Understanding the Regulation of STIM1-ORAI1 Interaction Using a Reaction-Diﬀusion Model

bioRxiv preprint doi: https://doi.org/10.1101/306530; this version posted April 23, 2018. The copyright holder for this preprint (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.

Understanding the regulation of STIM1-ORAI1 interaction using a reaction-diﬀusion model

Barbara Schmidt,1, 2, 3, ∗ Ivan Bogeski,3, 4, † Barbara A. Niemeyer,2, ‡ and Heiko Rieger1, § 1Department of Theoretical Physics, Saarland University, 66041 Saarbrücken,Germany 2Department of Molecular Biophysics, Saarland University, 66421 Homburg, Germany 3Department of Biophysics, Saarland University, 66421 Homburg, Germany 4Molecular Physiology, Institute of Cardiovascular Physiology, University Medical Center Georg-August-University, 37073 Göttingen,Germany (Dated: April 23, 2018) Release of Ca2+ from endoplasmatic retriculum (ER) Ca2+ stores causes stromal interaction molecules (STIM) in the ER membrane and ORAI proteins in the plasma membrane (PM) to interact and form the Ca2+ release activated Ca2+ (CRAC) channels, which represent a major Ca2+ entry route in non-excitable cells and thus control various cell functions. Extracellular reactive oxygen species (ROS) can modulate the CRAC current ICRAC via oxidation of ORAI1. We formulate a reaction-diffusion model to quantify the STIM1-ORAI1 interaction during CRAC channel formation and analyze different ORAI1 channel stoichiometries and different ratios of STIM1 and ORAI1 in comparison with experimental data. We incorporate the inhibition of ORAI1 channels by ROS into our model and calculate its contribution to the CRAC channel amplitude. We find that the possibility of reactions between CRAC channel subunits and established CRAC channels tunes the total amount of Ca2+ influx and determines which CRAC channel configuration is mostly preferred. High numbers of ROS-inhibited ORAI1 dimers (in comparison to non-inhibited ORAI1 dimers) are needed to induce a strong decrease of Ca2+ influx compared to the wildetype (WT) case. Keywords: ORAI1; STIM1; CRAC channel; reaction-diffusion-model; stoichiometry; ROS

I. INTRODUCTION proteins diffusing within the plasma membrane [9, 12– 14]. Depending on the STIM1-ORAI1 stochiometry different ORAI1 conductance states are reached open and Temporally and locally controlled changes of the intra- selectively conduct Ca2+ ions into the cell. cellular Ca2+ concentration drive a plethora of cellular Although the electrophysiological correlate has been functions [1–3]. While electrically excitable cells utilize 2+ 2+ voltage gated Ca2+ channels to achieve rapid changes in known as CRAC (Ca release activated Ca ) cur- intracellular Ca2+ concentration [2], immune cells require rent since 1991, the exact protein composition of the slower but long-lasting changes in intracellular Ca2+ con- complex has been a matter of debate. Several reports centration for activation and cytokine production [4, 5]. pointed towards dimeric ORAI1 channels at rest while In these cells activation of T-cell receptors and other PLC tetrameric and hexameric stoichiometries have been pro- coulped receptors results in a depletion of intracellular posed to form the ion conduction pore. Indeed recent re- Ca2+ stores (endoplasmatic reticulum, ER). This results sults obtained from using concatenated constructs as well in an increased intracellular Ca2+ concentration, which as the crystal structure of purified Drosophila Orai1 by itself is not sufficient to trigger long-term immune cell point towards hexameric Orai1 channels as the predom- activation and translocation of the nuclear factor of acti- inant species underlying ICRAC [15–17]. vated T-cells (NFAT). Thus extracellular Ca2+ needs to While the amplitude of ICRAC is thus determined by be ingested into the cell. the relative ratios of the STIM1 to ORAI1 protein lev- 2+ els [10, 18, 19], it is also modified by external factors. For long-lasting Ca influx the information about When immune cells enter an area of inflammation, they the filling state of the ER has to be conveyed to ion encounter environments rich in reactive oxygen species channels in the plasma membrane, which then provide (ROS). Exposure to ROS prevents ORAI1 from being ac- an entry pathway for extracellular Ca2+ [2, 6–10]. The 2+ tivated whereas preassembled STIM1-ORAI1 complexes drop in ER luminal Ca is sensed by stromal interac- are insensitive towards inhibition by ROS [20]. tion molecules (STIM), which undergo a conformational In [18] a Monod-Wynman-Changeux model is used to change, multimerize and move to regions near the plasma analyze the dependence of I on ORAI1 expression membrane, so called plasma membrane junctions (PMJ CRAC levels. In this model ORAI1 exists in two conformational [11, 12]). Here STIM1 proteins trap ORAI1 ion channel states (open and closed) with four binding sites of STIM1 each, which results in ten channel states in total. Analy- sis of ORAI1 complexes with less binding sites disagreed with the experimental data. More binding sites have not ∗Electronic address: [email protected] †Electronic address: [email protected] been tested. With the assumption that STIM1 binds to ‡Electronic address: [email protected] ORAI1 with negative cooperativity the model provides a § Electronic address: [email protected] reasonable fit to ICRAC . While for an ORAI1 expression bioRxiv preprint doi: https://doi.org/10.1101/306530; this version posted April 23, 2018. The copyright holder for this preprint (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. 2 level less than two (a. u.) the dominating state is the spot. Together with this restriction the formation of open ORAI1 conformation with four STIM1 bound OS4, STIM1-ORAI1 complexes results in differences of STIM1 for higher ORAI1 expression levels the open states with movement before and after releasing Ca2+ from ER. three and two STIM1 bound dominate and the state OS4 is nearly not occupied anymore [18]. While previous studies have used a reaction-diffusion system to model I [18, 21, 27, 28], these models The stochastic reaction diffusion model of [21] assumes CRAC were based on a tetrameric CRAC channel configuration that the ORAI1 proteins are already accumulated into and a single junctional interaction region. tetramers and that these ORAI1 complexes can trap one to four STIM1 dimers. This leads to four different Recent studies analyzing the CRAC channel stoi- CRAC channel states with different current capacities chiometries conclude that activated ORAI1 channels are contributing to the calculation of ICRAC and to CRAC present as hexameres. Yen et al. expressed hexameric channel currents reaching steady state values not earlier concatemers of human ORAI1 [15]. Their measured cur- than about 300 s. Furthermore the numbers of differ- rents reproduce the characteristics of CRAC channel cur- ent CRAC channel states in dependence of the cooper- rent which gives evidences that CRAC channels follow a ativity factors α and β is analyzed. It is found that for hexameric stoichometry. Single-molecule photobleaching all tested configurations (α, β) the best ratio of STIM1 experiments lead to the conclusion that ORAI1 forms monomers to ORAI1 tetramers is 7.5. In addition the dimers at resting state and that upon activation a mix- number of active channels depends not only on the total ture of dimers, tetramers and hexamers contributes to the number of ORAI1 proteins but also on the chosen coop- total CRAC current [16]. The ORAI1 concatemer analy- erativity. For negative cooperativity and a small number sis of [17] finds that concatemers of different sizes (dimer of ORAI1 proteins the tetrameric states are most domi- to hexamer) all lead to significant Ca2+ influx. Substi- nant, for a higher number of ORAI1 proteins the single tution of non-conducting subunits into different places in STIM1 bound states dominate. the concatemers shows, that the conducting capability of In [22] the diffusional behavior of STIM1 and ORAI1 the whole hexameric concatemer depends on the position in PMJ regions is addressed. Single-particle tracking and of the substituted subunit. This leads to two differnt photoactivation experiments are combined with Monte possibilities for the CRAC channels: a pure hexameric Carlo simulations to analyze STIM1 and ORAI1 diffu- arrangement and an assembly as trimer-of-dimers“. ” sion at PMJ regions in resting cells as well as in activated The ROS-mediated CRAC channel inhibition is an- cells. It is found that in resting cells STIM1 proteins fol- alyzed in [29]. Next to FRAP measurements to find low Brownian motion and ORAI1 motility is subdiffusive. differences in the diffusion parameter of inhibited and After ER-store depletion ORAI1 and STIM1 movement non-inhibited ORAI1, FRET measurements analyze the is mostly restricted to PMJ spots and the data show that interaction strength between STIM1 and ORAI1 and both proteins move together as a complex. Furthermore, between ORAI1 and ORAI1 for both WT and ROS- in activated cells more proteins are immobile than in rest- preincubated ORAI1. Altered diffusion and reaction being cells. havior together with the findings of an intramolecular The junctional regions between ER and plasma mem- locking of the CRAC channels by H O could explain the brane are not static [23] but the ER is remodeled by 2 2 reduced CRAC current of ORAI1 channels under H O STIM1 proteins. Activated STIM1 proteins are able to 2 2 influence. form elongated ER cisternae close to the plasma membrane, which increase in number and length during ER The goal of the present study is to transfer these in- depletion [24, 25]. The PM junctions seem to be pre- sights of CRAC channel stoichiometries into a new model determined since the puncta structures appear repeat- for CRAC channel formation in order to analyze the dif- edly at the same spots [26]. ferent possibilities of ORAI1 channel configurations and In [27] an integrated particle system model is com- their contribution to Ca2+ influx into the cell. bined with stochastic modeling using a spatially het- Therefore we combine dimeric, tetrameric and hexam- erogenous Gillespie algorithm to track single particles eric structures of ORAI1 channels and adjust the interac- while CRAC channel formation. The presented model al- tion regions to include as many junctional regions as can lows to observe the dynamics of single molecules as in sin- be observed in the experiment. Furthermore, we account gle molecule tracking experiments and allows to change for WT ORAI1 and ROS-preincubated ORAI1. rates of action according to the history of the molecules. Using a similar setup as [21] the diffusion of STIM1 The paper is organized as follows: In section II the complexes and the four different channels states is an- reaction-diffusion-model is introduced. We distinguish alyzed. Therefore the size of the PMJ is enlarged and two scenarios: the base case scenario and the H2O2 the channel states do not rest at one single PMJ spot. scenario, which deals with a mixture of inhibited and In the beginning none of the species show sub-diffusive non-inhibited ORAI1 channels. Consequently section III behavior but after 30 s the CRAC channel states move deals with the analytic, numeric and stochastic results. sub-diffusively with decreased diffusion rate, which is a Finally, we discuss (IV) our results. result of restricting these complexes to the small PMJ bioRxiv preprint doi: https://doi.org/10.1101/306530; this version posted April 23, 2018. The copyright holder for this preprint (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. 3

Ca2+ we now formulate our theoretical model to analyze the ORAI1 dimer ORAI1-STIM1 interaction during CRAC channel forma- plasma membrane tion and the resulting CRAC current. In the following we assume that the ER store is already depleted, which plasma membrane is experimentally realized by adding 1 µM of the SERCA junction inhibitor thapsigargin. Then we describe CRAC channel formation by the following four steps:

STIM1 multimer activated attached to PMJ CRAC channel 1. Multimerization of the STIM1 proteins ER ST membrane di 2. Diﬀusion of STIM1 and ORAI1 proteins to the Figure 1: Schematic representation of CRAC channel forma- PMJ tion 3. Attachment of STIM1 proteins to a PMJ

Ca2+ ROS 4. Binding of STIM1 and ORAI1 proteins at the PMJ

inhibited ORAI1 dimer The multimerization of the STIM1 proteins is given by: plasma membrane kmulti Sdimer + Sdimer )−−−−−−−−−−* S, (1) plasma membrane kdemulti junction

where Sdimer represents a STIM1 dimer (resting state configuration of STIM1) and S denotes a STIM1 multi- STIM1 multimer activated attached to PMJ CRAC channel mer (tetramer), which is able to form a CRAC channel ER ST membrane di subunit when combined with an ORAI1 dimer. The rates kpoly and kdepoly define the rates of multimerization and Figure 2: Schematic representation of CRAC channel forma- demultimerization respectively. Since after ER store de- tion under H2O2 pressure pletion a strong multimerization of STIM1 dimers is observed, one has kmulti kmulti. The stationary solution is given by: II. METHODS 1 k S = multi S2 . (2) 2 k dimer The formation of CRAC channels requires the inter- demulti action of two proteins, STIM1 and ORAI1. The STIM1 The ORAI1 dimers diffuse within the cell membrane, proteins are located at the ER membrane preassembled the STIM1 dimers and tetramers diffuse within the ER in form of dimers [30]. Similarly the ORAI1 proteins lo- plasma membrane. The diffusion rate within the PMJ is cated at the plasma membrane are assumed as dimers as assumed to be smaller than outside the plasma membrane smallest unit. As soon as the STIM1 EF-hands, which junction [22]. The different channel states (|Oi , |OOi reach into the ER lumen, sense a decrease in the luminal and |OOOi) and the STIM1 tetramers connected to the 2+ Ca concentration, the STIM1 proteins unfold and start PMJ (Srest) are assumed to rest at the PMJ. Further- to multimerize. These STIM1 multimers accumulate at more the reactions regions near the plasma membrane, the plasma mem- kattach brane junctions (PMJ). Here they attach to the plasma S + PMJ )−−−−−−−−−−* Srest (3) k membrane and trap the ORAI1 proteins. Already a detach channel consisting of four STIM1 and two ORAI1 (i. e. describe the process of STIM1 tetramers attaching to the in our model one CRAC channel subunit) is functional PMJ, which means these STIM1 tetrames Srest are fixed although with a low conductance. Also tetrameric or at the PMJ and are able to trap an ORAI1 dimer nearby. hexameric CRAC channel structures have been observed The core reaction scheme of CRAC channel formation [16]. These channels consisting of two or three CRAC is given by the following reactions, where Srest denotes channel subunits respectively yield an even higher Ca2+ the concentration of STIM1 tetramers fixed at the PMJ, influx per channel. Figure 1 schematically represents the O denotes the concentration of ORAI1 dimers within the different steps of CRAC channel formation. An exter- PMJ and Z1,Z2,Z3 denote the concentration of the three nal factor influencing the Ca2+ influx through CRAC different CRAC channel states: channels is the presence of ROS within the extracellular k1 space. ORAI1 proteins exposed to ROS become inacti- Srest + O )−*− Z1 (4) k vated, which means they can still form CRAC channels 2 k3 but the conductance of these inhibited channels is small Z1 + Z1 )−*− Z2 (5) in comparison to non-inhibited channels or even zero (cf. k4 figure 2). k5 Z2 + Z1 )−*− Z3 (6) Based on the experimental observation described above k6 bioRxiv preprint doi: https://doi.org/10.1101/306530; this version posted April 23, 2018. The copyright holder for this preprint (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. 4

+ parameter value 5 l + kmulti 4.8 · 10 mol·s 1 kmulti 0.01 s 6 l kattach 1.8 · 10 mol·s 1 kdetacht 0.3 s 6 l k1 1.2 · 10 mol·s 1 k2 1 s k3 α · k1 k4 β · k2 2 k5 α · k1 2 k6 β · k2 2 k7 α · k1 Figure 3: Schematic representation of the reaction scheme α 0.25 β 0.25

Table I: Reaction rate parameters for the reactions of the basic Resting STIM1 tetramers (Srest) form together with free reaction scheme ORAI1 dimers (O) CRAC channel subunits (Z1). Two of these subunits form an intermediate state (Z2). The fully open CRAC channel (Z ) is built out of an intermediate 3 rate constants for the forward reactions. Similar to state and another subunit. [21] we assume that STIM1 multimerizing is slower than Since CRAC channel formation and disassembly seems STIM1-ORAI1 binding. The process of attaching to the to be highly dynamic ([18] and [29]) we analyze the influ- membrane is assumed to be very fast, since just one (in- ence of an additional reaction between a hexamer CRAC stead of two) protein complex is involved. Furthermore, channel state Z and a CRAC channel subunit Z : 3 1 we assume strong negative cooperativity. With the default numerical values for the reaction rate parameters Z + Z −→k7 2 · Z . (7) 3 1 2 as given in table I the model provides a reasonable time This reaction destroys“ the fully open CRAC channel dependence of ICRAC . ” 2+ configuration and builds two intermediate CRAC channel The total Ca influx into the cell, ICRAC , is deter- 2+ mined by the number of channels N weighted with their states with lower Ca conductivity. Therefore we will Zi call this reaction stealing mechanism“. respective conductivity ci: ” Figure 3 shows a schematic representation of the re- I = c · N + c · N + c · N (10) action scheme. The yellow boxes indicate reactions only CRAC 1 Z1 2 Z2 3 Z3 allowed at the PMJ. The reaction rates k , k and k (on-rates) as well as with c1 = 0.01, c2 = 0.25 and c3 = 1.0. The number of 1 3 5 channels can be calculated via the formula: the rates k2, k4 and k6 (off-rates) are not chosen to be independent but are connected through a cooperativity N = Z · A · p , (11) parameter (α respectively β) to account for the findings Zi i cell PMJ of [18]. In analogy to [21] the dependency of the rates is 3 2 assumed to be: where Acell ≈ 2 · 10 µm denotes the size of the cell surface and pPMJ ≈ 15% describes the fraction of the 2n cell surface where ORAI1 proteins accumulate, the PMJ k1+2n = α · k1 , n ∈ (0, 1, 2) (8) 2n regions. k2n = β · k2 , n ∈ (0, 1, 2) . In the following we will analyze the reaction-diffusion As default we examine negative cooperativity (0 < α, β < model as follows: First, the core reactions without and 1) since we assume, that it gets harder to bind more and with stealing mechanism at the PMJ will be analyzed more proteins to an already established STIM1-ORAI1 analytically and numericallywith special emphasis on the complex. Nevertheless within the numerical analysis we steady state values for the channels states and for ICRAC . also examine positive cooperativity (α,β > 1). Assum- In a second step we will combine the reaction and diffu- ing that the reaction strength between a single CRAC sion part of the model into a stochastic reaction-diffusion channel subunit and a fully open CRAC channel is as model. Within this model the results of TIRF measure- strong as the reaction strength between a CRAC channel ments are used to describe and quantify the changes in subunit and an intermediate state, we take for the rate PMJ clusters. for the stealing mechanism: To account for diffusion in the stochastic model the model area is discretized in a grid of 100 × 100 grid cells 2 k7 = k5 = α · k1 . (9) called subvolumes each representing an area of ∆l×∆l = 0.1 µm × 0.1 µm. The diffusion of the proteins is treated Because STIM1 multimerization, STIM1 attachment to as reactions with reaction rates d = D/(∆l)2 assuming the PM and STIM1-ORAI1 binding are more preferred periodic boundary conditions. Numerical values for the than the respective backward reactions, we assume higher diffusion constants are given in table II. bioRxiv preprint doi: https://doi.org/10.1101/306530; this version posted April 23, 2018. The copyright holder for this preprint (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. 5

diﬀusion rate value A B

-H2O2 +Tg -H2O2 -Tg 2 DO 0.07 µm /s [13] 2 DS 0.1 µm /s [12] 2 DS2 0.05 µm /s [12]

PMJ 2 DO 0.03 µm /s [22]

PMJ 2 -H2O2 -Tg DS 0.03 µm /s [22] +H2O2 -Tg +H O -Tg +H O +Tg PMJ 2 C 2 2 2 2 D DS2 0.015 µm /s (*)

Table II: Diﬀusion constants for STIM1 and ORAI1 outside and within the PMJ, (*) assuming that as outside the PMJ the tetramers are half as fast as the dimers

-H2O2 +Tg The two-dimensional model area represents the cell +H2O2 +Tg membrane and the plasma membrane simultaneously. The interaction of ORAI1 and STIM1 is only possible at Figure 4: TRIF images of HEKS1 cells with GFP-tagged regions, where the ER membrane and the plasma mem- ORAI1, A: WT at t = 0 s, B: ROS preincubated cells at brane are close together, the plasma membrane junctions t = 0 s, C: WT at t = 300 s, D: ROS preincubated cells at PMJ. Therefore, some of the subvolumes of our model t = 300 s area are labeled PMJ. Reaction (1) and diffusion is possi- A B ble in all subvolumes, reactions (3) to (7) are just allowed 2 45 0.7 m 40 µ at the PMJ. 0.6 35 0.5 To determine how many subvolumes must be PMJ 30 we analyzed the ORAI1 cluster in HEKS1 cells (i. e. 25 0.4 HEK293 stably expressing STIM1 cells) via TIRF mi- 20 0.3 15 0.2 croscopy (cf. figure 4). After addition of the SERCA 10 inhibitor thapsigargin (1 µM) leading to passive ER 5 0.1 average number of Orai1 cluster 0 0 store depletion, the GFP-tagged ORAI1 proteins diffused 0 50 100 150 200 250 300 average size of Orai1 cluster in 0 50 100 150 200 250 300 within the cell membrane to the PMJs. Figure 4A shows t in s t in s a snapshot of two cells immediately after store depletion, Figure 5: Cluster analysis of TIRF images, A: average number figure 4C the same cells 300 s later. Analyzing in total 19 of ORAI1 clusters per cell over time, B: time dependence of cells via TIRF microscopy and with the help of imageJ the average size of ORAI1 clusters regarding number and mean size of ORAI1 clusters we find the following (cf. figure 5): Within the first 50 seconds the number of clusters rises to about 20 per cell and assumed to be empty. simultaneously the average size of the clusters increases rapidly from 0.3 µm2 to about 0.55 µm2. After this rapid rise the number of clusters doubles within the next 200 H2O2 scenario seconds until it reaches a value between 40 and 45. At the same time the average size of clusters drops slightly but then rises again to about 0.6 µm2. We analyze two different scenarios: The base case sce- In our analysis we increase the number of PMJ sub- nario described above and the H2O2 scenario to analyze volumes from one to six within the first 50 seconds and the influence of ROS. To account for the H2O2 prein- from five to eleven within the next 150 seconds. Simul- cubated cells we modify the reaction-diffusion scheme as taneously we increase their size from 0.3 µm2 to 0.6 µm2 follows: within the first 200 seconds in order to analyze the influ- • Additional to the CRAC channel states Z , Z ence of the PMJ formation. 1 2 and Z3, denoted for better readability as |Oi, Analogously we analyzed cells preincubated with ROS |OOi and |OOOi respectively, composed of STIM1 (figures 4B and D). Since size and amount of ORAI1 and ORAI1 proteins, new channel states consist- cluster were similar between the two analysis, the same ing of STIM1 and preincubated ORAI1 (OH ) or of settings in the model are used. STIM1 and a mixture of O and OH were included: H H H H H H H To analyze the reaction-diffusion system described O , OO , O O , OOO , OO O , H H H above we perform computer simulations using a Gillespie O O O . Monte Carlo algorithm [31] with an efficient implemen- tation technique [32] optimizing the computation time. • New reactions were introduced by exchanging the At the beginning of the simulation (t = 0 s) all proteins states O, |Oi, |OOi and |OOOi of reactions (4) to are homogeneously distributed and the ER Ca2+ store is (7) by the new states in every possible combination. bioRxiv preprint doi: https://doi.org/10.1101/306530; this version posted April 23, 2018. The copyright holder for this preprint (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. 6

• To model ICRAC a new parameter δ was introduced quantifying the degree of inhibition. We assume that the conductance of CRAC channel states con- dS = −k1 · S · O + k2 · Z1 (14) sisting of total ROS-inhibited ORAI1 is given by dt dO the fraction δ of the respective CRAC channel state = −k · S · O + k · Z of WT ORAI1. To model the conductance of mixed dt 1 2 1 CRAC channel states (consisting of WT and ROS- dZ Z2 1 = k · S · O − k · Z − k · 1 · 2 + 2 · k · Z inhibited ORAI1), we assume that each included dt 1 2 1 3 2 4 2 WT dimer contributes to the conductance as be- − k5 · Z2 · Z1 + k6 · Z3 fore and each included ROS-inhibited dimer con- 2 dZ2 Z1 tributes with fraction δ of the WT case. This means = k3 · − k4 · Z2 − k5 · Z2 · Z1 + k6 · Z3 H that the intermediate state OO is weighted dt 2 dZ with the factor (1 + δ) /2 and the mixed hexamer 3 = k · Z · Z − k · Z H H H 5 2 1 6 3 CRAC channel states OOO and OO O are dt weighted with the factors (2 + δ) /3 and (1 + 2δ) /3 respectively: and when including the stealing mechanism, the right hand sides of (14) are extended by: mix ICRAC = c1 · NZ1 + c2 · NZ2 + c3 · NZ3 dZ dZ + δ c1 · N|OH i + c2 · N|OH OH i + c3 · N|OH OH OH i 1,3 1,3 → − k7 · Z1 · Z3 (15) c2 dt dt + (1 + δ) · N H 2 |OO i dZ2 dZ2 → + 2 · k7 · Z1 · Z3 . c3 c3 dt dt + (2 + δ) · N H + (1 + 2δ) · N H H 3 |OOO i 3 |OO O i (12) The total amounts of ORAI1 (in whichever CRAC channel configuration) and of STIM1 respectively have In [29] the interactions between STIM1 and ORAI1 to be conserved, which means: proteins and between ORAI1 and ORAI1 proteins were analyzed. Foerster Resonance Energy Transfer (FRET) Otot = O(t)+ Z (t)+2 · Z (t)+3 · Z (t) , (16) values of STIM1 proteins with ORAI1 proteins inhib- 1 2 3 ited by H2O2 were significantly larger (0.24 ± 0.03) than FRET values of STIM1 proteins with WT ORAI1 Stot = S(t)+ Z (t)+2 · Z (t)+3 · Z (t) . (17) (0.15±0.01). In contrast, the ORAI1-ORAI1 subunit in- 1 2 3 teraction was reduced by 46%. Fluorescence recovery af- The second condition is always fulfilled when (16) is ful- ter photobleaching (FRAP) measurements revealed a 1.7 filled, since the right hand sides of the differential equa- times smaller rate of recovery for preincubated ORAI1 H tions for O and S are identical and we consider the fol- proteins [29]. Therefore the diffusion constant of O and lowing initial conditions: ˜ ˜ the reaction rates k1 and k2 as well as the cooperativity ˜ parametersα ˜ and β of the new reactions are defined as: S(0) = Stot (18) O(0) = Otot DOH = DO/1.7 (13) ˜ Z1(0) = 0 ki = ki · 1.6 for i ∈ (1, 2) Z2(0) = 0 α˜ = α · 0.46 Z3(0) = 0 . β˜ = β · 0.46 . Considering the reaction system without stealing (eqns (14)), the second equation of (14) can be rewritten as: III. RESULTS dZ dO dZ dZ 1 = − + 2 · 2 + 3 · 3 , (19) dt dt dt dt A. Analytical and numerical analysis of the Base Case Scenario which results in

Within the analysis of the base case scenario, we ex- Z1(t)= − (O(t)+2 · Z2(t)+3 · Z3(t)+ c0) , (20) amine two reaction systems. The ﬁrst reaction system consists of the core reactions only, the second reaction where c0 is determined by the initial condition (18), tot system includes the additional stealing mechanism. The which yields c0 = O . This is identical to the addi- core reaction system reads: tional condition above (16). bioRxiv preprint doi: https://doi.org/10.1101/306530; this version posted April 23, 2018. The copyright holder for this preprint (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. 7

Z / Otot, Z / Otot Z / Otot The stationary state of the reaction system (14) obeys: 2 3 1 -4 0.5 2.5⋅10 stat stat stat 0 = − k1 · S · O + k2 · Z1 (21) -4 0.4 2.0⋅10 stat2 Z1 stat stat stat 0 = k3 · − k4 · Z − k5 · Z · Z -4 2 2 2 1 0.3 1.5⋅10 stat + k6 · Z3 0.2 1.0 10-4 stat stat stat ⋅ 0 = k5 · Z2 · Z1 − k6 · Z3 . -5 0.1 5.0⋅10 These are three independent equations with five con- stat stat stat stat stat centration parameters (S ,O ,Z1 ,Z2 ,Z3 , ) 0 0 and six reaction rates ki. 0 1 2 3 4 5 With the cooperativity parameters α and β for the on- t in s and off-rates and using the abbreviations Figure 6: Time evolution of CRAC channel states Z1 (blue), α γ = (22) Z2 (red) and Z3 (green) according to the core reaction scheme β (eq (14), solid lines) and the reaction system with stealing mechanism (eq (15), dashed lines) for the rate parameters as k1 k = , given in table I and for Otot = 120000 and Stot = 240000 for k2 t ∈ [0 s, 5 s]. the equation system can be rewritten in terms of the stationary number of free ORAI1 and free STIM1 proteins: delay between tapsigargin addition and the steady state stat stat stat Ca2+ influx is larger than two seconds, which means that Z1 = k · S · O (23) the delay is also influenced by the diffusion of STIM1 and stat stat2 stat2 Z2 = 0.5 · γ · k · S · O ORAI1 proteins towards the PMJ. Figure 6 exemplifies 3 3 Zstat = 0.5 · γ3 · k2 · Sstat · Ostat . the time evolution of all three CRAC channel states nor- 3 malized to the total amount of ORAI1 (Otot) within the Together with the conservation laws (16) and (17) one first five seconds, with the parameters given in table I. stat The solid lines represent the core reaction system (14) gets a polynomial equation for Z1 , which can be solved numerically. All other stationary concentrations then fol- and the dashed lines represent the system with stealing low. mechanism (15). In both cases the single subunit state −4 Similarly we analyzed the reaction system with steal- Z1 is rarely occupied (less than 2 · 10 ), as on-reactions ing mechanism (eqns (15)): The additional stealing reac- are more preferred than off-reactions, while Z2 and Z3 tion (7) should help to regulate the formation of CRAC show more interesting features: channels. The corresponding stationary equation sys- The time course of Z2 and Z3 is determined by k1 and tem together with the two conservation laws (16) and k2. Analyzing the base case scenario without stealing (17) can be simplified to the following non-linear, non- mechanism shows the following: The larger k1 the steeper homogeneous equation system: the rise of Z2 within the first milliseconds, the larger k2 the faster the following drop of Z2. Similarly the rise ges stat stat stat stat O = O + Z1 + 2 · Z2 + 3 · Z3 (24) of Z3 is determined by the magnitude of k1. Large k2 ges stat stat stat stat yields a second (slower) rise of Z3 within the next five S = S + Z1 + 2 · Z2 + 3 · Z3 seconds. Furthermore k2 determines whether Z2 or Z3 stat k1 stat stat dominates after these five seconds, i. e. the larger k Z1 = S · O 2 k2 the more hexameric CRAC channel states are established stat k3 stat 2 k7 stat stat and the less tetrameric states are found. Analysis of the Z2 = (Z1 ) + Z1 · Z3 2k4 k4 base case scenario with stealing mechanism shows similar stat stat dependence of the time evolution of Z2 and Z3. The main stat k5 · Z1 · Z2 Z3 = stat , differences occur in the absolute values of these two states k6 + k7Z1 and that even for large k2 the hexameric state is less which is consistent with the basic solution for k7 = 0. occupied than the tetrameric state.

Time evolution of the CRAC channel states Inﬂuence of the rate parameters

The reaction systems (14) and (15) can be solved nu- In a second step we analysed the influence of the rate merically. In both reaction systems the stationary value parameters (k1, k2, α and β) on the steady state values. of the CRAC channels states is reached after about two Keeping all but the parameters displayed on the x-axis seconds. In experiments ([29]) it is observed that the fixed as given in table I, figures 7 and 8 show the results bioRxiv preprint doi: https://doi.org/10.1101/306530; this version posted April 23, 2018. The copyright holder for this preprint (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. 8

A B tot tot tot Zstat/ Otot Zstat/ OtotZstat/ O tot Zstat/ O , Zstat/ O , Zstat/ O A B 1 , 2 , 3 1 2 3 0.45 0.35 stat tot stat tot stat tot stat tot stat tot stat tot Z2 / O , Z3 / O Z1 / O Z2 / O , Z3 / O Z1 / O 0.4 0.3 -4 -3

0.5 0.5 2.5¤10 2.5 10 0.35 0.25 0.3 0.2 0.25 -4 -3

0.4 © 0.15 0.4 2.0£10 2.0 10 0.2 0.1 0.15 0.1 0.05 -4 -3

0.3 ¨ 0.3 1.5¢10 1.5 10 0.05 0 0 -0.05 -10 -8 -6 10-6 10-4 10-2 100 102 104 106 1x10 1x10 1x10 0.0001 0.01 1 100 -4 -3

0.2 § 0.2 1.0 10 1.0 10 k1 in l / (mol s) k2 in 1/s

-5 -4

0.1 ¦ 0.1 5.0¡10 5.0 10 Figure 7: Graphic representation of the values of the steady stat stat state conﬁguration (i. e. at t = 300 s) Z1 (blue), Z2 0 0 0 0 stat 0 0.05 0.1 0.15 0.2 0 0.5 1 1.5 2 (red) and Z3 (green) in dependence of the rate parameters

¥ β k1 (A) and k2 (B) for the core reaction system (eq (14), solid lines) and with stealing mechanism (eq (15), dashed lines). Figure 8: Graphic representation of the values of the steady If not varied as displayed on the x axis (log-scale!), the rate stat stat state configuration Z1 (blue, right y-axis), Z2 (red) and parameters are chosen as given in table I. stat Z3 (green) in dependence of α and β for the core reaction system (eq (14), solid lines) and with stealing mechanism (eq (15), dashed lines). If not varied as displayed on the x axis, for varying the respective parameters. Solid lines indicate the rate parameters are chosen as given in table I. the core reaction system, while dashed lines indicate the inclusion of the stealing reaction. Zstat/ Otot, Zstat/ Otot Zstat/ Otot 2 3 1 -4 0.4 4.0⋅10 Figure 7A shows the influence of the on-rate k1 on the stationary solution of the reaction schemes. In both -4 0.3 3.0⋅10 cases the behavior of Z1 is similar: Only in the case when the on-rate is small (between 10−2 l/(mol · s) and -4 102 l/(mol·s)) a lot of dimeric CRAC channels states can 0.2 2.0⋅10 be found. If the on-rate is even less than 10−3 l/(mol · s) -4 no channels at all are formed. The behavior of intermedi- 0.1 1.0⋅10 ate CRAC channel states on changes of k1 differs without (14) or with (15) stealing mechanism. In the second case 0 0 a larger on-rate yields to more tetrameric CRAC chan- 0 0.5 1 1.5 2 2.5 3 nel states up to the value 0.22. In the first case just for Stot / Otot on-rates between 10−1 l/(mol · s) to 105 l/(mol · s) a non negligible stationary value of Z2 is reached. As already Figure 9: Graphic representation of the values of the steady stat stat expected from the data of the time evolution analysis, the state configuration Z1 (blue, right y-axis), Z2 (red) and stat most dominant state of the core reaction system is the Z3 (green) in dependence of the ratio STIM1 / ORAI1. hexamer configuration for large on-rates. In case of core Solid lines indicate the core reaction scheme (eq (14)), dashed reactions with stealing mechanism the stationary value of lines show the corresponding values for the reaction scheme including the stealing mechanism (eq (15)). Rate parameters Z is smaller than the one of Z for large on-rates, which 3 2 are chosen as given in table I. means, that more tetramers than hexamers are formed. Keeping the on-rate fixed and varying the off-rate (figure 7B) results always in no noticeable values of Z1. This cooperativity parameter β (0.25) the steady state values is obvious from the data before, because in the exam- of Z2 and Z3 develop from zero to their respective con- ined interval the on-reactions are always more preferred stant value as in the analysis above. Z1 drops from 1 than the off-reactions. In the core reaction scenario the (α = 0) to 10−3 (α = 0.1) and than to less than 10−5 for tetramer configuration is more often adopted as the hex- α rising until 0.2. amer configuration as long as the off-rate is smaller than In contrast to this Z change more significantly on 10−3 1 and then drops to almost zero for larger off-rates. i s changes of the off-rate cooperativity parameter β, when In contrast to this the hexamer configuration starts at a α is fixed at 0.25 (cf. figure 8B). For the core reaction value of 0.177 for small off-rates, rises to a value of 0.344 −4 system Z1 rises linear from zero to 2.5 · 10 for β be- at k2 = 0.01 and than slightly drops again to 0.289 for tween zero and two. Similarly Z2 rises from zero to 0.29 even larger off-rates. In the reaction system with stealing and Z drops from 0.2 to 0.14 for β between 0.1 and two. mechanism the tetramer configuration is always favored, 3 while the gap between tetramer and hexamer configuration scales down from 0.2 for off-rates between 10−9 to ges ges 10−3 to 0.04 for larger off-rates. Dependency of ICRAC of the ratio S /O Figure 8A shows the dependence of the CRAC channel states on the on-rate cooperativity parameter α. Only Major parameters influencing ICRAC are the amount for small α (smaller than 0.05) compared to the off-rate and ratio of STIM1 and ORAI1 proteins. Figure 9 shows bioRxiv preprint doi: https://doi.org/10.1101/306530; this version posted April 23, 2018. The copyright holder for this preprint (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. 9

stat tot tot ICRAC / O , ICRAC / O Zstat/ Otot Zstat/ Otot Zstat/ Otot 0.3 tot tot 2 , 3 1 -3 S / O = 1 0.4 6.0⋅10 tot tot 0.25 S / O = 2 Stot / Otot = 3 -3 0.3 4.5⋅10 0.2

0.15 -3 0.2 3.0⋅10 0.1 0.1 1.5 10-3 ⋅ 0.05

0 0 0 0 5 10 15 20 0 5 10 15 20 Stot / Otot t in s Figure 11: Stochastic analysis of the temporal course of β ICRAC for different ratios of STIM1 / ORAI1. Solid lines indicate the core reaction scheme (eq (14)), dashed lines show Figure 10: Graphic representation of the values of the steady the corresponding values for the reaction scheme including stat stat the stealing mechanism (eq (15)). state configuration Z1 (blue, right y-axis), Z2 (red) and stat Z3 (green) in dependence of the ratio STIM1 / ORAI1 with additional increase of β (unbinding cooperativity parameter). Solid lines indicate the core reaction scheme (eq (14)), dashed STIM1 proteins to ORAI1 proteins. Figure 11 shows the lines show the corresponding values for the reaction scheme development of ICRAC normalized to the total available including the stealing mechanism (eq (15)). Constant param- amount of free ORAI1 dimers within the first 20 seconds eters are chosen as s given in table I and β is varied linear in for three different ratios STIM1 / ORAI1 for the core the interval [0.25, 6.25]. reaction scheme without (solid lines) and with (dashed lines) stealing mechanism. In contrast to the numerical analysis above the respective steady state value of ICRAC the results for the different stationary CRAC channel is reached after about eight to ten seconds not already tot states normalized to O . As soon as there are twice after about two seconds. This is because diffusion of or more as many STIM1 dimers than ORAI1 dimers the ORAI1 and STIM1 proteins are now taken into account. stationary values of Zi are constant. For ratios of STIM1 For all three ratios of STIM1 / ORAI1 (STIM1 / ORAI1 to ORAI1 below two we see a linear rise of the steady = 1, 2 and 3 in black, blue and red respectively) the state values Z2,3 form zero to their respective value at core reaction scheme without stealing mechanism leads STIM1 / ORAI1 = 2 in both cases. Z1 of the core reac- to a higher amount of Ca2+ influx compared to the reaction scheme first shows a steep linear and than slightly tion scheme with stealing mechanism. In both reaction slower rise to its final value. schemes, Ca2+ influx is highest for STIM1 / ORAI1 = In comparison, figure 10 shows the stationary values of Zi 3. It is slightly lower for STIM1 / ORAI1 = 2 and sig- tot and ICRAC normalized to O in dependence of the ratio nificantly lower for STIM1 / ORAI1 = 1. tot tot S /O with simultaneous rise of β (linear from 0.25 to stat Figure 12 shows the steady state values of Zi and 6.25). This scenario corresponds to the assumption that stat tot ICRAC normalized to O in dependence of the ratio it gets more difficult for CRAC channel units to build STIM1 / ORAI1. For both reaction schemes without up larger complexes as more and more STIM1 proteins and with stealing the numbers of tetramer and hexamer arrive at the PMJ. In this case all Zi first rise between tot tot tot tot CRAC channel states rise linear from STIM1 / ORAI1 = S /O = 0 and S /O = 2 (0.25 ≤ β ≤ 0.55). Sub- 0 to STIM1 / ORAI1 ' 2.5 and then stay at a constant sequently, Z1 and Z2 rise more slowly whereas Z3 drops value except for statistical fluctuations. The number of for larger β and larger ratios Stot/Otot. This results in CRAC channel subunits Z1 is low in comparison to the both reaction systems (without stealing (14), solid line, number of higher CRAC channel states. and with stealing (15), dashed line) in a slight decrease As in the numerical analysis the hexamer states are the of ICRAC . A similar behavior is seen in [28]. most dominant for the base case scenario without stealing mechanism and the tetramer states are the most dominant for the base case scenario with stealing mechanism. B. Stochastic analysis of the Base Case Scenaraio This results in lower ICRAC in the latter scenario. In contrast to the numerical analysis above, the high- Analysis of ICRAC in dependence of time and of the ratio stat est steady state value of ICRAC is reached at STIM1 / STIM1 / ORAI1 ORAI1 & 2.5 and not at exactly STIM1 / ORAI1 = 2. The latter ratio is the minimum number of STIM1 Main aspects of the analysis of the base case scenario tetramers needed to saturate all free ORAI1 dimers are the dependence of ICRAC of time t and of the ratio of available and therefore is the theoretical minimal ra- bioRxiv preprint doi: https://doi.org/10.1101/306530; this version posted April 23, 2018. The copyright holder for this preprint (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. 10

stat tot stat totstat tot stat tot stat tot stat totstat tot stat tot Z1 / O , Z2 / O , Z3 / O , ICRAC / O Z1 / O , Z2 / O , Z3 / O , ICRAC / O 0.3 0.25

0.25 0.2 0.2 0.15 0.15 0.1 0.1

0.05 0.05

0 0 0 1 2 3 4 5 0 0.1 0.2 0.3 0.4 0.5 tot tot 2 S / O DO in mm / s

Figure 12: Stochastic analysis of the steady state values (i. e. Figure 13: Stochastic analysis of the steady state values (i. e. stat stat stat stat stat stat at t = 300) of CRAC channel states Z1 , Z2 , Z3 (blue, at t = 300) of CRAC channel states Z1 , Z2 , Z3 (blue, stat stat red, green respectively) and of ICRAC (black) in dependence red, green respectively) and of ICRAC (black) in dependence of the ratio STIM1 / ORAI1. Solid lines indicate the core re- of the diﬀusion constant DO of the ORAI1 dimers according action scheme (eq (14)), dashed lines show the corresponding to the reaction scheme including the stealing mechanism (eq values for the reaction scheme including the stealing mecha- (15)). nism (eq (15)).

tot ICRAC / O 0.25 tot tot tio at which the highest value of I is reached. S / O = 1 mod CRAC Stot / Otot = 2 mod The stochastic analysis includes diﬀusion of STIM1 and 0.2 Stot / Otot = 3 mod ORAI1. In this case there is more than the minimum Stot / Otot = 1 amount of STIM1 needed to saturate all ORAI1 dimers, 0.15 Stot / Otot = 2 because it is possible, that free STIM1 tetramers and free Stot / Otot = 3 ORAI1 dimers are not at the same spot and therefore can 0.1 not react with each other. Are there about 25% more STIM1 proteins available than the minimal theoretical 0.05 amount needed the maximal Ca2+ inﬂux is reached. 0 In the following we perfom all analysis with the reac- 0 5 10 15 20 tions of the core system with stealing mechanism. t in s

Figure 14: Temporal course of ICRAC according to eq (15). Influence of the diffusion constant of ORAI1 Faded lines indicate the parameters as given in tables I and II, bold lines indicate the modified parameters according to eq. (13) and DÕ = DO/1.7 Comparing WT ORAI1 channels with ROS preincubated ORAI1 channels one experimentally measured parameter concerns the diffusion constant of ORAI1. influx seen in experiments ([29]) between the H2O2 sce- WT ORAI1 proteins are faster than ROS preincubated nario and the WT scenario. ORAI1 channels [29]. To analyze, whether this could influence the total Ca2+ influx into the cell, we altered the diffusion rate of the ORAI1 dimers outside and inside the PMJ areas in our model. Influence of altered reaction rates stat Figure 13 shows the amplitude of ICRAC as well as the number of active channels at steady state (i. e. at In a next step in [29] the interactions between t = 300 s) normalized to Otot in dependence of the dif- STIM1 and ORAI1 proteins and between ORAI1 and fusion constant of the ORAI1 dimers. The diffusion con- ORAI1 proteins were analyzed. According to this we stant DO outside the PMJ regions was varied between 0 changed the reaction parameters as described in eq and 0.5 mm2/s. To account for the slower diffusion of (13). Combined with the modified diffusion constant PMJ ˜ ORAI1 within the PMJ, DO was set to 3 · DO/7 in (DO = DO/1.7) the temporal course of ICRAC was analogy to the difference in the measured values of [13] examined. The results are shown in figure 14. The and [22] (compare table II). Apart from statistical fluctu- faded black, blue and red curves show the courses of ations the number of active channels in the steady state WT ORAI1 for the three ratios of STIM1 / ORAI1 = 1, stat and hence the value of ICRAC do not vary for different 2 and 3 respectively. These courses are being compared values of DO. Consequently, the lowered diffusion con- to the modified version (mod) of the base case scenario stant alone can not explain the drastic decrease of Ca2+ including the altered reaction rates and the altered bioRxiv preprint doi: https://doi.org/10.1101/306530; this version posted April 23, 2018. The copyright holder for this preprint (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. 11 diffusion constant (black, blue and red respectively). where the numbers of H in the exponent indicate how The differences between the basic reaction scheme and many ORAI1 dimers that interacted with ROS are part the modified version are small. of the respective CRAC channel. First, we exemplarily analyzed the temporal course of j all occurring Zi at default values. Figure 15A shows the To sum up, the analysis of the base case scenario leads total number of single CRAC channel subunits in the to the following conclusions: H2O2 scenario (black) compared to the base case scenario (blue). In addition, the two possible configurations of • ICRAC strongly depends on the ratio of STIM1 / ORAI1. Ca2+ influx is highest for STIM1 / ORAI1 CRAC channel subunits in the H2O2 scenario are shown in gray. We see that within the temporal course, the total & 2.5. numbers of subunit states stay constant in both scenar- • The dominant channel form of the steady state ios except for statistical fluctuations. In contrast, the value of Istat (at t = 300 s) depends on the pos- tot CRAC composition of Z1 in the H2O2 scenario changes within sibility of single CRAC channel subunits to disrupt 0 time: The number of WT subunits (Z1 ) increases, while hexameric channels (what we call stealing mech- H ” the number of ROS-inhibited subunits (Z1 ) decreases. anism“). Are the subunits not able to disrupt the The analysis of the tetramer and the hexamer CRAC fully open CRAC channels (core reactions, eqns. channel states shows similar features (figure 15B and C): (14)) the hexameric state is the most favored state. The total numbers of the respective channel configura- Including the stealing mechanism ( eq.(15)) leads tions stays constant in both scenarios, while the compo- to a lower number of hexamers and a higher num- sition of Ztot of the H O scenario changes: For small t 2+ i 2 2 ber of tetramers. The total amount of Ca influx a lot of total ROS-inhibited channels can be found. For is decreased in this case. larger t the number of total ROS-inhibited channels de- • Altering the diffusion rate of free ORAI1 dimers creases, while the numbers of mixed channel states and stat of homomeric WT channel states increase. does not result in significant changes of ICRAC . Comparing the total numbers of Zi of the two differ- • Altered reaction and diffusion rates according to ent scenarios we see the following: There are less single ˜ [29] (eq. (13) and DO = DO/1.7) do not signif- CRAC channel subunits, roughly equal tetramer CRAC icantly change the temporal course of ICRAC for channels and more hexamer CRAC channel states in the different ratios of STIM1 / ORAI1. base case scenario than in the H2O2 scenario. These differences as well as the dynamic changes in the compo- tot sition of Zi occur due to the differences in the reaction C. Stochastic analysis of the H2O2 Scenario rates between WT channels and partially or completely ˜ ˜ ROS-inhibited channels. While k1 and k2 are larger than In the next step we extended our model taking the k1 and k2, the rates for reactions between higher CRAC ˜ ˜ findings of an intramolecular locking of ORAI1 channels channel states k3 to k7 are smaller than for simple WT by H2O2 ([29]) into account. We introduce a new par- CRAC channel states k3 to k7 (cf. eq. (13) and table I). H ticle species O , which represents ORAI1 proteins that In the next step we varied these three parameters and reacted with ROS (cf. section II). Thus three parameters analyzed the respective temporal courses of ICRAC (figs are of major interest: 16A, 17A and 18A) and the steady state values of the • The ratio of the total amount of STIM1 proteins to different CRAC channel states Zi as well as of ICRAC the total amount of ORAI1 proteins (i. e. free O normalized to Otot (figs 16B, 17B and 18B). and OH as well as all ORAI1 proteins in whichever First, we analyzed the ratio Stot/Otot while the other CRAC channel configuration) Stot/Otot, two parameters were fixed at their respective default values (figure 16B). As in the base case scenario, the highest • the ratio of ROS-inhibited ORAI1 (free and bound Ca2+ influx is reached for Stot/Otot 2.5. Due to altered in CRAC channels) to the total amount of ORAI1 & reaction parameters in the H O scenario, less hexam- OH /Otot and 2 2 eric channels and more tetrameric and dimeric channels • the inhibition parameter δ (cf. eq. (12)). are formed. The absolute value of ICRAC is significantly smaller (≈ 35%) in the H O scenario since the Ca2+ As default values we choose Stot/Otot = 2, OH /Otot = 2 2 conductance of the ROS-inhibited ORAI1 channels (or 0.95 and δ = 0.1. channel parts) is just ten percent of the conductance of To count the different channel states we summed up all WT ORAI1 channels. different combinations occurring of each type of CRAC channel state, which means We compare the temporal course of ICRAC between the two scenarios for different ratios of Stot/Otot (figure 16A, 0 H tot tot tot tot tot tot Z1 = Z1 + Z1 , (25) S /O = 1: black, S /O = 2: blue, S /O = 3: 0 H 2H red). We see that in the base case scenario (solid lines) Z2 = Z2 + Z2 + Z2 and 0 H 2H 3H as well as in the H2O2 scenario (dashed lines) ICRAC Z3 = Z3 + Z3 + Z3 + Z3 reaches as stable state after the first five seconds. In bioRxiv preprint doi: https://doi.org/10.1101/306530; this version posted April 23, 2018. The copyright holder for this preprint (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. 12 A B C 0.2 0.25 0.18 0.18 0.16 0.16 0.2 0.14 0.14 0.12 0.12 0.15 0.1 0.1 0.08 0.08 0.1 0.06 0.06 0.04 0.05 0.04 0.02 0.02 0 0 0 0 50 100 150 200 250 300 0 50 100 150 200 250 300 0 50 100 150 200 250 300 t in s t in s t in s

Figure 15: A: Temporal courses of the number of CRAC channel subunits of the WT scenario (blue) and of the H2O2 scenario (black and gray) for t ∈ [0 s, 300 s], B: temporal courses of tetramer CRAC channel states of the WT scenario (blue) and of the H2O2 scenario (black and gray) for t ∈ [0 s, 300 s], C: temporal courses of hexamer CRAC channel states of the WT scenario (blue) and of the H2O2 scenario (black and gray) for t ∈ [0 s, 300 s]

A B value of OH /Otot aﬀects whether the value of Imix at I / Otot tot tot tot mix tot CRAC CRAC Z1 / O , Z2 / O , Z3 / O , ICRAC / O 0.25 0.25 Stot / Otot = 1 t = 300 s is the steady state value or not. Values of the t = 300 s Stot / Otot = 2 H tot 0.2 0.2 Stot / Otot = 3 case O /O = 0 (black) correspond to the base case H tot 0.15 0.15 scenario. O /O = 1 (green) correspond to all ORAI1

0.1 dimers interacted with ROS before building CRAC chan- 0.1 H tot 0.05 nels. O /O = 0.2 (blue) connotes that 20 % of ORAI1 0.05 0 dimers interacted with ROS before building CRAC chan- 0 0 1 2 3 4 5 0 50 100 150 200 250 300 Stot / Otot nels. In all three cases the value of ICRAC approached t in s a stable after about five to ten seconds. In contrast at H tot mix a ratio of O /O = 0.95, which means that 95 % of Figure 16: A: Temporal course of ICRAC (cf. eq(12)) for mix different ratios of Stot/Otot (base case scenario: solid lines, the available ORAI1 interacted with ROS, ICRAC rises H tot continuously within the 300 seconds. This is due to the H2O2 scenario: dashed lines) with fixed O /O = 0.95 and δ = 0.1, B values of the different CRAC channel states Zi and fact that a large amount of ORAI1 features the modified mix tot tot of ICRAC at t = 300 s depending on the ratio of S /O on- and off-rates of the H2O2 scenario. mix (base case scenario: solid lines, H2O2 scenario: dashed lines) Figure 17B shows the values of ICRAC at t = 300 s tot and of Zi normalized to O in dependence of the ratio H tot tot tot A B O /O (S /O = 2, δ = 0.1). The number of Z1 I / Otot tot tot tot mix tot CRAC Z1 / O , Z2 / O , Z3 / O , ICRAC / O 0.25 0.22 increases, whereas the number of Z3 decreases for higher OH / Otot = 0 0.2 H tot OH / Otot = 0.2 O /O . The number of Z stays at similar level within 0.18 t = 300 s 2 0.2 OH / Otot = 0.95 0.16 OH / Otot = 1 the whole interval. This behavior combined with a ten 0.15 0.14 mix 0.12 percent contribution of Zi to I (δ = 0.1) yields less 0.1 CRAC 0.1 mix 0.08 ICRAC the more ORAI1 dimers interacted with ROS (i. 0.06 0.05 H tot 0.04 e. the larger the ratio O /O ). In total the final value 0.02 mix H tot 0 0 0.2 0.4 0.6 0.8 1 of I for O /O = 1 is equal to ten percent of the 0 50 100 150 200 250 300 CRAC OH / Otot mix H tot t in s value of ICRAC for O /O = 0, which is as expected: With OH /Otot = 1 equation (12) simplifies to mix Figure 17: A: temporal course of ICRAC (cf. eq(12)) for differ- H tot tot tot mix H tot ent ratios of O /O with fixed S /O = 2 and δ = 0.1, B ICRAC (O /O = 1) = δ · (c1 · NZ1 + c2 · NZ2 + c3 · NZ3 ) , mix values of the different CRAC channel states Zi and of ICRAC (26) at t = 300 s depending on the ratio OH /Otot which is equal to multiplying equation (10) with δ. Finally the influence of δ for fixed ratios Stot/Otot = 2 H tot contrast to the base case scenario, in the H2O2 scenario and O /O = 0.95 is examined (figure 18B). In general mix mix this is not the final steady state value, since ICRAC rises the steady state value of ICRAC increases with increasing again after about 100 seconds. The first rise is due to δ, which is as expected, since the Ca2+ influx depends diffusion of the proteins to the PMJ and the first CRAC linear on δ (cf. equation 12). channel formation. The second rise is due to the mixture Comparing different values of δ the temporal courses mix of original and modified on- and off-rates and the high and absolute values of ICRAC differ much from each amount of ROS-inhibited ORAI1. other (figure 18A). Large δ leads to a faster increase of mix mix Analyzing the temporal course of ICRAC at different ICRAC (t), which is obvious from the data before (cf. fig- ratios of OH /Otot (cf. figure 17A) at the fixed ratio ures 15B and C): In the first seconds mainly total ROS- Stot/Otot = 2 and for δ = 0.1 shows, that the chosen inhibited CRAC channel states are formed. For large δ bioRxiv preprint doi: https://doi.org/10.1101/306530; this version posted April 23, 2018. The copyright holder for this preprint (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. 13

A B reaches a stable steady state value after less then I / Otot tot tot tot mix tot CRAC Z1 / O , Z2 / O , Z3 / O , ICRAC / O 0.2 0.22 δ = 0 30 seconds, or drops again after reaching a maxi- 0.18 0.2

¡ = 0.1 t = 300 s 0.16 0.18 mum value. = 0.5 0.14

¢ = 1 0.16 0.12 0.14 0.1 0.12 Simultaneously, one feature of the base case scenario re- 0.08 0.1 0.06 mains unchanged in the H2O2 scenario: If the number of 0.04 0.08 0.02 0.06 available STIM1 dimers is at least 2.5 times larger than 0 0.04 0 50 100 150 200 250 300 0 0.2 0.4 0.6 0.8 1 the total number of ORAI1 dimers, the highest values of

t in s £ mix ICRAC at t = 300 s are reached. mix Figure 18: A: temporal course of ICRAC (cf. eq(12)) for different values of δ with fixed Stot/Otot = 2 and OH /Otot = 0.95, mix IV. DISCUSSION B values of the different CRAC channels Zi and of ICRAC at t = 300 s depending on δ With the help of a reaction-diffusion model we analyzed the STIM1-ORAI1 stoichiometries during CRAC these states contribute strongly to Imix . CRAC channel formation, the influence of dynamic PM junc- For δ = 0 (black), which means CRAC channels in- tions and additionally focused on the effects of ROS including ROS preincubated ORAI1 dimers can not con- hibition. duct any Ca2+ into the cell, Imix rises within the total CRAC Within the base case scenario, which correlates to WT analyzed time interval (t ∈ [0 s, 300 s]). A similar behav- ORAI1 in experiments we find that the highest value ior is seen for small delta (δ = 0.1, blue). In the case that of the amplitude of I is reached when the ratio of channels including ROS preincubated ORAI1 contribute CRAC STIM1 / ORAI1 equals or is larger than 2 in the analyti- half as strong to Imix as the channels consisting of WT CRAC cal and numerical analysis and equals or is larger than 2.5 ORAI1 only (δ = 0.5, red) the temporal course of Imix CRAC in the stochastic analysis. The difference occurs, since in is almost stable after about 30 seconds. If the mixed and the stochastic case diffusion of the proteins is taken into the WT channels contribute in equal manner to Imix CRAC account and the minimal number of STIM1 does not suf- (δ = 1, green), the same rises to a maximum after 30 fice the free ORAI1 dimers, since they are possibly not seconds and than drops continuously again. at the same spot. These differences and especially these instabilities in Analyzing the numbers of active channels and the dis- the course of ICRAC arise, because the compositions tot tribution of those, it is found that the most frequently of the total numbers of CRAC channel states Zi are not stable either. Due to the different on- and off-rates occupied channel state is the hexameric channel state, as well as the different cooperativity parameters α followed by tetrameric channels for the core reaction sys- and β for WT ORAI1 and WT CRAC channel states tem. Taking into account a further reaction between and for ROS preincubated ORAI1 and mixed CRAC free ORAI1 dimers and fully open CRAC channel states (what we call stealing mechanism“), the most dominant channel states, the process of binding and unbinding of ” CRAC channel states stays dynamic. Therefore, also channel configuration is tetrameric followed by hexameric the predicted Ca2+ current, which is estimated by the states. In this case the total amount of ICRAC is lower numbers of different CRAC channel states is dynamic. than without stealing mechanism. The dimeric channel subunit plays a minor role in contributing to Ca2+ influx into the cell. This analysis indicates, that the most likely 2+ Summing up, the introduction of the new species, the channel configuration and with that the amount of Ca ORAI1 dimers which reacted with ROS before building influx can be controlled by the interplay between single CRAC channels, leads to changes of the predicted Ca2+ CRAC channel subunits and already established CRAC influx into the cell: channels. Analyzing variations of the diffusion constant of • As CRAC channels including ROS preincubated ORAI1 and changes in the reaction rate parameters (on- ORAI1 dimers contribute less to the Ca2+ cur- and off-rate as well as cooperativity parameters α and rent than simple WT CRAC channels, the total β) shows, that for small off-rates the tetramer CRAC mix ICRAC drops largely, when a lot of ROS preincu- channel state configuration is more often occupied than bated ORAI1 dimers are taken into account. the hexamer configuration in both cases, without and • Introducing the new species OH leads to dynamic with stealing mechanism. For larger off-rates the situ- binding and unbinding of the CRAC channel states ation changes: Considering the core reactions only, the mix hexamer configuration is more likely than the tetramer and therefore the temporal course of ICRAC differs from the course seen in the base case scenario. configuration. Considering the core reaction system with stealing mechanism, the tetramer configuration is still • Depending on the chosen set of parameters more often occupied, but the gap between the tetramer tot tot H tot mix (S /O , O /O and δ), ICRAC either con- and the hexamer configuration is much smaller. The in- tinuously rises within the examined 300 seconds, fluence of the on-rate cooperativity parameter α on the bioRxiv preprint doi: https://doi.org/10.1101/306530; this version posted April 23, 2018. The copyright holder for this preprint (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. 14 different channel states is negligible in the examined pa- tance, an intermediate tetrameric CRAC channel with rameter range. Large off-rate cooperativity parameter β medium conductance and a fully open (i. e. hexameric) leads to less hexamer CRAC channel states than small β CRAC channel state with full conductance. Our model and simultaneously more tetramer CRAC channel states. would lead to similar results if we assume the different Analytic and numeric analysis of the steady state value conductance states to be due to hexameric channels with of ICRAC in dependence of the on- and off-rates as well different number of bound STIM1 molecules. as the ratio of STIM1 / ORAI1 show, that increasing With the help of the introduced stealing mechanism“ ” both the unbinding cooperativity and the ratio STIM1 we can account for the dynamic reversible binding reac- stat / ORAI1 results in a slight decrease of ICRAC after the tions between free STIM1 and ORAI1 as seen in [22]. In highest value (for STIM1 / ORAI1 = 2) is reached. This contrast to these findings in our model the free proteins is in good agreement with the exerimental results of [28]. remain within the junctional region. In a further step the influence of ROS-inhibited chan- Previous models [18, 21, 22, 27] all assume tetramers nels was analyzed. Therefore the whole reaction-diffusion as highest ORAI1 complexes. All studies evolve the system was extended by a new type of species (the ROS best ratio of single STIM1 monomers to single ORAI1 preincubated ORAI1) and the formation of channel com- monomers to be roughly 2:1. Also in our model, which plexes was altered accordingly. Analysis show that still is adapted to tetrameric and hexameric CRAC channels, for the ratio of STIM1 / ORAI1 being equal or larger the ratio of STIM1 / ORAI1 must be at least two or 2+ than 2.5 the largest Ca influx is observed. In this case larger to gain highest Ca2+ influx. the maximum value of I , which is only 35% of the CRAC While the models of [21] and [27] assume a static area maximum value of the base case scenario, is reached. The as PMJ region, we allow a dynamic grow of the PMJ re- introduced inhibition parameter δ influences I (t) CRAC gions as seen in the cluster analysis of TIRF experiments. for given ratios STIM1 / ORAI1 and OH /Otot. For large amounts of OH with respect to the total amount In contrast to the previous models we can distinguish of ORAI1, ICRAC drops drastically. between the reaction-diffusion analysis of WT ORAI1 Alansary et al. [29] analyzed the influence of ROS on with STIM1 and the reaction-diffusion analysis of ROS- the amplitude of Ca2+ influx experimentally. In accor- inhibited ORAI1 with STIM1. We can tune the quan- dance to these experiments our analysis shows, that the tity of inhibited proteins and therefore can predict the magnitude of Ca2+ influx in dependence of the ratio of drop in ICRAC for preincubated ORAI1 is not only due to alterations in the diffusion constant of ORAI1 and in preincubated ORAI1 to the total amount of ORAI1. the ORAI1-ORAI1 and the ORAI1-STIM1 interaction, In summary the described model opens the possibility but that there is another mechanism needed to explain to predict Ca2+ influx into cells while modifying reaction the strong decrease of ICRAC . In [29] it is found that and diffusion parameters, the amount of ROS-inhibited the interaction of two transmembrane domains lock the ORAI1 proteins and the predefinition of PMJ regions. CRAC channel when preincubated with ROS. The intro- So far, assessing and tuning these parameters experimen- duction of the new channels into the model to account for tally is hard. Therefore our model can reveal new insights this locking shows, that with this modification the drastic in the complex and dynamic stoichiometry of STIM1 and decrease of ICRAC can be explained, while only changing ORAI1 proteins during CRAC channel formation. the reaction and diffusion parameters according to the Addressing the Orai-STIM interaction during CRAC changes found in the experiment does not yield such a channel formation may also rise the question of how dif- large decrease in ICRAC . ferent STIM and Orai homologs (i. e. STIM2, ORAI2 Recent experiments, which analyze the ORAI1 sto- and ORAI3) may influence the stoichiometry of the ichiometry of CRAC channels demonstrate that fully CRAC channels and the Ca2+ influx. For example re- functional ORAI channels exist as hexamers, in accor- cent studies [36] find that the CRAC channels consisting cance with the crystal structure [15, 17, 33]. Other ex- of a mixture of ORAI1 and Orai3 show redox insensi- periments indicate that CRAC channels can occur as a tivity. Further extensions of a model according to these a mixture of hexameric, tetrameric and dimeric chan- homologs may offer new insights into the complex anal- nel complexes or as hexamers with different conducting ysis of CRAC channel formation. states [16, 34]. A very recent report provides evidence for the existence of different conductance states of hexameric channels due to the ability of STIM1 dimers to crosslink neighbouring ORAI1 hexamers to provide a more efficient Author Contributions activation for a given number of STIM1 molecules [35]. Until now, there has been no model taking these new findings into account. We therefore close this gap and BS performed calculations, performed the experi- present a reaction-diffusion model in which we include ments, and analyzed the data. HR supervised and de- three types of channels and therefore three types of con- signed the theoretical aspects of the research, BAN ad- ducting states: A CRAC channel subunit with only one vised on biological aspects and supervised the experi- ORAI1 dimer bound to STIM1 proteins with low conduc- ments. BS, BAN, IB and HR wrote the manuscript. bioRxiv preprint doi: https://doi.org/10.1101/306530; this version posted April 23, 2018. The copyright holder for this preprint (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. 15

Acknowledgments search Foundation (DFG) within the Collaborative Re- search Center SFB 1027, projects A3 to HR and C4 to We thank Dalia Alansary for the help with the experi- BN and IB. mental work. This work was funded by the German Re-

[1] Berridge M J, Lipp P and Bootman M D, The versatility channels, Molecular Biology of Cell, 27(16):2542-2553 and universality of calcium signalling, Nature Reviews (2016) Molecular Cell Biology, 1, 11-21 (2000) [17] Cai X, Zhou Y, Nwokonko R M, Loktionova N A, [2] Clapham, David E., Calcium Signaling, Cell, 131, 6, Wnag X, Xin P, Trebak M, Wang Y and Gill D L, 1047-1058 (2007) The Orai1 Store-operated Calcium Channel Functions [3] Carafoli E, Calcium signaling: A tale for all seasons, as a Hexamer, The Journal of Biological Chemistry, PNAS, 99, 3, 1114-1122 (2002) 291(50):25764-25775 (2016) [4] Falcke M, Reading the patterns in living cells — the [18] Hoover P J and Lewis R S, Stoichiometric require- physics of ca2+ signaling, Advances in Physics, 53, 3, ments for trapping and gating of Ca2+ release-activated 255-440 (2004) Ca2+ (CRAC) channels by stromal interaction molecule [5] Lewis R S, Calcium Signaling Mechanisms in T Lympho- 1 (STIM1), Proc. Natl. Acad. Sci. U.S.A., 108, 32, 13299- cytes, Annu. Rev. Immunol. 19, 497-521 (2001) 13304 (2011) [6] Parekh A B and Putney Jr. J W, Store-Operated Cal- [19] Scrimgeour N, Litjens T, Ma L, Barritt G J and Rychkov cium Channels, Physiological Reviews, 85, 2, 757-810 G Y, Properties of Orai1 mediated store-operated cur- (2005) rent depend on the expression levels of STIM1 and Orai1 [7] Hoth M and Penner R, Depletion of intracellular calcium proteins, The Journal of Physiology, 587, 12, 2903-0918 stores activates a calcium current in mast cells, Nature, (2009) 355, 6358, 353-356, (1992) [20] Bogeski I, Kummerow C, Al-Ansary D, Schwarz E, [8] Muik M, Frischauf I, Derler I, Fahrner M, Bergsman J, Koehler R, Kozai D, Takahashi N, Peinelt C, Griesemer Eder P, Schindl R, Hesch C, Polzinger B, Fritsch R, Kahr D, Bozem M, Mori Y, Hoth M and Niemeyer B A, Dif- H, Madl J, Gruber H, Groschner K and Romanin C, Dy- ferential Redox Regulation of ORAI Ion Channels: A namic Coupling of the Putative Coiled-coil Domain of Mechanism to Tune Cellular Calcium Signaling, Science ORAI1 with STIM1 Mediates ORAI1 Channel Activa- Signaling, 3, 115 (2010) tion, The Journal of Biological Chemestry, 283, 12, 8014- [21] Peglow M, Niemeyer B A, Hoth M and Rieger H, Inter- 8022 (2008) play of channels, pumps and organelle location in cal- [9] Luik R M, Wang B, Prakriya M, Wu M M and Lewis R S, cium microdomain formation, New Journal of Physics, Oligomerization of STIM1 couples ER calcium depletion 15, 27pp (2013) to CRAC channel activation, Nature, 454(7203), 538-542 [22] Wu M M, Covington E D and Lewis R S, Single-molecule (2008) analysis of diffusion and trapping of STIM1 and ORAI1 [10] Derler I, Jardin I and Romanin C, Molecular mechanisms at endoplasmatic reticulum-plasma membrane junctions, of STIM/Orai communication, Am J Physiol Cell Phys- Molecular Biology of the Cell, 25(22):3672-85 (2014) iol, 310, C643-C662 (2016) [23] Shen W-W, Frieden Ma and Demaurex N, Remodeling [11] Wu M M, Buchanan JA, Luik R and Lewis R S, Ca2+ of the endoplasmic retriculum during store-operated cal- store depletion causes STIM1 to accumulate in ER re- cium entry, Biology of the Cell, 103 (8), 365-380 (2011) gions closely associated with the plasma membrane, The [24] SaücS, Bulla M, Nunes P, Orci L, Marchetti A, Antigny Journal of Cell Biology, 174, 6, 803-813 (2006) F, Bernheim L, Cosson P, Frieden M and Demaurex N, [12] Liou J, Fivaz M, Inoue T and Meyer T, Live-cell imaging STIML traps and gates Orai channesl without remod- reveals sequential oligomerization and local plasma mem- eling the cortical ER, THe company of Biologists, 128, brane targeting of stromal interaction molecule 1 after 1568-1579 (2015) Ca2+ store depletion, PNAS, 104, 22, 9301-9306 (2007) [25] Wu M M, Buchanan JA, Luik R M, and Lewis R S, Ca2+ [13] Park C Y, Hoover P J, Mullins F M, Bachhawat P, Cov- store depletion causes STIM1 to accumulate in ER re- ington E D, Raunser S, Walz T, Garcia K C, Dolmetsch R gions closely associated with the plasma membrane, The E and Lewis R S, STIM1 Clusters and Activates CRAC Journal of Cell Biology, 174, 6, 803-813 (2006) Channels via Direct Binding of a Cytosolic Domain to [26] Malli R, Naghdi S, Romanin C and Graier W F, Cy- Orai1, Cell, 136, 876-890 (2009) tosolic Ca2+ prevents the subplasmalemmal clustering of [14] Yuan J P, Zeng W, Dorwart M R, Choi Y-J, Worley P F STIM1: an intrinsic mechanism to avoid Ca2+ overload, and Muallem S, SOAR and the polybasic STIM1 domains Journal of Cell Science, 121(019), 3133-3139 (2008) gate and regulate Orai channels, Nature Cell Biology, 11, [27] Melunis J, Hershberg U, A spatially heterogenous Gille- 3, 337-343 (2009) spie algorithm modeling framework that enables individ- [15] Yen M, Lokteva L A and Lewis R S, Functional Analysis ual molecule history and tracking, Engineering Applica- of Orai1 concatemers Supports a Hexameric Stoichiom- tions of Artificial Intelligence, 62, 304 - 311 (2017) etry for the CRAC Channel, Biophysical Journal, 111, [28] Kilch T, Alansary D, Peglow M,DörrK, Rychkov G, 1897-1907 (2016) Rieger H, Peinelt C and Niemeyer B A, Mutations of [16] Li P, Miao Y, Dani A and Vig M, α-SNAP regulates dy- the Ca2+-sensing Stromal Interaction Molecule STIM1 namic, on-site assembly and calcium selectivity of Orai1 regulate Ca2+ influx by altered oligomerization of STIM1 bioRxiv preprint doi: https://doi.org/10.1101/306530; this version posted April 23, 2018. The copyright holder for this preprint (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. 16

and by destabilization of the Ca2+ channel Orai1 J. Biol. ture of the calcium release-activated calcium channel Chem. 288, 1653 (2013) Orai, Science, 338, 1308-1313 (2012) [29] Alansary D, Schmidt B, DörrK, Bogeski I, Rieger H, [34] Dynes J L, Amcheslavsky A and Cahalan M D, Genet- Kless A and Niemeyer B A, Thiol dependent intramolecu- ically targeted single-channel optical recording reveals lar locking of Orai1 channels, Scientific Reports, 6, 33347 multiple Orai1 gating states and oscillations in calcium (2016) influx, PNAS 113 2, 440-445 (2016) [30] Zhou Y, Wang X, Wang X, Loktionova N A, Cai X, [35] Zhou Y, Nwokonko R M, Cai X, Loktionova N A, Ab- Nwokonko R M, Vrana E, Wang Y, Rothberg B S and Gill dulqadir R, Xin P, Niemeyer B A, Wang Y, Trebak M D L, STIM1 dimers undergo unimolecular coupling to ac- and Gill D, Cross-linking of Orai1 channels by STIM pro- tivate Orai1 channels, Nature Communications, 6:8395 teins, PNAS, 115 15, E3398–E3407 (2018) 82015) [36] Saul S, Gibhardt C S, Schmidt B, Lis A, Pasieka B, Con- [31] Gillespie D T, A General Method for Numerically Simu- rad D, Jung P, Gaupp R, Wonnenberg B, Diler E, Stanisz lating the Stochastic Time Evolution of Coupled Chemi- H, Vogt T, Schwarz E C, Bischoff M, Herrmann M, Tsch- cal Reactions, Journal of Computational Physics 22, 403- ernig T, Kappl R, Rieger H, Niemeyer B A and Bogeski I, 434 (1976) A calcium-redox feedback loop controls human monocyte [32] Gibson M A and Bruck J, Efficient Exact Stochastic immune responses: The role of ORAI Ca2+ channels, Sci- Simulation of Chemical Systems with Many Species and ence Signaling, 9, 418 (2016) Many Channels, J. Phys. Chem. A, 104, 1876-1889 (1999) [33] Hou X, Pedi L, Diver M M, and Long S B,Crystal struc-