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Pankaj Mehta

Publications and source records attributed to Pankaj Mehta.

At least 19 recordsLinked to original sources

Parameter-free representations outperform single-cell foundation models on downstream benchmarks

Single-cell RNA sequencing (scRNA-seq) data exhibit strong and reproducible statistical structure. This has motivated the development of large-scale foundation models, such as TranscriptFormer, that use transformer-based architectures to learn a generative model for gene expression by embedding genes into a latent vector space. These embeddings have been used to obtain state-of-the-art (SOTA) performance on downstream tasks such as cell-type classification, disease-state prediction, and cross-species learning. Here, we ask whether similar performance can be achieved without utilizing computationally intensive deep learning-based representations. Using simple, interpretable pipelines that rely on careful normalization and linear methods, we obtain SOTA or near SOTA performance across multiple benchmarks commonly used to evaluate single-cell foundation models, including outperforming foundation models on out-of-distribution tasks involving novel cell types and organisms absent from the training data. Our findings highlight the need for rigorous benchmarking and suggest that the biology of cell identity can be captured by simple linear representations of single cell gene expression data.

q-bio.GN

Emergent frequency-dependent selection predicts mutation outcomes in complex ecological communities

Ecological interactions can dramatically alter evolutionary outcomes in complex communities. Yet, the framework of population genetics largely neglects interactions from a species-rich community. Here, we bridge this gap by using dynamical mean-field theory to integrate community ecology into classical population genetics models. We show that ecological interactions result in emergent frequency-dependent selection between parents and mutants, characterized by a single parameter measuring the strength of ecological feedbacks. This result generalizes classical population genetics models to highly diverse communities and enables predictions of mutation outcomes in these eco-evolutionary settings. We derive an analytic expression for fixation probability that extends Kimura's formula and reveals that ecological interactions strongly suppress the fixation of moderately beneficial mutations. This suppression arises because frequency-dependent selection leads to prolonged coexistence between parent and mutant lineages, which acts as a barrier to fixation. The strength of these effects increases with effective population size and the number of open niches in the ecosystem. Our study establishes a framework for integrating ecological interactions into population genetics, showing that evolutionary outcomes can be predicted using simple models even in the presence of complex community feedbacks.

q-bio.PE

What do the fundamental constants of physics tell us about life?

In the 1970s, the renowned physicist Victor Weisskopf famously developed a research program to qualitatively explain properties of matter in terms of the fundamental constants of physics. But there was one type of matter prominently missing from Weisskopf's analysis: life. Here, we develop Weisskopf-style arguments demonstrating how the fundamental constants of physics can be used to understand the properties of living systems. By combining biophysical arguments and dimensional analysis, we show that vital properties of chemical self-replicators, such as growth yield, minimum doubling time, and minimum power consumption in dormancy, can be quantitatively estimated using fundamental physical constants. The calculations highlight how the laws of physics constrain chemistry-based life on Earth, and if it exists, elsewhere in our universe.

physics.bio-ph

Randomness with constraints: constructing minimal models for high-dimensional biology

Biologists and physicists have a rich tradition of modeling living systems with simple models composed of a few interacting components. Despite the remarkable success of this approach, it remains unclear how to use such finely tuned models to study complex biological systems composed of numerous heterogeneous, interacting components. One possible strategy for taming this biological complexity is to embrace the idea that many biological behaviors we observe are ``typical'' and can be modeled using random systems that respect biologically-motivated constraints. Here, we review recent works showing how this approach can be used to make close connection with experiments in biological systems ranging from neuroscience to ecology and evolution and beyond. Collectively, these works suggest that the ``random-with-constraints'' paradigm represents a promising new modeling strategy for capturing experimentally observed dynamical and statistical features in high-dimensional biological data and provides a powerful minimal modeling philosophy for biology.

physics.bio-ph

The Future of Artificial Intelligence and the Mathematical and Physical Sciences (AI+MPS)

This community paper developed out of the NSF Workshop on the Future of Artificial Intelligence (AI) and the Mathematical and Physics Sciences (MPS), which was held in March 2025 with the goal of understanding how the MPS domains (Astronomy, Chemistry, Materials Research, Mathematical Sciences, and Physics) can best capitalize on, and contribute to, the future of AI. We present here a summary and snapshot of the MPS community's perspective, as of Spring/Summer 2025, in a rapidly developing field. The link between AI and MPS is becoming increasingly inextricable; now is a crucial moment to strengthen the link between AI and Science by pursuing a strategy that proactively and thoughtfully leverages the potential of AI for scientific discovery and optimizes opportunities to impact the development of AI by applying concepts from fundamental science. To achieve this, we propose activities and strategic priorities that: (1) enable AI+MPS research in both directions; (2) build up an interdisciplinary community of AI+MPS researchers; and (3) foster education and workforce development in AI for MPS researchers and students. We conclude with a summary of suggested priorities for funding agencies, educational institutions, and individual researchers to help position the MPS community to be a leader in, and take full advantage of, the transformative potential of AI+MPS.

cs.AI

Hopfield Networks as Models of Emergent Function in Biology

Hopfield models, originally developed to study memory retrieval in neural networks, have become versatile tools for modeling diverse biological systems in which function emerges from collective dynamics. In this review, we provide a pedagogical introduction to both classical and modern Hopfield networks from a biophysical perspective. After presenting the underlying mathematics, we build physical intuition through three complementary interpretations of Hopfield dynamics: as noise discrimination, as a geometric construction defining a natural coordinate system in pattern space, and as gradient-like descent on an energy landscape. We then survey recent applications of Hopfield networks a variety of biological setting including cellular differentiation and epigenetic memory, molecular self-assembly, and spatial neural representations.

physics.bio-ph

Collective gene dynamics leave signatures of decision landscapes in cell fate coordinates

Multicellular organisms contain a wide variety of highly specialized cell types. The consistency and robustness of developmental trajectories suggest that complex gene regulatory networks effectively act as low-dimensional cell fate landscapes. Prior work inspired by dynamical systems theory argues that cell fate transitions fall into universal decision-making classes, but the theory connecting these geometric landscapes to high-dimensional gene expression space is still in its infancy. Here, we introduce a phenomenological model that identifies experimental signatures of decision-making classes in single-cell RNA-sequencing time-series data. The model combines low-dimensional gradient-like dynamics with high-dimensional Hopfield networks to capture the interplay between cell fate, gene expression, and signaling. We apply the framework to experimental mouse data on maturing lung alveolar cells and lineage-traced hematopoietic differentiation and show that the measured cell fate dynamics are consistent with developmental landscapes containing intermediate progenitors and saddle points. We further show that the framework can be used to understand spatial patterning and cell fate organization, focusing on Notch signaling in lung airways. Together, these results provide evidence that collective transcriptomic dynamics carry signatures of landscape features associated with universal decision-making classes.

q-bio.CB

Inferring genotype-phenotype maps using attention models

Predicting phenotype from genotype is a central challenge in genetics. Traditional approaches in quantitative genetics typically analyze this problem using methods based on linear regression. These methods generally assume that the genetic architecture of complex traits can be parameterized in terms of an additive model, where the effects of loci are independent, plus (in some cases) pairwise epistatic interactions between loci. However, these models struggle to analyze more complex patterns of epistasis or subtle gene-environment interactions. Recent advances in machine learning, particularly attention-based models, offer a promising alternative. Initially developed for natural language processing, attention-based models excel at capturing context-dependent interactions and have shown exceptional performance in predicting protein structure and function. Here, we apply attention-based models to quantitative genetics. We analyze the performance of this attention-based approach in predicting phenotype from genotype using simulated data across a range of models with increasing epistatic complexity, and using experimental data from a recent quantitative trait locus mapping study in budding yeast. We find that our model demonstrates superior out-of-sample predictions in epistatic regimes compared to standard methods. We also explore a more general multi-environment attention-based model to jointly analyze genotype-phenotype maps across multiple environments and show that such architectures can be used for "transfer learning" - predicting phenotypes in novel environments with limited training data.

q-bio.GN

A theory of ecological invasions and its implications for eco-evolutionary dynamics

Predicting the outcomes of species invasions is a central goal of ecology, a task made especially challenging due to ecological feedbacks. To address this, we develop a general theory of ecological invasions applicable to a wide variety of ecological models: including Lotka-Volterra models, consumer resource models, and models with cross feeding. Importantly, our framework remains valid even when invading evolved (non-random) communities and accounts for invasion-driven species extinctions. We derive analytical expressions relating invasion fitness to invader abundance, shifts in the community, and extinction probabilities. These results can be understood through a new quantity we term ``dressed invasion fitness'', which augments the traditional notion of invasion fitness by incorporating ecological feedbacks. We apply our theory to analyze short-term evolutionary dynamics through a series of invasions by mutants whose traits are correlated with an existing parent. We demonstrate that, generically, mutants and parents can coexist, often by driving the extinction of low-abundance species. We validate theoretical predictions against experimental datasets spanning ecosystems from plants to microbial protists. Our work highlights the central role of ecological feedbacks in shaping community responses to invasions and mutations, suggesting that parent-mutant coexistence is widespread in eco-evolutionary dynamics.

q-bio.PE

A twenty-first century statistical physics of life

The molecular biology revolution of the last seventy five years has transformed our view of living systems. Scientific explanations of biological phenomena are now synonymous with the identification of the genes, proteins, and signaling molecules involved. The hegemony of the molecular paradigm has only become more pronounced as new technologies allow us to make measurements at scale. Combining this wealth of data with new ``artificial intelligence'' techniques is viewed as the future of biology. Here, we challenge this emerging ``common sense'', laying out a roadmap for developing a theoretical understanding of life. We argue that a twenty-first century theoretical biology must be founded on a new type of statistical physics suited to the living world. Rather than merely constructing statistical models, a statistical theory requires developing ``quantitative abstractions'' for understanding the gene-organism-environment triad. This necessitates overcoming four major challenges that distinguish living matter: (1) living systems are composed of a large number of heterogeneous parts rather than a large number of identical objects; (2) living systems control and manipulate the physical world in a manner that is extremely different from the ways considered in traditional statistical physics; (3) living systems necessarily operate out of equilibrium; (4) living systems are evolved objects with a function, resulting in new types of constraints that must be imposed on probabilistic ensembles. We conclude by discussing a few key themes that we view as promising directions for developing a statistical physics of life: typicality, localized biological control, a linear response of complex systems with non-reciprocal interactions, biological resource allocation, and learning and adaptation in overparameterized systems.

physics.bio-ph

A differentiable Gillespie algorithm for simulating chemical kinetics, parameter estimation, and designing synthetic biological circuits

The Gillespie algorithm is commonly used to simulate and analyze complex chemical reaction networks. Here, we leverage recent breakthroughs in deep learning to develop a fully differentiable variant of the Gillespie algorithm. The differentiable Gillespie algorithm (DGA) approximates discontinuous operations in the exact Gillespie algorithm using smooth functions, allowing for the calculation of gradients using backpropagation. The DGA can be used to quickly and accurately learn kinetic parameters using gradient descent and design biochemical networks with desired properties. As an illustration, we apply the DGA to study stochastic models of gene promoters. We show that the DGA can be used to: (i) successfully learn kinetic parameters from experimental measurements of mRNA expression levels from two distinct $\textit{E. coli}$ promoters and (ii) design nonequilibrium promoter architectures with desired input-output relationships. These examples illustrate the utility of the DGA for analyzing stochastic chemical kinetics, including a wide variety of problems of interest to synthetic and systems biology.

physics.bio-ph

Les Houches Lectures on Community Ecology: From Niche Theory to Statistical Mechanics

Ecosystems are among the most interesting and well-studied examples of self-organized complex systems. Community ecology, the study of how species interact with each other and the environment, has a rich tradition. Over the last few years, there has been a growing theoretical and experimental interest in these problems from the physics and quantitative biology communities. Here, we give an overview of community ecology, highlighting the deep connections between ecology and statistical physics. We start by introducing the two classes of mathematical models that have served as the workhorses of community ecology: Consumer Resource Models (CRM) and the generalized Lotka-Volterra models (GLV). We place a special emphasis on graphical methods and general principles. We then review recent works showing a deep and surprising connection between ecological dynamics and constrained optimization. We then shift our focus by analyzing these same models in "high-dimensions" (i.e. in the limit where the number of species and resources in the ecosystem becomes large) and discuss how such complex ecosystems can be analyzed using methods from the statistical physics of disordered systems such as the cavity method and Random Matrix Theory.

q-bio.PE

A universal niche geometry governs the response of ecosystems to environmental perturbations

How ecosystems respond to environmental perturbations is a fundamental question in ecology, made especially challenging due to the strong coupling between species and their environment. Here, we introduce a theoretical framework for calculating the steady-state response of ecosystems to environmental perturbations in generalized consumer-resource. Our construction is applicable to a wide class of systems, including models with non-reciprocal interactions, cross-feeding, and non-linear growth/consumption rates. Within our framework, all ecological variables are embedded into four distinct vector spaces and ecological interactions are represented by geometric transformations between these spaces. We show that near a steady state, such geometric transformations directly map environmental perturbations - in resource availability and mortality rates - to shifts in niche structure. We illustrate these ideas in a variety of settings including a minimal model for pH-induced toxicity in bacterial denitrification. We end by discussing the biological implications of our framework. In particular, we show that it is extremely difficult to distinguish cooperative and competitive interactions by measuring species' responses to external perturbations.

q-bio.PE

Phase transition to chaos in complex ecosystems with non-reciprocal species-resource interactions

Non-reciprocal interactions between microscopic constituents can profoundly shape the large-scale properties of complex systems. Here, we investigate the effects of non-reciprocity in the context of theoretical ecology by analyzing a generalization of MacArthur's consumer-resource model with asymmetric interactions between species and resources. Using a mixture of analytic cavity calculations and numerical simulations, we show that such ecosystems generically undergo a phase transition to chaotic dynamics as the amount of non-reciprocity is increased. We analytically construct the phase diagram for this model and show that the emergence of chaos is controlled by a single quantity: the ratio of surviving species to surviving resources. We also numerically calculate the Lyapunov exponents in the chaotic phase and carefully analyze finite-size effects. Our findings show how non-reciprocal interactions can give rise to complex and unpredictable dynamical behaviors even in the simplest ecological consumer-resource models.

physics.bio-ph

Geometry of ecological coexistence and niche differentiation

A fundamental problem in ecology is to understand how competition shapes biodiversity and species coexistence. Historically, one important approach for addressing this question has been to analyze consumer resource models using geometric arguments. This has led to broadly applicable principles such as Tilman's $R^*$ and species coexistence cones. Here, we extend these arguments by constructing a novel geometric framework for understanding species coexistence based on convex polytopes in the space of consumer preferences. We show how the geometry of consumer preferences can be used to predict species which may coexist and enumerate ecologically-stable steady states and transitions between them. Collectively, these results provide a framework for understanding the role of species traits within niche theory.

q-bio.PE

Emergent competition shapes the ecological properties of multi-trophic ecosystems

Ecosystems are commonly organized into trophic levels -- organisms that occupy the same level in a food chain (e.g., plants, herbivores, carnivores). A fundamental question in theoretical ecology is how the interplay between trophic structure, diversity, and competition shapes the properties of ecosystems. To address this problem, we analyze a generalized Consumer Resource Model with three trophic levels using the zero-temperature cavity method and numerical simulations. We find that intra-trophic diversity gives rise to ``emergent competition'' between species within a trophic level due to feedbacks mediated by other trophic levels. This emergent competition gives rise to a crossover from a regime of top-down control (populations are limited by predators) to a regime of bottom-up control (populations are limited by primary producers) and is captured by a simple order parameter related to the ratio of surviving species in different trophic levels. We show that our theoretical results agree with empirical observations, suggesting that the theoretical approach outlined here can be used to understand complex ecosystems with multiple trophic levels.

q-bio.PE

Integrating local energetics into Maxwell-Calladine constraint counting to design mechanical metamaterials

The Maxwell-Calladine index theorem plays a central role in our current understanding of the mechanical rigidity of discrete materials. By considering the geometric constraints each material component imposes on a set of underlying degrees of freedom, the theorem relates the emergence of rigidity to constraint counting arguments. However, the Maxwell-Calladine paradigm is significantly limited -- its exclusive reliance on the geometric relationships between constraints and degrees of freedom completely neglects the actual energetic costs of deforming individual components. To address this limitation, we derive a generalization of the Maxwell-Calladine index theorem based on susceptibilities that naturally incorporate local energetic properties such as stiffness and prestress. Using this extended framework, we investigate how local energetics modify the classical constraint counting picture to capture the relationship between deformations and external forces. We then combine this formalism with group representation theory to design mechanical metamaterials where differences in symmetry between local energy costs and structural geometry are exploited to control responses to external forces.

cond-mat.soft

Thermodynamic origins of topological protection in nonequilibrium stochastic systems

Topological protection has emerged as an organizing principle for understanding and engineering robust collective behavior in electronic and material systems. Recent work suggests that topology may also play a role in organizing stochastic processes relevant to biology and self-assembly. Here, we show that topological protection in chemical networks can be understood entirely in terms of nonequilibrium thermodynamics. We illustrate these ideas using simple examples inspired by the literature.

cond-mat.stat-mech