These models are composed of partial differential equations and boundary conditions that model the receptor-mediated activation of phospholipase C (PLC) and protein kinase C (PKC) enzymes in mammalian cells. PLC hydrolyzes the membrane lipid, PIP2, to produce the lipid second messenger, diacylglycerol (DAG), which mediates PKC activation at the plasma membrane. Following indications in the literature, the equations also capture the influences of the regulatory protein, MARCKS, and the lipid intermediate, phosphatidic acid (PA). These regulatory links revealed putative positive feedback loops.

The primary purpose of these models is to explain how the PLC/PKC pathway might be polarized in cells with a shallow gradient of receptor activation, as is the case during the response to a chemotactic ligand. This follows evidence that the abundance of DAG is polarized during the chemotactic migration of fibroblasts to PDGF, a prominent chemoattractant that directs fibroblast invasion of cutaneous wounds. Another purpose of the models is to predict the robustness of the polarization response with respect to the external gradient conditions and to perturbation of the regulatory mechanisms involved. Yet another purpose is to define thresholds for polarization that can be used for multiscale modeling of wound invasion, where the concentrations of PDGF and other factors change dynamically in space and time.

Variational Joint Filtering (VJF) is a flexible framework that online learns latent nonlinear state dynamics and filters latent states from high-dimensional spike trains.

VJF is amenable to real-time applications, enables experimentalist to monitor complex data in the ongoing experiments at an abstract level, and has the potential to automate analysis and experimental design in ways that testably track and modify behavior using stimuli designed to influence learning.

Understanding how animals update their decision-making behavior over time is an important problem in neuroscience. Decision-making strategies evolve over the course of learning, and continue to vary even in well-trained animals. However, the standard suite of behavioral analysis tools is ill-equipped to capture the dynamics of these strategies. We present a flexible method for characterizing time-varying behavior during decision-making experiments. With this approach, we can uncover the detailed evolution of an animal’s strategy during learning, including adaptation to time-varying task statistics, suppression of sub-optimal strategies, and shared behavioral dynamics between subjects within an experimental population.