Topography of Extracellular Matrix Mediates Vascular Morphogenesis and Migration Speeds in Angiogenesis
The physical properties of the ECM , such as density , heterogeneity , and stiffness , that affect cell behavior is also an area of current investigation ., Matrigel , a popular gelatinous protein substrate for in vitro experiments of angiogenesis , is largely composed of collagen and laminin and contains growth factors , all of which provide an environment conducive to cell survival ., In experiments of endothelial cells on Matrigel , increasing the stiffness of the gel or disrupting the organization of the cellular cytoskeleton , inhibits the formation of vascular cell networks 10 , 11 ., Cells respond to alterations in the mechanical properties of the ECM , for example , by upregulating their focal adhesions on stiffer substrates 12 ., For anchorage-dependent cells , including endothelial cells , increasing the stiffness of the ECM therefore results in increased cell traction and slower migration speeds 12 ., Measurements of Matrigel stiffness as a function of density show a positive relationship between these two mechanical properties 13 ., That is , as density increases , so does matrix stiffness ., In light of these two findings , it is not surprising that this experimental study also shows slower cell migration speeds as matrix density increases 13 ., Moreover , matrices with higher fiber density transfer less strain to the cell 14 and experiments of endothelial cells cultured on collagen gels demonstrate that directional sprouting , called branching , is induced by collagen matrix tension 15 ., Thus , via integrin receptors , the mechanical properties of the ECM influence cell-matrix interactions and modulate cell shape , cell migration speed , and the formation of vascular networks ., Understanding how individual cells interpret biochemical and mechanical signals from the ECM is only a part of the whole picture ., Morphogenic processes also require multicellular coordination ., In addition to the guidance cues cells receive from the ECM , they also receive signals from each other ., During new vessel growth , cells adhere to each other through cell-cell junctions , called cadherins , and in order to migrate , cells must coordinate integrin mediated focal adhesions with these cell-cell bonds ., This process is referred to as collective or cluster migration 16 ., During collective migration , cell clusters often organize as two-dimensional sheets 16 ., Cells also have the ability to condition the ECM for invasion by producing proteolytic enzymes that degrade specific ECM proteins 17 ., In addition , cells can synthesize ECM components , such as collagen and fibronectin 11 , 18 , and can further reorganize the ECM by the forces they exert on it during migration 10 , 11 , 14 ., Collagen fibrils align in response to mechanical loading and cells reorient in the direction of the applied load 14 ., Tractional forces exerted by vascular endothelial cells on Matrigel cause cords or tracks of aligned fibers to form promoting cell elongation and motility 11 ., As more experimental data are amassed , the ECM is emerging as the vital component to morphogenic processes ., In this work , we extend our cellular model of angiogenesis 19 and validate it against empirical measurements of sprout extension speeds ., We then use our model to investigate the effect of ECM topography on vascular morphogenesis and focus on mechanisms controlling cell shape and orientation , sprout extension speeds , and sprout morphology ., We show the dependence of sprout extension speed and morphology on matrix density , fiber network connectedness , and fiber orientation ., Notably , we observe that varying matrix fiber density affects the likelihood of capillary sprout branching ., The model predicts an optimal density for capillary network formation and suggests matrix heterogeneity as a mechanism for sprout branching ., We also identify unique ranges of matrix density that promote sprout extension or that interrupt normal angiogenesis , and show that maximal sprout extension speeds are achieved within a density range similar to the density of collagen found in the cornea ., Finally , we quantify the effects of proteolytic matrix degradation by the tip cell on sprout velocity and demonstrate that degradation promotes sprout growth at high densities , but has an inhibitory effect at lower densities ., Based on these findings , we suggest and discuss several ECM targeted pro- and anti-angiogenesis therapies that can be tested empirically ., We previously published a cell-based model of tumor-induced angiogenesis that captures endothelial cell migration , growth , and division at the level of individual cells 19 ., That model also describes key cell-cell and cell-matrix interactions , including intercellular adhesion , cellular adhesion to matrix components , and chemotaxis to simulate the early events in new capillary sprout formation ., In the present study , we extend that model to incorporate additional mechanisms for cellular motility and sprout extension , and use vascular morphogenesis as a framework to study how ECM topography influences intercellular and cell-matrix interactions ., The model is two-dimensional ., It uses a lattice-based cellular Potts model describing individual cellular interactions coupled with a partial differential equation to describe the spatio-temporal dynamics of vascular endothelial growth factor ., At every time step , the discrete and continuous models feedback on each other , and describe the time evolution of the extravascular tissue space and the developing sprout ., The cellular Potts model evolves by the Metropolis algorithm: lattice updates are accepted probabilistically to reduce the total energy of the system in time ., The probability of accepting a lattice update is given bywhere is the change in total energy of the system as a result of the update , is the Boltzmann constant , and is the effective temperature corresponding to the amplitude of cell membrane fluctuations ., A higher temperature corresponds to larger cell membrane fluctuation amplitudes ., The energy , , includes a term describing cell-cell and cell-matrix adhesion , a constraint controlling cellular growth , an effective chemotaxis potential , and a continuity constraint ., Mathematically , total energy is given by: ( 1 ) In the first term of Eq ., 1 , represents the binding energy between model constituents ., For example , describes the relative strength of cell-cell adhesion that occurs via transmembrane cadherin proteins ., Similarly , is a measure of the binding affinity between an endothelial cell and a matrix fiber through cell surface integrin receptors ., Each endothelial cell is associated with a unique identifying number , ., is the Kronecker delta function and ensures that adhesive energy only accrues at cell surfaces ., The second term in Eq ., 1 describes the energy expenditure required for cell growth and deformation ., Membrane elasticity is described by , denotes cell current volume , and is a specified target volume ., For proliferating cells , the target volume is double the initial volume ., This growth constraint delivers a penalty to total energy for any deviation from the target volume ., In the third term , the parameter is the effective chemical potential and influences the strength of chemotaxis relative to other parameters in the model ., This chemotaxis potential varies depending on cell phenotype ( discussed below ) and is proportional to the local VEGF gradient , , where denotes the concentration of VEGF ., Cells must simultaneously integrate multiple external stimuli , namely intercellular adhesion , chemotactic incentives , and adherence to extracellular matrix fibers ., To do so , endothelial cells deform their shape and dynamically regulate adhesive bonds ., In the model , however , it is possible that collectively these external stimuli may cause a cell to be pulled or split in two ., To prevent non-biological fragmentation of cells , we introduce a continuity constraint that preserves the physical integrity of each individual cell ., This constraint expresses that it is energetically expensive to compromise the physical integrity of a cell and is incorporated into the equation for total energy ( Eq . 1 ) in the last term , where is a continuity constraint that represents the effects of the cytoskeletal matrix of a cell ., is the current size of the endothelial cell with identifying number , and is a breadth first search count of the number of continuous lattice sites occupied by that endothelial cell ., Thus , signals that the physical integrity of the cell has been compromised and a penalty to total energy is incurred ., Cooperatively , the continuity constraint and the volume constraint implicitly describe the interactions holding the cell together ., The amount of VEGF available at the right hand boundary of the domain is estimated by assuming that in response to a hypoxic environment , quiescent tumor cells secrete a constant amount of VEGF and that VEGF decays at a constant rate ., It is reasonable to assume that the concentration of VEGF within the tumor has reached a steady state and therefore that a constant amount of VEGF , denoted , is available at the boundary of the tumor ., We use constant boundary conditions for the left ( ) and right boundaries and periodic boundary conditions in the y-direction ., A gradient of VEGF is established as VEGF diffuses through the stroma with constant diffusivity coefficient , decays at a constant rate , and is bound by endothelial cells , ., A complete description of the biochemical derivation of the function for endothelial cell binding and uptake of VEGF ( ) has been previously published 19 ., For more direct comparison to other mathematical models of angiogenesis models and to isolate the effects of ECM topology on vessel morphology , we assume that the diffusion coefficient for VEGF in tissue is constant ., This is a simplification , however , because the ECM is not homogeneous and VEGF can be bound to and stored in the ECM ., Realistically , the diffusion coefficient ( ) for VEGF in the ECM depends on both space and time ., We address the implications of this assumption in the Discussion ., Under these assumptions , the concentration profile of VEGF satisfies a partial differential equation of the form: ( 2 ) The inset in Figure 1A provides an illustration of the 166 µm×106 µm domain geometry ., We initialize the simulation by establishing the steady state solution to Eq ., 2 ., The activation and aggregation of endothelial cells , and subsequent breakdown of basement membrane in response to VEGF 20 is a pre-condition ( boundary condition ) to the simulation ., The breakdown of basement membrane allows endothelial cells to enter the extravascular space through a new vessel opening ., Our simulation starts with a single activated endothelial cell ∼10 µm in diameter that has budded from the parent vessel located adjacent to the left hand boundary 20 ., We use 10 µm only as an initial estimate of endothelial cell size 21 , 22 ., Once the simulation begins , the cells immediately deform in shape and elongate ., During the simulation , the VEGF field is updated iteratively with cell uptake information , for example as shown in Figure 1B , C ., VEGF data is processed by the cells at the cell membrane and incorporated into the model through the chemotaxis term in Eq ., 1 ., From the parent blood vessel , endothelial cells ( red ) migrate into the domain in response to VEGF that is supplied from a tumor located adjacent to the right hand boundary ., The space between represents the stroma and is composed of extracellular matrix fibers ( green ) and interstitial fluid ( blue ) ., The physical meanings of all symbols and their parameter values are summarized in Table 1 ., To more accurately capture the cell-cell and cell-matrix interactions that occur during morphogenesis , we implement several additional features to this model ., One improvement is the implementation of stalk cell chemotaxis ., Stalk cells are not inert , but actively respond to chemotactic signals 23 ., As a consequence , cells now migrate as a collective body , a phenomenon called collective or cohort migration 24 ., This modification , however , also makes it possible for individual cells , as well as the entire sprout body , to migrate away from the parent vessel , making it necessary to consider cell recruitment from the parent vessel ., Cell recruitment is another added feature ., During the early stages of angiogenesis , cells are recruited from the parent vessel to facilitate sprout extension 20 , 25 ., Kearney et al . 26 measured the number and location of cell divisions that occur over 3 . 6 hours in in vitro vessels 8 days old ( a detailed description of these experiments is provided in our discussion of model validation ) ., In these experiments , the sprout field is defined as the area of the parent vessel wall that ultimately gives rise to the new sprout and the sprout itself ., The sprout field is further broken down into regions based on distance from the parent vessel and these regions are classified as distal , proximal , and nascent ., The authors report that 90% of all cell divisions occur in the parent vessel and the remaining 10% occur at or near the base of the sprout in the nascent area of the sprout field ., On average , total proliferation accounts for approximately 5 new cells in 3 . 6 hours , or 20 cells in 14 hours ., This data suggests that there is significant and sufficient proliferation in the primary vessel to account for and facilitate initial sprout extension ., This data does not suggest that proliferation in other areas of the sprout field does not occur at other times ., In fact , it has been established that a new sprout can migrate only a finite distance into the stroma without proliferation and that proliferation is necessary for continued sprout extension 25 ., We model sprout extension through a cell-cell adhesion dependent recruitment of additional endothelial cells from the parent vessel ., As an endothelial cell at the base of the sprout moves into the stroma , cell-cell adhesion pulls a cell from the parent vessel along with it ., In practice , a new cell is added to the base of the sprout when and where the previous cell detaches from the parent vessel wall ( left boundary of the simulation domain ) ., We assume , based on the data presented in 26 , that there is sufficient proliferation in the parent vessel to provide the additional cells required for initial sprout extension while maintaining the physical integrity of the parent vessel ., As in our previous model , once a cell senses a threshold concentration of VEGF , given by , it becomes activated ., We recognize that cells have distinct phenotypes that dictate their predominate behavior ., Thus , we distinguish between tip cells , cells that are proliferating , and non-proliferating but migrating stalk cells ., Tip cells are functionally specialized cells that concentrate their internal cellular machinery to promote motility 23 ., Tip cells are highly migratory pathfinding cells and do not proliferate 25 , 26 ., To model the highly motile nature of the tip cell , we assign it the highest chemotactic coefficient , ., The remainder of the cells are designated as stalk cells and use adhesive binding to and release from the matrix fibers for support and to facilitate cohort migration ., Stalk cells also sense chemical gradients but are not highly motile phenotypes ., Thus , the stalk cells in the model are assigned a lower , that is weaker , chemotactic coefficient than the specialized tip cell ., Proliferating cells are located behind the sprout tip 23 , 26 and increase in size as they move through an 18 hour cell cycle clock in preparation for cell division 27 ., Cells that are proliferating can still migrate 26; it is only during the final stage of the cell cycle that endothelial cells stop moving and round up for mitosis ( personal communication with C . Little ) ., As we assume that the presence of VEGF increases cell survivability , we do not model endothelial cell apoptosis ., As described in our previous work 19 , we model the mesh-like anisotropic structure of the extracellular matrix by randomly distributing 1 . 1 µm thick bundles of individual collagen fibrils at random discrete orientations between −90 and 90 degrees ., Unless otherwise stated , model matrix fibers comprise approximately 40% of the total stroma and the distribution of the ECM is heterogeneous , with regions of varying densities as can be seen in Figure 1A and Figure 7D ., The cells move on top of the 2D ECM model and interact with the matrix fibers at the cell membrane through the adhesion term in Eq ., 1 ., To relate the density ( ) of this model fibrillar matrix to physiological values , we measure matrix fiber density as the ratio of the interstitium occupied by matrix molecules to total tissue space , , and compare it to measured values of the volume fraction of collagen fibers in healthy tissues 28 ., In order to isolate and control the effects of the matrix topology on cellular behavior and sprout morphology we look at a static ECM , that is we do not model ECM rearrangement or dynamic matrix fiber cross-linking and stiffness ., We do , however , consider endothelial cell matrix degradation in a series of studies presented in Results ., No single model has been proposed that incorporates every aspect of all processes involved in sprouting angiogenesis , nor is this level of complexity necessary for a model to be useful or predictive ., It is not our intention to include every bio-chemical or mechanical dynamic at play during angiogenesis ., We develop this two-dimensional cell-based model as a step towards elucidating cellular level dynamics fundamental to angiogenesis , including cell growth and migration , and cell-cell and cell-matrix interactions ., Consequently , we do not incorporate processes or dynamics at the intracellular level ., For example , we describe endothelial cell binding of VEGF to determine cell activation and to capture local variations in VEGF gradients , but neglect intracellular molecular pathways signaled downstream of the receptor-ligand complex ., Moreover , our focus is on early angiogenic events and therefore we also do not consider the effects of blood flow on remodeling of mature vascular beds ., Numerical studies of flow-induced vascular remodeling have been given attention in McDougall et al . 29 , and Pries and Secomb 30 , 31 ., As is the case in many other simulations of biological systems , when we do not have direct experimental measurements for all of the parameters , choosing these parameter values is not trivial ., A list of values and references for our model parameters is provided in Table 1 ., A parameter is derived from experimental data whenever possible , otherwise it is estimated and denoted ‘est’ ., Fortunately , a sensitivity analysis ( discussed later ) shows that the dynamics of our model are quite robust to substantial variations in some parameters and tells us exactly which parameters are most critical ., We can then choose from a range of parameter values that exhibits the general class of behavior consistent with experimental observations ., See Table 1 for these parameter ranges and Table 3 for the effect of parameter perturbations , as well as , supplemental Figures S1 and S2 for examples of cellular behavior under different parameter sets ., In the cellular Potts model , the relative value , not the absolute value , of the parameters corresponds to available physiological measurements and gives rise to a cell behavior observed experimentally ., For example , the Youngs modulus for human vascular endothelial cells is estimated at 2 . 01*105 Pa 32 ., The Youngs modulus of a collagen fiber in aqueous conditions is between 0 . 2–0 . 8 GPa 33 ., However , the modulus of a collagen gel network is much lower and is measured at 7 . 5 Pa 34 ., Although interstitial fluid compressibility ( water ) is estimated to be 2 . 2 GPa 35 , indicating its hard to compress under uniform pressure , it deforms easily , that is , the shear modulus is low and is measured at 10−6 Pa 36 ., The qualitative parameters corresponding to these quantitative measurements are where ., Thus , the elastic modulus of endothelial cells>matrix fibers>interstitial fluid ( 0 . 2 MPa>7 . 5 Pa>10−6 Pa ) and is reflected in the relative values of the corresponding parameters , , and ., In a similar manner , the coupling parameters , , describe the relative adhesion strengths among endothelial cells , matrix fibers , and interstitial fluid ., For instance , choosing reflects that fact that endothelial cells have a higher binding affinity to each other , via cadherin receptors and gap junctions for example , than they do to matrix fibers 37 , 38 ., The chemotactic potential , , is chosen so that its contribution to the change in total energy is the same order of magnitude as the contribution to total energy from adhesion or growth ., The difference between the concentration of VEGF at two adjacent lattice sites is on the order of 10−4 ., Therefore , to balance adhesion and growth , must be on the order of 106 ., We calibrate this parameter to maximize sprout extension speeds ., Similarly , the parameter for continuity , , is chosen so that cells will not dissociate ., This is achieved by setting greater than the collective contribution to total energy from the other terms ., By equating the time it takes an endothelial cell to divide during the simulation with the endothelial cell cycle duration of 18 hours , we convert Monte Carlo steps to real time units ., In the simulations reported in this paper , 1 Monte Carlo step is equivalent to 1 minute ., Since this model has several enhancements over the previous model 19 , there are a different number of parameters , which necessitates recalibration of all the parameters ., Therefore , some parameters take on different values ., The canonical benchmark for validating models of tumor-induced angiogenesis is the rabbit cornea assay 39 , 40 ., In this in vivo experimental model , tumor implants are placed in a corneal pocket approximately 1–2 mm from the limbus ., New vessel growth is measured with an ocular micrometer at 10× , which has a measurement error of ±0 . 1 mm or 100 µm ., Initially , growth is linear and sprout extension speeds are estimated at a rate of 0 . 5 mm/day , or 20 . 8±4 . 2 µm/hr ., Sprouts then progress at average speeds estimated to be between 0 . 25–0 . 50 mm/day , or 10 . 4–20 . 8±4 . 2 µm/hr ., More recent measurements of sprout extension speeds during angiogenesis are reported in Kearney et al . 26 ., In this study , embryonic stem cells containing an enhanced green fluorescent protein are differentiated in vitro to form primitive vessels ., Day 8 cell cultures are imaged within an ∼160 µm2 area at 1 minute intervals for 10 hours and show sprouting angiogenesis over this period ., The average extension speed for newly formed sprouts is 14 µm/hr and ranges from 5 to 27 µm/hr ., For cell survival , growth factor is present and is qualitatively characterized as providing a diffuse , or shallow , gradient ., No quantitative data pertaining to growth factor gradients or the effect of chemotaxis during vessel growth are reported 26 ., We use the above experimental models and reported extension speeds as a close approximation to our model of in vivo angiogenesis for quantitative comparison and validation ., We simulate new sprout formation originating from a parent vessel in the presence of a diffusible VEGF field , which creates a shallow VEGF gradient ., We measure average extension speeds over a 14 hour period in a domain 100 µm by 160 µm ., As was done in Kearney et al . 26 , we calculate average sprout velocities as total sprout tip displacement in time and measure this displacement as the distance from the base of the new sprout to the sprout tip ., Figure 1A shows average sprout extension speed over time for our simulated sprouts ., Reported speeds are an average of at least 10 independent simulations using the same initial VEGF profile and parameter set as given in Table 1 ., Error bars represent the standard error from the mean ., The average extension speeds of our simulated sprouts are within the ranges of average sprout speeds measured by both Kearney et al . 26 and Gimbrone et al . 39 ., Table 2 summarizes various morphological measurements for the simulated sprouts ., It shows that the average velocity , thickness , and cell size of the simulated sprouts compare favorably to relevant experimental measurements ., Sprout velocity is given at 10 hours for direct comparison to 26 and averaged over 14 hours ., Sprout thicknesses and cell size are within normal physiological ranges ., There are many different cell shapes and sizes and vessel morphologies , however , that can be obtained in vivo and in vitro given different environmental factors ( VEGF profile , ECM topology and stiffness , inhibitory factors , other cell types , etc . ) ., In this manuscript , we investigate several of these dependencies and as we discuss below specific model parameters can be tuned to reproduce different cellular interactions and environments ., Figure 1A indicates that average sprout extension speed changes as a function of time ., Within the first two hours , speeds average ∼30 µm/hr and the new sprout consists of only 1–2 endothelial cells ., At two hours , sprouts contain an average of 3 cells , and at 4 hours , there are a total of 5–6 cells ., Over time , as more cells are added to the developing sprout , cell-cell adhesion and cellular adhesion to the extracelluar matrix slow the sprout extension speed ., The inset in Figure 1A shows the geometry of the computational domain and simulated sprout development at 7 . 8 hours ., As shown , simulated sprouts are approximately one cell diameter wide , which compares quantitatively well to reported VEGF induced vessel diameters 41 , 42 ., Here and in all simulation snapshots , tip cells are identified with a ‘T’ ., In moving multicellular clusters , rear retraction is a collective process that involves many cells simultaneously 16 ., A natural result of the cell-based model is that cells exhibit rear retraction , which refers to the ability of a cell to release its trailing adhesive bonds with the extracellular matrix during migration ., Collective migration , another characteristic dynamic observed during sprout growth , is also evident during the simulations ( see videos ) ., The VEGF concentration profile in picograms ( pg ) at 7 . 8 hours is given in Figure 1B ., Higher concentrations of VEGF are encountered as the cells approach the tumor ., However , because cell uptake of VEGF is small compared to the amount of available VEGF , it is difficult to discern the heterogeneities in the VEGF profile from this figure ., Figure 1C is the VEGF gradient profile ( pg ) at 7 . 8 hours and is a better indicator of the changes in local VEGF concentration ., This image shows larger gradients in the proximity of the tip cell and along the leading edges of the new sprout ., On average , simulated sprouts migrate 160 µm and reach the domain boundary in approximately 15 . 6 hours , before any cells in the sprout complete their cell cycle and proliferate ., We do not expect to see proliferation in the new sprout because the simulation duration is less than the 18 hour cell cycle and the cell cycle clock is set to zero for newly recruited cells to simulate the very onset of angiogenesis ., In our simulations , sprout extension is facilitated by cell recruitment from the parent vessel ., Between 15 and 20 cells are typically recruited , which agrees with the number of cells we estimate would be available for recruitment based on parent vessel cell proliferation reported by Kearney et al . 26 ., In those experiments 26 , proliferation in the parent vessel was measured for day 8 sprouts , which likely has cells at various stages in their cell cycles ., Proliferation in the new sprout is another mechanism for sprout extension ., Thus , we consider the possibility that cells recruited from the parent vessel may be in different stages of their cell cycles by initializing the cell cycle clock of each recruited cell at randomly generated times ., We observe no differences in extension speeds , sprout morphology , or the number of cells recruited as a result of the assumption we make for cell cycle initialization ( or random ) ., This suggests that , in the model , stalk cell proliferation and cell recruitment from the parent vessel are complementary mechanisms for sprout extension ., By adjusting key model parameters , we are able to simulate various morphogenic phenomena ., For example , by increasing the chemotactic sensitivity of cells in the sprout stalk and decreasing the parameter controlling cellular adhesion to the matrix , , we are able to capture stalk cell migration and translocation along the side of a developing sprout ( Video S1 ) ., This phenomena , where stalk cells weaken their adhesive bonds to the extracellular matrix and instead use cell-cell adhesion to facilitate rapid migration , frequently occurs in embryogenesis ( personal communication with C . Little ) and is described as preferential migration to stretched cells 43 ., Compare Video S1 with Figure 1, ( f ) in Szabo et al . 2007 43 ., Figure S1 shows the morphology for one particular set of parameter values corresponding to weaker cell-cell and cell-matrix adhesion and stronger chemotaxis ., In this simulation , cells elongate to approximately 40 µm in length , fewer cells are recruited from the parent vessel , and the average extension speed at 14 hours slows to 6 . 8 µm/hr ., The length scale is consistent with experimental measurements of endothelial cell elongation 23 , 44 ., Figure 5 from Oakley et al . 1997 shows images from experiments using human fibroblasts stained for actin, ( e ) and tubulin, ( f ) on micro-machined grooved substratum 45 ., These experiments demonstrate that cells alter their shape , orientation , and polarity to align with the direction of the grooves ( double-headed arrow ) , exhibiting topographic , or contact , guidance ., Figure S2 is a simulation designed to mimic these experiments by isolating the cellular response to topographical guidance on similarly patterned substratum ., In this simulation , there is no chemotaxis and no cell-cell contact; cells respond only to topographical cues in the extracellular matrix ., Simulated cells alter their shape and orient in the direction of the matrix fibers ., Figure S2 bears a striking resemblance to the cell shapes observed in 45 ., We are also able to simulate interstitial invasion/migration by a single cell by turning off proliferation and cell recruitment but leaving all other parameters unchanged ( Video S2 ) ., This simulation is especially relevant in the context of fibroblast recruitment during wound healing and tumor cell invasion ( e . g . , glioblastoma , the most malignant form of brain cancer 46 ) , where understanding cell-matrix interactions and directed motility are critical mechanisms for highly motile or invasive cell phenotypes ., We design a set of numerical experiments allowing us to observe the onset of angiogenesis in extravascular environments of varying matrix fiber density ., We consider matrix fiber densities given as a fraction of the total interstitial area , ., As a measure of matrix orientation equivalency , the total fiber orientation in both the x and the y direction is calculated as we increased the matrix density ., The total x and total y fiber orientation do not vary with changes in total matrix density ., Besides varying the matrix density , all other parameters are held fixed ., All simulations last the same duration corresponding to approximately 14 hours ., The average rate at which the sprout grows and migrates , or its average extension sp
The extracellular matrix plays a critical role in orchestrating the events necessary for wound healing , muscle repair , morphogenesis , new blood vessel growth , and cancer invasion ., In this study , we investigate the influence of extracellular matrix topography on the coordination of multi-cellular interactions in the context of angiogenesis ., To do this , we validate our spatio-temporal mathematical model of angiogenesis against empirical data , and within this framework , we vary the density of the matrix fibers to simulate different tissue environments and to explore the possibility of manipulating the extracellular matrix to achieve pro- and anti-angiogenic effects ., The model predicts specific ranges of matrix fiber densities that maximize sprout extension speed , induce branching , or interrupt normal angiogenesis , which are independently confirmed by experiment ., We then explore matrix fiber alignment as a key factor contributing to peak sprout velocities and in mediating cell shape and orientation ., We also quantify the effects of proteolytic matrix degradation by the tip cell on sprout velocity and demonstrate that degradation promotes sprout growth at high matrix densities , but has an inhibitory effect at lower densities ., Our results are discussed in the context of ECM targeted pro- and anti-angiogenic therapies that can be tested empirically .
A cell migrating in the extracellular matrix environment has to pull on the matrix fibers to move ., When the matrix is too dense , the cell secretes enzymes to degrade the matrix proteins in order to get through ., And when the matrix is too sparse , the cell produces matrix proteins to locally increase the “foothold” ., How cells interact with the extracellular matrix is important in many processes from wound healing to cancer invasion ., We use a computational model to investigate the topography of the matrix on cell migration and coordination in the context of tumor induced new blood vessel growth ., The model shows that the density of the matrix fibers can have a strong effect on the extension speed and the morphology of a new blood vessel ., Further results show that matrix degradation by the cells can enhance vessel sprout extension at high matrix density , but impede sprout extension at low matrix density ., These results can potentially point to new targets for pro- and anti-angiogenesis therapies .
cardiovascular disorders/vascular biology, developmental biology/morphogenesis and cell biology, cell biology/morphogenesis and cell biology, cell biology/cell growth and division, mathematics, cell biology/cell adhesion, computational biology/systems biology