Probing Cellular Heterogeneity through Fuzzy Time Series Forecasting Models of Leading Edge Dynamics

In this paper, a new biological modeling approach is proposed for predicting complex heterogeneous subcellular behaviors. Cell protrusion which initiates cell migration has a significant amount of subcellular heterogeneity in micrometer length and minute time scales. It is driven by actin polymerization, e.g., pushing the plasma membrane forward, and then regulated by a multitude of actin regulators. While mathematical modeling is central to system-level understandings of cell protrusion, most of the modeling is based on the ensemble average of actin regulator dynamics at the cellular or population levels, preventing from capturing the heterogeneous cellular activities. With these in mind, a systematic modeling framework is proposed in this paper for predicting velocities of heterogeneous protrusion of migrating cells driven by multiple molecular mechanisms. The modeling framework is developed through the integration of the multiple AutoRegressive eXogenous (ARX) models employing probability density input variables. Unlike conventional ARX models, it provides an effective framework for modeling heterogeneous subcellular behaviors with complex nonlinearities and uncertainties of dynamic systems. To train and validate the proposed model, numerous subcellular time series are extracted from time-lapse movies of migrating PtK1 cells using spinning disk confocal microscope: The current edge velocities and fluorescent intensities of mDia1, actin at the leading edge are used as the input while the future cell edge velocities are selected as an output. It is demonstrated that the proposed approach is highly effective in predicting the future trends of heterogeneous cell protrusion. In particular, by capturing the various multiple activities from the dataset, it is expected that it would improve the understanding of the molecular mechanism underlying cellular and subcellular heterogeneity.