Mechanotransduction may occur through numerous mechanisms, including potentially through autocrine signaling in a dynamically changing extracellular space. We developed a computational model to analyze how alterations in the geometry of an epithelial lateral intercellular space (LIS) affect the concentrations of constitutively shed ligands inside and below the LIS. The model employs the finite element method to solve for the concentration of ligands based on the governing ligand diffusion-convection equations inside and outside of the LIS, and assumes idealized parallel plate geometry and an impermeable tight junction at the apical surface. Using the model, we examined the temporal relationship between geometric changes and ligand concentration, and the dependence of this relationship on system characteristics such as ligand diffusivity, shedding rate, and rate of deformation. Our results reveal how the kinetics of mechanical deformation can be translated into varying rates of ligand accumulation, a potentially important mechanism for cellular discrimination of varying rate-mechanical processes. Furthermore, our results demonstrate that rapid changes in LIS geometry can transiently increase ligand concentrations in underlying media or tissues, suggesting a mechanism for communication of mechanical state between epithelial and subepithelial cells. These results underscore both the plausibility and complexity of the proposed extracellular mechanotransduction mechanism.

Cells often communicate through the exchange of extracellular autocrine and/or paracrine signals. Changes in the local levels of these molecules, derived from alterations in production, metabolism or transport, are dynamically sensed, allowing cells to respond appropriately to their microenvironment (1). We have proposed a mode of mechanotransduction whereby cells respond to changes in the local extracellular concentration of autocrine ligands that are caused solely by deformation of the extracellular space (2). In support of this hypothesis, we demonstrated that the extracellular space in cultured human bronchial epithelial cells deforms under transcellular compressive stress, and that an autocrine ligand-receptor signaling loop is activated by the same mechanical stimulus (2). The essential components of autocrine ligand-receptor circuits are frequently found to be constitutively expressed and colocalized in the basolateral compartment of epithelial cells (3). In our previous work, a simple analytical relationship was derived to predict the steady-state ligand concentration in the local extracellular space before and after mechanical loading (2). While this steady-state analysis was essential in establishing the plausibility of the extracellular mechanotransduction mechanism, it could not address the kinetics of the process, and omitted potentially important effects of convection.

Here we develop a generalized finite-element solution of the one-dimensional diffusion-convection equation to evaluate the temporal changes in ligand concentration occurring in a dynamically collapsing interstitial space between epithelial cells. We introduce a new geometry for the model that accommodates the diffusion and convection of ligands shed into the lateral intercellular space, which is continuous with an underlying media reservoir. Employing the model, we explore the parameter space of the governing equations, examining the effect of ligand diffusivity, shedding rate, and rate of extracellular space change on the kinetics of ligand accumulation. The new model geometry reveals the transient effect of convection on ligand concentration changes in the underlying space (e.g., media for the in vitro case or tissues in vivo), suggesting a potential mechanism for communication of a change in the mechanical state of the epithelium to underlying tissues. Moreover, the model offers a novel explanation for how cells could discriminate between mechanical processes occurring over a range of rates in different physiological scenarios. We use insights gained from the model to propose two explanations for a selective contribution of the EGF family-ligand heparin-binding EGF (HB-EGF) to the transduction of mechanical stress via autocrine signaling in a collapsing extracellular space.

The transitional regime extends to a distance R^sub t^ = w/π from the LIS boundary. This distance was determined by matching the fluxes corresponding to Cartesian (w) and radial (πR^sub t^) lengths, through which the flux passes. We further approximate the velocity field in this domain as uniform, being equal to the bulk velocity at the LIS exit V^sub t^ = V^sub x^(x = h). The transitional regime was included to avoid numerical difficulties that can occur when switching coordinate systems. The approximations made in this domain have little impact on the overall concentration profile inside and outside of the LIS (data not shown).

The radial domain encompasses the region between R^sub t^ (end of the transitional domain) and R^sub 0^ = h/2 (where we assume the ligand concentration to be zero). Mathematically, the zero-concentration boundary would be infinitely far away from the LIS (i.e., R^sub 0^ [arrow right] ∞), but for efficient numerical simulations we determined that for a LIS height h = 15 µm (2), R^sub 0^ = 7.5 µm is sufficiently far away from the LIS boundary such that further increasing R^sub 0^ had little effect on the overall concentration profile (data not shown). Hence, for all of the simulations we fixed the value of R^sub 0^ = 7.5 µm to be half of the previously measured LIS height ft = 15 µm (2).