Abstract
Signaling networks are made up of limited numbers of molecules and yet can code information that controls different cellular states through temporal patterns and a combination of signaling molecules. In this study, we used a data-driven modeling approach, the Laguerre filter with partial least square regression, to describe how temporal and combinatorial patterns of signaling molecules are decoded by their downstream targets. The Laguerre filter is a time series model used to represent a nonlinear system based on Volterra series expansion. Furthermore, with this approach, each component of the Volterra series expansion is expanded by Laguerre basis functions. We combined two approaches, application of a Laguerre filter and partial least squares (PLS) regression, and applied the combined approach to analysis of a signal transduction network. We applied the Laguerre filter with PLS regression to identify input and output (IO) relationships between MAP kinases and the products of immediate early genes (IEGs). We found that Laguerre filter with PLS regression performs better than Laguerre filter with ordinary regression for the reproduction of a time series of IEGs. Analysis of the nonlinear characteristics extracted using the Laguerre filter revealed a priming effect of ERK and CREB on c-FOS induction. Specifically, we found that the effects of a first pulse of ERK enhance the subsequent effects on c-FOS induction of treatment with a second pulse of ERK, a finding consistent with prior molecular biological knowledge. The variable importance of projections and output loadings in PLS regression predicted the upstream dependency of each IEG. Thus, a Laguerre filter with partial least square regression approach appears to be a powerful method to find the processing mechanism of temporal patterns and combination of signaling molecules by their downstream gene expression.
Highlights
Signal transduction networks have a “bow-tie” architecture
We focus on using data-driven dynamics to look at input and output (IO) relationships between MAP kinases (MAPKs) and CREB and the immediate early gene products (IEGs; outputs), in PC12 cells
Our results suggest a priming effect of phosphorylated ERK (pERK) and phosphorylated CREB (pCREB) on c-FOS induction
Summary
A relatively small set of molecules comprising the signal network are capable of both receiving information from diverse environmental sources and inducing a wide variety of gene expression patterns [1]. This raises questions as to how signals are selectively encoded by a limited number of signaling molecules and selectively decoded by their downstream targets. We focus on using data-driven dynamics to look at IO relationships between MAP kinases (MAPKs) and CREB (inputs) and the immediate early gene products (IEGs; outputs), in PC12 cells. We chose to focus on the signaling system that processes the information on cell fate decisions in a number of molecular species
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