(362a) Causal Network Modeling of Calcium Wave Propagation in Rat Liver Lobules

The liver performs a wide variety of physiological functions such as regulation of intermediary metabolism, lipid synthesis, bile production and xenobiotic detoxification. Normal liver function requires tight regulation of intracellular processes as well as intercellular coordination. Regulation of intracellular localization and levels of Ca²⁺ is critical to maintain hepatocyte metabolism and bile secretion, and regulate proliferation, autophagy and apoptosis. Consequently, disruption of Ca²⁺dynamics can potentially lead to pathological conditions.

Evidence from whole tissue Ca²⁺ imaging studies points towards wave-like spatial patterns of cytosolic Ca²⁺ in response to circulating hormonal stimuli in liver lobules. Experimental studies have indicated that gap-junction mediated transfer of inositol 1,4,5-trisphosphate (IP₃) between adjacent hepatocytes is required for sequential induction of Ca²⁺ oscillations in neighboring cells, resulting in a spatial wave that spreads across a liver lobule. Alternatively, it has been proposed that paracrine signaling, spatial gradients of intracellular Ca²⁺ signaling components as well as mechanical stress induced by blood flow can lead to wave-like propagation of Ca²⁺ signals. In previous work, we developed an ODE based computational model that accounts for propagation of Ca²⁺ signals along a hepatocyte cord within a lobule. Based on simulation and analysis of the model, we predicted that in addition to gap junction mediated IP₃ exchange, spatial gradients in intracellular Ca²⁺ signaling components were required to yield a wave-like propagation of Ca²⁺signals.

In the present study, we evaluated the above hypotheses pertaining to calcium wave propagation by obtaining and analyzing a unique data set on lobular scale Ca²⁺ signal dynamics measured at single cell resolution. We adopted a data driven, bottom-up approach to characterize relative contributions of cell autonomous, IP₃ mediated and paracrine signaling mediated Ca²⁺ wave dynamics starting at the single cell level. We imaged cytosolic Ca²⁺ levels in response to hormonal stimuli in perfused rat liver, to obtain a large-scale data set on Ca²⁺ transients in 1300 hepatocytes measured at 4 second intervals for 1600 seconds. Consistent with previous results, we observed wave-like propagation of Ca²⁺ signals throughout liver lobules. We analyzed the data set in three distinct ways including deterministic modeling, correlation networks, and causal network modeling, to uncover the contribution of proposed alternative mechanisms to spatial patterns of Ca²⁺signals. Note that our interpretation and analysis was based on a simplification of cell-cell interactions and lobular organization in two dimensions, and hence would miss the interactions that occur in the actual three-dimensional liver tissue.

We initially utilized our ODE model and evaluated whether cell autonomous responses without intercellular molecular interaction/exchange can yield the observed experimental results. We employed a rejection sampling approach to identify parameters for 1300 individual cellular Ca²⁺ time traces. Starting with priors of uniformly distributed parameter values centered on the nominal values from previous ODE model, we fitted the Ca²⁺ time traces of each hepatocyte to obtain cell-specific posterior parameter distributions corresponding to good data fits. Spatially correlated shifts in parameter posterior distributions would have suggested the absence of entrainment of Ca²⁺ responses of physically adjacent hepatocytes, and therefore of intercellular communication. However, our simulations yielded large overlaps in the posterior distributions of model parameters for cells lying within hepatocyte cords. The absence of shifts in posterior parameter distributions suggested that spatial gradients alone do not account for the observed Ca²⁺ wave propagation.

We next computed pair-wise correlations of Ca²⁺ traces to develop an undirected correlation network that was analyzed for alignment with the spatial patterns of potential interactions between hepatocytes. Our analysis suggested that Ca²⁺ signal correlation was spatially restricted to clusters of hepatocytes that were not limited to cells lying within the hepatocyte cords. These results suggest additional mechanisms of Ca²⁺ response synchronization besides gap junction mediated molecular exchange, such as release of paracrine signals by hepatocytes in their immediate microenvironment.

In order to assess whether the observed spatially clustered correlations in Ca²⁺ signals could be interpreted for directed interactions, we performed data-driven causal network modeling based on transfer entropy estimates of pair-wise information transfer between cells. Note that these formal measures of information flow are based on Shannon’s information theory, and do not directly translate to the colloquial meaning of the term. Based on the findings from undirected correlation networks, all hepatocytes lying within 50µm of each other were considered as candidates for information transfer. Causal network analysis identified information transfer edges between co-localized hepatocytes lying within as well as across hepatocyte cords, further indicating that synchronization of hepatocyte Ca²⁺responses does not arise exclusively due to gap junction mediated molecular exchange. Additionally, we found that information transfer between adjacent hepatocytes lying along a hepatocyte cord was not unidirectionally aligned.

The results of our study indicate that gap junction mediated IP₃ transfer as well as paracrine signaling contribute simultaneously towards shaping spatio-temporal dynamics of calcium wave propagation in liver lobules . The two mechanisms possibly contribute towards islands of highly synchronized hepatocytes. Additionally, spatial gradients of intracellular Ca²⁺ signaling components between the extremities of liver lobules might lead to an apparent Ca²⁺ wave propagation originating from multiple foci. These novel aspects must be included in our computational model to accurately capture Ca²⁺ signal propagation in liver lobules.