently introduced. We join these two pieces of knowledge in order to argue that: 1) Only N-markers participate in the spontaneous dynamics of a normal tissue. The number of active markers decreases as the tissue approaches the transition point where it becomes a tumor. 2) Only T-markers participate in the spontaneous dynamics of tumors. The number of markers increases as the tumor becomes more malignant. 3) Both sets of genes are connected by the so-called NT-genes, i.e., genes that are simultaneously N- and T-markers. They should play a crucial role at the transition point and, possibly, when the tumor is exposed to a drug or therapy. 4) The pathways or mechanisms protecting the normal tissue from becoming a tumor may be described by a small perfect panel of N-genes. 5) The pathways or mechanisms guiding the evolution of tumors in a tissue may be described by a small perfect panel of T-genes. We illustrate the above statements with the analysis of expression data for prostate adenocarcinoma, one of the most heterogeneous tumors. In this case, there are about 1000 N-genes and 6000 T-genes, and the perfect N- and T-panels contain 11 and 8 genes, respectively. Additionally, we provide examples from lung adenocarcinoma and liver hepatocarcinoma.

Alzheimers disease (AD) is a devastating neurodegenerative disease whose etiology is poorly understood and for which current treatments provide only modest control of symptoms. To better investigate the causes and progression of the disease, the transgenic TgF344-AD rat model has emerged as a crucial tool. In this paper, we collect observations on the accumulation of amyloid-{beta}, changes in neuronal density, and a decline in cognitive performance in TgF344-AD and wild-type rats. We develop a compartmental ordinary differential equation model and determine its parameters by fitting the output to the experimental observations. Our model simulations support the hypothesis that the accumulation of amyloid-{beta} leads to a rapid decline in neuronal density followed by a significant loss in memory and learning ability. Our mathematical model can provide a bridge between AD research in rodent models and the human condition of AD.