One of the most commonly used models for describing individual cell migration in 2D is the persistent random walk (PRW) model,12C14 whose mathematical formulation was originally developed as modified Brownian motion. a simple power law to relate the mean square displacement to time, more accurately captures individual cell migration paths across a range of engineered 2D and 3D environments than does the more commonly used PRW model. We used the AD model parameters to distinguish cell movement profiles on substrates with different chemokinetic factors, geometries (2D vs 3D), substrate adhesivities, and compliances. Although the two models performed with equal precision for Elastase Inhibitor, SPCK superdiffusive cells, we suggest a simple AD model, of PRW, to describe cell trajectories in populations with a significant subdiffusive fraction, such as cells in confined, 3D environments. INTRODUCTION Cell migration is integral to a variety of physiological processes including organ development, tissue morphogenesis, wound healing, and immune response. A greater understanding of the motility effects Elastase Inhibitor, SPCK of environmental cues can inform the design of biotechnologies such as movement-directing scaffolds. Research into the relationship between cell migration and cues from the cellular microenvironment increasingly takes advantage of the capability to manipulate properties such as the extracellular matrix (ECM) compliance1C6 and density of cell adhesive ligands.7C11 Descriptive (i.e., empirical) models of migration dynamics facilitate analysis of microenvironment dependence Elastase Inhibitor, SPCK in part by assigning parameters to characterize cells, individually and in aggregate. One of the most commonly used models for describing individual cell migration in 2D is the persistent random walk (PRW) model,12C14 whose mathematical formulation was originally developed as modified Brownian motion. Until recently, the migration of adherent cells has been explored almost exclusively on 2D surfaces, but is now investigated in 3D as well, partly due to the advent of bioengineered environments capable of encapsulating cells and more closely capturing conditions.2,15C19 Despite its success on 2D surfaces, cell migration is often not well described by the PRW model at any appreciably long time scale in confined 3D environments. Indeed, 9%C46% of low persistent (in anomalous diffusion, the mean squared displacement grows as a power, < 2, by definition lending this model the flexibility to describe both sub- and superdiffusive motion. Variants of anomalous diffusion, in which may be constant or cell trajectories to the best of our knowledge. Given that many cells migrating in 3D are subdiffusive, we undertook to systematically characterize the trajectories of individual cells (and aggregate sample-wide migration) under various extracellular conditions using the AD model. We found that PRW and AD gave similar correlation coefficients for superdiffusive cells, but that the AD model was better at describing subdiffusive cells. The AD parameter more clearly differentiated subdiffusive cells from each other than did the PRW parameter (persistence time). The AD parameters as well as the PRW parameters were found to predictably vary with geometry, Elastase Inhibitor, SPCK elastic modulus, ECM composition, and ECM ligand density. Therefore, we suggest the AD model is a more robust model of individual cell movement, particularly in constrained, 3D environments. RESULTS The AD model outperforms PRW in describing individual subdiffusive cell motion We first quantified cell motility on supra-physiologically stiff surfaces: 2D coverslips coupled with full-length, integrin-binding (ECM) proteins. We created three different surfaces, inspired by proteins found in different tissues of the human body: bone, brain, and lung (Fig. ?(Fig.1).1). Independently, we perturbed MDA-MB-231 chemokinesis and adhesivity, chemically, by adding either epidermal growth factor (EGF; green) or a function-affecting antibody to 1 1 integrin (red) [Figs. 1(a)C1(c)]. On these rigid surfaces, regardless of the ECM protein cocktail or chemical perturbation, cells were largely (28%C84%) superdiffusive [1? 0.8, while 45% of subdiffusive cells had and distribution within each condition was typically unimodal and sensitive to the ECM adhesivity and soluble factors, highlighting the capability of the power-function model to describe a heterogeneous population of cells [Figs. Rabbit polyclonal to cyclinA 1(d)C1(f) and S2]. Regardless of the ECM protein cocktail or chemical perturbation, cells’ individual anomalous exponents spanned the entire possible range 0C2 but tended to have a majority of.