Diversity of Evoked Astrocyte Ca2+ Dynamics Quantified through Experimental Measurements and Mathematical Modeling

Abstract

Astrocytes are a major cell type in the mammalian brain. They are not electrically excitable, but generate prominent Ca2+ signals related to a wide variety of critical functions. The mechanisms driving these Ca2+ events remain incompletely understood. In this study, we integrate Ca2+ imaging, quantitative data analysis, and mechanistic computational modeling to study the spatial and temporal heterogeneity of cortical astrocyte Ca2+ transients evoked by focal application of ATP in mouse brain slices. Based on experimental results, we tune a single-compartment mathematical model of IP3-dependent Ca2+ responses in astrocytes and use that model to study response heterogeneity. Using information from the experimental data and the underlying bifurcation structure of our mathematical model, we categorize all astrocyte Ca2+ responses into four general types based on their temporal characteristics: Single-Peak, Multi-Peak, Plateau, and Long-Lasting responses. We find that the distribution of experimentally-recorded response types depends on the location within an astrocyte, with somatic responses dominated by Single-Peak (SP) responses and large and small processes generating more Multi-Peak responses. On the other hand, response kinetics differ more between cells and trials than with location within a given astrocyte. We use the computational model to elucidate possible sources of Ca2+ response variability: (1) temporal dynamics of IP3, and (2) relative flux rates through Ca2+ channels and pumps. Our model also predicts the effects of blocking Ca2+ channels/pumps; for example, blocking store-operated Ca2+ (SOC) channels in the model eliminates Plateau and Long-Lasting responses (consistent with previous experimental observations). Finally, we propose that observed differences in response type distributions between astrocyte somas and processes can be attributed to systematic differences in IP3 rise durations and Ca2+ flux rates.

How Receptor Surface Diffusion and Cell Rotation Increase Association Rates

“…For example, synaptic receptors on neural membranes undergo a transitory conformational change after binding a neurotransmitter, and during this time the receptor is unable to bind additional neurotransmitters. A similar scenario occurs, for example, in experiments where neuroactive compounds are released into extracellular space and bind to receptors on astrocytes [86]. Such a recharge time was recently shown to have a drastic effect in other contexts [46,47], and it would be interesting to see how it affects the association rates studied in the present work.…”

Computational Models for Calcium-Mediated Astrocyte Functions

“…Half of the single astrocyte models were so-called generic, meaning that they did not describe astrocytes in any specific anatomical brain location. Others, however, were specified to model astrocytes in the cerebrum (Farr and David, 2011 ; Witthoft and Karniadakis, 2012 ), cerebral cortex (Diekman et al, 2013 ; Witthoft et al, 2013 ; Mesiti et al, 2015b ; Kenny et al, 2018 ), cortex (De Pittà et al, 2009b ; Toivari et al, 2011 ), hippocampus (Riera et al, 2011a , b ; Chander and Chakravarthy, 2012 ), as well as the visual cortex (Gibson et al, 2007 ; Bennett et al, 2008b ) and somatosensory cortex (Bennett et al, 2008b ; Taheri et al, 2017 ). One third of the single astrocyte models took into account neurotransmitters in a simplistic way just as a stimulus, having either the neurotransmitter as a constant, step function, or something similar (see e.g., Larter and Craig, 2005 ; Gibson et al, 2007 ; Bennett et al, 2008b ; De Pittà et al, 2009a ; Dupont et al, 2011 ; Toivari et al, 2011 ; Witthoft and Karniadakis, 2012 ; Hadfield et al, 2013 ; Witthoft et al, 2013 ; Kenny et al, 2018 ).…”

“…Thus, these models had similar core structure with small variations. As an example, six modeled capacitive Ca 2+ entry (CCE) which is mediated via store-operated Ca 2+ (SOC) channels (Riera et al, 2011a , b ; Toivari et al, 2011 ; Handy et al, 2017 ; Taheri et al, 2017 ; Ding et al, 2018 ) and two modeled VGCCs (Zeng et al, 2009 ; Ding et al, 2018 ), as well as one had Ca 2+ flux via ryanodine receptors (RyRs) (López-Caamal et al, 2014 ) and three had Ca 2+ influx via TRP vanilloid-related channel 4 (TRPV4) (Witthoft and Karniadakis, 2012 ; Witthoft et al, 2013 ; Kenny et al, 2018 ). Only Diekman et al ( 2013 ) and Komin et al ( 2015 ) modeled mitochondrial Ca 2+ unitransporters (MCUs).…”

“…Some of the most recent models developed in this category were the models by Komin et al ( 2015 ), Handy et al ( 2017 ), and Taheri et al ( 2017 ). Komin et al ( 2015 ) presented two models, a reaction-diffusion model and a reaction model.…”

“…Most of the astrocyte models presented here are based on ordinary differential equations (ODEs), modeling well-stirred astrocytes (see e.g., Nadkarni and Jung, 2003 ; Ullah et al, 2006 ; Volman et al, 2007 ; De Pittà et al, 2009a ; Goldberg et al, 2010 ; Dupont et al, 2011 ; Valenza et al, 2011 ; Amiri et al, 2012a ; Wade et al, 2012 ; Hadfield et al, 2013 ; Tang et al, 2013 ; Lallouette et al, 2014 ; Wallach et al, 2014 ; Li et al, 2016a ; Chan et al, 2017 ; Guo et al, 2017 ; Handy et al, 2017 ; Taheri et al, 2017 ). These models make the assumption that chemical species have the same concentrations throughout the entire volume of the astrocyte, which can also be called as average concentrations.…”