⇦Chinese Physics Letters, 2017, Vol. 34, No. 9, Article code 098701 Temperature Impacts on Transient Receptor Potential Channel Mediated Calcium Oscillations in Astrocytes * Yu-Hong Zhang(张玉红), Hui Liu(柳辉), Ying-Rong Han(韩英荣), Ya-Fei Chen(陈雅斐), Su-Hua Zhang(张素花), Yong Zhan(展永)** Affiliations School of Sciences, Hebei University of Technology, Tianjin 300401 Received 12 October 2016 *Supported by the National Natural Science Foundation of China under Grant Nos 11175055 and 11547013, and the Natural Science Foundation of Hebei Province under Grant No A2015202268.
**Corresponding author. Email: zhany@hebut.edu.cn Citation Text: Zhang Y H, Liu H, Han Y R, Chen Y F and Zhang S H et al 2017 Chin. Phys. Lett. 34 098701 Abstract We computationally study the possible effects of thermosensitive transient receptor potential (TRP) channels on the spontaneous calcium oscillations in astrocytes at various temperatures. Based on the previous model and the result of thermosensitive TRP channels' open probabilities, some meaningful conclusions are obtained. It is shown that the occurrence of calcium oscillations depends on temperature and the molar heat capacity difference between the closed and open channels ($\Delta C_{\rm p}$). The data indicate that calcium oscillations in astrocytes occurred in the ranges of 7$^{\circ}\!$C–11$^{\circ}\!$C and 27$^{\circ}\!$C–30$^{\circ}\!$C when $\Delta C_{\rm p}$ is 16 kJ$\cdot$mol$^{-1}\cdot$K$^{-1}$, and calcium oscillations only occur in the range of 27$^{\circ}\!$C–30$^{\circ}\!$C when $\Delta C_{\rm p}$ is 2 kJ$\cdot$mol$^{-1}\cdot$K$^{-1}$. In this study, the frequency decreases rapidly at temperatures ranging from 7$^{\circ}\!$C to 11$^{\circ}\!$C, and there is a contrary result in the range of 27$^{\circ}\!$C–30$^{\circ}\!$C. DOI:10.1088/0256-307X/34/9/098701 PACS:87.16.Uv, 05.70.Ln © 2017 Chinese Physics Society Article Text Astrocyte is one of the major cell types found in the human central nervous system (CNS) that serves a wide range of adaptive functions.[1,2] It is also known that astrocytes participate in many housekeeping functions such as modulating neurotransmitter systems and synaptic information processing, ionic homeostasis, energy metabolism, regulating cerebral blood flow, and stabilizing the extracellular environment.[3-7] Ca$^{2+}$ signaling is the predominant form of astrocytic signaling activity. The increase of calcium concentration in the astrocytes can lead to a release of neurotransmitters and glutamate.[8-10] There are some spontaneous Ca$^{2+}$ responses including several compounds such as random profiles, rhythmic oscillations, and bursting activity. Fields found visualizing calcium signaling exist in astrocytes.[11] Many experiments about calcium oscillations in astrocytes have been reported recently.[12-15] A recent study showed that astrocyte TRPA1 channels have an effect on basal Ca$^{2+}$ levels.[16] Shibasaki et al. revealed that TRPV2 is functionally expressed in astrocytes in addition to neurons using a combination of histological and physiological methods.[17] It was reported that the TRPV4 channel is also expressed in astrocytes.[18] Shibasaki's experimental results suggested that thrombin-induced upregulation of TRPC3 contributes to the pathological activation of astrocytes.[19] It is generally known that TRP channels are activated by a wide range of stimuli including changes in temperature, pressure and inflammatory agents. A mathematical model of calcium oscillations in astrocytes was successfully designed to simulate the inositol 1,4,5-triphosphate (IP3)-dependent calcium-induced calcium release (CICR) process by Lavrentovich and Hemkin.[20] Using this model we try to simulate the effects of temperature on calcium oscillations in astrocytes mediated by TRP channels. Previous works showed that the oscillatory behavior can be initiated by small changes in cytosolic calcium concentration ($[{\rm Ca}^{2+}]_{\rm cyt}$), which is caused by varying the flux of extracellular Ca$^{2+}$ across the cell membrane into the cytosol.[20] The conclusion is adopted in this study. The model is described by three ordinary differential equations[20] $$\begin{align} \frac{dX}{dt}=\,&\upsilon _1 -k_1 X+\upsilon _3 -\upsilon _2 +k_2 (Y-X),~~ \tag {1} \end{align} $$ $$\begin{align} \frac{dY}{dt}=\,&\upsilon _2 -\upsilon _3 -k_2 (Y-X),~~ \tag {2} \end{align} $$ $$\begin{align} \frac{dZ}{dt}=\,&\upsilon _4 -k_3 Z,~~ \tag {3} \end{align} $$ where $X$, $Y$ and $Z$ represent Ca$^{2+}$ concentration in the cytosol, Ca$^{2+}$ concentration in the endoplasmic reticulum (ER) and IP$_{3}$ concentration in the cell, respectively, $$\begin{align} \upsilon _2 =\,&\upsilon _M \Big(\frac{X^2}{X^2+K_4^2 }\Big),\\ \upsilon _3 =\,&4\upsilon _N \Big(\frac{K_6^n X^n}{(X^n+K_6^n )({X^n+K_7^n })}\Big)\\ &\times \Big(\frac{Z^m}{Z^m+K_8^m }\Big)({Y-X}),\\ \upsilon _4 =\,&\upsilon _{\rm p} \Big(\frac{X^2}{X^2+K_5^2 }\Big). \end{align} $$ The term $\upsilon _1$ describes the calcium flow from the extracellular space to the cytosol, $k_1 X$ is the rate of calcium efflux from the cytosol to the extracellular space, $\upsilon _2$ is the flux from the sarcoplasmic or endoplasmic reticulum ATPase that fills the ER with Ca$^{2+}$ from the cytosol, and $\upsilon _3$ is the IP$_{3}$-mediated calcium flux from the ER into the cytosol. Because of the concentration gradient, $k_2 ({Y-X})$ describes the leakage flux from the ER into the cytosol, $\upsilon _4$ denotes the rate of IP$_{3}$ production, $k_3 Z$ describes the rate of IP$_{3}$ degradation. A detailed description of this model can be found in Ref. [20]. The increase of cytosolic calcium concentration ($[{\rm Ca}^{2+}]_{\rm cyt}$) represents a form of astrocyte excitability. TRP channels that are functionally expressed in astrocytes, also participate in the calcium oscillations in astrocytes. In this study, we ignore the effects of calcium channels on $[{\rm Ca}^{2+}]_{\rm cyt}$, and only consider the effects of thermosensitive TRP channels on $[{\rm Ca}^{2+}]_{\rm cyt}$. The open probability of a thermosensitive TRP channel is given by Voets[21] as follows: $$\begin{align} P_0 =\frac{1}{1+\exp \Big[-\frac{zF}{RT}(V-V_{1/2})\Big]},~~ \tag {4} \end{align} $$ where $z$ is the gating charge, $V$ is the transmembrane voltage, $F$ is the Faraday constant, $R$ is the universal gas constant, and $V_{1/2}$ represents the voltage for half-maximal activation. Here $V_{1/2}$ changes linearly with temperature according to $$ V_{1/2} =\frac{1}{zF}(\Delta H-T\Delta S), $$ and $$\begin{align} \Delta H=\,&\Delta H_0 +\Delta C_{\rm p} (T-T_0), \\ \Delta S=\,&\Delta S_0 +\Delta C_{\rm p} \ln (T/T_0), \end{align} $$ where $\Delta H$, $\Delta S$ and $\Delta C_{\rm p}$ represent the differences in enthalpy, entropy and molar heat capacity between the closed and open channel. Clapham and Miller put forward the hypothesis that the conformational change of thermosensitive TRP channel is accompanied by a change in molar heat capacity ($\Delta C_{\rm p}$).[22] Here $\Delta H_0$ and $\Delta S_0$ represent the differences in enthalpy and entropy at reference temperature $T_0$, respectively, and $T_0$ is a 'modulation' parameter sensitive to molecular variations such as sequence, mutations and splice variants.[22] We suppose that the open probability at the given temperature $T_0$ is written as $P'_0$. When the open probability changes with temperature, the influx rate of Ca$^{2+}$ into the cell can be rewritten as $$\begin{align} \upsilon _1 \to \upsilon _1 \times \frac{P_0 }{P'_0}.~~ \tag {5} \end{align} $$ That is to say, instead of a unique flow in Eq. (1), we use Eqs. (4) and (5) to simulate the influence of temperature on $[{\rm Ca}^{2+}]_{\rm cyt}$. In this study, Ca$^{2+}$ oscillations in astrocytes are observed when the open probability of TRP channels changes with temperature. Parameter values are selected from Ref. [20] for all simulations unless noted.
cpl-34-9-098701-fig1.png
Fig. 1. Temperature dependence of the open probability of TRP channels ($\Delta C_{\rm p} =16$ kJ$\cdot$mol$^{-1}\cdot$K$^{-1}$).
cpl-34-9-098701-fig2.png
Fig. 2. The occurrence of calcium oscillations depends on the temperature. (a) There is no calcium oscillations in the temperature ranges of $-$20$^{\circ}\!$C–7$^{\circ}\!$C, 11$^{\circ}\!$C–27$^{\circ}\!$C, and 30$^{\circ}\!$C–60$^{\circ}\!$C. (b) The curves of calcium oscillations at different temperatures (7$^{\circ}\!$C–11$^{\circ}\!$C). (c) The curves of calcium oscillations at different temperatures (27$^{\circ}\!$C–30$^{\circ}\!$C).
Figure 1 shows the effect of temperatures on the open probability of TRP channels. The given temperature $T_0$ is 30$^{\circ}\!$C in this model. Here $\Delta H_0 =180$ kJ$\cdot$mol$^{-1}$, $\Delta S_0 =0.5$ kJ$\cdot$mol$^{-1}\cdot$K$^{-1}$, $z=0.8$, and $V=-70$ mV. These parameter values are taken from the work of Voets.[21] The value of $\Delta C_{\rm p}$ is 16 kJ$\cdot$mol$^{-1}\cdot$K$^{-1}$ in Figs. 1 and 2. The open probability $P_0$ varies with temperature, as shown in Fig. 1. Here $P_0$ decreases gradually when the temperature increases from 1$^{\circ}\!$C to 18$^{\circ}\!$C, and $P_0$ reaches the minimum when the temperature is about 20$^{\circ}\!$C. Then, it increases gradually between 18$^{\circ}\!$C and 50$^{\circ}\!$C, and $P_0$ is 1 at about 50$^{\circ}\!$C. In the following the changes of cytosolic calcium concentration with time are discussed in the temperature ranges of $-$20$^{\circ}\!$C–60$^{\circ}\!$C. The curves of cytosolic calcium concentration are shown in Fig. 2(a) in the temperature ranges of $-$20$^{\circ}\!$C–7$^{\circ}\!$C, 11$^{\circ}\!$C–27$^{\circ}\!$C and 30$^{\circ}\!$C–60$^{\circ}\!$C. We can see that the curve drops rapidly to a lower value in the temperature ranges of 3$^{\circ}\!$C–7$^{\circ}\!$C, 11$^{\circ}\!$C–27$^{\circ}\!$C and 30$^{\circ}\!$C–35$^{\circ}\!$C. The curve rises rapidly to a higher value in the temperature ranges of $-$20$^{\circ}\!$C–3$^{\circ}\!$C and 35$^{\circ}\!$C–60$^{\circ}\!$C. As shown in Fig. 2(b), the curves of calcium oscillations are shown in the temperature range of 7$^{\circ}\!$C–11$^{\circ}\!$C. The frequency of calcium oscillations decreases with the increase of the temperature. The curves of calcium oscillations in the temperature range of 27$^{\circ}\!$C–30$^{\circ}\!$C are displayed in Fig. 2(c). The change of oscillations frequency is contrary to the conclusion of Fig. 2(b). From Figs. 2(a)–2(c), we can draw the conclusions that the occurrence of calcium oscillations depends on the temperature, and the frequency of calcium oscillations can be affected by the temperature. In this study, we illustrate that different conformational states (different $\Delta C_{\rm p}$) have different reactions at the same temperature. The curves of cytosolic calcium concentration are given in Fig. 3(a), where $\Delta C_{\rm p}$ is 2 kJ$\cdot$mol$^{-1}\cdot$K$^{-1}$ and 16 kJ$\cdot$mol$^{-1}\cdot$K$^{-1}$. The results show that calcium oscillations depend on $\Delta C_{\rm p}$ when the temperature is 10$^{\circ}\!$C. When $\Delta C_{\rm p}$ is 2 kJ$\cdot$mol$^{-1}\cdot$K$^{-1}$, there are no calcium oscillations, and when $\Delta C_{\rm p}$ is 16 kJ$\cdot$mol$^{-1}\cdot$K$^{-1}$, the calcium oscillations occur. The value of $\Delta C_{\rm p}$ is 2 kJ$\cdot$mol$^{-1}\cdot$K$^{-1}$ in Figs. 3(b) and 3(c). As shown in Fig. 3(b), the cytosolic calcium concentrations are related to the temperature. The curve drops rapidly to a lower value in the temperature ranges of $-$20$^{\circ}\!$C–27$^{\circ}\!$C and 30$^{\circ}\!$C–36$^{\circ}\!$C. The curve rises rapidly to a higher value in the temperature range of 36$^{\circ}\!$C–60$^{\circ}\!$C. The curves of calcium oscillations are shown in Fig. 3(c) in the temperature range of 27$^{\circ}\!$C–30$^{\circ}\!$C. The relationship between oscillation frequency and temperature is similar to the conclusion of Fig. 2(c). In this work, we adopt Clapham and Miller's point of view. Clapham and Miller suggested that TRP channel gating is accompanied by large changes in molar heat capacity ($\Delta C_{\rm p}$). However, the related experiment has not been found. In this study, we have a qualitative discussion about the possible effects of thermosensitive TRP channels on the spontaneous calcium oscillations in astrocytes. Based on the results of Clapham and Miller, we carry out the related research. Because conformational changes of thermosensitive TRP channel for different $\Delta C_{\rm p}$ are different, the physiological effects are not the same. From the above discussion, calcium oscillations occur in two ranges of temperature, as shown in Fig. 2. However, in Fig. 3, calcium oscillations only occur in a temperature range. This may be an inevitable result because of the adoption of Clapham and Miller's point of view. However, to date, no relative experiment has been reported. However, it also provides a possibility for experimental study. On the other hand, our simulations may depend on a number of simplified assumptions, and the periods of calcium oscillations obtained here seem to be larger than typical values.
cpl-34-9-098701-fig3.png
Fig. 3. (a) The occurrence of calcium oscillations depends on the selection of $\Delta C_{\rm p}$ when the temperature is 10$^{\circ}\!$C. (b) The upper and lower plots correspond to $[{\rm Ca}^{2+}]_{\rm cyt}$ in $-$20$^{\circ}\!$C–27$^{\circ}\!$C, 30$^{\circ}\!$C–36$^{\circ}\!$C and 36$^{\circ}\!$C–60$^{\circ}\!$C. (c) The curves of calcium oscillations at different temperatures (27$^{\circ}\!$C–30$^{\circ}\!$C).
In addition, we find that calcium oscillations do not occur near the physiological temperature of 36.5$^{\circ}\!$C in this study. Perhaps it is because we simplify the related factors of the impact of calcium concentration to a certain extent. For example, the change of calcium concentration in astrocytes is related not only to TRP channels, but also to calcium channels. However in this study, we only consider the influence of TRP channels. On the other hand, the activation of TRP channels depends not only on temperature, but also on other activated factors including pressure and stimulants. Here we only take into account the influence of temperature on the calcium oscillations mediated by TRP channels. It is well known that astrocytes can respond to a variety of stimuli by increasing their cytosolic Ca$^{2+}$ concentration and can release glutamate to signal adjacent neurons in turn. In this study, a theoretical model proposed in the literature is used to explore the possible effects of thermosensitive TRP channels on the spontaneous calcium oscillations in astrocytes. We find that Ca$^{2+}$ entry via thermosensitive TRP channels plays an important role in astrocytic Ca$^{2+}$ dynamics. From this study, we obtain some useful conclusions: Firstly, the results show that the occurrence of calcium oscillations depends on the selection of $\Delta C_{\rm p}$. Our data show that calcium oscillations in astrocytes occur in the ranges of 7$^{\circ}\!$C–11$^{\circ}\!$C and 27$^{\circ}\!$C–30$^{\circ}\!$C when $\Delta C_{\rm p}$ is 16 kJ$\cdot$mol$^{-1}\cdot$K$^{-1}$, and calcium oscillations only occur in the range of 27$^{\circ}\!$C–30$^{\circ}\!$C when $\Delta C_{\rm p}$ is 2 kJ$\cdot$mol$^{-1}\cdot$K$^{-1}$. Secondly, calcium oscillations in astrocytes are strongly dependent on temperature, and the frequency of calcium oscillations in astrocytes is also found to be related to the temperature. In our study, the frequency decreases rapidly at temperatures ranging from 7$^{\circ}\!$C to 11$^{\circ}\!$C, and there is a contrary result in the range of 27$^{\circ}\!$C–30$^{\circ}\!$C. References Brain Energy Metabolism: Focus on Astrocyte-Neuron Metabolic CooperationMechanisms of Disease: astrocytes in neurodegenerative diseaseNew roles for astrocytes: Redefining the functional architecture of the brainWhat is the role of astrocyte calcium in neurophysiology?The astrocyte odysseyResveratrol increases antioxidant defenses and decreases proinflammatory cytokines in hippocampal astrocyte cultures from newborn, adult and aged Wistar ratsGlutamate-mediated astrocyte–neuron signallingVisualizing Calcium Signaling in AstrocytesPharmacological characterization of the involvement of protein kinase C in oscillatory and non-oscillatory calcium increases in astrocytesSpontaneous and glutamate evoked calcium oscillations in rat hippocampal astrocytesLong-term facilitation of spontaneous calcium oscillations in astrocytes with endogenous adenosine in hippocampal slice culturesHippocampal short- and long-term plasticity are not modulated by astrocyte Ca2+ signalingTRPA1 Channels Are Regulators of Astrocyte Basal Calcium Levels and Long-Term Potentiation via Constitutive D-Serine ReleaseAstrocytes express functional TRPV2 ion channelsPathological potential of astroglia.Differential functions between TRPV2 and TRPV4 in astrocytes to regulate neuronal excitabilityA mathematical model of spontaneous calcium(II) oscillations in astrocytesA thermodynamic framework for understanding temperature sensing by transient receptor potential (TRP) channels
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