Publications HAL de Yvinec

2024

titre
A Lifshitz–Slyozov type model for adipocyte size dynamics: limit from Becker–Döring system and numerical simulation
article
Journal of Mathematical Biology, 2024, 88 (2), pp.16. ⟨10.1007/s00285-023-02036-x⟩
resume
Biological data show that the size distribution of adipose cells follows a bimodal distribution. In this work, we introduce a Lifshitz-Slyozov type model, based on a transport partial differential equation, for the dynamics of the size distribution of adipose cells. We prove a new convergence result from the related Becker-Doring model, a system composed of several ordinary differential equations, toward mild solutions of the Lifshitz-Slyozov model using distribution tail techniques. Then, this result allows us to propose a new advective-diffusive model, the second-order diffusive Lifshitz-Slyozov model, which is expected to better fit the experimental data. Numerical simulations of the solutions to the diffusive Lifshitz-Slyozov model are performed using a well-balanced scheme and compared to solutions to the transport model. Those simulations show that both bimodal and unimodal profiles can be reached asymptotically depending on several parameters. We put in evidence that the asymptotic profile for the second-order system does not depend on initial conditions, unlike for the transport Lifshitz-Slyozov model.
Accès au texte intégral et bibtex
https://hal.inrae.fr/hal-04525358/file/articleMeyerRibotYvinec.pdf BibTex

2023

titre
Long-time asymptotic of the Lifshitz-Slyozov equation with nucleation
article
Kinetic and Related Models , In press, ⟨10.3934/krm.2023041⟩
resume
We consider the Lifshitz-Slyozov model with inflow boundary conditions of nucleation type. We show that for a collection of representative rate functions the size distributions approach degenerate states concentrated at zero size for sufficiently large times. The proof relies on monotonicity properties of some quantities associated to an entropy functional. Moreover, we give numerical evidence on the fact that the convergence rate to the goal state is algebraic in time. Besides their mathematical interest, these results can be relevant for the interpretation of experimental data.
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https://hal.science/hal-04098262/file/ls-final_black.pdf BibTex

2022

titre
An overview of deep learning applications in precocious puberty and thyroid dysfunction
article
Frontiers in Endocrinology, 2022, 13, pp.959546. ⟨10.3389/fendo.2022.959546⟩
resume
In the last decade, deep learning methods have garnered a great deal of attention in endocrinology research. In this article, we provide a summary of current deep learning applications in endocrine disorders caused by either precocious onset of adult hormone or abnormal amount of hormone production. To give access to the broader audience, we start with a gentle introduction to deep learning and its most commonly used architectures, and then we focus on the research trends of deep learning applications in thyroid dysfunction classification and precocious puberty diagnosis. We highlight the strengths and weaknesses of various approaches and discuss potential solutions to different challenges. We also go through the practical considerations useful for choosing (and building) the deep learning model, as well as for understanding the thought process behind different decisions made by these models. Finally, we give concluding remarks and future directions.
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https://hal.science/hal-03824764/file/fendo-13-959546.pdf BibTex
titre
Averaging of a stochastic slow-fast model for population dynamics: application to the development of ovarian follicles
article
SIAM Journal on Applied Mathematics, 2022, 82 (1), pp.359-380. ⟨10.1137/21M1409615⟩
resume
We analyze a birth, migration and death stochastic process modeling the dynamics of a finite population, in which individuals transit unidirectionally across successive compartments. The model is formulated as a continuous-time Markov chain, whose transition matrix involves multiscale effects; the whole (or part of the) population affects the rates of individual birth, migration and death events. Using the slow-fast property of the model, we prove the existence and uniqueness of the limit model in the framework of stochastic singular perturbations. The derivation of the limit model is based on compactness and coupling arguments. The uniqueness is handled by applying the ergodicity theory and studying a dedicated Poisson equation. The limit model consists of an ordinary-differential equation ruling the dynamics of the first (slow) compartment, coupled with a quasi-stationary distribution in the remaining (fast) compartments, which averages the contribution of the fast component of the Markov chain on the slow one. We illustrate numerically the convergence, and highlight the relevance of dealing with nonlinear event rates for our application in reproductive biology. The numerical simulations involve a simple integration scheme for the deterministic part, coupled with the nested algorithm to sample the quasi-stationary distribution.
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https://hal.science/hal-03405177/file/ManuscritGB-FC-RY.pdf BibTex

2021

titre
The initial-boundary value problem for the Lifshitz-Slyozov equation with non-smooth rates at the boundary
article
Nonlinearity, 2021, 34 (04), pp.1975-2017. ⟨10.1088/1361-6544/abd3f3⟩
resume
We prove existence and uniqueness of solutions to the initialboundary value problem for the Lifshitz-Slyozov equation (a nonlinear transport equation on the half-line), focusing on the case of kinetic rates with unbounded derivative at the origin. Our theory covers in particular those cases with rates behaving as power laws at the origin, for which an inflow behavior is expected and a boundary condition describing nucleation phenomena needs to be imposed. The method we introduce here to prove existence is based on a formulation in terms of characteristics, with a careful analysis on the behavior near the singular boundary. As a byproduct we provide a general theory for linear continuity equations on a half-line with transport fields that degenerate at the boundary. We also address both the maximality and the uniqueness of inflow solutions to the Lifshitz-Slyozov model, exploiting monotonicity properties of the associated transport equation.
Accès au texte intégral et bibtex
https://hal.inrae.fr/hal-03109431/file/revision_v8_submitted.pdf BibTex
titre
Stochastic nonlinear model for somatic cell population dynamics during ovarian follicle activation
article
Journal of Mathematical Biology, 2021, 82 (3), pp.1-52. ⟨10.1007/s00285-021-01561-x⟩
resume
In mammals, female germ cells are sheltered within somatic structures called ovarian follicles, which remain in a quiescent state until they get activated, all along reproductive life. We investigate the sequence of somatic cell events occurring just after follicle activation, starting by the awakening of precursor somatic cells, and their transformation into proliferative cells. We introduce a nonlinear stochastic model accounting for the joint dynamics of the two cell types, and allowing us to investigate the potential impact of a feedback from proliferative cells onto precursor cells. To tackle the key issue of whether cell proliferation is concomitant or posterior to cell awakening, we assess both the time needed for all precursor cells to {awake}, and the corresponding increase in the total cell number with respect to the initial cell number. Using the probabilistic theory of first passage times, we design a numerical scheme based on a rigorous Finite State Projection and coupling techniques to compute the mean extinction time and the cell number at extinction time. We find that the feedback term clearly lowers the number of proliferative cells at the extinction time. We calibrate the model parameters using an exact likelihood approach. We carry out a comprehensive comparison between the initial model and a series of submodels, which helps to select the critical cell events taking place during activation, and suggests that awakening is prominent over proliferation.
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https://inria.hal.science/hal-02057983/file/main_finalversion.pdf BibTex
titre
Quasi-stationary distribution and metastability for the stochastic Becker-Döring model
article
Electronic Communications in Probability, 2021, 26, ⟨10.1214/21-ECP411⟩
resume
We study a stochastic version of the classical Becker-Döring model, a well-known kinetic model for cluster formation that predicts the existence of a long-lived metastable state before a thermodynamically unfavorable nucleation occurs, leading to a phase transition phenomena. This continuous-time Markov chain model has received little attention, compared to its deterministic differential equations counterpart. We show that the stochastic formulation leads to a precise and quantitative description of stochastic nucleation events thanks to an exponentially ergodic quasi-stationary distribution for the process conditionally on nucleation has not yet occurred.
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https://hal.science/hal-03110670/file/v15_12pages.pdf BibTex
titre
Pharmacological characterization of low molecular weight biased agonists at the follicle stimulating hormone receptor
article
International Journal of Molecular Sciences, 2021, 22 (18), pp.1-23. ⟨10.3390/ijms22189850⟩
resume
Follicle-stimulating hormone receptor (FSHR) plays a key role in reproduction through the activation of multiple signaling pathways. Low molecular weight (LMW) ligands composed of biased agonist properties are highly valuable tools to decipher complex signaling mechanisms as they allow selective activation of discrete signaling cascades. However, available LMW FSHR ligands have not been fully characterized yet. In this context, we explored the pharmacological diversity of three benzamide and two thiazolidinone derivatives compared to FSH. Concentration/activity curves were generated for Gαs, Gαq, Gαi, β-arrestin 2 recruitment, and cAMP production, using BRET assays in living cells. ERK phosphorylation was analyzed by Western blotting, and CRE-dependent transcription was assessed using a luciferase reporter assay. All assays were done in either wild-type, Gαs or β-arrestin 1/2 CRISPR knockout HEK293 cells. Bias factors were calculated for each pair of read-outs by using the operational model. Our results show that each ligand presented a discrete pharmacological efficacy compared to FSH, ranging from super-agonist for β-arrestin 2 recruitment to pure Gαs bias. Interestingly, LMW ligands generated kinetic profiles distinct from FSH (i.e., faster, slower or transient, depending on the ligand) and correlated with CRE-dependent transcription. In addition, clear system biases were observed in cells depleted of either Gαs or β-arrestin genes. Such LMW properties are useful pharmacological tools to better dissect the multiple signaling pathways activated by FSHR and assess their relative contributions at the cellular and physio-pathological levels
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https://hal.science/hal-03351267/file/ijms-22-09850-v2.pdf BibTex

2020

titre
Multiscale population dynamics in reproductive biology: singular perturbation reduction in deterministic and stochastic models
article
ESAIM: Proceedings and Surveys, 2020, 67, pp.72-99. ⟨10.1051/proc/202067006⟩
resume
In this study, we describe different modeling approaches for ovarian follicle population dynamics, based on either ordinary (ODE), partial (PDE) or stochastic (SDE) differential equations, and accounting for interactions between follicles. We put a special focus on representing the populationlevel feedback exerted by growing ovarian follicles onto the activation of quiescent follicles. We take advantage of the timescale difference existing between the growth and activation processes to apply model reduction techniques in the framework of singular perturbations. We first study the linear versions of the models to derive theoretical results on the convergence to the limit models. In the nonlinear cases, we provide detailed numerical evidence of convergence to the limit behavior. We reproduce the main semi-quantitative features characterizing the ovarian follicle pool, namely a bimodal distribution of the whole population, and a slope break in the decay of the quiescent pool with aging.
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https://inria.hal.science/hal-03047923/file/proc206706.pdf BibTex
titre
Mathematical modeling approaches of cellular endocrinology within the hypothalamo-pituitary-gonadal axis
article
Molecular and Cellular Endocrinology, 2020, 518, ⟨10.1016/j.mce.2020.110877⟩
resume
The reproductive neuroendocrine axis, or hypothalamo-pituitary-gonadal (HPG) axis, is a paragon of complex biological system involving numerous cell types, spread over several anatomical levels communicating through entangled endocrine feedback loops. The HPG axis exhibits remarkable dynamic behaviors on multiple time and space scales, which are an inexhaustible source of studies for mathematical and computational biology. In this review, we will describe a variety of modeling approaches of the HPG axis from a cellular endocrinology viewpoint. We will in particular investigate the questions raised by some of the most striking features of the HPG axis: (i) the pulsatile secretion of hypothalamic and pituitary hormones, and its counterpart, the cell signaling induced by frequency-encoded hormonal signals, and (ii) the dual, gametogenic and glandular function of the gonads, which relies on the tight control of the somatic cell populations ensuring the proper maturation and timely release of the germ cells.
Accès au texte intégral et bibtex
https://inria.hal.science/hal-03046096/file/accepted-10.1016_j.mce.2020.110877.pdf BibTex

2019

titre
Analysis and calibration of a linear model for structured cell populations with unidirectional motion : Application to the morphogenesis of ovarian follicles
article
SIAM Journal on Applied Mathematics, 2019, 79 (1), pp.207-229. ⟨10.1137/17M1161336⟩
resume
We analyze a multi-type age dependent model for cell populations subject to unidirectional motion, in both a stochastic and deterministic framework. Cells are distributed into successive layers; they may divide and move irreversibly from one layer to the next. We adapt results on the large-time convergence of PDE systems and branching processes to our context, where the Perron-Frobenius or Krein-Rutman theorem cannot be applied. We derive explicit analytical formulas for the asymptotic cell number moments, and the stable age distribution. We illustrate these results numerically and we apply them to the study of the morphodynamics of ovarian follicles. We prove the structural parameter identifiability of our model in the case of age independent division rates. Using a set of experimental biological data, we estimate the model parameters to fit the changes in the cell numbers in each layer during the early stages of follicle development.
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https://hal.science/hal-01852560/file/M116133_published_version.pdf BibTex
titre
Biased signaling and allosteric modulation at the FSHR
article
Frontiers in Endocrinology, 2019, 10, pp.148. ⟨10.3389/fendo.2019.00148⟩
resume
Knowledge on G protein-coupled receptor (GPCRs) structure and mechanism of activation has profoundly evolved over the past years. The way drugs targeting this family of receptors are discovered and used has also changed. Ligands appear to bind a growing number of GPCRs in a competitive or allosteric manner to elicit balanced signaling or biased signaling (i.e., differential efficacy in activating or inhibiting selective signaling pathway(s) compared to the reference ligand). These novel concepts and developments transform our understanding of the follicle-stimulating hormone (FSH) receptor (FSHR) biology and the way it could be pharmacologically modulated in the future. The FSHR is expressed in somatic cells of the gonads and plays a major role in reproduction. When compared to classical GPCRs, the FSHR exhibits intrinsic peculiarities, such as a very large NH2-terminal extracellular domain that binds a naturally heterogeneous, large heterodimeric glycoprotein, namely FSH. Once activated, the FSHR couples to Gαs and, in some instances, to other Gα subunits. G protein-coupled receptor kinases and β-arrestins are also recruited to this receptor and account for its desensitization, trafficking, and intracellular signaling. Different classes of pharmacological tools capable of biasing FSHR signaling have been reported and open promising prospects both in basic research and for therapeutic applications. Here we provide an updated review of the most salient peculiarities of FSHR signaling and its selective modulation.
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https://hal.science/hal-02362523/file/Landomiel-FCE2019.pdf BibTex

2018

titre
Advances in computational modeling approaches of pituitary gonadotropin signaling
article
Expert Opinion on Drug Discovery, 2018, 13 (9), pp.799-813. ⟨10.1080/17460441.2018.1501025⟩
resume
Pituitary gonadotropins play an essential and pivotal role in the control of human and animal reproduction within the hypothalamic-pituitary-gonadal (HPG) axis. The computational modeling of pituitary gonadotropin signaling encompasses phenomena of different natures such as the dynamic encoding of gonadotropin secretion, and the intracellular cascades triggered by gonadotropin binding to their cognate receptors, resulting in a variety of biological outcomes. We overview historical and ongoing issues in modeling and data analysis related to gonadotropin secretion in the field of both physiology and neuro-endocrinology. We mention the different mathematical formalisms involved, their interest and limits. We discuss open statistical questions in signal analysis associated with key endocrine issues. We also review recent advances in the modeling of the intracellular pathways activated by gonadotropins, which yields promising development for innovative approaches in drug discovery. The greatest challenge to be tackled in computational modeling of pituitary gonadotropin signaling is the embedding of gonadotropin signaling within its natural multi-scale environment, from the single cell level, to the organic and whole HPG level. The development of modeling approaches of G protein-coupled receptor signaling, together with multicellular systems biology may lead to unexampled mechanistic understanding with critical expected fallouts in the therapeutic management of reproduction.
Accès au texte intégral et bibtex
https://hal.science/hal-01913612/file/computational_gonado_2ndrevision_withauthors.pdf BibTex
titre
The Becker-Doring Process: Pathwise Convergence and Phase Transition Phenomena
article
Journal of Statistical Physics, 2018, 177 (5), pp.506-527. ⟨10.1007/s10955-019-02377-2⟩
resume
In this note, we prove alaw of large numbersfor an infinite chemical reactionnetwork for phase transition problems called the stochastic Becker-Döring process.Under a general condition on the rate constants we show the convergence in lawand pathwise convergence of the process towards the deterministic Becker-Döringequations. Moreover, we prove that the non-equilibrium potential, associated to thestationary distribution of the stochastic Becker-Döring process, approaches the rela-tive entropy of the deterministic limit model. Thus, the phase transition phenomenathat occurs in the infinite dimensional deterministic modelis also present in the finitestochastic model.In this note, we prove alaw of large numbersfor an infinite chemical reactionnetwork for phase transition problems called the stochastic Becker-Döring process.Under a general condition on the rate constants we show the convergence in lawand pathwise convergence of the process towards the deterministic Becker-Döringequations. Moreover, we prove that the non-equilibrium potential, associated to thestationary distribution of the stochastic Becker-Döring process, approaches the rela-tive entropy of the deterministic limit model. Thus, the phase transition phenomenathat occurs in the infinite dimensional deterministic modelis also present in the finitestochastic model.
Accès au texte intégral et bibtex
https://hal.science/hal-01852561/file/2018_Yvinec_SBD.pdf BibTex

2017

titre
β-arrestin signalling and bias in hormone-responsive GPCRs
article
Molecular and Cellular Endocrinology, 2017, 449, pp.28-41. ⟨10.1016/j.mce.2017.01.052⟩
resume
G protein-coupled receptors (GPCRs) play crucial roles in the ability of target organs to respond to hormonal cues. GPCRs’ activation mechanisms have long been considered as a two-state process connecting the agonist-bound receptor to heterotrimeric G proteins. This view is now challenged as mounting evidence point to GPCRs being connected to large arrays of transduction mechanisms involving heterotrimeric G proteins as well as other players. Amongst the G protein-independent transduction mechanisms, those elicited by β-arrestins upon their recruitment to the active receptors are by far the best characterized and apply to most GPCRs. These concepts, in conjunction with remarkable advances made in the field of GPCR structural biology and biophysics, have supported the notion of ligand-selective signalling also known as pharmacological bias. Interestingly, recent reports have opened intriguing prospects to the way β-arrestins control GPCR-mediated signalling in space and time within the cells. In the present paper, we review the existing evidence linking endocrine-related GPCRs to β-arrestin recruitement, signalling, pathophysiological implications and selective activation by biased ligands and/or receptor modifications. Emerging concepts surrounding β-arrestin-mediated transduction are discussed in the light of the peculiarities of endocrine systems.
Accès au texte intégral et bibtex
https://hal.science/hal-01604784/file/2017_EReiter_MolCellEndocrinol_2.pdf BibTex
titre
Human luteinizing hormone and chorionic gonadotropin display biased agonism at the LH and LH/CG receptors
article
Scientific Reports, 2017, 7 (1), pp.1-11. ⟨10.1038/s41598-017-01078-8⟩
resume
Human luteinizing hormone (LH) and chorionic gonadotropin (hCG) have been considered biologically equivalent because of their structural similarities and their binding to the same receptor; the LH/CGR. However, accumulating evidence suggest that LH/CGR differentially responds to the two hormones triggering differential intracellular signaling and steroidogenesis. The mechanistic basis of such differential responses remains mostly unknown. Here, we compared the abilities of recombinant rhLH and rhCG to elicit cAMP, β-arrestin 2 activation, and steroidogenesis in HEK293 cells and mouse Leydig tumor cells (mLTC-1). For this, BRET and FRET technologies were used allowing quantitative analyses of hormone activities in real-time and in living cells. Our data indicate that rhLH and rhCG differentially promote cell responses mediated by LH/CGR revealing interesting divergences in their potencies, efficacies and kinetics: rhCG was more potent than rhLH in both HEK293 and mLTC-1 cells. Interestingly, partial effects of rhLH were found on β-arrestin recruitment and on progesterone production compared to rhCG. Such a link was further supported by knockdown experiments. These pharmacological differences demonstrate that rhLH and rhCG act as natural biased agonists. The discovery of novel mechanisms associated with gonadotropin-specific action may ultimately help improve and personalize assisted reproduction technologies.
Accès au texte intégral et bibtex
https://hal.science/hal-01594546/file/2017_Riccetti_ScientificReports_%7B45340015-375A-4432-9B1B-3F14AAA2F2D8%7D.pdf BibTex
titre
Quasi steady state approximation of the small clusters in Becker–Döring equations leads to boundary conditions in the Lifshitz–Slyozov limit
article
Communications in Mathematical Sciences, 2017, 15 (5), pp.1353-1384. ⟨10.4310/CMS.2017.v15.n5.a7⟩
resume
The following paper addresses the connection between two classical models of phase transition phenomena describing different stages of clusters growth. The first one, the Becker-Doring model (BD) that describes discrete-sized clusters through an infinite set of ordinary differential equations. The second one, the Lifshitz-Slyozov equation (LS) that is a transport partial differential equation on the continuous half-line x is an element of (0, + infinity). We introduce a scaling parameter epsilon > 0, which accounts for the grid size of the state space in the BD model, and recover the LS model in the limit epsilon -> 0. The connection has been already proven in the context of outgoing characteristic at the boundary x = 0 for the LS model when small clusters tend to shrink. The main novelty of this work resides in a new estimate on the growth of small clusters, which behave at a fast time scale. Through a rigorous quasi steady state approximation, we derive boundary conditions for the incoming characteristic case, when small clusters tend to grow.
Accès au texte intégral et bibtex
https://hal.science/hal-01608844/file/BD_LS_finalversion.pdf BibTex

2016

titre
Computational modeling approaches in gonadotropin signaling
article
Theriogenology, 2016, 86 (1), pp.22-31. ⟨10.1016/j.theriogenology.2016.04.015⟩
resume
Follicle-stimulating hormone (FSH) and luteinizing hormone (LH) play essential roles in animal reproduction. They exert their function through binding to their cognate receptors, which belong to the large family of G protein-coupled receptors (GPCRs). This recognition at the plasma membrane triggers a plethora of cellular events, whose processing and integration ultimately lead to an adapted biological response. Understanding the nature and the kinetics of these events is essential for innovative approaches in drug discovery. The study and manipulation of such complex systems requires the use of computational modeling approaches combined with robust in vitro functional assays for calibration and validation. Modeling brings a detailed understanding of the system and can also be used to understand why existing drugs do not work as well as expected, and how to design more efficient ones.
Accès au texte intégral et bibtex
https://hal.science/hal-01409338/file/MAARYPCAP_16_therio.pdf BibTex
titre
Profiling of FSHR negative allosteric modulators on LH/CGR reveals biased antagonism with implications in steroidogenesis
article
Molecular and Cellular Endocrinology, 2016, 436, pp.10-22. ⟨10.1016/j.mce.2016.07.013⟩
resume
Biased signaling has recently emerged as an interesting means to modulate the function of many G protein-coupled receptors (GPCRs). Previous studies reported two negative allosteric modulators (NAMs) of follicle-stimulating hormone receptor (FSHR), ADX68692 and ADX68693, with differential effects on FSHR-mediated steroidogenesis and ovulation. In this study, we attempted to pharmacologically profile these NAMs on the closely related luteinizing hormone/chorionic gonadotropin hormone receptor (LH/CGR) with regards to its canonical Gs/cAMP pathway as well as to β-arrestin recruitment in HEK293 cells. The NAMs' effects on cAMP, progesterone and testosterone production were also assessed in murine Leydig tumor cell line (mLTC-1) as well as rat primary Leydig cells. We found that both NAMs strongly antagonized LH/CGR signaling in the different cell models used with ADX68693 being more potent than ADX68692 to inhibit hCG-induced cAMP production in HEK293, mLTC-1 and rat primary Leydig cells as well as β-arrestin 2 recruitment in HEK293 cells. Interestingly, differential antagonism of the two NAMs on hCG-promoted steroidogenesis in mLTC-1 and rat primary Leydig cells was observed. Indeed, a significant inhibition of testosterone production by the two NAMs was observed in both cell types, whereas progesterone production was only inhibited by ADX68693 in rat primary Leydig cells. In addition, while ADX68693 totally abolished testosterone production, ADX68692 had only a partial effect in both mLTC-1 and rat primary Leydig cells. These observations suggest biased effects of the two NAMs on LH/CGR-dependent pathways controlling steroidogenesis. Interestingly, the pharmacological profiles of the two NAMs with respect to steroidogenesis were found to differ from that previously shown on FSHR. This illustrates the complexity of signaling pathways controlling FSHR- and LH/CGR-mediated steroidogenesis, suggesting differential implication of cAMP and β-arrestins mediated by FSHR and LH/CGR. Together, our data demonstrate that ADX68692 and ADX68693 are biased NAMs at the LH/CGR in addition to the FSHR. These pharmacological characteristics are important to consider for potential contraceptive and therapeutic applications based on such compounds.
Accès au texte intégral et bibtex
https://hal.science/hal-01409332/file/MMARYetal_16_mce_profiling.pdf BibTex
titre
First passage times in homogeneous nucleation: Dependence on the total number of particles
article
Journal of Chemical Physics, 2016, 144 (3), pp.1-17. ⟨10.1063/1.4940033⟩
resume
Motivated by nucleation and molecular aggregation in physical, chemical, and biological settings, we present an extension to a thorough analysis of the stochastic self-assembly of a fixed number of identical particles in a finite volume. We study the statistics of times required for maximal clusters to be completed, starting from a pure-monomeric particle configuration. For finite volumes, we extend previous analytical approaches to the case of arbitrary size-dependent aggregation and fragmentation kinetic rates. For larger volumes, we develop a scaling framework to study the first assembly time behavior as a function of the total quantity of particles. We find that the mean time to first completion of a maximum-sized cluster may have a surprisingly weak dependence on the total number of particles. We highlight how higher statistics (variance, distribution) of the first passage time may nevertheless help to infer key parameters, such as the size of the maximum cluster. Finally, we present a framework to quantify formation of macroscopic sized clusters, which are (asymptotically) very unlikely and occur as a large deviation phenomenon from the mean-field limit. We argue that this framework is suitable to describe phase transition phenomena, as inherent infrequent stochastic processes, in contrast to classical nucleation theory.
Accès au texte intégral et bibtex
https://hal.science/hal-01353266/file/RYvinec_preprint_2.pdf BibTex

2014

titre
Adiabatic reduction of a model of stochastic gene expression with jump Markov process
article
Journal of Mathematical Biology, 2014, 68 (5), pp.1051-1070. ⟨10.1007/s00285-013-0661-y⟩
resume
This paper considers adiabatic reduction in a model of stochastic gene expression with bursting transcription considered as a jump Markov process. In this model, the process of gene expression with auto-regulation is described by fast/slow dynamics. The production of mRNA is assumed to follow a compound Poisson process occurring at a rate depending on protein levels (the phenomena called bursting in molecular biology) and the production of protein is a linear function of mRNA numbers. When the dynamics of mRNA is assumed to be a fast process (due to faster mRNA degradation than that of protein) we prove that, with appropriate scalings in the burst rate, jump size or translational rate, the bursting phenomena can be transmitted to the slow variable. We show that, depending on the scaling, the reduced equation is either a stochastic differential equation with a jump Poisson process or a deterministic ordinary differential equation. These results are significant because adiabatic reduction techniques seem to have not been rigorously justified for a stochastic differential system containing a jump Markov process. We expect that the results can be generalized to adiabatic methods in more general stochastic hybrid systems.
Accès au texte intégral et bibtex
https://hal.science/hal-01136285/file/2014_Yivinec_Journal%20of%20Mathematical%20Biology%20%28Preprint%29_1 BibTex

2013

titre
Dynamic behavior of stochastic gene expression models in the presence of bursting
article
SIAM Journal on Applied Mathematics, 2013, 73 (5), pp.1830-1852. ⟨10.1137/12090229X⟩
resume
This paper considers the behavior of discrete and continuous mathematical models for gene expression in the presence of transcriptional/translational bursting. We treat this problem in generality with respect to the distribution of the burst size as well as the frequency of bursting, and our results are applicable to both inducible and repressible expression patterns in prokaryotes and eukaryotes. We have given numerous examples of the applicability of our results, especially in the experimentally observed situation that burst size is geometrically or exponentially distributed.
Accès au texte intégral et bibtex
https://hal.inrae.fr/hal-02650825/file/2013_MMackey_SiamJApplMath_1.pdf BibTex

2012

titre
First passage times in homogeneous nucleation and self-assembly
article
Journal of Chemical Physics, 2012, 137 (24), pp.1-18. ⟨10.1063/1.4772598⟩
resume
Motivated by nucleation and molecular aggregation in physical, chemical, and biological settings, we present a thorough analysis of the general problem of stochastic self-assembly of a fixed number of identical particles in a finite volume. We derive the backward Kolmogorov equation (BKE) for the cluster probability distribution. From the BKE, we study the distribution of times it takes for a single maximal cluster to be completed, starting from any initial particle configuration. In the limits of slow and fast self-assembly, we develop analytical approaches to calculate the mean cluster formation time and to estimate the first assembly time distribution. We find, both analytically and numerically, that faster detachment can lead to a shorter mean time to first completion of a maximum-sized cluster. This unexpected effect arises from a redistribution of trajectory weights such that upon increasing the detachment rate, paths that take a shorter time to complete a cluster become more likely.
Accès au texte intégral et bibtex
https://hal.inrae.fr/hal-02649185/file/2012_RYvinec_arXiv%3A1211.1093_1.pdf BibTex

2011

titre
Molecular distributions in gene regulatory dynamics
article
Journal of Theoretical Biology, 2011, 274 (1), pp.84--96. ⟨10.1016/j.jtbi.2011.01.020⟩
resume
We show how one may analytically compute the stationary density of the distribution of molecular constituents in populations of cells in the presence of noise arising from either bursting transcription or translation, or noise in degradation rates arising from low numbers of molecules. We have compared our results with an analysis of the same model systems (either inducible or repressible operons) in the absence of any stochastic effects, and shown the correspondence between behaviour in the deterministic system and the stochastic analogs. We have identified key dimensionless parameters that control the appearance of one or two steady states in the deterministic case, or unimodal and bimodal densities in the stochastic systems, and detailed the analytic requirements for the occurrence of different behaviours. This approach provides, in some situations, an alternative to computationally intensive stochastic simulations. Our results indicate that, within the context of the simple models we have examined, bursting and degradation noise cannot be distinguished analytically when present alone.
Accès au texte intégral et bibtex
https://hal.science/hal-00651585/file/MCMMTRY_10_MolecularDistributions.pdf BibTex