Marie Doumic

Marie Doumic
National Institute for Research in Computer Science and Control | INRIA · MAMBA - Modelling and Analysis for Medical and Biological Applications

Ph.D.

About

105
Publications
7,771
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Introduction
I am a researcher at INRIA, the French National Institute for Research in Applied Mathematics and Computer Science, and "ingénieur en chef des Ponts et Forêts". My research field is PDE (sometimes combined with stochastic processes and statistics) for growing and dividing populations, with two main application fields: protein polymerization occurring in amyloid diseases (a wide range of diseases among which we can quote Alzheimer's, Huntington's, Creuzfeld-Jakob's diseases), and cell division.
Additional affiliations
March 2007 - December 2008
Ecole Normale Supérieure de Paris
Position
  • Researcher
January 2009 - present
Sorbonne University
Position
  • Researcher
Education
September 1999 - June 2000
Université Paris Dauphine-PSL
Field of study
  • NonLinear Applied Analysis
September 1996 - August 2000
Ecole Normale Supérieure de Paris
Field of study
  • Mathematics

Publications

Publications (105)
Preprint
Full-text available
In the absence of telomerase, telomere shortening triggers the DNA damage checkpoint and replicative senescence, a potent tumor suppressor mechanism. Paradoxically, this same process is also associated with oncogenic genomic instability. Yet, the precise mechanism that connects these seemingly opposing forces remains poorly understood. To directly...
Article
Full-text available
Telomere shortening ultimately causes replicative senescence. However, identifying the mechanisms driving replicative senescence in cell populations is challenging due to the heterogeneity of telomere lengths and the asynchrony of senescence onset. Here, we present a mathematical model of telomere shortening and replicative senescence in Saccharomy...
Preprint
Depolymerization reactions constitute frequent experiments, for instance in biochemistry for the study of amyloid fibrils. The quantities experimentally observed are related to the time dynamics of a quantity averaged over all polymer sizes, such as the total polymerised mass or the mean size of particles. The question analysed here is to link this...
Preprint
Shrinkage of large particles, either through depolymerisation (i.e. progressive shortening) or through fragmentation (breakage into smaller pieces) may be modelled by discrete equations, of Becker-D\''oring type, or by continuous ones. In this note, we review two kinds of inverse problems: the first is the estimation of the initial size-distributio...
Preprint
To provide a mechanistic explanation of sustained {then} damped oscillations observed in a depolymerisation experiment, a bi-monomeric variant of the seminal Becker-D\"oring system has been proposed in \cite{DFMR}. When all reaction rates are constant, the equations are the following: \begin{align*}\frac{dv}{dt} & =-vw+v\sum_{j=2}^{\infty}c_{j}, \q...
Article
Full-text available
Systems describing the long-range interaction between individuals have attracted a lot of attention in the last years, in particular in relation with living systems. These systems are quadratic, written under the form of transport equations with a nonlocal self-generated drift. We establish the localisation limit, that is the convergence of nonloca...
Preprint
Progressive shortening of telomeres ultimately causes replicative senescence and is linked with aging and tumor suppression. Studying the intricate link between telomere shortening and senescence at the molecular level and its population-scale effects over time is challenging with current approaches but crucial for understanding behavior at the org...
Preprint
Full-text available
Systems describing the long-range interaction between individuals have attracted a lot of attention in the last years, in particular in relation with living systems. These systems are quadratic, written under the form of transport equations with a nonlocal self-generated drift. We establish the localisation limit, that is the convergence of nonloca...
Article
Full-text available
Aggregation of ubiquitinated cargo by oligomers of the protein p62 is an important preparatory step in cellular autophagy. In this work a mathematical model for the dynamics of these heterogeneous aggregates in the form of a system of ordinary differential equations is derived and analyzed. Three different parameter regimes are identified, where ei...
Preprint
The present paper provides a new representation of the solution to the fragmentation equation as a power series in the Banach space of Radon measures endowed with the total variation norm. This representation is used to justify how the fragmentation kernel, which is one of the two key parameters of the fragmentation equation, can be recovered from...
Article
Full-text available
Background: Telomerase-negative cells have limited proliferation potential. In these cells, telomeres shorten until they reach a critical length and induce a permanently arrested state. This process called replicative senescence is associated with genomic instability and participates in tissue and organismal ageing. Experimental data using single-...
Article
Full-text available
The dynamics by which polymeric protein filaments divide in the presence of negligible growth, for example due to the depletion of free monomeric precursors, can be described by the universal mathematical equations of ‘pure fragmentation’. The rates of fragmentation reactions reflect the stability of the protein filaments towards breakage, which is...
Preprint
Modelling, analysing and inferring triggering mechanisms in population reproduction is fundamental in many biological applications. It is also an active and growing research domain in mathematical biology. In this chapter, we review the main results developed over the last decade for the estimation of the division rate in growing and dividing popul...
Preprint
Full-text available
Background: Telomerase-negative cells have limited proliferation potential. In these cells, telomeres shorten until they reach a critical length and induce a permanently arrested state. This process called replicative senescence is associated with genomic instability and participates in tissue and organismal ageing. Experimental data using single-c...
Article
Full-text available
To model the morphogenesis of rod-shaped bacterial micro-colony, several individual-based models have been proposed in the biophysical literature. When studying the shape of micro-colonies, most models present interaction forces such as attraction or filial link. In this article, we propose a model where the bacteria interact only through non-overl...
Preprint
Full-text available
To model the morphogenesis of rod-shaped bacterial micro-colony, several individual-based models have been proposed in the biophysical literature. When studying the shape of micro-colonies, most models present interaction forces such as attraction or filial link. In this article, we propose a model where the bacteria interact only through non-overl...
Article
Full-text available
The division of amyloid protein fibrils is required for the propagation of the amyloid state, and is an important contributor to their stability, pathogenicity and normal function. Here, we combine kinetic nanoscale imaging experiments with analysis of a mathematical model to resolve and compare the division stability of amyloid fibrils. Our theore...
Preprint
Full-text available
Aggregation of ubiquitinated cargo by oligomers of the protein p62 is an important preparatory step in cellular autophagy. In this work a mathematical model for the dynamics of these heterogeneous aggregates in the form of a system of ordinary differential equations is derived and analyzed. Three different parameter regimes are identified, where ei...
Preprint
Given nonstationary data, one generally wants to extract the trend from the noise by smoothing or filtering. However, it is often important to delineate a third intermediate category, that we call high frequency (HF) features: this is the case in our motivating example, which consists in experimental measurements of the time-dynamics of depolymeris...
Article
Full-text available
The dynamics of aggregation and structural diversification of misfolded, host-encoded proteins in neurodegenerative diseases are poorly understood. In many of these disorders, including Alzheimer’s, Parkinson’s and prion diseases, the misfolded proteins are self-organized into conformationally distinct assemblies or strains. The existence of intras...
Article
Full-text available
In this article, in order to understand the appearance of oscillations observed in protein aggregation experiments, we propose, motivate and analyse mathematically the differential system describing the kinetics of the following reactions: {V + W ->(k) 2W, W + C-i ->(ai) C-i+1,C- 1 <= i <= n, C-i + V ->(bi) Ci-1 + 2V, 2 <= i <= n, with n finite or...
Preprint
Is it possible to estimate the dependence of a growing and dividing population on a given trait in the case where this trait is not directly accessible by experimental measurements, but making use of measurements of another variable? This article adresses this general question for a very recent and popular model describing bacterial growth, the so-...
Preprint
Full-text available
Aggregation of misfolded forms from host-encoded proteins is key to the pathogenesis of a number of neurodegenerative disorders, including prion diseases, Alzheimer's disease and Parkinson's disease. In prion diseases, the cellular prion protein PrPC can misfold into PrPSc and auto-organize into conformationally distinct assemblies or strains. A pl...
Article
Full-text available
The prion protein (PrP) misfolds and assembles into a wide spectrum of self-propagating quaternary structures, designated PrPSc. These various PrP superstructures can be functionally different, conferring clinically distinctive symptomatology, neuropathology and infectious character to the associated prion diseases. However, a satisfying molecular...
Preprint
Full-text available
The division of amyloid protein fibrils is required for the propagation of the amyloid state, and is an important contributor to their stability, pathogenicity and normal function. Here, we combine kinetic nano-scale imaging experiments with analysis of a mathematical model to resolve and compare the division of amyloid fibrils. Our theoretical res...
Article
Full-text available
This study is devoted to the long-term behavior of nucleation, growth and fragmentation equations, modeling the spontaneous formation and kinetics of large polymers in a spatially homogeneous and closed environment. Such models are, for instance, commonly used in the biophysical community in order to model in vitro experiments of fibrillation. We i...
Preprint
We consider the fragmentation equation $\dfrac{\partial}{\partial t}f (t, x) = --B(x)f (t, x) + \int\_{ y=x}^{ y=\infty} k(y, x)B(y)f (t, y)dy,$ and address the question of estimating the fragmentation parameters-i.e. the division rate $B(x)$ and the fragmentation kernel $k(y, x)$-from measurements of the size distribution $f (t, $\times$)$ at vari...
Article
The aim of this study is to generalise recent results of the two last authors on en-tropy methods for measure solutions of the renewal equation to other classes of structured population problems. Specifically, we develop a generalised relative entropy inequality for the growth-fragmentation equation and prove asymptotic convergence to a steady-stat...
Preprint
The aim of this study is to generalise recent results of the two last authors on en-tropy methods for measure solutions of the renewal equation to other classes of structured population problems. Specifically, we develop a generalised relative entropy inequality for the growth-fragmentation equation and prove asymptotic convergence to a steady-stat...
Article
We consider the fragmentation equation∂f∂t(t,x)=−B(x)f(t,x)+∫y=xy=∞k(y,x)B(y)f(t,y)dy, and address the question of estimating the fragmentation parameters - i.e. the division rate B(x) and the fragmentation kernel k(y,x) - from measurements of the size distribution f(t,⋅) at various times. This is a natural question for any application where the si...
Preprint
This study is devoted to the long-term behavior of nucleation, growth and fragmentation equations, modeling the spontaneous formation and kinetics of large polymers in a spatially homogeneous and closed environment. Such models are, for instance, commonly used in the biophysical community in order to model in vitro experiments of fibrillation. We i...
Article
Full-text available
In mammals, Prion pathology refers to a class of infectious neuropathologies whose mechanism is based on the self-perpetuation of structural information stored in the pathological conformer. The characterisation of the PrP folding landscape has revealed the existence of a plethora of pathways conducing to the formation of structurally different ass...
Data
Multi-wavelength static light scattering data, allowing us to have a correspondence between the elution volume measured by SEC (in ml) and the size of the polymers going through the SEC device (in the number of monomers, denoted mer). (EPS)
Data
Details on the static light scattering (SLS) scales. (PDF)
Data
Details on the size exclusion chromatography (SEC) scales. (PDF)
Data
Normalised initial distribution for the three experiments considered, at 1μM (dark blue), 3μM (red) and 7μM (green). We can observe that they superimpose very well. (EPS)
Data
Comparison between SLS (black dots) data and second moment computed from SEC data (red points) for the three experiments, from left to right: 1μM, 3μM and 7μM. (EPS)
Data
Noise measurement of the empty cuvette for the SLS device. (EPS)
Article
Full-text available
We give here an explicit formula for the following critical case of the growth-fragmentation equation ∂/∂tu(t,x)+∂/∂x(gxu(t,x))+bu(t,x)=bα2u(t,αx), u(0,x)=u0(x) ∂∂tu(t,x)+∂∂x(gxu(t,x))+bu(t,x)=bα2u(t,αx), u(0,x)=u0(x) for some constants g > 0, b > 0 and α >1 - the case α = 2 being the emblematic binary fission case. We discuss the links between...
Preprint
We give here an explicit formula for the following critical case of the growth-fragmentation equation $$\frac{\partial}{\partial t} u(t, x) + \frac{\partial}{\partial x} (gxu(t, x)) + bu(t, x) = b\alpha^2 u(t, \alpha x), \qquad u(0, x) = u\_0 (x),$$ for some constants $g > 0$, $b > 0$ and $\alpha > 1$ - the case $\alpha = 2$ being the emblematic bi...
Article
Full-text available
In the formation of large clusters out of small particles, the initializing step is called the nucleation, and consists in the spontaneous reaction of agents which aggregate into small and stable polymers called nuclei. After this early step, the polymers are involved in a number of reactions such as polymerization, fragmentation and coalescence. S...
Article
Full-text available
We study the asymptotic behaviour of the following linear growth-fragmentation equation $${\partial\over\partial t} u(t,x) + {\partial\over\partial x}(xu(t,x)) + B(x)u(t,x) = 4B(2x) u(t,2x),$$ and prove that under fairly general assumptions on the division rate $B(x)$, its solution converges towards an oscillatory function, explicitly given by the...
Preprint
We study the asymptotic behaviour of the following linear growth-fragmentation equation$$\dfrac{\partial}{\partial t} u(t,x) + \dfrac{\partial}{\partial x} \big(x u(t,x)\big) + B(x) u(t,x) =4 B(2x)u(t,2x),$$ and prove that under fairly general assumptions on the division rate $B(x),$ its solution converges towards an oscillatory function,explicitel...
Article
Strategic Workforce Planning is a company process providing best in class, economically sound, workforce management policies and goals. Despite the abundance of literature on the subject, this is a notorious challenge in terms of implementation. Reasons span from the youth of the field itself to broader data integration concerns that arise from gat...
Preprint
Strategic Workforce Planning is a company process providing best in class, economically sound, workforce management policies and goals. Despite the abundance of literature on the subject, this is a notorious challenge in terms of implementation. Reasons span from the youth of the field itself to broader data integration concerns that arise from gat...
Article
Full-text available
Self-assembly of proteins is a biological phenomenon which gives rise to spontaneous formation of amyloid fibrils or polymers. The starting point of this phase, called nucleation exhibits an important variability among replicated experiments.To analyse the stochastic nature of this phenomenon, one of the simplest models considers two populations of...
Preprint
Self-assembly of proteins is a biological phenomenon which gives rise to spontaneous formation of amyloid fibrils or polymers. The starting point of this phase, called nucleation exhibits an important variability among replicated experiments.To analyse the stochastic nature of this phenomenon, one of the simplest models considers two populations of...
Article
Estimating reaction rates and size distributions of protein polymers is an important step for understanding the mechanisms of protein misfolding and aggregation, a key feature for amyloid diseases. This study aims at setting this framework problem when the experimental measurements consist in the time-dynamics of a moment of the population (i.e. fo...
Article
Full-text available
In eukaryotes, the absence of telomerase results in telomere shortening, eventually leading to replicative senescence, an arrested state that prevents further cell divisions. While replicative senescence is mainly controlled by telomere length, the heterogeneity of its onset is not well understood. This study proposes a mathematical model based on...
Article
Full-text available
Self-assembly of proteins into amyloid aggregates is an important biological phenomenon associated with human diseases such as Alzheimer's disease. Amyloid fibrils also have potential applications in nano-engineering of biomaterials. The kinetics of amyloid assembly show an exponential growth phase preceded by a lag phase, variable in duration as s...
Article
Full-text available
The spike trains are the main components of the information processing in the brain. To model spike trains several point processes have been investigated in the literature. And more macroscopic approaches have also been studied, using partial differential equation models. The main aim of the present article is to build a bridge between several poin...
Article
Full-text available
We illustrate the use of statistical tools (asymptotic theories of standard error quantification using appropriate statistical models, bootstrapping, and model comparison techniques) in addition to sensitivity analysis that may be employed to determine the information content in data sets. We do this in the context of recent models [S. Prigent, A....
Article
Full-text available
Fragmentation and growth-fragmentation equations is a family of problems with varied and wide applications. This paper is devoted to description of the long time time asymptotics of two critical cases of these equations, when the division rate is constant and the growth rate is linear or zero. The study of these cases may be reduced to the study of...
Article
Full-text available
More than twenty types of proteins can adopt misfolded conformations, which can co-aggregate into amyloid fibrils, and are related to pathologies such as Alzheimers disease. This article surveys mathematical models for aggregation chain reactions, and discuss the ability to use them to understand amyloid distributions. Numerous reactions have been...
Article
In the formation of large clusters out of small particles, the initializing step is called the nucleation, and consists in the spontaneous reaction of agents which aggregate into small and stable polymers called nucleus. After this early step, the polymers are involved into a bunch of reactions such as polymerization, fragmentation and coalescence....
Article
Full-text available
Many organisms coordinate cell growth and division through size control mechanisms: cells must reach a critical size to trigger some cell cycle event. Bacterial division is often assumed to be controlled in this way, but experimental evidence to support this assumption is still lacking. Theoretical arguments show that size control is required to ma...
Article
Full-text available
We consider the growth-fragmentation equation and we address the problem of estimating the division rate from the stable size distribution of the population, which is easily measured, but non-smooth. We propose a method based on the Mellin transform for growth-fragmentation equations with self-similar kernels. We build a sequence of functions which...
Article
Study of growth-fragmentation equations and application in biology
Data
This text contains details about parameter estimation of the Bik kinetics model as well as additional information on numerical simulations for therapeutics optimization. (PDF)
Article
Full-text available
Src tyrosine kinases are deregulated in numerous cancers and may favor tumorigenesis and tumor progression. We previously described that Src activation in NIH-3T3 mouse fibroblasts promoted cell resistance to apoptosis. Indeed, Src was found to accelerate the degradation of the pro-apoptotic BH3-only protein Bik and compromised Bax activation as we...
Article
Full-text available
Protein polymerization consists in the aggregation of single monomers into polymers that may fragment. Fibrils assembly is a key process in amyloid diseases. Up to now, protein aggregation was commonly mathematically simulated by a polymer size-structured ordinary differential equations (ODE) system, which is infinite by definition and therefore le...
Data
Parameter estimation considering each curve separately. Time evolution of PolyQ41 polymerized mass for an initial PolyQGST concentration equal to . The experimental results are plotted in dotted line and the best-fit curve in solide line. is set to 3. Best-fit parameters are . (TIF)
Data
Parameter estimation for Experimental Set 1 when is set to 3. Time evolution of the adimensioned PolyQ41 polymerized mass for an initial PolyQGST concentration equal to (A), (B), (C). Dotted curves represent experimental results. The solid curve is the best-fit. The global error in adimensioned norm was equal to 40% and the optimal parameters are v...
Data
Left: Size distribution of the fragmentation rate for an aggregation of size 20, following a uniform distribution (black) or a mechanical-based distribution (red) of fragmentation. Right: Simulated normalized reaction progress curves of amyloid formation for a uniform distribution (black) and a mechanical-based distribution (red) of fragmentation....
Data
Full-text available
Model derivation from ODE to PDE. (PDF)
Data
Parameter estimation for Experimental Set 1 when is set to 1. Time evolution of the adimensioned PolyQ41 polymerized mass for an initial PolyQGST concentration equal to (A), (B), (C). Dotted curves represent experimental results. The solid curve is the best-fit. The global error in in adimensioned norm was equal to 11%. The best-fit parameters are...
Data
Examples of simulated size distribution of the aggregates for a uniform distribution (black) and a mechanical-based distribution (red) of fragmentation. See above for the numerical values. (TIF)
Data
Full-text available
Application to PolyQ41 polymerization. (PDF)