Meaningful local signalling in sinoatrial node identified by random matrix theory and PCA

The sinoatrial node (SAN) is the pacemaker of the heart. Recently calcium signals, believed to be crucially important in rhythm generation, have been imaged in intact SAN and shown to be heterogeneous in various regions of the SAN with a lot of analysis relying on visual inspection rather than mathematical tools. Here we apply methods of random matrix theory (RMT) developed for financial data and various biological data sets including β-cell collectives and electroencephalograms (EEG) to analyse correlations in SAN calcium signals using eigenvalues and eigenvectors of the correlation matrix. We use principal component analysis to locate signalling modules corresponding to localization properties the eigenvectors corresponding to high eigenvalues. We find that the top eigenvector captures the global behaviour of the SAN i.e. action potential (AP) induced calcium transient. In some cases, the eigenvector corresponding to the second highest eigenvalue yields a pacemaker region whose calcium signals predict the AP. Furthermore, using new analytic methods, we study the relationship between covariance coefficients and distance, and find that even inside the central zone, there are non-trivial long range correlations, indicating intercellular interactions in most cases. Lastly, we perform an analysis of nearest-neighbour eigenvalue distances and find that it coincides with universal Wigner surmise under all available experimental conditions, while the number variance, which captures eigenvalue correlations, is sensitive to experimental conditions. Thus RMT application to SAN allows to remove noise and the global effects of the AP-induced calcium transient and thereby isolate the local and meaningful correlations in calcium signalling.