Deriving time-varying cellular motility parameters via wavelet analysis

Cell migration, which is regulated by intracellular signaling pathways (ICSP) and extracellular matrix (ECM), plays an indispensable role in many physiological and pathological process such as normal tissue development and cancer metastasis. However, there is a lack of rigorous and quantitative tools for analyzing the time-varying characteristics of cell migration in heterogeneous microenvironment, resulted from, e.g. the time-dependent local stiffness due to microstructural remodeling by migrating cells. Here, we develop a wavelet-analysis approach to derive the time-dependent motility parameters from cell migration trajectories, based on the time-varying persistent random walk model. In particular, the wavelet denoising and wavelet transform are employed to analyze migration velocities and obtain the wavelet power spectrum. Subsequently, the time-dependent motility parameters are derived via Lorentzian power spectrum. Our results based on synthetic data indicate the superiority of the method for estimating the intrinsic transient motility parameters, robust against a variety of stochastic noises. We also carry out a systematic parameter study and elaborate the effects of parameter selection on the performance of the method. Moreover, we demonstrate the utility of our approach via analyzing experimental data ofin vitrocell migration in distinct microenvironments, including the migration of MDA-MB-231 cells in confined micro-channel arrays and correlated migration of MCF-10A cells due to ECM-mediated mechanical coupling. Our analysis shows that our approach can be as a powerful tool to accurately derive the time-dependent motility parameters, and further analyze the time-dependent characteristics of cell migration regulated by complex microenvironment.