Generalized Turing Patterns and Their Selective Realization in Spatiotemporal Systems

We consider the pattern formation problem in coupled identical systems after the global synchronized state becomes unstable. Based on analytical results relating the coupling strengths and the instability of each spatial mode (pattern) we show that these spatial patterns can be selectively realized by varying the coupling strengths along different paths in the parameter space. Furthermore, we discuss the important role of the synchronized state (fixed point versus chaotic attractor) in modulating the temporal dynamics of the spatial patterns.Comment: 9 pages, 3 figure

Frequency decomposition of conditional Granger causality and application to multivariate neural field potential data

It is often useful in multivariate time series analysis to determine statistical causal relations between different time series. Granger causality is a fundamental measure for this purpose. Yet the traditional pairwise approach to Granger causality analysis may not clearly distinguish between direct causal influences from one time series to another and indirect ones acting through a third time series. In order to differentiate direct from indirect Granger causality, a conditional Granger causality measure in the frequency domain is derived based on a partition matrix technique. Simulations and an application to neural field potential time series are demonstrated to validate the method.Comment: 18 pages, 6 figures, Journal publishe

Analyzing Stability of Equilibrium Points in Neural Networks: A General Approach

Networks of coupled neural systems represent an important class of models in computational neuroscience. In some applications it is required that equilibrium points in these networks remain stable under parameter variations. Here we present a general methodology to yield explicit constraints on the coupling strengths to ensure the stability of the equilibrium point. Two models of coupled excitatory-inhibitory oscillators are used to illustrate the approach.Comment: 20 pages, 4 figure

Systematic inference of functional phosphorylation events in yeast metabolism

Motivation: Protein phosphorylation is a post-translational modification that affects proteins by changing their structure and conformation in a rapid and reversible way, and it is an important mechanism for metabolic regulation in cells. Phosphoproteomics enables high-throughput identification of phosphorylation events on metabolic enzymes, but identifying functional phosphorylation events still requires more detailed biochemical characterization. Therefore, development of computational methods for investigating unknown functions of a large number of phosphorylation events identified by phosphoproteomics has received increased attention. Results: We developed a mathematical framework that describes the relationship between phosphorylation level of a metabolic enzyme and the corresponding flux through the enzyme. Using this framework, it is possible to quantitatively estimate contribution of phosphorylation events to flux changes. We showed that phosphorylation regulation analysis, combined with a systematic workflow and correlation analysis, can be used for inference of functional phosphorylation events in steady and dynamic conditions, respectively. Using this analysis, we assigned functionality to phosphorylation events of 17 metabolic enzymes in the yeast Saccharomyces cerevisiae, among which 10 are novel. Phosphorylation regulation analysis cannot only be extended for inference of other functional post-translational modifications but also be a promising scaffold formulti-omics data integration in systems biology