Stéphanie Portet

The interplay between reaction kinetics and diffusion leads to a wide range of spatiotemporal behaviors in reaction–diffusion (RD) systems. This article presents a theoretical and computational study of a RD system inspired by experimental observations of the Rho-GEF-Myosin signaling network controlling cell contraction dynamics. The temporal reaction system dynamics range from periodicity to bistability. By employing a dual hybrid dynamical systems approach of numerical bifurcation analysis and Floquet theory, we characterize the spatiotemporal dynamics when stable limit-cycle oscillators or homogeneous time-periodic solutions undergo the process of Floquet–Turing-diffusion-driven-instability (FTDDI). FTDDI refers to the emergence of spatially nonuniform patterns when diffusion destabilizes an otherwise temporally stable limit cycle of the underlying reaction kinetics. For the temporal reaction system, numerical bifurcation allows us to identify regions in a two-parameter space defining the stability of the uniform steady states and regions where the system exhibits limit cycles, which are characterized by employing the Floquet theory. In the presence of spatial variations, Floquet theory classifies regions where diffusion destabilizes the limit cycle or maintains their homogeneous stability and the emerging spatiotemporal dynamics of the full system, far from equilibrium. In the bistable regime, diffusion differentiates regions into those that exhibit classical Turing diffusion-driven instability, leading to pattern formation; and those that exhibit FTDDI, leading to space-time periodic patterns, spatially inhomogeneous patterns, oscillatory pulses, and wave propagation, and those that remain unaffected by diffusion. These findings provide theoretical insights into understanding complex spatiotemporal dynamics relevant to biological, chemical, and ecological spatiotemporal systems.

Intermediate filaments form an essential structural network, spread throughout the cytoplasm, and play a key role in cell mechanics, intracellular organization, and molecular signaling. The maintenance of the network and its adaptation to the cell's dynamic behavior relies on several mechanisms implicating cytoskeletal crosstalk which are not fully understood. Mathematical modeling allows us to compare several biologically realistic scenarios to help us interpret experimental data. In this study we observe and model the dynamics of the vimentin intermediate filaments in single glial cells seeded on circular micropatterns following microtubule disruption by nocodazole treatment. In these conditions, the vimentin filaments move towards the cell center and accumulate before eventually reaching a steady state. In the absence of microtubule-driven transport, the motion of the vimentin network is primarily driven by actin-related mechanisms. To model these experimental findings, we hypothesize that vimentin may exist in two states, mobile and immobile, and switch between the states at unknown (either constant or nonconstant) rates. Mobile vimentin is assumed to advect with either constant or nonconstant velocity. We introduce several biologically realistic scenarios using this set of assumptions. For each scenario, we use differential evolution to find the best parameter sets resulting in a solution that most closely matches the experimental data and then the assumptions are evaluated using the Akaike information criterion. This modeling approach allows us to conclude that our experimental data are best explained by a spatially dependent trapping of intermediate filaments or a spatially dependent speed of actin-dependent transport.

In this paper, we provide a simple ODEs model with a generic nonlinear incidence rate function and incorporate two treatments, blocking the virus binding and inhibiting the virus replication to investigate the impact of calibration on model predictions for the SARS-CoV-2 infection dynamics. We derive conditions of the infection eradication for the long-term dynamics using the basic reproduction number, and complement the characterization of the dynamics at short-time using the resilience and reactivity of the virus-free equilibrium are considered to inform on the average time of recovery and sensitivity to perturbations in the initial virus free stage. Then, we calibrate the treatment model to clinical datasets for viral load in mild and severe cases and immune cells in severe cases. Based on the analysis, the model calibrated to these different datasets predicts distinct scenarios: eradication with a non reactive virus-free equilibrium, eradication with a reactive virus-free equilibrium, and failure of infection eradication. Moreover, severe cases generate richer dynamics and different outcomes with the same treatment. Calibration to different datasets can lead to diverse model predictions, but combining long- and short-term dynamics indicators allows the categorization of model predictions and determination of infection severity.

Intermediate laments form an essential structural network, spread throughout the cytoplasm andplay a key role in cell mechanics, intracellular organization and molecular signaling. The maintenanceof the network and its adaptation to the cell's dynamic behavior relies on several mechanismsimplicating cytoskeletal crosstalk which are not fully understood. Mathematical modeling allows usto compare several biologically realistic scenarios to help us interpret experimental data. In thisstudy, we observe and model the dynamics of the vimentin intermediate laments in single glial cellsseeded on circular micropatterns following microtubule disruption by nocodazole treatment. In theseconditions, the vimentin laments move towards the cell center and accumulate before eventuallyreaching a steady-state. In absence of microtubule-driven transport, the motion of the vimentinnetwork is primarily driven by actin-related mechanisms. To model these experimental ndings, wehypothesize that vimentin may exist in two states, mobile and immobile, and switches between thestates at unknown (either constant or non-constant) rates. Mobile vimentin are assumed to advectwith either constant or non-constant velocity. We introduce several biologically realistic scenariosusing this set of assumptions. For each scenario, we use dierential evolution to nd the bestparameter sets resulting in a solution that most closely matches the experimental data, then theassumptions are evaluated using the Akaike Information Criterion. This modeling approach allowsus to conclude that our experimental data are best explained by a spatially dependent trapping ofintermediate laments or a spatially dependent speed of actin-dependent transport.

Fluorescence Recovery After Photobleaching (FRAP) has been extensively used to understand molecular dynamics in cells. This technique when applied to soluble, globular molecules driven by diffusion is easily interpreted and well understood. However, the classical methods of analysis cannot be applied to anisotropic structures subjected to directed transport, such as cytoskeletal filaments or elongated organelles transported along microtubule tracks. A new mathematical approach is needed to analyze FRAP data in this context and determine what information can be obtain from such experiments. To address these questions, we analyze fluorescence intensity profile curves after photobleaching of fluorescently labelled intermediate filaments anterogradely transported along microtubules. We apply the analysis to intermediate filament data to determine information about the filament motion. Our analysis consists of deriving equations for fluorescence intensity profiles and developing a mathematical model for the motion of filaments and simulating the model. Two closed forms for profile curves were derived, one for filaments of constant length and one for filaments with constant velocity, and three types of simulation were carried out. In the first type of simulation, the filaments have random velocities which are constant for the duration of the simulation. In the second type, filaments have random velocities which instantaneously change at random times. In the third type, filaments have random velocities and exhibit pausing between velocity changes. Our analysis shows: the most important distribution governing the shape of the intensity profile curves obtained from filaments is the distribution of the filament velocity. Furthermore, filament length which is constant during the experiment, had little impact on intensity profile curves. Finally, gamma distributions for the filament velocity with pauses give the best fit to asymmetric fluorescence intensity profiles of intermediate filaments observed in FRAP experiments performed in polarized migrating astrocytes. Our analysis also shows that the majority of filaments are stationary. Overall, our data give new insight into the regulation of intermediate filament dynamics during cell migration.

Vimentin is a highly charged intermediate filament protein that inherently forms extended dimeric coiled-coils, which serve as the basic building blocks of intermediate filaments. Under low ionic strength conditions, vimentin filaments dissociate into uniform tetrameric complexes of two anti-parallel oriented, half-staggered coiled-coil dimers. By addition of salt, vimentin tetramers spontaneously reassemble into filaments in a time-dependent process: i) lateral assembly of tetramers into unit-length filaments (ULFs); ii) longitudinal annealing of ULFs; iii) longitudinal assembly of filaments coupled with subsequent radial compaction. To independently determine the lateral and longitudinal assembly kinetics, we measure with a stopped-flow instrument the static light scattering signal at two different wavelengths (405 and 594 nm) with a temporal resolution of 3 ms, and analyze the signals based on Rayleigh-Gans theory. This theory considers that the intensity of the scattered light depends not only on the molecular weight of the scattering object but also on its shape. This shape-dependence is more pronounced at shorter wavelengths, allowing us to decompose the scattered light signal into its components arising from lateral and longitudinal filament assembly. We demonstrate that both the lateral and longitudinal filament assembly kinetics increase with salt concentration. Significance statement: The proper formation of intermediate filament (IF) networks in the cytoplasm is important for numerous cell functions. Here, we present a stopped-flow method for measuring the in-vitro assembly kinetics of intermediate filaments with a temporal resolution of 3 ms using static light scattering at two different wavelengths. This allows us to compute the shape factor of the assembly products based on Rayleigh-Gans light scattering theory. From the shape factor, we can separately measure the lateral assembly of tetramers into unit-length filaments (ULFs), and the longitudinal annealing of ULFs and longer filaments. For the IF protein vimentin, we find that with increasing salt concentrations, both the lateral and longitudinal assembly rates increase, and unstable, hyper-aggregated assembly complexes emerge.

Recent experimental observations reveal that local cellular contraction pulses emerge via a combination of fast positive and slow negative feedbacks based on a signal network composed of Rho, GEF and Myosin interactions [22]. As an examplary, we propose to study a plausible, hypothetical temporal model that mirrors general principles of fast positive and slow negative feedback, a hallmark for activator-inhibitor models. The methodology involves (ⅰ) a qualitative analysis to unravel system switching between different states (stable, excitable, oscillatory and bistable) through model parameter variations; (ⅱ) a numerical bifurcation analysis using the positive feedback mediator concentration as a bifurcation parameter, (ⅲ) a sensitivity analysis to quantify the effect of parameter uncertainty on the model output for different dynamic regimes of the model system; and (ⅳ) numerical simulations of the model system for model predictions. Our methodological approach supports the role of mathematical and computational models in unravelling mechanisms for molecular and developmental processes and provides tools for analysis of temporal models of this nature.

We consider models for the importation of a new variant COVID-19 strain in a location already seeing propagation of a resident variant. By distinguishing contaminations generated by imported cases from those originating in the community, we are able to evaluate the contribution of importations to the dynamics of the disease in a community. We find that after an initial seeding, the role of importations becomes marginal compared to that of community-based propagation. We also evaluate the role of two travel control measures, quarantine and travel interruptions. We conclude that quarantine is an efficacious way of lowering importation rates, while travel interruptions have the potential to delay the consequences of importations but need to be applied within a very tight time window following the initial emergence of the variant.