Philippe Tracqui

Necrotic core thickness and positive arterial remodeling index: Emergent biomechanical factors for evaluating the risk of plaque rupture

Fibrous cap thickness is often considered as diagnostic of the degree of plaque instability. Necrotic core area (Core(area)) and the arterial remodeling index (Remod(index)), on the other hand, are difficult to use as clinical morphological indexes: literature data show a wide dispersion of Core(area) thresholds above which plaque becomes unstable. Although histopathology shows a strong correlation between Core(area) and Remod(index), it remains unclear how these interact and affect peak cap stress (Cap(stress)), a known predictor of rupture. The aim of this study was to investigate the change in plaque vulnerability as a function of necrotic core size and plaque morphology. Cap(stress) value was calculated on 5,500 idealized atherosclerotic vessel models that had the original feature of mimicking the positive arterial remodeling process described by Glagov. Twenty-four nonruptured plaques acquired by intravascular ultrasound on patients were used to test the performance of the associated idealized morphological models. Taking advantage of the extensive simulations, we investigated the effects of anatomical plaque features on Cap(stress). It was found that: 1) at the early stages of positive remodeling, lesions were more prone to rupture, which could explain the progression and growth of clinically silent plaques and 2) in addition to cap thickness, necrotic core thickness, rather than area, was critical in determining plaque stability. This study demonstrates that plaque instability is to be viewed not as a consequence of fibrous cap thickness alone but rather as a combination of cap thickness, necrotic core thickness, and the arterial remodeling index.

The motility of normal and cancer cells in response to the combined influence of the substrate rigidity and anisotropic microstructure

Cell adhesion and migration are strongly influenced by extracellular matrix (ECM) architecture and rigidity, but little is known about the concomitant influence of such environmental signals to cell responses, especially when considering cells of similar origin and morphology, but exhibiting a normal or cancerous phenotype. Using micropatterned polydimethylsiloxane substrates (PDMS) with tunable stiffness (500 kPa, 750 kPa, 2000 kPa) and topography (lines, pillars or unpatterned), we systematically analyse the differential response of normal (3T3) and cancer (SaI/N) fibroblastic cells. Our results demonstrate that both cells exhibit differential morphology and motility responses to changes in substrate rigidity and microtopography. 3T3 polarisation and spreading are influenced by substrate microtopography and rigidity. The cells exhibit a persistent type of migration, which depends on the substrate anisotropy. In contrast, the dynamic of SaI/N spreading is strongly modified by the substrate topography but not by substrate rigidity. SaI/N morphology and migration seem to escape from extracellular cues: the cells exhibit uncorrelated migration trajectories and a large dispersion of their migration speed, which increases with substrate rigidity.

In vitro angiogenesis is modulated by the mechanical properties of fibrin gels and is related to αvβ3 integrin localization

SummaryThis study deals with the role of the mechanical properties of matrices in in vitro angiogenesis. The ability of rigid fibrinogen matrices with fibrin gels to promote capillarylike structures was compared. The role of the mechanical properties of the fibrin gels was assessed by varying concentration of the fibrin gels. When the concentration of fibrin gels was decreased from 2 mg/ml to 0.5 mg/ml, the capillarylike network increased. On rigid fibrinogen matrices, capillarylike structures were not formed. The extent of the capillarylike network formed on fibrin gels having the lowest concentration depended on the number of cells seeded. The dynamic analysis of capillarylike network formation permitted a direct visualization of a progressive stretching of the 0.5 mg/ml fibrin gels. This stretching was not observed when fibrin concentration increases. This analysis shows that 10 h after seeding, a prearrangement of cells into ringlike structures was observed. These ringlike structures grew in size. Between 16 and 24 h after seeding, the capillarylike structures were formed at the junction of two ringlike structures. Analysis of the αvβ3 integrin localization demonstrates that cell adhesion to fibrinogen is mediated through the αvβ3 integrin localized into adhesion plaques. Conversely, cell adhesion to fibrin shows a diffuse and dot-contact distribution. We suggest that the balance of the stresses between the tractions exerted by the cells and the resistance of the fibrin gels triggers an angiogenic signal into the intracellular compartment. This signal could be associated with modification in the αvβ3 integrin distribution.

Spatiotemporal dynamics of actin-rich adhesion microdomains: influence of substrate flexibility

In this study we analyse the formation and dynamics of specific actin-rich structures called podosomes. Podosomes are very dynamic punctual adhesion sites tightly linked to the actin cytoskeleton. Mechanical properties of substrates are emerging as important physical modulators of anchorage-dependent processes involved in the cellular response. We investigate the influence of substrate flexibility on the dynamic properties of podosomes. We used mouse NIH-3T3 fibroblasts, transfected with GFP-actin and cultured on polyacrylamide collagen-coated substrates of varying stiffness. Static and dynamic features of cell morphologies associated with an optical flow analysis of the dynamics of podosomes revealed that: (1) they have constant structural properties, i.e. their shape factor and width do not change with the substrate flexibility; (2) the lifespan of podosomes and mean minimum distance between them depend on the substrate flexibility; (3) there is a variation in the displacement speed of the rosette of podosomes. Moreover, the rosettes sometimes appear as periodically emergent F-actin structures, which suggests that a two-level self-organisation process may drive first, the formation of clusters of podosomes and second, the organisation of these clusters into oscillating rings. Such dynamic features give new perspectives regarding the potential function of podosomes as mechanosensory structures.

From passive diffusion to active cellular migration in mathematical models of tumour invasion

Mathematical models of tumour invasion appear as interesting tools for connecting the information extracted from medical imaging techniques and the large amount of data collected at the cellular and molecular levels. Most of the recent studies have used stochastic models of cell translocation for the comparison of computer simulations with histological solid tumour sections in order to discriminate and characterise expansive growth and active cell movements during host tissue invasion. This paper describes how a deterministic approach based on reaction-diffusion models and their generalisation in the mechano-chemical framework developed in the study of biological morphogenesis can be an alternative for analysing tumour morphological patterns. We support these considerations by reviewing two studies. In the first example, successful comparison of simulated brain tumour growth with a time sequence of computerised tomography (CT) scans leads to a quantification of the clinical parameters describing the invasion process and the therapy. The second example considers minimal hypotheses relating cell motility and cell traction forces. Using this model, we can simulate the bifurcation from an homogeneous distribution of cells at the tumour surface toward a nonhomogeneous density pattern which could characterise a pre-invasive stage at the tumour-host tissue interface.

Mapping elasticity moduli of atherosclerotic plaque in situ via atomic force microscopy.

Several studies have suggested that evolving mechanical stresses and strains drive atherosclerotic plaque development and vulnerability. Especially, stress distribution in the plaque fibrous capsule is an important determinant for the risk of vulnerable plaque rupture. Knowledge of the stiffness of atherosclerotic plaque components is therefore of critical importance. In this work, force mapping experiments using atomic force microscopy (AFM) were conducted in apolipoprotein E-deficient (ApoE(-/-)) mouse, which represents the most widely used experimental model for studying mechanisms underlying the development of atherosclerotic lesions. To obtain the elastic material properties of fibrous caps and lipidic cores of atherosclerotic plaques, serial cross-sections of aortic arch lesions were probed at different sites. Atherosclerotic plaque sub-structures were subdivided into cellular fibrotic, hypocellular fibrotic and lipidic rich areas according to histological staining. Hertzs contact mechanics were used to determine elasticity (Youngs) moduli that were related to the underlying histological plaque structure. Cellular fibrotic regions exhibit a mean Young modulus of 10.4±5.7kPa. Hypocellular fibrous caps were almost six-times stiffer, with average modulus value of 59.4±47.4kPa, locally rising up to ∼250kPa. Lipid rich areas exhibit a rather large range of Youngs moduli, with average value of 5.5±3.5kPa. Such precise quantification of plaque stiffness heterogeneity will allow investigators to have prospectively a better monitoring of atherosclerotic disease evolution, including arterial wall remodeling and plaque rupture, in response to mechanical constraints imposed by vascular shear stress and blood pressure.

Mechanical signalling and angiogenesis. The integration of cell-extracellular matrix couplings.

In vitro angiogenesis assays have shown that the couplings between fibrin gel and cell traction forces trigger biogel pre-patterning, consisting, in the formation of lacunae which evolve toward capillary-like structures (CLS) networks. Depending on the experimental conditions (number of seeded cells, gel elasticity,...), this pre-patterning can be enhanced or inhibited. A theoretical model based on a description of the cell-biogel biochemical and mechanical interactions is proposed as a basis for understanding how integrating these interactions can lead to the pre-patterning of the biogel. We showed that the critical parameter values corresponding to the bifurcation of the model solutions correspond to threshold values of the experimental variables. Furthermore, simulations of the mechanocellular model give rise to dynamic remodelling patterns of the biogel which are in good agreement both with the lacunae morphologies and with the time and space scales derived from the in vitro angiogenesis assays. Special attention has been paid in the simulations to cell proteolytic activity and to the amplitude of cell traction forces. We finally discussed how modelling guided experiments can be inferred from these results.

Modelling Biological Gel Contraction by Cells: Mechanocellular Formulation and Cell Traction Force Quantification

Traction forces developed by most cell types play a significant role in the spatial organisation of biological tissues. However, due to the complexity of cell-extracellular matrix interactions, these forces are quantitatively difficult to estimate without explicitly considering cell properties and extracellular mechanical matrix responses. Recent experimental devices elaborated for measuring cell traction on extracellular matrix use cell deposits on a piece of gel placed between one fixed and one moving holder. We formulate here a mathematical model describing the dynamic behaviour of the cell-gel medium in such devices. This model is based on a mechanical force balance quantification of the gel visco-elastic response to the traction forces exerted by the diffusing cells. Thus, we theoretically analyzed and simulated the displacement of the free moving boundary of the system under various conditions for cells and gel concentrations. This modelis then used as the theoretical basis of an experimental device where endothelial cells are seeded on a rectangular biogel of fibrin cast between two floating holders, one fixed and the other linked to a force sensor. From a comparison of displacement of the gel moving boundary simulated by the model and the experimental data recorded from the moving holder displacement, the magnitude of the traction forces exerted by the endothelial cell on the fibrin gel was estimated for different experimental situations. Different analytical expressions for the cell traction term are proposed and the corresponding force quantifications are compared to the traction force measurements reported for various kind of cells with the use of similar or different experimental devices.

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.

A computational model of cell migration coupling the growth of focal adhesions with oscillatory cell protrusions

Cell migration is a highly integrated process where actin turnover, actomyosin contractility, and adhesion dynamics are all closely linked. In this paper, we propose a computational model investigating the coupling of these fundamental processes within the context of spontaneous (i.e. unstimulated) cell migration. In the unstimulated cell, membrane oscillations originating from the interaction between passive hydrostatic pressure and contractility are sufficient to lead to the formation of adhesion spots. Cell contractility then leads to the maturation of these adhesion spots into focal adhesions. Due to active actin polymerization, which reinforces protrusion at the leading edge, the traction force required for cell translocation can be generated. Computational simulations first show that the model hypotheses allow one to reproduce the main features of fibroblast cell migration and established results on the biphasic aspect of the cell speed as a function of adhesion strength. The model also demonstrates that certain temporal parameters, such as the adhesion proteins recycling time and adhesion lifetimes, influence cell motion patterns, particularly cell speed and persistence of the direction of migration. This study provides some elements, which allow a better understanding of spontaneous cell migration and enables a first glance at how an individual cell would potentially react once exposed to a stimulus.