(309a) 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.