Computational Modeling of Spatiotemporal Ca²⁺Signal Propagation Along Hepatocyte Cords

Abstract

Objective The purpose of the present study is to model the dynamics of lobular Ca2+ wave propagation induced by an extracellular stimulus and to analyze the effect of spatially systematic variations in cell-intrinsic signaling parameters on sinusoidal Ca2+ response. Methods We developed a computational model of lobular scale Ca2+ signaling that accounts for receptor-mediated initiation of cell-intrinsic Ca2+ signal in hepatocytes and its propagation to neighboring hepatocytes through gap junction-mediated molecular exchange. Results Analysis of the simulations showed that a pericentral-to-periportal spatial gradient in hormone sensitivity and/or rates of IP3 synthesis underlies the Ca2+ wave propagation. We simulated specific cases corresponding to localized disruptions in the graded pattern of these parameters along a hepatic sinusoid. Simulations incorporating locally altered parameters exhibited Ca2+ waves that do not propagate throughout the hepatic plate. Increased gap junction coupling restored normal Ca2+ wave propagation when hepatocytes with low Ca2+ signaling ability were localized in the mid-lobular or the pericentral region. Conclusion Multiple spatial patterns in intracellular signaling parameters can lead to Ca2+ wave propagation that is consistent with the experimentally observed spatial patterns of Ca2+ dynamics. Based on simulations and analysis, we predict that increased gap junction-mediated intercellular coupling can induce robust Ca2+ signals in otherwise poorly responsive hepatocytes, at least partly restoring the sinusoidally oriented Ca2+ waves. Significance Our bottom-up model of agonist-evoked spatial Ca2+ patterns can be integrated with detailed descriptions of liver histology to study Ca2+ regulation at the tissue level.

Causality Analysis and Cell Network Modeling of Spatial Calcium Signaling Patterns in Liver Lobules

“…We next sought to determine whether a combination of the causal influence network and a dynamic model of hepatocyte Ca 2+ response can yield propagating Ca 2+ waves consistent with experimental observations. We started with a previously-published dynamic model of hepatocyte Ca 2+ response (Verma et al, 2016 ) and extended the model to incorporate cell-cell connectivity suggested by the causal influence network (see Methods). In addition, we modified the model parameters to incorporate zonation patterns of signaling components based on results from recently published single cell RNA-seq study (Halpern et al, 2017 ).…”

“…We started with a receptor oriented, ordinary differential equation (ODE)-based model of Ca 2+ signal propagation in a cord of hepatocytes detailed in Verma et al ( 2016 ). Here, we consider the complex spatial features of a liver lobule by allowing the hepatocytes to be connected with more than two other hepatocytes, as was the case in the original model of Verma et al ( 2016 ). In the present computational model, the state of every cell “i” and its interaction with a set of adjacent cells represented by the index “j” is defined by the following system of ODEs:…”

“…The model assumed constant total intracellular Ca 2+ for all hepatocytes. Additional details of model development can be found in Verma et al ( 2016 ). See Tables 1 , 2 for parameter descriptions, their nominal ranges and initial values for model species.…”

“…For instance, Schuster et al ( 2002 ) present a detailed discussion of computational models developed for describing Ca 2+ spiking, as well as propagation of Ca 2+ waves through co-localized cells. In previous work, we used a computational model to predict that zonation of intracellular signaling components as well as gap junction-mediated IP 3 exchange between immediate neighbors are required for the propagation of a Ca 2+ signal through a chain of connected hepatocytes (Verma et al, 2016 ). A recent study employing single cell RNA sequencing provided evidence in support of our predictions of lobular gradients of intracellular signaling components at the mRNA level (Halpern et al, 2017 ).…”

Computational Modeling in Liver Surgery

“…A variety of mathematical models of hepatic signaling processes were developed, mostly using ordinary differential equations (ODEs). Aspects covered by such models include, e.g., the origin of zonation patterning (e.g., Wnt/β-catenin signaling pathway, Kogan et al, 2012 ; Benary et al, 2013 ), the propagation of calcium waves at the lobular scale involved in the regulation of diverse hepatic functions (Verma et al, 2016 ), or the link between the circadian clock and hepatic metabolism (Woller et al, 2016 ). These models elucidate important features in the regulation and signaling of hepatic function.…”