Effects of Transmitters and Amyloid-Beta Peptide on Calcium Signals in Rat Cortical Astrocytes: Fura-2AM Measurements and Stochastic Model Simulations

Background To better understand the complex molecular level interactions seen in the pathogenesis of Alzheimer's disease, the results of the wet-lab and clinical studies can be complemented by mathematical models. Astrocytes are known to become reactive in Alzheimer's disease and their ionic equilibrium can be disturbed by interaction of the released and accumulated transmitters, such as serotonin, and peptides, including amyloid- peptides (A). We have here studied the effects of small amounts of A25–35 fragments on the transmitter-induced calcium signals in astrocytes by Fura-2AM fluorescence measurements and running simulations of the detected calcium signals. Methodology/Principal Findings Intracellular calcium signals were measured in cultured rat cortical astrocytes following additions of serotonin and glutamate, or either of these transmitters together with A25–35. A25–35 increased the number of astrocytes responding to glutamate and exceedingly increased the magnitude of the serotonin-induced calcium signals. In addition to A25–35-induced effects, the contribution of intracellular calcium stores to calcium signaling was tested. When using higher stimulus frequency, the subsequent calcium peaks after the initial peak were of lower amplitude. This may indicate inadequate filling of the intracellular calcium stores between the stimuli. In order to reproduce the experimental findings, a stochastic computational model was introduced. The model takes into account the major mechanisms known to be involved in calcium signaling in astrocytes. Model simulations confirm the principal experimental findings and show the variability typical for experimental measurements. Conclusions/Significance Nanomolar A25–35 alone does not cause persistent change in the basal level of calcium in astrocytes. However, even small amounts of A25–35, together with transmitters, can have substantial synergistic effects on intracellular calcium signals. Computational modeling further helps in understanding the mechanisms associated with intracellular calcium oscillations. Modeling the mechanisms is important, as astrocytes have an essential role in regulating the neuronal microenvironment of the central nervous system.


Introduction
Alzheimer's disease (AD) is a progressive and irreversible neurodegenerative disorder that leads to cognitive impairment and emotional disturbances. Symptoms result from the degeneration of brain tissue, seen as shrinkage of certain brain regions, which are involved in cognitive processes, learning, and memory formation (reviewed in [1]). In addition to brain shrinkage, AD patients suffer from accumulation of amyloid-beta (Ab) containing neuritic plaques and neurofibrillary tangles (tau protein in neuronal somata), which are considered as hallmarks of AD. Though the pathological changes in the brain can be detected using MRI and PET imaging techniques, the exact molecular mechanisms leading to the severe symptoms are not yet known.
Early diagnosis together with a possibility of specific targeted treatment would provide the patients with more years of quality life.
Amyloid plaques containing aggregated Ab fragments have been shown to disturb the homeostasis of intracellular calcium ions (Ca 2z ) and contribute to the altered Ca 2z signaling in the brain cells [1]. The plaques typically consist of 39-42 amino acid Ab fragments, and the plasma ratio of 42 and 40 amino acids long fragments (Ab42/Ab40) is suggested of being useful for identifying the risk of developing mild cognitive impairment and AD [2,3]. Based on the classification of amino acids by Branden and Tooze [4], 25 amino acids out of the total 42 have hydrophobic side chains in Ab42. Therefore, Ab42 tends to aggregate easier than the shorter Ab fragments. Ab42 and the shorter 11 amino acids long synthetic derivative (Ab25-35) are both fragments which are widely used in Alzheimer's disease research (see recent studies [5][6][7][8][9][10]) with specifically Ab25-35 having Ca 2z -mediated neurotoxic properties [11,12].
So far the in vitro studies of the effects of Ab peptide on the cellular Ca 2z responses have failed to give any definite answers to the mechanisms involved. Together with the longer fragments, Ab25-35 has been shown to depress hippocampal long-term potentiation [13] and to potentiate the long-term depression [14], both of which depend on the increases in intracellular Ca 2z concentration in neurons. Ab25-35 has been shown to induce transient changes in intracellular Ca 2z concentration in astrocytes [15,16]. These effects may be important in explaining the loss of new memory formation and learning seen in AD. The detailed mechanisms behind the Ab-induced neuronal and glial Ca 2z fluctuations, as well as the changes triggered by these, require further studies.
One of the central functions of astrocytes is gliotransmitter/ neurotransmitter release and uptake in the neuronal synaptic cleft of the tripartite synapse [17] together with more complex regulation of the neuronal microenvironment [18][19][20][21][22][23]. Astrocytes thus have a vital role in the synaptic information processing and in the metabolism of the central nervous system. Astrocytes release transmitters and have receptors and transporters for different neurotransmitters in their plasma membranes, such as for serotonin (5-hydroxytryptamine; 5-HT), ATP, and glutamate [17,24]. Astrocytes, as well as other glial cells, use both spontaneous and stimulated variations of the Ca 2z concentration for intra-and intercellular signaling [25,26]. Previous electrophysiological and Ca 2z imaging studies have shown how already micromolar concentration of 5-HT cause transient release of Ca 2z from intracellular stores followed by prolonged transmembrane inward Ca 2z flow [17,27]. We here have used rat cortical astrocytes, similarly to our earlier studies on Ab25-35 and Ab1-40 [16], to study the special effects of Ab25-35 to Ca 2z signals when added together with transmitters. We now show that Ab25-35 increases the initial peak of Ca 2z release when added together with 5-HT, compared to the effects of 5-HT alone.
Despite the rapid advancements in computing technology, it is currently not possible to model mathematically the biological systems of realistic complexity over interesting time scales by only using the molecular dynamic approach [28]. Typically, the details of the state of the system (such as the position, orientation, and momentum of individual particles) are excluded in the modeling of whole-cell level phenomena. Here, we describe a model of astrocyte Ca 2z signals as a macroscopic flow of Ca 2z ions rather than as a model of each individual Ca 2z channel in the membranes. In the case of AD, abnormal Ca 2z signals could be among the first hallmarks of disturbed brain function (the correlation between Ca 2z and Ab is reviewed in [29]). A computational model which closely mimics the experimentally measured Ca 2z signals in rat cortical astrocytes helps in understanding the interaction of the various components of Ca 2z dynamics in healthy cells versus the cells with dysfunctional metabolism.

Experimental methods and data
Ethics Statement. Confluent primary astrocyte cultures were prepared from cortices of newborn Sprague-Dawley rat pups as previously described [30], with minor modifications. Pups were killed by decapitation according to the procedure conforming to the Public Health Service Policy on Humane Care and Use of Laboratory Animals and approved by the Albany Medical College Institutional Animal Care and Use Committee for Dr. H.K. Kimelberg, Protocol ID 006038 entitled ''Neurotransmitter receptors and ion channels on astrocytes''.
Cell culture. Primary astrocyte cultures were prepared from new-born Sprague-Dawley rat pups. In brief, the cerebral hemispheres were removed, freed from the meninges and mechanically dissociated using Dispase (Sigma, St. Louis, MO, USA) into culture medium (Eagle's Medium with Earle's salts, Gibco, U.K.) supplemented with 10% heat-inactivated horse serum (HS, Gibco, U.K.), 25 mM sodium bicarbonate and antibiotics (penicillin and streptomycin). Deoxyribonuclease I (Sigma, St. Louis, MO, USA) was added to prevent cell clumping during the second extraction. Cells were grown on coverslips in culture dishes and kept at 37uC in an air-ventilated humidified incubator containing 5% CO 2 . The medium was first changed after one day and subsequently twice a week. About 95% of the cells routinely stained positively for glial fibrillary acidic protein (GFAP+), with polyclonal rabbit anti-cow GFAP used as the primary antibody and either rhodamine or fluorescein conjugated gamma & light chain goat anti-rabbit IgGs as secondary antibody. The studies were performed on cells kept for 1 to 4 weeks in culture.
Calcium imaging. Fura-2-acetoxymethyl ester (Fura-2AM) is a membrane penetrating derivative of the radiometric Ca 2z indicator Fura-2 used to measure intracellular Ca 2z concentrations by fluorescence. Inside the cell, the acetoxymethyl groups in Fura-2AM are removed by cellular esterases resulting to generate Fura-2, the pentacarboxylate Ca 2z indicator. The ratio of the emissions at 340 and 380 nm wavelengths is directly correlated to the amount of intracellular Ca 2z concentration (as presented in [17]). Calcium imaging of Fura-2AM-loaded astrocytes was performed using a monochromator based spectrophotofluorimetric system (Model RF D-4010 Deltascan, PTI, USA, PC computer and software together with Nikon Diaphot microscope) with dual excitation at the 340 and 380 nm wavelengths, bandpass of 2 nm and the fluorescence emission measurements at 510 nm wavelength. Astrocytes on the coverslips were loaded for 30 minutes at 37uC in a HEPES-buffered Ringer's solution containing 4 mM Fura-2AM (Molecular Probes, Inc., Eugine, OR). The coverslips were then rinsed and placed in a Sykes-Moore Culture Chamber (Bellco Biotech, Vineland, NJ, USA). Experiments were made at room temperature. For determining the effects of transmitters, a stable baseline for intracellular Ca 2z concentration was first obtained, after which the solution was replaced normally for 30 s by a buffer solution containing 5-HT or glutamate. After this the transmitter was rinsed away by several successive applications of a fresh buffer solution. Results are shown as a ratio of the emissions obtained by the two wavelengths of 340 nm and 380 nm.
Solutions. Solutions of the following composition were used and the chemicals were obtained from Sigma, St.Louis, MO. USA, if not otherwise stated.  [17,27]), or 50 mM L-glutamate were added in the recording chamber.
The obtained experimental data together with the known components affecting cellular Ca 2z concentration (presented in Figure 1) were used to design the type of the computational model. Because of the variability of detected Ca 2z levels (see Figure 2), stochasticity was introduced into the computational model which was validated by the data obtained from Fura-2AM measurements.

Stochastic model for Ca 2z signals
Computational modeling, in general, means mathematical description of the functional properties of the system components and the analysis of the model predictions. One of the challenges in computational modeling is the lack of precise experimental data for model components. In other words, a specific experimental data set with proper statistics is needed for selecting relevant range of values for model parameters. Validation of the model is typically done by comparing the predicted output of the model with the experimental data. To ensure the relevant parameter values, a computational model for Ca 2z signaling in astrocytes by Di Garbo et al. [31] was taken as a reference model. The model takes into account the physiological phenomena known to be the major contributors in the intracellular Ca 2z oscillations. In summary, it describes the Ca 2z concentration in cytosol as a six-component system (a graphical illustration in Figure 1). Namely, 1) Ca 2z leak from/to extracellular matrix (ECM), 2) capacitive Ca 2z entry (CCE) from ECM, 3) Ca 2z entry via ionotropic receptors, 4) Ca 2z leak from intracellular stores, such as endoplasmic reticulum (ER), 5) storage of Ca 2z to ER via sarco(endo)plasmic Ca 2z ATPase (SERCA) pumps, and 6) Ca 2z release from ER mediated by inositol 1,4,5-trisphosphate (IP 3 ). The reference model carefully addresses a widely accepted mechanism for astrocytic Ca 2z increases via the canonical G protein/phospholipase C (PLC)/IP 3 pathway [32] where the IP 3 released into the cytosol binds to its receptor (IP 3 R) on ER, the Ca 2z channels open, and Ca 2z ions inside the ER are liberated to cytosol causing a sharp rise in the cytosolic concentration of free Ca 2z which is normally kept very low (see also [33,34]). The parameters used for both the reference model (deterministic; Di Garbo et al. [31]) and the here developed stochastic model are presented in Table 1.
The kinetics of biological processes are typically stochastic, i.e. random, in nature [28]. Therefore, the cellular functions cannot be properly understood with purely deterministic models (see, e.g., [35][36][37]) and both the intrinsic and extrinsic stochastic phenomena need to be accounted for in silico models. Intrinsic stochasticity is caused by the dynamics of the system from the random timing of individual reaction events. The importance of intrinsic stochasticity becomes obvious in systems with low numbers of molecules. However, stochasticity included in the model may not always be able to explain the large diversity observed in experimental measurements (as shown in [38]). The low numbers make individual reaction events, which change molecular numbers by one or two, more significant. At the same time the extrinsic stochasticity is caused by the system interacting with other stochastic systems in the cell or its environment. Mathematically, stochasticity means that the trajectories for each simulation are slightly different from one another and computationally intensive simulations are often required to follow the time evolution of the system dynamics. Our earlier studies [39,40] have shown the potential of stochastic differential equations in the kinetics of signal transduction and ion channels. Mathematical analysis alone may be able to completely describe all the properties of interest in the case of simple random systems. However, mathematical analysis is For the explanation of model components 1-6, see text. In short, according to general knowledge, the primary messengers pass their effects via their respective receptors and G proteins on the plasma membrane. Once activated, the G protein activates the membrane-bound phospholipase C (PLC). Furthermore, active PLC propagates its signal by cleaving a lipid molecule phosphatidyl-inositol 4,5-bisphosphate (PIB) that is in attendance in small quantities in the inner half of the plasma membrane lipid bilayer. By disassociating the sugar-phosphate head of the PIB, PLC generates two separate second messenger molecules; inositol 1,4,5-trisphosphate (IP 3 ) and diacylglyserol (DAG). While DAG remains embedded in the plasma membrane, hydrophilic IP 3 diffuses into the cytosol, binds to its receptor (IP 3 R) on ER causing Ca 2z liberation to cytosol. doi:10.1371/journal.pone.0017914.g001 not possible for more complex stochastic models, i.e. the complex stochastic models are analytically intractable.
The exact method to model chemical reactions, when diffusion is not taken into account, is the discrete-state chemical master equation (CME, [41]). However, the CME can rarely be solved and thus an algorithm called Gillespie stochastic simulation algorithm (SSA, [42,43]) has been developed. The SSA presents an easy way to simulate the actual CME process and it is used more and more in computational modeling studies. In many cases, the SSA is slow to simulate and thus, we have chosen to introduce stochasticity into the reference model [31,44] by the chemical Langevin equation (CLE, [45]), that is one type of stochastic differential equation. The CLE represents the continuous-state Markov model approximated from the exact CME. The CLE is much faster to simulate than the actual SSA when large volumes are considered but it can produce negative values when low concentrations are simulated [39]. However, for the system modeled in this study the CLE produce realistic results and can be thus used. When making the stochastic extension of the model, we need to assume volumes for the cytosol (V cytosol ) and ER (V ER ) (see Table 1 for more information).
To describe the time-series behavior of the model, a set of equations (Equations 1-4) was introduced. ½Ca 2z cyt , ½Ca 2z ER , and ½IP 3 represent concentrations of cytosolic Ca 2z , Ca 2z in the ER, and cytosolic IP 3 , respectively. The fraction of active IP 3 receptors on the ER membrane was termed IP 3 R. In the stochastic terms of Equations 1-4,W W = ½W 1 ,:::,W 12 T stands for the Brownian motion andW W (t)*N(0 0,tI). Furthermore, N A represents the Avogadro's number.
Due to the lack of fully understanding the phenomena related to CCE, the rate regulating capacitive Ca 2z influx was assumed to be a nonlinear function of ½Ca 2z ER , as described in [31]: Earlier experimental results (cited in [31]) indicated that the transient component in cytosolic Ca 2z concentration was induced by the activation of the metabotropic receptor (mR) due to stimuli/input-evoked Ca 2z release from the intracellular stores, whereas the activation of the ionotropic receptor (iR) mediated the sustained component (similarly to our results; see Results and Figure 3A). In the reference model by Di Garbo et al. [31], ATP has an effect on ½Ca 2z cyt via both ionotropic and metabotropic receptors. The same is here assumed to 5-HT. Thus, the parts of the model (Equations 6 and 7) describing the ATP-induced Ca 2z response in [31] is here used with some modifications to activate the model for astrocytic Ca 2z signaling with 5-HT and Ab. In this study, the rate of Ca 2z influx, induced by ionotropic receptors, from ECM to cytosol was modeled as in [31]: Similarly, the activation of G protein and PLCb pathways, induced by metabotropic receptors, to promote the IP 3 production were reformed from [31,46] and modeled as: The remaining rate terms used in Equations 1-4 were taken from [46] and are explicitly formulated as Equations 8-16.

Results
To specifically study how the non-aggregated Ab25-35 affects the metabotropic 5-HT receptor function, we added small amyloid peptide concentrations together with the transmitter and measured the ratio of emissions at 340 and 380 nm in Fura-2AM loaded rat cortical astrocytes in primary cultures. In some experiments L-glutamate was also added in aim to study the possible differences between glutamate and 5-HT receptor activation in these cells. The ratio of emissions is directly correlated to cytosolic Ca 2z concentration ½Ca 2z cyt . A deterministic model, introduced by Di Garbo et al. [31], was used as a reference model to which stochasticity was introduced by CLE in aim to reproduce the Ca 2z data measured with the used experimental conditions. Below we present the results obtained by combining the Fura-2AM measurements and computational simulations.

Effects of 5-HT on the levels of cytosolic Ca 2z
When the experiments were performed in solutions with normal external Ca 2z , the addition of 5-HT every time induced a transient peak together with a more sustained increase in ½Ca 2z cyt (Figures 3A and 4). When a lesser amount of 1 mM 5-HT was added for 20 seconds in Ca 2z free medium, a single peak was seen, indicating release of Ca 2z from intracellular stores ( Figure 3B). The simulation of this is seen in Figure 3D. In Figures 3C and 3D, one realization of the chemical Langevin equation is printed in gray while the black traces represent the means and standard deviations for 1000 realizations. The lack of external Ca 2z caused three of the components to be restrained in the six-component computational model, namely: 1) Ca 2z leak from extracellular matrix (ECM), 2) capacitive Ca 2z entry from ECM, and 3) Ca 2z entry via ionotropic receptors. When rates n LM , n CCE , and n iR were set to zero the model simulations indeed produced fast transients without any sustained component. The model simulation closely resembled the experimental peak, except the peak duration was found to be shorter in simulations than in experiments (compare Figures 3B and 3D). With external Ca 2z present, the simulation (illustrated in Figure 3C) shows a sustained component which, however, is shorter than seen in the experiments (compare Figures 3A and 3C).

Effects of Ab25-35 on the basal levels of cytosolic Ca 2z
Our earlier studies [16] showed that only 36% of astrocytes responded to Ab25-35 additions by transient increase in ½Ca 2z cyt , which returned back to baseline level after 1-4 minutes. In the present study, the mean value for the baseline ½Ca 2z cyt in control astrocytes was 2.39+0.40 (mean in ratio 340/380 units + s.d.; n = 32), and 2.69+0.60 (n = 8) in those astrocytes which were similarly cultured and then incubated with 200 nM Ab25-35 for 48 h (see the baseline at t = 0 … 180 s in Figure 2). There is no significant difference in the baseline values of the control and Ab25-35-treated astrocytes (p = 0.098, which is w0.05; statistics were made using Anova module, Statistica, Statsoft Inc.), indicating that Ab25-35 does not cause persistent change in the basal level of calcium in these cells.

Synergistic effects of Ab25-35 and transmitters on the levels of cytosolic Ca 2z
The mean amplitude of ½Ca 2z cyt increase with simultaneous addition of 5-HT and Ab25-35 was statistically significantly different (pv0.001) from the amplitude when 5-HT alone was added. 100% (n = 43) of studied astrocytes, with or without Ab25-35 present, responded to 10 mM 5-HT with a transient peak of increased ½Ca 2z cyt . Ab25-35 addition did not significantly change the mean duration or time constant of the first Ca 2z peak, but increased the peak amplitude, which reflects the magnitude of Ca 2z release from intracellular stores (compare traces in Figures 4 and 5). 1 mM Ab25-35, when added simultaneously with 10 mM 5-HT, caused a significant 163% increase in the mean Ca 2z peak amplitude (n = 5) from the control value of ½Ca 2z cyt induced by 5-HT alone (n = 13). A lesser 75% increase was detected in cells incubated with 200 nM Ab25-35 for 48 h prior to adding 5-HT (n = 6, Figure 2). Astrocytes were also incubated with 10 nM Ab25-35, but the detected 5-HT-induced changes in ½Ca 2z cyt were then not significantly different from the control values.
Glutamate has earlier been shown to induce increase in intracellular Ca 2z [17], and also in the present study 50 mM glutamate induced increase in intracellular Ca 2z in 25% (n = 4) out of 16 astrocytes. Incubation of astrocytes with 10 nM or 200 nM Ab25-35 for 48 h increased the number of cells responding to glutamate to two cells out of four tested. When Ab25-35 was added simultaneously with glutamate, 100% (n = 6) of astrocytes responded with a Ca 2z increase (data not shown). Furthermore, this study revealed another interesting interaction between intracellular Ca 2z and glutamate: glutamate seems to be able to decrease ½Ca 2z cyt , which has first been elevated by 5-HT, and to inhibit the Ca 2z -oscillations and return the Ca 2z levels close to baseline (Figures 4,  5, and 6A). Glutamate may thus be able, by activating separate metabotropic receptors, to both increase ½Ca 2z cyt via release from intracellular stores and influx through L-type Ca 2z channels, and inhibit the Ca 2z channel-mediated Ca 2z influx and oscillations. This phenomenon was seen in every cell tested (in 8 control astrocytes, 10 astrocytes incubated with 10 or 200 nM of Ab25-35, and 12 astrocytes where Ab25-35 had been added simultaneously with glutamate). These effects of glutamate were not included in the computational model and synergistic effects of 5-HT and glutamate with Ab peptide fragments require further testing.

The importance of intracellular Ca 2z stores in Ca 2z
signaling The ability of recurrent additions of the transmitter to induce a Ca 2z release from intracellular stores was tested using different frequencies of stimuli. If the stimuli (simultaneous addition of Ab25-35 and 5-HT in experimental measurements) were given to the system more frequently, the peak amplitudes of the latter measurements were lower. This indicated the incomplete recovery from the desensitization of the receptor or the inadequate filling of the intracellular Ca 2z stores between the stimuli. However, the more sustained components, originating from Ca 2z flux through plasma membrane, were similar, regardless of the frequency of stimuli. Simulations run with less/more frequent stimuli mimicked the experimental measurements (compare Figures 6A, 6B and 7). Thus, the Ca 2z responses in simulations indeed depend on the  preceding events. The more sustained component of Ca 2z release seemed to remain both in the experimental results and simulations, regardless of the frequencies of the stimuli. In Figures 6B and 7, one realization of the chemical Langevin equation is printed in gray while the black traces represent the means and standard deviations for 1000 realizations.

Discussion
One of the hallmarks of AD are the neuritic Ab plaques. It is still an unresolved question how Ab fragments start to form aggregates and at what concentrations they begin to affect the cellular interactions in the brain. We have here shown that even small amounts of Ab25-35 fragments in the rat cortical astrocytes can, together with 5-HT and glutamate, induce meaningful changes in the intracellular Ca 2z concentration. Ab25-35 together with 5-HT caused an enhanced first peak of intracellular Ca 2z representing the release from intracellular stores mediated by 5-HT2A receptor. The glutamate induced increase in Ca 2z release from stores would most probably be mediated by a Group I (type 1 or 5) mGluR found in cortical astrocytes [17]. The observed additional inhibitory effect of glutamate could be the result of the activation of the group II metabotropic glutamate receptors which are known to reduce the voltage-sensitive Ca 2z currents and be potential targets for neurological disorders (see [47,48]).
In this study, we used data and a computational model to characterize the Ca 2z transients associated with synergistic effects of Ab25-35 and transmitter 5-HT in rat cortical astrocytes. To our knowledge, this is the first such study. In the experimental part of this study, it was shown that 5-HT and Ab25-35, when added together, clearly increased the amplitudes of the Ca 2z signals. Addition of Ab25-35, 5-HT, or glutamate alone was not able to induce that several-fold increment to the intracellular Ca 2z , which was seen when Ab25-35 and 5-HT were added together. The abnormal increase in intracellular Ca 2z may in its turn trigger a complex cascade of a variety of molecular events in the intracellular signaling pathways [16,17,[49][50][51][52][53]. The measured Ca 2z signals indicate the activation of 5-HT2A receptor followed by G protein, PLC, and IP 3 mediated Ca 2z release from intracellular Ca 2z stores. An additional Ca 2z influx through voltage-sensitive and -insensitive Ca 2z channels might be involved, as presented in [27]. Changes in astrocytic Ca 2z signaling are prone to cause widespread alterations in neuronal network function and can lead to neurological disorders (reviewed in [54]).
In the computational part of this study, a mathematical model by Di Carbo et al. [31], for simulating intracellular Ca 2z processes, was selected to be the basis for developing a more adequate model. Other models presenting Ca 2z signaling in astrocytes (such as in [55]) include the flux of Ca 2z from/to ECM, pumping Ca 2z to ER, and Ca 2z release from ER. The model selected for the present study includes six components which affect the intracellular Ca 2z concentration: 1) Ca 2z leak from/to ECM, 2) capacitive Ca 2z entry from ECM, 3) Ca 2z entry via ionotropic receptors, 4) Ca 2z leak from intracellular stores, such as ER, 5) storage of Ca 2z to ER via SERCA pumps, and 6) Ca 2z release from ER mediated by IP 3 . Due to different experimental setups, some of the components in the six-component model had to be restrained. The hypothesis about Ca 2z liberation from the intracellular stores was first experimentally verified, and then reproduced by simulations. The simulations supported the experimental findings in both Ca 2z free media and with normal extracellular Ca 2z containing environment. The variability of biological signals cannot be accurately mimicked by deterministic models alone, which justified the use of stochastic methods.
A mathematical model, presented in this study, integrates data from several experimental sources and thus provides a way to computationally follow Ca 2z changes in biologically relevant conditions. Here, the stochastic model was able to reproduce the Ca 2z signals seen in the experimental Fura-2AM measurements.  Potential pitfall of modeling, in general, is the inadequate experimental data. Experiments should originally be designed also to fulfill the demands of a modeling approach, including the need of considerable amount of repetitions, relevant statistics, and adequate metadata. When new components, describing cellular functions, will be added in the model, it will help to explore further the possible mechanisms behind the measured Ca 2z signals. This may advance the study of astrocytic Ca 2z signals and their effects on neuronal networking in the central nervous system, by adding information of the intracellular targets activated by Ca 2z transients (studies on astrocytic Ca 2z waves are reviewed in [56]). Calcium transients are known to affect the important intracellular Ca 2z sensitive peptides, such as protein kinases and phosphatases. In addition, the passage of Ca 2z signals could lead to the priming of the astrocytes, thus modifying forthcoming astrocytic responses, setting the cellular basis for plasticity in glial cells [56]. Leissring et al. [57] have discussed the possibility that mutations in presenilin 1 (one of the factors in familial AD involved in the accumulation of amyloid b fragments in the brain) may change the activity of the ER Ca 2z -ATPases, e.g., SERCA. ATPases are associated with pumping the cytosolic Ca 2z into the ER lumen, leading eventually to higher concentration of Ca 2z in ER. Amyloid b peptide accumulation may lead to higheramplitude [Ca 2z ] cyt signals, have an effect on other Ca 2z -induced release, and increase intracellular IP 3 sensitivity [57]. Thus, the exceptional cytosolic Ca 2z signals via ER, overfilled with Ca 2z , may explain the Ca 2z changes detected in the familial AD. Possible extension of the here developed stochastic model could be the incorporation of some specific IP 3 R model into the proposed model to study the role of altered IP 3 sensitivity on the overall Ca 2z signaling.
The simulations run with our stochastic model did not take into account the possibility that the synergistic effects of Ab25-35 and 5-HT could be due to increased activation of, e.g., SERCA pumps. In addition, the pitfall of the here introduced stochastic model is that it does not take into account spontaneous Ca 2z signaling in astrocytes (modeled, e.g., in [55]). To include these phenomena into our stochastic model would need further studies and tuning of model parameters. Progressive inclusion of additional components could lead to a still more realistic model of the Ca 2z signaling in astrocytes. In general, a better understanding of the involvement of astrocytes in the developing pathology of Alzheimer's disease is of great importance for the future development of diagnosis and treatment. Early diagnosis of AD is important for initiating treatment and for understanding the pathobiology of the disease [58]. Ab-induced astrocyte activation is thought to have a critical role in the mechanisms of neurodegeneration in AD [59], as astrocytes signal to neurons in response to a physiological stimulus (see, e.g., [60]). The active participation of astrocytes in synaptic processes is of utmost importance for physiology of the nervous system [61,62]. Studies combining experimental and computational experiments, like the present one, are required as they may provide us novel viewpoints and help explaining the possible mechanisms behind certain experimental findings.