THE ROLE OF IP3R CLUSTERING IN Ca 2 + SIGNALING

Transcription

1 THE ROLE OF IP3R CLUSTERING IN Ca 2 + SIGNALING ALEXANDER SKUPIN alexander.skupinbmi.de MARTIN FALCKE falckebmi. de Max-Delbriick-Center for Molecular Medince, Departement of Mathematical Cell Physiology, Robert-Rossle-Str. 10, Berlin, Germany Ca 2 + is the most important second messenger controlling a variety of intracellular processes by oscillations of the cytosolic Ca 2 + concentration. These oscillations occur by Ca 2 + release from the endoplasmic reticulum (ER) into the cytosol through channels and the re-uptake of Ca 2 + into the ER by pumps. A common channel type present in many cell types is the inositol trisphosphate receptor (IP3R), which is activated by IP3 and Ca 2 + itself leading to Ca2+ induced Ca 2 + release (CICR). We have shown in an experimental study [15], that Ca 2 + oscillations are sequences of random spikes that occur by wave nucleation. We use here our recently developed model for Ca 2 + dynamics in 3 dimension to illuminate the role of IP3R clustering within spatial extended systems. Keywords: cell signaling; calcium oscillations; modeling; clustering 1. Introduction Calcium is a ubiquitous messenger used by cells to control a variety of different physiological processes like muscle contraction, gene expression or secretion. Most importantly Ca2+ translates external stimuli into intracellular responses by a transient increase of the cytosolic Ca2+ concentration [2, 4, 7, 18J, which can act on distinct pathways or protein functions in dependence on their durations, strength and expressed components. The increase of cytosolic Ca 2 + is often caused by Ca 2 + release from internal stores, especially from the endoplasmic reticulum (ER) and the sarcoplasmic reticulum by release channels. The nonlinear properties of these channels combined with other complex control mechanisms within cells, as e.g. buffer reactions and pumps, lead to a rich spectrum of different Ca2+ signals including traveling waves and global oscillations [7J. Figure 1 exhibits an example. A versatilely used pathway is the inositol 1,4,5-trisphosphate (IP3) pathway leading to intracellular Ca2+ responses. If a plasma membrane receptor detects a signal molecule, as e.g. serotonin, a phospholipase C (PLC) is activated by a G protein and produces IP3 at the cell membrane. IP3 diffuses into the cytosol where it can be bound by receptor channels (IP3R) on the membrane of the ER. If IP3 and Ca 2 + are bound to an 1P3R, it can open and Ca 2 + will diffuse into the cytosol. The released Ca2+ is pumped back into the ER by Sacro-Endoplasmic Reticulum 15

2 16 A. Skupin & M. Faleke A 'JJ\lliJWWJ <l <l u.. B ]WllWJ :: t : f.. : 40 J 30 J : : : : u t (5) t (5) Fig. 1. Ca 2 + oscillations in experiment and simulation. Upper panels show the fluorescent signals t:.f = F / Fo as the ratio of the measured signal F divided by the initial signal strength Fo visualizing the cytosolic Ca 2 + concentration. Lower panels exhibit the inter spike intervals (ISIs), i.e. the time between two successive fluorescent maxima. A: Experimentally measured spontaneous Ca 2 + oscillations of a PLA cell (for more details see [15].) B: Simulated Ca 2 + oscillation of a cell with 16 randomly distributed channel clusters consisting of a random number of channels between 3 and 15 each. The Ca2+ base level is [Ca 2 +]o = 35 nm and [IP3]= 80 nm. Calcium ATPases (SERCAs) pumps. The open probability of IP 3 Rs depends on the IP 3 concentration and the calcium concentration in the cytosol [7, 11, 17]. It increases with increasing IP 3 concentration. It is low for low calcium concentration, increases with increasing Ca2+ and finally decreases again for even higher concentrations. This behavior leads to Calcium Induced Calcium Release (CICR) as Ca2+ released by one channel diffuses in the cytosol and increases the open probability of adjacent channels. Ca2+ terminates its own release by inhibiting the channels at high Ca2+ concentrations. The localized release, Ca 2 + binding to buffers and removal of Ca2+ by pumps cause huge concentration gradients close to open clusters. IP 3 Rs are grouped into randomly distributed channel clusters on the ER membrane containing 1-40 channels and separated by 1-7 Il-m. This spatial inhomogeneity combined with the SERCA pumps and Ca2+ buffers causes huge concentration differences close to open clusters. Ca2+ oscillations have been intensively studied in both experiments and theory. Most traditional models neglect concentration gradients, and thus describe Ca2+ dynamics by ordinary differential equations [13]. But we have shown recently in an experimental work [15], that intracellular Ca 2 + oscillations using IP 3 receptors are sequences of random spikes initiated by the local stochastic behavior of ion channels transformed into a global Ca 2 + signal by wave nucleation. A Ca2+ signal originates from the opening of a single channel, called "blip", which might cause opening of other channels within the cluster yielding in an elemental event called "puff" [3,5,7-9]. A puff can activate neighboring clusters and if a supercritical number of puffs arises, Ca2+ release spreads through the whole cell. This nucleation process carries the fluctuations of the state of individual channels

3 The Role of [P3R Clustering in Ca H Signaling 17 up to the cell level. The question is now, why cells build distinct channel cluster and do not use a diffuse arrangement of channels or work with one huge cluster. While the influence of IP3R clustering has been studied on the level of a single cluster [10] and in two dimensions with a reduced model for the IP3R [14], an investigation of this issue in three dimensions and the above depicted hierarchical picture still lacks. In order to close this gap we use here our recently developed method of modeling Ca2+ dynamics in 3d [16] to explore the role of IP3R clustering in a bottom up approach. 2. Methods and Results 2.1. [PaR Model A commonly used IP3R model is the DeYoung-Keizer (DK) model. The DK model assumes each IP3R to consist of four identical subunits having 3 binding sites each. One for IP3, one for Ca 2 + activating the subunit and another one for Ca2+, which inhibits the subunit. Since each binding site can be free or occupied a single subunit has 2 3 different states X ijk and 12 possible transitions, which can be visualized on a cube as shown in Fig. 2A. The first index of Xijk specifies IP3 binding and is 1 if IP3 is bound and 0 otherwise. Analogously the second index indicates Ca2+ binding to the activating site and the last one corresponds to Ca 2 + binding to the dominant inhibiting site. A subunit is active in the state X 110 only and a channel will open if at least three of the four subunits are activated. The transitions between the states Xijk occur by stochastic binding and dissociation of signaling molecules to the corresponding binding sites. The rates for binding depend on the particular rate constants ai and on the Ca2+ concentration C and the IP3 concentration I, respectively as shown in Fig. 2A, whereas dissociation occurs with constant rates bi. The binding of Ca 2 + to the activating as well as to B ER \ I cytosol.channe, cell Fig. 2. A: Scheme of the DeYoung-Keizer model for a single subunit. A subunit is active, if 1P3 is bound and Ca 2 + is only bound to the activating site, i.e. in state X110. A channel opens if at least 3 of its 4 subunits are active. See text for more details and Table 1 for values of rates bi and rate constants ai. B: Sketch of our two compartment model. We overlay the two compartments, i.e. each point in space within our spherical cell corresponds to the ER and the cytosol simultaneously.

4 18 A. Skupin fj M. Faleke Table 1. Rates of the DK model used within simulations. al bl a2 b2 a3 b3 a4 b4 a5 b5 20 (J.tMs)-1 20 s (J.tMS) s (J.tMs)-l 20 s-l (J.tMs)-l 0.1 S-l 10 (J.tMs) s-l rate co.nstant for 1P3 binding with no inhibiting Ca 2 + bound rate of 1P3 dissociation with no inhibiting Ca 2 + bound rate constant for Ca2+ binding to the inhibiting site with 1P3 bound rate of Ca 2 + dissociation from the inhibiting site with 1P3 bound rate constant for 1P3 binding with inhibiting Ca 2 + bound rate of 1P3 dissociation with inhibiting Ca 2 + bound rate constant for Ca 2 + binding to the inhibiting site with no IP3 bound rate of Ca2+ dissociation from the inhibiting site with no IP3 bound rate constant for Ca 2 + binding to the activating site rate of Ca 2 + dissociation to the activating site the inhibiting site leads to a bell shaped open probability in dependence on Ca 2 + representing a key element of CICR CellModel We assume the cell is a sphere. The ER is a tubular network spreading throughout the whole cell. Therefore we describe the cell by a two-compartment model as sketched in Fig. 2B. The two compartments interact through open channels, the leak flux and by SERCA pumps. Opening and closing of channels, the Ca2+ pump flux into the ER and the reaction of Ca2+ with buffers determines the concentration dynamics in the cytosol and the ER, i.e. we have two reaction diffusion systems (RDSs), each for one compartment, which are coupled by the Ca 2 + fluxes. However, we are only interested in the cytosolic Ca2+ dynamics and need the concentration within the ER to determine the channel fluxes. Thus we use the single channel approximation derived in [1] for the flux J of an open channel 8F D as / DJtDcO'e - tanh (as' / DJtDcO'e) _ J= "DC V c E V c E (E-Ca2+), (1) 1 + F. /DE+DcO' E V DcDE e which depends on the diffusion coefficients of Ca2+ within the cytosol Dc and the ER DE, the channel radius a, the flux constant O'e and on the average concentrations within the compartments. For channel clusters with more than one open channel, we scale the radius by the cubic root of the number of open channels N open, i.e. a = as \I N open, taking the increase of the source volume due to channel opening into account. With Eq. (1) we can neglect the spatially resolved dynamics within the ER. In the following we will take one mobile [B] and one immobile [Bi] (with DBi = 0) buffer into account yielding in a system of three coupled PDEs. In order to derive an analytical solution we linearize the PDEs around the resting state where no channels are open and all three components (Ca 2 +, mobile and immobile buffer) are homogeneously distributed and in equilibrium. After rescaling time t ---'> tit and space r ---'> rll with the diffusion time T = (k+[b]t)-l and length L =

5 The Role of IP3R Clustering in Ca 2 + Signaling 19 J DCa(k+(BJT )-1 the resulting system in dimensionless units defined in Table 2 takes the form (16] (2a) (2b) (2c) where the first equation describes the dimensionless free Ca 2 + concentration and the other two correspond to the scaled free mobile and immobile buffer concentrations, resp. The first term in Eq. (2a) corresponds to diffusion of Ca2+, whereas the next four terms describe the reactions with buffers and the coupling with the ER by the pumps and the leak flux (O' p and 0'1 respectively). The last term specifies release of Ca2+ by channels, which we assume to be delta sources. Nevertheless we incorporate their spatial character by using Eq. (1) for the scaled flux o'. The two remaining equations in (2) describe the buffers dynamics. The dimensionless resting conditions are given by eo = (Ca 2 +Jo/K, bo = (eo + 1)-1 and bi,o = (eo;;; + 1)-1 depending on the buffer dissociation constant K of the mobile buffer and the ratio ;;; of the dissociation constants of the two buffer types. For the linear system of PDEs (2) we derived an analytical solution by means of coupled Green's functions for a spherical cell with noflux boundary condition at the cell membrane (16). The solution for the concentration dynamics can now be used as a natural environment for localized IP 3 R clusters to study the interplay of their nonlinear stochastic opening behavior and the feedback on Ca2+. Therefore we couple the global deterministic solution to the local stochastic channel behavior by a Gillespie algorithm described in (12J. Table 2. Definition of dimensionless parameters. c b bi e d T i T ER CTi CT K, K,E [Ca2+J/K [Bl/[B1T [Bi]/[BilT [E]/KE DB/Dca [BJT/K [BiJT/K [BdTki /[BJTk- P;lk+[B1T J"'k+[B]T 2FK K/Ki K/KE dimensionless free Ca 2 + concentration dimensionless free mobile buffer concentration dimensionless free immobile buffer concentration dimensionless free Ca 2 + concentration within the ER ratio of the diffusion coefficients time separation of the mobile buffer time separation of the immobile buffer ratio of buffer influence scaled fluxes of CTI and CT p scaled channel flux ratio of the dissociation constants of the mobile and immobile buffer ratio of the dissociation constants of the cytosolic and lumenal buffer

6 20 A. Skupin fj M. Falcke B N=2 C N=32 0 z '" c d:.- il I illlllllllill : fiji" ",[.:, 1 o: 1: : : : : J t (5) t (5) Fig. 3. A: Sketch of the spatial arrangement for the clustering analysis. Clusters are put on a regular grid around the origin. Band C : Representative examples of the channel dynamics. Upper panels show number of open channels and the lower panels the amount of inhibited subunits for a cell with 128 channels in total, which are distributed on N clusters Results For the following investigation we use the parameters of the DK model listed in Table 1 and standard parameters for the RDS listed in Table 3 reflecting typical properties of eukaryotic cells. Our results do not depend qualitatively on this explicit choice, but can differ in a quantitative manner for different parameters. To study the influence of 1P3R clustering we vary the N in the cell arranged on a regular grid with a grid constant d as depicted in Fig. 3A. The grid constant influences the spatial coupling between the clusters as the pumps will decrease the Ca2+ signal at adjacent clusters with increasing separation d and thus decrease the probability for a global event. Figure 3B and C exhibits two representative examples of the cooperative channel behavior for a cell with 128 channels distributed equally on N clusters separated R Table fj,m 8nm 220 fj,m2/s 70 fj,m 2 /s 95 fj,m 2 /s 50 nm 90 nm 25 fj,m 600 (fj,ms)-l 100 s-l 30 fj,m 600 (fj,ms)-l 100 s-l 86 s-l s-l i'::j 0.01 s-l Standard values of parameters used for simulations. cell radius channel radius diffusion coefficient of cytosolic Ca 2 + diffusion coefficient of lumenal Ca 2 + diffusion coefficient of mobile buffer cytosolic Ca 2 + base level IP3 concentration total mobile buffer concentration on rate of the mobile buffer dissociation rate of the mobile buffer total immobile buffer concentration on rate of the immobile buffer dissociation rate of the immobile buffer pump rate channel flux constant leak flux constant implicitly given by Pp and [Ca2+]o

7 The Role of 1P3R Clustering in Ca2+ Signaling 21 by d = 1 J.Lm. The upper panels show the number of open channels N open and the lower panels depict the degree of inhibition R inh, which is zero if no subunit is inhibited and one for total inhibition. We observe for two clusters each consisting of 64 channels a relatively regular spiking caused by the self amplifying character of CICR. If one channel of a cluster opens, it will open other channels of the cluster, too, leading to an increase of the cytosolic Ca 2 + concentration which will activate the second cluster. The resulting high [Ca2+] leads to a almost complete inhibition of channels terminating the spike. If we distribute the 128 channels on 32 clusters, i.e. each cluster has 4 channels, the amplitude and frequency decreases, since the spatial coupling is decreased. Thus we observe a higher uncoordinated background activity, i.e. opening events of very few channels, that leads rarely to global events as the puffs are too small to nucleate a global wave. To characterize such oscillations we will determine in the following the mean amplitude and the mean period Tav by averaging over the ISIs, here given by the time between to successive maxima of open channels. Cells can control the number of IP3R and the degree of clustering. Thus, we are interested in how cells can tune spiking with these two variables. We compare a stimulated cell with the above mentioned high [IP3] and a cell with a lower IP3 concentration. It turned out that cells with high [IP3] and a sufficiently high number of channels exhibit a saturated behavior as can be seen in fig. 4. Here the squares show T av and the number of open channels for a cell with a fixed number of channels Nch = 320, which are distributed equally on N clusters separated by d = 1 J.Lm. Both, T av and the amplitude exhibit only small fluctuations indicating the strong coupling between the clusters. This behavior changes if we switch to low IP3 concentrations as can be seen by the dots in fig. 4. Here each cluster contains 100 channels, i.e. by increasing the we increase the number of channels. The amplitudes increase by increasing the. Thereby Tav decreases from about 50 s for 2 clusters to about 20 s for 15 clusters. That is A 60 B f, OJ 60 "0.-2 > + C. f i l-'" E 30 IjJ IjJ 30 ill i IjJ! + + f t Fig. 4. Comparison of a cell with [IP3]=50 nm and a fixed number of channels distributed equally on clusters (squares) with a cell with [IP3 ]=10 nm, where each cluster consists of 100 channels (dots). A: Dependence of the mean period Tav on the. B: Averaged maximal amplitude of the channel oscillations. (All error bars denote SEM.)

8 22 A. Skupin E9 M. Faleke in the range of the mean period of the saturated cell and is due to the increased nucleation probability by the increased number of channels. For even more clusters, T av increases again since inhibition obstructs the more regular behavior. That is a consequence of the increased amplitudes shown in Fig. 4B for higher amounts of clusters and channels leading to higher Ca2+ concentrations. We observe a steep increase of the amplitudes up to the level of the saturated cell of about 45 channels. From that point on a further expression of channels is less sufficient as the amplitude increases slower and exhibits larger variations. Interestingly this cross over point of the amplitudes coincides with the fastest oscillation period in 4A. To analyze the effect of channel distribution further we use a grid with a grid constant d = 1.5 m and less channels to avoid a saturated behavior. Figure 5 exhibits Tav and the amplitude for two different cell setups. The dots correspond to Neh= 128 and the squares mark Nch= 256. The mean periods in Fig. 5A exhibit a pronounced change for less than ten channels per cluster. Another property is shown by the amplitudes. Althol}gh the squares have the double amount of channels compared to the dots, the average maximal amplitude is only slightly increased caused by self inhibition. These results suggest that cells with 128 channels have a larger dynamic range for frequency coding. In addition T av exhibits a more pronounced change than the amplitude and could be used for a robust control mechanism. We now return to the question about diffusive arranged channels. In a third approach to the analysis of the cluster distribution, we preserve the channel density by scaling the grid constant with the cubic root of the number of channels per cluster, i.e. d = dl (Nch/Ncl)1/3, where d 1 denotes the minimal grid constant for one channel per cluster. In Fig. 6 we compare two cells with the same [IP3] and Ca2+ base level concentration but with two different number of channels Nch and minimal grid constants d1. Both setups, the one with Nch = 128 and dp)= 1 m denoted by the squares and the setup with Nch = 256 and d2) = 1.5 m shown by the dots, exhibit a minimum in Tav' as shown in Fig. 6A. That means, cells with a more A 160 B 40 IDID IjJ ifi I!J t "0 '" 80 f '. -2 > a. 20 f-'" + E + 40 ID 10 ID [!][!J Fig. 5. Influence of clustering with a conserved number of channels (triangles denote N c h=128 and squares Nch = 256, i.e. each square has doubled amount of channels as the corresponding dots) and a fixed grid constant d = 1.5!-lm. A: Mean period Tav against the. B: Amplitude dependence for two different total number of channels within the cell.

9 The Role of IPa R Clustering in Ca 2 + Signaling 23 A 60 B CD " f t 1. ID Q. l- E rn ill '" 10 I!l Fig. 6. Influence of clustering with a conserved channel density. A: The comparison of T av for a cell with Nch = 128 channels and dl =1 m (squares) and a cell with Nch = 256 channels and dl =1.5 m (dots) demonstrate that the minimal Tav is not a simple effect of the density. B: The amplitudes exhibit a constant region and show, that diffusively arranged channels do not create global oscillations for physiological regions, as the period increases and the amplitude goes to zero for increasing. diffusive arrangement of channels can decrease T av and increase the amplitude by clustering of IP3Rs. That is due to the existence of an optimal coupling strength for systems with discrete excitable stochastic elements [14]. Once the minimal Tav is reached, further clustering results again in slower oscillations, since inhibition blocks the channel clusters. Further we see that oscillations with a lower channel density (dots) are slower compared to those with a higher density (squares). The two minima of T av for the two setups occur at distinct cluster numbers and T av values, but in both minima each cluster has 16 channels. We observe for both realizations a plateau of the amplitudes for a relatively large range from about 8 to 23 clusters. In this range the cell with the larger amount of channels exhibits a nearly doubled average amplitude, whereas the amplitude is only slightly higher for few clusters due to inhibition and goes to zero for a diffusive arrangement of channels at larger cluster numbers. Interestingly the minimal periods are in this range of constant amplitudes what might indicate a stabilized regime. 3. Discussion In this paper we used our recently developed method for modeling Ca2+ dynamics in three dimensions to investigate the role of IP3R clustering. We found that spike amplitudes and lsi depend on the degree of clustering, cluster configuration and. We found optimal configurations and numbers of channels with respect to a variety of properties. Reliable fast spiking can be obtained with about 10 channels per clusters and cluster densities of about 0.01 {tm- 3. That would wean numbers of channels per cell which are about one order of magnitude smaller than those estimated from IP3 binding experiments (see [9] and references therein). Remarkably, expressing move IP3 or increasing the degree of clustering does not improve

10 24 A. Skupin f3 M. Faleke regularity or accelerate spiking. It is currently believed that Ca2+ oscillations use frequency encoding. Small channel numbers appear more suitable for that purpose than large ones. Clustering of channels consistently improved spiking with respect to regularity of ISIs and amplitudes of spikes. If we assume that the ability to spike and to use frequency coding is the purpose of the Ca2+ signaling pathway, our results indicate that it can be achieved with surprisingly small channel numbers and if channels cluster. References [1] Bentele, K. and Falcke, M., Quasi-Steady Approximation for Ion Channel Currents, Biophys. J., 93: , [2] Berridge, M., Inositol trisphosphate and calcium signalling, Nature, 361: , [3] Berridge, M., Elementary and global aspects of calcium signalling, J. Physiol., 499: , [4] Berridge, M., Lipp, P. and Bootman, M., The versatility and universality of calcium signalling, Nature Rev. Mol. Cell Biol., ,2000. [5] Bootman, M., Niggli, E., Berridge, M., and Lipp, P., Imaging the hierarchical Ca 2 + signalling in HeLa cells, J. Physiol, 499: , [6] Falcke, M., On the role of stochastic channel behavior in intracellular Ca 2 + dynamics, Biophys. J., 84:42-56, [7] Falcke, M., Reading the patterns in living cells - the Physics of Ca2+ signaling, Advances in Physics, 53: , [8] Marchant, J., Callamaras, N., and Parker, 1., Initiation of IP3-mediated Ca 2 + waves in Xenopus oocytes, The EMBO J., 18: , [9] Marchant, J. and Parker, 1., Role of elementary Ca 2 + puffs in generating repetitive Ca2+ oscillations, The EMBO Journal, 20:65-76, 200l. [10] Meinhold, L. and Schmansky-Geier, L., Analytical description of stochastic calcium periodicity PRE, 66: (R), [11] Putney, J. and Bird, G., The inositolphosphate-calcium signaling system in nonexcitable cells, Endocrine Reviews, 14: , [12] Rudiger, S. et al., Hybrid Stochastic and Deterministic Simulations of Calcium Blips, Biophys. J., 93: , [13] Schuster, S., Marhl, M., and HOfer, T., Modelling of simple and complex calcium oscillations, Eur. J. Biochem., 269: , 200l. [14] Shuai, J. and Jung, P., Optimal ion channel clustering for intracellular calcium signaling, PNAS, 100: , [15] Skupin, A. et al., How does intracellular Ca 2 + oscillate: By chance or by the Clock, Biophys. J., 94: , [16] Skupin, A. and Falcke, M., How to model Ca2+ dynamics in 3D, submitted, [17] Taylor, C., Inositol trisphosphate receptors: Ca 2 + -modulated intracellular Ca 2 + channels, Biochimica and Biophysica Acta, 1436:19-33, [18] Tsien, R. and Tsien, R., Calcium channels, stores and oscillations, Annu. Rev. Cell Biol., 6: , 1990.