Determining the Roles of Inositol Trisphosphate Re

Authors: Silvia Honda Takada Juliane Midori Ikebara Erica de Sousa Débora Sterzeck Cardoso Rodrigo Ribeiro Resende Henning Ulrich Martin Rückl Sten Rüdiger Alexandre Hiroaki Kihara

Publish Date: 2016/10/22

Volume: 54, Issue: 9, Pages: 6870-6884

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Abstract

It is well known that calcium Ca2+ is involved in the triggering of neuronal death Ca2+ cytosolic levels are regulated by Ca2+ release from internal stores located in organelles such as the endoplasmic reticulum Indeed Ca2+ transit from distinct cell compartments follows complex dynamics that are mediated by specific receptors notably inositol trisphosphate receptors IP3Rs Ca2+ release by IP3Rs plays essential roles in several neurological disorders however details of these processes are poorly understood Moreover recent studies have shown that subcellular location molecular identity and density of IP3Rs profoundly affect Ca2+ transit in neurons Therefore regulation of IP3R gene products in specific cellular vicinities seems to be crucial in a wide range of cellular processes from neuroprotection to neurodegeneration In this regard microRNAs seem to govern not only IP3Rs translation levels but also subcellular accumulation Combining new data from molecular cell biology with mathematical modelling we were able to summarize the state of the art on this topic In addition to presenting how Ca2+ dynamics mediated by IP3R activation follow a stochastic regimen we integrated a theoretical approach in an easytoapply cell biologycoherent fashion Following the presented premises and in contrast to previously tested hypotheses Ca2+ released by IP3Rs may play different roles in specific neurological diseases including Alzheimer’s disease and Parkinson’s diseaseHU is grateful for grants from Fundação de Amparo à Pesquisa do Estado de São Paulo FAPESP 2012/508804 and Conselho Nacional de Desenvolvimento Científico e Tecnológico CNPq 486294/20129 and 467465/20142 Brazil SR acknowledges support from the Deutsche Forschungsgemeinschaft RU1660/21 and IRTG 1740 AHK is grateful for grants from FAPESP 2014/167116 and CNPq 308608/20143 Alexandre Hiroaki Kihara acknowledges the support from grant numbers FAPESP 2011/501510 e FAPESP 2015/501220In this appendix we will give a brief description of the main equations solved to obtain Fig 2 The system we solved is shown in Supplementary Fig 1 It consists of two parts which are solved in a coupled socalled hybrid way The left of Supplementary Fig 1 shows the system of equation schematically It consists of ordinary differential equations ODEs one for each cluster which represent the evolution of the calcium concentration at the cluster This equation takes into account the effect of diffusion of calcium as well as the chemical reactions with calciumbinding proteins The solution of this equation controls the rate of opening of calcium channels in the cluster Equations for adjacent clusters are coupled by a modified diffusional termsBriefly we set up a biophysical model for spread of intracellular Ca2+ release in an 8 × 8 array of clusters of channels The IP3 concentration is here assumed to be homogenous in the dendrite The model builds on our earlier modelling work 74 based on an FEM solver for partial differential equations In an effort to reduce the model’s complexity we here aim to replace the detailed reactiondiffusion model of Ca2+ with sets of coupled ordinary differential equations where each cluster is represented by one ODE FEM simulations show that the spatiotemporal concentration field of Ca2+ ‘lives’ on three different scales in terms of its concentration and spatial extension First if a channel is open its feedback by binding Ca2+ released by the channel outweighs any other contribution The local nanodomain can take on concentrations of 100 μM and more Second if a channel is closed it experiences highly variable dynamics because of openings and closings of channels in the same cluster These occur at microdomain concentrations of about 1–10 μM Third if a cluster is inactive ie no open channel for some time there is diffusion of Ca2+ from other active cluster leading to a bulk concentration which is much smaller than the former contributions but may become sufficient to trigger the inactive clusterHere maxx y is the maximum value of x and y This concentration c i t then provides the concentration at a closed channel relevant for the Ca2+binding events of that channel Intracluster feedback is proportional to the number of open channels γ c The coefficient α controls coupling strength between clusters and C i denotes the set of direct neighbours of cluster i on a onedimensional lattice of clusters Lastly if a channel is open we set its concentration to a fixed large value 100 μMFor the second part of the model we have to define discrete and stochastic gating transitions of each channel in each cluster Each channels gating transitions including its opening and closing are modelled by a Markov chain Conversely the opening of a channel regulated by gating controls the calcium concentration around the channel and the cluster The transition of the Markov chain represent processes of the DeYoung–Keizerntype as described in the main text Further details on the model can be found in Rückl and Rüdiger to be publishedThe right panel in Supplementary Fig 1 illustrates the numerical methods to solve the hybrid equations The Markov chains are represented by Master equations which are solved by numerically computing stochastic representations We employ a method based on the Gillespie method which was modified here to take into account the concentrations and propensities changing in time 81 The coupled ODEs are solved time discretized by a standard timestepping scheme

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