arXiv subjects

Madhav Mani

Publications and source records attributed to Madhav Mani.

7 recordsLinked to original sources

arXiv2026

Sandscapes: self-modifying energy landscapes with emergent branching and flips

Energy landscapes provide a common framework for describing learning, embryonic development, and collective dynamics. Although such landscapes may evolve over time, their dynamics are typically prescribed externally rather than generated by the system itself. Here we get inspiration from biology to introduce sandscapes : self-modifying landscapes in which the motions of interacting agents continuously reshape the landscape that governs their own trajectories. We derive sandscapes from a minimal model of interacting Hopfield units, where the basins of each attractor are modulated by their occupancies. Sandscapes spontaneously generate sequential symmetry breaking and differentiation trees, with local branching described by coupled Ising dynamics. We then drive the dynamics of sandscapes (using local proliferation common in biology) and leverage catastrophe theory to show that sandscapes self-organize toward flip bifurcations, suggesting a generic mechanism for the emergence of ubiquitous binary cell-fate decisions. We further demonstrate that sandscapes can act as generative models of developmental trajectories : starting from terminal states alone, we reconstruct realistic hematopoietic differentiation trees with multiple layers of intermediate progenitor states. More broadly, our results identify sandscapes as a general principle of adaptive dynamics, explaining how feedback between agents and landscapes produces branching, criticality, and self-organization across learning and biology.

q-bio.QM↗

arXiv2025

The Environment-Dependent Regulatory Landscape of the E. coli Genome

All cells respond to changes in both their internal milieu and the environment around them through the regulation of their genes. Despite decades of effort, there remain huge gaps in our knowledge of both the function of many genes (the so-called y-ome) and how they adapt to changing environments via regulation. Here we describe a joint experimental and theoretical dissection of the regulation of a broad array of over 100 biologically interesting genes in E. coli across 39 diverse environments, permitting us to discover the binding sites and transcription factors that mediate regulatory control. Using a combination of mutagenesis, massively parallel reporter assays, mass spectrometry and tools from information theory and statistical physics, we go from complete ignorance of a promoter's environment-dependent regulatory architecture to predictive models of its behavior. As a proof of principle of the biological insights to be gained from such a study, we chose a combination of genes from the y-ome, toxin-antitoxin pairs, and genes hypothesized to be part of regulatory modules; in all cases, we discovered a host of new insights into their underlying regulatory landscape and resulting biological function.

q-bio.GN↗

arXiv2023

A Waddington landscape for prototype learning in generalized Hopfield networks

Networks in machine learning offer examples of complex high-dimensional dynamical systems reminiscent of biological systems. Here, we study the learning dynamics of Generalized Hopfield networks, which permit a visualization of internal memories. These networks have been shown to proceed through a 'feature-to-prototype' transition, as the strength of network nonlinearity is increased, wherein the learned, or terminal, states of internal memories transition from mixed to pure states. Focusing on the prototype learning dynamics of the internal memories we observe a strong resemblance to the canalized, or low-dimensional, dynamics of cells as they differentiate within a Waddingtonian landscape. Dynamically, we demonstrate that learning in a Generalized Hopfield Network proceeds through sequential 'splits' in memory space. Furthermore, order of splitting is interpretable and reproducible. The dynamics between the splits are canalized in the Waddington sense -- robust to variations in detailed aspects of the system. In attempting to make the analogy a rigorous equivalence, we study smaller subsystems that exhibit similar properties to the full system. We combine analytical calculations with numerical simulations to study the dynamical emergence of the feature-to-prototype transition, and the behaviour of splits in the landscape, saddles points, visited during learning. We exhibit regimes where saddles appear and disappear through saddle-node bifurcations, qualitatively changing the distribution of learned memories as the strength of the nonlinearity is varied -- allowing us to systematically investigate the mechanisms that underlie the emergence of Waddingtonian dynamics. Memories can thus differentiate in a predictive and controlled way, revealing new bridges between experimental biology, dynamical systems theory, and machine learning.

cond-mat.dis-nn↗

arXiv2020

Dimensionality-Reduction in the Drosophila Wing as Revealed by Landmark-Free Measure-ments of Phenotype

Organismal phenotypes emerge from a complex set of genotypic interactions. While technological advances in sequencing provide a quantitative description of an organism's genotype, characterization of an organism's physical phenotype lags far behind. Here, we relate genotype to the complex and multi-dimensional phenotype of an anatomical structure using the Drosophila wing as a model system. We develop a mathematical approach that enables a robust description of biologically salient phenotypic variation. Analysing natural phenotypic variation, and variation generated by weak perturbations in genetic and environmental conditions during development, we observe a highly constrained set of wing phenotypes. In a striking ex-ample of dimensionality reduction, the nature of varieties produced by the Drosophila developmental pro-gram is constrained to a single integrated mode of variation in the wing. Our strategy demonstrates the emergent simplicity manifest in the genotype-to-phenotype map in the Drosophila wing and may represent a general approach for interrogating a variety of genotype-phenotype relationships.

physics.bio-ph↗

arXiv2019

The Role of Intracellular Interactions in the Collective Polarization of Tissues and its Interplay with Cellular Geometry

Planar cell polarity (PCP), the coherent in-plane polarization of a tissue on multicellular length scales, provides directional information that guides a multitude of developmental processes at cellular and tissue levels. While it is manifest that cells utilize both intracellular and intercellular mechanisms, how the two produce the collective polarization remains an active area of investigation. We study the role of intracellular interactions in the large-scale spatial coherence of cell polarities, and scrutinize the role of intracellular interactions in the emergence of tissue-wide polarization. We demonstrate that nonlocal cytoplasmic interactions are necessary and sufficient for the robust long-range polarization, and are essential to the faithful detection of weak directional signals. In the presence of nonlocal interactions, signatures of geometrical information in tissue polarity become manifest. We investigate the deleterious effects of geometric disorder, and determine conditions on the cytoplasmic interactions that guarantee the stability of polarization. These conditions get progressively more stringent upon increasing the geometric disorder. Another situation where the role of geometrical information might be evident is elongated tissues. Strikingly, our model recapitulates an observed influence of tissue elongation on the orientation of polarity. Eventually, we introduce three classes of mutants: lack of membrane proteins, cytoplasmic proteins, and local geometrical irregularities. We adopt core-PCP as a model pathway, and interpret the model parameters accordingly, through comparing the in silico and in vivo phenotypes. This comparison helps us shed light on the roles of the cytoplasmic proteins in cell-cell communication, and make predictions regarding the cooperation of cytoplasmic and membrane proteins in long-range polarization.

physics.bio-ph↗

arXiv2017

Abortive Initiation as a Bottleneck for Transcription in the Early Drosophila Embryo

Gene transcription is a critical step in gene expression. The currently accepted physical model of transcription predicts the existence of a physical limit on the maximal rate of transcription, which does not depend on the transcribed gene. This limit appears as a result of polymerase "traffic jams" forming in the bulk of the 1D DNA chain at high polymerase concentrations. Recent experiments have, for the first time, allowed one to access live gene expression dynamics in the Drosophila fly embryo in vivo under the conditions of heavy polymerase load and test the predictions of the model. Our analysis of the data shows that the maximal rate of transcription is indeed the same for the Hunchback, Snail and Knirps gap genes, and modified gene constructs in nuclear cycles 13, 14, but the experimentally observed value of the maximal transcription rate corresponds to only 40 % of the one predicted by this model. We argue that such a decrease must be due to a slower polymerase elongation rate in the vicinity of the promoter region. This effectively shifts the bottleneck of transcription from the bulk to the promoter region of the gene. We suggest a quantitative explanation of the difference by taking into account abortive transcription initiation. Our calculations based on the independently measured abortive initiation constant in vitro confirm this hypothesis and find quantitative agreement with MS2 fluorescence live imaging data in the early fruit fly embryo. If our explanation is correct, then the transcription rate cannot be increased by replacing "slow codons" in the bulk with synonymous codons, and experimental efforts must be focused on the promoter region instead. This study extends our understanding of transcriptional regulation, re-examines physical constraints on the kinetics of transcription and re-evaluates the validity of the standard TASEP model of transcription.

physics.bio-ph↗

arXiv2017

Active Tension Network model reveals an exotic mechanical state realized in epithelial tissues

It is now widely recognized that mechanical interactions between cells play a crucial role in epithelial morphogenesis, yet understanding the mechanisms through which stress and deformation affect cell behavior remains an open problem due to the complexity inherent in the mechanical behavior of cells and the difficulty of direct measurement of forces within tissues. Theoretical models can help by focusing experimental studies and by providing the framework for interpreting measurements. To that end, "vertex models" have introduced an approximation of epithelial cell mechanics based on a polygonal tiling representation of planar tissue. Here we formulate and analyze an Active Tension Network (ATN) model, which is based on the same polygonal representation of epithelial tissue geometry, but in addition i) assumes that mechanical balance is dominated by cortical tension and ii) introduces tension dependent local remodeling of the cortex, representing the active nature of cytoskeletal mechanics. The tension-dominance assumption has immediate implications for the geometry of cells, which we demonstrate to hold in certain types of Drosophila epithelial tissues. We demonstrate that stationary configurations of an ATN form a manifold with one degree of freedom per cell, corresponding to "isogonal" - i.e. angle preserving - deformations of cells, which dominate the dynamic response to perturbations. We show that isogonal modes account for approximately 90% of experimentally observed deformation of cells during the process of ventral furrow formation in Drosophila. Other interesting properties of our model include the exponential screening of mechanical stress and a negative Poisson ratio response to external uniaxial stress. We also provide a new approach to the problem of inferring local cortical tensions from the observed geometry of epithelial cells in a tissue

q-bio.TO↗