Computational Modeling of Extracellular Mechanotransduction

Abstract

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.

Migration of connective tissue-derived cells is mediated by ultra-low concentration gradient fields of EGF

“…40-ng/mL, 80-ng/mL, or 400-ng/mL, while EGF concentration within the SKC chamber was initially set to 0-ng/mL. Experimental measurement of EGF transport within the channel over time generated a diffusivity value of 2.0×10 −6 cm 2 /s, which is well within the range of published EGF diffusivities shown in Table 1 [38–41] Our device-measured EGF diffusivity of 2.0×10 −6 cm 2 /s was then used to generate mathematically precise EGF concentration profiles within the bridged µLane as a function of time and position shown in Figure 1C. As seen, the data illustrate that a steady-state EGF concentration distribution is established after approximately 18 hours.…”

Putting the Squeeze on Airway Epithelia

“…In a follow-up study, Tschumperlin et al used finite-element methods to calculate the potential concentrations of ligands in the lateral intercellular space (52). Using reasonable assumptions, they found that alterations in the geometry of the lateral intercellular space could impact the concentrations of constitutively shed ligands inside and below the cell layer.…”

“…In their model, the maximal change in volume of the lateral intercellular space occurred ϳ10 min after the application of compressive stress. Finally, they used a three-dimensional imaging technique, with better temporal and spatial resolution than had been available at the time their initial work was done, to observe the evolution of mechanotransduction responses through changes in the concentration of local EGF ligands such as heparin-binding EGF (HB-EGF) and transforming growth factor ␣ (TGF-␣) (52). They found that highly localized changes in ligand concentrations can be induced through mechanical loading, depending on both local deformations and the effects of ligand convection.…”

Quantification of three-dimensional dynamics of intercellular geometry under mechanical loading using a weighted directional adaptive-threshold method

“…Our results thus serve to focus future efforts on understanding the dynamics of mechanotransduction events that occur in synchrony with the measured deformations. These quantitative imaging results also provide an essential input for mathematical models [11] that relate changes in local geometry to autocrine signaling, helping to refine our understanding of the dynamics of extracellular mechanotransduction. Most importantly, the improved imaging and image analysis methods detailed here offer an enhanced capacity to capture and quantify dynamic, three dimensional cellular deformations under loading.…”