Nonlinear Dynamics

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.

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.

Phytoplankton sustain all marine ecosystems and are key components of the carbon cycle being responsible for ~50% of the global primary production. A major hypothesis to explain their coexistence with highly efficient lytic viruses is antiviral resistance. Although intracellular and extracellular mechanisms have been shown to underly such resistance and while its determinism is commonly associated to a genomic polymorphism or a (random or virus induced) phenotypic plasticity, comparisons of the impact of those molecular determinants on phytoplankton-virus population dynamic are genuinely lacking. We combined 12 epidemiological models with an unprecedented set of parameter estimates derived from experimental studies of the ubiquitous species Ostreococcus tauri and its prasinoviruses to provide such comprehensive predictions. We show that 'bet-hedging' strategies corresponding to random phenotypic switches between susceptible and resistant cells provide the strongest barrier to virus emergence. When such resistance is associated to intracellular mechanisms the virus' R0 is at least halved because of the strong 'dilution effect' produced by the 'dead-end' hosts. In addition, once the virus has spread, both random and virus-induced phenotypic plasticity strongly stabilize the otherwise 'boom and bust' phytoplankton-virus dynamics, which is highly consistent with the experimental dynamics observed for such interactions.

Nitrogen dioxide (NO2) is a widespread air pollutant associated with the risk and prevalence of various respiratory infectious diseases. Epidemiological studies have reported associations between NO2 exposure and COVID-19 incidence, and biological evidence indicates that NO2 exposure increases vulnerability to infection. Motivated by these findings and by the scarcity of mechanistic epidemic models that incorporate air pollutant data, here we introduce an NO2- and mobility-informed metapopulation model and study the first COVID-19 wave in Oklahoma. County-level NO2 concentrations enter the infection rates through a first-order parameterization, alongside high-resolution mobility patterns capturing heterogeneous inter-county connectivity. Using numerical simulations, we demonstrate that higher environmental sensitivity produces earlier and more synchronized outbreaks across counties, while lower sensitivity yields delayed, asynchronous trajectories. When fitted to county-level COVID-19 incidence data, our model outperformed the classic SIR model (fitted independently in each county) in over 75% of counties in Oklahoma across all standard error metrics. The improvements were even more pronounced in forecasting tasks across epidemic stages, with county-level win rates against the SIR model of 59.74% (surge), 87.01% (peak), 80.52% (post-peak), and 88.31% (decline) by nRMSE. To isolate the contribution of NO2, we compared our model against a mobility-only model with NO2 removed and homogeneous infection rates across counties. The NO2 term improved county-level forecasts during the surge (94.81% of counties by nRMSE), post-peak (88.31%), and peak (62.34%) stages, though not during the early and decline stages, suggesting that NO2 information can generate better forecasts than mobility alone during periods of high incidence. Our results demonstrate that environmental exposure can enter the transmission structure of a mechanistic epidemic model directly and that doing so yields measurable forecasting gains.

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.

Background. Classical macroparasite models commonly represent worm burden heterogeneity through prescribed Poisson or negative-binomial (NB) distributions, while transmission dynamics are formulated in terms of aggregate quantities such as mean worm burden and prevalence. We revisit these assumptions using a stratified worm burden (SWB) framework that explicitly tracks the distribution of parasite burdens across heterogeneous host classes and allows demographic turnover, transmission, and interventions to be analyzed within a unified model. Methods. We derive equilibrium distributions of the SWB system under homogeneous and heterogeneous infection processes and compare them with the classical Poisson and NB distributions used in macroparasite epidemiology and control policymaking. The framework is then extended to include host demography, coupled human-snail transmission dynamics, and periodic mass drug administration (MDA). Corresponding SWB and NB-type MacDonald models are calibrated to comparable endemic prevalence and mean worm burden, allowing direct comparison of potential transmission breakpoints and intervention outcomes. Results. In the absence of demographic turnover, the SWB framework naturally generates Poisson and NB equilibrium distributions as limiting cases of homogeneous and heterogeneous infection processes. Incorporating demographic recruitment and mortality alters these benchmark distributions, producing endemic burden structures that differ systematically from their classical counterparts. Analysis of coupled human-snail systems reveals that transmission breakpoints and bistable equilibria occur only within a relatively restricted region of SWB parameter space. In contrast, comparable NB-MacDonald formulations exhibit breakpoint behavior over substantially broader parameter ranges with the net effect of overestimating the likelihood of interruption of transmission. Although calibrated models can reproduce near identical endemic prevalence and mean worm burden, they often generate markedly different responses to MDA, including differences in rebound dynamics, persistence, and elimination thresholds. Conclusions. The SWB framework links classical statistical descriptions of worm aggregation to mechanistic burden-resolved population dynamics, clarifying how endemic distributions emerge and how they are modified by demography and control interventions. Our results suggest that transmission breakpoints are not a universal feature of helminth systems but depend strongly on model structure, and that predictions of elimination and post-treatment recovery may be considerably more model-dependent than implied by prevalence-based calibration alone. The SWB approach therefore provides a flexible alternative framework for evaluating parasite transmission dynamics and predicting the outcomes of control strategies.

Mechanistic models of infectious disease transmission provide a framework for understanding and predicting disease dynamics, but statistical inference is often computationally prohibitive. This challenge is especially pronounced for models with high-dimensional structures and many unknown parameters, where trajectory matching may require thousands of evaluations of an expensive likelihood function. We developed a surrogate-assisted optimization framework that uses Bayesian optimization to reduce the number of evaluations of the underlying mechanistic model required for parameter inference. We evaluated the approach using simulated fitting problems based on age-structured susceptible-exposed-infected-recovered models with 4, 8, and 16 age classes and a 210-compartment age-structured rotavirus transmission model. Applying surrogate-assisted optimization substantially reduced the number of likelihood evaluations required to identify good parameter estimates, with larger improvements as model dimensionality increased. In the rotavirus model, the surrogate Bayesian optimization approach reached the benchmark after approximately 0.7 hours, compared with approximately 9.4 hours using traditional Nelder-Mead optimization. These results demonstrate that surrogate-assisted optimization can substantially reduce the computational burden of trajectory matching for complex mechanistic transmission models, particularly for higher-dimensional inference problems.

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.

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.

Simulation models are widely used to support counterfactual inference in settings where direct experimental validation is difficult or infeasible. However, for phenomenological models calibrated to observational time series, goodness-of-fit does not necessarily establish that the structural assumptions underlying such inferences are uniquely supported by the data. Here, we examine this issue using a published COVID-19 transmission model for Japan that incorporates empirical inputs including human mobility, variant prevalence, and vaccination and has been used to estimate the effects of alternative vaccination scenarios. Using the publicly archived code together with a reconstructed substitute for a restricted-access input file required by the released implementation, we first reproduced the published model behaviour. We then performed two complementary computational stress tests. First, the vaccination-related input was suppressed and the remaining parameters were re-estimated against the original epidemic trajectory. Second, as a complementary test of trajectory-level flexibility, the model was refitted to synthetic target series with qualitatively different temporal structures while retaining the empirical mobility and variant inputs. The model retained substantial fitting capacity in both tests: suppression of the vaccination-related input caused only a limited deterioration in fit to the original trajectory, while qualitatively different synthetic trajectories could also be reproduced through parameter adjustment. Variation in fitted parameters across these conditions was also consistent with compensatory parameter behaviour. These results do not imply that vaccination had no effect or that the original model is invalid. Rather, they provide empirical evidence that, in this case, goodness-of-fit to the observed epidemic trajectory alone does not uniquely support the structural interpretation required for vaccination-related counterfactual inference. The study illustrates the value of reproducible computational stress testing as a complement to, rather than a substitute for, formal identifiability or model-comparison analyses.

The dentate gyrus' principal neuron, the granule cell (GC), plays a key role in pattern separation, transforming similar inputs into dissimilar outputs. We used a new measure based on information theory to evaluate this transformation in an experimentally derived in silico GC model with realistic ion channel distributions across its dendrites. We found that model performance aligned well with current-clamp recordings from mouse brain slices. However, it was also possible to find artificial parameter combinations in the model that functionally outperformed the recorded cells while matching their action potential shapes. Rather than maximising computational power, the biologically realistic GC model balanced energy efficiency against increased functionality in a Pareto optimal way: No possible parameter combination was found to improve one of the objectives without impairing the other. Interestingly, immature GCs adopted a different weighted trade-off with a stronger emphasis on energy efficiency than pattern separation, but they remained Pareto optimal over their putative developmental trajectory. Our results support the idea that evolution favours neurons that can satisfy functional and energetic demands simultaneously.

To resolve how the gut microbiota shapes human health, it is essential to quantify the exchange of chemicals between microbes and the host. Much as the dose of a drug determines its pharmacological effect, the magnitude of a specific chemical flux determines its impact. Here, we establish from first principles how fluxes can be estimated by integrating key parameters from human digestive physiology and microbial metabolism. We apply this framework to three cases: the exchange of fermentation products, the production of toxins by bacterial pathogens, and nitrogen homeostasis. Our analysis identifies three directly measurable host-level parameters which, in concert with microbial activity, shape flux magnitudes: intestinal transit time, absolute microbial abundance in feces, and fecal mass loss. The simultaneous quantification of these parameters provides a feasible yet essential step toward a mechanistic and quantitative description of gut microbiota-host interactions across health and disease.

Genetics shape cocaine behavior and abuse liability, but the underlying neurophysiological effects remain understudied. In male C57BL/6J, B6129SF2/J, and DO/J mice, we report conserved and divergent cocaine induced neuroplasticity in the accumbens shell following 5 days of cocaine and 10 to 14 days of abstinence.

Primary sulcal patterns, the spatial arrangement of the earliest cortical folds, emerge prenatally and remain essentially stable after birth. Alterations are associated with cognitive outcomes and hold promise as clinical biomarkers. However, detecting abnormalities is challenging due to the high topological variability and complexity of normal individual sulcal patterns. Here, we introduce an unsupervised generative model that quantifies individual sulcal pattern deviations against a normative baseline learned from 10,349 typically developing subjects spanning early childhood through adulthood. We combine a generative reconstruction error with a discriminator trained on diffusion-generated pseudo-atypical graphs to leverage their complementary strengths in sensitivity and robustness. The discriminator captures subtle anomalies and is robust to demographic and data quality variations, whereas the generative model enables severity stratification and demonstrates cross-site generalizability. Across two clinical cohorts spanning subtle to overt sulcal abnormalities (congenital heart disease and polymicrogyria), our model captured global and localized condition-related deviations and linked them to neurodevelopmental outcomes. By enabling population-scale, individualized quantification of sulcal deviations, this framework provides a foundation for future clinical risk stratification.

While lysosomal lipid dysregulation is implicated in Parkinsons disease (PD), identifying the precise enzymatic drivers remains limited by the lack of subcellularly resolved metabolic mapping. Leveraging endosome-origin plasma extracellular vesicle (PsEV) lipidomics, we identified a profound bidirectional disruption of the ceramide-sphingomyelin (SM) axis in PD, driven by asymmetric upregulation of sphingomyelin phosphodiesterase 1 (SMPD1) and sphingomyelin synthase 1 (SGMS1). BODIPY-C5 SM tracking revealed that SMPD1 perturbation severely impairs lysosomal SM turnover. Crucially, this SMPD1-driven hydrolysis forces a salvage pathway collapse, bottlenecked by SPHK1/SGPL1 downregulation, which precipitates oxidative membrane damage and PINK1/Parkin-dependent mitophagy failure. We robustly validated this multi-pathway dysfunction across orthogonal in vitro, in vivo mouse, and postmortem human brain models. Furthermore, SMPD1/SGMS1 expression distinctly stratifies clinical phenotypes, marking the aggressive Postural Instability/Gait Difficulty (PIGD) subtype. Our findings establish SMPD1-mediated lysosomal impairment and ceramide-SM imbalance as a core biochemical axis in PD pathophysiology.

Acute glucose-stimulated beta-cell secretion is a key dimension of beta-cell function, but the hyperglycemic clamp used to assess it is technically demanding and resource-intensive, limiting its use at scale. We aimed to develop and validate the oral glucose tolerance test (OGTT) Early C-peptide (OEC) Index for estimating clamp-derived acute C-peptide response to glucose (ACPRg). We defined OEC as the 0-60-min incremental C-peptide area under the curve (AUC) normalized to the geometric mean of incremental and total glucose AUCs, with a fasting-glucose correction of 100/G0. OEC was evaluated in paired OGTT-clamp data from RISE Adult Medication (baseline n=257; internal validation) and BetaFat (baseline n=70; external validation). Predictive R^2 and Pearson r for log-ACPRg were assessed using participant-level 5-fold cross-validation in RISE and external validation without refitting in BetaFat, with the C-peptidogenic, insulinogenic, and CIR30 indices as comparators. In RISE Adult, cross-validated R^2 for OEC was 0.47, 0.61, and 0.54 at baseline, 12, and 15 months, respectively, with corresponding Pearson r of 0.69, 0.78, and 0.74; nested cross-validation showed only modest attenuation. Applied without refitting in BetaFat, OEC yielded R^2 of 0.55, 0.41, and 0.39 at baseline, 12, and 24 months, with corresponding r of 0.76, 0.70, and 0.64. OEC had higher predictive R^2 point estimates than all three comparators at every visit in both cohorts. OEC provides a simple, transparent OGTT-based estimate of acute beta-cell secretory capacity that retained predictive performance in BetaFat and may broaden access to physiological assessment of early beta-cell function.

Postmenopausal women are vulnerable to metabolic dysfunction. Compelling evidence suggests this is because they lack the protective effects of estrogens. We have shown that circulating estrogens regulate daily eating and activity rhythms in female mice and protect them from obesity and metabolic dysfunction. However, few studies have investigated whether postmenopausal women have disrupted eating and sleep-activity rhythms that could contribute to metabolic dysfunction. The purpose of this cross-sectional study was to investigate the relationship between sleep and eating rhythms and metabolic risk in postmenopausal women with overweight or obesity. Seven days of sleep and food intake behavior data were collected from postmenopausal women with overweight or obesity. Sleep timing was assessed using wrist-worn actigraphy and sleep logs. First and last calorie intake times were collected daily using text messaging. Visceral adipose tissue (DXA), insulin resistance (Matsuda index), blood pressure, and triglycerides were analyzed as markers of metabolic risk. In 122 postmenopausal women (mean {+/-} SD: 58.1 {+/-} 3.6 yr, 33.2 {+/-} 5.2 kg/m2 BMI), we found that later sleep onset was associated with greater visceral adipose tissue (p=0.0007), but not insulin resistance, blood pressure, or triglycerides. Next, we used a random forest model to quantify the relative contributions of sleep and meal timing variables to predict visceral adipose tissue. The top predictors of visceral adipose tissue were time of sleep onset, sleep duration, and time of last caloric intake. These data suggest that interventions that advance sleep onset may reduce metabolic risk in postmenopausal women.

Directed evolution enables the engineering of proteins with novel or improved functions, yet existing approaches often require extensive manual intervention and are difficult to sustain over long evolutionary trajectories. Here we introduce PRIME (Protein-primed Replication for In vivo Mutagenesis and Evolution), a plasmid-based orthogonal DNA replication system for continuous directed evolution in Escherichia coli. PRIME harnesses protein-primed DNA replication to establish an autonomous replicon that operates independently of the host genome. Coupling this system to an error-prone DNA polymerase enables targeted diversification of constructs encoded on the orthogonal plasmid while preserving genomic integrity. Using only standard laboratory equipment, we demonstrate the evolution of a construct expressing msfGFP with an 11.8-fold increase in fluorescence. The platform is fully compatible with standard molecular biology workflows and requires no specialised instrumentation. We further demonstrate its portability across bacterial hosts by establishing PRIME in Pseudomonas putida. PRIME thus provides a broadly accessible framework for continuous in vivo evolution, with wide-ranging applications in protein engineering and synthetic biology.

Quiescence is a reversible proliferation arrest enabling cells to adapt to environmental changes, yet the post-transcriptional mechanisms governing its transitions remain poorly understood. Here, we map genome-wide alternative polyadenylation (APA) dynamics across 15 time points of quiescence transitions in fission yeast using 3'-end RNA sequencing. We reveal that APA undergoes extensive remodeling: driving global 3'UTR lengthening during early quiescence entry, 3' UTR shortening upon quiescence establishment, and progressive reversal to proliferative-state lengths during quiescence exit. Integrating 3' UTR dynamics with differential expression analysis, we identify candidate genes potentially regulated through APA-mediated 3' UTR mechanisms. We demonstrate that sod2, encoding mitochondrial superoxide dismutase, autoregulates its mRNA and protein levels via APA-dependent 3' UTR changes. Disrupting proximal APA site of sod2 in a mitophagy-deficient (atg43{Delta}) background exacerbates quiescence maintenance defects and mitochondrial dysfunction. We further identify Pabp as an upstream regulator of sod2 APA. This study establishes the temporal APA remodeling during quiescence transitions and reveals a Pabp-APA-sod2 regulatory axis governing post-transcriptional control of cellular quiescence.

Microglia represent a highly dynamic and heterogeneous cell type that is critically implicated in states of health and pathology. Microglial morphological subgroups have been identified that correspond to functional characteristics determining health-related outcomes. The identification of states based on morphological characteristics will therefore provide invaluable insights into the microglia-specific functional mechanisms driving treatment effects. The application of clustering analyses enables the detection of groupings within samples reflecting differences in morphological features. Here we propose the application of three custom-created modules to be used within the open-source software CellProfiler. These modules enable the automated detection of clusters present within the sample of microglia, as well as the assessment of the abundance of these clusters across conditions. The application of the analysis is conducted in a highly user-friendly manner, with a user interface integrated into the pipeline, enabling the performance of the analysis with only minimal user input. The workflow thereby includes the conduction of an outlier assessment, followed by hierarchical clustering and k-means clustering and the generation of interactive graphs to determine the number of microglia states present in the sample. Bar plots displaying the abundance of the microglia states across conditions included in the sample will be created. This approach will facilitate faster and more comparable detection of microglial morphological clusters across studies.