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.