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Intermediate filament (IF) proteins assemble into highly flexible filaments that organize into complex cytoplasmic networks: keratins in all types of epithelia, vimentin in endothelia, and desmin in muscle. Since IF elongation proceeds via end-to-end annealing of unit-length filaments and successively of progressively growing filaments, it is important to know how their remarkable flexibility, i.e., their persistence length [Formula: see text] , influences the assembly kinetics. In fact, their [Formula: see text] ranges between 0.3 μm (keratin K8/K18) and 1.0 μm (vimentin and desmin), and thus is orders of magnitude lower than that of microtubules and F-actin. Here, we present a unique mathematical model, which implements the semiflexible nature of the three IF types based on published semiflexible polymers theories and depends on a single free parameter [Formula: see text]. Calibrating this model to filament mean length dynamics of the three proteins, we demonstrate that the persistence length is indeed essential to accurately describe their assembly kinetics. Furthermore, we reveal that the difference in flexibility alone does not explain the significantly faster assembly rate of keratin filaments compared with that of vimentin. Likewise, desmin assembles approximately six times faster than vimentin, even though both their filaments exhibit the same [Formula: see text] value. These data strongly indicate that differences in their individual amino acid sequences significantly impact the assembly rates. Nevertheless, using a single [Formula: see text] value for each of these three key representatives of the IF protein family, our advanced model does accurately describe the length distribution and mean length dynamics and provides effective filament assembly rates. It thus provides a tool for future investigations on the impact of posttranslational modifications or amino acid changes of IF proteins on assembly kinetics. This is an important issue, as the discovery of mutations in IF genes causing severe human disease, particularly for desmin and keratins, is steadily increasing.

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.

The activation of 2'-5'-oligoadenylate synthetase (OAS) enzymes by direct interaction with viral double-stranded RNA (dsRNA) is a key part of the innate immune response to viral infection. A downstream effect of the OAS-dsRNA interaction is to degrade the single-stranded RNA to prevent the spread of the virus. The activation of OAS2, one of the members of the OAS family, depends on dsRNA length. Combining in vitro experiments and mathematical modelling, we test different hypotheses for the OAS2 activation mechanisms by its cofactor dsRNA. After model calibration and selection, the cooperative binding of multiple OAS2 to a single dsRNA is shown to best represent the effect of its cofactor length on enzyme activity.

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 statementThe 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.

Several cellular activities, such as directed cell migration, are coordinated by an intricate network of biochemical reactions which lead to a polarised state of the cell, in which cellular symmetry is broken, causing the cell to have a well defined front and back. Recent work on balancing biological complexity with mathematical tractability resulted in the proposal and formulation of a famous minimal model for cell polarisation, known as the wave pinning model. In this study, we present a three-dimensional generalisation of this mathematical framework through the maturing theory of coupled bulk-surface semilinear partial differential equations in which protein compartmentalisation becomes natural. We show how a local perturbation over the surface can trigger propagating reactions, eventually stopped in a stable profile by the interplay with the bulk component. We describe the behaviour of the model through asymptotic and local perturbation analysis, in which the role of the geometry is investigated. The bulk-surface finite element method is used to generate numerical simulations over simple and complex geometries, which confirm our analysis, showing pattern formation due to propagation and pinning dynamics. The generality of our mathematical and computational framework allows to study more complex biochemical reactions and biomechanical properties associated with cell polarisation in multi-dimensions.

International audience; Noise affects all biological processes from molecules to cells, organisms and populations. Although the effect of noise on these processes is highly variable, evidence is accumulating which shows natural stochastic fluctuations (noise) can facilitate biological functions. Herein, we investigate the effect of noise on the transport of intermediate filaments in cells by comparing the stochastic and deterministic formalizations of the bidirectional transport of intermediate filaments, long elastic polymers transported along microtubules by antagonistic motor proteins (Dallon et al., 2019; Portet et al., 2019). By numerically exploring discrepancies in timescales and attractors between both formalizations, we characterize the impact of stochastic fluctuations on the individual and ensemble transport. Biologically, we find that noise promotes the collective movement of intermediate filaments and increases the efficiency of its regulation by the biochemical properties of motor-cargo interactions. While stochastic fluctuations reduce the impact of the initial distributions of motor proteins in cells, the number of binding sites and the affinity of motor-cargo interactions are the key parameters controlling transport efficiency and efficacy.

Using a stochastic model, we assess the risk of importation-induced local transmission chains in locations seeing few or no local transmissions and evaluate the role of quarantine in the mitigation of this risk. We find that the rate of importations plays a critical role in determining the risk that case importations lead to local transmission chains, more so than local transmission characteristics, i.e. strength of social distancing measures (NPI). The latter influences the severity of the outbreaks when they do take place. Quarantine after arrival in a location is an efficacious way to reduce the rate of importations. Locations that see no or low-level local transmission should ensure that the rate of importations remains low. A high level of compliance with post-arrival quarantine followed by testing achieves this objective with less of an impact than travel restrictions or bans.

Summary Local cell contraction pulses play important roles in tissue and cell morphogenesis. Here, we improve a chemo-optogenetic approach and apply it to investigate the signal network that generates these pulses. We use these measurements to derive and parameterize a system of ordinary differential equations describing temporal signal network dynamics. Bifurcation analysis and numerical simulations predict a strong dependence of oscillatory system dynamics on the concentration of GEF-H1, an Lbc-type RhoGEF, which mediates the positive feedback amplification of Rho activity. This prediction is confirmed experimentally via optogenetic tuning of the effective GEF-H1 concentration in individual living cells. Numerical simulations show that pulse amplitude is most sensitive to external inputs into the myosin component at low GEF-H1 concentrations and that the spatial pulse width is dependent on GEF-H1 diffusion. Our study offers a theoretical framework to explain the emergence of local cell contraction pulses and their modulation by biochemical and mechanical signals., Graphical Abstract, Highlights • Cell contraction dynamics are investigated via acute chemo-optogenetic perturbations • A theoretical model predicts GEF-H1-dependent switches in pulsatile Rho dynamics • Experimental manipulations of cytosolic GEF-H1 levels confirm model predictions • Local pulsatile dynamics are generated by coupling feedback regulation and diffusion, Kamps et al. derive a reaction-diffusion system that generates subcellular activity pulses of the cell contraction regulator Rho. System parameters are obtained by combining perturbation-response analyses with theoretical investigations. Multiple switches in activity dynamics, which are dependent on the positive feedback mediator GEF-H1, are predicted by theory and confirmed experimentally.

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.

Breast cancer is the most common cancer in women worldwide. Hormone receptor breast cancers are the most common ones and, about 2 out of every 3 cases of breast cancer are estrogen receptor (ER) positive. Selective ER modulators, such as tamoxifen, are the first line of endocrine treatment of breast cancer. Despite the expression of hormone receptors some patients develop tamoxifen resistance and 50% present de novo tamoxifen resistance. Recently, we have demonstrated that activated mammalian target of rapamycin (mTOR) is positively associated with overall survival and recurrence free survival in ER positive breast cancer patients who were later treated with tamoxifen. Since altered expression of protein kinase B (PKB)/Akt in breast cancer cells affect N-myristoyltransferase 1 (NMT1) expression and activity, we investigated whether mTOR, a downstream target of PKB/Akt, regulates NMT1 in ER positive breast cancer cells (MCF7 cells). We inhibited mTOR by treating MCF7 cells with rapamycin and observed that the expression of NMT1 increased with rapamycin treatment over the period of time with a concomitant decrease in mTOR phosphorylation. We further employed mathematical modelling to investigate hitherto not known relationship of mTOR with NMT1. We report here for the first time a collection of models and data validating regulation of NMT1 by mTOR.

International audience; Intermediate filaments are long elastic fibers that are transported by the microtubule-associated motor proteins kinesin and dynein inside the cell. How elastic filaments are efficiently transported by antagonistic motors is not well understood and is difficult to measure with current experimental techniques. Adapting the tug-of-war paradigm for vesiclelike cargos, we develop a mathematical model to describe the motion of an elastic filament punctually bound to antagonistic motors. As observed in cells, up to three modes of transport are obtained; dynein-driven retrograde, kinesin-driven anterograde fast motions, and a slow motion. Motor properties and initial conditions that depend on intracellular context regulate the transport of filaments. Filament elasticity is found to affect both the mode and the efficiency of transport. We further show that the coordination of motors along the filament emerges from the interplay between intracellular context and elastic properties of filaments.

International audience; Intermediate filaments are a key component of the cytoskeleton. Their transport along microtubules plays an essential role in the control of the shape and structural organization of cells. To identify the key parameters responsible for the control of intermediate filament transport, we generated a model of elastic filament transport by microtubule-associated dynein and kinesin. The model is also applicable to the transport of any elastically-coupled cargoes. We investigate the effect of filament properties such as number of motor binding sites, length, and elasticity on motion of filaments. Additionally, we consider the effect of motor properties, i.e. off rates, on filament transport. When one motor has a catch bond off rate it dictates the motion, whereas when motors have the same type of off rate filaments can alternate between retrograde and anterograde motions. The elasticity of filaments optimizes the filament transport and the coordination of motors along the length of the filament.

A complex network model for the spread of Dutch Elm Disease in an urban forest is formulated. American elms are the focus of the model. Each elm can be in one of five states, a combination of their life and epidemiological status. Each tree is also potentially a host to a population of elm bark beetles, the vectors of Dutch Elm Disease. The epidemiological dynamics of trees is governed by a stochastic process that takes into account the dispersal of spore-carrying beetles between trees and potential contacts between tree root systems. The model describes seasonal variations of beetle activity and population dynamics. Numerical simulations and sensitivity analyses of the model are carried out. In this introductory paper, we use data from the City of Winnipeg, where Dutch Elm Disease is prevalent, and focus on two neighbourhoods representative of a residential area and an area with urban parks.

An SIR infectious disease propagation model is considered that incorporates mobility of individuals between a large urban centre and smaller satellite cities. Because of the difference in population sizes, the urban centre has standard incidence and satellite cities have mass action incidence. It is shown that the general basic reproduction number \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {R}}_{0}$$\end{document}R0 acts as a threshold between global asymptotic stability of the disease free equilibrium and disease persistence. The case of Winnipeg (MB, Canada) and some neighbouring satellite communities is then considered numerically to complement the mathematical analysis, highlighting the importance of taking into account not only \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {R}}_{0}$$\end{document}R0 but also other measures of disease severity. It is found that the large urban centre governs most of the behaviour of the general system and control of the spread is better achieved by targeting it rather than reducing movement between the units. Also, the capacity of a satellite city to affect the general system depends on its population size and its connectivity to the main urban centre.

Keratin intermediate filament networks are part of the cytoskeleton in epithelial cells. They were found to regulate viscoelastic properties and motility of cancer cells. Due to unique biochemical properties of keratin polymers, the knowledge of the mechanisms controlling keratin network formation is incomplete. A combination of deterministic and stochastic modeling techniques can be a valuable source of information since they can describe known mechanisms of network evolution while reflecting the uncertainty with respect to a variety of molecular events. We applied the concept of piecewise-deterministic Markov processes to the modeling of keratin network formation with high spatiotemporal resolution. The deterministic component describes the diffusion-driven evolution of a pool of soluble keratin filament precursors fueling various network formation processes. Instants of network formation events are determined by a stochastic point process on the time axis. A probability distribution controlled by model parameters exercises control over the frequency of different mechanisms of network formation to be triggered. Locations of the network formation events are assigned dependent on the spatial distribution of the soluble pool of filament precursors. Based on this modeling approach, simulation studies revealed that the architecture of keratin networks mostly depends on the balance between filament elongation and branching processes. The spatial distribution of network mesh size, which strongly influences the mechanical characteristics of filament networks, is modulated by lateral annealing processes. This mechanism which is a specific feature of intermediate filament networks appears to be a major and fast regulator of cell mechanics.

A model is developed to study the in vivo intermediate filament organization in terms of repartition between four different structural states: soluble proteins, particles, short, and long filaments. An analysis is conducted, showing that the system has a unique, globally asymptotically stable equilibrium. By means of sensitivity analysis, the influence of parameters on the system is studied. It is shown that, in agreement with biological observations, posttranslational modifications of intermediate filament proteins resulting in filament solubilization are the main regulators of the intermediate filament organization. A high signalling-dependent solubilization of filaments favours the intermediate filament aggregation in particles.

In vitro assembly of intermediate filament proteins is a very rapid process. It starts without significant delay by lateral association of tetramer complexes into unit-length filaments (ULFs) after raising the ionic strength from low salt to physiological conditions (100 mM KCl). We employed electron and scanning force microscopy complemented by mathematical modeling to investigate the kinetics of in vitro assembly of human recombinant vimentin. From the average length distributions of the resulting filaments measured at increasing assembly times we simulated filament assembly and estimated specific reaction rate parameters. We modeled eight different potential pathways for vimentin filament elongation. Comparing the numerical with the experimental data we conclude that a two-step mechanism involving rapid formation of ULFs followed by ULF and filament annealing is the most robust scenario for vimentin assembly. These findings agree with the first two steps of the previously proposed three-step assembly model (Herrmann, H., and Aebi, U. (1998) Curr. Opin. Struct. Biol. 8, 177-185). In particular, our modeling clearly demonstrates that end-to-end annealing of ULFs and filaments is obligatory for forming long filaments, whereas tetramer addition to filament ends does not contribute significantly to filament elongation.

Keratin are among the most abundant proteins in epithelial cells. Functions of the keratin network in cells are shaped by their dynamical organization. Using a collection of experimentally-driven mathematical models, different hypotheses for the turnover and transport of the keratin material in epithelial cells are tested. The interplay between turnover and transport and their effects on the keratin organization in cells are hence investigated by combining mathematical modeling and experimental data. Amongst the collection of mathematical models considered, a best model strongly supported by experimental data is identified. Fundamental to this approach is the fact that optimal parameter values associated with the best fit for each model are established. The best candidate among the best fits is characterized by the disassembly of the assembled keratin material in the perinuclear region and an active transport of the assembled keratin. Our study shows that an active transport of the assembled keratin is required to explain the experimentally observed keratin organization., 27 pages, 11 Figures

This paper discusses the role of nonlinearities in the physical description of key biomolecules that participate in crucial subcellular processes, namely actin, microtubules and ions crowding around these filaments. The assembly kinetics of actin is that of a nonlinear process that is governed by coupled nonlinear equations involving monomer concentration and filament number as the dynamical variables. The dendritic growth of actin networks in cell motility phenomena is described by the coupling of actin filaments to the protein Arp2/3. We then discuss how coupled differential equations describing the interactions between ions in solution and the filament they surround can lead to solitonic signal transmission. We also investigate the role of nonlinear dynamics in the formation of microtubules. Space-flight laboratory experiments have shown that the self-organization of microtubules is sensitive to gravitational conditions. We propose a model of self-organization of microtubules in a gravitational field based on the dominant chemical kinetics. The pattern formation of microtubule concentration is obtained in terms of a moving kink. Finally, we present a model of elastic properties of microtubules describing a microtubule as an elastic rod. We found that when the microtubule is subjected to bending forces, the tangent angle satisfies a Sine-Gordon equation whose solutions describe kink and anti-kink bending modes that may propagate at a range of velocities along the length of the microtubule.

This Letter discusses the role of key physical and chemical effects in the emergence of pattern formation in microtubule assemblies in vitro under the influence of gravity. The roles of chemical kinetics, diffusion, gravitational drift and electrostatic interactions affected by thermal fluctuations are discussed. The subtle interplay of these factors leads to the observed self-organization phenomena exhibiting the features of a typical polar liquid crystal phase.

We review and model the experimental parameters which characterize elastic properties of microtubules. Three macroscopic estimates are made of the anisotropic elastic moduli, accounting for the molecular forces between tubulin dimers: for a longitudinal compression of a microtubule, for a lateral force and for a shearing force. These estimates reflect the anisotropies in these parameters observed in several recent experiments.

Because cells are sensitive to mechanical forces, weightlessness might act on stress-dependent cell changes. Human breast cancer cells MCF-7, flown in space in a Photon capsule, were fixed after 1.5, 22 and 48 h in orbit. Cells subjected to weightlessness were compared to 1 g in-flight and ground controls. Post-flight, fluorescent labeling was performed to visualize cell proliferation (Ki-67), three cytoskeleton components and chromatin structure. Confocal microscopy and image analysis were used to quantify cycling cells and mitosis, modifications of the cytokeratin network and chromatin structure. Several main phenomena were observed in weightlessness: The perinuclear cytokeratin network and chromatin structure were looser; More cells were cycling and mitosis was prolonged. Finally, cell proliferation was reduced as a consequence of a cell-cycle blockade; Microtubules were altered in many cells. The results reported in the first point are in agreement with basic predictions of cellular tensegrity. The prolongation of mitosis can be explained by an alteration of microtubules. We discuss here the different mechanisms involved in weightlessness alteration of microtubules: i) alteration of their self-organization by reaction-diffusion processes, and a mathematical model is proposed, ii) activation or deactivation of microtubules stabilizing proteins, acting on both microtubule and microfilament networks in cell cortex.

The Gross–Pitaevskii regime of a Bose–Einstein condensate is investigated using a fully non-linear approach. The confining potential first adopted is that of a linear ramp. An infinite class of new analytical solutions of this linear ramp potential approximation to the Gross–Pitaevskii equation is found which are characterised by pronounced large-amplitude oscillations close to the boundary of the condensate. The limiting case within this class is a nodeless ground state which is known from recent investigations as an extension of the Thomas–Fermi approximation. We have found the energies of the oscillatory states to lie above the ground state energy but recent experimental work, especially on spatially confined superconductors, indicates that such states may be easily occupied and made manifest at finite temperatures. We have also investigated their stability using a Poincare section analysis as well as a linear perturbation approach. Both these techniques demonstrate stability against small perturbations. Finally, we have discussed the relevance of these quasi-one-dimensional solutions in the context of the fully three-dimensional condensates. This has been argued on the basis of numerical work and asymptotic approximations.

Background: In the MCF7 human breast cancer cell line, several patterns of cytokeratin networks are observed, depending on the intracellular localization. Our hypothesis is that architectural variations of cytokeratin networks depend on local tensions or forces appearing spontaneously in the cytoplasm. The aim of this work was to discriminate between the different patterns and to quantitate these variations. Materials and Methods: Image analysis procedures were developed to extract cytokeratin filament networks visualized by immunofluorescence and confocal microscopy. Two methods were used to segment sets of curvilinear objects. The first, the ‘‘mesh-approach,’’ based on classical methods of mathematical morphology, takes into account global network topology. The second, the ‘‘filamentapproach’’ (novel), is meant to account for individual element morphology. These methods and their combination allow the computation of several features at two levels of geometry: global (network topology) and local (filament morphology). Results: Variations in cytokeratin networks are characterized by their connectivity, density, mesh structure, and filament shape. The connectivity and the density of a network describe its location in a local ‘‘stress-force’’ zone or in a ‘‘relaxed’’ zone. The mesh structure characterizes the intracellular localization of the network. Moreover, the filament shape reflects the intracellular localization and the occurrence of a ‘‘stress-force’’ zone. Conclusions: These features permitted the quantitation of differences within the network patterns and within the specific filament shapes according to the intracellular localization. Further experiments on cells submitted to external forces will test the hypothesis that the architectural variations of intermediate filaments reflect intracytoplasmic tensions. Cytometry 35:203‐213, 1999. r 1999 Wiley-Liss, Inc.

Recent space-flight experiments performed by Tabony's team provided further evidence that a microgravity environment strongly affects the spatio-temporal organization of microtubule assemblies. Characteristic time and length scales were found that govern the organization of oriented bundles under Earth's gravitational field (GF). No such organization has been observed in a microgravity environment. This paper discusses physical mechanisms resulting in pattern formation under gravity and its disappearance in microgravity. The subtle interplay between chemical kinetics, diffusion, gravitational drift, thermal fluctuations, electrostatic interactions and liquid crystalline characteristics provides a plausible scenario.

A mechanism of intermediate filament disassembly regulation is proposed in which disassembly is regulated by the amount of proteins assembled in networks. It is also hypothesized that a delay might exist between regulation and actual disassembly. Under realistic biological conditions of assembly and disassembly, it is shown that such a delay is harmless and does not destabilize the organization of intermediate filaments in networks. However, for high rates of disassembly, the model predicts that delay can destabilize the organization, with the intermediate filament material oscillating between organizations mainly in networks and in nonfilamentous particles.

An aggregation model with explicit expression of association rate constants is considered to study in vitro type III intermediate filament length distribution dynamics. Different assumptions on the properties of filaments and probability of aggregation are considered, leading to four models. Fitting of model responses to experimental data leads to the identification of the most appropriate model to represent each time point of the assembly. A combination of models allows the construction of a mixed model that represents well the complete assembly dynamics: it is found that the rate constants decrease with respect to filament size when the aggregation involves at least one short filament, whereas for longer filaments they are almost independent of size. The flexible nature of filaments is thus important in the assembly of intermediate filaments.

SPECIFIC AIMThis study aims to investigate the role of gravity in signal transduction across the cytoskeleton to the nucleus. According to our hypothesis, gravity was considered as an external forc...

The salt-induced in vitro assembly of cytoplasmic intermediate filament (IF) proteins such as vimentin is characterized by a very rapid lateral association of soluble tetrameric subunits into 60-nm-long full-width "unit-length" filaments (ULFs). We have demonstrated for this prototype IF protein that filament elongation occurs by the longitudinal annealing of ULFs into short IFs. These IFs further longitudinally anneal and thus constitute a progressively elongating filament population that over time yields filaments of several microm in length. Previously, we provided a mathematical model for the kinetics of the assembly process based on the average length distribution of filaments as determined by time-lapse electron and atomic force microscopy. Thereby, we were able to substantiate the concept that end-to-end-annealing of both ULFs and short filaments is obligatory for the formation of long IFs (Kirmse, R.; Portet, S.; Mucke, N. Aebi, U.; Herrmann, H.; Langowski, J. J. Biol. Chem. 2007, 282, 18563-18572). As the next step in understanding the mechanics of IF formation, we have expanded our mathematical model to describe the quantitative aspects of IF assembly by taking into account geometry constraints as well as the diffusion properties of rodlike linear aggregates. Thereby, we have developed a robust model for the time-dependent filament length distribution of IFs under standard conditions.

A model is developed to study the in vivo intermediate filament organization in terms of repartition between four different structural states: soluble proteins, particles, short, and long filaments. An analysis is conducted, showing that the system has a unique, globally asymptotically stable equilibrium. By means of sensitivity analysis, the influence of parameters on the system is studied. It is shown that, in agreement with biological observations, posttranslational modifications of intermediate filament proteins resulting in filament solubilization are the main regulators of the intermediate filament organization. A high signalling-dependent solubilization of filaments favours the intermediate filament aggregation in particles.

We propose two systems of ordinary differential equations modeling the assembly of intermediate filament networks. The first one describes the in vitro intermediate filament assembly dynamics. The second one deals with the in vivo evolution of cytokeratin, which is the intermediate filament protein expressed by epithelial cells. The in vitro model is then briefly analyzed in a simplified case.

Parameters characterizing elastic properties of microtubules, measured in several recent experiments, reflect an anisotropic character. We describe the microscopic dynamical properties of microtubules using a discrete model based on an appropriate lattice of dimers. Adopting a harmonic approximation for the dimer–dimer interactions and estimating the lattice elastic constants, we make predictions regarding vibration dispersion relations and vibration propagation velocities. Vibration frequencies and velocities are expressed as functions of the elastic constants and of the geometrical characteristics of the microtubules. We show that vibrations which propagate along the protofilament do so significantly faster than those along the helix.

We investigate the conditions enabling actin filaments to act as electrical transmission lines for ion flows along their lengths. We propose a model in which each actin monomer is an electric element with a capacitive, inductive, and resistive property due to the molecular structure of the actin filament and viscosity of the solution. Based on Kirchhoff's laws taken in the continuum limit, a nonlinear partial differential equation is derived for the propagation of ionic waves. We solve this equation in two different regimes. In the first, the maximum propagation velocity wave is found in terms of Jacobi elliptic functions. In the general case, we analyze the equation in terms of Fisher-Kolmogoroff modes with both localized and extended wave characteristics. We propose a new signaling mechanism in the cell, especially in neurons.

Tabony and co-workers [C. Papaseit, N. Pochon, and J. Tabony, Proc. Natl. Acad. Sci. U.S.A. 97, 8364 (2000)] showed that the self-organization of microtubules from purified tubulin solutions is sensitive to gravitational conditions. In this paper, we propose two models of spatial and orientational self-organization of microtubules in a gravitational field. First, the spatial model is based on the dominant chemical kinetics. The pattern formation of microtubule concentration is obtained (1) in terms of a moving kink in the limit when the disassembly rate is negligible, and (2) for the case of no free tubulin and only assembled microtubules present. Second, the orientational pattern of striped microtubule domains is consistent with predictions from a phenomenological Landau-Ginzburg free energy expansion in terms of an orientational order parameter.

At a macroscopic level of large bending motions, a continuum medium model is proposed describing a microtubule as an elastic rod. Compressional and shear deformations are excluded as less relevant biophysically. When the microtubule is subjected to a constant bending force, it is found that the dynamics of the angular deviation, with respect to the rectilinear configuration of the microtubule, is governed by a Sine-Gordon Equation. Particular analytical solutions of this equation are found which describe kink and anti-kink bending modes which may propagate at various subsonic speeds along the length of the microtubule. Kinetic energies of these modes are calculated for different propagation velocities and compared with thermal and ATP hydrolysis energies. Viscous damping is shown to be negligible for long microtubules and fast moving bending deformations.

A model is introduced for the transmission dynamics of a vector-borne disease with two vector strains, one wild and one pathogen-resistant; resistance comes at the cost of reduced reproductive fitness. The model, which assumes that vector reproduction can lead to the transmission or loss of resistance (reversion), is analyzed in a particular case with specified forms for the birth and force of infection functions. The vector component can have, in the absence of disease, a coexistence equilibrium where both strains survive. In the case where reversion is possible, this coexistence equilibrium is globally asymptotically stable when it exists. This equilibrium is still present in the full vector-host system, leading to a reduction of the associated reproduction number, thereby making elimination of the disease more feasible. When reversion is not possible, there can exist an additional equilibrium with only resistant vectors.

Intermediate filaments (IFs) participate in directed cell migration, but how the IF network becomes polarized in motile cells is unclear. Leduc and Etienne-Manneville show that the turnover of IF mainly relies on actin-driven retrograde flow and microtubule-driven anterograde and retrograde transport. During cell migration, Cdc42-mediated polarity signaling inhibits dynein-dependent transport to promote the polarization of the IF network., Intermediate filaments (IFs) are key players in the control of cell morphology and structure as well as in active processes such as cell polarization, migration, and mechanoresponses. However, the regulatory mechanisms controlling IF dynamics and organization in motile cells are still poorly understood. In this study, we investigate the mechanisms leading to the polarized rearrangement of the IF network along the polarity axis. Using photobleaching and photoconversion experiments in glial cells expressing vimentin, glial fibrillary acidic protein, and nestin, we show that the distribution of cytoplasmic IFs results from a continuous turnover based on the cooperation of an actin-dependent retrograde flow and anterograde and retrograde microtubule-dependent transports. During wound-induced astrocyte polarization, IF transport becomes directionally biased from the cell center toward the cell front. Such asymmetry in the transport is mainly caused by a Cdc42- and atypical PKC–dependent inhibition of dynein-dependent retrograde transport. Our results show how polarity signaling can affect the dynamic turnover of the IF network to promote the polarization of the network itself.