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PubMed2025

Bistable Mutation-Selection Equilibria and Violations of Fisher's Theorem in Tetraploids: Insights from Nonlinear Dynamics.

Polyploidy and whole genome duplication (WGD) are widespread biological phenomena with substantial cellular, meiotic, and genetic effects. Despite their prevalence and significance across the tree of life, population genetics theory for polyploids is not well developed. The lack of theoretical models limits our understanding of polyploid evolution and restricts our ability to harness polyploidy for crop improvement amidst increasing environmental stress. To address this gap, we developed and analyzed deterministic models of mutation-selection balance for tetraploids under polysomic (autotetraploid) and disomic (allotetraploid) inheritance patterns and arbitrary dominance relationships. We also introduced a new mathematical framework based on ordinary differential equations and nonlinear dynamics for analyzing the models. We find that autotetraploids approach Hardy-Weinberg Equilibrium 33% faster than allotetraploids, but the different tetraploid inheritance models show little differences in mutation load and allele frequency at mutation-selection balance. Our model also reveals two bistable points of mutation-selection balance for dominant alleles with biased mutation rates over a wide range of selection coefficients in the tetraploid models compared to bistability in only a narrow range for diploids. Finally, using discrete time simulations, we explore the temporal dynamics of allele frequency and fitness change and compare these dynamics to the predictions of Fisher's Fundamental Theorem of Natural Selection. While Fisher's predictions generally hold, we show that the bistable dynamics for dominant mutations fundamentally alter the associated temporal dynamics. Overall, this work develops foundational theoretical models that will facilitate the development of population genetic models and methodologies to study evolution in empirical tetraploid populations.

Fisher’s Fundamental Theorem↗

PubMed2025

Balanced state of networks of winner-take-all units.

Irregularly timed action potentials, or spikes, are pervasively observed in the brain activity of awake mammals. However, the role of this temporal irregularity in neural computation is still not well understood. In canonical network models irregular spiking emerges via balanced, fluctuating input currents, leading to collective responses that track inputs linearly. How networks characterized by irregular spiking could support flexible nonlinear dynamics needed for general-purpose computation remains under ongoing debate. Here we characterize the dynamics of networks whose elementary unit is not a single neuron but a small group of neurons, with distinct tunings, that compete at each timestep via a winner-take-all (WTA) interaction. While WTA has long been proposed as an elementary functional motif in the brain and represents a powerful computational primitive, how large networks of such units behave has received less investigation. We show that these networks, like classic excitatory-inhibitory balanced networks, exhibit a chaotic fluctuation-driven regime characterized by sustained irregular activity resembling realistic cortical spiking, which we interpret as a multidimensional balance spread over several competing neural populations with different tunings. We develop a mean-field theory for the network, which shows how irregular spiking sustained by time-varying input fluctuations can support flexible nonlinear collective dynamics. Using the theory we predict and verify network regimes in which input fluctuations alone yield multistability, stable sequence generation, or complex heterogeneous firing rate dynamics-three core dynamical primitives thought to underlie memory-dependent neural computation-via consistent Poisson-like spiking produced through chaos. Thus, networks of WTA units support a chaotic fluctuation-driven regime characterized by irregular spiking that can power complex nonlinear collective dynamics. This represents a new model of brain activity capable of simultaneously reproducing realistic spike trains and diverse nonlinear firing rate patterns well posed for flexible computation, and which can be trained or fit to data.

Models, Neurological↗

PubMed2025

Learning neural dynamics through instructive signals.

Rapid learning is essential for flexible behavior, but its basis in the brain remains unknown. Here we introduce the PRISM plasticity rule, a unifying mechanistic model of three well-established, fast-acting synaptic plasticity rules-in hippocampus, cerebellum and mushroom body-which relies exclusively on pre-synaptic activity and an "instructive signal" from another brain area. Using a multi-region network model we show that guiding PRISM plasticity with instructive signals enables the network to quickly learn extremely flexible nonlinear dynamics underlying behaviorally relevant computations, as well as to emulate unknown external system dynamics from real-time error signals, which we demonstrate with comprehensive simulations supported by exact mathematical theory. Thus, PRISM plasticity guided by instructive signals is well-suited to rapidly learn general-purpose neural computations-in contrast to canonical Hebbian rules. Finally, we show how including this plasticity rule in artificial learning algorithms can solve long-range temporal credit assignment, a long-standing challenge in machine learning.

cerebellum↗

PubMed2026

Non-linear predictive modeling and comprehensive meta-analysis of rectal temperature in Santa Inês sheep: a systematic review of thermal challenges and biometerological trends.

A systematic and bibliometric review, combined with a meta-analysis, was used to adjust an equation for estimating the physiological responses of Santa Inês sheep subjected to different thermal challenges. The systematic review compiled data on physiological responses and the thermal environment, which were then used in the meta-analysis to adjust regression models. The bibliometric analysis mapped the relationships among studies, highlighting their usefulness in interpreting research findings and biases. Addressing prior methodological critiques, the core of this study involves replacing the linear approach with a non-linear segmented regression model to accurately define the Thermal Neutral Zone (TNZ). The Segmented Regression Model was crucial, establishing the upper limit of the Thermal Neutral Zone (TNZ) at an air temperature (tair) of 34.64 °C, where trectal begins to increase abruptly. The model, while identifying a biologically significant breakpoint, exhibited a moderate Multiple R-squared of 0.3529, highlighting the high heterogeneity and methodological variability in the current Santa Inês literature. This non-linear approach offers a biologically superior tool for identifying the onset of thermal distress.

Animals↗

PubMed2024

Use of 3D chaos game representation to quantify DNA sequence similarity with applications for hierarchical clustering.

A 3D chaos game is shown to be a useful way for encoding DNA sequences. Since matching subsequences in DNA converge in space in 3D chaos game encoding, a DNA sequence's 3D chaos game representation can be used to compare DNA sequences without prior alignment and without truncating or padding any of the sequences. Two proposed methods inspired by shape-similarity comparison techniques show that this form of encoding can perform as well as alignment-based techniques for building phylogenetic trees. The first method uses the volume overlap of intersecting spheres and the second uses shape signatures by summarizing the coordinates, oriented angles, and oriented distances of the 3D chaos game trajectory. The methods are tested using: (1) the first exon of the beta-globin gene for 11 species, (2) mitochondrial DNA from four groups of primates, and (3) a set of synthetic DNA sequences. Simulations show that the proposed methods produce distances that reflect the number of mutation events; additionally, on average, distances resulting from deletion mutations are comparable to those produced by substitution mutations.

Animals↗

PubMed2025

APNet, an explainable sparse deep learning model to discover differentially active drivers of severe COVID-19.

MOTIVATION: Computational analyses of bulk and single-cell omics provide translational insights into complex diseases, such as COVID-19, by revealing molecules, cellular phenotypes, and signalling patterns that contribute to unfavourable clinical outcomes. Current in silico approaches dovetail differential abundance, biostatistics, and machine learning, but often overlook nonlinear proteomic dynamics, like post-translational modifications, and provide limited biological interpretability beyond feature ranking. RESULTS: We introduce APNet, a novel computational pipeline that combines differential activity analysis based on SJARACNe co-expression networks with PASNet, a biologically informed sparse deep learning model, to perform explainable predictions for COVID-19 severity. The APNet driver-pathway network ingests SJARACNe co-regulation and classification weights to aid result interpretation and hypothesis generation. APNet outperforms alternative models in patient classification across three COVID-19 proteomic datasets, identifying predictive drivers and pathways, including some confirmed in single-cell omics and highlighting under-explored biomarker circuitries in COVID-19. AVAILABILITY AND IMPLEMENTATION: APNet's R, Python scripts, and Cytoscape methodologies are available at https://github.com/BiodataAnalysisGroup/APNet.

COVID-19↗

PubMed2026

Decoding Nonlinearities in AAV-Based Gene Therapy Using PBPK Modelling.

The objective of this research was to develop a physiologically based pharmacokinetic (PBPK) model for AAV-based gene therapy, which can capture the nonlinearity observed in both viral vector and transgene product pharmacokinetics (PK) across a wide range of doses, while accounting for the effect of immunogenicity. To develop the PBPK model, previously published PK data generated in mice using AAV8 vector containing the transgene for a non-binding monoclonal antibody was used. Immunocompetent mice were administered with AAV at a wide range of doses (1E8, 1E9, 5E9, 1E10, 2E10, 1E11, 2E11, 1E12, and 1E13vg per mouse), and the PK of transgene and transgene product (i.e., antibody) in plasma and/or tissue was collected. The nonlinearity in transgene product concentrations was characterized using a saturable production process and a concentration-dependent antibody elimination rate was used to characterize the effect of anti-drug antibody (ADA) on transgene product. The model successfully described the PK of both the vector and the transgene product across all dose levels and accurately captured the sigmoidal dose-exposure-response relationship for AAV. Notably, the model described a dose-dependent ADA response, with the high dose group exhibiting an earlier onset and faster rate of transgene product elimination. Lower dose group showed delayed onset and minimal ADA-mediated elimination of transgene product. Overall, the PBPK model presented here effectively characterizes vector and transgene product kinetics in mice and demonstrates utility in preclinical-to-clinical translation and dose optimization of AAV-based gene therapies.

Animals↗

PubMed2026

NLCD: A method to discover nonlinear causal relations among genes.

Distinguishing correlation from causation is a fundamental challenge in many scientific fields, including biology, especially when interventions like randomized controlled trials are infeasible and only observational data are available. Methods based on statistical tests of conditional independence within the Mendelian Randomization framework can detect causality between two observed variables that are each associated with a third instrumental variable. However, these methods for detecting causal relationships between traits (e.g., two gene expression or clinical traits associated with a genetic variant, all observed in the same population) often assume a linear relationship, thereby hindering the discovery of causal gene networks from genomics data. We have developed NLCD, a method for NonLinear Causal Discovery from genomics data based on nonlinear regression modeling and conditional feature importance scoring. NLCD uses these techniques to extend the statistical tests in an existing linear causal discovery method called the Causal Inference Test (CIT). We benchmarked NLCD against current state-of-the-art methods: CIT, Findr, and MRPC. On simulated datasets, NLCD performs comparably to most methods in detecting linear relations (Average AUPRC (Area Under the Precision-Recall Curve) of NLCD = 0.94, CIT = 0.94, Findr = 0.94, and MRPC = 0.99), and outperforms them in detecting nonlinear (sine and sawtooth type) relations between two genes (Average AUPRC of NLCD = 0.76, CIT = 0.60, Findr = 0.56, and MRPC = 0.73). When tested on a nonlinear subset of a yeast genomic dataset to recover known causal relations involving transcription factors, NLCD and CIT performed comparable to each other and slightly better than Findr and MRPC (Average AUPRC of NLCD = 0.82, CIT = 0.81, Findr = 0.71, and MRPC = 0.54). On application to a human genomic dataset, NLCD revealed active causal gene pairs (IRF1 → PSME1 and HLA-C → HLA-T) in the muscle tissue, and clarified the promises and challenges in discovering causal gene networks in tissues under in vivo human settings.

Humans↗

PubMed2026

Global disparities in COVID-19 vaccine coverage associated with trajectories of SARS-CoV-2 adaptation.

BACKGROUND: Vaccination serves as an effective intervention for health promotion and disease prevention across the socioecological systems and has played an important role during the COVID-19 pandemic. However, global disparities in vaccine coverage have increased uncertainty about the trajectories of viral adaptation, and the potential interplay between SARS-CoV-2 adaptation and vaccine rollout warrants further quantification. METHODS: Using over 13 million SARS-CoV-2 genomes across 86 countries from March 2020 to September 2022, we analyzed nonlinear associations between SARS-CoV-2 adaptation and vaccination coverage, considering public health and social measures, international travel, and infection dynamics, before and after the emergence of Omicron. Additionally, we examined the relationship between SARS-CoV-2 adaptation and COVID-19 mortality. RESULTS: During the pre-Omicron period, we found positive associations between nonsynonymous to synonymous divergence (dN/dS) ratios in the S1 subunit and medium levels of adjusted vaccine coverage (effect size: 0.96 [95% CI 0.47, 1.45]), while the association became insignificant at high levels (effect size: -1.89 [95% CI -4.20, 0.43]). However, no significant associations were found when Omicron dominated, possibly due to the immune escape ability of Omicron variants and the complex immune landscape shaped by mass hybrid immunity. Moreover, we observed evidence of dynamic interdependence and positive correlations between COVID-19 mortality and SARS-CoV-2 adaptation, with COVID-19 mortality interpreted as a proxy for uncontrolled viral spread. CONCLUSIONS: Our findings suggest a complex nonlinear relationship between vaccine-induced immunity and SARS-CoV-2 adaptation, with high vaccine coverage potentially linked to lower positive selection. We also observed directional coupling between COVID-19 mortality and SARS-CoV-2 adaptation. This may have implications for fair and fast vaccination in pandemic preparedness and response. CLINICAL TRIAL NUMBER: Not applicable.

Humans↗

PubMed2025

Multiscale dispersion entropy of resting-state EEG in older adults with Alzheimer's disease, mild cognitive impairment, and remitted major depressive disorder.

BackgroundMultiscale dispersion entropy (MDEnt) is a nonlinear EEG measure that quantifies brain complexity across time scales, reflecting both local and global brain dynamics. Previous research indicates lower complexity at short time scales in Alzheimer's disease (AD) compared to mild cognitive impairment (MCI) and healthy controls (HCs), with MCI also showing lower values than HCs. Major depressive disorder (MDD) has also been preliminarily linked to reduced complexity during acute episodes.ObjectiveTo assess whether MDEnt at short time scales can distinguish AD from MCI and HCs, and to examine complexity differences across additional groups, remitted MDD (rMDD) and rMDD + MCI, while exploring associations with cognitive performance.MethodsThe study included 316 older adults: 44 HCs, 46 with rMDD, 114 with MCI, 71 with rMDD + MCI, and 41 with AD. Resting-state, eyes-closed EEGs were analyzed using MDEnt at 24 ms (short) and 60 ms (long) time scales. Cognitive function was measured with the Montreal Cognitive Assessment and a composite cognitive score.ResultsShort time scale complexity was lowest in AD, followed by MCI, and highest in HCs; rMDD presence had no impact. Only AD showed reduced complexity at long time scales. Complexity at both time scales was significantly correlated with cognitive performance.ConclusionsThis study highlights the value of MDEnt to assess complexity at short time scale and differentiate individuals with AD, MCI, or HCs. Reduced complexity in these individuals may underlie their cognitive impairment. In contrast, our study suggests that any MDD impact on complexity is likely related to active depressive symptoms.

Humans↗

PubMed2025

New insights into multistability and complex resonances driven by subthreshold periodic signals in a neuronal model.

Understanding how neurons respond to weak external signals is crucial for accurate signal transmission and processing in both individual nerve cells and interconnected neuronal networks. One mechanism for the detection of these responses is through resonances. In this paper, we numerically investigate the firing patterns induced in a silent Huber-Braun neuron by a sinusoidal external force. We observe complex resonance patterns, including a sequence of frequency-locking exhibited in a Devil's Staircase structure. Furthermore, we also explore the emergence of multistability induced by the nonlinear resonance. This multistability manifests as the coexistence of three attractors, such as periodic spiking, chaotic spiking, and subthreshold oscillations. The dynamical behaviors are comprehensively analyzed using time series, bifurcation diagrams, phase portraits, and the basin of attraction. In addition, we compute the maximum Lyapunov exponent to verify chaotic regimes, and estimate the fractal dimension of basin boundaries using the uncertainty exponent. We also analyze the energy consumption of resonance-induced firing patterns and coexisting attractors. The results presented in this paper have important implications for understanding the detection of subthreshold signals and the encoding of stimulus information within a neuron's firing patterns.

Basins of attraction↗

PubMed2026

Pattern Formation in a Spatial Public Goods Dilemma due to Diffusive or Directed Motion.

The costly provision of public goods serves as a model problem for the evolution of cooperative behavior, presenting a social dilemma between the collective benefits of shared resources and the individual incentive to free-ride in resource production. The spatial structure of populations can also impact cooperation over public goods, as diffusion of public goods and intentional motion of individuals towards regions with greater resources can interact with population and public goods dynamics to produce heterogeneous patterns in the spatial distribution of strategies and resources. In this paper, we build off a model introduced by Young and Belmonte for the reaction dynamics of interacting individuals and an explicit public good, deriving a system of PDEs that describes the spatial profiles of strategies and the public good in the presence of both diffusive motion of individuals and resources and chemotaxis-like directed motion of individuals in response to gradients in the concentration of public goods. Through linear stability analysis, we show that spatial patterns in strategic and public goods profiles can emerge due to either Turing instability with high defector diffusivity or a directed-motion instability through strong sensitivity of cooperators towards increasing resource concentration. We further explore the emergent spatial patterns with a mix of weakly nonlinear stability analysis and numerical simulation, showing that, for a wide range of reaction parameters, diffusion-driven instability appears to increase cooperation and public goods across the spatial domain, while directed motion of cooperators towards public goods tends to decrease cooperation and environmental quality across the environment.

Models, Biological↗

PubMed2026

Modelling time-varying genetic effects on binary disease risk via functional Mendelian randomization.

MOTIVATION: Genome-wide association studies have identified thousands of genetic variants associated with complex traits, establishing Mendelian randomization (MR) as a powerful framework for causal inference using variants as natural experiments. However, existing MR methods treat causal effects as static, relying on cross-sectional exposure measurements and ignoring how genetic predispositions to disease operate dynamically across the life course. Recovering age-specific causal effect functions from longitudinal data requires combining functional data representations of exposure trajectories with instrumental variable estimation strategies suitable for binary disease endpoints, a methodological gap that has remained unaddressed. RESULTS: We develop a functional MR framework for binary outcomes that integrates functional principal component analysis with two-stage residual inclusion (2SRI), ensuring consistent estimation under the nonlinear logistic link function that renders standard instrumental variable estimators inconsistent. Simulations across different causal effect trajectory shapes, varying measurement densities, and varying instrument strengths demonstrate accurate recovery of time-varying genetically predicted effects with minimal bias. Applied to UK Biobank data, the framework identifies an age-specific causal effect of genetically predicted body mass index on type 2 diabetes risk concentrated in early mid-adulthood and progressively attenuating thereafter. Concordance between the proposed 2SRI estimator applied to type 2 diabetes and the established continuous-outcome functional MR estimator applied to the paired glycated haemoglobin marker in the same cohort provides indirect empirical support for the validity of the proposed approach. AVAILABILITY AND IMPLEMENTATION: The method is implemented in the R package mvfmr, with a full tutorial vignette.

Mendelian Randomization Analysis↗

PubMed2026

Association of time-averaged systemic immune-inflammation indices with in-hospital mortality after intracerebral hemorrhage: a retrospective study.

BACKGROUND: Systemic inflammation plays a central role in secondary brain injury following intracerebral hemorrhage (ICH). Although inflammatory indices such as the neutrophil-to-lymphocyte ratio (NLR), systemic immune-inflammation index (SII), and systemic inflammation response index (SIRI) are linked to poor outcomes, their associations with mortality are commonly assumed to be linear, potentially overlooking nonlinear patterns where mortality risk rises steeply at higher levels. METHODS: We conducted a retrospective study using the MIMIC-IV database, including 440 patients with non-traumatic ICH who were alive and remained in the ICU for at least 72 h after admission. Mean NLR, SII, and SIRI were calculated from measurements obtained during this period. Multivariable logistic regression and restricted cubic spline (RCS) analyses were applied to assess their independent and nonlinear associations with in-hospital mortality. Model discrimination and calibration were internally validated using 1,000 bootstrap resamples. RESULTS: The in-hospital mortality rate was 26.1%. After multivariable adjustment, NLR and SIRI remained independently associated with mortality. Patients in the highest SIRI quartile had the highest risk of death (aOR = 5.12; 95% CI: 2.57-12.24; p < 0.001). RCS analysis revealed a significant nonlinear association between SIRI and mortality (p-nonlinearity < 0.05), showing a steep risk increase at higher SIRI levels. Adding SIRI to the base model provided a modest improvement in discrimination (AUC 0.762 to 0.785, p = 0.045) and significantly improved risk reclassification (cNRI = 0.4778, p < 0.001; IDI = 0.0240, p = 0.0151). CONCLUSIONS: Among patients with ICH who met the 72-hour eligibility criterion, higher 72-hour average SIRI was independently associated with in-hospital mortality. As a time-averaged measure, SIRI should be interpreted as a dynamic marker integrating the initial inflammatory state and the early clinical course rather than as a purely baseline prognostic factor. Although adding SIRI to the base model modestly improved discrimination and risk reclassification, it should be considered a candidate prognostic marker requiring external validation before clinical application.

Humans↗

PubMed2026

Decoding spatiotemporal fibrotic and cellular immunosuppression of therapeutic T cells in live pancreatic ductal adenocarcinoma.

Pancreatic ductal adenocarcinoma (PDA) is profoundly immunosuppressive. To help define this behavior, we present integrated experimental and computational frameworks to elucidate therapeutic T cell dynamics. Through the development of TME-CARTographer (TME-CART), a computational pipeline integrating high-dimensional data, graph theory, behavior analysis, and deep learning (DL), we present quantitative insights on 4D T cell-TME interactions in live PDA tumors. Mapping physical immunosuppression demonstrates that collagen fiber architectures direct migration while concomitantly limiting off-axis movement, creating immune exclusion zones. Expanding these findings, we establish that the collagen matrix harbors and spatially organizes immunosuppressive myeloid cells to serve as cooperative co-modulators of T cell behaviors, including migration, sampling, repulsion, and sequestration. Consistent with these findings, DL defines both linear and nonlinear collagen matrix and cellular neighborhood interactions as drivers of T cell behavior. The TME-CART DL framework also accurately predicts shifts in immunosuppression following depletion of myeloid cells. Overall, we identify synergistic barriers impeding anti-tumor T cell behaviors and present TME-CART as a discovery platform for interpreting complex 4D data to enhance the understanding and design of immunotherapies.

Journal Article↗