Understanding how species persist under interacting stressors is a central challenge in ecology. We develop a spatially explicit reaction-diffusion framework to investigate competing species in landscapes shaped by climate variability, pollution, resource heterogeneity, and cooperation. Here, temperature follows low-frequency oscillations, while pollution and resources diffuse from localized sources. Growth is governed by a dynamic carrying capacity integrating abiotic stress with an endogenous, pollution-sensitive cooperation field. Numerical simulations reveal the spontaneous emergence of persistent spatial organization, including dominance segregation and stable competitive boundaries. Quantitative analyses-using boundary geometry, fractal dimension, and spatial entropy-demonstrate a transition from intermixed initial states to low-complexity, quasi-stationary configurations. Coexistence occurs through distinct strategies: one species occupies more area, while the other maintains higher local densities. Cooperation enhances resilience but collapses in polluted zones, creating heterogeneous "social buffering." We further introduce a hybrid inverse modeling framework using a Swin Transformer to infer high-dimensional parameters from only two temporal snapshots. Trained on synthetic data, the model accurately recovers demographic, diffusive, and environmental-sensitivity parameters. While it achieves reliable short-term spatial predictions, long-term forecasts diverge due to the intrinsic sensitivity of nonlinear systems. This unified framework links sparse observations to mechanistic dynamics, advancing biodiversity forecasting under accelerating global change.

Phylogenetic reconciliation seeks to explain host-symbiont co-evolution by mapping parasite trees onto host trees through events such as cospeciation, duplication, host switching, and loss. Finding an optimal reconciliation that ensures time feasibility is computationally hard when timing information is incomplete, and the complexity remains open when host switches are restricted by a fixed maximum distance $d$. While the case $d=2$ is known to be polynomial, larger values are unresolved. In this paper, we study the cases $d=3$ and $d=4$. We show that although arbitrarily large cycles may occur, it suffices to check only bounded-size cycles (we provide a complete list), provided the reconciliation satisfies acyclicity (i.e., time-feasibility) in a stronger sense. These results do not resolve the general complexity, but highlight structural properties that advance the understanding of distance-bounded reconciliations.

Current genomic foundation models (GFMs) rely on extensive neural computation to implicitly approximate conserved biological motifs from single-nucleotide inputs. We propose Gengram, a conditional memory module that introduces an explicit and highly efficient lookup primitive for multi-base motifs via a genomic-specific hashing scheme, establishing genomic "syntax". Integrated into the backbone of state-of-the-art GFMs, Gengram achieves substantial gains (up to 14%) across several functional genomics tasks. The module demonstrates robust architectural generalization, while further inspection of Gengram's latent space reveals the emergence of meaningful representations that align closely with fundamental biological knowledge. By establishing structured motif memory as a modeling primitive, Gengram simultaneously boosts empirical performance and mechanistic interpretability, providing a scalable and biology-aligned pathway for the next generation of GFMs. The code is available at this https URL, and the model checkpoint is available at this https URL.

Generative modeling of peptide sequences requires navigating a discrete and highly constrained space in which many intermediate states are chemically implausible or unstable. Existing discrete diffusion and flow-based methods rely on reversing fixed corruption processes or following prescribed probability paths, which can force generation through low-likelihood regions and require countless sampling steps. We introduce Minimal-action discrete Schrödinger Bridge Matching (MadSBM), a rate-based generative framework for peptide design that formulates generation as a controlled continuous-time Markov process on the amino-acid edit graph. To yield probability trajectories that remain near high-likelihood sequence neighborhoods throughout generation, MadSBM 1) defines generation relative to a biologically informed reference process derived from pre-trained protein language model logits and 2) learns a time-dependent control field that biases transition rates to produce low-action transport paths from a masked prior to the data distribution. We finally introduce guidance to the MadSBM sampling procedure towards a specific functional objective, expanding the design space of therapeutic peptides; to our knowledge, this represents the first-ever application of discrete classifier guidance to Schrödinger bridge-based generative models.

Cell size is a fundamental determinant of cellular physiology, influencing processes such as growth, division, and function. In this study, we develop a segmented mathematical framework to investigate how different control mechanisms operating across multiple phases of the cell cycle affect fibroblast population dynamics. Building on our previous work modeling sizer, timer, and adder strategies, we extend the analysis by introducing phase-specific control schemes in the S and G2 phases, incorporating nonlinear growth dynamics and cell death. Using agent-based stochastic simulations, we examine how these mechanisms shape steady-state size distributions and respond to parameter variations. Our results reveal that the steady-state cell size distribution is primarily governed by division kernels and phase-specific control strategies, and appears remarkably robust to cell death modalities. We identify a fundamental trade-off between extrinsic and intrinsic growth feedbacks: while population-density-dependent regulation tightly limits total cell numbers, cell-size-dependent regulation acts as a proportional homeostatic mechanism, suppressing relative size variability. Furthermore, we demonstrate that population recovery is accelerated by the retention of proliferation-competent large cells. This study provides biologically relevant insights into the complex interplay between growth, division, and homeostasis, with implications for understanding tissue repair and disease progression.

The efficacy of anti-cancer therapies is severely limited by the emergence of drug resistance. While genetic drivers are well-characterized, growing evidence suggests that non-genetic mechanisms, particularly those involving drug-tolerant persisters (DTPs), play a pivotal role in solid tumor relapse. To elucidate the evolutionary dynamics of DTP-induced resistance, we develop a stochastic agent-based model (ABM) of solid tumor evolution that couples macroscopic population dynamics with microscopic epigenetic state inheritance during the cell cycle. Our simulations accurately reproduce the temporal progression of relapse observed in experimental studies, capturing the dynamic transition from sensitive cells to DTPs, and ultimately to stable resistant phenotypes under prolonged therapy. By explicitly modeling the epigenetic plasticity of individual cells, our model bridges the gap between cellular heterogeneity and population-level tumor evolution. Furthermore, we performed \textit{in silico} clinical trials using virtual patient cohorts to evaluate therapeutic outcomes, demonstrating that optimized adaptive treatment strategies can significantly delay tumor relapse compared to standard dosing. This study provides a quantitative framework for dissecting DTP-driven resistance mechanisms and designing more effective, biologically informed therapeutic strategies.

The BioModels database is one of the premier databases for computational models in systems biology. The database contains over 1000 curated models and an even larger number of non-curated models. All the models are stored in the machine-readable format, SBML. Although SBML can be translated into the human readable Antimony format, analyzing the models can still be time consuming. In order to bridge this gap, a LLM (large language model) assistant was created to analyze the BioModels and allow interaction between the user and the model using natural language. By doing so, a user can easily and rapidly extract the salient points in a given model. Our analysis workflow involved 'chunking' BioModels and converting them to plain text using llama3, and then embedding them in a ChromaDB database. The user-provided query was also embedded, and a similarity search was performed between the query and the BioModels in ChromaDB to extract the most relevant BioModels. The BioModels were then used as context to create the most accurate output in the chat between the user and the LLM. This approach greatly minimized the chance of hallucination and kept the LLM focused on the problem at hand.

The COVID-19 pandemic has profoundly affected global health, driven by the remarkable transmissibility and mutational adaptability of the SARS-CoV-2 virus. Five major variants of concern, Alpha, Beta, Gamma, Delta, and Omicron, have been identified. By August 2022, over 12.95 million full-length SARS-CoV-2 genome sequences had been deposited in the Global Initiative on Sharing Avian Influenza Data (GISAID) database, offering an unprecedented opportunity to investigate viral evolution and epistatic interactions. Recent advances in epistatic inference, exemplified by Direct Coupling Analysis (DCA) (Zeng et al., Phys. Rev. E, 2022), have generated numerous Circos plots illustrating genetic inter-dependencies. In this study, we constructed a dataset of 1,984 Circos plots and developed a convolutional neural network (CNN) framework to classify and identify the corresponding genomic variants. The CNN effectively captured complex epistatic features, achieving an accuracy of 99.26\%. These findings demonstrate that CNN-based models can serve as powerful tools for exploring higher-order genetic dependencies, providing deeper insights into the evolutionary dynamics and adaptive mechanisms of SARS-CoV-2.

Recent advances in metagenomics have revealed macroecological patterns or "laws" describing robust statistical regularities across microbial communities. Stochastic logistic models (SLMs), which treat species as independent -- akin to ideal gases in physics -- and incorporate environmental noise, reproduce many single-species patterns but cannot account for the pairwise covariation observed in microbiome data. Here we introduce an interacting stochastic logistic model (ISLM) that minimally extends the SLM by sampling an ensemble of random interaction networks chosen to preserve these single-species laws. Using dynamical mean-field theory, we map the model's phase diagram -- stable, chaotic, and unbounded-growth regimes -- where the transition from stable fixed-point to chaos is controlled by network sparsity and interaction heterogeneity via a May-like instability line. Going beyond mean-field theory to account for finite communities, we derive an estimator of an effective stability parameter that quantifies distance to the edge of instability and can be inferred from the width of the distribution of pairwise covariances in empirical species-abundance data. Applying this framework to synthetic data, environmental microbiomes, and human gut cohorts indicates that these communities tend to operate near the edge of instability. Moreover, gut communities from healthy individuals cluster closer to this edge and exhibit broader, more heterogeneous associations, whereas dysbiosis-associated states shift toward more stable regimes -- enabling discrimination across conditions such as Crohn's disease, inflammatory bowel syndrome, and colorectal cancer. Together, our results connect macroecological laws, interaction-network ensembles, and May's stability theory, suggesting that complex communities may benefit from operating near a dynamical phase transition.

Microbes constantly interact with their environment by depleting and transforming food sources. Theoretical studies have mainly focused on Lotka-Volterra models, which do not account for food source dynamics. In contrast, consumer-resource models, which consider food source dynamics, are less explored. In particular, it is still unclear what physical mechanisms control oscillatory dynamics at a single population level, a phenomenon which can only be captured by a consumer-resource model. Here, we present a minimalistic consumer-resource model of a single microbial population with growth and death dynamics, consuming a continuously replenishing substrate. Our model reveals that decaying oscillations can occur around steady state if and only if the timescale of microbial adaptation to food supply changes exceeds the death timescale. This interplay of timescales allows us to rationalize the emergence of oscillatory dynamics when adding various biophysical ingredients to the model. We find that microbial necromass recycling or complementary use of multiple food sources reduces the parameter range for oscillations and increases the decay rate of oscillations. Requiring multiple simultaneous food sources has the opposite effect. Essentially, facilitating growth reduces the likelihood of oscillations around a fixed point. We further demonstrate that such damped oscillatory behavior is correlated with persistent oscillatory behavior in a noisy environment. We hope our work will motivate further investigations of consumer-resource models to improve descriptions of environments where food source distributions vary in space and time.

Tactile localization is the seemingly simple ability to 'tell' where a touch has occurred. However, how this ability is assessed, and what conclusions are drawn from experiments, depends on the theoretical ideas that inspire the research. Here, we review both theoretical frameworks and methodological approaches based on a systematic web-based literature search on tactile localization. After presenting current theories of tactile localization, we discuss task characteristics that differentiate current methodology for tactile localization into at least 8 distinct types of experimental tasks. We describe these tasks, discuss their, often implicit, underlying assumptions and cognitive requirements, and relate them to the theoretical approaches. We then compare, in an exemplary manner, the tactile localization results reported by a subset of studies and demonstrate how some methods are associated with specific biases, illustrating that the choice of experimental method significantly affects the conclusions drawn from the results. Our review suggests that the field currently lacks a clear concept of the specific processes induced by the various experimental tasks and, thus, calls for concerted efforts to clarify and unify currently diverse, fragmented, and partly inconsistent theoretical underpinnings of tactile spatial processing, flanked by dedicated data sharing to allow across-study analysis.

Multispecific antibodies offer transformative therapeutic potential by engaging multiple epitopes simultaneously, yet their efficacy is an emergent property governed by complex molecular architectures. Rational design is often bottlenecked by the inability to predict how subtle changes in domain topology influence functional outcomes, a challenge exacerbated by the scarcity of comprehensive experimental data. Here, we introduce a computational framework to address part of this gap. First, we present a generative method for creating large-scale, realistic synthetic functional landscapes that capture non-linear interactions where biological activity depends on domain connectivity. Second, we propose a graph neural network architecture that explicitly encodes these topological constraints, distinguishing between format configurations that appear identical to sequence-only models. We demonstrate that this model, trained on synthetic landscapes, recapitulates complex functional properties and, via transfer learning, has the potential to achieve high predictive accuracy on limited biological datasets. We showcase the model's utility by optimizing trade-offs between efficacy and toxicity in trispecific T-cell engagers and retrieving optimal common light chains. This work provides a robust benchmarking environment for disentangling the combinatorial complexity of multispecifics, accelerating the design of next-generation therapeutics.

Molecular generative models, often employing GPT-style language modeling on molecular string representations, have shown promising capabilities when scaled to large datasets and model sizes. However, it remains unclear and subject to debate whether these models adhere to predictable scaling laws under fixed computational budgets, which is a crucial understanding for optimally allocating resources between model size, data volume, and molecular representation. In this study, we systematically investigate the scaling behavior of molecular language models across both pretraining and downstream tasks. We train 300 models and conduct over 10,000 experiments, rigorously controlling compute budgets while independently varying model size, number of training tokens, and molecular representation. Our results demonstrate clear scaling laws in molecular models for both pretraining and downstream transfer, reveal the substantial impact of molecular representation on performance, and explain previously observed inconsistencies in scaling behavior for molecular generation. Additionally, we publicly release the largest library of molecular language models to date to facilitate future research and development. Code and models are available at this https URL.

Dynamic models are widely used to mathematically describe biological phenomena that evolve over time. One important area of application is leukaemia research, where leukaemia cells are genetically modified in preclinical studies to explore new therapeutic targets for reducing leukaemic burden. In advanced experiments, these studies are often conducted in mice and generate time-resolved data, the analysis of which may reveal growth-inhibiting effects of the investigated gene modifications. However, the experimental data is often times evaluated using statistical tests which compare measurements from only two different time points. This approach does not only reduce the time series to two instances but also neglects biological knowledge about cell mechanisms. Such knowledge, translated into mathematical models, expands the power to investigate and understand effects of modifications on underlying mechanisms based on experimental data. We utilise two population growth models -- an exponential and a logistic growth model -- to capture cell dynamics over the whole experimental time horizon and to consider all measurement times jointly. This approach enables us to derive modification effects from estimated model parameters. We demonstrate that the exponential growth model recognises simulated scenarios more reliably than the other candidate model and than a statistical test. Moreover, we apply the population growth models to evaluate the efficacy of candidate gene knockouts in patient-derived xenograft (PDX) models of acute leukaemia.

Self-supervised fMRI foundation models have shown promising transfer performance, yet most rely on predefined region-level parcellations that discard fine-grained voxel information and introduce atlas-dependent biases. We propose Omni-fMRI, an atlas-free foundation model that operates directly on voxel-level signals. To enable scalable pretraining on 49,497 fMRI sessions across nine datasets, Omni-fMRI introduces a dynamic patching mechanism that substantially reduces computational cost while preserving informative spatial structure. To support reproducibility and fair comparison, we establish a comprehensive benchmark suite spanning 11 datasets and a diverse set of resting-state and task-based fMRI tasks. Experimental results demonstrate that Omni-fMRI consistently outperforms existing foundation models, providing a scalable and reproducible framework for atlas-free brain representation learning. Code and logs are available.

Rooted phylogenetic networks allow biologists to represent evolutionary relationships between present-day species by revealing ancestral speciation and hybridization events. A convenient and well-studied class of such networks are `tree-child networks' and a `ranking' of such a network is a temporal ordering of the ancestral speciation and hybridization events. In this short note, we investigate the question of counting such rankings on any given binary (or semi-binary) tree-child network. We also consider a class of binary tree-child networks that have exactly one ranking, and investigate further the relationship between ranked-tree child networks and the class of `normal' networks. Finally, we provide an explicit asymptotic expression for the expected number of rankings of a tree-child network chosen uniformly at random.

Biological systems operate under persistent noise, which can alter system states and induce transitions between attractors. Here, we study the attractor dynamics of Boolean networks focusing on the transitions between attractors induced by noise. By computing transition probabilities between attractors, we present methods at the attractor level to determine dominance, stability, and diversity of attractors, and systematically compare local and global noise. Whereas global noise leads to attractor behavior dictated primarily by basin sizes, local noise produces structured transition patterns characterized by enhanced stability, non-trivial dominance patterns, and broader exploration of the attractor space. Our work offers insight into the dynamics of attractors, showing the importance of transition patterns under noise.

Multimodal protein language models deliver strong performance on mutation-effect prediction, but training such models from scratch demands substantial computational resources. In this paper, we propose a fine-tuning framework called InstructPLM-mu and try to answer a question: \textit{Can multimodal fine-tuning of a pretrained, sequence-only protein language model match the performance of models trained end-to-end? } Surprisingly, our experiments show that fine-tuning ESM2 with structural inputs can reach performance comparable to ESM3. To understand how this is achieved, we systematically compare three different feature-fusion designs and fine-tuning recipes. Our results reveal that both the fusion method and the tuning strategy strongly affect final accuracy, indicating that the fine-tuning process is not trivial. We hope this work offers practical guidance for injecting structure into pretrained protein language models and motivates further research on better fusion mechanisms and fine-tuning protocols.

DNA language models are increasingly used to represent genomic sequence, yet their effectiveness depends critically on how raw nucleotides are converted into model inputs. Unlike natural language, DNA offers no canonical boundaries, making fixed tokenizations a brittle design choice under shifts, indels, and local repeats. We introduce \modelname{}, a masked DNA language model that incorporates a learnable adaptive segmentation module to produce context-dependent, variable-length units. Building on a dynamic segmentation procedure, \modelname{} learns to allocate finer granularity to functionally enriched regions while compressing repetitive or redundant sequence. We pre-train \modelname{} on the human reference genome (HG38) and evaluate it on the Nucleotide Transformer and Genomic Benchmarks, where it consistently improves over strong fixed-tokenization baselines. Further analyses and ablations indicate that the learned segmentation is structured rather than incidental: the model preferentially uses shorter units around promoters and exons, and longer units in repetitive regions, yielding representations that are both mutation-resilient and biologically-informed.

We prove a Large Deviation Principle for {\color{blue} jump-Markov } Processes on sparse large disordered network with disordered connectivity. The network is embedded in a geometric space, with the probability of a connection a (scaled) function of the spatial positions of the nodes. This type of model has numerous applications, including neuroscience, epidemiology and social networks. We prove that the rate function (that indicates the asymptotic likelihood of state transitions) is the same as for a network with all-to-all connectivity. We apply our results to a stochastic $SIS$ epidemiological model on a disordered networks, and determine Euler-Lagrange equations that dictate the most likely transition path between different states of the network.

Foundation models are emerging as a powerful paradigm for fMRI analysis, but current approaches face a dual bottleneck of data- and training-efficiency. Atlas-based methods aggregate voxel signals into fixed regions of interest, reducing data dimensionality but discarding fine-grained spatial details, and requiring extremely large cohorts to train effectively as general-purpose foundation models. Atlas-free methods, on the other hand, operate directly on voxel-level information - preserving spatial fidelity but are prohibitively memory- and compute-intensive, making large-scale pre-training infeasible. We introduce SLIM-Brain (Sample-efficient, Low-memory fMRI Foundation Model for Human Brain), a new atlas-free foundation model that simultaneously improves both data- and training-efficiency. SLIM-Brain adopts a two-stage adaptive design: (i) a lightweight temporal extractor captures global context across full sequences and ranks data windows by saliency, and (ii) a 4D hierarchical encoder (Hiera-JEPA) learns fine-grained voxel-level representations only from the top-$k$ selected windows, while deleting about 70% masked patches. Extensive experiments across seven public benchmarks show that SLIM-Brain establishes new state-of-the-art performance on diverse tasks, while requiring only 4 thousand pre-training sessions and approximately 30% of GPU memory comparing to traditional voxel-level methods.