On the Adjacency Matrix of RyR2 Cluster Structures

In the heart, electrical stimulation of cardiac myocytes increases the open probability of sarcolemmal voltage-sensitive Ca2+ channels and flux of Ca2+ into the cells. This increases Ca2+ binding to ligand-gated channels known as ryanodine receptors (RyR2). Their openings cause cell-wide release of Ca2+, which in turn causes muscle contraction and the generation of the mechanical force required to pump blood. In resting myocytes, RyR2s can also open spontaneously giving rise to spatially-confined Ca2+ release events known as “sparks.” RyR2s are organized in a lattice to form clusters in the junctional sarcoplasmic reticulum membrane. Our recent work has shown that the spatial arrangement of RyR2s within clusters strongly influences the frequency of Ca2+ sparks. We showed that the probability of a Ca2+ spark occurring when a single RyR2 in the cluster opens spontaneously can be predicted from the precise spatial arrangements of the RyR2s. Thus, “function” follows from “structure.” This probability is related to the maximum eigenvalue (λ1) of the adjacency matrix of the RyR2 cluster lattice. In this work, we develop a theoretical framework for understanding this relationship. We present a stochastic contact network model of the Ca2+ spark initiation process. We show that λ1 determines a stability threshold for the formation of Ca2+ sparks in terms of the RyR2 gating transition rates. We recapitulate these results by applying the model to realistic RyR2 cluster structures informed by super-resolution stimulated emission depletion (STED) microscopy. Eigendecomposition of the linearized mean-field contact network model reveals functional subdomains within RyR2 clusters with distinct sensitivities to Ca2+. This work provides novel perspectives on the cardiac Ca2+ release process and a general method for inferring the functional properties of transmembrane receptor clusters from their structure.Author Summary: Many transmembrane receptors have been shown to aggregate into supramolecular clusters that enhance sensitivity to external stimuli in a variety of cell types. Advances in super-resolution microscopy have enabled researchers to study these structures with sufficient detail to distinguish the precise locations of individual receptors. In the heart, efforts have been successful in imaging calcium release channels, which are found in clusters of up to ∼ 100 in the sarcoplasmic reticulum membrane of cardiac myocytes. We showed in a recent study how the precise cluster structure affects the frequency of spontaneous release events known as calcium “sparks.” Here we have developed an analytical model of calcium spark initiation that clearly illustrates how the structure controls spark likelihood. We then applied this model to a collection of channel cluster structures obtained using super-resolution microscopy, revealing spatial gradients in the functional properties of individual channels. This work provides insight into the calcium release process in the heart and a framework for evaluating functional heterogeneity in populations of receptor clusters using structural information alone.