A Multiscale Model to Predict Neuronal Cell Deformation with Varying Extracellular Matrix Stiffness and Topography

Predicting neurite extension for varying extracellular matrix stiffness and topography

Neurite extension is a dynamic process and is dependent on the microenvironment. The mechanical properties of the extracellular matrix (ECM), such as stiffness and topography influence the microenvironment and affects neurite extension; however, the mechanistic basis for this dynamic response of neurite extension remains elusive. In this study, we develop a computational model that predicts neurite extension dynamics process as the stiffness and patterned topography of ECM changes. The model includes the contribution of receptors integrin and neural cellular adhesion molecule toward the growth of neurite tip. We use non-linear finite element analysis (FEA) to model the neuronal cell, neurite, and the ECM, which is then coupled to the force-deformation receptor properties obtained from molecular dynamics simulations. Using an empirical relation, we develop a neurite extension algorithm that simulates the dynamic process of growth cone induced by growth cone extension, receptor density, and rupture. We investigate the dependence of neurite extension on ECM stiffness using three distinct materials, the effect of width and spacing of continuous (cylindrical) and discontinuous (pillar) patterned topography, as well as the topography steepness and stiffness gradient. We find that an increasing stiffness and width of patterned topography results in increased neurite extension, but the magnitude of the increase differs depending on the growth cone extension and receptor density between them. These findings will aid in vitro studies in determining an ECM with appropriate mechanical properties, such as stiffness and topography that will improve neurite extension, thus resulting in the formation of functional neurons.

Local tissue heterogeneity may modulate neuronal responses via altered axon strain fields: insights about innervated joint capsules from a computational model

In innervated collagenous tissues, tissue scale loading may contribute to joint pain by transmitting force through collagen fibers to the embedded mechanosensitive axons. However, the highly heterogeneous collagen structures of native tissues make understanding this relationship challenging. Recently, collagen gels with embedded axons were stretched and the resulting axon signals were measured, but these experiments were unable to measure the local axon strain fields. Computational discrete fiber network models can directly determine axon strain fields due to tissue scale loading. Therefore, this study used a discrete fiber network model to identify how heterogeneous collagen networks (networks with multiple collagen fiber densities) change axon strain due to tissue scale loading. In this model, a composite cylinder (axon) was embedded in a Delaunay network (collagen). Homogeneous networks with a single collagen volume fraction and two types of heterogeneous networks with either a sparse center or dense center were created. Measurements of fiber forces show higher magnitude forces in sparse regions of heterogeneous networks and uniform force distributions in homogeneous networks. The average axon strain in the sparse center networks decreases when compared to homogeneous networks with similar collagen volume fractions. In dense center networks, the average axon strain increases compared to homogeneous networks. The top 1% of axon strains are unaffected by network heterogeneity. Based on these results, the interaction of tissue scale loading, collagen network heterogeneity, and axon strains in native musculoskeletal tissues should be considered when investigating the source of joint pain.

Long-range mechanical signaling in biological systems

Cells can respond to signals generated by other cells that are remarkably far away. Studies from at least the 1920's showed that cells move toward each other when the distance between them is on the order of a millimeter, which is many times the cell diameter. Chemical signals generated by molecules diffusing from the cell surface would move too slowly and dissipate too fast to account for these effects, suggesting that they might be physical rather than biochemical. The non-linear elastic responses of sparsely connected networks of stiff or semiflexible filament such as those that form the extracellular matrix (ECM) and the cytoskeleton have unusual properties that suggest multiple mechanisms for long-range signaling in biological tissues. These include not only direct force transmission, but also highly non-uniform local deformations, and force-generated changes in fiber alignment and density. Defining how fibrous networks respond to cell-generated forces can help design new methods to characterize abnormal tissues and can guide development of improved biomimetic materials.