(533g) Modeling the Spatio-Temporal Dynamics of Calcium Signal Propagation in 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. Free Ca²⁺ in the intracellular domain participates in the regulation of hepatic functions such as energy metabolism, bile secretion, proliferation and apoptosis. Regulation of cytosolic Ca²⁺ is particularly important in hepatocytes, the cells responsible for the bulk of metabolic and detoxification activities in the liver. Consequently, disruption of Ca²⁺ dynamics can potentially lead to pathological conditions. Extracellular stimulants such as hormones elicit a signaling cascade involving phospholipase C (PLC) cleavage of PI-4,5-P₂, IP₃ generation, and subsequent Ca²⁺ release from intracellular stores. Gap-junction mediated transfer of IP₃ molecules between adjacent hepatocytes induces, in neighboring hepatocytes, Ca²⁺ oscillations that spread through the tissue. This cell-cell interaction leads to a coordinated response at the tissue level. Measuring lobular Ca²⁺ responses upon treatment of perfused rodent livers with PLC-activating agonists has revealed a remarkable spatial organization. For low stimulus levels, Ca²⁺ signals in liver lobules start near a specific lobular locus, in the pericentral region, and propagate towards the periportal region in a wave-like fashion.

Although the behavior of Ca²⁺ signal propagation at the lobular scale is understood fairly well, the contribution of hepatocyte-specific Ca²⁺ signaling components to the lobular scale Ca²⁺ wave propagation remains largely unknown. In the present study, we performed a causality analysis of time series data on Ca²⁺ signals in single hepatocytes to identify a cell-cell influence network underlying the Ca²⁺ wave propagation in liver lobules. We also developed a computational model of spatio-temporal Ca²⁺signaling and cell-cell interactions to predict the coordinated changes in the intracellular Ca²⁺ signaling parameters sufficient to yield the lobular scale Ca²⁺ propagation dynamics identified in the time series data analysis.

We acquired time-resolved images of Ca²⁺ spikes caused by different vasopressindoses in the isolated perfusedrat liver at the lobular level. We segmented the acquired images to obtain hepatocyte-specific cytosolic Ca²⁺ profiles. For a given time lag, we estimated pairwise transfer entropies (TEs) for Ca²⁺ signal information received by a hepatocyte from all the other hepatocytes within the two-dimensional lobular visual field to obtain hepatocyte- and lag-specific empirical TE distributions. For each hepatocyte, we identified the set of statistically significant causal influences by comparing the TE values from its immediate neighbors with the hepatocyte-specific empirical TE distribution. Our analysis revealed that at the lobular scale, for the vasopressin levels employed in the experiment, Ca²⁺ waves propagate from the pericentral to the periportal region along the hepatocyte cords. However, the transfer entropy analysis revealed that the direction of causal influence between successive neighboring hepatocytes may not be consistently in the pericentral-to-periportal direction, i.e., in some instances, Ca²⁺ signal information may â??flowâ? in the direction opposite to lobular scale Ca²⁺ wave propagation between neighboring hepatocytes lying within a hepatocyte cord.

We utilized a computational modeling approach to explore how such local switches in the direction of Ca²⁺ signal influence could arise, and evaluated their influence on the overall lobular scale wave propagation. We developed an ODE based computational model of cytosolic Ca²⁺ spiking in hepatocytes to identify the spatial patterns of cell-intrinsic Ca²⁺ signaling parameters that can reproduce the experimentally observed lobular Ca²⁺ wave propagation. Our model consists of individual hepatocytes in which the intracellular Ca²⁺ signals are elicited via a G-protein coupled receptor mediated pathway. The hepatocytes are oriented along a cord and exchange IP₃ with the adjacent hepatocytes via gap junctions. Model simulations revealed that 1) gap junction coupling results in coordination of Ca²⁺ spikes in hepatocytes along a cord, despite variability in intracellular Ca²⁺ signaling parameters across cells, and 2) correlated spatial gradients of intracellular Ca²⁺ signaling parameters are required for yielding unidirectional flow of Ca²⁺ waves at the lobular scale. In the absence of gap junction coupling, Ca²⁺ spikes did not occur sequentially along a hepatocyte cord in response to stimuli that lasted over extended periods of time. Disruption of spatial gradients of intracellular signaling parameters resulted in local deviations from the overall direction of Ca²⁺ wave propagation along hepatocyte cords.

Next, we tested the effect of local disruptions in cell-specific Ca²⁺ signaling ability of hepatocytes on the lobular scale Ca²⁺ wave propagation. Inability of hepatocytes to respond to Ca²⁺ agonists may contribute to aberrant bile trafficking and promote cholestasis. We initialized our model of a hepatocyte cord in which a randomly distributed subset of hepatocytes was insensitive to Ca²⁺ agonists. Simulations revealed that Ca²⁺ waves do not propagate throughout the lobule when Ca²⁺ signals are not elicited in a subset of hepatocytes. Furthermore, increase in the strength of gap junction coupling was sufficient to restore the lobular scale Ca²⁺ signaling pattern even in the presence of local disruptions in Ca²⁺ response, suggesting that efficient intercellular communication can yield robust lobular scale Ca²⁺ response despite local insufficiencies in Ca²⁺ signaling.

In summary, we have developed and illustrated a computational model based approach to analyze and interpret time series data on Ca²⁺ signals in single cells in intact liver tissue. Our results led to new predictions on the role of gap junctions in overriding the cell-intrinsic variability towards a robust and spatially-organized lobular scale Ca²⁺ response to external stimuli.