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. This revised version was published online in June 2006 with corrections to the Cover Date.     

Cells Actively Stiffen Fibrin Networks by Generating Contractile Stress

During wound healing and angiogenesis, fibrin serves as a provisional extracellular matrix. We use a model system of fibroblasts embedded in fibrin gels to study how cell-mediated contraction may influence the macroscopic mechanical properties of their extracellular matrix during such processes. We demonstrate by macroscopic shear rheology that the cells increase the elastic modulus of the fibrin gels. Microscopy observations show that this stiffening sets in when the cells spread and apply traction forces on the fibrin fibers. We further show that the stiffening response mimics the effect of an external stress applied by mechanical shear. We propose that stiffening is a consequence of active myosin-driven cell contraction, which provokes a nonlinear elastic response of the fibrin matrix. Cell-induced stiffening is limited to a factor 3 even though fibrin gels can in principle stiffen much more before breaking. We discuss this observation in light of recent models of fibrin gel elasticity, and conclude that the fibroblasts pull out floppy modes, such as thermal bending undulations, from the fibrin network, but do not axially stretch the fibers. Our findings are relevant for understanding the role of matrix contraction by cells during wound healing and cancer development, and may provide design parameters for materials to guide morphogenesis in tissue engineering.     

Cells Actively Stiffen Fibrin Networks by Generating Contractile Stress

During wound healing and angiogenesis, fibrin serves as a provisional extracellular matrix. We use a model system of fibroblasts embedded in fibrin gels to study how cell-mediated contraction may influence the macroscopic mechanical properties of their extracellular matrix during such processes. We demonstrate by macroscopic shear rheology that the cells increase the elastic modulus of the fibrin gels. Microscopy observations show that this stiffening sets in when the cells spread and apply traction forces on the fibrin fibers. We further show that the stiffening response mimics the effect of an external stress applied by mechanical shear. We propose that stiffening is a consequence of active myosin-driven cell contraction, which provokes a nonlinear elastic response of the fibrin matrix. Cell-induced stiffening is limited to a factor 3 even though fibrin gels can in principle stiffen much more before breaking. We discuss this observation in light of recent models of fibrin gel elasticity, and conclude that the fibroblasts pull out floppy modes, such as thermal bending undulations, from the fibrin network, but do not axially stretch the fibers. Our findings are relevant for understanding the role of matrix contraction by cells during wound healing and cancer development, and may provide design parameters for materials to guide morphogenesis in tissue engineering.     

The relative magnitudes of endothelial force generation and matrix stiffness modulate capillary morphogenesis in vitro

When suspended in collagen gels, endothelial cells elongate and form capillary-like networks containing lumens. Human blood outgrowth endothelial cells (HBOEC) suspended in relatively rigid 3 mg/ml floating collagen gels, formed in vivo-like, thin, branched multi-cellular structures with small, thick-walled lumens, while human umbilical vein endothelial cells (HUVEC) formed fewer multi-cellular structures, had a spread appearance, and had larger lumens. HBOEC exert more traction on collagen gels than HUVEC as evidenced by greater contraction of floating gels. When the stiffness of floating gels was decreased by decreasing the collagen concentration from 3 to 1.5 mg/ml, HUVEC contracted gels more and formed thin, multi-cellular structures with small lumens, similar in appearance to HBOEC in floating 3 mg/ml gels. In contrast to floating gels, traction forces exerted by cells in mechanically constrained gels encounter considerable resistance. In constrained collagen gels (3 mg/ml), both cell types appeared spread, formed structures with fewer cells, had larger, thinner-walled lumens than in floating gels, and showed prominent actin stress fibers, not seen in floating gels. These results suggest that the relative magnitudes of cellular force generation and apparent matrix stiffness modulate capillary morphogenesis in vitro and that this balance may play a role in regulating angiogenesis in vivo.     

ECM concentration and cell-mediated traction forces play a role in vascular network assembly in 3D bioprinted tissue

Tissue vascularization is critical to enable oxygen and nutrient supply. Therefore, establishing expedient vasculature is necessary for the survival of tissue after transplantation. The use of biomechanical forces, such as cell-induced traction forces, may be a promising method to encourage growth of the vascular network. Three-dimensional (3D) bioprinting, which offers unprecedented versatility through precise control over spatial distribution and structure of tissue constructs, can be used to generate capillary-like structures in vitro that would mimic microvessels. This study aimed to develop an in vitro, 3D bioprinted tissue model to study the effect of cellular forces on the spatial organization of vascular structures and tissue maturation. The developed in vitro model consists of a 3D bioprinted polycaprolactone (PCL) frame with a gelatin spacer hydrogel layer and a gelatin–fibrin–hyaluronic acid hydrogel layer containing normal human dermal fibroblasts and human umbilical vein endothelial cells printed as vessel lines on top. The formation of vessel-like networks and vessel lumens in the 3D bioprinted in vitro model was assessed at different fibrinogen concentrations with and without inhibitors of cell-mediated traction forces. Constructs containing 5 mg/ml fibrinogen had longer vessels compared to the other concentrations of fibrinogen used. Also, for all concentrations of fibrinogen used, most of the vessel-like structures grew parallel to the direction the PCL frame-mediated tensile forces, with very few branching structures observed. Treatment of the 3D bioprinted constructs with traction inhibitors resulted in a significant reduction in length of vessel-like networks. The 3D bioprinted constructs also had better lumen formation, increased collagen deposition, more elaborate actin networks, and well-aligned matrix fibers due to the increased cell-mediated traction forces present compared to the non-anchored, floating control constructs. This study showed that cell traction forces from the actomyosin complex are critical for vascular network assembly in 3D bioprinted tissue. Strategies involving the use of cell-mediated traction forces may be promising for the development of bioprinting approaches for fabrication of vascularized tissue constructs.     

On the mechanochemical theory of biological pattern formation with application to vasculogenesis

We first describe the Murray-Oster mechanical theory of pattern formation, the biological basis of which is experimentally well documented. The model quantifies the interaction of cells and the extracellular matrix via the cell-generated forces. The model framework is described in quantitative detail. Vascular endothelial cells, when cultured on gelled basement membrane matrix, rapidly aggregate into clusters while deforming the matrix into a network of cord-like structures tessellating the planar culture. We apply the mechanical theory of pattern formation to this culture system and show that neither strain-biased anisotropic cell traction nor cell migration are necessary for pattern formation: isotropic, strain-stimulated cell traction is sufficient to form the observed patterns. Predictions from the model were confirmed experimentally.     

Phorbol ester induces cultured endothelial cells to invade a fibrin matrix in the presence of fibrinolytic inhibitors

We have previously shown that the tumor promoter 4 beta-phorbol 12-myristate 13-acetate (PMA) induces capillary endothelial cells grown to confluency on the surface of three-dimensional collagen gels to invade the underlying matrix and to form capillary-like tubular structures, a phenomenon mimicking angiogenic processes that occur in vivo (Montesano and Orci: Cell, 42:469-477, 1985). Since angiogenesis frequently occurs within a fibrin-rich extracellular matrix, we have examined the ability of PMA-treated endothelial cells to invade fibrin gels. Control endothelial cells grown on fibrin gels formed a confluent monolayer on the gel surface and did not invade the underlying matrix. Treatment of the cultures with PMA resulted in a progressive lysis of the substrate without invasion of the fibrin matrix. However, if the cells were treated with PMA either in the presence of fibrinolytic inhibitors (Trasylol, epsilon-aminocaproic acid) or in the absence of detectable plasminogen, dissolution of the substrate was prevented, and the endothelial cells invaded the fibrin gel, forming vessel-like tubular structures similar to those previously observed with collagen gels. These results demonstrate that the invasive and morphogenetic events induced by PMA do not necessarily require an interaction between endothelial cells and collagen fibrils but can also occur with other biologically relevant substrata. They also suggest (1) that invasion may occur via a plasmin-independent mechanism and (2) that in vivo, neutralization of excess proteolytic activity may play an important permissive role in angiogenesis and other invasive processes by preventing uncontrolled matrix degradation.     

Investigating metalloproteinases MMP-2 and MMP-9 mechanosensitivity to feedback loops involved in the regulation of in vitro angiogenesis by endogenous mechanical stresses

Angiogenesis is a complex morphogenetic process regulated by growth factors, but also by the force balance between endothelial cells (EC) traction stresses and extracellular matrix (ECM) viscoelastic resistance. Studies conducted with in vitro angiogenesis assays demonstrated that decreasing ECM stiffness triggers an angiogenic switch that promotes organization of EC into tubular cords or pseudo-capillaries. Thus, mechano-sensitivity of EC with regard to proteases secretion, and notably matrix metalloproteinases (MMPs), should likely play a pivotal role in this switching mechanism. While most studies analysing strain regulation of MMPs used cell cultured on stretched membranes, this work focuses on MMP expression during self-assembly of EC into capillary-like structures within fibrin gels, i.e. on conditions that mimics more closely the in vivo cellular mechanical microenvironment. The activity of MMP-2 and MMP-9, two MMPs that have a pivotal role in capillaries formation, has been monitored in pace with the progressive elongation of EAhy926 cells that takes place during the emergence of cellular cords. We found an increase of the zymogen proMMP-2 that correlates with the initial stages of EC cords formation. However, MMP-2 was not detected. ProMMP-9 secretion decreased, with levels of MMP-9 kept at a rather low value. In order to analyse more precisely the observed differences of EAhy926 response on fibrin and plastic substrates, we proposed a theoretical model of the mechano-regulation of proMMP-2 activation in the presence of type 2 tissue inhibitor of MMPs (TIMP-2). Using association/dissociation rates experimentally reported for this enzymatic network, the model adequately describes the synergism of proMMP-2 and TIMP-2 strain activation during pseudo-capillary morphogenesis. All together, these results provide a first step toward a systems biology approach of angiogenesis mechano-regulation by cell-generated extracellular stresses and strains.     

Paracrine regulation of angiogenesis by different cell types in the aorta ring model

The development of blood vessels during angiogenesis is the result of paracrine interactions between tube-forming endothelial cells and angiogenic factor-producing nonendothelial cells. This process can be reproduced and studied under chemically defined culture conditions by culturing vascular explants in three-dimensional gels of extracellular matrix. Rings of rat or mouse aorta cultured in collagen, fibrin or basement membrane gels produce angiogenic outgrowths composed of a mixed population of endothelial cells and nonendothelial cells. Aortic angiogenesis is regulated by endogenous angiogenic factors, inflammatory cytokines, chemokines, extracellular matrix molecules, and proteolytic enzymes produced by cells of the vessel wall in response to the injury of the dissection procedure. In this paper, we review how macrophages, mural cells and fibroblasts regulate different stages of the angiogenic process, from the formation of immature endothelial sprouts to the reabsorption of the neovessels. We also describe how aortic cultures can be used to study interactions between angiogenic outgrowths and nonvascular cell types such as bone marrow macrophages, platelets or cancer cells. Morphologic, genetic and functional studies of this model have provided invaluable information on how vessels form, mature, interact with nonvascular cell types, and are eventually reabsorbed. Further analysis of the paracrine cross-talk between aortic endothelial and nonendothelial cells is likely to provide new insights into the angiogenic process and its key mechanisms.