On the significance of membrane unfolding in mechanosensitive cell spreading: Its individual and synergistic effects.

Mechanosensitivity of cell spread area to substrate stiffness has been established both through experiments and different types of mathematical models of varying complexity including both the mechanics and biochemical reactions in the cell. What has not been addressed in previous mathematical models is the role of cell membrane dynamics on cell spreading, and an investigation of this issue is the goal of this work. We start with a simple mechanical model of cell spreading on a deformable substrate and progressively layer mechanisms to account for the traction dependent growth of focal adhesions, focal adhesion induced actin polymerization, membrane unfolding/exocytosis and contractility. This layering approach is intended to progressively help in understanding the role each mechanism plays in reproducing experimentally observed cell spread areas. To model membrane unfolding we introduce a novel approach based on defining an active rate of membrane deformation that is dependent on membrane tension. Our modeling approach allows us to show that tension-dependent membrane unfolding plays a critical role in achieving the large cell spread areas experimentally observed on stiff substrates. We also demonstrate that coupling between membrane unfolding and focal adhesion induced polymerization works synergistically to further enhance cell spread area sensitivity to substrate stiffness. This enhancement has to do with the fact that the peripheral velocity of spreading cells is associated with contributions from the different mechanisms by either enhancing the polymerization velocity at the leading edge or slowing down of the retrograde flow of actin within the cell. The temporal evolution of this balance in the model corresponds to the three-phase behavior observed experimentally during spreading. In the initial phase membrane unfolding is found to be particularly important.

Simulation and in vivo experimentation predict AdamTS-A location of function during caudal visceral mesoderm migration in Drosophila.

BACKGROUND: Caudal visceral mesoderm (CVM) cells migrate as a loose collective along the trunk visceral mesoderm (TVM) and are surrounded by extracellular matrix (ECM). In this study, we examined how one extracellular protease, AdamTS-A, facilitates CVM migration. RESULTS: A comparison of mathematical simulation to experimental results suggests that location of AdamTS-A action in CVM cells is on the sides of the cell not in contact with the TVM, predominantly at the CVM-ECM interface. CVM migration from a top-down view showed CVM cells migrating along the outside of the TVM substrate in the absence of AdamTS-A. Moreover, overexpression of AdamTS-A resulted in similar, but milder, mis-migration of the CVM. These results contrast with the salivary gland where AdamTS-A is proposed to cleave connections at the trailing edge of migrating cells. Subcellular localization of GFP-tagged AdamTS-A suggests that this protease is not limited to functioning at the trailing edge of CVM cells. CONCLUSION: Using both in vivo experimentation and mathematical simulations, we demonstrated that AdamTS-A cleaves connections between CVM cells and the ECM on all sides not attached to the TVM. Clearly, AdamTS-A has a more expansive role around the entire cell in cleaving cell-ECM attachments in cells migrating as a loose collective.

Multiscale phenomena and patterns in biological systems: special issue in honour of Hans Othmer.

This special issue on "Multiscale phenomena and patterns in biological systems" is an homage to the seminal contributions of Hans Othmer. He has remained at the forefront of multiscale modelling and pattern formation in biology for over half a century, developing models for molecular signalling networks, the mechanics of cellular movements, the interactions between multiple cells and their contributions to tissue patterning and dynamics. The contributions in this special issue follow Hans' legacy in using advanced mathematics to understand complex biological processes.

Center or periphery? Modeling the effects of focal adhesion placement during cell spreading.

Focal adhesions are often observed at the cell's periphery. We provide an explanation for this observation using a system-level mathematical model of a cell interacting with a two-dimensional substrate. The model describes the biological cell as a hypoelastic continuum material whose behavior is coupled to a deformable, linear elastic substrate via focal adhesions that are represented by collections of linear elastic attachments between the cell and the substrate. The evolution of the focal adhesions is coupled to local intracellular stresses which arise from mechanical cell-substrate interactions. Using this model we show that the cell has at least three mechanisms through which it can control its intracellular stresses: focal adhesion position, size, and attachment strength. We also propose that one reason why focal adhesions are typically located on the cell periphery instead of its center is because peripheral focal adhesions allow the cell to be more sensitive to changes in the microenvironment. This increased sensitivity is caused by the fact that peripherally located focal adhesions allow the cells to modulate its intracellular properties over a much larger portion of the cell area.

The role of the microenvironment in tumor growth and invasion.

Mathematical modeling and computational analysis are essential for understanding the dynamics of the complex gene networks that control normal development and homeostasis, and can help to understand how circumvention of that control leads to abnormal outcomes such as cancer. Our objectives here are to discuss the different mechanisms by which the local biochemical and mechanical microenvironment, which is comprised of various signaling molecules, cell types and the extracellular matrix (ECM), affects the progression of potentially-cancerous cells, and to present new results on two aspects of these effects. We first deal with the major processes involved in the progression from a normal cell to a cancerous cell at a level accessible to a general scientific readership, and we then outline a number of mathematical and computational issues that arise in cancer modeling. In Section 2 we present results from a model that deals with the effects of the mechanical properties of the environment on tumor growth, and in Section 3 we report results from a model of the signaling pathways and the tumor microenvironment (TME), and how their interactions affect the development of breast cancer. The results emphasize anew the complexities of the interactions within the TME and their effect on tumor growth, and show that tumor progression is not solely determined by the presence of a clone of mutated immortal cells, but rather that it can be 'community-controlled'.

Multi-scale models of cell and tissue dynamics.

Cell and tissue movement are essential processes at various stages in the life cycle of most organisms. The early development of multi-cellular organisms involves individual and collective cell movement; leukocytes must migrate towards sites of infection as part of the immune response; and in cancer, directed movement is involved in invasion and metastasis. The forces needed to drive movement arise from actin polymerization, molecular motors and other processes, but understanding the cell- or tissue-level organization of these processes that is needed to produce the forces necessary for directed movement at the appropriate point in the cell or tissue is a major challenge. In this paper, we present three models that deal with the mechanics of cells and tissues: a model of an arbitrarily deformable single cell, a discrete model of the onset of tumour growth in which each cell is treated individually, and a hybrid continuum-discrete model of the later stages of tumour growth. While the models are different in scope, their underlying mechanical and mathematical principles are similar and can be applied to a variety of biological systems.