arXiv subjects

Paul François

Publications and source records attributed to Paul François.

12 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

Learning the principles of T cell antigen discernment

T cells are central to the adaptive immune response, capable of detecting pathogenic antigens while ignoring healthy tissues with remarkable specificity and sensitivity. Quantitatively understanding how T cell receptors (TCRs) discriminate among antigens requires biophysical models and theoretical analysis of signaling networks. Here, we review current theoretical frameworks of antigen recognition in the context of modern experimental and computational advances. Antigen potency spans a continuum and exhibits nonlinear effects within complex mixtures, challenging discrete classification and simple threshold-based models. This complexity motivates the development of models such as adaptive kinetic proofreading, which integrate both activating and inhibitory signals. Advances in high-throughput technologies now generate large-scale, quantitative datasets, enabling the refinement of such models through statistical and machine learning approaches. This convergence of theory, data, and computation promises deeper insights into immune decision-making and opens new avenues for rational immunotherapy design.

q-bio.MN↗

arXiv2024

Unclocklike oscillators with frequency memory for the entrainment of biological clocks

Entrainment experiments on the vertebrate segmentation clock have revealed that embryonic oscillators actively change their internal frequency to adapt to the driving signal. This is neither consistent with a one-dimensional clock model nor with a limit-cycle model, but rather suggests a new "unclocklike" behavior. In this work, we propose simple, biologically realistic descriptions of such internal frequency adaptation, where a phase oscillator activates a memory variable controlling the oscillator's frequency. We study two opposite limits for the control of the memory variable, one with a smooth phase-averaging memory field, and the other with a pulsatile, phase-dependent activation. Both models recapitulate intriguing properties of the entrained segmentation clock, such as very broad Arnold tongues and an entrainment phase plateauing with detuning. We compute analytically multiple properties of such systems, such as entrainment phases and cycle shapes. We further describe new phenomena, including hysteresis in entrainment, bistability in the frequency of the entrained oscillator, and probabilistic entrainment. Our work shows that oscillators with frequency memory can exhibit new classes of unclocklike properties, that can be tested through experimental entrainment.

physics.bio-ph↗

arXiv2024

Waves, patterns and bifurcations: a tutorial review on the vertebrate segmentation clock

Proper vertebrae formation relies on a tissue-wide oscillator called the segmentation clock. Individual cellular oscillators in the presomitic mesoderm are modulated by intercellular coupling and external signals, leading to the propagation of oscillatory waves of genetic expression eventually stabilizing into a static pattern. Here, we review 4 decades of biophysical models of this process, starting from the pioneering Clock and Wavefront model by Cooke and Zeeman, and the reaction-diffusion model by Meinhardt. We discuss how modern descriptions followed advances in molecular description and visualization of the process, reviewing phase models, delayed models, systems-level, and finally geometric models. We connect models to high-level aspects of embryonic development from embryonic scaling to wave propagation, up to reconstructed stem cell systems. We provide new analytical calculations and insights into classical and recent models, leading us to propose a geometric description of somitogenesis organized along two primary waves of differentiation.

q-bio.MN↗

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↗

arXiv2019

Attack and defence in cellular decision-making: lessons from machine learning

Machine learning algorithms can be fooled by small well-designed adversarial perturbations. This is reminiscent of cellular decision-making where ligands (called antagonists) prevent correct signalling, like in early immune recognition. We draw a formal analogy between neural networks used in machine learning and models of cellular decision-making (adaptive proofreading). We apply attacks from machine learning to simple decision-making models, and show explicitly the correspondence to antagonism by weakly bound ligands. Such antagonism is absent in more nonlinear models, which inspired us to implement a biomimetic defence in neural networks filtering out adversarial perturbations. We then apply a gradient-descent approach from machine learning to different cellular decision-making models, and we reveal the existence of two regimes characterized by the presence or absence of a critical point for the gradient. This critical point causes the strongest antagonists to lie close to the decision boundary. This is validated in the loss landscapes of robust neural networks and cellular decision-making models, and observed experimentally for immune cells. For both regimes, we explain how associated defence mechanisms shape the geometry of the loss landscape, and why different adversarial attacks are effective in different regimes. Our work connects evolved cellular decision-making to machine learning, and motivates the design of a general theory of adversarial perturbations, both for in vivo and in silico systems.

physics.bio-ph↗

arXiv2018

Numerical parameter space compression and its application to microtubule dynamic instability

Physical models of biological systems can become difficult to interpret when they have a large number of parameters. But the models themselves actually depend on (i.e. are sensitive to) only a subset of those parameters. Rigorously identifying this subset of "stiff" parameters has been made possible by the development of parameter space compression (PSC). However, PSC has only been applied to analytically-solvable physical models. We have generalized this powerful method by developing a numerical approach to PSC that can be applied to any computational model. We validated our method against analytically-solvable models of random walk with drift and protein production and degradation. We then applied our method to an active area of biophysics research, namely to a simple computational model of microtubule dynamic instability. Such models have become increasingly complex, perhaps unnecessarily. By adding two new parameters that account for prominent structural features of microtubules, we identify one that can be "compressed away" (the "seam" in the microtubule) and another that is essential to model performance (the "tapering" of microtubule ends). Furthermore, we show that the microtubule model has an underlying, low-dimensional structure that explains the vast majority of our experimental data. We argue that numerical PSC can identify the low-dimensional structure of any computational model in biophysics. The low-dimensional structure of a model is easier to interpret and identifies the mechanisms and experiments that best characterize the system.

physics.bio-ph↗

arXiv2017

Untangling the hairball: fitness based asymptotic reduction of biological networks

Complex mathematical models of interaction networks are routinely used for prediction in systems biology. However, it is difficult to reconcile network complexities with a formal understanding of their behavior. Here, we propose a simple procedure (called $\bar φ$) to reduce biological models to functional submodules, using statistical mechanics of complex systems combined with a fitness-based approach inspired by $\textit{in silico}$ evolution. $\bar φ$ works by putting parameters or combination of parameters to some asymptotic limit, while keeping (or slightly improving) the model performance, and requires parameter symmetry breaking for more complex models. We illustrate $\bar φ$ on biochemical adaptation and on different models of immune recognition by T cells. An intractable model of immune recognition with close to a hundred individual transition rates is reduced to a simple two-parameter model. $\bar φ$ extracts three different mechanisms for early immune recognition, and automatically discovers similar functional modules in different models of the same process, allowing for model classification and comparison. Our procedure can be applied to biological networks based on rate equations using a fitness function that quantifies phenotypic performance.

physics.bio-ph↗

arXiv2016

Phenotypic spandrel: absolute discrimination and ligand antagonism

We consider the general problem of sensitive and specific discrimination between biochemical species. An important instance is immune discrimination between self and not-self, where it is also observed experimentally that ligands just below discrimination threshold negatively impact response, a phenomenon called antagonism. We characterize mathematically the generic properties of such discrimination, first relating it to biochemical adaptation. Then, based on basic biochemical rules, we establish that, surprisingly, antagonism is a generic consequence of any strictly specific discrimination made independently from ligand concentration. Thus antagonism constitutes a "phenotypic spandrel": a phenotype existing as a necessary by-product of another phenotype. We exhibit a simple analytic model of discrimination displaying antagonism, where antagonism strength is linear in distance from detection threshold. This contrasts with traditional proofreading based models where antagonism vanishes far from threshold and thus displays an inverted hierarchy of antagonism compared to simpler models. The phenotypic spandrel studied here is expected to structure many decision pathways such as immune detection mediated by TCRs and FC$ε$RIs, as well as endocrine signalling/disruption.

q-bio.MN↗

arXiv2015

The case for absolute ligand discrimination : modeling information processing and decision by immune T cells

Some cells have to take decision based on the quality of surroundings ligands, almost irrespective of their quantity, a problem we name "absolute discrimination". An example of absolute discrimination is recognition of not-self by immune T Cells. We show how the problem of absolute discrimination can be solved by a process called "adaptive sorting". We review several implementations of adaptive sorting, as well as its generic properties such as antagonism. We show how kinetic proofreading with negative feedback implements an approximate version of adaptive sorting in the immune context. Finally, we revisit the decision problem at the cell population level, showing how phenotypic variability and feedbacks between population and single cells are crucial for proper decision.

q-bio.CB↗

arXiv2015

Embryonic Elongation controlled by Graded Cell Fate: A Molecular Dynamics Approach

Regression of Hensen's node from anterior to posterior is driving the elongation and patterning of avian embryo body. Recent experiments link gradient of presomitic mesoderm cell motility to displacement of the node and body axis elongation. Ingression of new cells into presomitic mesoderm tissue also contributes to the process. At present, movements of presomitic mesoderm can be tracked at single cell precision. Yet, mechanisms that couple these movements to regression and axis elongation are largely unknown. In this work we develop a computational approach to study regression of Hensen's node and the elongation of anterior-posterior body axis. Based on our simulations we propose that regression and the elongation are a result of the influx of new mesoderm cells mediated by cell density gradient. Addition of new cells leads to expansion of tissue in anterior-posterior direction (elongation) and pushes node towards posterior (regression). Motility gradient of cells further aids regression by biasing tissue expansion towards more motile posterior. We show that our model reproduces experimentally observed differences in presomitic mesoderm cell movements and regression of Hensen's node in various embryo phenotypes.

q-bio.QM↗

arXiv2013

Principles of Adaptive Sorting Revealed by In Silico Evolution

Many biological networks have to filter out useful information from a vast excess of spurious interactions. We use computational evolution to predict design features of networks processing ligand categorization. The important problem of early immune response is considered as a case-study. Rounds of evolution with different constraints uncover elaborations of the same network motif we name adaptive sorting. Corresponding network substructures can be identified in current models of immune recognition. Our work draws a deep analogy between immune recognition and biochemical adaptation.

q-bio.MN↗