Agent-based model of angiogenesis simulates capillary sprout initiation in multicellular networks

We developed an agent-based model of endothelial sprout initiations based on time-lapse confocal imaging in vitro that outperforms Monte Carlo simulations, suggesting that sprout location and frequency are not purely stochastic behaviors

Quantifying the Proteolytic Release of Extracellular Matrix-Sequestered VEGF with a Computational Model

BACKGROUND: VEGF proteolysis by plasmin or matrix metalloproteinases (MMPs) is believed to play an important role in regulating vascular patterning in vivo by releasing VEGF from the extracellular matrix (ECM). However, a quantitative understanding of the kinetics of VEGF cleavage and the efficiency of cell-mediated VEGF release is currently lacking. To address these uncertainties, we develop a molecular-detailed quantitative model of VEGF proteolysis, used here in the context of an endothelial sprout. METHODOLOGY AND FINDINGS: To study a cell's ability to cleave VEGF, the model captures MMP secretion, VEGF-ECM binding, VEGF proteolysis from VEGF165 to VEGF114 (the expected MMP cleavage product of VEGF165) and VEGF receptor-mediated recapture. Using experimental data, we estimated the effective bimolecular rate constant of VEGF165 cleavage by plasmin to be 328 M(-1) s(-1) at 25 degrees C, which is relatively slow compared to typical MMP-ECM proteolysis reactions. While previous studies have implicated cellular proteolysis in growth factor processing, we show that single cells do not individually have the capacity to cleave VEGF to any appreciable extent (less than 0.1% conversion). In addition, we find that a tip cell's receptor system will not efficiently recapture the cleaved VEGF due to an inability of cleaved VEGF to associate with Neuropilin-1. CONCLUSIONS: Overall, VEGF165 cleavage in vivo is likely to be mediated by the combined effect of numerous cells, instead of behaving in a single-cell-directed, autocrine manner. We show that heparan sulfate proteoglycans (HSPGs) potentiate VEGF cleavage by increasing the VEGF clearance time in tissues. In addition, we find that the VEGF-HSPG complex is more sensitive to proteases than is soluble VEGF, which may imply its potential relevance in receptor signaling. Finally, according to our calculations, experimentally measured soluble protease levels are approximately two orders of magnitude lower than that needed to reconcile levels of VEGF cleavage seen in pathological situations

Module-based multiscale simulation of angiogenesis in skeletal muscle

<p>Abstract</p> <p>Background</p> <p>Mathematical modeling of angiogenesis has been gaining momentum as a means to shed new light on the biological complexity underlying blood vessel growth. A variety of computational models have been developed, each focusing on different aspects of the angiogenesis process and occurring at different biological scales, ranging from the molecular to the tissue levels. Integration of models at different scales is a challenging and currently unsolved problem.</p> <p>Results</p> <p>We present an object-oriented module-based computational integration strategy to build a multiscale model of angiogenesis that links currently available models. As an example case, we use this approach to integrate modules representing microvascular blood flow, oxygen transport, vascular endothelial growth factor transport and endothelial cell behavior (sensing, migration and proliferation). Modeling methodologies in these modules include algebraic equations, partial differential equations and agent-based models with complex logical rules. We apply this integrated model to simulate exercise-induced angiogenesis in skeletal muscle. The simulation results compare capillary growth patterns between different exercise conditions for a single bout of exercise. Results demonstrate how the computational infrastructure can effectively integrate multiple modules by coordinating their connectivity and data exchange. Model parameterization offers simulation flexibility and a platform for performing sensitivity analysis.</p> <p>Conclusions</p> <p>This systems biology strategy can be applied to larger scale integration of computational models of angiogenesis in skeletal muscle, or other complex processes in other tissues under physiological and pathological conditions.</p

Elongation, proliferation & migration differentiate endothelial cell phenotypes and determine capillary sprouting

<p>Abstract</p> <p>Background</p> <p>Angiogenesis, the growth of capillaries from preexisting blood vessels, has been extensively studied experimentally over the past thirty years. Molecular insights from these studies have lead to therapies for cancer, macular degeneration and ischemia. In parallel, mathematical models of angiogenesis have helped characterize a broader view of capillary network formation and have suggested new directions for experimental pursuit. We developed a computational model that bridges the gap between these two perspectives, and addresses a remaining question in angiogenic sprouting: how do the processes of endothelial cell elongation, migration and proliferation contribute to vessel formation?</p> <p>Results</p> <p>We present a multiscale systems model that closely simulates the mechanisms underlying sprouting at the onset of angiogenesis. Designed by agent-based programming, the model uses logical rules to guide the behavior of individual endothelial cells and segments of cells. The activation, proliferation, and movement of these cells lead to capillary growth in three dimensions. By this means, a novel capillary network emerges out of combinatorially complex interactions of single cells. Rules and parameter ranges are based on literature data on endothelial cell behavior in vitro. The model is designed generally, and will subsequently be applied to represent species-specific, tissue-specific in vitro and in vivo conditions.</p> <p>Initial results predict tip cell activation, stalk cell development and sprout formation as a function of local vascular endothelial growth factor concentrations and the Delta-like 4 Notch ligand, as it might occur in a three-dimensional in vitro setting. Results demonstrate the differential effects of ligand concentrations, cell movement and proliferation on sprouting and directional persistence.</p> <p>Conclusion</p> <p>This systems biology model offers a paradigm closely related to biological phenomena and highlights previously unexplored interactions of cell elongation, migration and proliferation as a function of ligand concentration, giving insight into key cellular mechanisms driving angiogenesis.</p

Computational Model of Gab1/2-Dependent VEGFR2 Pathway to Akt Activation.

PMC3689841Vascular endothelial growth factor (VEGF) signal transduction is central to angiogenesis in development and in pathological conditions such as cancer, retinopathy and ischemic diseases. However, no detailed mass-action models of VEGF receptor signaling have been developed. We constructed and validated the first computational model of VEGFR2 trafficking and signaling, to study the opposing roles of Gab1 and Gab2 in regulation of Akt phosphorylation in VEGF-stimulated endothelial cells. Trafficking parameters were optimized against 5 previously published in vitro experiments, and the model was validated against six independent published datasets. The model showed agreement at several key nodes, involving scaffolding proteins Gab1, Gab2 and their complexes with Shp2. VEGFR2 recruitment of Gab1 is greater in magnitude, slower, and more sustained than that of Gab2. As Gab2 binds VEGFR2 complexes more transiently than Gab1, VEGFR2 complexes can recycle and continue to participate in other signaling pathways. Correspondingly, the simulation results show a log-linear relationship between a decrease in Akt phosphorylation and Gab1 knockdown while a linear relationship was observed between an increase in Akt phosphorylation and Gab2 knockdown. Global sensitivity analysis demonstrated the importance of initial-concentration ratios of antagonistic molecular species (Gab1/Gab2 and PI3K/Shp2) in determining Akt phosphorylation profiles. It also showed that kinetic parameters responsible for transient Gab2 binding affect the system at specific nodes. This model can be expanded to study multiple signaling contexts and receptor crosstalk and can form a basis for investigation of therapeutic approaches, such as tyrosine kinase inhibitors (TKIs), overexpression of key signaling proteins or knockdown experiments.JH Libraries Open Access Fun

Mechanistic modelling of dynamic MRI data predicts that tumour heterogeneity decreases therapeutic response

Mechanistic modelling of dynamic MRI data predicts that tumour heterogeneity decreases therapeutic respons

Tipping the Balance: Robustness of Tip Cell Selection, Migration and Fusion in Angiogenesis

Vascular abnormalities contribute to many diseases such as cancer and diabetic retinopathy. In angiogenesis new blood vessels, headed by a migrating tip cell, sprout from pre-existing vessels in response to signals, e.g., vascular endothelial growth factor (VEGF). Tip cells meet and fuse (anastomosis) to form blood-flow supporting loops. Tip cell selection is achieved by Dll4-Notch mediated lateral inhibition resulting, under normal conditions, in an interleaved arrangement of tip and non-migrating stalk cells. Previously, we showed that the increased VEGF levels found in many diseases can cause the delayed negative feedback of lateral inhibition to produce abnormal oscillations of tip/stalk cell fates. Here we describe the development and implementation of a novel physics-based hierarchical agent model, tightly coupled to in vivo data, to explore the system dynamics as perpetual lateral inhibition combines with tip cell migration and fusion. We explore the tipping point between normal and abnormal sprouting as VEGF increases. A novel filopodia-adhesion driven migration mechanism is presented and validated against in vivo data. Due to the unique feature of ongoing lateral inhibition, ‘stabilised’ tip/stalk cell patterns show sensitivity to the formation of new cell-cell junctions during fusion: we predict cell fates can reverse. The fusing tip cells become inhibited and neighbouring stalk cells flip fate, recursively providing new tip cells. Junction size emerges as a key factor in establishing a stable tip/stalk pattern. Cell-cell junctions elongate as tip cells migrate, which is shown to provide positive feedback to lateral inhibition, causing it to be more susceptible to pathological oscillations. Importantly, down-regulation of the migratory pathway alone is shown to be sufficient to rescue the sprouting system from oscillation and restore stability. Thus we suggest the use of migration inhibitors as therapeutic agents for vascular normalisation in cancer

A multiscale hybrid model for pro-angiogenic calcium signals in a vascular endothelial cell

Cytosolic calcium machinery is one of the principal signaling mechanisms by which endothelial cells (ECs) respond to external stimuli during several biological processes, including vascular progression in both physiological and pathological conditions. Low concentrations of angiogenic factors (such as VEGF) activate in fact complex pathways involving, among others, second messengers arachidonic acid (AA) and nitric oxide (NO), which in turn control the activity of plasma membrane calcium channels. The subsequent increase in the intracellular level of the ion regulates fundamental biophysical properties of ECs (such as elasticity, intrinsic motility, and chemical strength), enhancing their migratory capacity. Previously, a number of continuous models have represented cytosolic calcium dynamics, while EC migration in angiogenesis has been separately approached with discrete, lattice-based techniques. These two components are here integrated and interfaced to provide a multiscale and hybrid Cellular Potts Model (CPM), where the phenomenology of a motile EC is realistically mediated by its calcium-dependent subcellular events. The model, based on a realistic 3-D cell morphology with a nuclear and a cytosolic region, is set with known biochemical and electrophysiological data. In particular, the resulting simulations are able to reproduce and describe the polarization process, typical of stimulated vascular cells, in various experimental conditions.Moreover, by analyzing the mutual interactions between multilevel biochemical and biomechanical aspects, our study investigates ways to inhibit cell migration: such strategies have in fact the potential to result in pharmacological interventions useful to disrupt malignant vascular progressio

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

Establishment and Validation of Computational Model for MT1-MMP Dependent ECM Degradation and Intervention Strategies

MT1-MMP is a potent invasion-promoting membrane protease employed by aggressive cancer cells. MT1-MMP localizes preferentially at membrane protrusions called invadopodia where it plays a central role in degradation of the surrounding extracellular matrix (ECM). Previous reports suggested a role for a continuous supply of MT1-MMP in ECM degradation. However, the turnover rate of MT1-MMP and the extent to which the turnover contributes to the ECM degradation at invadopodia have not been clarified. To approach this problem, we first performed FRAP (Fluorescence Recovery after Photobleaching) experiments with fluorescence-tagged MT1-MMP focusing on a single invadopodium and found very rapid recovery in FRAP signals, approximated by double-exponential plots with time constants of 26 s and 259 s. The recovery depended primarily on vesicle transport, but negligibly on lateral diffusion. Next we constructed a computational model employing the observed kinetics of the FRAP experiments. The simulations successfully reproduced our FRAP experiments. Next we inhibited the vesicle transport both experimentally, and in simulation. Addition of drugs inhibiting vesicle transport blocked ECM degradation experimentally, and the simulation showed no appreciable ECM degradation under conditions inhibiting vesicle transport. In addition, the degree of the reduction in ECM degradation depended on the degree of the reduction in the MT1-MMP turnover. Thus, our experiments and simulations have established the role of the rapid turnover of MT1-MMP in ECM degradation at invadopodia. Furthermore, our simulations suggested synergetic contributions of proteolytic activity and the MT1-MMP turnover to ECM degradation because there was a nonlinear and marked reduction in ECM degradation if both factors were reduced simultaneously. Thus our computational model provides a new in silico tool to design and evaluate intervention strategies in cancer cell invasion