Abstract

The dynamics of filopodia interacting with the surrounding extracellular matrix (ECM) play a key role in various cell-ECM interactions, but their mechanisms of interaction with the ECM in 3D environment remain poorly understood. Based on first principles, here we construct an individual-based, force-based computational model integrating four modules of 1) filopodia penetration dynamics; 2) intracellular mechanics of cellular and nuclear membranes, contractile actin stress fibers, and focal adhesion dynamics; 3) structural mechanics of ECM fiber networks; and 4) reaction-diffusion mass transfers of seven biochemical concentrations in related with chemotaxis, proteolysis, haptotaxis, and degradation in ECM to predict dynamic behaviors of filopodia that penetrate into a 3D ECM fiber network. The tip of each filopodium crawls along ECM fibers, tugs the surrounding fibers, and contracts or retracts depending on the strength of the binding and the ECM stiffness and pore size. This filopodium-ECM interaction is modeled as a stochastic process based on binding kinetics between integrins along the filopodial shaft and the ligands on the surrounding ECM fibers. This filopodia stochastic model is integrated into migratory dynamics of a whole cell in order to predict the cell invasion into 3D ECM in response to chemotaxis, haptotaxis, and durotaxis cues. Predicted average filopodia speed and that of the cell membrane advance agreed with experiments of 3D HUVEC migration at r2 > 0.95 for diverse ECMs with different pore sizes and stiffness.

Highlights

  • Cell migration in the three dimensional extracellular matrix (ECM) plays a crucial role in a wide variety of biophysical processes, such as wound healing, morphogenesis, angiogenesis, tumor growth, and cancer invasion [1,2]

  • We are interested in how filopodia gain traction forces from the surrounding collagen fibers in the degradable ECM

  • Detailed mechanisms of filopodia dynamics have previously been studied for 2D behaviors: filopodia traction dynamics, including motor-clutch mechanism at the filopodial shaft, frictional slippage, and load-and-fail phenomena at hard and soft ECMs [4]; filopodial protrusion due to actin polymerization and depolymerization [5,6,7]; the formation of focal complexes (FCs) [8,9] and retraction force generation at the filopodial tip [10]; and filopodium buckling instability [11]

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Summary

Introduction

Cell migration in the three dimensional extracellular matrix (ECM) plays a crucial role in a wide variety of biophysical processes, such as wound healing, morphogenesis, angiogenesis, tumor growth, and cancer invasion [1,2]. Filopodia play many important roles in interacting with ECM. Detailed mechanisms of filopodia dynamics have previously been studied for 2D behaviors: filopodia traction dynamics, including motor-clutch mechanism at the filopodial shaft, frictional slippage, and load-and-fail phenomena at hard and soft ECMs [4]; filopodial protrusion due to actin polymerization and depolymerization [5,6,7]; the formation of focal complexes (FCs) [8,9] and retraction force generation at the filopodial tip [10]; and filopodium buckling instability [11]

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