OPEN Optimal microdomain crosstalk between

SUBJECT AREAS: and mitochondria COMPUTATIONAL 21 BIOPHYSICS for Ca oscillations SIGNALLING Hong Qi1, Linxi Li1 & Jianwei Shuai1,2,3

Received 1Department of Physics, Xiamen University, Xiamen 361005, China, 2State Key Laboratory of Cellular Stress Biology, Innovation 29 July 2014 Center for Biology, Xiamen University, Xiamen 361005, China, 3Fujian Provincial Key Laboratory of Theoretical and Accepted Computational Chemistry, Xiamen University, Xiamen 361005, China. 24 December 2014

1 1 Published ACa2 signaling model is proposed to consider the crosstalk of Ca2 ions between endoplasmic reticulum 23 January 2015 (ER) and mitochondria within microdomains around inositol 1, 4, 5-trisphosphate receptors (IP3R) and the 21 mitochondrial Ca uniporter (MCU). Our model predicts that there is a critical IP3R-MCU distance at which 50% of the ER-released Ca21 is taken up by mitochondria and that mitochondria modulate Ca21 signals differently when outside of this critical distance. This study highlights the importance of the 21 Correspondence and IP3R-MCU distance on Ca signaling dynamics. The model predicts that when MCU are too closely 21 21 requests for materials associated with IP3Rs, the enhanced mitochondrial Ca uptake will produce an increase of cytosolic Ca should be addressed to spike amplitude. Notably, the model demonstrates the existence of an optimal IP3R-MCU distance (30– 85 nm) for effective Ca21 transfer and the successful generation of Ca21 signals in healthy cells. We suggest J.S. (jianweishuai@ that the space between the inner and outer mitochondria membranes provides a defense mechanism against xmu.edu.cn) 21 occurrences of high [Ca ]Cyt. Our results also hint at a possible pathological mechanism in which 21 abnormally high [Ca ]Cyt arises when the IP3R-MCU distance is in excess of the optimal range.

he calcium ion (Ca21) is a ubiquitous intracellular signal controlling diverse cellular functions, such as muscle cell contraction, neurotransmitter release from neurons and astrocytes, metabolic processes, egg activation, and cell maturation, differentiation and death1.Ca21 signals commonly appear as repetitive T 21 21 spikes of cytosolic Ca concentration ([Ca ]Cyt), with signaling information encoded in the frequency, ampli- 2 21 tude and duration of these oscillations . The complex spatial-temporal profiles of [Ca ]Cyt depend heavily on the endoplasmic reticulum (ER) and mitochondria3 which act as the two major intracellular Ca21 stores. 21 While it has been widely accepted that the inositol 1, 4, 5-trisphosphate receptors (IP3R) function as Ca release channels on the ER membrane1, mitochondria were previously considered only to function as Ca21-sinks under pathological conditions when there is an abnormally high cellular Ca213. This view on mitochondria began 21 to change in the 1990s with two landmark studies demonstrating that non-pathological elevations of [Ca ]Cyt are 21 21 4 21 accompanied by a marked rise of Ca concentrations ([Ca ]Mt) and that [Ca ]Mt 21 5 responds dynamically to physiological oscillations of [Ca ]Cyt . Experimental observations indicated that mito- chondria can accumulate Ca21 through the mitochondrial Ca21 uniporter (MCU) which is located on the inner 6 21 21 mitochondrial membrane (IMM) . In despite of its low Ca affinity, the MCU is exposed to a high [Ca ]Cyt 7,8 21 generated in microdomain around the channel pore of open IP3Rs , thus even when global [Ca ]Cyt is low a high 21 21 value of [Ca ]Mt may be observed. As a result, mitochondria can serve as buffers of cytoplasmic Ca under both pathological and non-pathological conditions. Although it is now generally believed that mitochondria function as a dynamic Ca21 sequestration system to shape cytosolic Ca21 oscillations, and therefore regulate many physiological processes6, the detailed mechanism underlying how mitochondria influence global Ca21 signals remains elusive. Contradictory mechanisms have 21 9–11 been suggested on how mitochondrial Ca uptake regulates IP3R activity, including up-regulation , down- regulation12,13 and complete independence14. Furthermore, although mitochondrial Ca21 uptake via MCU depends primarily on the spacing between the ER and mitochondria15, the working distance between the two organelles remains unclear due to the complexity of the intracellular environment and the lack of spatial resolution in the experimental observations. Indeed, the existing estimates of the distances between the ER and mitochondria vary hugely, from less than 10 nm to more than 200 nm16. A recent paper published in

SCIENTIFIC REPORTS | 5 : 7984 | DOI: 10.1038/srep07984 1 www.nature.com/scientificreports

PNAS17 even argued that the mitochondria may not act as a signifi- ER and mitochondria on Ca21 signaling (Fig. 1(a)). As a result, the cant dynamic buffer of cytosolic Ca21 under physiological model has three compartments: (Cyt), ER and mitochondria conditions. (Mt). As shown in Fig. 1(a), the dynamics of the free [Ca21] in these Computational models provide a valuable tool for understanding compartments is determined by the Ca21 fluxes from various chan- of the mechanisms underlying Ca21 signal transduction18 and the nels and pumps and by buffering processes with various Ca21 bind- dynamics of Ca21 release from the ER has been extensively mod- ing (BP), given by, 19–23 21 eled . Some models only focused on mitochondrial Ca 2z 24,25 d½Ca dynamics . Dash and co-workers developed a detailed kinetic Cyt ~jout{jin zjout{jin zj , ð1Þ model for MCU to match published data sets on mitochondrial dt ER ER Mt Mt CaCyt Ca21 uptake25. However, the involvement of both the ER and mito- z chondria in Ca21 dynamics has only been considered in a limited d½Ca2 ER ~V =V (jin {jout)zj , ð2Þ number of models18,26–30. In the earlier models18,26, it was postulated dt Cyt ER ER ER CaER 21 21 that the MCU substantially sequesters Ca when [Ca ]Cyt , 1 mM, 2z in contrast to experimental evidence that the MCU actually seques- d½Ca Mt in out 21 3,31 28 ~V =V (j {j )zj : ð3Þ ters Ca in the range of 10–20 mM . Dupont et al. modeled the dt Cyt Mt Mt Mt CaMt effect of Hint2, a mitochondrial , on cytosolic Ca21 dynamics in . However, in these models the maximum value of ER 21 21 21 21 luminal [Ca ] ([Ca ]ER) is in the order of several to several tens of Here [Ca ] represents the free [Ca ], V the volume of three com- 1 mM, deviating drastically from most of the measured figures of 100– partments, jin the Ca2 flux from outside to inside, and jout the oppos- 32 21 21 900 mM , and the value of [Ca ]Mt was also significantly under- ite flux. The three terms jCa represent Ca dissociated from the estimated. More importantly, except the model proposed by Szopa BP. 29 21 21 et al. , none of them take into account the high [Ca ]Cyt microdo- In each compartment, Ca can be buffered by various BPs. The main, which is critical for mitochondrial Ca21 signaling. The model kinetics between free Ca21 and BP is described by a simple chemical considered by Szopa et al.29 is a modification of the model from reaction ref. 26, analyzing the influence of microdomain on the period and z koni ~ shape of calcium oscillations. They supposed that MCU sense ele- Cai BPi ' CaBPi, i Cyt, ER or Mt, vated Ca21 concentration which is directly equal to that in ER29. This koffi assumption is incoherent with the experimental observation that giving [Ca21] in microdomain is about several tens of mM, which is about Cyt ~ { 2z { 10-fold higher than that in the bulk cytosol7 and about 10-fold lower jCai koffi½CaBPi koni½Ca i(½BPTot i ½CaBPi), ð4Þ than that in ER32. Thus, there is a lack of model to quantitatively where [BP]Tot_i and [CaBP]i represent the total concentration of BP investigate how the crosstalk between the ER and mitochondria con- 21 trols Ca21 signaling. and the concentration of Ca -bound BP in each compartment, kon and k denote the on and off rate constants of Ca21 with the BP, Here we consider a more realistic model to investigate the role of off mitochondria in Ca21 signaling to couple the ER and mitochondria respectively. 21 based on the Ca microdomain. A cytosolic microdomain is specif- 21 21 ically considered in order to discuss the MCU dynamics and so each Ca fluxes in ER component. The Ca effluxes from the ER to MCU specifically responds to the local high Ca21 concentration in cytosol are given by the IP3R release and a passive leakage with the concentration gradient across the ER membrane as their driving microdomain generated by a cluster of IP3Rs. Our results dem- onstrate the critical role of mitochondrial Ca21 uptake in modulating force, i.e., IP R-released Ca21 signaling. We show that the location of the MCU out~ z 2z { 2z 3 j (vIP3RPoIP3R cLeak)(½Ca ½Ca ), ð5Þ 21 ER ER Cyt relative to IP3Rs is a key determinant for modulating Ca signals. There is a critical IP3R-MCU distance at which 50% of the ER- with vIP3R being the maximal efflux from the IP3Rs in the ER 21 21 released Ca is taken up by mitochondria and that mitochondria membrane, PoIP3R the open fraction of IP3Rs, and cLeak the Ca modulate Ca21 signals differently when outside of this critical dis- leak constant. tance. When the IP3R-MCU distance is greater than the critical The IP3R channel is an assembly of four equivalent subunits, each 21 21 21 distance mitochondrial Ca uptake stimulates ER-Ca release by of which is mutually gated by IP3 and Ca . The gating dynamics of 21 19 rapidly reducing the amplitude of the [Ca ]Cyt signal within the each IP3R subunit is described by the Li-Rinzel model and we microdomain and suppressing the inhibition dynamics of high assumed that the channel is open if at least three of its subunits 21 [Ca ]Cyt on IP3R. However, when the distance is less than the critical are in the active state20. Thus, we get the following expression for 21 distance, mitochondrial Ca uptake demonstrates a different effect PoIP3R: on IP3R dynamics. Initially strong mitochondrial uptake forces 21 [Ca ]Cyt to a low level, thus preventing the strong activation z 21 2 dynamics of [Ca ] on IP R. This leads to strong IP R inhibition ½IP3 ½Ca Cyt Cyt 3 3 P ~s4 z4s3 (1-s ), s ~ h: ð6Þ 21 oIP3R act act act act z 2z z on the decay of subsequent [Ca ]Cyt spikes. Thus, our model pre- ½IP3 d1 ½Ca Cyt d5 dicts that when MCU are too closely associated with IP3Rs, the 21 enhanced mitochondrial Ca uptake will produce an increase of Here sact is the probability in the active state of the subunit, [IP3] 21 cytosolic Ca spike amplitude. As a result, there is an optimal spa- is the IP3 concentration, and the slowly gating variable h is given cing about 30–85 nm between the ER and mitochondria for genera- by tion of experimentally observed Ca21 oscillations in living cells. z dh ~ { { ~ ½IP3 d1 ~ 2z Modelling coupled ER and mitochondria Ca21 ah(1 h) bhh, ah a2d2 , bh a2½Ca Cyt, ð7Þ dt ½IP3zd3 dynamics 21 A ‘‘closed’’ cell model, which does not include Ca exchange where ai and di are constants. between cytosol and external medium through the plasma mem- The cytosolic Ca21 can be pumped back into ER by active SERCA brane, is considered to investigate the coupling effects between the which is given by,

SCIENTIFIC REPORTS | 5 : 7984 | DOI: 10.1038/srep07984 2 www.nature.com/scientificreports

Figure 1 | The model design. (a) The schematic diagram of the components and fluxes included in the model. When a cell is stimulated to generate 21 21 IP3,IP3 binds to IP3R and triggers Ca release from the ER through IP3Rs. The Ca in the cytsol can be pumped back into ER by SERCA. (b) IP3Rs and 21 21 MCUs in close proximity form a microdomain, a half 3-dimensional cytosolic space separated by ER membrane. A high microdomain [Ca ] ([Ca ]Mic) 21 21 can be generated upon opening of IP3Rs which in turn leads to Ca uptake into mitochondria through MCUs. Ca is extruded from mitochondria back into the cytosol by NCX. (c) The four-state model of MCU monomer with binding and unbinding rates.

2z 2 Whereas MICU1 acts as a regulator, MCU represents the core vSERCA½Ca 21 jin ~ Cyt , ð8Þ pore-forming component responsible for mitochondrial Ca ER 2 z 2z 2 37,38 kSERCA ½Ca Cyt uptake . Recent experimental and bioinformatic analysis reveals that MCU is an oligomer37 and most likely a tetramer39. Considering 21 21 where vSERCA and kSERCA are maximum SERCA pump flux and the biphasic dependence of MCU on [Ca ]Cyt, i.e., fast Ca SERCA activation constants. -dependent activation and slow Ca21-dependent inactivation of the MCU31, we simply propose that each monomer has two Ca21 binding Ca21 fluxes in mitochondrial component. Mitochondrial Ca21 sites, one for activation and another for inhibition. Therefore a uptake through MCU is driven primarily by the large voltage monomer can exist in 4 states of s00,s10,s01 and s11 with the first across IMM. Besides the IMM voltage, it has been shown that index for activation binding site and the second index for inhibition MCU flux is also regulated by MICU33. For simplicity, in our binding site and with 1 for binding and 0 unbinding (Fig. 1(c)). model we only consider the role of MICU1 which has been well Similar as the IP3R, we posit that the MCU is open if either 3 or 4 investigated in experiment. Then the MCU influx can be expressed as of the 4 monomers are in the active state (s10). Thus, the MCU open in ~ fraction is given by, jMt vMCUDWRMICUPoMCU: ð9Þ 4 3 PoMCU~(x10) z4(x10) (1-x10), ð12Þ Here vMCU is the maximal flux of MCU, DW is the voltage driving force, RMICU represents the MICU1 regulatory term, and PoMCU where xij denotes the probability of a monomer in states sij. The describes the open fraction of MCU. dynamical equations governing the state of a monomer are The IMM voltage Y is 150 , 180 mV (negative inside). Although 21 the net Ca flux into the mitochondria might associate with a reduc- dx 21 00 2z 2z tion in voltage, some evidence suggests that mitochondrial Ca ~(c2x01{b2½Ca x00){(b1½Ca x00{c1x10), dt Mic Mic uptake does not appear to alter Y significantly during physiological condition34. With the assumption of constant Y, the driving force for dx10 z z MCU can be given by35 ~(b ½Ca2 x {c x ){(b ½Ca2 x {c x ), dt 1 Mic 00 1 10 2 Mic 10 2 11 { bF(y-y ) bF(y y0) 0 bF(y-y0) DW~ e RT sinh( ), ð10Þ dx RT RT 01 ~(c x {b ½Ca2z x ){(c x {b ½Ca2z x ), ð13Þ dt 1 11 1 Mic 01 2 01 2 Mic 00

Here F, R, and T are the Faraday constant, the gas constant and the with x00 1 x01 1 x10 1 x11 5 1. 35 21 Kelvin temperature, respectively; b and Y0 are fitting parameters . Ca is extruded from mitochondria primarily by NCX which 1 21 As a regulatory subunit, MICU1 senses [Ca21] in mitochondrial swaps 3 Na ions with 1 Ca ion during each exchange cycle, 35 intermembrane space to set a threshold for MCU33. The influx rate of Thus, the kinetic of outward calcium flux can be described as MCU only becomes substantial when the extra-mitochondrial 21 36 [Ca ] reaches values above 3 mM . As a result, the regulation of z 3 z ½Na ½Ca2 MICU1 to MCU activity has a sharp activation threshold (k ) out~ Cyt Mt MICU jMt vNCX 3 z , ð14Þ 36 3 z z z 2 with an apparent Hill coefficient equal to 4 : kNa ½Na Cyt kNCX ½Ca Mt

1 1 where [Na ]Cyt is Na concentration in the cytosol, vNCX is maximal 2z 4 ½Ca Mic NCX activity, both kNa and kNCX are activation constants for NCX. RMICU~ , ð11Þ 4 z 2z 4 kMICU ½Ca Mic Microdomain crosstalk between the ER and mitochondria. Now 21 21 where [Ca ]Mic is the microdomain [Ca ]Cyt that MCU is exposed we describe a microdomain model that represents the crosstalk to, which will be discussed later. occurring between closely situated ER and mitochondria

SCIENTIFIC REPORTS | 5 : 7984 | DOI: 10.1038/srep07984 3 www.nature.com/scientificreports

(Fig. 1(b)). The interacting players are IP3Rs and MCUs in the the distance between IMM and ER membrane. As a result, Eq. 16 21 microdomain. A microdomain of local high [Ca ]Cyt produced by represents the microdomain coupling between the ER and mito- 21 nearby open IP3Rs is essential for high capacity Ca transport into chondria in our model. mitochondria via MCU. It has been reported that 90% of IP3Rs are located close to mitochondria and the majority of MCU sense the Parameter values. The parameters used in this model are listed in 21 29 high [Ca ]Mic in the vicinity of IP3Rs . Here we make a specific Table 1 (see supplementary material). They are categorized on the 21 assumption that MCU senses the local high [Ca ]Mic generated by basis of their source to: (a) those extracted directly from experimental 21 the opening of clustered IP3Rs, but other Ca handling components, data; (b) those obtained from previously published models; or (c) the such as IP3Rs, SERCA, NCX, etc., are determined by the global free parameters which were fit to experimental results. The model 21 21 averaged [Ca ]Cyt. The pros and cons of our method will be presented in this study permits simultaneous calculation of [Ca ] discussed in the last section of the paper. changes in the 3 compartments. Currently, it is difficult to measure 1 It has been suggested that each mitochondrial Ca21 uptake site experimentally Ca2 concentrations in the cytosol and ER or 21 40 must face multiple IP3Rs for effective mitochondrial Ca uptake . mitochondria simultaneously because of the highly dynamic 21 46 Recent experiment evidence indicates that IP3Rs are typically dis- nature of the Ca signals that occur within organelles . Only a 46,47 tributed in clusters on the ER membrane, with each cluster contain- few existing experimental data sets consist of measurements 41,42 ing a handful of IP3Rs . Patch clamp experiments also show that from all 3 compartments. The free parameters used in our model 21 the Ca current (IsIP3R) passing through a single open IP3R is line- were extrapolated from fits to these data sets. 21 21 arly correlated with the concentration gradient ([Ca ]ER - [Ca ]Cyt) 43 across the ER membrane with a slope of SIP3R 5 0.3 pA/mM . Results 21 21 Considering the closely distributed IP3Rs, we treat the Ca flux from The Ca oscillations. Our first priority was to determine whether 21 21 clustered IP3Rs as a Ca current from a point source at cluster the model realistically simulated cellular Ca dynamics. As shown in 21 center. As a result, an effective Ca current from clustered IP3Rs Fig. 2a, when setting [IP3] 5 0.5 mM our model generates baseline is expressed as Ca21 oscillations occurring as a series of discrete spikes. The values for basal and stimulated [Ca21] for the cytosol, mitochondria and ER 38,48 z z in the model are in close accord with experimental data . The d~n P I , I ~S (½Ca2 {½Ca2 ): ð15Þ IP3R oIP3R sIP3R sIP3R IP3R ER Cyt oscillations period is in the order of several ten seconds, as seen in many experimental observations with non-exitable cells2,48. The Ca21 spikes show relatively rapid rising phases and slow falling phases, Here, P is the IP R open probability given by Eq. 6 and n is oIP3R 3 IP3R mimicking those seen in experimental recordings49. The cytosolic the IP R number in a cluster. According to Ref. 41, we consider a 3 and mitochondrial [Ca21] oscillate almost in phase, with [Ca21] typical cluster with n 5 4. These 4 IP Rs are in tight association, Cyt IP3R 3 as the leader, while the ER [Ca21] is in anti-phase with them, also as organized in a square pattern. observed experimentally13,47. Around the center of IP R cluster, the open IP Rs will generate a 3 3 Having established that the salient features of the Ca21 dynamics very sharp distribution of [Ca21] due to rapid Ca21 diffusion pro- Cyt of our model are in good agreement with existing experimental ducing a microdomain of high [Ca21] . Here we also assume that Cyt observations, we examined the effect of manipulating the mechan- the ER membrane acts as a flat boundary to limit the Ca21 diffusion isms modulated by the crosstalk of the ER and mitochondria. Thus, in a half 3-dimensional space, i.e. the cytosolic microdomian we also performed simulations in which mitochondria were absent (Fig. 1(b)). Using hemispherical symmetry of Ca21 diffusion from from the model (Fig. 2b). The minimal values of [Ca21] are a point release source, the sharp distribution around the release point ER 311 mM and 276 mM in the absence and in the presence of mito- can be established with a signal equation analogous to the linear cable chondria, respectively (Fig. 2), indicating that more Ca21 ions are equation44,45. As a solution of the linearized reaction-diffusion equa- 21 45 released from the ER during each spiking cycle in the presence of tion, the microdomain [Ca ] is given by 21 mitochondria. The maximal values of [Ca ]Cyt are 5.6 mM and 2.5 mM in the absence and in the presence of mitochondria, respect- d 2z ~ ({r=l)z 2z ively (Fig. 2), showing that mitochondria can significantly decrease ½Ca Mic e ½Ca Cyt, ð16Þ 21 4prFDc [Ca ]Cyt oscillation amplitude.

21 with Ca oscillation modulated by IP3R-MCU distance. Next we qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 21 looked at the effect of IP3R-MCU distance on Ca oscillation in ~ z 2z l Dc=(konCyt½BPMicKd=(Kd ½Ca Cyt)): ð17Þ detail. Fig. 3 compares oscillating [Ca21] trajectories in microdomain, ER, mitochondria, and cytosol during a single cycle at varying IP3R-MCU distances. By decreasing the IP3R-MCU 21 Here, Dc is the diffusion coefficient for free Ca . The parameter l is distance from infinity (we used simulations in which mitochondria 21 an important factor that determines the sharp decay of [Ca ] within were absent from the model as the infinite IP3R-MCU distance), the 21 21 a microdomain, which accounts for the Ca diffusion and binding to [Ca ]Mic in microdomain increases according to Eq. 16 against BPs. [BP]Mic is the total concentration of BP in the microdomain and distance (Fig. 3a), giving an increase in mitochondrial Ca21 uptake. 44,45 21 21 Kd is its dissociation constant . One can see that the [Ca ]Mic As a result, the minimal [Ca ]ER steadily decreases (Fig. 3b) and the 21 21 within a microdomain becomes the cellular average [Ca ]Cyt when [Ca ]Mt spike amplitude steadily increases until saturating at about there are no open IP3Rs. 65 mM (Fig. 3c). However, an unexpected finding is that the 21 21 Eq. 16 describes the [Ca ] distribution at distance r around the [Ca ]Cyt spike amplitude first decreases but then increases as the point source, i.e., the IP3R cluster center. In our model the parameter distance decreases (Fig. 3d). r is the distance between the MCU and the IP3R cluster center, which 21 21 we will call the IP3R-MCU distance in the paper. Thus, [Ca ]Mic is The critical IP3R-MCU distance. The amplitudes of [Ca ]Mic, 21 21 21 the microdomain Ca concentration that the MCU sees. [Ca ]Mt, and [Ca ]Cyt are plotted in detail as a function of Considering MCUs located on IMM, here we also simply assume distance from 10 to 150 nm at [IP3] 5 0.5 mM in Fig. 4a and 4b. A 21 21 that the outer mitochondrial membrane (OMM) has little effect on sharp increase is observed for [Ca ]Mic and [Ca ]Cyt at r , 30 nm, 21 21 6 21 the Ca diffusion as it has high permeability to Ca . If we suppose and [Ca ]Cyt reaches its minimum at r 5 30 nm. Fig. 4b also shows 21 the IMM and ER membrane are parallel, parameter r also represents that the [Ca ]Cyt spiking period increases monotonically from 30 to

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21 decreasing distance at r , 20 nm, how can [Ca ]Cyt spiking amplitudes increase (violet line with diamonds in Fig. 4b), while the total amount of Ca21 released from the ER decreases (black line with squares in Fig. 4c) but mitochondrial Ca21 uptake fraction increases (green line with stars in Fig. 4c)? In order to further examine this conflicting effect of distance on 21 21 [Ca ]Cyt spike amplitude and the amount of ER-released Ca ,we investigated how mitochondrial Ca21 uptake modulates the spike 21 width, the spike rising time and decay time of [Ca ]Cyt at varying IP3R-MCU distance. Here the spike width is defined as the duration 21 at half maximum of [Ca ]Cyt spike amplitude, the rising time is 21 defined as the duration from twice of the minimal [Ca ]Cyt to the peak of the response, and the decay time as the duration from the 21 peak of the response to twice of the minimal [Ca ]Cyt. An example of definition of these parameters is marked in Fig. 2a for spike curve at distance r 5 35 nm. We first discuss the simple situation at r . rcrt. As shown in Fig. 4d when r . rcrt, the spike width increases with decreasing distance, which primarily arises from an increase in the duration of the decay time, whereas the rising time is rapid and shows little change with distance. As r decreases, the ability of mitochondrial Ca21 uptake 21 increases, leading to a decrease in [Ca ]Cyt amplitude. The decrease 21 21 in [Ca ]Cyt amplitude in turn leads to a weakening of the Ca inhibition of IP3R dynamics, resulting in the prolonged spike decay time with decreasing distance. Differently, at r , rcrt, as the IP3R-MCU distance decreases, even though the rising time increases (black line in Fig. 4d), the spike width actually becomes smaller due to a decrease in the decay time (blue and red lines in Fig. 4d). At this small distance, the rising time consists of both a slow rising phase and an abrupt rising phase. As an example, the slow rising and abrupt rising phases for a spike at distance r 5 10 nm are indicated by arrows in Fig. 3a&b. The mito- 21 Figure 2 | Mitochondria serve as Ca reservoirs. (a) Oscillations of: chondrial Ca21 uptake is so strong that, at the beginning of each 21 21 [Ca ]Mic in the IP3R-MCU microdomain, [Ca ]Cyt in the cytosol, oscillating cycle, most of the ER-released Ca21 ions are directly dri- 21 21 [Ca ]Mt in mitochondria, and [Ca ]ER in the ER in the presence of 21 ven into mitochondria, leading to a rapid increase of [Ca ]Mt mitochondria with a IP3R-MCU distance of 35 nm. The width at half (Fig. 3c), but a very slow increase of [Ca21] (Fig. 3d). With low 21 Cyt maximum, the rising duration and decay duration of [Ca ]Cyt spike are 21 21 [Ca ]Cyt, there are a small fraction of activating IP3Rs which remain marked in the second panel of (a). (b) Oscillations of: [Ca ]Cyt in the 21 21 open for a long time, resulting in a slow rise phase for [Ca ]Cyt (e.g. cytosol, and [Ca ]ER in the ER in the absence of mitochondria. [IP3] 5 5 21 the gray dash line for r 10 nm in Fig. 3d with time from 0 to 0.5 mM. The unit of [Ca ]ismM. 21 30 sec). Such a long duration with low [Ca ]Cyt actually contributes 21 little to the spike width. When [Ca ]Mt increases to approach to its 50 sec, following the increased ability of mitochondria to take up saturation state, most of the ER-released Ca21 ions will then diffuse 21 21 21 21 Ca as the IP3R-MCU distance diminishes. The [Ca ]Cyt spiking into cytosol. Because of the Ca induced Ca release, there occurs 21 amplitude is determined by the number of Ca ions that diffuse into an abrupt increase in the numbers of open IP3Rs, generating a spike the cytosol, which is related to the total amount of Ca21 ions released (e.g. the gray dash line for r 5 10 nm in Fig. 3d with time from 30 to from ER through IP3Rs and the fraction which are taken by 35 sec). 21 mitochondria. In the model, the total amount of Ca released With shorter IP3R-MCU distance, the mitochondria become more from the ER through IP3R and the fraction accumulated by saturated prior to the abrupt rising phase, and thus during the abrupt mitochondria through MCU during each oscillating cycle are rising phase the Ca21 ions released from the ER diffuse more into 21 plotted in Fig. 4c as a function of IP3R-MCU distance. The cytosol, generating a higher amplitude spike in [Ca ]Cyt (violet line fraction of mitochondrial Ca21 uptake increases monotonically with diamonds in Fig. 4b at r , 30 nm). In turn, the elevated 21 with decreasing distance indicating an increase in the ability of the [Ca ]Cyt peak induces a strong inhibitory effect on IP3R dynamics, 21 mitochondria to take up Ca at closer distances. Our simulation such that spikes decay faster as the IP3R-MCU distance decreases shows that at 30 nm distance, about 50% of the ER-released Ca21 (red line with circles in Fig. 4d). ions are taken up by mitochondria (see green line with stars in The changes with distance seen in the amount of Ca21 ions Fig. 4c). As a consequence, rcrt 5 30 nm acts as a critical distance released from the ER during the rise and decay phases can then 21 21 for mitochondria to modulate cytosolic Ca signaling: At r . rcrt, explain why the total amount of ER-released Ca reaches a max- 21 more ER-released Ca ions will diffuse into the cytosol than be taken imum around r 5 20 nm. At r . rcrt, as the rising time is fast and up by mitochondria; whilst at r , rcrt, mitochondria will capture the little affected by distance (close to 6 s as shown in Fig. 4d), the majority of Ca21 ions released from ER. elevation in the total amount of ER-released Ca21 with decreasing distance mainly related to the increase of the decay phase. By 21 Ca dynamics modulated by IP3R-MCU distance. Surprisingly, decreasing r at rcrt . r . 20 nm, although the amount of ER-released Fig. 4c also shows another unexpected finding that the total Ca21 ions during the decay phase decreases because of the shortened amount of Ca21 released from the ER first increases with distance decay duration (red line in Fig. 4d), the amount of ER-released Ca21 down to r 5 20 nm and then decreases at smaller distance (see black ions during the rising phase increases because of the prolonged rising line with squares in Fig. 4c). This raises a critical question: with duration (black line in Fig. 4d). As a result, the total amount of Ca21

SCIENTIFIC REPORTS | 5 : 7984 | DOI: 10.1038/srep07984 5 www.nature.com/scientificreports

21 21 21 21 Figure 3 | The time evolution of [Ca ]Mic (a), [Ca ]ER (b), [Ca ]Mt (c) and [Ca ]Cyt (d) in an oscillating cycle at distance r 5 200 (green), 100 (purple), 40 (red), 20 (dark) and 10 nm (grey). The brown lines in (b) and (d) are in the absence of mitochondria. In (a) and (b) the duration of an abrupt 21 increase in Ca release is marked by arrows for r 5 10 nm. [IP3] 5 0.5 mM.

21 released by ER keeps increasing with decreasing r for rcrt . r . [Ca ]Cyt spike amplitude is mainly determined by the amount of 20 nm. However, at very short distance of r , 20 nm, during the Ca21 released during the abrupt rising phase of a Ca21 response, rising phase the ER-released Ca21 ions almost saturate both mito- giving an increasing relationship with decreasing distance. In con- chondria and the cytosol, giving a maximal Ca21 amount released by trast to this, the change in the total amount of ER-released Ca21 ER during the rising phase (see the open circles in Fig. 4c at r , mainly follows the behavior of the spike decay time, giving a decreas- 20 nm). Then, the change of the total amount of ER-released Ca21 is ing relationship with decreasing distance at r , 20 nm. 21 typically determined by the change of decay time, leading to a The synchronization of the oscillation phases between [Ca ]Cyt, 21 21 21 decrease in the total amount of ER-released Ca with decreasing [Ca ]ER, and [Ca ]Mt is also modulated by the IP3R-MCU distance. 21 distance at r , 20 nm. Our data (not shown here) indicate that at r . rcrt, [Ca ]Cyt peaks 21 21 Thus we can see how the apparently paradoxical relationship first, followed by [Ca ]ER minimum and then [Ca ]Mt peak, due to 21 21 between [Ca ]Cyt spike amplitude and total amount of ER-released an increase of the amount of ER-released Ca ions diffusing into the 21 Ca at IP3R-MCU distances ,20 nm develops. At r , 20 nm, the cytosol at greater distances. However, when r , rcrt, more ER-

21 21 21 Figure 4 | Ca dynamics modulated by the IP3R-MCU distance. (a) The spike amplitudes of [Ca ]Mic (triangles) and [Ca ]Mt (circles). (b) The spike 21 21 amplitudes of [Ca ]Cyt (diamonds) and spike period (spheres). (c) The total amount of Ca released from the ER through IP3Rs during each cycle 21 (squares), the amount of Ca released from the ER through IP3Rs during the rising time (circles), and the fraction delivered to mitochondria through 21 MCU (stars). (d) The spike width (triangles), the rising time (squares) and the decay time (circles) of [Ca ]Cyt oscillations. [IP3] 5 0.5 mM.

SCIENTIFIC REPORTS | 5 : 7984 | DOI: 10.1038/srep07984 6 www.nature.com/scientificreports

21 [IP3] range. Outside of such distance range the Ca oscillations always occur even at infinitely high [IP3] (Fig. 5b). 21 [Ca ]Cyt oscillations with limited amplitudes regulate a host of 1 21 vital cell functions . A global [Ca ]Cyt less than 3.5 mM is usually 38,48 21 observed in living cell . However, high [Ca ]Cyt will trigger and 51 21 modulate . Fig. 5c shows the maximal [Ca ]Cyt values seen in our model plotted against IP3R-MCU distance for different 21 [IP3]. One can see that a rapid elevation in [Ca ]Cyt amplitude is 21 observed at IP3R-MCU distances around 10 nm. A global [Ca ]Cyt which is smaller than 4.0 or 5.0 mM (i.e. dashed or dotted line in Fig. 5c) is typically obtained with IP3R-MCU distances of 20 to 85 nm or distances of 15 to 150 nm, respectively.

Robustness with varying clustered IP3R number. In above study, we only consider a cluster in which nIP3R 5 4IP3Rs correspond to a single MCU. Experimental evidence suggests that IP3R clusters 41,42 typically contain a handful (,4) of IP3Rs . Next we discuss the robustness of the model’s behavior upon slight changes in nIP3R (from 4 to 3, and 5). By calculating the fraction of Ca21 ions accumulated by mitochondria compared to the total amount of Ca21 released from the ER, we see that the critical distance is changed to 20 nm for nIP3R 5 3 and 35 nm for nIP3R 5 5 (Fig. 6(a)). Fig. 6(b) gives the value of [IP3] at the right bifurcation point against distance with varying nIP3R. A common region to find the right bifurcation [IP3] is obtained with distances of 33 to 93 nm. 21 Fig. 6(c) shows the maximal [Ca ]Cyt plotted against IP3R-MCU 21 distances for varying nIP3R. A global [Ca ]Cyt which is smaller than 4.0 or 5.0 mM (i.e. dashed or dotted line in Fig. 6(c)) is 21 Figure 5 | Ca dynamics modulated by [IP3]. (a) The bifurcation diagram (the stable steady states and the maxima and minima of Ca21 oscillations) of the model with [IP3] as the bifurcation parameter at distance r 5 200 (green), 100 (purple), 40 (red), 20 (dark) and 10 nm (grey). (b) The value of [IP3] at the right bifurcation point plotted against distance. The inset is the bifurcation diagram at distance r 5 60 nm, in which the arrow marks the right bifurcation point. (c) The maximal 21 [Ca ]Cyt against the IP3R-MCU distance for [IP3] 5 0.1 (lozenges), 0.5 (squares), 1.0 (circles), 2.0 (triangles), and 5.0 mM (stars). The dashed and 21 dotted lines represent [Ca ]Cyt 5 4 and 5 mM, respectively.

21 21 released Ca ions are sequestered into mitochondria, so [Ca ]Mt 21 21 peaks first, followed by [Ca ]ER minimum and then [Ca ]Cyt peak.

21 Ca dynamics modulated by [IP3]. In the following discussion, we 21 investigate how [IP3] controlled [Ca ]Cyt oscillations can be modulated by the IP3R-MCU distance. The bifurcation diagram 21 21 for [Ca ]Cyt oscillation (i.e. the steady state of [Ca ]Cyt or the 21 maximum and minimum of [Ca ]Cyt oscillation) with [IP3] as the bifurcation parameter is plotted at different IP3R-MCU distances in 21 Fig. 5a. When IP3 levels are low, [Ca ]Cyt can be seen to remain in a low stable steady state. Beyond a certain threshold value of [IP3], 21 [Ca ]Cyt undergoes periodical oscillations. We also found that, at distance range of 27–122 nm, the system only demonstrates 21 sustained Ca oscillations when [IP3] values are in an intermediate range, evolving into a stable steady state at higher [IP3] (Fig. 5b). Such a bifurcation diagram for r 5 60 nm is depicted in the inset of Fig. 5b. Similar bifurcation behavior has been observed in the experimental Ca21 waves in Xenopus laevis oocytes. In oocytes it has been shown that repetitive Ca21 waves 50 occur only at intermediate [IP3] between 0.1 and 1 mM . Thus, as 21 21 shown in the inset of Fig. 5b, r 5 60 nm is the optimum IP3R-MCU Figure 6 | Robustness of Ca dynamics on nIP3R. (a) The fraction of Ca distance in which our model replicates these experimental accumulated by mitochondria of the total amount of Ca21 released from 50 observations. According to the experiment , for a biologically the ER during each oscillating cycle plotted against IP3R-MCU distance. 21 meaningful Ca oscillation model there should be a right (b) The value of [IP3] at the right bifurcation point against distance. 21 bifurcation point for high [IP3], beyond which there occurs no (c) The maximal [Ca ]Cyt against the IP3R-MCU distance at saturating 21 21 Ca oscillation. As plotted in Fig. 5b, only in the range of r of 27– [IP3] 5 5.0 mM. The dashed and dotted lines represent [Ca ]Cyt 5 4 and 21 122 nm the model can produce Ca oscillations in an intermediate 5 mM, respectively. Here nIP3R 5 3 (stars), 4 (circles) and 5 (triangles).

SCIENTIFIC REPORTS | 5 : 7984 | DOI: 10.1038/srep07984 7 www.nature.com/scientificreports

typically obtained with IP3R-MCU distances of 25 to 85 nm or taken up by mitochondria. At distances smaller than rcrt mitochon- 21 distances of 20 to 110 nm, respectively. dria can take up more Ca , while at distances larger than rcrt, more Taken together, compared with experimental observations38,48,50,51, Ca21 ions diffuse from the ER into the cytosol. This leads to mito- the simulation results shown in Fig. 5 and Fig. 6 suggest that the chondria displaying different kinds of Ca21 signal modulation 21 optimal IP3R-MCU distance for physiological Ca signaling should depending on their distance from the ER. The effects of mitochon- be around 30 to 85 nm. When the IP3R-MCU distance is between 30 dria on the spike amplitude, spike width, and rising and decay time of 21 21 and 85 nm, as illustrated in Fig. 6(a) approximately 15–55% of ER- [Ca ]Cyt spikes, the synchronization phase among [Ca ]Cyt, 21 21 21 21 released Ca ions can be taken up by mitochondria, compatible with [Ca ]ER and [Ca ]Mt, and the total amount of Ca released from 52,53 experimental measurements made in various cells . Our model the ER are all substantially modulated by how the IP3R-MCU dis- thus suggests that mitochondria, typically working at a short distance tance deviates from this critical value. 21 from the ER (but larger than rcrt), serve as Ca sinks, sequestering To explore experimentally the consequences of mitochondrial Ca21 ions released from the ER. Ca21 uptake on global Ca21 signals, mitochondrial Ca21 uptake is often prevented directly by applying an MCU inhibitor14 or modu- Discussion lated by using agents which either depolarize or hyperpolarize the Since the 1990s, the manner in which mitochondrial Ca21 uptake mitochondrial and thus dissipate or increase the 21 10,14 through MCU shapes intracellular Ca21 signaling has attracted much driving force for Ca uptake into the organelle . How mitochon- 21 attention6. The key questions presently debated are: to what extent drial Ca uptake affects IP3R release mechanism is still under invest- 21 mitochondria acquire Ca21; what impact mitochondria have on cyto- igation. Some researchers have argued that mitochondrial Ca 21 solic Ca21 signals; and what dimensions the ER/mitochondria Ca21 uptake may provide a positive modulation of Ca release by sup- 21 9–11 microdomain might have. To address these questions, we con- pressing the negative feedback of high [Ca ]Cyt on IP3R . Others 21 structed a Ca21 signaling model to consider the Ca21 crosstalk within have suggested that mitochondrial Ca uptake exerts a negative control on [Ca21] by preventing the positive feedback of Ca21 microdomains between IP3Rs and MCU. A 4-states MCU model has Cyt 12,13 been suggested based on the latest experimental results31,37–39. The on IP3R . 21 MCU is exposed to the microdomain Ca21 concentration which is In our simulations, the ability of mitochondria to take up Ca is 34,36 released from the nearby clustered IP3Rs , rather than the bulk changed by varying the IP3R-MCU distance and so the mitochon- cytosolic Ca21 concentration. As a result, the model replicates the drial modulation on IP3R dynamics has been examined. Our model 1 shape, amplitude, period, and kinetics of the Ca21 spikes observed in indicates that altering mitochondrial Ca2 uptake induces a nontri- 21 experimental data, allowing us to examine the effects of mitochon- vial change on [Ca ]Cyt amplitude, which can reconcile the conflict- 21 drial Ca21 uptake on cytosolic Ca21 signals. ing results of the change of [Ca ]Cyt amplitude observed in various 9–13 From experimental observations, it has been suggested that mito- experiments . When IP3R-MCU distance is larger than the critical 21 21 chondrial Ca21 uptake contributes significantly to the physiological distance rcrt, mitochondrial Ca uptake is weak and more Ca ions 1 regulation of cytosolic Ca2138. Regarding the recent controversy diffuse into cytosol, the enhancement of mitochondrial Ca2 uptake 21 whether mitochondria act as significant buffers to cytosolic Ca21 causes a decreasing [Ca ]Cyt spike peak, exerting a weakened inhibi- under physiological conditions17, our model indicates that mito- tion effect on IP3R dynamics, resulting in a prolonged decay time of chondria can accumulate large quantities of Ca21 under physio- spikes. Thus, at this region, mitochondrial Ca21 uptake offers a pos- 21 21 logical conditions (about 15–55% of the total released from the itive modulation of Ca release by reducing [Ca ]Cyt amplitude to ER) at IP3R-MCU distances of 30–85 nm. Furthermore, our model suppress the inhibition dynamics (i.e. the negative feedback) of high 21 indicates that the distance between the ER and mitochondria appears [Ca ]Cyt on IP3R during decay time of spikes (Fig. 7), similar as 21 to be an important factor in modulating Ca signaling, especially suggested in refs 9, 10, 11. While, when IP3R-MCU distance is smal- considering that mitochondria can be highly mobile organelles54. ler than the critical distance, mitochondria take more Ca21 ions than 21 There is a critical IP3R-MCU distance rcrt (around 20 to 35 nm those diffusing into cytosol, the strong mitochondrial Ca uptake 21 21 depending on nIP3R) at which half of the Ca released by the ER is will force [Ca ]Cyt at a small value to prevent the strong activation

21 21 21 Figure 7 | Schematic representation of how mitochondria modulate [Ca ]Cyt. IP3R channel is regulated by Ca in a biphasic manner: a lower [Ca ]Cyt 21 21 21 promotes Ca release and causes its elevation whereas higher [Ca ]Cyt inhibits Ca release. There is a critical distance at which 50% of the IP3R-released 21 21 21 Ca ions are taken up by mitochondria. When r,rcrt, mitochondrial Ca uptake exerts a negative control on IP3R-released Ca by preventing the 21 21 21 positive effect of low [Ca ]Cyt on IP3R; whilst when r . rcrt, mitochondrial Ca uptake provides a positive modulation on IP3R-released Ca by 21 21 suppressing the negative effect of high [Ca ]Cyt on IP3R. Ca oscillations merely occur for moderate values of [IP3] (orange range) with physiological amplitude (gray range), so the optimal distance of IP3R-MCU should be within the intersection zone between the gray and orange range.

SCIENTIFIC REPORTS | 5 : 7984 | DOI: 10.1038/srep07984 8 www.nature.com/scientificreports

21 26,29 dynamics (i.e. the positive feedback) of [Ca ]Cyt on IP3R (Fig. 7), by a simple Hill equation or by the Monod-Wyman-Changeux similar as proposed in refs 12, 13. Thus, our model shows that this type allosteric regulation24,27,28. In contrast to these models, we intro- weak activation effect causes a small Ca21 release from ER, giving a duced a mechanistic kinetic model to discuss in detail the binding slow rising phase. When mitochondria approach to saturation and and unbinding processes of Ca21 to MCU. Second, the numerical 21 21 21 [Ca ]Cyt increases beyond the threshold of excitable dynamics, an simulation about the peak values of [Ca ]ER or/and [Ca ]Mt were 21 24,26–30 abrupt rising phase occurs to generate a [Ca ]Cyt spike, giving a high usually underestimated in most of the models . For example, the 21 21 [Ca ]Cyt amplitude and then inducing a strong inhibitory effect on concentration of free Ca in the ER is typically in the range of a few IP3R dynamics to shorten the decay time of spikes. hundred micromolars. Our model is capable of reproducing the 21 21 21 An unexpected prediction with the model is that when the IP3R- observed magnitudes of [Ca ]Cyt, [Ca ]ER and [Ca ]Mt. MCU distance is less than the critical distance, even though mito- In 2013, Szopa et al. suggested a model to explicitly take into chondrial Ca21 uptake keeps increasing with decreasing distance, the account the existence of Ca21 microdomain between the ER and total amount of Ca21 released from the ER decreases while the cyto- mitochondria to discuss the mitochondrial Ca21 uptake29. 21 21 solic Ca spike amplitude increases. The [Ca ]Cyt peak is mainly However, the assumption in the model that MCU directly senses 21 21 determined by the amount of Ca released during the abrupt rising the [Ca ]ER may be not very appropriate, particularly in view of 21 phase of spikes. At shorter IP3R-MCU distances, the mitochondria the existing sharp Ca gradients in the microdomain against the become almost saturated before the abrupt rising phase, and thus distance between the IP3R and MCU. Previously, there are mainly during the abrupt rising phase more of the Ca21 ions released from two basic ways to handle Ca21 microdomain in the whole-cell mod- the ER diffuse more into cytosol, generating a higher amplitude of els. The first approach involved the separation of a specified small 21 21 [Ca ]Cyt. However, the change in the total amount of Ca release region from the cell. But this subspace is simply treated as another from the ER seen with decreasing distance is mainly determined by well-mixed compartment57,58, and thus this approach cannot capture the release of Ca21 occurring during the decay phase of spike. The the fact of sharp Ca21 concentration gradients in the microdo- 21 43,44 enhanced inhibitory effect of higher amplitude [Ca ]Cyt spikes on main . Sneyd et al. used an alternative approach to divide the cell 59,60 IP3R dynamics in turn leads to a shortening of the decay time of the into a few separate domains, connected by many boundary fluxes . spikes, resulting in a decrease in the total Ca21 amount released from Although this is a powerful approach, it greatly increases the com- ER with decreased IP3R-MCU distance. plexity of the model, leading to extreme computational difficulties. 21 The existence of high [Ca ]Mic in microdomains has been put Different from these methods, a new approach has been suggested forward as one way to resolve the apparent paradox that even though in the present paper. For simplicity, all the IP3Rs dynamics and 21 21 the Ca affinity of the MCU is low (Kd of 10–20 mM) highly efficient SERCA are determined by the bulk [Ca ]Cyt. As a result, the bulk mitochondrial Ca21 uptake still occurs under physiological condi- Ca21 concentrations in cytosol, ER and mitochondria can be exam- 21 3 tions with low micromolar global [Ca ]Cyt . However, an intriguing ined in deterministic ODE which actually assuming that the cytoso- question related to the role of the microdomain is the distance lic, ER and mitochondrial compartments are mixed homogenously. between the ER and mitochondria that would be required to control Upon such well mixed compartments, a microdomain is specifically distinct cellular processes. The distance from the ER membrane to considered to discuss the MCU dynamics which is crucial for mito- OMM was originally estimated to be in excess of 100 nm16, recently it chondrial Ca21 uptake. The microdomain consists of a cluster of has been suggested that this distance could be in the order of IP3Rs and a MCU separated at a short distance. Treated as a point 15,55 30 nm . A key prediction of our model is that the optimal distance release source for the clustered IP3Rs which dynamics is controlled 21 21 between the IP3R and MCU is about 30–85 nm. This arises when by bulk [Ca ]Cyt, a sharp distribution of [Ca ]Mic can be built up in 21 21 parameters for [IP3] and [Ca ] are derived from the experimental the microdomain. Each MCU responds to the local high [Ca ]Mic 21 21 observations that Ca oscillations generally occur for intermediate generated by the clustered IP3Rs, rather than the bulk [Ca ]Cyt.Asa 50 21 21 values of IP3 and that physiological [Ca ]Cyt amplitudes seldom result, this method avoids the simulation of the Ca diffusion in exceed 3.5 mM in living cells38,48, which are illustrated in Fig. 7. microdomain between the ER membrane and IMM. Considering that the thickness between OMM and IMM is around Peglow et al.30 discussed a three-dimensional model to analyze the 20 nm56, our model predicts that the optimal gap between the ER influence of the distance between mitochondria and the CRAC chan- membrane and OMM should be approximately 10–65 nm, which is nel on the plasma membrane, which is responsible for Ca21 influx in good agreement with measurements obtained via electron micro- from the outside of the cell, on global Ca21 oscillation. They con- scopy and tomography15,31,55. firmed that the relative position between mitochondria and the Interestingly, our simulation also provides a reason for why MCUs CRAC channels controls the global Ca21 signal. Their simulation need to be located ,20 nm away from the OMM. In experiment, results showed that close mitochondria will lower the microdomain 21 21 21 elevations in the magnitude of [Ca ]Cyt during typical agonist [Ca ] right at the CRAC channels and prevent the Ca -dependent 21 21 induced responses could lead to a triggering of [Ca ]Cyt-induced inactivation of CRAC channels, leading to higher Ca influx and 51 21 apoptosis . Maintaining a distance between IMM and OMM of thereby increasing global [Ca ]Cyt. They found that the global 21 20 nm may present a defense mechanism to keep the global [Ca ]Cyt monotonously changes with the mitochondria-CRAC dis- 21 [Ca ]Cyt at a small physiological range. Our model highlights the tance from 0.1 to 2 mm. A similar result is obtained in our model at r importance of the IP3R-MCU distance and suggests that potential . rcrt. 21 pathological mechanisms for generating elevated [Ca ]Cyt and lead- As a fact, our model does not realistically consider the spatial 21 6,51 21 ing to possibly [Ca ]Cyt-induced apoptosis would be found in structure and so many important factors of Ca signaling have been disorders in which the optimal distance between the ER and mito- ignored. In the model the microdomain is modeled as a radially chondria is disturbed. Considering that when untethered to the ER, symmetric hemisphere and so the linearized reaction-diffusion equa- 54 21 mitochondria can be highly mobile organelles and that little is tion has been applied to obtain a simple expression for [Ca ]Mic. The known of the physiological stimuli governing the distance between mitochondrial boundary is actually ignored. One may expect that the 21 the ER and mitochondria, or how the tethers between the ER and mitochondrial boundary effect may modulate the sharp [Ca ]Mic 21 mitochondria function or are disrupted during pathology, future distribution. The Ca release from the clustered IP3Rs are treated as research elucidating how the IP3R-MCU distance is maintained the point release source, which is correct for far away MCU. But if and controlled is essential. MCU is too close to IP3Rs, a better treatment is to consider the spatial Finally, we discuss the advantages and limitations of our model. distribution of IP3Rs. The model also assumes that OMM has no First, the previous published models typically simulated MCU either effect on the Ca21 diffusion as it has high permeability to Ca21.A

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60. Means, S. A. & Sneyd, J. Spatio-temporal calcium dynamics in pacemaking units Additional information of the interstitial cells of Cajal. J. Theor. Biol. 267, 137–152 (2010). Supplementary information accompanies this paper at http://www.nature.com/ scientificreports Competing financial interests: The authors declare no competing financial interests. Acknowledgments How to cite this article: Qi, H., Li, L. & Shuai, J. Optimal microdomain crosstalk between We would like to acknowledge many useful conversations with George Dickinson, Ian endoplasmic reticulum and mitochondria for Ca21 oscillations. Sci. Rep. 5, 7984; Parker and Jeffery Lock in University of California, Irvine. We also thank Ke Jiang and Yu DOI:10.1038/srep07984 (2015). Jiang in Xiamen University for help with numerical simulations. This work was supported by the China National Funds for Distinguished Young Scholars under grant 11125419, the This work is licensed under a Creative Commons Attribution-NonCommercial- National Natural Science Foundation of China under grant 31370830, the Fujian Province NoDerivs 4.0 International License. The images or other third party material in Funds for Leading Scientist in Universities and ICAM branches cost sharing fund. this article are included in the article’s Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Author contributions Commons license, users will need to obtain permission from the license holder H.Q. and J.S. conceived and designed the model. H.Q. performed the numerical in order to reproduce the material. To view a copy of this license, visit http:// simulations. L.L. contributed to the writing of the programs. H.Q. and J.S. wrote the paper. creativecommons.org/licenses/by-nc-nd/4.0/

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