A Physical View of Tissue Biology

The cells in our bodies must fit together seamlessly in tissues and organs, adopting specific shapes to function properly. It is vital to understand the rules that control this if we will be able to use tissue engineering for regenerative medicine. Studies have revealed that mechanical forces are fundamental shapers of cells and tissues. They further suggest that, if used in a combinatorial manner, a small number of force-generating properties—namely cell-cell adhesion, cell-matrix adhesion, protrusion, and contractility—could orchestrate the movement of tissues into new structures. An exciting new challenge in biophysics is to interpret the functions of molecules, as defined by cell biology, within the framework of the elementary forces that shape cells and tissues.

Surface Energetics

When cells aggregate, they tend to do so in ways that seem to minimize their overall surface area. Soap bubbles also aggregate by surface minimization and this represent an energy minimum in which forces are balanced. Several years ago, we discovered a striking example of this phenomenon in the eye (Hayashi and Carthew, 2004). The eye epithelium is composed of 800 repeating units of a small number of cells (Figure 1). Within each unit, two primary pigment cells surround four central cone cells and are in turn framed by secondary and tertiary pigment cells in a highly reproducible pattern. We varied the number of cone cells in each unit, and we found that they packed into configurations that precisely resembled those of free soap bubble aggregates of the same number (Figure 2). In other words, cone cells changed shape so that the entire cluster reached an energetically favorable state, as also occurs with soap bubbles.

Cells are not soap bubbles and so a more biological depiction of surface energy is needed. Interfacial tension is a measure of the energy required to increase the surface of contact between fluid-like entities like cells. This tension is a function of simple surface tension as well as biological components such as cell-cell adhesion, which reduces interfacial tension, and the actin cytoskeleton, which contributes positively to interfacial tension. We have developed a cell-based mathematical model for interfacial tension that simulates the way that cells are configured in the eye. Beginning with virtual cells of random shape, a computer simulation allows the cells to change shape so as to achieve a minimal interfacial tension for the entire eye unit (Figure 3). The modeling quantitatively recapitulates the precise cell shapes found in the eye (Hilgenfeldt et al., 2008). This mathematical approach to modeling cell shapes in epithelia is one of just a few being developed in the world. 

Cell-cell adhesion can play an important role in tissue integrity. What about in the shaping of tissue? Cells in the eye express two kinds of cell-cell adhesion molecules: E-cadherin and N-cadherin. All cells contain E-cadherin; however, only the four cone cells contain N-cadherin. The cadherin protein molecules become localized in a thin band of lateral cell membrane corresponding to the adherens junction, which is the major site of adhesion between cells. Cadherins in one membrane bind to cadherins located in the membrane of a neighboring cell across the intercellular gap, increasing the adherence of one cell with its neighbor. Adhesion between facing membranes decreases interfacial tension making expansion of the cell-cell interface energetically favorable. However, the expansion of one interface affects other cell-cell interfaces due to constraints on the overall size of the cell membrane. Shape changes in one cell induce shape changes in others, and alteration of the elastic energy of the membranes around all cells. Ultimately, the mechanical energy of the entire unit needs to be minimized globally in order to find an equilibrium configuration for the unit of cells.

We use experimental genetics and computer modeling to understand how cadherin molecules control morphogenesis (Gemp et al., 2011). Comparison of model simulations with experimental data for mutants in which certain cells produce altered levels of cadherin have found that (i) the model describes characteristic shape changes in such mutants, (ii) the simulations distinguish between different mechanisms of how cadherin levels are attained and controlled, and (iii) the model incorporates important dynamical features in morphogenesis, such as the temporal sequence of cadherin expression and cell-cell contact remodeling.

The objective of our biomechanical modeling is to understand how cells naturally form tissues of defined structure with the goal to use this knowledge for regenerative medicine and tissue engineering.