INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

Calcium (Ca²⁺) plays a central role in determining cellular activity in animals controlling functions such as contraction, excitability, proliferation, secretion, or cell defense via protein modification or gene expression (Bootman et al., 2001; Campbell, 1983). The eukaryotic cell has two main sources of Ca²⁺, an influx through channels in the plasma membrane, and release from internal stores, the major store being the endoplasmic reticulum (ER). Ca²⁺ enters the ER through sarcoplasmic and endoplasmic reticulum Ca²⁺-activated ATPase (SERCA) pumps and is bound to proteins such as calreticulin (CRT) and grp78 (BiP). It is released into the cytosol through inositol 1,4,5 trisphosphate (IP₃) or ryanodine receptors. In cell signaling, much of the focus has been on changes in cytosolic signals that comprise a spatio-temporal pattern leading to different cell responses (Berridge et al., 1998). It is now clear that the cell also has a signaling system within the endoplasmic reticulum (Camacho and Lechleiter, 1995; Llewellyn and Llewelyn-Roderick, 1998; Urano et al., 2000). Here, changes in Ca²⁺ or unfolded protein levels communicate to other parts of the cell, including the nucleus and plasma membrane, to determine whether a cell recovers from stress, crosses a cell cycle checkpoint, or dies by apoptosis. In particular, loss of Ca²⁺ from the ER signals a rapid opening of Ca²⁺ channels in the plasma membrane, leading to a global Ca²⁺ signal and refilling of the ER store. In the longer term, loss of ER Ca²⁺ signals chaperone gene expression and activation of ER proteases (Jeffery et al., 2000). Others, have shown that over-expression of calreticulin alters cytosolic Ca²⁺ signals in a way that cannot be explained by a chaperone acting simply to change store capacity (Lievremont et al., 1997; Llewelyn-Roderick et al., 1998). Thus, if calreticulin is to be a signaling protein within the ER, it must interact with domains facing the inner lumen.

It has been proposed that calreticulin could interact with the IP₃R (Camacho and Lechleiter, 1995) or SERCA 2b (John et al., 1998), the predominant isoform in nonmuscle cells, both of which have potential ER lumenal domains. Three questions now arise: 1) what are the initiating signals within the ER, and how do these communicate throughout the cell; 2) does calreticulin play a role as a signal protein not only storing but controlling Ca²⁺; and 3) what role do the components, IP₃, the IP₃R, and SERCA pump, play in calreticulin mediated Ca²⁺ responses. This current work focuses on questions 2 and 3.

This paper simplifies the Ca²⁺ mobilization pathway by removing capacitative Ca²⁺ entry and addresses the affect on ER mobilized Ca²⁺. Thus, our strategy was first to define the effect of calreticulin over-expression on cytosolic Ca²⁺ signals in individual cells and then to develop a mathematical model that predicted the mechanism by which calreticulin caused such changes (Fig. 1). The model has enabled us to assess the relative importance of the two major ER transmembrane regulators of cytosolic Ca²⁺, the IP₃ receptor, and the SERCA pump in HeLa cells, which have no ryanodine receptors.

View larger version (21K): [in this window] [in a new window]   FIGURE 1   Flow diagram demonstrating the central role of mathematical modeling for determining signal protein function. Proposed strategy to incorporate three separate work blocks: 1) manipulation and ion measurement from a cell system, 2) mathematical modeling, and 3) fitting and analysis to investigate the role of ER-signal proteins in calcium mobilization.

Our results show that calreticulin over-expression induces transient-decline oscillations, defined as nonuniform oscillations occurring upon the recovery phase of a single transient. To investigate calreticulin component interactions within the ER, we developed a mechanistic model based initially on the De Young and Keizer (1992) model. Our model was optimized for IP₃ concentration, IP₃R regulation, and SERCA pump activity to minimize the difference between the predicted Ca²⁺ signal and that determined experimentally. Each of the components was restricted by the experimental data, enabling us to determine the most likely candidate for calreticulin-mediated Ca²⁺ oscillations. The results show that each of the three components have oscillatory potential, but highlight for the first time that the SERCA pump is the most likely source for Ca²⁺ oscillations. We show that incorporation of a buffering factor into the model does not affect the qualitative conclusions. The generation of new experimental data, combined with novel mathematics, has predicted an interaction between calreticulin and the SERCA pump, which supports our hypothesis that intralumenal communication within the ER plays a key role in cell signaling.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

Materials

Fura-2 AM was purchased from Molecular Probes (Leiden, Netherlands). A stock was prepared in dimethyl sulfoxide (1 mg/ml). All tissue culture reagents were obtained from Life Technologies/Gibco-BRL (Cleveland, OH) and other reagents unless specified were purchased from Sigma (St. Louis, MO).

Cell culture, loading of Fura-2

Stable transfected HeLa cell cultures with green fluorescent protein (GFP)-calreticulin chimera were routinely grown to 70 to 80% confluency in DMEM supplemented with 10% fetal calf serum 400 µg/ml G418 antibiotic. They were detached from dishes and seeded onto coverslips. Twenty-four hours later the adherent cells were incubated for 20 min in complete DMEM containing 2 µM Fura-2AM at 37°C. The cells were then washed and rested for 10 min in a minimal physiological buffer (10 mM Hepes, pH 7.4, 121 mM NaCl, 5 mM KCl, 0.8 mM MgCl₂, 5 mM glucose, and 0.1% bovine serum albumin) containing 1 mM CaCl₂ to allow complete cleavage of the ester form of the indicator.

Fluorescent measurement of intracellular calcium

The cover slips were placed into an observation chamber mounted on a Zeiss Axiovert 100. All experiments were performed using a 40×, 1.3 NA oil objective. Ratio images (excitation at 340 and 380 nm; emission at 515 nm) were captured at 2-s intervals using an ORCA-1 cooled CCD camera (Hamamatsu Inc., Welwyn Garden City, UK) from the same field a GFP-calreticulin image was recorded (excitation at 475 nm; emission at 515 nm). The buffer was changed to a calcium-free environment (1 mM EGTA). After 1 min of recording the basal ratio, a supra-maximal concentration of 80 µM ATP was added. Following this, images were acquired for a further 5 min. Separately, the size of the intracellular pool, before and after IP₃-mediated Ca²⁺ release was estimated by the addition of a SERCA pump inhibitor thapsigargin (1 µM). Sequences were acquired and analyzed using AQM-2000 (Kinetic Imaging Inc., Wirral, UK).

Evaluation of calcium recovery characteristics

Individual cells were assigned as either GFP-calreticulin positive (CRT_P) or GFP-calreticulin negative (CRT_N). Data were extracted for each individual wavelength, a background subtracted, and the ratiometric value calculated. Cells (149 CRT_P and 98 CRT_N) were selected from appropriate fields (n = 18). The characteristics of each response, the basal ratio (R_bs), peak ratio (R_pk), and the duration period for the recovery phase (T_d) were determined and number of oscillations (N_os) during the recovery period counted for each individual cell. Estimated contribution of the plasma membrane Ca²⁺-ATPase (PMCA) pump to Ca²⁺ recovery was determined by the amount of Ca²⁺ remaining in the ER pool compared with the amount in the pool to start. This was estimated by calculating the total area under the curve for 39 CRT_P and 34 CRT_N cells after the addition of thapsigargin. Individual cell data for CRT_P and CRT_N cells were pooled to produce mean and standard deviation values, which were compared with a statistical t-test.

A linear relationship between experimental fluorescent ratiometric values and Ca²⁺ concentration was assumed. To compare experimental fluorescent data with simulated Ca²⁺ traces both sets of data were normalized to basal levels equal to 1.0.

Modeling of calcium dynamics

A "closed" cell model, which does not include Ca²⁺ influx from the extra-cellular medium, was developed to investigate the effects of calreticulin on the three main components of the Ca²⁺ mobilization pathway: 1) IP₃ production, 2) IP₃ receptor regulation, and 3) SERCA and PMCA pump activity. This model incorporated the De Young and Keizer (1992) equations for Ca²⁺ flow through the IP₃R and input and decay of IP₃. The model considers ER-Ca²⁺ release through the IP₃R (J_IP3R), reuptake via the SERCA pump (J_SERCA), and extrusion from the cell by the PMCA pump (J_PMCA).

The calcium dynamics for this model are expressed by this ordinary differential equation:

(1)

in which J denotes the fluxes of processes that increase and decrease cytosolic calcium concentration ([Ca²⁺]_cyt), respectively. X denotes the percentage of recycled Ca²⁺ available to reenter the ER, whereas Y denotes the percentage of Ca²⁺ pumped out of the cell.

De Young and Keizer's (1992) equation for Ca²⁺ flow through the IP₃R was included in the model. This equation incorporated calcium dependence on receptor open probability (Bezprozvanny et al., 1991) and IP₃ binding data (Joseph et al., 1989). The flow of Ca²⁺ through the IP₃R is given by:

(2)

in which r₁ is the ratio of ER to cytosolic volume, v₁ and v₂ are maximal Ca²⁺ fluxes for the IP₃R and the passive leak, and d₁, d₂, d₃, and d₅ are the receptor dissociation constants for IP₃, Ca²⁺ inhibition, IP₃, and Ca²⁺ activation, respectively.

Physiological cytosolic calcium concentration ([Ca²⁺]_cyt) is maintained by a combination of sequestration of Ca²⁺ back into the ER via the SERCA pump and extrusion from the cell via the PMCA pump. We have assumed that the PMCA pump has similar kinetic properties to SERCA. Ca²⁺ extrusion via the PMCA and Ca²⁺ uptake by the SERCA pump (Lytton et al., 1992) is governed by this Hill-type equation

(3)

V_max is the maximal activity of the pump, and K_1/2 is the activation concentration. The Hill coefficient, n, represents the number of cooperative calcium sites required for pump activity.

The model also includes De Young and Keizer's (1992) equation of input and decay for [IP₃]:

(4)

in which I_R is the rate constant for loss of IP₃, [IP₃]* is the steady-state concentration, I_P the pulse amplitude, and p(t) controls the timing of IP₃ pulses denoted by 0 or 1.

Parameter values unless optimized are given in Table 1.

Controlling the timing of the oscillator

In all conditions IP₃ must be elevated to release calcium from the ER. It was assumed that the Ca²⁺ transient seen in CRT_N cells was due to IP₃ mediated mobilization of Ca²⁺; hence one pulse of IP₃ with a 2.5-s duration was required. For each oscillator the onset and duration of each simulated oscillation, governed by the experimental data, was determined using a time dependent oscillatory trace.

IP₃ as the oscillator

IP₃ pulses were regulated according to Eq. 4 where generation and decay of IP₃ was governed by p(t) denoted by 0 or 1. When IP₃ did not act as the oscillator, the IP₃ profile defaulted to that of CRT_N cells (one pulse with a 2.5-s duration).

IP₃R as the oscillator

Opening and closing of the receptor was mimicked by changing the dissociation constants for IP₃ (d₁) and activation by Ca²⁺ (d₂) resulting in a transition from an open to a closed state. Investigation of possible dissociation constants concluded that the best fit could be achieved by switching the dissociation for 1) IP₃ (d₁) between 2 µM and 0.13 µM and 2) activation by Ca²⁺ (d₂) between 0.5 µM and 1.049 µM. When the receptor was not the oscillator it was assumed to remain in a state whereby the channel was open (S₁₁₀) (De Young and Keizer, 1992).

SERCA as the oscillator

Oscillations from SERCA pump activity were generated by switching the activation concentration (K_1/2SERCA) between the optimized parameter value (denoted by 1) and a predetermined multiplication factor (1.75), which generated oscillations of the required amplitude.

Effect of buffering on Ca²⁺ model

To implement buffering into the model, we assumed that 90% of Ca²⁺ entering the cytoplasm was immediately absorbed by buffers. As a result the total cytosolic Ca²⁺ flux shown previously in Eq. 1 was multiplied by the factor  (Sneyd et al., 1995) (in which  = 0.1):

(5)

Parameter estimation

Computer simulation of the models applied the 4^th-order Runge-Kutta method to predict cytosolic Ca²⁺ traces. The system of equations was modeled using the ModelMaker software (Cherwell Scientific, Oxford).

An evaluation of the difference between model simulations and experimental data was applied to adjust selected model parameter values. This adjustment of parameter values was achieved through optimization, applying the Simplex method, built in to the ModelMaker software, to minimize the difference between predicted and observed values. At the end of each optimization a chi-squared value (an indication of the error between predicted and observed values) was generated. Optimized parameter values were entered into the model and the model reoptimized. This iterative process continued until the chi-squared value did not improve and the visual comparison of simulated overlaid with experimental data was satisfactory.

	RESULTS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

Effects of calreticulin over-expression on calcium dynamics

The effect of calreticulin over-expression on the calcium recovery profile after mobilization of IP₃-mediated release was measured. To isolate the recovery process from further calcium entry across the plasma membrane all experiments were conducted with HeLa cells in a calcium-free buffer subjected to maximal levels of agonist (80 µM ATP). A typical field of cells (Fig. 2 a), containing calreticulin positive cells (CRT_P) and calreticulin negative cells (CRT_N) (Fig. 2 b) is shown. Qualitative comparison of calcium dynamics in CRT_N versus CRT_P cells showed a dramatic difference during the recovery phase of the calcium transient. CRT_N cells (Fig. 2 d) exhibited a smoothed exponential recovery, whereas an oscillatory pattern was apparent in the CRT_P cells (Fig. 2 c). Quantitative analysis of the characteristics defining the calcium recovery profiles (see Fig. 2 c) was performed for 149 CRT_P and 98 CRT_N cells. These data were pooled to produce the mean and standard deviation values shown in Table 2. A statistical t-test was performed on these data to determine any significant difference between CRT_N and CRT_P cells. This test highlighted no significant difference between basal ratio (R_bs), peak ratio (R_pk) after addition of ATP and hence peak/basal factor change for CRT_P and CRT_N cells. CRT_P cells were found to have a longer recovery phase (T_d) of ~1.3 fold. CRT_N cells exhibited slight oscillatory behavior located only at the peak of the response (mean N_os = 2 ± 2) and rarely during the recovery phase. Whereas CRT_P cells exhibited oscillations throughout the entire recovery period (mean N_os = 6 ± 2). Nineteen CRT_N and 14 CRT_P cells were selected to represent the population. A limited model of the system was applied to this group of cells to elucidate interactions between principal components in generating the Ca²⁺ response seen experimentally.

View larger version (91K): [in this window] [in a new window]   FIGURE 2   Experimental data depicting calcium mobilization. Field of HeLa cells loaded with a calcium indicator Fura-2 (A) and the corresponding GFP-calreticulin image (B). */+, Represents CRTP and CRTN cells, respectively. Cytoplasmic calcium profiles representing ratio (340/380 nm) against time (seconds) for CRTP (C) and CRTN (D) cells. Arrow indicates addition of 80 µM ATP. Measured parameters have been defined as: basal ratio (Rbs), peak ratio (Rpk), the duration time for the recovery period (Td), and the number of oscillations during the recovery period (Nos) are shown (C).

Fitting simulated calcium response to experimental data

An iterative process was implemented to optimize simulated cytosolic Ca²⁺ traces against experimental data. The model focused on the interaction of three key elements: 1) the generation and decay of IP₃; 2) calcium release from the ER through the IP₃R; and 3) calcium reuptake into the ER via the SERCA pump and extrusion from the cell via the PMCA pump. Both the PMCA and the SERCA pump are responsible for removing Ca²⁺ from the cytosol. To ascertain the relative contribution from each pump we determined how much Ca²⁺ was present in the thapsigargin-sensitive pool before and after IP₃-mediated Ca²⁺ release. In these HeLa cells ~60% of calcium was pumped out of the cell via the PMCA pump, while 40% was recycled back into the ER, the relative contributions have been incorporated into the calcium balance equation (Eq. 1). Significantly in this minimal "closed" model the ER store is never completely depleted.

Our implementation enabled, via optimization, the experimental data to influence IP₃ levels and SERCA pump activity. The simulated Ca²⁺ trace for each model was normalized and optimized against the corresponding experimental data. As a result a new set of parameter values were predicted for IP₃ generation and decay (I_P and I_R) and SERCA pump activity (K_1/2SERCA and V_maxSERCA). The iterative optimization process has been described previously in Materials and Methods.

CRT_N optimizations

Nineteen CRT_N (cells expressing normal levels of calreticulin) models were developed and optimized. For each CRT_N cell, mean, and standard deviation parameter values were pooled (Table 3). To correlate the effectiveness of the fit between simulated and experimental data, R² values were calculated where an R² value of 100% equals a perfect fit. A typical CRT_N optimized simulation is shown (Fig. 3 a), which produced a good fit against its experimental counterpart (mean R² = 88%). The optimized parameters for CRT_N cells revealed that on average a single IP₃ pulse with an amplitude (I_P) of 93 nM s¹ was required to maintain a Ca²⁺ transient. This IP₃ pulse was degraded at a rate (I_R) of 0.010 s¹. Maximal activity of the SERCA pump (V_maxSERCA) was optimized with a mean value of 238 nM s¹ and a half activation (K_1/2SERCA) of 229 nM.

View larger version (33K): [in this window] [in a new window]   FIGURE 3   Simulation of condition-constrained models. Simulation plots of a typical cell modeled and optimized for the following conditions: CRTN cell (A); CRTP cell with IP3 oscillating (B); CRTP cell where IP3R opens and closes (C); and SERCA pump switching (D). For each condition, normalized experimental Ca2+ (experimental Ca2+), model-simulated Ca2+ (simulated Ca2+), and model-simulated IP3 (simulated IP3) traces are plotted against time.

The model was then applied to investigate the potential of components of the calcium mobilization pathway to act as possible oscillators. We conducted a series of constrained in silico experiments assigning each component separately as the oscillator and optimizing model parameters against experimental data.

Condition modeling to investigate possible oscillators

Fourteen CRT_P (cells over-expressing GFP-calreticulin) cells were selected, and seven condition-constrained models were developed where we assumed that one, two, or three components had an affect on the response seen. Model simulations for each of these cells were optimized against experimental data to investigate the possible source of the oscillatory behavior seen in Fig. 2 c. The three possible components investigated were 1) changeable levels of IP₃ concentration, 2) alternating dissociation constants for IP₃ and activation by Ca²⁺ to mimic opening and closing of the IP₃ receptor, and 3) switching levels of SERCA pump sensitivity, enabling varying pump activity. Of the seven models developed, the closest fit of simulated against experimental data was selected for each of the three oscillatory components, where all of the parameters were optimized.

Optimization of each oscillatory condition model generated a new set of parameter values represented by the mean and standard deviation values pooled for all 14 CRT_P cells (Table 3). A graphical representation of a typical CRT_P cell highlighting the experimental data (Experimental Ca²⁺), and the effect of the oscillatory components on the simulated cytosolic Ca²⁺ trace (Simulated Ca²⁺) and the simulated IP₃ trace (Simulated IP₃) are shown in Fig. 3 (b-d).

When IP₃ acted as the oscillator a fit with a mean R² value of 93% was generated. To achieve this, an amplitude (I_P) of 15 nM s¹ was required for each oscillation; this parameter was sixfold lower than that seen for CRT_N cells. An additional consequence of oscillating IP₃ levels was a degradation rate (I_R) eightfold higher than that in CRT_N cells. Maximal Ca²⁺ uptake of the SERCA pump was similar to CRT_N cells (V_maxSERCA = 245 nM s¹) with the activation constant (K_1/2SERCA) 2.8-fold more sensitive.

When opening and closing of the IP₃R generated oscillations optimization resulted in a fit with a mean R² value of 86%. To achieve this, more IP₃ (2.8-fold) was produced at the peak compared with CRT_N cells, with a degradation rate 1.3-fold faster. A slight reduction (13%) in the maximal uptake of the SERCA pump (V_maxSERCA) was seen, whereas the activation constant (K_1/2SERCA) almost halved. A characteristic of this and other IP₃R versions was an overshoot of oscillations at the top third of the recovery phase.

To enable the SERCA pump to act as the oscillator the activation constant (K_1/2SERCA) for the pump switched between 247 and 431 nM, generating a fit with an R² value of 89%. To achieve this, less IP₃ (20%) was produced (I_P) at the peak compared with CRT_N cells with a degradation rate (I_R) 25% slower. The activation constant for the SERCA pump (K_1/2SERCA) was similar to CRT_N cells, whereas maximal activity (V_maxSERCA) increased by 20%.

Summarizing the optimization results for each oscillator IP₃ generated the best fit of experimental and simulated data with an R² value of 93% followed by SERCA pump in which R² = 89% then IP₃R R² = 86%. A t-test comparing the accuracy of the optimization procedure assessing R² values for each of the three oscillating CRT_P conditions highlighted no significant difference between the IP₃R optimizations and those for the SERCA pump. As a result of both of these observations IP₃, IP₃R, and the SERCA pump must all be considered equally as potential oscillators for calreticulin-mediated release.

Effect of adding a buffering factor to the model

It is well established that calcium concentrations are strongly buffered in living cells, but how buffers affect the movement of Ca²⁺ remains unclear. Thus, inclusion of an equation for buffering into mathematical models for Ca²⁺ oscillations is important. Information on the spatial distribution, timing, and concentration of macromolecules is required to fully understand the role of buffering in cells. However, to a first approximation, buffering can be estimated with the application of a global buffering factor. To elucidate any potential effects of buffering on the current conclusions a buffering factor (Sneyd et al., 1995) in the cytoplasm was added to the model (Eq. 5). Buffering factors ranging from 99% ( = 0.01) down to 50% ( = 0.5) of Ca²⁺ buffered in the cytoplasm were considered. A Ca²⁺ buffering factor of 99% ( = 0.01) was unable to generate oscillations for all conditions before and after parameter optimization, however factors from 90 to 50% produced oscillations before and after optimization. As a result it was assumed that 90% of Ca²⁺ entering the cytoplasm was buffered ( = 0.1). The model, including buffering, was reoptimized to determine if addition of this factor qualitatively affected the current conclusions. For a given CRT_P cell modeled without buffering and optimized under the three given conditions, 1) IP₃ pulsing (Fig. 3 b), 2) IP₃R opening and closing (Fig. 3 c), and 3) switching SERCA pump sensitivity (Fig. 3 d), the associated R² values calculated were 95, 87, and 94%, respectively. For this cell modeled with buffering and reoptimized for all three conditions the R² values calculated were 93 (Fig. 4 b), 86 (Fig. 4 c), and 87% (Fig. 4 d). Qualitatively the addition of buffering to the model did not affect the conclusions of this paper; oscillations were generated for all three components therefore, each oscillator still remains a potential candidate for calreticulin-mediated Ca²⁺ oscillations.

View larger version (17K): [in this window] [in a new window]   FIGURE 4   Effect of buffering on model optimizations. CRTP simulation traces after the addition of a buffering factor () where 90% of cytosolic Ca2+ is buffered ( = 0.1). (A) Experimental trace (experimental Ca2+) for a typical CRTP cell. (B-D) Highlight the same CRTP cell modeled (simulated Ca2+) for IP3 pulsing (B), IP3R opening and closing (C), and SERCA sensitivity switching (D). Plots in these panels (B-D) should be compared with those simulated (simulated Ca2+) where buffering has not been included (Fig. 3, B-D).

Transforming a CRT_N to a CRTp response

To distinguish between the three components and isolate out the oscillator the outcome from directly translating a CRT_N cell was investigated by applying just the oscillator. At all confidence levels no significant difference between the basal activation constant (K_1/2SERCA) and the maximal uptake (V_maxSERCA) of the SERCA pump could be found for CRT_N cells and CRT_P cells where the SERCA pump was the oscillator (Table 3). This led us to investigate whether the main difference between control (CRT_N) cells and those over-expressing calreticulin (CRT_P) was an effect whereby the sensitivity of the SERCA pump switched, resulting in Ca²⁺ oscillations. To achieve this, CRT_P cells were remodeled where only the oscillator was active, all parameter values irrespective of previous optimizations were assigned CRT_N optimized values (Table 2). This would determine whether the imposed oscillatory component alone was able to induce CRT_P behavior. We superimposed the CRT_P simulated traces upon a typical CRT_N experimental trace. This highlighted that IP₃ pulsing (Fig. 5 b) or opening and closing of the IP₃R (Fig. 5 c) alone was unable to convert a CRT_N to a CRT_P response similar to the experimental traces shown in Fig. 5 a. This was achieved, however, by switching the sensitivity of the SERCA pump alone (Fig. 5 d). This successful transformation of a CRT_N to a CRT_P cell highlights that the SERCA pump is the most suitable candidate for the Ca²⁺ oscillations seen as a result of over-expression of calreticulin.

View larger version (16K): [in this window] [in a new window]   FIGURE 5   Transforming a CRTN response to a CRTP. Comparison of normalized CRTN (gray lines) and CRTP (black lines) response profiles against time. (A) Typical CRTN overlaid with a typical CRTP experimental Ca2+ response. (B-D) Use the same experimental CRTN trace and the oscillatory properties of the same CRTP cell as shown in A. (B) CRTN experimental profile compared against a simulated CRTP trace where only IP3 oscillates. (C) CRTN experimental trace with a simulated CRTP profile where only the IP3R opens and closes. (D) CRTP trace with a simulated CRTP trace where the sensitivity of the SERCA pump alternates.

	DISCUSSION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

We demonstrate in the current study that the development and implementation of a mathematical model forms an integral and important tool in the process for determining the role of ER-located signal proteins (Fig. 1). We have shown that over-expression of calreticulin generated a transient decline oscillatory profile not present in control cells and those over-expressing another ER Ca²⁺-binding chaperone grp78 (BiP) (data not shown). These experimental data have enabled us to predict the oscillatory outcome from each of the components investigated. This highlighted for the first time the potential oscillatory role of the SERCA pump. Conversion of a CRT_N to a CRT_P response has indicated that the SERCA pump is the most likely candidate for calreticulin-mediated Ca²⁺ oscillations. This suggested that the effect of calreticulin was due to a direct interaction with the lumenal domain of an ER protein, and not the direct result of a change in ER free-Ca²⁺ (Llewellyn and Llewelyn-Roderick, 1998). It has been suggested that the SERCA pump may play a role in regulating ER calcium, thereby affecting capacitative calcium entry (Putney, 1986). Our conclusions from the minimal "closed" model supported the hypothesis that signaling within the ER involves interactions between ER Ca²⁺-binding proteins and other components of the Ca²⁺-signaling system and that calreticulin acts as a signaling protein.

To identify which of the three potential key candidates were responsible for the transient-decline oscillations, a model based upon the De Young and Keizer (1992) model was applied. The model demonstrated that IP₃ oscillations generated a good fit with experimental data. It has been proposed that IP₃ oscillations may be produced through a positive or negative feedback mechanism incorporating phospholipase C (Cuthbertson and Chay, 1991; Meyer and Stryer, 1991). However, it is unlikely that IP₃ can fluctuate at the rate required to sustain such a calcium profile. Furthermore, there is no obvious direct mechanism whereby calreticulin within the ER could affect IP₃ synthesis or degradation in the cytosol. Thus, the most likely mechanism for transient-decline oscillations may be derived from an interaction between calreticulin and the lumenal domains of either the IP₃R or the SERCA pump. It has been proposed that calreticulin could stabilize the open conformation of the IP₃R prolonging Ca²⁺ release (Camacho and Lechleiter, 1995) or that calreticulin can interact with SERCA2b to inhibit Ca²⁺ uptake (John et al., 1998). It has also been demonstrated that IP₃R subtypes could encode Ca²⁺ oscillatory behavior (Miyakawa et al., 1999). In our optimized model, the SERCA pump and IP₃R generated similar fits of simulated against experimental data. These two potential oscillators were separated by their ability to convert a normal cell recovery profile (CRT_N) to transient-decline oscillations observed in cells over-expressing calreticulin (CRT_P). Thus, this is the first model to propose that the regulation of the SERCA pump can cause cytosolic Ca²⁺ oscillations directly by alternating Ca²⁺ sensitivity for SERCA pump activation. The molecular source of SERCA modulated oscillations now needs to be determined.

The most likely explanation is an on-off binding of calreticulin to the SERCA pump, hence switching its activation state. By identifying and mutating SERCA pump binding sites on calreticulin we can manipulate this potential interaction and measure its downstream effect on calcium mobilization. Additionally, uncaging IP₃ (Fink et al., 1999), using estimates from our model, would provide an elegant approach to separate the contribution of IP₃ pulsing from SERCA switching in calreticulin positive cells.

The simulated model, in general, fitted well with experimental data. However, near the peak the fit deviated slightly, indicating an ill-defined complexity not taken into account by the model. The addition of buffering reduced this deviation where previous fits had overshot. In agreement with previous studies (Wagner and Keizer, 1994) the effect of a global buffer decreased the amplitude of both the IP₃R and SERCA oscillations. It has previously been shown that oscillatory responses are identical irrespective of the buffering equations applied (Wagner and Keizer, 1994). We selected to implement a global buffer factor () (Sneyd et al., 1995) to remove artifacts that may arise from inaccurate parameter estimations. Our qualitative observations were not altered by the inclusion of a buffering factor. The marked decrease in oscillatory amplitude after the inclusion of a buffering factor suggests that an interplay of more than one oscillator either functioning independently during the recovery period or working in concert chaotically or phase dependently would enhance the simulated response. This would require further investigation with particular emphasis on the interaction between the oscillators and their phase relationships.

Our results show how vital it is to combine mathematical modeling with manipulation and measurement of signals in individual living cells if hypotheses in cell signaling are to be properly tested. Ultimately, we can envisage a time-resolved, high-throughput (many manipulations), and high-content (single cell) screening approach to determine the physiological outcome of genetically altered cells, where specific mechanisms are addressed. Mathematical modeling, together with complementary computational methods, will play a central role in the acquisition, mining, and interpretation of such experimental data (Endy and Brent, 2001). Most importantly robust models constructed and developed with "real" data will allow us to predict how intra and extracellular signals are decoded and their effects on cellular outcomes. In this work we have demonstrated the valuable use of a robust mathematical model in elucidating interactions in cell signaling and thus influencing future experimental design. We have shown for the first time that an interaction between calreticulin and the SERCA pump acts as a cause of cytosolic Ca²⁺ oscillations. This extends the role of calreticulin to act as a signal protein in addition to being a storage protein within the ER.