arXiv Quantitative Biology @arxiv_bio@qoto.org

We investigate predictions of stochastic compartmental models on the severity of disease outbreaks. The models we consider are the Susceptible-Infected-Susceptible (SIS) for bacterial infections, and the Susceptible -Infected-Removed (SIR) for airborne diseases. Stochasticity enters the compartmental models as random fluctuations of the contact rate, to account for uncertainties in the disease spread. We consider three types of noise to model the random fluctuations: the Gaussian white and Ornstein-Uhlenbeck noises, and the logarithmic Ornstein-Uhlenbeck (logOU). The advantages of logOU noise are its positivity and its ability to model the presence of superspreaders. We utilize homological bifurcation plots from Topological Data Analysis to automatically determine the shape of the long-time distributions of the number of infected for the SIS, and removed for the SIR model, over a range of basic reproduction numbers and relative noise intensities. LogOU noise results in distributions that stay close to the endemic deterministic equilibrium even for high noise intensities. For low reproduction rates and increasing intensity, the distribution peak shifts towards zero, that is, disease eradication, for all three noises; for logOU noise the shift is the slowest. Our study underlines the sensitivity of model predictions to the type of noise considered in contact rate.

Alzheimer's disease (AD) is a complex neurodegenerative disorder characterized by the accumulation of amyloid-beta (A$β$) and phosphorylated tau (p-tau) proteins, leading to cognitive decline measured by the Alzheimer's Disease Assessment Scale (ADAS) score. In this study, we develop and analyze a system of ordinary differential equation models to describe the interactions between A$β$, p-tau, and ADAS score, providing a mechanistic understanding of disease progression. To ensure accurate model calibration, we employ Bayesian inference and Physics-Informed Neural Networks (PINNs) for parameter estimation based on Alzheimer's Disease Neuroimaging Initiative data. The data-driven Bayesian approach enables uncertainty quantification, improving confidence in model predictions, while the PINN framework leverages neural networks to capture complex dynamics directly from data. Furthermore, we implement an optimal control strategy to assess the efficacy of an anti-tau therapeutic intervention aimed at reducing p-tau levels and mitigating cognitive decline. Our data-driven solutions indicate that while optimal drug administration effectively decreases p-tau concentration, its impact on cognitive decline, as reflected in the ADAS score, remains limited. These findings suggest that targeting p-tau alone may not be sufficient for significant cognitive improvement, highlighting the need for multi-target therapeutic strategies. The integration of mechanistic modelling, advanced parameter estimation, and control-based therapeutic optimization provides a comprehensive framework for improving treatment strategies for AD.

In this paper we generalise a simple discrete time stochastic SIR type model defined by Tuckwell and Williams. The SIR model by Tuckwell and Williams assumes a homogeneous population, a fixed infectious period, and a strict transition from susceptible to infected to recovered. In contrast, our model introduces two groups, $A$ and $B$, where group $B$ has a higher risk of infection due to increased contact rates. Additionally, the duration in the infected class follows a probability distribution rather than being fixed. Finally, individuals in group $B$ can transition directly to the recovered class R, allowing us to analyze the impact of this preventive measure on disease spread. Finally, we apply this model to the spread of HIV, analyzing how risk behaviors, rapid testing, and PrEP-like therapies influence the epidemic dynamics.

Vaccination policies play a central role in public health interventions and models are often used to assess the effectiveness of these policies. Many vaccines are leaky, in which case the observed vaccine effectiveness depends on the force of infection. Within models, the immunity parameters required for agent-based models to achieve observed vaccine effectiveness values are further influenced by model features such as its transmission algorithm, contact network structure, and approach to simulating vaccination. We present a method for determining parameters in agent-based models such that a set of target immunity values is achieved. We construct a dataset of desired population-level immunity values against various disease outcomes considering both vaccination and prior infection from COVID-19. This dataset incorporates immunological data, data collection methodologies, immunity models, and biological insights. We then describe how we choose minimal parameters for continuous waning immunity curves that result in those target values being realized in simulations. We use simulations of the household secondary attack rates to establish a relationship between the protection per infection attempt and overall immunity, thus accounting for the dependence of protection from acquisition on model features and the force of infection.

Physical colors, i.e. reflected or emitted lights entering the eyes from a visual environment, are converted into perceived colors sensed by humans by neurophysiological mechanisms. These processes involve both three types of photoreceptors, the LMS cones, and spectrally opponent and non-opponent interactions resulting from the activity rates of ganglion and lateral geniculate nucleus cells. Thus, color perception is a phenomenon inherently linked to an experimental environment (the visual scene) and an observing apparatus (the human visual system). This is clearly reminiscent of the conceptual foundation of both relativity and quantum mechanics, where the link is between a physical system and the measuring instruments. The relationship between color perception and relativity was explicitly examined for the first time by the physicist H. Yilmaz in 1962 from an experimental point of view. The main purpose of this contribution is to present a rigorous mathematical model that, by taking into account both trichromacy and color opponency, permits to explain on a purely theoretical basis the relativistic color perception phenomena argued by Yilmaz. Instead of relying directly on relativistic considerations, we base our theory on a quantum interpretation of color perception together with just one assumption, called trichromacy axiom, that summarizes well-established properties of trichromatic color vision within the framework of Jordan algebras. We show how this approach allows us to reconcile trichromacy with Hering's opponency and also to derive the relativistic properties of perceived colors without any additional mathematical or experimental assumption.

Biophysical models of human brain represent the latter as a graph of inter-connected neural regions. Building from the model by Naskar et al. (Network Neuroscience 2021), our motivation was to understand how these brain regions can be connected at neural level to implement some inhibitory control, which calls for inhibitory connectivity rarely considered in such models. In this model, regions are made of inter-connected excitatory and inhibitory pools of neurons, but are long-range connected only via excitatory pools (mutual excitation). We thus extend this model by generalizing connectivity, and we analyse how connectivity affects the behaviour of this model. Focusing on the simplest paradigm made of a Control area and a Target area, we explore four typical kinds of connectivity: mutual excitation, Target inhibition by Control, Control inhibition by Target, and mutual inhibition. For this, we build an analytical sensitivity framework, nesting up sensitivities of isolated pools, of isolated regions, and of the full system. We show that inhibitory control can emerge only in Target inhibition by Control and mutual inhibition connectivities. We next offer an analysis of how the model sensitivities depends on connectivity structure, depending on a parameter controling the strength of the self-inhibition within Target region. Finally, we illustrate the effect of connectivity structure upon control effectivity in response to an external forcing in the Control area. Beyond the case explored here, our methodology to build analytical sensitivities by nesting up levels (pool, region, system) lays the groundwork for expressing nested sensitivities for more complex network configurations, either for this model or any other one.

There is a morphodynamic component to synaptic learning by which changes in dendritic spine head size are associated with the strengthening or weakening of the synaptic connection between two neurons, in response to the temporal correlation of local presynaptic and postsynaptic signals. Morphological factors are in turn sculpted by the dynamics of the actin cytoskeleton. We use Dynamical Graph Grammars (DGGs) implemented within a computer algebra system to model how networks of actin filaments can dynamically grow or shrink, reshaping the spine head. DGGs provide a well-defined way to accommodate dynamically changing system structure such as active cytoskeleton represented using dynamic graphs, within nonequilibrium statistical physics under the master equation. We show that DGGs can also incorporate biophysical forces between graph-connected objects at a finer time scale, with specialized DGG kinetic rules obeying biophysical constraints of Galilean invariance, conservation of momentum, and dissipation of conserved global energy. We use graph-local energy functions for cytoskeleton networks interacting with membranes, and derive DGG rules from the specialization of dissipative stochastic dynamics to a mutually exclusive and exhaustive collection of graph-local neighborhood types for the rule left hand sides. Dissipative rules comprise a stochastic version of gradient descent dynamics. Thermal noise rules use a Gaussian approximation of each position coordinate to sample jitter-like displacements. We designed and implemented DGG grammar sub-models including actin network growth, non-equilibrium statistical mechanics, and filament-membrane mechanical interaction to regulate the re-writing of graph objects. From a biological perspective, we observe regulatory effects of three actin-binding proteins on the membrane size and find evidence supporting mechanisms of membrane growth.

We present a numerical framework for solving neural field equations on surfaces using Radial Basis Function (RBF) interpolation and quadrature. Neural field models describe the evolution of macroscopic brain activity, but modeling studies often overlook the complex geometry of curved cortical domains. Traditional numerical methods, such as finite element or spectral methods, can be computationally expensive and challenging to implement on irregular domains. In contrast, RBF-based methods provide a flexible alternative by offering interpolation and quadrature schemes that efficiently handle arbitrary geometries with high-order accuracy. We first develop an RBF-based interpolatory projection framework for neural field models on general surfaces. Quadrature for both flat and curved domains are derived in detail, ensuring high-order accuracy and stability as they depend on RBF hyperparameters (basis functions, augmenting polynomials, and stencil size). Through numerical experiments, we demonstrate the convergence of our method, highlighting its advantages over traditional approaches in terms of flexibility and accuracy. We conclude with an exposition of numerical simulations of spatiotemporal activity on complex surfaces, illustrating the method's ability to capture complex wave propagation patterns.

This work aligns deep learning (DL) with human reasoning capabilities and needs to enable more efficient, interpretable, and robust image classification. We approach this from three perspectives: explainability, causality, and biological vision. Introduction and background open this work before diving into operative chapters. First, we assess neural networks' visualization techniques for medical images and validate an explainable-by-design method for breast mass classification. A comprehensive review at the intersection of XAI and causality follows, where we introduce a general scaffold to organize past and future research, laying the groundwork for our second perspective. In the causality direction, we propose novel modules that exploit feature co-occurrence in medical images, leading to more effective and explainable predictions. We further introduce CROCODILE, a general framework that integrates causal concepts, contrastive learning, feature disentanglement, and prior knowledge to enhance generalization. Lastly, we explore biological vision, examining how humans recognize objects, and propose CoCoReco, a connectivity-inspired network with context-aware attention mechanisms. Overall, our key findings include: (i) simple activation maximization lacks insight for medical imaging DL models; (ii) prototypical-part learning is effective and radiologically aligned; (iii) XAI and causal ML are deeply connected; (iv) weak causal signals can be leveraged without a priori information to improve performance and interpretability; (v) our framework generalizes across medical domains and out-of-distribution data; (vi) incorporating biological circuit motifs improves human-aligned recognition. This work contributes toward human-aligned DL and highlights pathways to bridge the gap between research and clinical adoption, with implications for improved trust, diagnostic accuracy, and safe deployment.

Many networks that arise in nature and applications are effectively low-dimensional in the sense that their connectivity structure is dominated by a few dimensions. It is natural to expect that dynamics on such networks might also be low-dimensional. Indeed, recent results show that low-rank networks produce low-dimensional dynamics whenever the network is isolated from external perturbations or noise. However, networks in nature are rarely isolated. We show that recurrent networks with low-rank structure often produce high-dimensional dynamics in the presence of high-dimensional perturbations. Counter to intuition, dynamics in these networks are \textit{suppressed} in directions that are aligned with the network's low-rank structure, a phenomenon we term "low-rank suppression." Our results clarify important, but counterintuitive relationships between a network's connectivity structure and the structure of the dynamics it generates.

Stick insect stepping patterns have been studied for insights about locomotor rhythm generation and control, because the underlying neural system is relatively accessible experimentally and produces a variety of rhythmic outputs. Harnessing the experimental identification of effective interactions among neuronal units involved in stick insect stepping pattern generation, previous studies proposed computational models simulating aspects of stick insect locomotor activity. While these models generate diverse stepping patterns and transitions between them, there has not been an in-depth analysis of the mechanisms underlying their dynamics. In this study, we focus on modeling rhythm generation by the neurons associated with the protraction-retraction, levitation-depression, and extension-flexion antagonistic muscle pairs of the mesothoracic (middle) leg of stick insects. Our model features a reduced central pattern generator (CPG) circuit for each joint and includes synaptic interactions among the CPGs; we also consider extensions such as the inclusion of motoneuron pools controlled by the CPG components. The resulting network is described by an 18-dimensional system of ordinary differential equations. We use fast-slow decomposition, projection into interacting phase planes, and a heavy reliance on input-dependent nullclines to analyze this model. Specifically, we identify and elucidate dynamic mechanisms capable of generating a stepping rhythm, with a sequence of biologically constrained phase relationships, in a three-joint stick insect limb model. Furthermore, we explain the robustness to parameter changes and tunability of these patterns. In particular, the model allows us to identify possible mechanisms by which neuromodulatory and top-down effects could tune stepping pattern output frequency.

We propose and analyze a model for the dynamics of the flow into and out of a nest for the arboreal turtle ant $\textit{Cephalotes goniodontus}$ during foraging to investigate a possible mechanism for the emergence of oscillations. In our model, there is mixed dynamic feedback between the flow of ants between different behavioral compartments and the concentration of pheromone along trails. On one hand, the ants deposit pheromone along the trail, which provides a positive feedback by increasing rates of return to the nest. On the other hand, pheromone evaporation is a source of negative feedback, as it depletes the pheromone and inhibits the return rate. We prove that the model is globally asymptotically stable in the absence of pheromone feedback. Then we show that pheromone feedback can lead to a loss of stability of the equilibrium and onset of sustained oscillations in the flow in and out of the nest via a Hopf bifurcation. This analysis sheds light on a potential key mechanism that enables arboreal turtle ants to effectively optimize their trail networks to minimize traveled path lengths and eliminate graph cycles.

Free-ranging dogs (Canis familiaris) thrive in diverse landscapes, including those heavily modified by humans. This study investigated the influence of resource availability on their spatial ecology across 52 rural and 41 urban sites, comparing urban and rural environments. Census-based surveys were conducted to understand the distribution of dogs and resources, while territory-based observations were carried out across different seasons to capture temporal variability in dog populations and resource availability. Dog and resource density were significantly higher in urban areas, supporting the Resource Dispersion Hypothesis (RDH). Territory size (TS) varied seasonally, decreasing significantly (by 21%) post-mating, likely reflecting shifts in resource demands and distribution. TS was positively correlated with resource heterogeneity, dispersion, patch richness, and male-to-female ratio, but not with group size, which remained stable across seasons and resource gradients. This suggests that while resource availability and sex ratio influence space use, social factors play a key role in shaping group dynamics. These findings highlight the complex interplay between resource availability, social behaviour, and human influences in shaping the spatial ecology of free-ranging dogs and have important implications for their management and disease control, informing targeted interventions such as spay/neuter programs and responsible waste management in both urban and rural landscapes.

Agent-based modeling (ABM) is a powerful computational approach for studying complex biological and biomedical systems, yet its widespread use remains limited by significant computational demands. As models become increasingly sophisticated, the number of parameters and interactions rises rapidly, exacerbating the so-called curse of dimensionality and making comprehensive parameter exploration and uncertainty analyses computationally prohibitive. Surrogate modeling provides a promising solution by approximating ABM behavior through computationally efficient alternatives, greatly reducing the runtime needed for parameter estimation, sensitivity analysis, and uncertainty quantification. In this review, we examine traditional approaches for performing these tasks directly within ABMs -- providing a baseline for comparison -- and then synthesize recent developments in surrogate-assisted methodologies for biological and biomedical applications. We cover statistical, mechanistic, and machine-learning-based approaches, emphasizing emerging hybrid strategies that integrate mechanistic insights with machine learning to balance interpretability and scalability. Finally, we discuss current challenges and outline directions for future research, including the development of standardized benchmarks to enhance methodological rigor and facilitate the broad adoption of surrogate-assisted ABMs in biology and medicine.

The vast majority of scientific contributions in the field of computational systems biology are based on mathematical models. These models can be broadly classified as either dynamic (kinetic) models or steady-state (constraint-based) models. They are often described in specific markup languages whose purpose is to aid in the distribution and standardization of models. Despite numerous established standards in the field, reproducibility remains problematic due to the substantial effort required for compliance, diversity of implementations, and the lack of proportionate rewards for researchers. This article explores the application of event sourcing - a software engineering technique where system state is derived from sequential recorded events - to address reproducibility challenges in computational systems biology. Event sourcing, exemplified by systems like git, offers a promising solution by maintaining complete, immutable records of all changes to a model. Through examples including leader and follower applications, local and remote computation, and contribution tracking, this work demonstrates how event-sourced systems can automate standards compliance, provide comprehensive audit trails, enable perfect replication of processes, facilitate collaboration, and generate multiple specialized read models from a single event log. An implementation of the outlined principles has the potential to transform computational systems biology by providing unprecedented transparency, reproducibility, and collaborative capabilities, ultimately accelerating research through more effective model reuse and integration. An event-sourced approach to modeling in computational systems biology may act as an example to related disciplines and contribute to ending the reproducibility crisis plaguing multiple major fields of science.

The highly pathogenic avian influenza (HPAI) H5 clade 2.3.4.4b has triggered an unprecedented global panzootic. As the frequency and scale of HPAI H5 outbreaks continue to rise, understanding how wild birds contribute to shape the global virus spread across regions, affecting poultry, domestic and wild mammals, is increasingly critical. In this review, we examine ecological and evolutionary studies to map the global transmission routes of HPAI H5 viruses, identify key wild bird species involved in viral dissemination, and explore infection patterns, including mortality and survival. We also highlight major remaining knowledge gaps that hinder a full understanding of wild birds role in viral dynamics, which must be addressed to enhance surveillance strategies and refine risk assessment models aimed at preventing future outbreaks in wildlife, domestic animals and safeguard public health.

This work investigates how biodiversity is affected in a cyclic spatial May-Leonard model with hierarchical and non-hierarchical rules. Here we propose a generalization of the traditional rock-paper-scissors model by considering highly reactive species, i. e., species that react in a stronger manner compared to the others in respect to either competition or reproduction. These two classes of models, called here Highly Competitive and Highly Reproductive models, may lead to hierarchical and non-hierarchical dynamics, depending on the number of highly reactive species. The fundamental feature of these models is the fact that hierarchical models may as well support biodiversity, however, with a higher probability of extinction than the non-hierarchical ones, which are in fact more robust. This analysis is done by evaluating the probability of extinction as a function of mobility. In particular, we have analyzed how the dominance scheme changes depending on the highly reactive species for non-hierarchical models, where the findings lead to the conclusion that highly reactive species are usually at a disadvantage compared to the others. Moreover, we have investigated the power spectrum and the characteristic length of each species, including more information on the behavior of the several systems considered in the present work.

Information processing in the brain is coordinated by the dynamic activity of neurons and neural populations at a range of spatiotemporal scales. These dynamics, captured in the form of electrophysiological recordings and neuroimaging, show evidence of time-irreversibility and broken detailed balance suggesting that the brain operates in a nonequilibrium stationary state. Furthermore, the level of nonequilibrium, measured by entropy production or irreversibility appears to be a crucial signature of cognitive complexity and consciousness. The subsequent study of neural dynamics from the perspective of nonequilibrium statistical physics is an emergent field that challenges the assumptions of symmetry and maximum-entropy that are common in traditional models. In this review, we discuss the plethora of exciting results emerging at the interface of nonequilibrium dynamics and neuroscience. We begin with an introduction to the mathematical paradigms necessary to understand nonequilibrium dynamics in both continuous and discrete state-spaces. Next, we review both model-free and model-based approaches to analysing nonequilibrium dynamics in both continuous-state recordings and neural spike-trains, as well as the results of such analyses. We briefly consider the topic of nonequilibrium computation in neural systems, before concluding with a discussion and outlook on the field.

Microtubules (MTs) are dynamic protein filaments essential for intracellular organization and transport, particularly in long-lived cells such as neurons. The plus and minus ends of neuronal MTs switch between growth and shrinking phases, and the nucleation of new filaments is believed to be regulated in both healthy and injury conditions. We propose stochastic and deterministic mathematical models to investigate the impact of filament nucleation and length-regulation mechanisms on emergent properties such as MT lengths and numbers in living cells. We expand our stochastic continuous-time Markov chain model of filament dynamics to incorporate MT nucleation and capture realistic stochastic fluctuations in MT numbers and tubulin availability. We also propose a simplified partial differential equation (PDE) model, which allows for tractable analytical investigation into steady-state MT distributions under different nucleation and length-regulating mechanisms. We find that the stochastic and PDE modeling approaches show good agreement in predicted MT length distributions, and that both MT nucleation and the catastrophe of large-length MTs regulate MT length distributions. In both frameworks, multiple mechanistic combinations achieve the same average MT length. The models proposed can predict parameter regimes where the system is scarce in tubulin, the building block of MTs, and suggest that low filament nucleation regimes are characterized by high variation in MT lengths, while high nucleation regimes drive high variation in MT numbers. These mathematical frameworks have the potential to improve our understanding of MT regulation in both healthy and injured neurons.

Background: The integration and analysis of multi-modal data are increasingly essential across various domains including bioinformatics. As the volume and complexity of such data grow, there is a pressing need for computational models that not only integrate diverse modalities but also leverage their complementary information to improve clustering accuracy and insights, especially when dealing with partial observations with missing data. Results: We propose Generalized Probabilistic Canonical Correlation Analysis (GPCCA), an unsupervised method for the integration and joint dimensionality reduction of multi-modal data. GPCCA addresses key challenges in multi-modal data analysis by handling missing values within the model, enabling the integration of more than two modalities, and identifying informative features while accounting for correlations within individual modalities. The model demonstrates robustness to various missing data patterns and provides low-dimensional embeddings that facilitate downstream clustering and analysis. In a range of simulation settings, GPCCA outperforms existing methods in capturing essential patterns across modalities. Additionally, we demonstrate its applicability to multi-omics data from TCGA cancer datasets and a multi-view image dataset. Conclusion: GPCCA offers a useful framework for multi-modal data integration, effectively handling missing data and providing informative low-dimensional embeddings. Its performance across cancer genomics and multi-view image data highlights its robustness and potential for broad application. To make the method accessible to the wider research community, we have released an R package, GPCCA, which is available at https://github.com/Kaversoniano/GPCCA.