arXiv subjects

Massimo Vergassola

Publications and source records attributed to Massimo Vergassola.

At least 19 recordsLinked to original sources

arXiv2025

Fast decisions with biophysically constrained gene promoter architectures

Cells integrate signals and make decisions about their future state in short amounts of time. A lot of theoretical effort has gone into asking how to best design gene regulatory circuits that fulfill a given function, yet little is known about the constraints that performing that function in a small amount of time imposes on circuit architectures. Using an optimization framework, we explore the properties of a class of promoter architectures that distinguish small differences in transcription factor concentrations under time constraints. We show that the full temporal trajectory of gene activity allows for faster decisions than its integrated activity represented by the total number of transcribed mRNA. The topology of promoter architectures that allow for rapidly distinguishing low transcription factor concentrations result in a low, shallow, and non cooperative response, while at high concentrations, the response is high and cooperative. In the presence of non-cognate ligands, networks with fast and accurate decision times need not be optimally selective, especially if discrimination is difficult. While optimal networks are generically out of equilibrium, the energy associated with that irreversibility is only modest, and negligible at small concentrations. Instead, our results highlight the crucial role of rate-limiting steps imposed by biophysical constraints.

q-bio.MN↗

arXiv2025

Defects, parcellation, and renormalized negative diffusivities in non-homogeneous oscillatory media

Spatial non-homogeneities can synchronize clusters of spatially-extended oscillators in different frequency plateaus. Motivated by physiological rhythms, we fully characterize the phase diagram of a Ginzburg-Landau (GL) model with a gradient of frequencies. For large gradients and diffusion, the rest state is stable, and the linear spectrum around it maps onto the non-Hermitian Bloch-Torrey equation. When complex pairs of eigenvalues turn unstable, precursors of plateaus grow, separated by defects where the GL amplitude vanishes. Nonlinear effects either saturate the amplitude of plateaus or lead to a phase-locked state, with saddle-node bifurcations separating the two regimes. In the region of plateaus, we trace the formation of defects to a non-linear renormalization of the diffusivity, and determine the scaling of their number and length vs dynamical parameters.

nlin.PS↗

arXiv2025

Optimal trajectories for Bayesian olfactory search in turbulent flows: the low information limit and beyond

In turbulent flows, tracking the source of a passive scalar cue requires exploiting the limited information that can be gleaned from rare, stochastic encounters with the cue. When crafting a search policy, the most challenging and important decision is what to do in the absence of an encounter. In this work, we perform high-fidelity direct numerical simulations of a turbulent flow with a stationary source of tracer particles, and obtain quasi-optimal policies (in the sense of minimal average search time) with respect to the empirical encounter statistics. We study the trajectories under such policies and compare the results to those of the infotaxis heuristic. In the presence of a strong mean wind, the optimal motion in the absence of an encounter is zigzagging (akin to the well-known insect behavior "casting") followed by a return to the starting location. The zigzag motion generates characteristic $t^{1/2}$ scaling of the rms displacement envelope. By passing to the limit where the probability of detection vanishes, we connect these results to the classical linear search problem and derive an estimate of the tail of the arrival time pdf as a stretched exponential, which agrees with Monte Carlo results. We also discuss what happens as the wind speed decreases.

physics.flu-dyn↗

arXiv2025

Exploring Bayesian olfactory search in realistic turbulent flows

The problem of tracking the source of a passive scalar in a turbulent flow is relevant to flying insect behavior and several other applications. Extensive previous work has shown that certain Bayesian strategies, such as "infotaxis," can be very effective for this difficult "olfactory search" problem. More recently, a quasi-optimal Bayesian strategy was computed under the assumption that encounters with the scalar are independent. However, the Bayesian approach has not been adequately studied in realistic flows which exhibit spatiotemporal correlations. In this work, we perform direct numerical simulations (DNS) of an incompressible flow at $\mathrm{Re}_λ\simeq150,$ while tracking Lagrangian particles which are emitted by a point source and imposing a uniform mean flow with several magnitudes (including zero). We extract the spatially-dependent statistics of encounters with the particles, which we use to build Bayesian policies, including generalized ("space-aware") infotactic heuristics and quasi-optimal policies. We then assess the relative performance of these policies when they are used to search using scalar cue data from the DNS, and in particular study how this performance depends on correlations between encounters. Among other results, we find that quasi-optimal strategies continue to outperform heuristics in the presence of strong mean flow but fail to do so in the absence of a mean flow. We also explore how to choose optimal search parameters, including the frequency and threshold concentration of observation.

physics.flu-dyn↗

arXiv2024

Uncovering multiscale structure in the variability of larval zebrafish navigation

Animals chain movements into long-lived motor strategies, exhibiting variability across scales that reflects the interplay between internal states and environmental cues. To reveal structure in such variability, we build Markov models of movement sequences that bridges across time scales and enables a quantitative comparison of behavioral phenotypes among individuals. Applied to larval zebrafish responding to diverse sensory cues, we uncover a hierarchy of long-lived motor strategies, dominated by changes in orientation distinguishing cruising versus wandering strategies. Environmental cues induce preferences along these modes at the population level: while fish cruise in the light, they wander in response to aversive stimuli, or in search for appetitive prey. As our method encodes the behavioral dynamics of each individual fish in the transitions among coarse-grained motor strategies, we use it to uncover a hierarchical structure in the phenotypic variability that reflects exploration-exploitation trade-offs. Across a wide range of sensory cues, a major source of variation among fish is driven by prior and/or immediate exposure to prey that induces exploitation phenotypes. A large degree of variability that is not explained by environmental cues unravels motivational states that override the sensory context to induce contrasting exploration-exploitation phenotypes. Altogether, by extracting the timescales of motor strategies deployed during navigation, our approach exposes structure among individuals and reveals internal states tuned by prior experience.

physics.bio-ph↗

arXiv2024

Fluctuating landscapes and heavy tails in animal behavior

Animal behavior is shaped by a myriad of mechanisms acting on a wide range of scales, which hampers quantitative reasoning and the identification of general principles. Here, we combine data analysis and theory to investigate the relationship between behavioral plasticity and heavy-tailed statistics often observed in animal behavior. Specifically, we first leverage high-resolution recordings of C. elegans locomotion to show that stochastic transitions among long-lived behaviors exhibit heavy-tailed first passage time distributions and correlation functions. Such heavy tails can be explained by slow adaptation of behavior over time. This particular result motivates our second step of introducing a general model where we separate fast dynamics on a quasi-stationary multi-well potential, from non-ergodic, slowly varying modes. We then show that heavy tails generically emerge in such a model, and we provide a theoretical derivation of the resulting functional form, which can become a power law with exponents that depend on the strength of the fluctuations. Finally, we provide direct support for the generality of our findings by testing them in a C. elegans mutant where adaptation is suppressed and heavy tails thus disappear, and recordings of larval zebrafish swimming behavior where heavy tails are again prevalent.

cond-mat.stat-mech↗

arXiv2023

Optimal policies for Bayesian olfactory search in turbulent flows

In many practical scenarios, a flying insect must search for the source of an emitted cue which is advected by the atmospheric wind. On the macroscopic scales of interest, turbulence tends to mix the cue into patches of relatively high concentration over a background of very low concentration, so that the insect will only detect the cue intermittently and cannot rely on chemotactic strategies which simply climb the concentration gradient. In this work, we cast this search problem in the language of a partially observable Markov decision process (POMDP) and use the Perseus algorithm to compute strategies that are near-optimal with respect to the arrival time. We test the computed strategies on a large two-dimensional grid, present the resulting trajectories and arrival time statistics, and compare these to the corresponding results for several heuristic strategies, including (space-aware) infotaxis, Thompson sampling, and QMDP. We find that the near-optimal policy found by our implementation of Perseus outperforms all heuristics we test by several measures. We use the near-optimal policy to study how the search difficulty depends on the starting location. We discuss additionally the choice of initial belief and the robustness of the policies to changes in the environment. Finally, we present a detailed and pedagogical discussion about the implementation of the Perseus algorithm, including the benefits -- and pitfalls -- of employing a reward shaping function.

physics.flu-dyn↗

arXiv2021

Affinity maturation for an optimal balance between long-term immune coverage and short-term resource constraints

In order to target threatening pathogens, the adaptive immune system performs a continuous reorganization of its lymphocyte repertoire. Following an immune challenge, the B cell repertoire can evolve cells of increased specificity for the encountered strain. This process of affinity maturation generates a memory pool whose diversity and size remain difficult to predict. We assume that the immune system follows a strategy that maximizes the long-term immune coverage and minimizes the short-term metabolic costs associated with affinity maturation. This strategy is defined as an optimal decision process on a finite dimensional phenotypic space, where a pre-existing population of naive cells is sequentially challenged with a neutrally evolving strain. We unveil a trade-off between immune protection against future strains and the necessary reorganization of the repertoire. This plasticity of the repertoire drives the emergence of distinct regimes for the size and diversity of the memory pool, depending on the density of naive cells and on the mutation rate of the strain. The model predicts power-law distributions of clonotype sizes observed in data, and rationalizes antigenic imprinting as a strategy to minimize metabolic costs while keeping good immune protection against future strains.

q-bio.PE↗

arXiv2019

Hunchback promoters can readout morphogenetic positional information in less than a minute

The first cell fate decisions in the developing fly embryo are made very rapidly : hunchback genes decide in a few minutes whether a given nucleus follows the anterior or the posterior developmental blueprint by reading out the positional information encoded in the Bicoid morphogen. This developmental system constitutes a prototypical instance of the broad spectrum of regulatory decision processes that combine speed and accuracy. Traditional arguments based on fixed-time sampling of Bicoid concentration indicate that an accurate readout is not possible within the short times observed experimentally. This raises the general issue of how speed-accuracy tradeoffs are achieved. Here, we compare fixed-time sampling strategies to decisions made on-the-fly, which are based on updating and comparing the likelihoods of being at an anterior or a posterior location. We found that these more efficient schemes can complete reliable cell fate decisions even within the very short embryological timescales. We discuss the influence of promoter architectures on the mean decision time and decision error rate and present concrete promoter architectures that allow for the fast readout of the morphogen. Lastly, we formulate explicit predictions for new experiments involving Bicoid mutants.

q-bio.MN↗

arXiv2016

Complete coverage of space favors modularity of the grid system in the brain

Grid cells in the entorhinal cortex fire when animals that are exploring a certain region of space occupy the vertices of a triangular grid that spans the environment. Different neurons feature triangular grids that differ in their properties of periodicity, orientation and ellipticity. Taken together, these grids allow the animal to maintain an internal, mental representation of physical space. Experiments show that grid cells are modular, i.e. there are groups of neurons which have grids with similar periodicity, orientation and ellipticity. We use statistical physics methods to derive a relation between variability of the properties of the grids within a module and the range of space that can be covered completely (i.e. without gaps) by the grid system with high probability. Larger variability shrinks the range of representation, providing a functional rationale for the experimentally observed co-modularity of grid cell periodicity, orientation and ellipticity. We obtain a scaling relation between the number of neurons and the period of a module, given the variability and coverage range. Specifically, we predict how many more neurons are required at smaller grid scales than at larger ones.

q-bio.NC↗

arXiv2016

Infomax strategies for an optimal balance between exploration and exploitation

Proper balance between exploitation and exploration is what makes good decisions, which achieve high rewards like payoff or evolutionary fitness. The Infomax principle postulates that maximization of information directs the function of diverse systems, from living systems to artificial neural networks. While specific applications are successful, the validity of information as a proxy for reward remains unclear. Here, we consider the multi-armed bandit decision problem, which features arms (slot-machines) of unknown probabilities of success and a player trying to maximize cumulative payoff by choosing the sequence of arms to play. We show that an Infomax strategy (Info-p) which optimally gathers information on the highest mean reward among the arms saturates known optimal bounds and compares favorably to existing policies. The highest mean reward considered by Info-p is not the quantity actually needed for the choice of the arm to play, yet it allows for optimal tradeoffs between exploration and exploitation.

cs.LG↗

arXiv2015

The Impact of Environmental Fluctuations on Evolutionary Fitness Functions

The concept of fitness as a measure for a species's success in natural selection is central to the theory of evolution. We here investigate how reproduction rates which are not constant but vary in response to environmental fluctuations, influence a species' prosperity and thereby its fitness. Interestingly, we find that not only larger growth rates but also reduced sensitivities to environmental changes substantially increase the fitness. Thereby, depending on the noise level of the environment, it might be an evolutionary successful strategy to minimize this sensitivity rather than to optimize the reproduction speed. Also for neutral evolution, where species with exactly the same properties compete, variability in the growth rates plays a crucial role. The time for one species to fixate is strongly reduced in the presence of environmental noise. Hence, environmental fluctuations constitute a possible explanation for effective population sizes inferred from genetic data that often are much smaller than the census population size.

q-bio.PE↗

arXiv2015

Evolutionary Fitness in Variable Environments

One essential ingredient of evolutionary theory is the concept of fitness as a measure for a species' success in its living conditions. Here, we quantify the effect of environmental fluctuations onto fitness by analytical calculations on a general evolutionary model and by studying corresponding individual-based microscopic models. We demonstrate that not only larger growth rates and viabilities, but also reduced sensitivity to environmental variability substantially increases the fitness. Even for neutral evolution, variability in the growth rates plays the crucial role of strongly reducing the expected fixation times. Thereby, environmental fluctuations constitute a mechanism to account for the effective population sizes inferred from genetic data that often are much smaller than the census population size.

q-bio.PE↗

arXiv2014

Odor Landscapes in Turbulent Environments

The olfactory system of male moths is exquisitely sensitive to pheromones emitted by females and transported in the environment by atmospheric turbulence. Moths respond to minute amounts of pheromones and their behavior is sensitive to the fine-scale structure of turbulent plumes where pheromone concentration is detectible. The signal of pheromone whiffs is qualitatively known to be intermittent, yet quantitative characterization of its statistical properties is lacking. This challenging fluid dynamics problem is also relevant for entomology, neurobiology and the technological design of olfactory stimulators aimed at reproducing physiological odor signals in well-controlled laboratory conditions. Here, we develop a Lagrangian approach to the transport of pheromones by turbulent flows and exploit it to predict the statistics of odor detection during olfactory searches. The theory yields explicit probability distributions for the intensity and the duration of pheromone detections, as well as their spacing in time. Predictions are favorably tested by using numerical simulations, laboratory experiments and field data for the atmospheric surface layer. The resulting signal of odor detections lends to implementation with state-of-the-art technologies and quantifies the amount and the type of information that male moths can exploit during olfactory searches.

q-bio.QM↗

arXiv2010

Statistical distribution of quantum entanglement for a random bipartite state

We compute analytically the statistics of the Renyi and von Neumann entropies (standard measures of entanglement), for a random pure state in a large bipartite quantum system. The full probability distribution is computed by first mapping the problem to a random matrix model and then using a Coulomb gas method. We identify three different regimes in the entropy distribution, which correspond to two phase transitions in the associated Coulomb gas. The two critical points correspond to sudden changes in the shape of the Coulomb charge density: the appearance of an integrable singularity at the origin for the first critical point, and the detachement of the rightmost charge (largest eigenvalue) from the sea of the other charges at the second critical point. Analytical results are verified by Monte Carlo numerical simulations. A short account of some of these results appeared recently in Phys. Rev. Lett. {\bf 104}, 110501 (2010).

cond-mat.stat-mech↗

arXiv2009

Phase Transitions in the Distribution of Bipartite Entanglement of a Random Pure State

Using a Coulomb gas method, we compute analytically the probability distribution of the Renyi entropies (a standard measure of entanglement) for a random pure state of a large bipartite quantum system. We show that, for any order q>1 of the Renyi entropy, there are two critical values at which the entropy's probability distribution changes shape. These critical points correspond to two different transitions in the corresponding charge density of the Coulomb gas: the disappearance of an integrable singularity at the origin and the detachement of a single-charge drop from the continuum sea of all the other charges. These transitions respectively control the left and right tails of the entropy's probability distribution, as verified also by Monte Carlo numerical simulations of the Coulomb gas equilibrium dynamics.

cond-mat.stat-mech↗

arXiv2008

Large Deviations of the Maximum Eigenvalue for Wishart and Gaussian Random Matrices

We present a simple Coulomb gas method to calculate analytically the probability of rare events where the maximum eigenvalue of a random matrix is much larger than its typical value. The large deviation function that characterizes this probability is computed explicitly for Wishart and Gaussian ensembles. The method is quite general and applies to other related problems, e.g. the joint large deviation function for large fluctuations of top eigenvalues. Our results are relevant to widely employed data compression techniques, namely the principal components analysis. Analytical predictions are verified by extensive numerical simulations.

cond-mat.stat-mech↗

arXiv2008

Belief Propagation and Beyond for Particle Tracking

We describe a novel approach to statistical learning from particles tracked while moving in a random environment. The problem consists in inferring properties of the environment from recorded snapshots. We consider here the case of a fluid seeded with identical passive particles that diffuse and are advected by a flow. Our approach rests on efficient algorithms to estimate the weighted number of possible matchings among particles in two consecutive snapshots, the partition function of the underlying graphical model. The partition function is then maximized over the model parameters, namely diffusivity and velocity gradient. A Belief Propagation (BP) scheme is the backbone of our algorithm, providing accurate results for the flow parameters we want to learn. The BP estimate is additionally improved by incorporating Loop Series (LS) contributions. For the weighted matching problem, LS is compactly expressed as a Cauchy integral, accurately estimated by a saddle point approximation. Numerical experiments show that the quality of our improved BP algorithm is comparable to the one of a fully polynomial randomized approximation scheme, based on the Markov Chain Monte Carlo (MCMC) method, while the BP-based scheme is substantially faster than the MCMC scheme.

cs.IT↗