INBIO : Méthodes expérimentales et computationnelles pour la modélisation des processus cellulaires

Universal observations in Biology are sometimes described as "laws". In E. coli, experimental studies performed over the past six decades have revealed major growth laws relating ribosomal mass fraction and cell size to the growth rate. Because they formalize complex emerging principles in biology, growth laws have been instrumental in shaping our understanding of bacterial physiology. Here, we discovered a novel size law that connects cell size to the inverse of the metabolic proteome mass fraction and the active fraction of ribosomes. We used a simple whole-cell coarse-grained model of cell physiology that combines the proteome allocation theory and the structural model of cell division. This integrated model captures all available experimental data connecting the cell proteome composition, ribosome activity, division size and growth rate in response to nutrient quality, antibiotic treatment and increased protein burden. Finally, a stochastic extension of the model explains non-trivial correlations observed in single cell experiments including the adder principle. This work provides a simple and robust theoretical framework for studying the fundamental principles of cell size determination in unicellular organisms.

Across diverse biological systems-ranging from neural networks to intracellular signaling and genetic regulatory networks-the information about changes in the environment is frequently encoded in the full temporal dynamics of the network nodes. A pressing data-analysis challenge has thus been to efficiently estimate the amount of information that these dynamics convey from experimental data. Here we develop and evaluate decoding-based estimation methods to lower bound the mutual information about a finite set of inputs, encoded in single-cell high-dimensional time series data. For biological reaction networks governed by the chemical Master equation, we derive model-based information approximations and analytical upper bounds, against which we benchmark our proposed model-free decoding estimators. In contrast to the frequently-used k-nearest-neighbor estimator, decoding-based estimators robustly extract a large fraction of the available information from high-dimensional trajectories with a realistic number of data samples. We apply these estimators to previously published data on Erk and Ca2+ signaling in mammalian cells and to yeast stress-response, and find that substantial amount of information about environmental state can be encoded by non-trivial response statistics even in stationary signals. We argue that these single-cell, decoding-based information estimates, rather than the commonly-used tests for significant differences between selected population response statistics, provide a proper and unbiased measure for the performance of biological signaling networks.

Optimizing the production of recombinant proteins is a problem of major industrial and pharmaceutical importance. Secretion of the protein by the host cell considerably simplifies downstream purification processes. However, for many proteins, this is also the limiting production step. Current solutions involve extensive engineering of the chassis cell to facilitate protein trafficking and limit protein degradation triggered by excessive secretion-associated stress. Here, we propose instead a regulation-based strategy in which induction is dynamically adjusted to an optimal strength based on the current stress level of the cells. Using a small collection of hard-to-secrete proteins, a bioreactor-based platform with automated cytometry measurements, and a systematic assay to quantify secreted protein levels, we demonstrate that the secretion sweet spot is indicated by the appearance of a subpopulation of cells that accumulate high amounts of proteins, decrease growth, and face significant stress, that is, experience a secretion burnout. In these cells, adaptations capabilities are overwhelmed by a too strong production. Using these notions, we show for a single-chain antibody variable fragment that secretion levels can be improved by 70% by dynamically keeping the cell population at optimal stress levels using real-time closed-loop control.

Mathematical models have been used successfully at diverse scales of biological organization, ranging from ecology and population dynamics to stochastic reaction events occurring between individual molecules in single cells. Generally, many biological processes unfold across multiple scales, with mutations being the best studied example of how stochasticity at the molecular scale can influence outcomes at the population scale. In many other contexts, however, an analogous link between micro- and macro-scale remains elusive, primarily due to the challenges involved in setting up and analyzing multi-scale models. Here, we employ such a model to investigate how stochasticity propagates from individual biochemical reaction events in the bacterial innate immune system to the ecology of bacteria and bacterial viruses. We show analytically how the dynamics of bacterial populations are shaped by the activities of immunity-conferring enzymes in single cells and how the ecological consequences imply optimal bacterial defense strategies against viruses. Our results suggest that bacterial populations in the presence of viruses can either optimize their initial growth rate or their population size, with the first strategy favoring simple immunity featuring a single restriction modification system and the second strategy favoring complex bacterial innate immunity featuring several simultaneously active restriction modification systems.

Discrete-state continuous-time Markov processes are an important class of models employed broadly across the sciences. When the system size becomes large, standard approaches can become intractable to exact solution and numerical simulation. Approximations posed on a continuous state space are often more tractable and are presumed to converge in the limit as the system size tends to infinity. For example, an expansion of the master equation truncated at second order yields the Fokker--Planck equation, a widely used continuum approximation equipped with an underlying process of continuous state. Surprisingly, in [C. R. Doering, K. V. Sargsyan, and L. M. Sander, Multiscale Model. Simul., 3 (2005), pp. 283--299] it is shown that the Fokker--Planck approximation may exhibit exponentially large errors, even in the infinite system-size limit. Crucially, the source of this inaccuracy has not been addressed. In this paper, we focus on the family of continuous-state approximations obtained by arbitrary-order truncations. We uncover how the exponentially large error stems from the truncation by quantifying the rapid error decay with increasing truncation order. Furthermore, we explain why this discrepancy only comes to light in a subset of problems. The approximations produced by finite truncation beyond second order lack underlying stochastic processes. Nevertheless, they retain valuable information that explains the previously observed discrepancy by bridging the gap between the continuous and discrete processes. The insight conferred by this broader notion of “continuum approximation,” where we do not require an underlying stochastic process, prompts us to revisit previously expressed doubts regarding continuum approximations. In establishing the utility of higher-order truncations, this approach also contributes to the extensive discussion in the literature regarding the second-order truncation: while recognizing the appealing features of an associated stochastic process, in certain cases it may be advantageous to dispense of the process in exchange for the increased approximation accuracy guaranteed by higher-order truncations.

Understanding and characterising biochemical processes inside single cells requires experimental platforms that allow one to perturb and observe the dynamics of such processes as well as computational methods to build and parameterise models from the collected data. Recent progress with experimental platforms and optogenetics has made it possible to expose each cell in an experiment to an individualised input and automatically record cellular responses over days with fine time resolution. However, methods to infer parameters of stochastic kinetic models from single-cell longitudinal data have generally been developed under the assumption that experimental data is sparse and that responses of cells to at most a few different input perturbations can be observed. Here, we investigate and compare different approaches for calculating parameter likelihoods of single-cell longitudinal data based on approximations of the chemical master equation (CME) with a particular focus on coupling the linear noise approximation (LNA) or moment closure methods to a Kalman filter. We show that, as long as cells are measured sufficiently frequently, coupling the LNA to a Kalman filter allows one to accurately approximate likelihoods and to infer model parameters from data even in cases where the LNA provides poor approximations of the CME. Furthermore, the computational cost of filtering-based iterative likelihood evaluation scales advantageously in the number of measurement times and different input perturbations and is thus ideally suited for data obtained from modern experimental platforms. To demonstrate the practical usefulness of these results, we perform an experiment in which single cells, equipped with an optogenetic gene expression system, are exposed to various different light-input sequences and measured at several hundred time points and use parameter inference based on iterative likelihood evaluation to parameterise a stochastic model of the system.

We consider a generic biological process described by a dynamical system, subject to an input signal with a high-frequency periodic component. The rapid oscillations of the input signal induce inherently multiscale dynamics, motivating order-reduction techniques. It is intuitive that the system behaviour is well approximated by its response to the averaged input signal. However, changes to the high-frequency component that preserve the average signal are beyond the reach of such intuitive reasoning. In this study, we explore system response under the influence of such an input signal by exploiting the timescale separation between high-frequency input variations and system response time. Employing the asymptotic method of multiple scales, we establish that, in some circumstances, the intuitive approach is simply the leading-order asymptotic contribution. We focus on higher-order corrections that capture the response to the details of the high-frequency component beyond its average. This approach achieves a reduction in system complexity while providing valuable insight into the structure of the response to the oscillations. We develop the general theory for nonlinear systems, while highlighting the important case of systems affine in the state and the input signal, presenting examples of both discrete and continuum state spaces. Importantly, this class of systems encompasses biochemical reaction networks described by the chemical master equation and its continuum approximations. Finally, we apply the framework to a nonlinear system describing mRNA translation and protein expression previously studied in the literature. The analysis shines new light on several aspects of the system quantification and both extends and simplifies results previously obtained.

This study describes a method for controlling the production of protein in individual cells using stochastic models of gene expression. By combining modern microscopy platforms with optogenetic gene expression, experimentalists are able to accurately apply light to individual cells, which can induce protein production. Here we use a finite state projection based stochastic model of gene expression, along with Bayesian state estimation to control protein copy numbers within individual cells. We compare this method to previous methods that use population based approaches. We also demonstrate the ability of this control strategy to ameliorate discrepancies between the predictions of a deterministic model and stochastic switching system.

.Motivated by recent laboratory experiments, we study microbial populations with light-inducible genetic differentiation that generates a two-species microbial consortium relevant for bioproduction. First, we derive a hierarchy of models describing the evolution of the microbial populations, each with decreasing complexity. This sequential order reduction reveals the connections between several popular classes of models used in this context. Second, we demonstrate the analytical insight the order reduction provides by studying the optimal control of such a reduced-order system of nonlinear ordinary differential equations. Appealing to Pontryagin's maximum principle, we find different optimal control structures within different regions of the parameter space. Explicit solutions are obtained in a subset of parameter space, while, for the remainder of parameter space, closed-form solutions are obtained that depend on a scalar value that solves a particular transcendental equation. We show that a unique solution of the scalar equation exists and lies in a known compact interval, making its numerical approximation particularly easy. The analytical results are verified against direct numerical calculations.Keywordsmicrobial consortiabioengineeringoptimal controlmathematical modelingMSC codes92-1093C1534H0549K15

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La résistance aux antibiotique est de plus en plus courante. En particulier, la fraction croissante d'Escherichia coli commensaux et pathogènes exprimant des bêta-lactamases à spectre étendu et/ou des carbapénémases est alarmante. E. coli est une cause majeure d'infections courantes telles que les infections urinaires, qui touchent plus de 150 millions de personnes dans le monde. Il est important de noter que de nombreuses infections récidivent. Il est donc essentiel de comprendre en profondeur la sensibilité des isolats cliniques d'E. coli aux bêta-lactamines pour proposer des traitements efficaces.Les bactéries peuvent échapper aux traitements de différentes manières. Les bactéries résistantes se développent et se divisent normalement en présence d'antibiotiques. Leur caractérisation est facile à l'aide de tests de diagnostic standard. Les bactéries tolérantes se contentent de survivre en présence d'antibiotiques et repoussent lorsque l'antibiotique est retiré ou dégradé. Ce comportement biphasique complique la prédiction des résultats du traitement. La résilience au traitement est notamment observée dans la tolérance collective aux antibiotiques, où les cellules mortes libèrent des bêta-lactamases qui dégradent l'antibiotique dans l'environnement. Les approches standard ne sont pas adaptées pour quantifier et comprendre le rôle de la résistance et/ou de la résilience.Nos principaux objectifs sont de quantifier la dynamique de la mort cellulaire au cours de traitements répétés et de quantifier l'impact des différentes conditions environnementaux sur la mort cellulaire. Tout d'abord, nous avons développé de nouveaux protocoles pour résoudre les problèmes de variabilité dans les mesures de densité optique, et pour effectuer des tests d'unités formant colonies d'une manière efficace. Grâce à ces techniques, nous avons généré un vaste ensemble de données décrivant l'impact de traitements répétés sur différents isolats cliniques. Nous avons calibré un modèle, précédemment développé par l'équipe, de la réponse de la population aux antibiotiques et de l'évolution de l'environnement dans le contexte de tolérance collective aux antibiotiques. Nous avons calibré le modèle sur l'ensemble de données, et nous avons montré que le modèle tient compte de l'évolution temporelle de la biomasse et du nombre de cellules vivantes. En outre, nous avons démontré qu'en utilisant ce modèle, nous pouvons prédire le nombre de cellules vivantes à partir des mesures de la biomasse.Dans ce travail, nous avons mis en évidence l'écart entre l'in vitro et l'in vivo en évaluant l'effet de différentes conditions de croissance sur la survie des cellules. Pour relever ce défi, nous avons étudié la réponse bactérienne dans l'urine humaine et dans le milieu de Mueller-Hinton (milieu utilisé pour les antibiogrammes standard), ainsi que dans un milieu défini avec différentes sources de carbone. Tout d'abord, nous avons observé une meilleure survie dans l'urine par rapport au milieu Mueller-Hinton, mais ce résultat variait en fonction de la souche et de la concentration d'antibiotique. Il est intéressant de noter que les données expérimentales ont montré que la concentration en nutriments n'avait pas d'effet sur le taux de croissance, mais un effet important sur la capacité de charge et la réponse aux antibiotiques. Grâce à l'étalonnage du modèle et à l'analyse des valeurs des paramètres du modèle, nous avons identifié des processus biologiques qui pourraient expliquer les différences entre le comportement des bactéries dans différents milieux.

Posté sur BioRxiv le 4 août 2021

International audience

International audience