248 research outputs found
Mathematical modelling and numerical simulations of actin dynamics in the eukaryotic cell
The aim of this article is to study cell deformation and cell movement by considering both the mechanical and biochemical properties of the cortical network of actin filaments and its concentration. Actin is a polymer that can exist either in fil- amentous form (F-actin) or in monometric form (G-actin) (Chen et al. 2000) and the filamentous form is arranged in a paired helix of two protofilaments (Ananthakrish- nan et al. 2006). By assuming that cell deformations are a result of the cortical actin dynamics in the cell cytoskeleton, we consider a continuum mathematical model that couples the mechanics of the network of actin filaments with its bio-chemical dy- namics. Numerical treatment of the model is carried out using the moving grid finite element method (Madzvamuse et al. 2003). Furthermore, by assuming slow deforma- tions of the cell, we use linear stability theory to validate the numerical simulation results close to bifurcation points. Far from bifurcation points, we show that the math- ematical model is able to describe the complex cell deformations typically observed in experimental results. Our numerical results illustrate cell expansion, cell contrac- tion, cell translation and cell relocation as well as cell protrusions. In all these results, the contractile tonicity formed by the association of actin filaments to the myosin II motor proteins is identified as a key bifurcation parameter
Hybrid data-based modelling in oncology: successes, challenges and hopes
International audienceIn this review we make the statement that hybrid models in oncology are required as a mean for enhanced data integration. In the context of systems oncology, experimental and clinical data need to be at the heart of the models developments from conception to validation to ensure a relevant use of the models in the clinical context. The main applications pursued are to improve diagnosis and to optimize therapies.We first present the Successes achieved thanks to hybrid modelling approaches to advance knowledge, treatments or drug discovery. Then we present the Challenges than need to be addressed to allow for a better integration of the model parts and of the data into the models. And Finally, the Hopes with a focus towards making personalised medicine a reality. Mathematics Subject Classification. 35Q92, 68U20, 68T05, 92-08, 92B05
Proceedings of the XXXIInd Seminar of the French-Speaking Society for Theoretical Biology; Saint-Flour (Cantal), France, 10–13 June, 2012
International audienc
Cortical Factor Feedback Model for Cellular Locomotion and Cytofission
Eukaryotic cells can move spontaneously without being guided by external
cues. For such spontaneous movements, a variety of different modes have been
observed, including the amoeboid-like locomotion with protrusion of multiple
pseudopods, the keratocyte-like locomotion with a widely spread lamellipodium,
cell division with two daughter cells crawling in opposite directions, and
fragmentations of a cell to multiple pieces. Mutagenesis studies have revealed
that cells exhibit these modes depending on which genes are deficient,
suggesting that seemingly different modes are the manifestation of a common
mechanism to regulate cell motion. In this paper, we propose a hypothesis that
the positive feedback mechanism working through the inhomogeneous distribution
of regulatory proteins underlies this variety of cell locomotion and
cytofission. In this hypothesis, a set of regulatory proteins, which we call
cortical factors, suppress actin polymerization. These suppressing factors are
diluted at the extending front and accumulated at the retracting rear of cell,
which establishes a cellular polarity and enhances the cell motility, leading
to the further accumulation of cortical factors at the rear. Stochastic
simulation of cell movement shows that the positive feedback mechanism of
cortical factors stabilizes or destabilizes modes of movement and determines
the cell migration pattern. The model predicts that the pattern is selected by
changing the rate of formation of the actin-filament network or the threshold
to initiate the network formation
Multiscale modelling of vascular tumour growth in 3D: the roles of domain size & boundary condition
We investigate a three-dimensional multiscale model of vascular tumour growth, which couples blood flow, angiogenesis, vascular remodelling, nutrient/growth factor transport, movement of, and interactions between, normal and tumour cells, and nutrient-dependent cell cycle dynamics within each cell. In particular, we determine how the domain size, aspect ratio and initial vascular network influence the tumour's growth dynamics and its long-time composition. We establish whether it is possible to extrapolate simulation results obtained for small domains to larger ones, by constructing a large simulation domain from a number of identical subdomains, each subsystem initially comprising two parallel parent vessels, with associated cells and diffusible substances. We find that the subsystem is not representative of the full domain and conclude that, for this initial vessel geometry, interactions between adjacent subsystems contribute to the overall growth dynamics. We then show that extrapolation of results from a small subdomain to a larger domain can only be made if the subdomain is sufficiently large and is initialised with a sufficiently complex vascular network. Motivated by these results, we perform simulations to investigate the tumour's response to therapy and show that the probability of tumour elimination in a larger domain can be extrapolated from simulation results on a smaller domain. Finally, we demonstrate how our model may be combined with experimental data, to predict the spatio-temporal evolution of a vascular tumour
Spatio-temporal Models of Lymphangiogenesis in Wound Healing
Several studies suggest that one possible cause of impaired wound healing is
failed or insufficient lymphangiogenesis, that is the formation of new
lymphatic capillaries. Although many mathematical models have been developed to
describe the formation of blood capillaries (angiogenesis), very few have been
proposed for the regeneration of the lymphatic network. Lymphangiogenesis is a
markedly different process from angiogenesis, occurring at different times and
in response to different chemical stimuli. Two main hypotheses have been
proposed: 1) lymphatic capillaries sprout from existing interrupted ones at the
edge of the wound in analogy to the blood angiogenesis case; 2) lymphatic
endothelial cells first pool in the wound region following the lymph flow and
then, once sufficiently populated, start to form a network. Here we present two
PDE models describing lymphangiogenesis according to these two different
hypotheses. Further, we include the effect of advection due to interstitial
flow and lymph flow coming from open capillaries. The variables represent
different cell densities and growth factor concentrations, and where possible
the parameters are estimated from biological data. The models are then solved
numerically and the results are compared with the available biological
literature.Comment: 29 pages, 9 Figures, 6 Tables (39 figure files in total
A Modular Fibrinogen Model that Captures the Stress-Strain Behavior of Fibrin Fibers
We tested what to our knowledge is a new computational model for fibrin fiber mechanical behavior. The model is composed of three distinct elements: the folded fibrinogen core as seen in the crystal structure, the unstructured α-C connector, and the partially folded α-C domain. Previous studies have highlighted the importance of all three regions and how they may contribute to fibrin fiber stress-strain behavior. Yet no molecular model has been computationally tested that takes into account the individual contributions of all these regions. Constant velocity, steered molecular dynamics studies at 0.025 Å/ps were conducted on the folded fibrinogen core and the α-C domain to determine their force-displacement behavior. A wormlike chain model with a persistence length of 0.8 nm (Kuhn length = 1.6 nm) was used to model the mechanical behavior of the unfolded α-C connector. The three components were combined to calculate the total stress-strain response, which was then compared to experimental data. The results show that the three-component model successfully captures the experimentally determined stress-strain behavior of fibrin fibers. The model evinces the key contribution of the α-C domains to fibrin fiber stress-strain behavior. However, conversion of the α-helical coiled coils to β-strands, and partial unfolding of the protein, may also contribute
Robustness Analysis and Behavior Discrimination in Enzymatic Reaction Networks
Characterizing the behavior and robustness of enzymatic networks with numerous variables and unknown parameter values is a major challenge in biology, especially when some enzymes have counter-intuitive properties or switch-like behavior between activation and inhibition. In this paper, we propose new methodological and tool-supported contributions, based on the intuitive formalism of temporal logic, to express in a rigorous manner arbitrarily complex dynamical properties. Our multi-step analysis allows efficient sampling of the parameter space in order to define feasible regions in which the model exhibits imposed or experimentally observed behaviors. In a first step, an algorithmic methodology involving sensitivity analysis is conducted to determine bifurcation thresholds for a limited number of model parameters or initial conditions. In a second step, this boundary detection is supplemented by a global robustness analysis, based on quasi-Monte Carlo approach that takes into account all model parameters. We apply this method to a well-documented enzymatic reaction network describing collagen proteolysis by matrix metalloproteinase MMP2 and membrane type 1 metalloproteinase (MT1-MMP) in the presence of tissue inhibitor of metalloproteinase TIMP2. For this model, our method provides an extended analysis and quantification of network robustness toward paradoxical TIMP2 switching activity between activation or inhibition of MMP2 production. Further implication of our approach is illustrated by demonstrating and analyzing the possible existence of oscillatory behaviors when considering an extended open configuration of the enzymatic network. Notably, we construct bifurcation diagrams that specify key parameters values controlling the co-existence of stable steady and non-steady oscillatory proteolytic dynamics
Predicting drug pharmacokinetics and effect in vascularized tumors using computer simulation
In this paper, we investigate the pharmacokinetics and effect of doxorubicin and cisplatin in vascularized tumors through two-dimensional simulations. We take into account especially vascular and morphological heterogeneity as well as cellular and lesion-level pharmacokinetic determinants like P-glycoprotein (Pgp) efflux and cell density. To do this we construct a multi-compartment PKPD model calibrated from published experimental data and simulate 2-h bolus administrations followed by 18-h drug washout. Our results show that lesion-scale drug and nutrient distribution may significantly impact therapeutic efficacy and should be considered as carefully as genetic determinants modulating, for example, the production of multidrug-resistance protein or topoisomerase II. We visualize and rigorously quantify distributions of nutrient, drug, and resulting cell inhibition. A main result is the existence of significant heterogeneity in all three, yielding poor inhibition in a large fraction of the lesion, and commensurately increased serum drug concentration necessary for an average 50% inhibition throughout the lesion (the IC50 concentration). For doxorubicin the effect of hypoxia and hypoglycemia (“nutrient effect”) is isolated and shown to further increase cell inhibition heterogeneity and double the IC50, both undesirable. We also show how the therapeutic effectiveness of doxorubicin penetration therapy depends upon other determinants affecting drug distribution, such as cellular efflux and density, offering some insight into the conditions under which otherwise promising therapies may fail and, more importantly, when they will succeed. Cisplatin is used as a contrast to doxorubicin since both published experimental data and our simulations indicate its lesion distribution is more uniform than that of doxorubicin. Because of this some of the complexity in predicting its therapeutic efficacy is mitigated. Using this advantage, we show results suggesting that in vitro monolayer assays using this drug may more accurately predict in vivo performance than for drugs like doxorubicin. The nonlinear interaction among various determinants representing cell and lesion phenotype as well as therapeutic strategies is a unifying theme of our results. Throughout it can be appreciated that macroscopic environmental conditions, notably drug and nutrient distributions, give rise to considerable variation in lesion response, hence clinical resistance. Moreover, the synergy or antagonism of combined therapeutic strategies depends heavily upon this environment
- …