Multiple effects of gradient coupling on network synchronization

Functional Implications of Cardiac Mitochondria Clustering

The spatio-temporal organization of mitochondria in cardiac myocytes facilitates myocyte-wide, cluster-bound, mitochondrial inner membrane potential oscillatory depolarizations, commonly triggered by metabolic or oxidative stressors. Local intermitochondrial coupling can be mediated by reactive oxygen species (ROS) that activate inner membrane pores to initiate a ROS-induced-ROS-release process that produces synchronized limit cycle oscillations of mitochondrial clusters within the whole mitochondrial network. The network's dynamic organization, structure and function can be assessed by quantifying dynamic local coupling constants and dynamic functional clustering coefficients, both providing information about the network's response to external stimuli. In addition to its special organization, the mitochondrial network of cardiac myocytes exhibits substrate-sensitive coupling constants and clustering coefficients. The myocyte's ability to form functional clusters of synchronously oscillating mitochondria is sensitive to conditions such as substrate availability (e.g., glucose, pyruvate, β-hydroxybutyrate), antioxidant status, respiratory chain activity, or history of oxidative challenge (e.g., ischemia-reperfusion). This underscores the relevance of quantitative methods to characterize the network's functional status as a way to assess the myocyte's resilience to pathological stressors.

Onset of synchronization in weighted complex networks: the effect of weight-degree correlation

By numerical simulations, we investigate the onset of synchronization of networked phase oscillators under two different weighting schemes. In scheme-I, the link weights are correlated to the product of the degrees of the connected nodes, so this kind of networks is named as the weight-degree correlated (WDC) network. In scheme-II, the link weights are randomly assigned to each link regardless of the node degrees, so this kind of networks is named as the weight-degree uncorrelated (WDU) network. Interestingly, it is found that by increasing a parameter that governs the weight distribution, the onset of synchronization in WDC network is monotonically enhanced, while in WDU network there is a reverse in the synchronization performance. We investigate this phenomenon from the viewpoint of gradient network, and explain the contrary roles of coupling gradient on network synchronization: gradient promotes synchronization in WDC network, while deteriorates synchronization in WDU network. The findings highlight the fact that, besides the link weight, the correlation between the weight and the node degree is also important to the network dynamics.

Spatio-temporal oscillations of individual mitochondria in cardiac myocytes reveal modulation of synchronized mitochondrial clusters

Mitochondrial networks in cardiac myocytes under oxidative stress show collective (cluster) behavior through synchronization of their inner membrane potentials (DeltaPsi(m)). However, it is unclear whether the oscillation frequency and coupling strength between individual mitochondria affect the size of the cluster and vice versa. We used the wavelet transform and developed advanced signal processing tools that allowed us to capture individual mitochondrial DeltaPsi(m) oscillations in cardiac myocytes and examine their dynamic spatio-temporal properties. Heterogeneous frequency behavior prompted us to sort mitochondria according to their frequencies. Signal analysis of the mitochondrial network showed an inverse relationship between cluster size and cluster frequency as well as between cluster amplitude and cluster size. High cross-correlation coefficients between neighboring mitochondria clustered longitudinally along the myocyte striations, indicated anisotropic communication between mitochondria. Isochronal mapping of the onset of myocyte-wide DeltaPsi(m) depolarization further exemplified heterogeneous DeltaPsi(m) among mitochondria. Taken together, the results suggest that frequency and amplitude modulation of clusters of synchronized mitochondria arises by means of strong changes in local coupling between neighboring mitochondria.

Complete periodic synchronization in coupled systems

Recently, complete chaotic synchronization in coupled systems has been well studied. In this paper, we study complete synchronization in coupled periodic oscillators with diffusive and gradient couplings. Eight typical types of critical curve for the transverse Lyapunov exponent of standard mode, which give rise to different synchronization-desynchronization patterns, are classified. All possible desynchronous behaviors including steady state, periodic state, quasiperiodic state, low-dimensional chaotic state, and two types of high-dimensional chaotic state are identified, and two classical synchronization-desynchronizaiton bifurcations--the shortest wavelength bifurcation and Hopf bifurcation from synchronous periodic state--are classified.