Modeling the Diffusive Behavior of 3D Stem Cell Migration

Design of 3D scaffolds that can facilitate proper survival, proliferation, and differentiation of progenitor cells is a challenge for clinical applications involving large connective tissue defects, with cell migration within scaffolds a critical process governing tissue integration.  In previous work, we have quantified how physical properties of 3D scaffolds, such as pore diameter, modulus, and integrin-binding peptides, as independently tunable parameters, govern the motility and infiltration of marrow-derived stem cells (MSCs). The relationships between migration speed, displacement, and total path length were found to be strongly dependent on pore size, most likely resulting from the non-intuitive convolution of pore diameter and void chamber diameter yielding different geometric environments experienced by the cells within. 

A looming challenge in the quantification of cell motility in these complex microenvironments is whether or not we will be able to predict the extent of cell infiltration given a set of scaffold physical parameters. We are building computational models, based on anomalous diffusion, to determine whether or not MSC migration on 2D polyacrylamide substrates, with tunable stiffness and integrin-binding peptides, is predictive of MSC migration in more complex 2.5D and 3D microenvironments.  An anomalous diffusion model of cell motility exhibits superior fitting to the canonical persistent random walk (PRW) model since it is able to capture both the superdiffusive and subdiffusive behavior of MSC migration within 3D microenvironments.  This model relates the mean squared displacement (MSD) to time by a power law and is characterized by two parameters, a diffusion coefficient and a scaling index.  To develop a predictive quantitative model of cell motility, we are determining diffusion coefficients and scaling indices using migration paths from single cell tracking experiments and correlating these model parameters to specific physicochemical cues from the microenvironment.  Experimentally, we have observed that MSC migration speed has a biphasic dependence on the density of surface-bound RGD, but only at intermediate substrate stiffness.  This biphasic relationship was observed in 3D gels, but only when the pores were much larger than the average cell diameter, and therefore likely a quasi-2D environment.  In smaller pore diameters, where migration was truly 3D, this biphasic dependence disappeared.  We are currently designing novel "2.5D" substrates, wherein cells cannot infiltrate the scaffold, but still experience topographical cues and ridges that approximate 3D macroporous scaffolds.  We hypothesize that this hybrid microenvironment will bridge our computational efforts in 2D and 3D, and allow us to predict 3D migration given the scaffolds pore size, modulus, and density of integrin-binding peptides.  This information on MSC motility could be very powerful for future intelligent scaffold design for MSC-directed bone regeneration in vivo.