MUSICS

MUSICS - 2024

2024Activity reportProject-TeamMUSICS

RNSR: 202424549J

Research center Inria Lyon Centre
In partnership with:Université Claude Bernard (Lyon 1), CNRS, Ecole normale supérieure de Lyon
Team name: MUltiScale Interacting Cell Systems
In collaboration with:Institut Camille Jordan, Laboratoire de Biologie et Modélisation de la Cellule
Domain:Digital Health, Biology and Earth
Theme:Modeling and Control for Life Sciences

Keywords

Computer Science and Digital Science

A6. Modeling, simulation and control
A6.1. Methods in mathematical modeling
A6.1.1. Continuous Modeling (PDE, ODE)
A6.1.2. Stochastic Modeling
A6.1.3. Discrete Modeling (multi-agent, people centered)
A6.1.4. Multiscale modeling
A6.2. Scientific computing, Numerical Analysis & Optimization
A6.2.1. Numerical analysis of PDE and ODE
A6.2.3. Probabilistic methods
A6.2.4. Statistical methods
A6.3.1. Inverse problems
A6.3.3. Data processing
A8.12. Optimal transport

1 Team members, visitors, external collaborators

Research Scientists

Thomas Lepoutre [Team leader, INRIA, Researcher, from Jul 2024]
Mostafa Adimy [INRIA, Senior Researcher, from Jul 2024]
Aymeric Baradat [CNRS, Researcher, from Jul 2024]
Samuel Bernard [CNRS, Researcher, from Jul 2024]
Clément Erignoux [INRIA, ISFP, from Jul 2024]
Olivier Gandrillon [CNRS, Senior Researcher, from Jul 2024]
Michèle Romanos [CNRS, from Jul 2024]

Faculty Members

Thibault Espinasse [UNIV LYON I, Associate Professor, from Jul 2024]
Laurent Pujo-Menjouet [UNIV LYON I, Associate Professor, from Jul 2024]
Léon Tine [UNIV LYON I, Associate Professor, from Jul 2024, HDR]

Post-Doctoral Fellows

Mohammed Elghandouri [INRIA, Post-Doctoral Fellow, from Nov 2024]
Thi Nhu Thao Nguyen [CNRS, Post-Doctoral Fellow, from Jul 2024]

PhD Students

Charlotte Camus [INRIA, from Jul 2024]
Maxime Estavoyer [INRIA, from Jul 2024]
Clemence Fournie [CNRS, from Jul 2024]
Grégoire Ranson [UNIV YORK, from Jul 2024]

Administrative Assistants

Claire Alexandre [INRIA]
Sylvie Boyer [INRIA]

Visiting Scientists

Pablo Amster [Univ Buenos Aires , from Sep 2024 until Nov 2024]
Claudia Pio Ferreira [GOUV BRESIL, from Sep 2024 until Oct 2024]

2 Overall objectives

MUltiScale Interacting Cell Systems, or MUSICS, is an newly created Inria team at the Centre Inria de Lyon devoted to the multiscale modelling and analysis of cellular dynamics. It is jointly supported by members of the ICJ (Institut Camille Jordan, University Lyon 1, CNRS and Inria), and the LBMC (ENS Lyon, CNRS) under the leadership of Thomas Lepoutre (Inria and ICJ). MUSICS inherits in part the staff and the research topics of the late Inria team Dracula, headed by Mostafa Adimy, that was set up in 2011.

3 Research program

Biological systems can be described at many organization scales, starting from the molecular level, to cellular, whole body, and all the way up to the population level. Each scale is rich and complex in its own right, but also interact with other scales and this is a crucial feature.

Yet it contains a much higher level of complexity, both in terms of computations and modelling. The historical, reductionist approach that has been used in molecular biology for the past 30 years consists in inferring the biological function, often at the tissue or whole body level, from molecular observations. There are several areas where this approach does not work so well. If the average cellular phenotype is not representative of the whole population phenotype, no matter how finely individual cells will be characterised, there will be a mismatch between the prediction and the observation. For the reductionist approach to work, it must take into account what happens when cells are brought together, that is, the tissue ecology. Cell population dynamics, in a broad sense, is the study of the phenomena that occur when many cells are brought in together, interact, proliferate, differentiate and die. One major difficulty that arises when analyzing such systems stems from the fact that those different scales do not behave independently but display strong, constant and dynamic interactions. In this context, the idea of a privileged level of causation loses its meaning, calling for new formal tools and approaches that aim at capturing the so-called “circular causality”, where causation moves both upward and downward 40. Upward causation is the set of processes by which the elements at lower levels interact and produce changes at higher levels. For example, a modification in the function of a gene product will alter the proliferation capacity of a cell that will alter the tissue composition. Downward causation is the set of constraints imposed by the higher levels on the dynamics at lower levels. For example, the generation at the tissue level of a gradient of a morphogen will result in a change in gene expression in individual cells. The gradient is a property of the tissue, not individual cells. Despite the variety of existing techniques to handle causality, this complexity of living systems poses new challenges and calls for the development of new tools. The MUSICS project is devoted to the development of tools and methods to study multiscale processes in biology with potential applications in medicine.

MUSICS will mainly focus on the cellular level, taking into account interactions at smaller spatial (and faster) scales (e.g. cellular content, gene expression), or at larger spatial scales (e.g. tissue, organism). The cell, as the structural unit of living organisms, has always played a key role in biology. With the rise of molecular biology and genomics, the role of the cell had been somewhat relegated to the background, in favour of molecular data acquired on large numbers of cells. The existence, extent and role of intercellular diversity was largely underestimated. Molecular biology was until recently based upon the assumption (or approximation) of the existence of an “average cell” that could be characterised from population measurements. This view proved to be not only wrong, but irrelevant 39. Rather, cellular diversity seems to be a key feature to understand biological systems and dynamics.

What has dramatically changed in the last decade is the access to this diversity, notably through the revolution of single cell data. We now have access to gene expression at the resolution of the (single) cell for a large number of genes (thousands) in a large number of (individual) cells (up to millions) 43. The recent years have witnessed an explosion in both the amount and the diversity of single-cell omics data. This has led to new opportunities to develop computationally efficient and statistically sound models and methods, with many challenges ahead 37.

One of the main drivers for cellular variability lies within the gene expression process that is intrinsically stochastic 36. Notably, the observable regime for gene expression, when analysed at the single cell level, can be characterised as bursty 42. This means that mRNA production occurs in brief episodes (bursts), generating a characteristic gamma distribution of mRNA transcripts when analysed over a sufficiently large amount of individual cells 38. Such variability is often not taken into account at all in current modelling schemes. For example in a recent paper which developed a model of multicellular gene expression that accounts for intra- and intercellular gene regulation 41, gene expression is reduced to a binary variable.

It is therefore critical to develop new modelling approaches in which the molecular-based variability is correctly taken into account at the molecular level, so that its impact at higher levels (cellular and tissular) can be analysed.

Similarly, the way such molecular variability is constrained by higher levels should also be incorporated into the modelling process. Finally, we will build on our expertise in developing population models that can be analysed mathematically in order to be able to derive relevant predictions in simplified situations (corresponding to mean-field limits, for instance). This leads to a structure of the project into three thematic axes of different size (more members in the first one, and fewer in the two others).

Axis 1
Modelling and theoretical analysis in population dynamics. This methodological axis concerns population dynamics in general. This leads to the study of questions related to existence, uniqueness and asymptotic behaviour for population models, described in terms of partial differential equations (PDEs), integro-differential equations, or delay differential equations. Moreover, we have a strong focus on an intermediate description: structured population dynamics. This is the biggest axis and concerns most members of the teams.
Axis 2
Simulate efficiently large populations of individuals with internal dynamics influenced by the population (chemical signalling, overcrowding $\dots$ ). This approach is not only adapted when the coupling of scales is strong but can also be used to test the validity approximation of weak coupling used in population models. This can also guide the construction of new simplified models (based on numerical observations). Moreover, internal dynamics assessed on the data will be encoded in the simulation tool with the addition of nonlinear feedback loops. The axis is notably computational but contains also the analysis of large population limit.
Axis 3
Understand, analyse and infer the internal dynamics from data with a mechanistic description. This challenge is more related to statistical inference (mechanistic description has consequences on the structure of the noise) and leads to difficult questions linked to large deviations and optimal transportation. Axis 3 mixes some deep theoretical questions related to stochastic hybrid models with direct confrontations to data.

Only such multiscale modelling approaches will allow to investigate one of the most challenging characteristics of living systems, namely the circular causality that drives them 40.

Figure 1: Non-exhaustive view of interacting scales.

4 Application domains

Detailed in the research program

5 Highlights of the year

The team was created in July 2024!

5.1 Awards

Léon Tine was awarded the Maurice Audin mathematics prize for his research into the mathematical modelling of mechanisms linked to physics and biology. link

6 New software, platforms, open data

6.1 New software

6.1.1 Simuscale

Name:
Multiscale simulation of cell populations
Keywords:
Ode, Simulation, Multiscale, Multi-agent
Scientific Description:
SiMuScale is a C++ simulation framework that models both intra- and extra-cellular processes at different time scales. Its decoupled architecture allows for an easy and parsimonious extension of the model with e.g. a new kind of intra-cellular formalism.
Functional Description:
Simuscale is a multiscale, individual-based modelling platform written in C++ for performing numerical simulations of heterogeneous populations of individual cells evolving in time and interacting physically and biochemically. Models are described at two levels: cellular level and population level. The cellular level describes the dynamics of single cells, as defined by the modeller. Cells have an internal state that includes default properties such as cell size and position, and may also include any other cell-specific state, such as gene or protein expression. The population level describes the mechanical constraints and biochemical interactions between cells. Cells evolve in bounded 3D domain, and can divide or die. Simuscale implements the physical simulator that manages the simulations at the population level. It delegates the details of cellular dynamics to each cell. This makes Simuscale modular, as it can accommodate any number of cell models with the same simulation, including models with different modelling formalisms. Biochemical interactions occur between cells that are in contact with each other, through intercellular signals. Intercellular signals can be known to all or to a subset of the cells only. Simuscale expects an input file describing the initial cell population and numerical options, it runs a simulation over a specified time interval, updating the cell population at given time steps, and generates an output file containing the state of each cell at each time step, and the tree of cell divisions and deaths.
Release Contributions:
Includes diffusive signals (nonlocal) across the whole simulation domain
URL:
https://gitlab.inria.fr/bernard1/simuscale
Publications:
hal-04489553, hal-04400510
Contact:
Samuel Bernard
Participants:
Carole Knibbe, David Parsons, Fabien Crauste, Olivier Gandrillon, Raphael Bournhonesque, Samuel Bernard
Partners:
CNRS, UCBL Lyon 1

7 New results

Preliminary remarks: some results of the year have been obtained within the Dracula Inria Team.

7.1 Mathematical modelling of the motility regime switching in Myxobacteria

Participants: Maxime Estavoyer, Thomas Lepoutre.

Maxime Estavoyer has studied in 5 the modelling of motility regime switching in Myxobacteria. This has taken the form of accurate numerical simulations in particular shed light on the fact that the existence of a faster group speed may not always results in an acceleration of the invasion. In an asymptotic (scalar and not anymore a system) limit of fast exchange Maxime Estavoyer and Thomas Lepoutre have established the existence of a threshold for such an advantage. Namely, there exists a $θ^{*}$ such that for a speed advantage smaller that $θ^{*}$ the invasion is not accelerated whereas it is accelerated above the threshold. This corrresponds to a transition between pulled and pushed fronts 16.

7.2 Results on stability for HIV

Participants: Mostafa Adimy, Laurent Pujo-Menjouet.

In 2, an examination is conducted on a model derived from the inquiry into the efficacy of HIV Pre-Exposure Prophylaxis (PrEP) within high-risk populations. To achieve this objective, we employ an SI model coupled with an age-structured equation to delineate the dynamics of individuals under PrEP protection, incorporating an infected-dependent rate of new users recruited from the susceptible population. This nonlinear term is contingent upon a factor dedicated to the political or economic context of a government. Local asymptotic stability for both disease-free and endemic equilibria is established, and global asymptotic stability for the disease-free steady-state is demonstrated. To address the system’s behavior, a reduction of the partial differential equation is undertaken, presenting it as a coupled system of differential equations and a delayed difference equation. Lastly, persistence is substantiated when the endemic equilibrium is realized.

7.3 Modelling the antigen–antibody complex activity

Participants: Mostafa Adimy, Charlotte Dugourd-Camus.

Using the laws of chemical reactions, we propose in 10 a new approach to modelling the antigen–antibody complex activity. The resulting expression covers not only purely competitive or purely independent binding but also synergistic binding which, depending on the antibodies, can promote either neutralization or enhancement of viral activity. The results indicate that efficient viral neutralization is associated with purely independent antibody binding, whereas strong viral activity enhancement is expected in the case of purely competitive antibody binding. Finally, data collected during a secondary dengue infection were used to validate the model. The dataset includes sequential measurements of virus and antibody titres during viremia in patients. Data fitting shows that the two antibodies are in strong competition, as the synergistic binding is low. This contributes to the high levels of virus titres and may explain the antibody-dependent enhancement phenomenon. Besides, the mortality of infected cells is almost twice as high as that of susceptible cells, and the heterogeneity of viral kinetics in patients is associated with variability in antibody responses between individuals. Other applications of the model may be considered, such as the efficacy of vaccines and antibody-based therapies.

7.4 Mathematical modelling of dialog between yeast cells

Participants: Thomas Lepoutre.

In 6 with Vincent Calvez, Nicolas Meunier and Nicolas Muller, we develop a model to describe some aspects of communication between yeast cells. It consists in a coupled system of two one-dimensional non-linear advection-diffusion equations in which the advective field is given by the Hilbert transform. We give some sufficient condition for the blow-up in finite time of the coupled system (formation of a singularity). We provide a biological interpretation of these mathematical results.

7.5 Modelling prion and Alzheimer

7.5.1 Alzheimer and inflammation

Participants: Laurent Pujo-Menjouet, Léon Tine.

In 9, we introduce and study a new model for the progression of Alzheimer's disease incorporating the interactions of Aβ-monomers, oligomers, microglial cells and interleukins with neurons through different mechanisms such as protein polymerization, inflammation processes and neural stress reactions. In order to understand the complete interactions between these elements, we study a spatially-homogeneous simplified model that allows to determine the effect of key parameters such as degradation rates in the asymptotic behavior of the system and the stability of equilibriums. We observe that inflammation appears to be a crucial factor in the initiation and progression of Alzheimer's disease through a phenomenon of hysteresis, which means that there exists a critical threshold of initial concentration of interleukins that determines if the disease persists or not in the long term. These results give perspectives on possible anti-inflammatory treatments that could be applied to mitigate the progression of Alzheimer's disease. We also present numerical simulations that allow to observe the effect of initial inflammation and concentration of monomers in our model.

7.5.2 Prion replication

Participants: Laurent Pujo-Menjouet.

Prion diseases, or transmissible spongiform encephalopathies (TSEs), are neurodegenerative disorders caused by the accumulation of misfolded conformers (PrPSc) of the cellular prion protein (PrPC). During the pathogenesis, the PrPSc seeds disseminate in the central nervous system and convert PrPC leading to the formation of insoluble assemblies. As for conventional infectious diseases, variations in the clinical manifestation define a specific prion strain which correspond to different PrPSc structures. In 17, we implemented the recent developments on PrPSc structural diversity and tissue response to prion replication into a stochastic reaction-diffusion model using an application of the Gillespie algorithm. We showed that this combination of non-linearities can lead prion propagation to behave as a complex system, providing an alternative to the current paradigm to explain strain-specific phenotypes, tissue tropisms, and strain co-propagation while also clarifying the role of the connectome in the neuro-invasion process.

7.5.3 Estimation of nucleation

Participants: Léon Tine.

In 20, we are interested in the modeling of Alzheimer’s disease from the angle of the amyloid cascade hypothesis, where the pathogenic agent is the Aβ protein in its oligomeric form. The formation dynamics of this pathogenic form is modeled by a Becker–Doring type model where APP (Amyloid Precursor Protein) protein, after cleavage by specific enzymes, forms monomeric Aβ proteins, which, by polymerization and/or nucleation, lead to the formation of oligomeric Aβ. We propose an optimal control problem to estimate the rate of nucleation which seems to be at the base of this amyloid cascade hypothesis and for which no (experimental) measurement exists for the moment.

7.6 In silico modelling of CD8 T cell immune response

Participants: Samuel Bernard, Olivier Gandrillon, Thi Nhu Thao Nguyen.

The CD8 T cell immune response operates at multiple temporal and spatial scales, including all the early complex biochemical and biomechanical processes, up to long term cell population behavior. In order to model this response, we devised in 21 a multiscale agent-based approach using Simuscale software. Within each agent (cell) of our model, we introduced a gene regulatory network (GRN) based upon a piecewise deterministic Markov process formalism. Cell fate – differentiation, proliferation, death – was coupled to the state of the GRN through rule-based mechanisms. Cells interact in a 3D computational domain and signal to each other via cell–cell contacts, influencing the GRN behavior. Results show the ability of the model to correctly capture both population behavior and molecular timedependent evolution. We examined the impact of several parameters on molecular and population dynamics, and demonstrated the add-on value of using a multiscale approach by showing the influence of molecular parameters, particularly protein degradation rates, on the outcome of the response, such as effector and memory cell counts.

7.7 Selection and refinement in ensembles of executable gene regulatory networks

Participants: Olivier Gandrillon.

In 4, we present a Design of Experiment strategy to use as a second stage after the inference process. It is specifically fitted for identifying the next most informative experiment to perform for deciding between multiple network topologies, in the case where proposed GRNs are executable models. This strategy first performs a topological analysis to reduce the number of perturbations that need to be tested, then predicts the outcome of the retained perturbations by simulation of the GRNs and finally compares predictions with novel experimental data. Results: We apply this method to the results of our divide-and-conquer algorithm called WASABI, adapt its gene expression model to produce perturbations and compare our predictions with experimental results. We show that our networks were able to produce in silico predictions on the outcome of a gene knock-out, which were qualitatively validated for 48 out of 49 genes. Finally, we eliminate as many as two thirds of the candidate networks for which we could identify an incorrect topology, thus greatly improving the accuracy of our predictions. Conclusion: These results both confirm the inference accuracy of WASABI and show how executable gene expression models can be leveraged to further refine the topology of inferred GRNs. We hope this strategy will help systems biologists further explore their data and encourage the development of more executable GRN models

7.8 A new collision avoidance model with semi implicit random batch resolution

Participants: Léon Tine.

Research on crowd simulation has important and wide range of applications. The main difficulty is how to lead all particles with a same and simple rule, especially when particles are numerous. In 8, we firstly propose a two dimensional agent-based collision avoidance model, which is a N-particles Newtonian system. The collision interaction force, imminent interaction force and following interaction force are designed, so that particles can be guided to their respective destinations without collisions. The proposed agent-based model is then extended to the corresponding mean field limit model as N→∞. Secondly, notice that direct simulation of the N-particles Newtonian system is very time-consuming, since the computational complexity is of order O(N2). In contrast, we propose an efficient hybrid resolution strategy to reduce the computational complexity. It is a combination of the Random Batch method (Shi Jin, Lei Li, and Jian-Guo Liu. Random batch methods (RBM) for interacting particle systems. Journal of Computational Physics, 400:108877, 2020.) and the method based on local particles Newtonian system. Thanks to this hybrid resolution strategy, the computational complexity is reduced to O(N). Finally, various tests are presented to show robustness and efficiency of our collision avoidance model and the hybrid resolution strategy.