Quantitative Biology

We introduce a novel method for estimating COVID-19 time-varying parameters. These parameters are in the context of an SIRD compartmental differential equations. The time-dependent parameters are the transmission rate $\beta(t)$, recovery rate $\gamma(t)$, and mortality rate $\mu(t)$. The method harnesses the novel Kolmogorov-Arnold Network (KAN), which is a type of artificial neural network. In KAN, we learn activation functions that are represented using Fourier series, hence the abbreviation KAN-F. We define three KAN-F functions $\widehat{\beta}$, $\widehat{\gamma}$, $\widehat{\mu}$ that model the true parameters $\beta(t)$, $\gamma(t)$, $\mu(t)$, respectively. The objective loss function that has to be minimized is subject to Physics-Informed Neural Network (PINN) or Epi-DNN. We estimate the COVID-19 time-dependent parameters using COVID-19 data of three South-East Asian countries: Indonesia, Singapore, Malaysia. The time period of choice for the data coincides with the period where SARS-CoV-2 Delta variant (B.1.617.2) was dominant. Using Epi-DNN and KAN-F, we are able to estimate $\beta(t)$, $\gamma(t)$, and $\mu(t)$, with decent accuracy and comparative efficiency. The total number of training epochs for Indonesia is 4316 steps, for Singapore is 8408 steps, and for Malaysia is 8000 steps. For all countries, each of the three functions $\widehat{\beta}$, $\widehat{\gamma}$, and $\widehat{\mu}$ has the same KAN-F architecture of 2 hidden layers. Specifically, we implement 8 input neurons, 17 neurons for the first hidden layer, 35 neurons for the second hidden layer, and 1 output neuron. The number of Fourier terms for each activation function is $30$.

Phylogenetic inference traditionally relies on aligned characters under substitution models, but this framework becomes less reliable when alignments are unstable or when evolution is dominated by insertions, deletions, repeats, and other structural changes. We adapt Ladderpath as an alignment-free distance approach for phylogenetic inference. Motivated by algorithmic information theory, Ladderpath decomposes sequences into derived, reusable units (``ladderons'', rather than fixed-length $k$-mers) organized hierarchically, from which pairwise distances are computed. The premise is that shared derived sequence structure, including repeated or reused segments that are poorly represented by column-wise substitutions, can retain phylogenetic information. The bacteriophage T7 known lineage, the cpSSR repeat-rich marker, and a cytochrome~$c$ protein dataset confirm that Ladderpath recovers topologies consistent with the known experimental history or with established alignment-based methods. Its advantage emerges under stress: in block-translocation and indel-dominated simulations Ladderpath remains stable while alignment-dependent pipelines deteriorate; on banana mitochondrial and plastome genomes it scales to genome length and captures the expected contrast between organellar histories, all from unaligned input. These results support Ladderpath as an alignment-free, structurally informed method that could complement standard pipelines in cases where higher-order sequence structure carries phylogenetic signal.

Proteins function through coordinated motion across multiple spatial and temporal scales, underpinning processes such as ligand binding, allostery, and catalysis. However, accessing long-timescale conformational change through molecular dynamics (MD) simulations remains prohibitively expensive for systematic exploration across diverse systems. Here, we present DyneTrion, a generative protein dynamics emulator that jointly enforces geometric symmetry, structural consistency and temporal coherence within a single framework. DyneTrion uses a tri-attention architecture that integrates invariant point attention (IPA) for SE(3)-robust geometric updates, spatial attention anchored to a reference conformation to preserve structural integrity, and temporal attention to model correlated evolution across time frames. Across 100-ns MD trajectory simulation benchmarks, DyneTrion reproduces MD-derived flexibility, ensemble distributions and interaction observables while maintaining stereochemical validity during extrapolation. To evaluate long time-scale generalization, we introduce dynamicPDB, a dataset of over 10,000 proteins with up to 1-$\mu$s all-atom trajectories at 10-ps resolution and accompanying physical annotations. On microsecond trajectories, DyneTrion preserves free-energy landscapes and metastable-state populations, and it supports large conformational propagation in apo-to-holo transitions and fast folders. Together, DyneTrion provides a scalable path from static structure prediction toward time-resolved, ensemble-faithful protein modeling. The code is publicly available at this https URL

In this paper, we propose a new model to estimate the impact of an intervention on human hosts of a vector-borne infection, such as dengue, which occurs in yearly outbreaks of different magnitudes. The model applies to these outbreaks and, in fact, is independent of their intensity, that is, it does not require the steady-state assumption. The model takes as input the officially reported age-dependent number of cases of a vector-borne infection. It is deterministic and does not account for stochasticity. Our objective is to estimate the impact of the intervention (the efficacy), and we rely on the observed fact that the age distribution of the proportion of cases of the infections transmitted by the same vector is independent of both the intensity of transmission and the geographic area studied, at least for Brazilian regions. This finding is highlighted in the main text and forms the basis of our calculations. A hypothetical intervention is simulated using a dengue vaccine, which allows the determination of the optimal strategy for a vaccination campaign.

Biomechanical models are used to quantify and optimize human movement in clinical rehabilitation, sports science, and occupational health. Personalizing these models requires accurate identification of anatomical landmarks and body segment parameters, which can be derived from 3D body surface scans. Registering these surfaces to a canonical template is essential for automated landmark detection and model scaling. However, fitting parametric body models to real-world 3D point clouds remains challenging: non-linear optimization can converge to suboptimal solutions when target poses deviate substantially from the default pose of a template. We present BODIESReg, an open-source registration pipeline that addresses this initialization problem by constructing a pose-aligned mesh before distance minimization begins. In automatic mode, BODIESReg can be used for end-to-end registration without user intervention and processes multiple scans in batch. We evaluated BODIESReg on two complementary datasets: CHI3D, a synthetic dataset containing complex human poses, and MorphoMotion, a set of real-world 3D optical scans. Automatic registration succeeded for 82.9% of CHI3D scans and for all MorphoMotion scans. Among successful registrations, mean surface-fit error were below 10 mm across both datasets. For cases where automatic initialization fails, we provide interactive tools for manual pose correction and correspondence selection. BODIESReg supports large-scale registration of 3D body scans for biomechanical research.

Standard phylogenetic reconstruction techniques often yield unrooted phylogenetic networks; these are subsequently rooted to infer evolutionary history. A common problem in this process is to determine the structural classes to which the resulting network will belong. In this paper, we investigate unrooted networks in which the choice of any root results in a valid rooted phylogenetic network, a property we define as {\em robustly orientable}. We then establish a strict structural condition for this class, specifically, that an unrooted network is robustly orientable if and only if it contains no sink components. We also show that if an unrooted network is level-$2$ or less, or if it is tree-based, then it is robustly orientable. Furthermore, we define an unrooted network to be {\em robustly class $\mathcal C$} if the choice of any root results in a network belonging to class $\mathcal C$. We demonstrate that an unrooted network is robustly tree-child or robustly stack-free if and only if it is level-$1$ or less. Finally, we show that a phylogenetic network is robustly normal if and only if it is a phylogenetic tree.

The primate visual system is typically divided into two streams - the ventral stream, responsible for object recognition, and the dorsal stream, responsible for encoding spatial relations and motion. Recent studies have shown that convolutional neural networks (CNNs) pretrained on object recognition tasks are remarkably effective at predicting neuronal responses in the ventral stream, shedding light on the neural mechanisms underlying object recognition. However, similar models of the dorsal stream remain underdeveloped due to the lack of large scale datasets encompassing dorsal stream areas. To address this gap, we present STSBench, a dataset of large-scale, single neuron recordings from over 2,000 neurons in the superior temporal sulcus (STS), a nearly 50-fold increase over existing dorsal stream datasets, collected while Rhesus macaques viewed thousands of unique, natural videos. We show that our dataset can be used for benchmarking encoding models of dorsal stream neuronal responses and reconstructing visual input from neural activity.

We describe a model of perceptual inference in primary visual cortex (V1) equivalent to a minimal diffusion model whose function can be readily understood from its parameters. The model is based on sparse coding with a non-factorial prior over latent variables in the form of an unconstrained, pairwise interaction matrix, extending standard sparse coding inference to a general recurrent dynamical system. We efficiently train these recurrent dynamics using a denoising score-matching objective and implicit differentiation. After training on natural images, the learned interaction matrix mirrors the structure of horizontal connections in superficial layers of V1 that link neurons of similar orientation tuning. This model exhibits exceptionally good denoising performance, restoring image features such as extended contours amid extreme visual ambiguity, nearly matching the behavior of standard, black-box diffusion architectures in generalization regime. Owing to the model's simplicity, the network's Jacobian can be decomposed directly in terms of the interaction matrix between latent variables, revealing mechanistically how the recurrent dynamics assign high probability over a continuous family of natural structural deformations. Intriguingly, within this circuit, a large fraction of latent variables learn to disconnect from visual input altogether, essentially forming a hierarchical representation that appears to enforce global consistency among image features. Together, the model and results bridge two distinct domains: for neuroscience, it generates concrete, testable hypotheses regarding functional connectivity in recurrent neural circuits during perceptual inference tasks; for machine learning, it elucidates the internal mechanisms learned by diffusion models that allow them to generate infinitely many novel images from a finite training set.

Attempts to quantify biological complexity often consider intrinsic structural properties at a chosen hierarchical level and resolution, such as counts of body parts and their degree of differentiation. These measures are inherently \emph{syntactic}, being concerned with the information needed to specify an arrangement rather than the biological functions performed. Syntactic complexity alone is therefore not sophisticated enough of a measure to fully address the role of complexity as either a driver or consequence of evolution. We propose to study the counterpart, \emph{semantic} complexity: the subset of structural features whose variation has a measurable effect on organismal fitness. We illustrate this distinction in a simple mathematical model of tagmosis with functional constraints, symmetry breaking, and specialisation. We find that the total syntactic complexity evolved as selection drives lineages toward globally optimal fitness is path-dependent, revealing two evolutionary modes: a driven mode, in which semantic and syntactic complexity rise together, and an entropic mode, in which syntactic complexity drifts upward under a near-neutral evolution. Historical contingencies in early specialisation, combined with multi-optima fitness landscapes, govern how long lineages stay in each mode. Those on paths that do not lead directly to the highest-fitness states remain in the driven mode for longer and can eventually reach comparable fitness, but only by evolving morphologies with greater syntactic complexity.

Collective migration of epithelial monolayers emerges from the interplay between mechanical interactions and biochemical signalling. Here, we present a phenomenological mechanobiological framework linking cell-scale orientational interactions to tissue-scale mechanics. We distinguish reversible and irreversible head-on and glancing collisions, showing that reversible interactions store orientational mechanical energy while preserving collision geometry, whereas irreversible interactions dissipate energy and alter cell orientation. The balance between energy storage and dissipation governs collective migration, mechanical feedback, and density-dependent processes including cell jamming and live cell extrusion. These interactions regulate cell elasticity, contractility, and adhesion, thereby modifying epithelial surface tension and the effective viscoelastic response of the monolayer. We quantify these effects using orientational interaction potentials, an effective second virial coefficient, and dimensionless measures of stored and dissipated orientational energy. The relative contribution of these mechanisms increases with cell packing density, becoming dominant near the jamming transition. This framework provides a constitutive interpretation connecting collision-induced orientation dynamics with emergent epithelial rheology and suggests how density-dependent interaction regimes shape collective migration and tissue viscoelasticity.

Brain field potentials are scale-free: their power spectra follow a $1/f^{\beta}$ law whose aperiodic exponent $\beta$ tracks cortical state, and sleep depth in particular is a shift in $\beta$. We ask whether a transformer endowed with an explicit renormalization-group (RG) inductive bias the RG-Flow Transformer, which couples ordinary self-attention to a scale-aware stream with a learnable anomalous dimension $\gamma$, block-spin coarse-graining, and an entropy-gated synchronization bridge has an advantage over a parameter-matched vanilla transformer on \emph{real, scarce} EEG. Using the PhysioNet Sleep-EDF corpus with a strict leakage-free by-subject hold-out, we (i) benchmark RG-Flow against a param-matched vanilla transformer and a hierarchy-only ablation on 5-class AASM sleep staging, (ii) sweep the per-subject data budget to look for the inductive-bias crossover predicted when data are scarce, and (iii) test whether RG-Flow's learned $\gamma$ tracks the measured spectral exponent $\beta$ out-of-sample a quantity the vanilla model does not possess. Across $5$ subjects and $5$ seeds under leave-one-subject-out cross-validation, RG-Flow and the vanilla transformer are statistically indistinguishable on 5-class staging (77.3\% vs 77.0\% accuracy; paired $p=0.294$), and the predicted scarce-data crossover does not appear: vanilla is numerically ahead at every data-limited budget. What does separate the models is interpretability RG-Flow recovers the continuous spectral exponent out-of-sample ($\beta$-recovery $R^2 = 0.416$), a capability the vanilla architecture has no analogue for.

AlphaFold2's 93 million parameters, shaped by the evolutionary record of protein structure encoded in the Protein Data Bank and in sequence alignments, are conventionally treated only as machinery for converting sequence to structure. We propose they are also a scientific object that can be analyzed directly: a learned encoding of protein conformational organization that can be probed and characterized. By smoothing the Evoformer's weight tensors with a Gaussian convolution and scaling the result, we show that the trained model produces physically structured conformational landscapes. Under perturbation, ubiquitin's native contacts break in the order established by decades of folding experiments. For KaiB, five independently trained models agree that the alternative fold is not recovered under perturbation. For alpha-synuclein, five models produce five different but coherent landscapes, mapping where the training signal has determined the representation and where it has not. Matched-power noise controls confirm that random corruption of equal magnitude produces debris, not conformations. The model learned to predict static structures; the conformational organization visible under perturbation was not an explicit training target, suggesting it emerged as a byproduct of that objective. AlphaFold2's weights appear to encode structural constraints, shaped by evolutionary and structural training data, that extend beyond what unperturbed inference reveals. We call the approach of reading them neural spectroscopy, and Scaled Gaussian Convolution one such protocol.

Alignment-free methods in phylogenetic tree construction have major benefits in computational efficiency over alignment-based methods, but most sacrifice sequence information to pairwise distances, losing the statistical power of maximum likelihood (ML) inference. We describe ML-MAWS, an algorithm that fills this gap by encoding Minimal Absent Words (MAWs) as a binary presence/absence character matrix and estimating using an ML tree under the Lewis Mkv model using ascertainment bias correction. MAWs are obtained in linear time through the traversal of a suffix automaton. The pipeline incorporates strand-aware intersection filtering that retains only MAWs absent from both DNA orientations, entropy-based multi-length selection via Shannon entropy maximization to select the most informative lengths of MAWs, and parsimony-informative character capping to retain the most discriminative columns. We tested ML-MAWS on 14 benchmark datasets of bacterial, mitochondrial, viral, and simulated genomes with normalized Robinson-Foulds distances and matching split distances against published reference trees. The results show that while the binary encoding of MAWs can lead to higher topological error than continuous-valued distance baselines on closely related genomes, ML-MAWS is the first MAW-based method to provide per-branch bootstrap support and a rigorous probabilistic framework with ascertainment bias correction capabilities lacking from all existing alignment-free methods.

Large language models (LLMs) demonstrate remarkable reasoning capabilities, yet their stateless architecture fundamentally limits deployment in long-horizon research workflows requiring multi-session continuity and quantitative rigor. Here we present Ensemble QSP, a multi-agent framework featuring a three-layer hierarchical memory architecture that keeps injected context bounded and constant in project duration (mid-term project state: median 301 tokens, max 4,050, across 104 runs) by capping each state category and evicting completed work, enabling continuous autonomous operation without context degradation. The system orchestrates five specialist worker agents under domain-expert principal investigators, enforcing physical constraints through physics-based checklists and structured-domain knowledge. Comprehensive benchmarking demonstrates robust autonomous pharmacokinetic-pharmacodynamic model selection without human intervention, consistent result quality across both lower-cost and frontier LLMs, improved PK parameter recovery relative to single-agent baselines, and stable model selection across linguistically diverse prompts of the same task. Feature-level ablation across physiologically based pharmacokinetic (PBPK) models spanning a broad complexity range shows that PI-agent oversight improves debugging efficiency while preserving final accuracy across conditions. The architecture is structurally domain-agnostic, adding a new scientific domain requires only a new PI agent configuration.

We model human motor cortex, recorded during rest and motor-imagery BCI conditions, as a port-Hamiltonian system: a conservative interconnection (skew-symmetric coupling between band-limited neural phasors) together with a dissipative port whose state-dependent decay is set by a graph-neural-network surrogate. The Hamiltonian is resolved into five interpretable frequency sub-energies, and a phase-locking prior measured from the recordings gates the learned functional connectome so that coupling is admitted only where phase coherence is present. A metriplectic formulation places the resting cortex at a non-equilibrium steady state sustained by an explicit metabolic port, with a fluctuation-dissipation-consistent noise channel governed by a single arousal temperature. Fitting the model to 'FitTrainN' phasor samples from the PhysioNet EEG Motor Movement/Imagery database, under a leakage-free split with three subjects held out entirely, yields a held-out kinematic reconstruction error of 'FitTestMSE' that is stable across random seeds. We then score the free-running model against model-independent dynamical invariants it did not author: it reproduces near-critical avalanche branching ($\sigma\approx1$) but not yet the aperiodic $1/f$ spectral slope or the long-range temporal correlations of real cortex a concrete, falsifiable gap that we trace to specific, testable upgrades. The port-Hamiltonian structure supplies neuroanatomically grounded stimulation ports with stability guarantees, positioning the model as a physically principled, structure-preserving substrate for closed-loop neuromodulation.

Predicting species distributions using occupancy models accounting for imperfect detection is now commonplace in ecology. Recently, modeling spatial and temporal autocorrelation was proposed to alleviate the lack of replication in occupancy data, which often prevents model identifiability. However, how such models perform in highly heterogeneous datasets where missing or single-visit data dominates remains an open question. Motivated by a heterogeneous fine-scale butterfly occupancy dataset, we evaluate the performance of a multi-season occupancy model with spatial and temporal random effects to a skewed (Poisson) distribution of the number of surveys per site, overlap of covariates between occupancy and detection submodels, and spatiotemporal clustering of observations. Results showed that the model is robust to heterogeneous data and covariate overlap. However, when spatiotemporal gaps were added, site occupancy was biased towards the average occupancy, itself overestimated. Random effects did not correct the influence of gaps, due to identifiability issues of variance and autocorrelation parameters. Occupancy analysis of two butterfly species further confirmed these results. Overall, multi-season occupancy models with autocorrelation are robust to heterogeneous data and covariate overlap, but still present identifiability issues and are challenged by severe data gaps, which contaminate predictions even in data-rich areas.