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

Abstract

Dynamics as well as localization of Ca2+ transients plays a vital role in liver function under homeostatic conditions, repair, and disease. In response to circulating hormonal stimuli, hepatocytes exhibit intracellular Ca2+ responses that propagate through liver lobules in a wave-like fashion. Although intracellular processes that control cell autonomous Ca2+ spiking behavior have been studied extensively, the intra- and inter-cellular signaling factors that regulate lobular scale spatial patterns and wave-like propagation of Ca2+ remain to be determined. To address this need, we acquired images of cytosolic Ca2+ transients in 1300 hepatocytes situated across several mouse liver lobules over a period of 1600 s. We analyzed this time series data using correlation network analysis, causal network analysis, and computational modeling, to characterize the spatial distribution of heterogeneity in intracellular Ca2+ signaling components as well as intercellular interactions that control lobular scale Ca2+ waves. Our causal network analysis revealed that hepatocytes are causally linked to multiple other co-localized hepatocytes, but these influences are not necessarily aligned uni-directionally along the sinusoids. Our computational model-based analysis showed that spatial gradients of intracellular Ca2+ signaling components as well as intercellular molecular exchange are required for lobular scale propagation of Ca2+ waves. Additionally, our analysis suggested that causal influences of hepatocytes on Ca2+ responses of multiple neighbors lead to robustness of Ca2+ wave propagation through liver lobules.

A Spatial Model of Hepatic Calcium Signaling and Glucose Metabolism Under Autonomic Control Reveals Functional Consequences of Varying Liver Innervation Patterns Across Species

“…In the simulation with uncoupled hepatocytes, intracellular Ca 2+ dynamics are unsynchronized, with the Ca 2+ spikes for each hepatocyte showing its own intrinsic frequency (Figure 3E, left). Gap junction coupling leads to synchronized waves that start in the PC region and propagate toward the PP region, consistent with Ca 2+ dynamics reported in recent literature (Figure 3E, middle and right; Verma et al, 2018;Gaspers et al, 2019). While the period of Ca 2+ waves is very similar between the two coupled systems, stronger gap junction connectivity resulted in a shorter lag time (defined as the time between calcium spike maxima of the extreme PC and PP hepatocytes) and a larger Ca 2+ wave velocity compared with the system with strong gap junction connectivity.…”

“…We developed a multi-scale multi-organ model of autonomic control of hepatic glucose metabolism through regulation of systemic, intercellular, and intracellular signaling (Figure 1). Built on previous efforts to account for metabolic zonation and blood flow along porto-central axis within a liver lobule (Ashworth et al, 2016), and intra and intercellular calcium signaling along a liver sinusoid (Verma et al, 2016(Verma et al, , 2018, the present model combines these earlier models with a new model of hepatic innervation and regulation of systemic hormonal levels to account for CNS control of organismal scale signaling and hepatic calcium dynamics and glucose metabolism (Figure 1). We simulated the multi-scale model to explore hepatic glucose output and systemic glucose recovery under a range of biological conditions, including increased intensity and duration of exercise, and denervation of the adrenal gland and liver.…”

“…Ca 2+ spiking occurs due to the positive feedback by IP 3 -induced Ca 2+ release and Ca 2+ -stimulated IP 3 formation. We model the induction of Ca 2+ signals by extracellular catecholamine (epinephrine and norepinephrine) stimulus through α 1adrenergic receptor activation, however, similar Ca 2+ dynamics can be induced by other extracellular stimuli such as vasopressin (Assimacopoulos-Jeannet et al, 1977;Schöfl et al, 1993;Verma et al, 2018). The equations for intracellular Ca 2+ fluxes and IP 3 receptor dynamics are retained from Meyer and Stryer (1991) with the exception of IP 3 synthesis, which is related to the hormone receptor dynamics instead of constant receptor activation in the original Meyer and Stryer (1991) model.…”

“…Detailed description of parameters and initial conditions for the lobular scale Ca 2+ portion of the model can be found in Tables 1, 2, respectively. We explicitly consider the zonation profiles of the following parameters: α 1 -adrenergic receptors exhibit a decreasing PC to PP gradient (Halpern et al, 2017;Verma et al, 2018). Therefore, the intracellular Ca 2+ signaling parameters k r and k IP3 are initialized as decreasing gradients from the PC to PP region (k r ∈ [0.5, 0.6]; k IP3 ∈ [0.5, 1]).…”

“…Intracellular and Lobular Scale Ca 2+ Signaling Under a hormone stimulus, hepatocytes typically exhibit interspike intervals of 100 s (Robb- Gaspers and Thomas, 1995;Verma et al, 2018). Based on this rough estimate of inter-spike interval for catecholamine induced Ca 2+ spikes in hepatocytes, nominal parameter values and initial conditions used in simulations are listed in Tables 1, 2, respectively.…”