Fig. 1.

Progressive and incremental reduction in system dynamic range is associated with dysfunction in coupled systems. A: incremental destabilization of a state defined as normal (N) through successive pseudo-stable states (I–V, solid black line) arises as a consequence of persistent (mal)adaptation that attempts to rebalance the network following perturbation. Intuitively, progressive network destabilization is expected to be associated with successively greater dysfunction (i.e., increasing step size) owing to the residual effect of successive malfunctions. In this scheme, the first two pseudo-stable states (I, II) are associated with small changes in interlinked systems [e.g., arrhythmia susceptibility (blue), cell death (green), and metabolic dysfunction (orange)], but a normal phenotype is maintained [cardiac function (red)]. However, the crossing of a threshold of system dysfunction, possibly as a consequence of failure to attenuate perturbation, accelerates these abnormalities and causes a steep decline in cardiac function. This scheme also illustrates that arrhythmia-linked genetic mutations may profoundly reduce basal network complexity (gray line) and introduce a heightened propensity to arrhythmia (dashed blue line) that is exacerbated by progression through successive pseudo-stable states (i–iv). B: the progressive instability and dysfunction described in A is reproduced in bifurcation diagrams generated by a model of the third-order system of differential equations describing cardiovascular dynamics developed by Parthimos and colleagues (111). This mathematical model of Ca²⁺ cycling incorporates terms that describe the activities of voltage- and receptor-operated Ca²⁺ channels (VOCC and ROC), Na⁺/Ca²⁺ exchanger (NCX), Ca²⁺ extrusion via plasma membrane ATPase (PMCA), sarcoplasmic (SR) reticulum Ca²⁺-ATPase (SERCA), and ryanodine receptor type 2 (RyR2) (111). Here we plotted the loci of maxima and minima of Ca²⁺ oscillatory activity for values of RyR2 activity (an index of the open state probability of RyRs or alternatively, proportional to the number of RyRs on the SR membrane) in a single cell (red lines) and two Ca²⁺-coupled cardiac cells (blue lines/points). In each scenario, continuous lines correspond to periodic solutions, whereas widely distributed points represent chaotic solutions or other hallmark types of nonlinear dynamics. Modeling of Ca²⁺ dynamics in single cells, where there is zero potential for intercellular desynchronization, results in entirely periodic solutions (red lines). Specific patterns of oscillatory behavior at various values of RyR2 activity (indicated by arrows) are shown in the series of panels N and I–IV. Inset, periodic windows of profoundly reduced complexity and low periodicity (gray shading) are superimposed over the bifurcation diagrams.