Protein phosphorylation driven by intracellular calcium oscillations: a kinetic analysis.

Given the ubiquitous nature of signal-induced Ca2+ oscillations, the question arises as to how cellular responses are affected by repetitive Ca2+ spikes. Among these responses, we focus on those involving protein phosphorylation. We examine, by numerical simulations of a theoretical model, the situation where a protein is phosphorylated by a Ca(2+)-activated kinase and dephosphorylated by a phosphatase. This reversible phosphorylation system is coupled to a mechanism generating cytosolic Ca2+ oscillations; for definiteness, this oscillatory mechanism is based on the process of Ca(2+)-induced Ca2+ release. The analysis shows that the average fraction of phosphorylated protein increases with the frequency of repetitive Ca2+ spikes; the latter frequency generally rises with the extent of external stimulation. Protein phosphorylation therefore provides a mechanism for the encoding of the external stimulation in terms of the frequency of signal-induced Ca2+ oscillations. Such a frequency encoding requires precise kinetic conditions on the Michaelis-Menten constants of the kinase and phosphatase, their maximal rates, and the degree of cooperativity in kinase activation by Ca2+. In particular, the most efficient encoding of Ca2+ oscillations based on protein phosphorylation occurs in conditions of zero-order ultrasensitivity, when the kinase and phosphatase are saturated by their protein substrate. The kinetic analysis uncovers a wide variety of temporal patterns of phosphorylation that could be driven by signal-induced Ca2+ oscillations.     

Decoding calcium signals by multifunctional CaM kinase.

Multifunctional Ca2+/calmodulin-dependent protein kinase (CaM kinase) is one of the three major protein kinases coordinating cellular responses to hormones and neurotransmitters. It mediates the action of Ca2+ on neurotransmitter synthesis and release, on carbohydrate metabolism and on the cytoskeleton. CaM kinase has structural/functional properties that facilitate its response to distinctive attributes of Ca2+ signals which often involve transient increases that span a narrow concentration range and increases that are pulsatile rather than persistent. The kinase responds to the narrow working range of Ca2+ signals by the use of calmodulin as the Ca2+ sensor. It is activated by the binding of calmodulin to an autoinhibitory domain that keeps the kinase inactive in the basal state. The transient nature of the signal is accommodated by autophosphorylation of this autoinhibitory domain which allows the kinase to remain partially active after calmodulin dissociates and thereby switches it to a Ca(2+)-independent species. The pulsatile nature of Ca2+ signals may also be decoded by CaM kinase. Autophosphorylation traps calmodulin on autophosphorylated subunits by greatly reducing its off-rate. At high frequency of stimulation, calmodulin would remain trapped during the brief interval between Ca2+ oscillations and each successive rise in Ca2+ would recruit more calmodulin. This may enable a stimulus frequency dependent activation of CaM kinase.     

Amplitude of circadian oscillations entrained by 24-h light-dark cycles

An intriguing property of circadian clocks is that their free-running period is not exactly 24h. Using models for circadian rhythms in Neurospora and Drosophila, we determine how the entrainment of these rhythms is affected by the free-running period and by the amplitude of the external light-dark cycle. We first consider the model for Neurospora, in which light acts by inducing the expression of a clock gene. We show that the amplitude of the oscillations of the clock protein entrained by light-dark cycles is maximized when the free-running period is smaller than 24h. Moreover, if the amplitude of the light-dark cycle is very strong, complex oscillations occur when the free-running period is close to 24h. In the model for circadian rhythms in Drosophila, light acts by enhancing the degradation of a clock protein. We show that while the amplitude of circadian oscillations entrained by light-dark cycles is also maximized if the free-running period is smaller than 24h, the range of entrainment is centered around 24h in this model. We discuss the physiological relevance of these results in regard to the setting of the free-running period of the circadian clock.     

Collective oscillations of coupled cell cycles

Problems with networks of coupled oscillators arise in multiple contexts, commonly leading to the question about the dependence of network dynamics on network structure. Previous work has addressed this question in Drosophila oogenesis, in which stable cytoplasmic bridges connect the future oocyte to the supporting nurse cells that supply the oocyte with molecules and organelles needed for its development. To increase their biosynthetic capacity, nurse cells enter the endoreplication program, a special form of the cell cycle formed by the iterated repetition of growth and synthesis phases without mitosis. Recent studies have revealed that the oocyte orchestrates nurse cell endoreplication cycles, based on retrograde (oocyte to nurse cells) transport of a cell cycle inhibitor produced by the nurse cells and localized to the oocyte. Furthermore, the joint dynamics of endocycles has been proposed to depend on the intercellular connectivity within the oocyte-nurse cell cluster. We use a computational model to argue that this connectivity guides, but does not uniquely determine the collective dynamics and identify several oscillatory regimes, depending on the timescale of intercellular transport. Our results provide insights into collective dynamics of coupled cell cycles and motivate future quantitative studies of intercellular communication in the germline cell clusters.     

The manipulation of calcium oscillations by harnessing self-organisation

This paper investigates how self-organisation might be harnessed for the manipulation and control of calcium oscillations. Calcium signalling mechanisms are responsible for a number of important functions within biological systems, such as fertilization, secretion, contraction, neuronal signalling and learning. In this paper, calcium oscillations are investigated as a biological periodic process. Within biological systems such periodic behaviour is one of the outcomes from self-organisation. The understanding of periodic processes in living systems can enable more accurate diagnosis and physiologically suitable clinical therapies to be proposed, for diseases such as cancer, epilepsy, cardiac diseases and other dynamic diseases. In this paper these ideas are investigated by means of the calcium-induced calcium release (CICR) model and a number of representative simulations of intra and inter-cellular calcium oscillations are used to illustrate the manipulation and control of these oscillations in normal and pathological situations.     

Frequency decoding of fast calcium oscillations by calpain

We report the development of a novel procedure for generating fast, high-frequency Ca2+ oscillations in vitro and the frequency-dependent activation of m-calpain, the Ca2+-activated intracellular cysteine protease. The procedure is based upon liberating Ca2+ from a cage, DM-Nitrophen, by repetitive UV laser pulses and its concomitant binding by a 'slow' chelator, 1,4,7,10-tetraazacyclododecane-N,N',N",N"'-tetraacetate (DOTA). It is shown that a full control over the pattern of oscillations can be readily achieved because the half-life of individual spikes is determined by DOTA concentration and pH, whereas peak amplitude can be adjusted by light intensity. Frequency is only limited by the physical parameters of the light source. The sensitivity of calpain activation to the frequency of Ca2+ oscillations was monitored by the cleavage of microtubule-associated protein 2, a very sensitive physiological substrate of the enzyme. One hundred transients at a peak Ca2+ concentration of 10 microM were presented at various pH values and frequencies ranging from 1 to 50 Hz. At pH 6.0 and 7.0 significant activation occurred at high frequencies (20 and 50 Hz), but here Ca2+ accumulated due to the overlap of transients; at low frequencies (1 and 3 Hz) where Ca2+ accumulation was negligible, there was no calpain activation. At pH 8.0, where individual transients do not overlap even at 50 Hz, frequency-dependence of activation is seen when calpain is sensitized to Ca2+ by autolysis and by the addition of a phospholipid, phosphatidylinositol-4,5-bisphosphate. Our results show that calpain is sensitive to the frequency of fast Ca2+ oscillations in vitro, which is of potential physiological significance.     

Frequency decoding of calcium oscillations

Background

Calcium (Ca^2 +) oscillations are ubiquitous signals present in all cells that provide efficient means to transmit intracellular biological information. Either spontaneously or upon receptor ligand binding, the otherwise stable cytosolic Ca^2 + concentration starts to oscillate. The resulting specific oscillatory pattern is interpreted by intracellular downstream effectors that subsequently activate different cellular processes. This signal transduction can occur through frequency modulation (FM) or amplitude modulation (AM), much similar to a radio signal. The decoding of the oscillatory signal is typically performed by enzymes with multiple Ca^2 + binding residues that diversely can regulate its total phosphorylation, thereby activating cellular program. To date, NFAT, NF-κB, CaMKII, MAPK and calpain have been reported to have frequency decoding properties.

Scope of review

The basic principles and recent discoveries reporting frequency decoding of FM Ca^2 + oscillations are reviewed here.

Major conclusions

A limited number of cellular frequency decoding molecules of Ca^2 + oscillations have yet been reported. Interestingly, their responsiveness to Ca^2 + oscillatory frequencies shows little overlap, suggesting their specific roles in cells.

General significance

Frequency modulation of Ca^2 + oscillations provides an efficient means to differentiate biological responses in the cell, both in health and in disease. Thus, it is crucial to identify and characterize all cellular frequency decoding molecules to understand how cells control important cell programs.     

Cytoplasmic calcium oscillations: a two pool model

Cytosolic calcium oscillations induced by a wide range of agonists, particularly those which stimulate phosphoinositide metabolism, are the result of a periodic release of stored calcium. The formation of inositol 1,4,5 trisphosphate (Ins(1,4,5)P3) seems to play an important role because it can initiate this periodic behaviour when injected or perfused into a variety of cells. A two pool model has been developed to explain how Ins(1,4, 5)P3 sets up these calcium oscillations. It is proposed that Ins(1,4,5)P3 acts through its specific receptor to create a constant influx of primer calcium (Ca2+p) made up of calcium released from the Ins(1,4,5)P3-sensitive pool (ISCS) together with an influx of external calcium. This Ca2+p fails to significantly elevate cytosolic calcium because it is rapidly sequestered by the Ins(1,4,5)P3-insensitive (IICS) stores of calcium distributed throughout the cytosol. Once the latter have filled, they are triggered to release their stored calcium through a process of calcium-induced calcium release to give a typical calcium spike (Ca2+s). In many cells, each Ca2+s begins at a discrete initiation site from which it then spreads through the cell as a wave. The two pool model can account for such waves if it is assumed that calcium released from one IICS diffused across to excite its neighbours thereby setting up a self-propagating wave based on calcium-induced calcium release.     

Agonist-dependent phosphorylation of the inositol 1,4,5-trisphosphate receptor: A possible mechanism for agonist-specific calcium oscillations in pancreatic acinar cells.

The properties of inositol 1,4,5-trisphosphate (IP3)-dependent intracellular calcium oscillations in pancreatic acinar cells depend crucially on the agonist used to stimulate them. Acetylcholine or carbachol (CCh) cause high-frequency (10-12-s period) calcium oscillations that are superimposed on a raised baseline, while cholecystokinin (CCK) causes long-period (>100-s period) baseline spiking. We show that physiological concentrations of CCK induce rapid phosphorylation of the IP3 receptor, which is not true of physiological concentrations of CCh. Based on this and other experimental data, we construct a mathematical model of agonist-specific intracellular calcium oscillations in pancreatic acinar cells. Model simulations agree with previous experimental work on the rates of activation and inactivation of the IP3 receptor by calcium (DuFour, J.-F., I.M. Arias, and T.J. Turner. 1997. J. Biol. Chem. 272:2675-2681), and reproduce both short-period, raised baseline oscillations, and long-period baseline spiking. The steady state open probability curve of the model IP3 receptor is an increasing function of calcium concentration, as found for type-III IP3 receptors by Hagar et al. (Hagar, R.E., A.D. Burgstahler, M.H. Nathanson, and B.E. Ehrlich. 1998. Nature. 396:81-84). We use the model to predict the effect of the removal of external calcium, and this prediction is confirmed experimentally. We also predict that, for type-III IP3 receptors, the steady state open probability curve will shift to lower calcium concentrations as the background IP3 concentration increases. We conclude that the differences between CCh- and CCK-induced calcium oscillations in pancreatic acinar cells can be explained by two principal mechanisms: (a) CCK causes more phosphorylation of the IP3 receptor than does CCh, and the phosphorylated receptor cannot pass calcium current; and (b) the rate of calcium ATPase pumping and the rate of calcium influx from the outside the cell are greater in the presence of CCh than in the presence of CCK.     

How yeast cells synchronize their glycolytic oscillations: a perturbation analytic treatment

Of all the lifeforms that obtain their energy from glycolysis, yeast cells are among the most basic. Under certain conditions the concentrations of the glycolytic intermediates in yeast cells can oscillate. Individual yeast cells in a suspension can synchronize their oscillations to get in phase with each other. Although the glycolytic oscillations originate in the upper part of the glycolytic chain, the signaling agent in this synchronization appears to be acetaldehyde, a membrane-permeating metabolite at the bottom of the anaerobic part of the glycolytic chain. Here we address the issue of how a metabolite remote from the pacemaking origin of the oscillation may nevertheless control the synchronization. We present a quantitative model for glycolytic oscillations and their synchronization in terms of chemical kinetics. We show that, in essence, the common acetaldehyde concentration can be modeled as a small perturbation on the "pacemaker" whose effect on the period of the oscillations of cells in the same suspension is indeed such that a synchronization develops.     

Metabolic cycles as an underlying basis of biological oscillations

The evolutionary origins of periodic phenomena in biology, such as the circadian cycle, the hibernation cycle and the sleep-wake cycle, remain a mystery. We discuss the concept of temporal compartmentalization of metabolism that takes place during such cycles, and suggest that cyclic changes in a cell's metabolic state might be a fundamental driving force for such biological oscillations.     

Calcium homeostasis in bovine somatotrophs: calcium oscillations and calcium regulation by growth hormone-releasing hormone and somatostatin.

The free intracellular calcium ion concentration ([Ca2+]i) was measured in single cells of a population containing 65-80% somatotrophs, using the fluorescent Ca(2+)-indicator Fura-2 and digital imaging microscopy. Spontaneous oscillations in [Ca2+]i ranging in frequency up to 1.5 oscillations per minute were observed in 30% of somatotrophs. These Ca2+ oscillations were blocked by the Ca2+ channel blocker CoCl2 and were thus proposed to be the result of influx of Ca2+ into the cell, possibly as the result of spontaneous electrical activity. GHRH (10-100 nM) increased [Ca2+]i in 61% of the cells studied, although the amplitude and dynamics of the response varied from cell to cell. Typically [Ca2+]i rose from 170 +/- 26 nM to 321 +/- 44 nM (n = 13) in response to a challenge with 66 nM GHRH. GHRH also increased the frequency of Ca2+ oscillations in a number of cells, and some previously quiescent cells showed Ca2+ oscillations following addition of GHRH. Forskolin, which raises cAMP levels in bovine anterior pituitary cells, also stimulated a sustained rise in [Ca2+]i in 10 out of 14 cells tested. Somatostatin (SS) (10-80 nM) rapidly reduced basal [Ca2+]i, blocked Ca2+ oscillations, and blocked the [Ca2+]i response to GHRH. The Ca2+ channel blocker CoCl2 (4 mM) had similar actions on [Ca2+]i to those of SS. These results suggest that GHRH and SS may regulate GH release by modulating Ca2+ entry into the cell through the cell membrane. The [Ca2+]i oscillations seen in a proportion of the somatotrophs were modulated in frequency by GHRH and SS, and are probably generated by influx of Ca2+ through channels in the cell membrane. Thus GH secretion may be regulated by changes in the mean level of [Ca2+]i, which in turn, may be influenced by the frequency of [Ca2+]i oscillations in bovine somatotrophs.     

Signal transduction by the platelet integrin alpha IIb beta 3: induction of calcium oscillations required for protein-tyrosine phosphorylation and ligand-induced spreading of stably transfected cells.

We demonstrate an example of signal transduction by an integrin and have begun to define the pathway through which this signaling is achieved. We constructed a stably transfected derivative of 293 cells (ATCC 1573) that expresses the platelet integrin GPIIbIIIa (alpha IIb beta 3). This cell line, clone B, adheres to and spreads on fibrinogen, a ligand for alpha IIb beta 3, while the parent cell line does not. Stimulation of these cells either by adhesion to fibrinogen or with antiserum directed against alpha IIb beta 3 results in induction of calcium oscillations, followed by tyrosine phosphorylation of at least one protein of molecular weight approximately 125 kDa. We establish that this phosphorylation, as well as the morphological rearrangements, requires the mobilization of calcium.     

Differential regulation of intracellular calcium oscillations by mitochondria and gap junctions

Fluctuations of intracellular Ca²⁺ ([Ca²⁺]_i) regulate a variety of cellular functions. The classical Ca²⁺ transport pathways in the endoplasmic reticulum (ER) and plasma membrane are essential to [Ca²⁺]_i oscillations. Although mitochondria have recently been shown to absorb and release Ca²⁺ during G protein-coupled receptor (GPCR) activation, the role of mitochondria in [Ca²⁺]_i oscillations remains to be elucidated. Using fluo-3-loaded human teratocarcinoma NT2 cells, we investigated the regulation of [Ca²⁺]_i oscillations by mitochondria. Both the muscarinic GPCR agonist carbachol and the ER Ca²⁺-adenosine triphosphate inhibitor thapsigargin (Tg) induced [Ca²⁺]_i oscillations in NT2 cells. The [Ca²⁺]_i oscillations induced by carbachol were unsynchronized among individual NT2 cells; in contrast, Tg-induced oscillations were synchronized. Inhibition of mitochondrial functions with either mitochondrial blockers or depletion of mitochondrial DNA eliminated carbachol—but not Tg-induced [Ca²⁺]_i oscillations. Furthermore, carbachol-induced [Ca²⁺]_i oscillations were partially restored to mitochondrial DNA-depleted NT2 cells by introduction of exogenous mitochondria. Treatment of NT2 cells with gap junction blockers prevented Tg-induced but not carbachol-induced [Ca²⁺]_i oscillations. These data suggest that the distinct patterns of [Ca²⁺]_i oscillations induced by GPCR and Tg are differentially modulated by mitochondria and gap junctions.     

Activation of calcium oscillations by thapsigargin in parotid acinar cells.

The tumor promoter thapsigargin releases Ca2+ from intracellular stores by specific inhibition of microsomal Ca-ATPase activity without inositol phosphate formation. Recent studies of the actions of thapsigargin support the concept that the level of Ca2+ within the inositol (1,4,5)-trisphosphate (IP3)-sensitive intracellular pool regulates the Ca2+ permeability of the plasma membrane. We examined the effects of thapsigargin on intracellular Ca2+ concentration ([Ca2+]i) in single rat parotid cells using digital fluorescence microscopy. In the absence of extracellular Ca2+ (Ca2+o), thapsigargin transiently increased [Ca2+]i. Following the thapsigargin-induced [Ca2+]i transient, carbachol in the continued absence of Ca2+o was unable to raise [Ca2+]i, indicating that thapsigargin mobilizes Ca2+ from the IP3-sensitive store. In the converse experiment, carbachol prevented a rise of [Ca2+]i by thapsigargin, suggesting that the IP3- and thapsigargin-sensitive Ca2+ pools are the same. Depletion of Ca2+ from the IP3-sensitive pool by thapsigargin enhanced plasma membrane Ca2+ permeability. Thapsigargin triggered sustained Ca2+ oscillations in Ca2(+)-containing medium which are highly reminiscent of agonist-induced oscillations in these cells. Carbachol addition rapidly raised IP3 levels during oscillations triggered by thapsigargin but did not elevate [Ca2+]i, indicating that the IP3-sensitive pool remains continuously depleted during [Ca2+]i fluctuations. The results from this study rule out the involvement of the IP3-sensitive pool in the mechanisms involved in thapsigargin-induced (and by analogy, agonist-induced) oscillations in parotid cells.     

Reversed predator–prey cycles are driven by the amplitude of prey oscillations

Ecoevolutionary feedbacks in predator–prey systems have been shown to qualitatively alter predator–prey dynamics. As a striking example, defense–offense coevolution can reverse predator–prey cycles, so predator peaks precede prey peaks rather than vice versa. However, this has only rarely been shown in either model studies or empirical systems. Here, we investigate whether this rarity is a fundamental feature of reversed cycles by exploring under which conditions they should be found. For this, we first identify potential conditions and parameter ranges most likely to result in reversed cycles by developing a new measure, the effective prey biomass, which combines prey biomass with prey and predator traits, and represents the prey biomass as perceived by the predator. We show that predator dynamics always follow the dynamics of the effective prey biomass with a classic ¼‐phase lag. From this key insight, it follows that in reversed cycles (i.e., ¾‐lag), the dynamics of the actual and the effective prey biomass must be in antiphase with each other, that is, the effective prey biomass must be highest when actual prey biomass is lowest, and vice versa. Based on this, we predict that reversed cycles should be found mainly when oscillations in actual prey biomass are small and thus have limited impact on the dynamics of the effective prey biomass, which are mainly driven by trait changes. We then confirm this prediction using numerical simulations of a coevolutionary predator–prey system, varying the amplitude of the oscillations in prey biomass: Reversed cycles are consistently associated with regions of parameter space leading to small‐amplitude prey oscillations, offering a specific and highly testable prediction for conditions under which reversed cycles should occur in natural systems.     

Reciprocal regulation of calcium dependent and calcium independent cyclic AMP hydrolysis by protein phosphorylation

The hydrolysis of cyclic nucleotide second messengers takes place through multiple cyclic nucleotide phosphodiesterases (PDEs). The significance of this diversification is not fully understood. Here we report the differential regulation of low K(m) Ca2+-activated (PDE1C) and Ca2+-independent, rolipram-sensitive (PDE4) PDEs by protein phosphorylation in the neuroendocrine cell line AtT20. Incubation of cells with 8-(4-chlorophenylthio)-cyclic AMP (CPT-cAMP) enhanced PDE4 and reduced PDE1C activity. These effects were blocked by H89 indicating mediation by cAMP-dependent protein kinase (PKA), furthermore in broken cell preparations PKA produced the same reciprocal changes of PDE activities. Calyculin A, an inhibitor of protein phosphatases 1 and 2 A, stimulated PDE4 and enhanced the inhibitory effect of CPT-cAMP on PDE1C. The reduction of PDE1C activity was characterized by a marked attenuation of the activation by Ca2+/calmodulin. Stimulation of PDE4 activity by CPT-cAMP or calyculin A was attributable to PDE4D3 and these effects could also be reproduced in human embryonic kidney cells expressing epitope-tagged PDE4D3. Together, these data show reciprocal regulation of PDE1C and PDE4D by PKA, which represents a novel scheme for plasticity in intracellular signalling.     

Regulation of sperm flagellar motility by calcium and cAMP-dependent phosphorylation

There is substantial evidence that cAMP-dependent phosphorylation is involved in the activation of motility of spermatozoa as they are released from storage in the male reproductive tract. This evidence includes observations that in vivo activation of motility can be inhibited by protein kinase inhibitors, can be reversed by protein phosphatase treatment of demembranated spermatozoa, and is associated with phosphorylation of sperm proteins, and observations that spermatozoa that have not been activated in vivo can be activated in vitro by cAMP-dependent phosphorylation. Activation in vivo can often be triggered by conditions that increase intracellular pH, but the relevance of this to in vivo activation under natural conditions and the steps between pH increase and cAMP increase have not been fully established. The relationships between changes in the protein substrates for cAMP-dependent phosphorylation and changes in axonemal function are still unknown. Sperm chemotaxis to egg secretions is widespread; in the sea urchin Arbacia, the egg jelly peptide resact has been identified as a chemoattractant. Response to chemoattractants involves changes in asymmetry of flagellar bending waves, and similar changes in asymmetry can be produced in vitro by increases in [Ca++]. Temporal changes in resact receptor occupancy might lead to transient changes in intracellular [Ca++] and the asymmetry of flagellar bending, but many links in this hypothetical sequence remain to be established. Both of these signalling systems offer immediate opportunities for investigations of biochemical pathways leading to easily assayable biological responses. However, complications resulting from interactions between these two systems need to be considered.     

GnRH-induced cytosolic calcium oscillations in pituitary gonadotrophs: phase resetting by membrane depolarization.

Cultured rat pituitary gonadotrophs under whole-cell voltage clamp conditions respond to the hypothalamic hormone GnRH with synchronized oscillatory changes in both cytosolic Ca2+ concentration ([Ca2+]i) and [Ca2+]i-activated, apamin-sensitive K+ current (IK(Ca)). We found, and report here for the first time, that in GnRH-stimulated cells a brief depolarizing pulse can elicit a transient [Ca2+]i rise similar to the endogenous cycle. Furthermore, Ca2+ entry during a single depolarizing pulse was found to shift the phase of subsequent endogenous [Ca2+]i oscillations, which thereafter continue to occur at their previous frequency before the pulse. Application of two consecutive depolarizing pulses showed that the size of the [Ca2+]i rise evoked by the second pulse depended on the time lapsed between two consecutive pulses, indicating that each endogenous or evoked [Ca2+]i rise cycle leaves the Ca2+ release mechanism of the gonadotroph in a refractory state. Recovery from this condition can be described by an exponential function of the time lapsed between the pulses (time constant of ca. 1 s). We propose that the underlying mechanism in both refractoriness after endogenous cycles and phase resetting by a brief pulse of Ca2+ entry involves the InsP3 receptor-channel molecule presumed to be located on the cytosolic aspect of the endoplasmic reticulum membrane.