Spontaneous calcium signaling of cartilage cells: from spatiotemporal features to biophysical modeling

Abstract

Intracellular calcium ([Ca²⁺]_i) oscillation is a fundamental signaling response of cartilage cells under mechanical loading or osmotic stress. Chondrocytes are usually considered as nonexcitable cells with no spontaneous [Ca²⁺]_i signaling. This study proved that chondrocytes can exhibit robust spontaneous [Ca²⁺]_i signaling without explicit external stimuli. The intensity of [Ca²⁺]_i peaks from individual chondrocytes maintain a consistent spatiotemporal pattern, acting as a unique “fingerprint” for each cell. Statistical analysis revealed lognormal distributions of the temporal parameters of [Ca²⁺]_i peaks, as well as strong linear correlations between their means and sds. Based on these statistical findings, we hypothesized that the spontaneous [Ca²⁺]_i peaks may result from an autocatalytic process and that [Ca²⁺]_i oscillation is controlled by a threshold-regulating mechanism. To test these 2 mechanisms, we established a multistage biophysical model by assuming the spontaneous [Ca²⁺]_i signaling of chondrocytes as a combination of deterministic and stochastic processes. The theoretical model successfully explained the lognormal distribution of the temporal parameters and the fingerprint feature of [Ca²⁺]_i peaks. In addition, by using antagonists for 10 pathways, we revealed that the initiation of spontaneous [Ca²⁺]_i peaks in chondrocytes requires the presence of extracellular Ca²⁺, and that the PLC–inositol 1,4,5-trisphosphate pathway, which controls the release of calcium from the endoplasmic reticulum, can affect the initiation of spontaneous [Ca²⁺]_i peaks in chondrocytes. The purinoceptors and transient receptor potential vanilloid 4 channels on the plasma membrane also play key roles in the spontaneous [Ca²⁺]_i signaling of chondrocytes. In contrast, blocking the T-type or L-type voltage-gated calcium channel promoted the spontaneous calcium signaling. This study represents a systematic effort to understand the features and initiation mechanisms of spontaneous [Ca²⁺]_i signaling in chondrocytes, which are critical for chondrocyte mechanobiology.—Zhou, Y., Lv, M., Li, T., Zhang, T., Duncan, R., Wang, L., Lu, X. L. Spontaneous calcium signaling of cartilage cells: from spatiotemporal features to biophysical modeling.

Chondrocytes, the only cell population in articular cartilage, are responsible for the homeostasis of cartilage extracellular matrix (ECM). Residing in the ECM, chondrocytes have no direct access to the circulatory or nervous systems, relying instead on other intercellular communication methods. One of the intercellular communication pathways is through calcium ions, a fundamental second messenger (1) in cell signaling. Oscillation of the intracellular calcium ([Ca²⁺]_i) concentration, known as calcium signaling, is an intracellular activity with highly versatile patterns. [Ca²⁺]_i signaling can induce ATP release from plasma membrane, and the diffusion of extracellular ATP can induce calcium responses in neighboring cells (2). Calcium wave propagation represents an effective intercellular communication method (3). Cells employ various strategies to initiate [Ca²⁺]_i signaling (4). Some excitable cells, such as neurons or cardiac muscle cells, can initiate [Ca²⁺]_i peaks spontaneously. Most musculoskeletal cells, on the other hand, can have calcium responses under external stimuli, such as mechanical loading (5–7) or fluid flow (8–10). In chondrocytes, [Ca²⁺]_i signaling can be induced and regulated by hydrostatic pressure (11), fluid flow (12), mechanical stimulation (13, 14), or osmotic stress (15, 16). Recently, spontaneous [Ca²⁺]_i signaling has been discovered in chondrocytes in monolayer culture or tissue explants (17–19). However, because of the variety of experimental conditions, the characteristics of the observed spontaneous [Ca²⁺]_i peaks vary significantly among different studies. In contrast to the neuronal or cardiac cells, chondrocytes are generally considered to be nonexcitable cells in terms of the calcium signaling. Little is known about the initiation mechanisms of the spontaneous [Ca²⁺]_i signaling in chondrocytes.

[Ca²⁺]_i signaling, as a tool for cell self-regulation, orchestrates cellular functions to varying degrees in many eukaryotes. One would expect the pattern of [Ca²⁺]_i signaling parameters to be deterministic (20). However, there is huge variability among the [Ca²⁺]_i signals of the same cell type in the same environment. If the [Ca²⁺]_i activities are controlled by multiple parallel or independent processes, the spatiotemporal parameters of the [Ca²⁺]_i fluctuations should follow a standard gaussian normal distribution according to the central limit theorem (21). However, the spatiotemporal characteristics of [Ca²⁺]_i peaks (e.g., number for multiple peaks from a single cell, time it takes to reach a peak from the baseline) of the same cell population were found to follow a lognormal distribution rather than a normal distribution (22, 23). Little knowledge is available to interpret this statistical distribution profile of the [Ca²⁺]_i peak parameters.

It is understood that [Ca²⁺]_i signaling in cells is mainly due to the influx or outflux of Ca²⁺ ions from the cytosol space, but the mechanisms regulating the ion transports remain partially understood. For chondrocytes under physical stimuli, several essential pathways that are involved in the [Ca²⁺]_i signaling have been identified. For example, extracellular Ca²⁺ sources (24), ATP release, extracellular ATP transport (25), and purinoceptors on the plasma membrane (26, 27) all play critical roles in the Ca²⁺ influx for the stimulated chondrocytes. Endoplasmic reticulum (ER) (28) functions as the major cytosol Ca²⁺ reservoir. Its release is controlled by the PLC related pathway (29). In addition, mechanical sensitive ion channels [e.g., piezo-type mechanosensitive ion channel component (PIEZO) 1 and -2 channels] (30), transient receptor potential vanilloid 4 (TRPV4) (16), and voltage-gated ion channels on the plasma membrane (31, 32) can all facilitate Ca²⁺ transport. For chondrocytes without external stimuli, however, the pathways regulating the spontaneous [Ca²⁺]_i oscillation remain largely unknown. In this study, we investigated the biophysics of spontaneous [Ca²⁺]_i signaling of in situ chondrocytes. In addition to the spatiotemporal parameters of [Ca²⁺]_i peaks, the roles of 10 essential pathways were examined. Based on the experimental data, a biophysical model was proposed to describe the initiation and developing mechanisms of the spontaneous [Ca²⁺]_i peaks, as well as the statistical features of their spatiotemporal parameters.

MATERIALS AND METHODS

Chemicals and reagents

DMEM, calcium-free HBSS, ITS Plus Premix, and sodium pyruvate were purchased from Thermo Fisher Scientific (Waltham, MA, USA). l-proline, ascorbate 2-phosphate, dexamethasone, DMSO, 18α-glycyrrhetinic acid (18α-GA), EGTA (cell-impermeable), NNC 55-0396 hydrate, apyrase, pyridoxal-phosphate-6-azophenyl-2′,4′-disulfonate (PPADS), neomycin, GSK205, NNC 55-0396, verapamil, gadolinium chloride (GdCl3), HEPES, and thapsigargin were obtained from MilliporeSigma (Burlington, MA, USA).

Cartilage explant culture

Cylindrical cartilage explants were harvested from the femoral condyle heads of 3–6 mo-old fresh bovine knee joints (Green Village Packing, Green Village, NJ, USA) using a 3-mm diameter biopsy punch. Explant thickness was controlled at 2 mm using a custom-designed cutting tool to guarantee 2 parallel-end surfaces of the cylindrical samples (Fig. 1A). Cartilage explants were cultured at 37°C and 100% humidity in chondrogenic medium (DMEM, 1% ITS Plus Premix, 50 μg/ml l-proline, 0.1 μM dexamethasone, 0.9 mM sodium pyruvate, 50 μg/ml ascorbate 2-phosphate) (33) for 3 d, which allowed the chondrocytes inside the explant to adapt to the in vitro culture environment.

Figure 1.

Harvest of fresh cartilage explant and fluorescent calcium imaging of in situ chondrocytes. A) Fresh cartilage explants were harvested from the central region of femoral condyle heads of bovine knee joint. B) Half cylindrical cartilage explant was dyed with Fluo-8 AM, placed in an imaging chamber filled with DMEM medium, and imaged on a confocal microscope. Imaging area was at the central region of the cross-section area, which was 200 µm below the articular surface. Fluorescent images of the in situ chondrocytes located 50 µm inside the tissue were taken at 1.5 s per frame for 16 min (scale bar, 50 µm). C) A typical [Ca²⁺]_i intensity curve of chondrocyte with 2 spontaneous peaks. Spatiotemporal parameters of the [Ca²⁺]_i peaks include number of peaks, normalized maximum magnitude of a peak (m₁), time from baseline to the peak (t₁), and time from peak value to 50% relaxation (t₂).

Calcium imaging of in situ chondrocytes

A cartilage explant was split into 2 identical halves using a cutting tool (ASI Instruments, Warren, MI, USA), and cells in both halves were loaded with 5 μM Fluo-8 AM (AAT Bioquest, Sunnyvale, CA, USA) in DMEM for 40 min (34–36). The samples were then washed for 5 min in 37°C DMEM medium (with 10 mM HEPES) 3 times. Two halves from 1 explant were separated into the control and treatment groups, respectively (see details below). The halved cylindrical sample was placed in a DMEM filled imaging chamber with the cross-section area facing down (Fig. 1B). The imaging chamber was fixed on a confocal microscope (LSM510; Carl Zeiss, Jena, Germany), and the sample was left untouched for 15 min to recover from any agitation due to handling (37). The imaging focal plane was positioned at a distance of ∼50 µm from the cross-section surface (the average size of chondrocyte is ∼10 µm). Calcium images of chondrocytes were captured every 1.5 s for 16 min by a ×20 objective lens with a Zeiss LSM510 confocal microscope (488 nm laser excitation, 505–550 nm emission filter), while the sample was kept undisturbed (Fig. 1B).

Fluctuation of [Ca²⁺]_i intensity over time was extracted and analyzed as previously described (3, 19, 38–40). In brief, the average fluorescent intensity of each cell in the images was extracted and normalized to the basal intensity value when the cell was at rest. The change of imaging intensity should be positively correlated with the oscillation of [Ca²⁺]_i concentration. A cell was defined as responsive if it displayed a [Ca²⁺]_i peak with a magnitude 4 times higher than its noise level of the baseline (41). The responsive percentage was defined as the fraction of cells showing [Ca²⁺]_i oscillation over all viable cells. The number of [Ca²⁺]_i peaks during the 16-min recording period was counted for all the responsive cells. The spatiotemporal parameters of the [Ca²⁺]_i peaks were defined following a standard protocol, as shown in Fig. 1C (19, 39), which include the normalized maximum magnitude of a peak (m₁), the time from baseline to the peak (t₁), and time from the peak value to 50% relaxation (t₂).

Pathway study

In addition to the control experiments described above, the other half of the cartilage explants were randomly assigned into one of the 10 antagonist treatment groups. All studied pathways are illustrated in Fig. 2A. The effects of extracellular calcium sources on the calcium signaling were investigated with 3 different treatments. 1) Extracellular calcium chelating (EGTA): 10 mM EGTA was added into the medium to remove all free extracellular Ca²⁺ (24, 42). 2) Extracellular calcium source depletion: calcium-free HBSS medium was used during the imaging (2, 39). 3) Gap junction blocking: 75 μM 18α-GA medium (0.375% v/v DMSO) was used to block the gap junctions between chondrocytes (25, 43). Gap junctions can facilitate the rapid exchange of Ca²⁺ and other small molecules (e.g., ATP) between the interconnected cells. Four more treatment groups were designed to study the involvement of the [Ca²⁺]_i stores. 4) Extracellular ATP hydrolysis: 10 U/ml apyrase was added to hydrolyze the extracellular ATP released by cells (44, 45). ATP can activate the purinoceptors on the plasma membrane, including P2Y receptors, which can further activate the PLC–inositol 1,4,5-trisphosphate (IP₃) pathway and induce the release of ER stored calcium. 5) ER calcium store depletion: 1 μM thapsigargin (TG) medium (0.065% v/v DMSO) was used to deplete the Ca²⁺ in ER (46, 47). 6) PLC-IP₃ pathway blocking: PLC activity was inhibited by 11 mM neomycin (39, 48). 7) Purinoceptor blocking: Sample was treated with 167 μM PPADS, a nonselective P2 purinoceptor antagonist (49, 50). In addition, 3 types of ion channels on plasma membrane were studied. 8) Mechanosensitive ion channels: Sample was treated with 20 μM GdCl₃. 9) TRPV4 channel: 10 μM GSK205 was used to block the TRPV4 channel (16, 51). 10) Voltage-gated calcium channel (VGCC): 17.7 µM NNC 55-0396 was used to block the T-type VGCC (52, 53); 100 µM verapamil was used to block the L-type VGCC (54–56).

Figure 2.

Calcium signaling pathways and their effects on the calcium responsive percentage of chondrocytes. A) Ten treatment groups were designed to understand the roles of several essential pathways in the spontaneous calcium signaling of in situ chondrocytes. The pathways include extracellular Ca²⁺ source, intracellular ER calcium store, purinoceptors, mechanosensitive channel, TRPV4 channel, T-type VGCC (T-VGCC) and L-type VGCC (L-VGCC), and intercellular gap junctions on plasma membrane. The corresponding antagonist of each pathway is listed in black. Length scales of the components involved in calcium signaling are listed at the bottom for reference. B–D) Responsive percentage of in situ chondrocytes, defined as the number of cells with spontaneous [Ca²⁺]_i peaks divided by the total number of cells in the recorded fluorescent videos. Responsive percentages of the antagonist-treated samples and their corresponding controls are compared in each plot. Data are shown as means + sd with data points overlapped. ***P < 0.001.

Concentrations of all drugs were determined in previous studies in which effective inhibition was demonstrated in chondrocytes. The diffusion coefficients of these chemicals in cartilage were in the range from 0.3 × 10⁻¹¹ to 29.0 × 10⁻¹¹ m²/s (57). Thus, a 30-min treatment time was anticipated to be sufficient for the antagonist chemicals to diffuse and reach the extracellular space of the imaged chondrocytes (50 µm below the surface).

Biophysical model of a spontaneous [Ca²⁺]_i peak

In chondrocytes, the intracellular cytosol Ca²⁺ concentration is about 0.1 μM (i.e., ∼10⁵ Ca²⁺ ions in cytosol assuming a cell volume around 1000 µm³). Stochastic movement of these Ca²⁺ ions could activate a single channel and form small Ca²⁺ puffs (58), Ca²⁺ signals confined in small cytoplasmic region. Many studies found that small Ca²⁺ puffs, usually at suborganelle level (<100 nm) (59–62), represent the basic units in a cellular-level [Ca²⁺]_i fluctuation (60). A local Ca²⁺ puff can stochastically propagate and trigger Ca²⁺ puffs in surrounding areas. Thus a Ca²⁺ puff could be an autocatalytic process (i.e., the reaction products could function as the catalyst for the same reaction). Accumulation of small Ca²⁺ puffs could eventually be strong enough to activate a major calcium signaling pathway, such as the store operated calcium channels (∼1 µm). Activation of a major calcium pathway can lead to a cellular level (∼10 µm) calcium signaling event. For example, such cascading actions can cause the Ca²⁺ release from the ER [Ca²⁺]_i store, which is known as the calcium-induced calcium release (63, 64). Based on these facts, we assume that the spontaneous [Ca²⁺]_i peaks in chondrocytes are initiated by the stochastic Ca²⁺ puffs as an autocatalytic process. This assumption is also based on the general belief that the initiation of biologic signaling could be a stochastic and random process (65). In contrast, the initiation of cellular-level calcium signaling is well known to be controlled by specific pathways and cell organelles, such as the 10 pathways listed in Fig. 2A. The activation of these pathways and organelles belong to deterministic activities. Thus, in our biophysical model, spontaneous [Ca²⁺]_i signaling in chondrocytes is considered a hybrid stochastic-deterministic process.

To predict the profile of [Ca²⁺]_i peaks, we divide each [Ca²⁺]_i peak into 3 consequent stages (see Supplemental Data for equations of the biophysical model). 1) Exponential initiation stage: According to the autocatalytic assumption for calcium signaling, a certain amount of Ca²⁺ influx could induce further Ca²⁺ influx. Here, the rate of such induction is assumed to be proportional to the current [Ca²⁺]_i concentration. A parameter, , is defined as the average rate coefficient of calcium-induced calcium influx, indicating the rate of an autocatalytic process for current [Ca²⁺]_i concentration to induce Ca²⁺ influx. By mathematical deduction, the [Ca²⁺]_i concentration rises at an exponential rate during this stage. 2) Logistic rising stage: The exponential increase of [Ca²⁺]_i concentration in stage I ceases at a certain point, as the prolonged high [Ca²⁺]_i level is toxic to cells (22). After the [Ca²⁺]_i concentration exceeds a certain threshold, the [Ca²⁺]_i peak enters stage II, at which the calcium influx and outflux from cytosol compete with each other, slowing down the net increase of [Ca²⁺]_i. Here, a parameter, , is defined as the average rate coefficient of calcium-induced calcium outflux. At this stage, and constants orchestrate the net [Ca²⁺]_i amount in cytosol. The outcome is a dampening of the net Ca²⁺ influx speed, leading to an S-shaped curve (logistic curve) for the [Ca²⁺]_i concentration at this stage. At the end of this stage, calcium outflux equals to the influx, and [Ca²⁺]_i concentration in cytosol reaches its peak value. 3) Reciprocal relaxation stage: After reaching the peak [Ca²⁺]_i, calcium outflux dominates calcium influx, and [Ca²⁺]_i concentration starts to decrease toward the baseline. Here we assume that the [Ca²⁺]_i concentration at the decreasing stage follows a reciprocal function of time. Using this simplified triple-stage mathematical model, spontaneous [Ca²⁺]_i peaks of chondrocytes can be curve-fitted by optimizing the and constants (MatLab Software; MathWorks, Natick, MA, USA).

Statistics

Temporal parameters of [Ca²⁺]_i peaks from all control groups were pooled together, and the logarithmic values of these parameters were examined with the Shapiro–Wilk normality test (66). The spatiotemporal parameters from different antagonist-treated groups and their corresponding controls were compared using 1-way ANOVA, and the difference was detected using post hoc Bonferroni tests for the logarithmic values of the parameters. χ² test was used to compare the [Ca²⁺]_i responsive percentages between different groups. Differences with a value of P < 0.05 were considered significant. The means and sd of spatiotemporal parameters of all explants were pooled together, and Pearson’s correlation coefficients were calculated to evaluate the linear relationship between the means and sd. Pearson’s correlation coefficients of <0.19, 0.20–0.39, 0.40–0.59, 0.60–0.79, and >0.80 are considered as very weak, weak, moderate, strong, and very strong correlations, respectively (67). In addition, the spatiotemporal similarity of multiple [Ca²⁺]_i peaks from the same cell was quantified. The consistency of the peak magnitudes from each cell was evaluated by Cronbach’s α value, which is considered to be “acceptable” and “good” when the value is >0.7 and >0.8, respectively (68). The similarity of multiple [Ca²⁺]_i peaks was determined by calculating the 1-dimensional cross-correlation coefficient. The coefficient equals 1 for 2 identical [Ca²⁺]_i peaks.

RESULTS

Responsive percentage of chondrocytes

The numbers of tested cartilage explants and analyzed cells for all pathway groups are summarized in Table 1. All cartilage explants in the control group demonstrated robust spontaneous [Ca²⁺]_i signaling in the chondrocytes (Supplemental Video S1). The average [Ca²⁺]_i responsive percentage of in situ chondrocytes from all the control groups was 19.24% for n = 61 cartilage explants. To avoid sample-to-sample variation, each antagonist-treated sample was pair-compared with its corresponding control from the same explant. The responsive percentage in the Ca²⁺-free medium (5.69%) group was significantly lower than that of the corresponding control group (19.14%) (Fig. 2B). After adding EGTA in the medium to chelate the extracellular Ca²⁺, [Ca²⁺]_i activities were almost completely abolished; only 4 responsive cells were found in 3 cartilage explants (0.88% responsive). Neither the hydrolysis of extracellular ATP with apyrase nor the blockage of intercellular gap junctions showed any significant influence on the responsive percentage of cells. When the PLC-IP₃ pathway was inhibited (control: 19.41% vs. treated: 7.18%) or the ER calcium store was depleted (control: 18.26% vs. treated: 10.77%), the responsive percentages decreased significantly. Blocking the purinoceptors on the plasma membrane also reduced the number of responsive cells (control: 20.99% vs. treated: 14.05%). For the ion channels, the responsive percentage of cells was decreased after blocking TRPV4 (control: 19.45% vs. treated: 12.46%) or mechanosensitive channels (control: 14.81% vs. treated: 6.48%). In contrast, blocking T-type VGCC significantly increased the responsive percentage of cells (control: 20.79% vs. treated: 30.47%), and blocking the L-type VGCC also promoted the spontaneous calcium signaling (control: 23.57% vs. treated: 63.71%).

TABLE 1.

Number of the total cartilage explants and chondrocytes analyzed in spontaneous [Ca²⁺]_i signaling

	Extracellular source			Intracellular store				Ca2+ ion channel
Experimental design	EGTAchelator	Ca2+free	Gap junct.	Extracel ATP	ER store	PLC-IP3	P2 receptor	Mech channel	TRPV4	T-VGCC	L-VGCC
Chemical reagent	EGTA	HBSS	18α-GA	Apyrase	Thapsigargin	Neomycin	PPADS	GdCl3	GSK205	NNC 55-0396	Verapamil
Explant (n)	3	5	4	6	7	8	4	6	5	5	6
Cells/explant in control group	167 ± 24	196 ± 18	140 ± 28	184 ± 43	180 ± 36	140 ± 20	176 ± 23	201 ± 39	189 ± 46	162 ± 61	111 ± 19
Cells/explant in drug-treated group	152 ± 52	169 ± 11	139 ± 32	172 ± 26	161 ± 46	132 ± 35	183 ± 21	178 ± 40	189 ± 45	161 ± 40	109 ± 19

Junct., junction; L-VGCC, L-type VGCC; T-VGCC, T-type VGCC.

Spatiotemporal parameters of [Ca²⁺]_i peaks

The magnitude of [Ca²⁺]_i peaks in the treated group was shown in the form of relative percentage in comparison with its corresponding control group (Fig. 3). Original data in the form of absolute values + sd with data points overlapped are presented in Supplemental Fig. S1. The magnitude of [Ca²⁺]_i peaks reduced significantly when extracellular ATP was hydrolyzed or the gap junction was blocked (Fig. 3A). The peak magnitude also decreased when the purinoceptors, the mechanosensitive channels, or TRPV4 channels were blocked. Instead, the peak magnitude increased when L-type VGCC was blocked. A responsive chondrocyte could have multiple [Ca²⁺]_i peaks in the recorded time period. The average number of [Ca²⁺]_i peaks from the control group was 2.68 ± 1.60 (n = 1714 cells). As shown in Fig. 3B, when purinoceptors were blocked, the number of peaks was significantly reduced (−24.31%, P < 0.001). When the Ca²⁺ in the ER calcium store was depleted or TRPV4 channel was blocked, the average number of peaks significantly increased (ER calcium store depletion: +37.84%, P < 0.001; TRPV4 blocking: +45.31%, P < 0.001). For all the other pathway inhibited groups, no significant changes were detected. The time required to reach a [Ca²⁺]_i peak (Fig. 3C) increased significantly in the purinoceptors blocked group (+57.57%, P < 0.01) and L-type VGCC blocked group (+29.93%, P < 0.01), whereas no significant difference was detected in the other groups. When Ca²⁺-free medium was used or the TRPV4 channel was blocked, the peak relaxation time was significantly shortened (Ca²⁺-free: −52.69%, P < 0.01; TRPV4 blocking: −41.51%, P < 0.001) (Fig. 3D). The peak relaxation times were increased significantly when PLC-IP₃ (+49.01%, P < 0.05) or L-type VGCC (+70.59%, P < 0.001) was blocked. The representative calcium peak traces from all groups are provided in Supplemental Fig. S2.

Figure 3.

Spatiotemporal parameters of spontaneous [Ca²⁺]_i peaks and the effects of pathway antagonists. Data from all treated groups were normalized to their corresponding control sample (Ctrl). A) Magnitude of [Ca²⁺]_i peaks. B) Number of [Ca²⁺]_i peaks in the responsive chondrocytes. C) Time to reach a peak from baseline. D) Peak relaxation time. Data are shown as means + sd. *P < 0.05, **P < 0.01, ***P < 0.001.

Statistical features of the spatiotemporal parameters

In all groups, distribution of the temporal parameters was skewed and asymmetric. The distribution can be optimally fitted in a lognormal form (Fig. 4A). The Shapiro-Wilk normality test was performed on the logarithmic value of both temporal parameters of [Ca²⁺]_i peaks (n = 331 peaks). No statistical significance was detected (time to reach a peak: P = 0.797; peak relaxation time: P = 0.768), which proves the lognormal distribution of the 2 temporal parameters. As an illustration, the distributions of times to reach a peak were plotted in both regular (Fig. 4A) and logarithmic scales (Fig. 4B).

Figure 4.

Statistical analysis of the spatiotemporal parameters of the spontaneous [Ca²⁺]_i peaks. A, B) Statistical distribution of time to reach a peak plotted at a regular (A) and a logarithmic (B) scale. The distribution trends were plotted in the lognormal form (A) and gaussian normal form (B). Shapiro-Wilk normality test indicates that the distribution in logarithmic scale follows a gaussian normal form (P = 0.797). C) Mean and sd of spatiotemporal parameters of each explant were plotted together, and the correlation between the means and sd were tested. Pearson’s r value was calculated to confirm the linear relationship; the value r > 0.8 indicates a very strong linear correlation.

The means and sd of spatiotemporal parameters were calculated and plotted together (Fig. 4C). Pearson’s test indicated a very strong (P > 0.8) linear correlation between the mean and the corresponding sd (n = 98 explants, including both control and treated groups) of all spatiotemporal parameters, because Pearson’s r = 0.827 for the magnitude of peaks, r = 0.907 for time to reach a peak, and r = 0.925 for the peak relaxation time. A strong linear correlation between the mean and sd implies that a threshold control mechanism is responsible for regulating the [Ca²⁺]_i peaks (69, 70).

Fingerprint-like feature of the spontaneous [Ca²⁺]_i peaks

Multiple [Ca²⁺]_i peaks from the same chondrocyte were segmented and stacked together to examine their similarity in spatiotemporal pattern (Fig. 5A). The [Ca²⁺]_i peaks from 9 randomly selected chondrocytes are shown in Fig. 5B, and the peaks from the same cell maintain a unique and consistent shape. A 1-dimensional cross-correlation coefficient (where 1 indicates a perfect match) was calculated and shown in the plot to quantify the consistency between peaks. Magnitudes of multiple [Ca²⁺]_i peaks were examined by the internal consistency test for all responsive cells. The Cronbach’s α coefficients of the peak magnitudes from the same cell were >0.8, indicating “good” internal consistency (Table 2). Therefore, each cell has a unique profile for its [Ca²⁺]_i peaks, which represents a fingerprint-like feature of the cells (Fig. 5B).

Figure 5.

Fingerprint-like feature of [Ca²⁺]_i peaks for each individual cell. A) [Ca²⁺]_i peaks from a single cell at different times displayed almost identical spatiotemporal patterns. B) [Ca²⁺]_i peaks released by the same chondrocyte were stacked to illustrate the fingerprint-like feature. Each plot has 2 [Ca²⁺]_i peaks from an individual chondrocyte. One-dimensional (1D) cross-correlation coefficient was calculated to evaluate the similarity between the 2 peaks. Coefficient of 1 indicates a perfect match.

TABLE 2.

Consistency of the [Ca²⁺]_i peak magnitudes from each cell

Number of peaks in 1 cell	Cell number	Cronbach’s α coefficients
2	438	0.823
3	367	0.835
4	288	0.844
5	190	0.899
6	96	0.890

Cronbach’s α coefficients were calculated to evaluate the

consistency of the [Ca²⁺]_i peak magnitudes from each cell.

The consistency is “good” if the value is >0.8.

Multistage biophysical model of [Ca²⁺]_i peaks

Using the new biophysical model, curve-fitting for the 3 stages of a [Ca²⁺]_i peak was performed. The multistage model provides a satisfying fit to the peaks with high R² values (>0.90) (Fig. 6A). The calcium induced calcium influx constant () and calcium induced calcium outflux constant () were obtained from each drug treatment group. When Ca²⁺-free medium was used or the TRPV4 channel was blocked, increased significantly (Ca²⁺-free: +89.08%; TRPV4 blocking: +74.58%) (Fig. 6B), implying an increase of the autocatalytic reaction rate for Ca²⁺ influx. decreased significantly when the T-type VGCC was blocked (−27.47%). increased when Ca²⁺-free medium was used (+90.35%) or TRPV4 was blocked (+159.42%) (Fig. 6C), whereas the decreased significantly when the T-type VGCC was blocked (−30.90%). No significant difference was detected between the other groups. Therefore, extracellular Ca²⁺ was the driving factor to induce the autocatalytic reaction of Ca²⁺, although other Ca²⁺ channels or pathways could also affect the threshold level to initiate a cellular-level [Ca²⁺]_i event.

Figure 6.

Curve-fitting of [Ca²⁺]_i peaks using a simplified multistage biophysical model. A) Typical curve fitting of [Ca²⁺]_i peaks using the new theoretical model in this study. s₁ is the exponential initiation stage, s₂ denotes the logistic rising stage, and s₃ is the reciprocal relaxation stage. R² values of the curve fitting in each stage are reported. B, C) Autocatalytic-related parameters of the spontaneous [Ca²⁺]_i peaks were calculated for all treated groups using the theoretical model. Parameters from all treated groups were normalized to their corresponding control. B) The calcium induced calcium influx constant, in Supplemental Eq. S1, indicates the reaction rate for current [Ca²⁺]_i concentration to induce Ca²⁺ influx in the autocatalytic process. C) The calcium induced calcium outflux constant, in Supplemental Eq. S3, indicates the reaction rate for current [Ca²⁺]_i concentration to induce Ca²⁺ outflux in the autocatalytic process. Data are shown as means + sd; **P < 0.01, ***P < 0.001.

DISCUSSION

Spontaneous calcium signaling

Spontaneous calcium signaling was mainly discovered in electrically excitable cells such as neurons and cardiomyocytes (1, 71). Recently, spontaneous calcium signaling has been documented in a few nonexcitable cells, such as bone cells (72), mesenchymal stem cells (73), and chondrocytes (17). Because the phenotype and behaviors of chondrocytes change significantly in different environments, characteristics of their spontaneous calcium signaling (e.g., the responsive percentage) varied drastically among the monolayer seeded (74), agarose construct seeded (16), and in situ cells (17). It is not widely accepted that chondrocytes, as a metabolically inactive cell population, can have spontaneous calcium peaks. In this study, robust spontaneous calcium signaling of in situ chondrocytes was consistently recorded in over 60 (number of samples in the control groups) cartilage explant samples from 18 bovine knee joints. Robust spontaneous [Ca²⁺]_i peaks were even observed 24 h after the loading of fluorescent dye into cells (Supplemental video S2). Therefore, spontaneous calcium signaling exists in chondrocytes. The spatiotemporal characteristics of the spontaneous peaks were further analyzed and employed for the establishment of a new calcium signaling model.

Autocatalytic process has been extensively revealed in cell calcium signaling, such as the store-operated calcium entry, which is a central mechanism in balancing cellular calcium (75–77). In this study, we assumed that the spontaneous calcium signaling in chondrocytes is an autocatalytic process (78, 79) at the cellular level, where the reaction products could catalyze the reaction with a feedback mechanism; a small change of [Ca²⁺]_i concentration can further induce more cellular activities to strengthen the change until a threshold is met. Temporal parameters of an autocatalytic process often follow a lognormal distribution (80). In our biophysical model, assuming the [Ca²⁺]_i concentration threshold for the transition from exponential stage to logistic stage is , according to Supplemental Eq. S2, the time duration for stage I should be . When the dominant variant term complies with the central limit theorem, should follow a normal gaussian distribution. Thus the temporal parameter , which is the duration of stage I, should follow a lognormal distribution (20). Similarly, the durations of stages II and III, and t₃, should also follow lognormal distributions in the biophysical model. Therefore, our model for the spontaneous calcium signaling in chondrocytes, which is based on the autocatalytic process assumption, can explain the lognormal distribution of temporal parameters observed in the experimental data. It should be noted that the autocatalytic reaction in this study only refers to calcium intensity trace in a single calcium peak (i.e., the increase of [Ca²⁺]_i concentration owing to a positive feedback mechanism). As the amount of Ca²⁺ ions involved in stochastic calcium puffs is usually much smaller than those involved in cellular-level calcium events, the magnitude of the stochastic term in the model should be negligibly small in comparison with the deterministic term. Therefore, the magnitude of a [Ca²⁺]_i peak at cellular level is mainly regulated by the deterministic term, which remains as a constant for each individual cell. This partially explains the fingerprint-like feature of [Ca²⁺]_i peaks in a chondrocyte (i.e., the magnitudes of [Ca²⁺]_i peaks from the same chondrocyte remain relatively stable over time), as indicated by the internal consistency test.

The [Ca²⁺]_i trace of cells could be determined by many complex and competing cellular activities, such as the collective behaviors of all calcium ions, channels and their interactions. In this study, we found a strong linear relationship between the mean and sd of the spatiotemporal parameters (Fig. 4C). According to previous mathematical analysis, such a correlation often indicates that the parameter itself could be controlled by a threshold regulating mechanism (81–83). Because the high [Ca²⁺]_i level is toxic or lethal to a cell (22), some of the calcium channels and pathways can be deactivated by the excessive [Ca²⁺]_i concentration. Such a threshold characteristic has been noticed or proposed to describe the dynamics of the IP₃ pathway in [Ca²⁺]_i signaling (84–86), the calcium release from sarcoplasmic reticulum (87), and the activity of ryanodine sensitive Ca²⁺ channels (88). In the spontaneous calcium signaling of chondrocytes, the threshold regulating mechanism may play critical roles in both the initiation and the spatiotemporal features of a [Ca²⁺]_i peak. Small fluctuations of Ca²⁺ movement at a suborganelle level can accumulate over time until reaching the activation threshold of a neighboring calcium channel, the activation of which can initiate a cellular-level [Ca²⁺]_i peak. Once a [Ca²⁺]_i signal is initiated, the next transition point of the [Ca²⁺]_i trace could be regulated by [Ca²⁺]_i concentration, which may activate or deactivate certain channels or pathways. Therefore, such threshold characteristics in [Ca²⁺]_i signaling provide justification for a multistage model of a single [Ca²⁺]_i peak.

When certain calcium or cation channels on the plasma membrane are activated, such as the mechanosensitive and TRPV4 channels, extracellular calcium ions are transported into the cytosol. The elevation of [Ca²⁺]_i can further induce many cellular activities, one of which is the release of ATP. The released ATP can come back and activate the P2 receptors (e.g., P2Y family) and ion channels (e.g., P2X7) on cell membrane (89). Activation of P2Y receptors further activates the PLC-IP₃ pathway (90), which can induce the release of the ER store. Action of the ER store may cause store-operated calcium entry (91). It is now believed that [Ca²⁺]_i centration can be regulated by the actions of all plasma membrane channels, pumps, and the membrane channels on the ER and nucleus. These actions could have identical or competing effects on the cytosol calcium concentration. Nevertheless, the trace of a single calcium peak should be affected by some autocatalytic processes.

Extracellular Ca²⁺ source

The ability of local Ca²⁺ puffs to successfully evolve into a cellular-level event is dependent on the availability of calcium signaling pathways and the activation threshold of pathways. Inhibition of a pathway by an antagonist could significantly elevate the activation threshold, lowering the possibility for Ca²⁺ puffs to induce a [Ca²⁺]_i peak at a cellular level. In this study, we investigated the roles of several essential pathways related to [Ca²⁺]_i signaling in chondrocytes. These pathways can be grouped into 3 categories: extracellular Ca²⁺ source, intracellular Ca²⁺ store, and Ca²⁺ ion channels on the plasma membrane. Several studies concluded that the stimulated calcium signaling in chondrocytes required an extracellular Ca²⁺ source (13, 14). Previously, we also found that no calcium signaling can be initiated in osteocytes or osteoblasts when placing the cells in Ca²⁺-free medium. In this study, when Ca²⁺ chelator EGTA was added into the medium, only 4 chondrocytes in 3 cartilage explants exhibited spontaneous [Ca²⁺]_i peaks. However, bathing cartilage explant in the Ca²⁺-free medium did not reduce the spontaneous [Ca²⁺]_i oscillation to the same level as EGTA treatment, although the responsive percentage was significantly lower than that of the control (5.69 vs. 19.14%). This inconsistency could be caused by the unique composition of cartilage ECM, in which the abundant GAG chains are negatively charged. To maintain electrical neutrality, these charged molecules trap a large number of cations, including Ca²⁺, in the interstitial fluid across the ECM. Bathing the cartilage explant in Ca²⁺-free medium may not be able to fully deplete the Ca²⁺ ions trapped in the ECM, which could be used by the chondrocytes to initiate a [Ca²⁺]_i peak. In contrast, EGTA (MW: 380.35 g/mol) could diffuse into the tissue, actively chelate the remaining Ca²⁺ ions, and fully abolish the extracellular Ca²⁺ source. These results from 2 groups imply that the responsive rate of spontaneous [Ca²⁺]_i signaling could be positively correlated to the amount of extracellular Ca²⁺. In articular cartilage, Ca²⁺ concentration in the extracellular environment is usually around 1 mM (92), whereas intracellular cytosol Ca²⁺ concentration can be as low as 0.1 μM. Such a large concentration gradient could induce Ca²⁺ influx from extracellular space into the intracellular cytosol, which has been conjectured as a potential driving force to initiate spontaneous calcium signaling (93, 94). This conjecture is supported by our experimental data. When the extracellular Ca²⁺ concentration was significantly reduced by placing tissue in Ca²⁺-free medium, the spontaneous signaling was dampened. Moreover, the [Ca²⁺]_i peaks observed in the calcium-free medium implies that even a small amount of extracellular Ca²⁺, such as that trapped by GAG chains, could be used by chondrocytes to initiate spontaneous [Ca²⁺]_i peaks, although the successful rate would be significantly reduced.

Extracellular ATP and ER Ca²⁺ store

ATP can be released by chondrocytes under mechanical stimuli or after calcium signaling events (90) and is highly involved in the activation of GPCRs (95). Activation of GPCRs can, in turn, induce more ATP release from chondrocytes (96). As we found previously (2, 3), diffusion of extracellular ATP is an important mechanism for calcium wave propagation between neighboring osteocytes. In chondrocytes, ATP can activate purinoceptors (89), including P2X and P2Y receptors. P2X receptors are ATP-gated ion channels that can directly facilitate Ca²⁺ transport (90). P2Ys can trigger the activation of the PLC-IP₃ pathway (90) and cause Ca²⁺ release from the ER. Binding of free Ca²⁺ to the IP₃ receptor can further activate PLC-IP₃ pathway, representing an autocatalytic mechanism. In this study, inhibition of PLC-IP₃ pathway via neomycin and depletion of the ER Ca²⁺ store via thapsigargin both significantly reduced the responsive percentage (Fig. 2C), indicating that extracellular ATP diffusion and the release of the ER store could also be an initiation mechanism of the spontaneous [Ca²⁺]_i peaks in chondrocytes. Extracellular ATP can come either from the cell itself or from the neighboring cells. The extracellular ATP hydrolyzing reagent, apyrase, showed limited influence on the spontaneous calcium signaling in this study. Fast movement of apyrase (MW: ∼47 kDa) could be hindered by the dense ECM of cartilage, and thus the hydrolysis efficiency is restricted for a timely removal of the ATP released by chondrocytes. In contrast, inhibitors of the purinoceptors, PLC pathway, and ER store all reduced the responsive percentage of chondrocytes.

Ca²⁺ ion channels

Mechanosensitive ion channels (such as PIEZO1 and -2) can sense external stimulation via converted biochemical signals (94). The TRPV4 channel is a Ca²⁺-permeable channel that can be regulated by the osmolality and mechanical stimuli (97, 98). These channels on plasma membrane have long been considered to be the initiator of [Ca²⁺]_i peaks induced by physical stimuli. Our results revealed that these physical signal–sensitive channels also play critical roles in spontaneous calcium signaling in chondrocytes. Blocking these channels can significantly inhibit the spontaneous [Ca²⁺]_i peaks in chondrocytes. According to the mechanism we proposed, accumulation of calcium puffs at the suborganelle level and its cascading events might activate these physical signal–sensitive channels (13) and further induce a cellular-level calcium event. For example, blocking mechanical sensitive channels (99) can affect the functions of transient receptor potential channels and GPCRs, which might impair the autocatalytic initiation mechanism of spontaneous [Ca²⁺]_i signaling. In contrast, blocking either T-type or L-type VGCC significantly promoted the spontaneous calcium responses in chondrocytes. Inhibition of VGCCs with the same reagents has been shown to block the physical stimulation–induced calcium responses in chondrocyte and bone cells (39, 72, 100). The promotion effects observed here may imply different roles of VGCCs in the initiation of spontaneous calcium signaling vs. the stimuli-induced calcium responses. Actions of VGCCs may prevent the accumulation or escalation of small calcium puffs at suborganelle level, and further inhibit the activation of local calcium pathways that can initiate a spontaneous calcium peak. Another potential mechanism might be related to the enhanced ER stress caused by the VGCC inhibitors (101), which can lead to a highly disturbed Ca²⁺ homeostasis (102). However, our previous study recorded the calcium responses of osteocytes immediately before and after the exposure to these 2 reagents, and no promoted calcium responses were observed (39). VGCCs play critical roles in the differentiation, proliferation, and metabolic activities of chondrocytes (55). We previously showed that blockage of T-type VGCC reduced load-induced osteoarthritis in mice (51). The functions of VGCCs in the spontaneous calcium signaling of chondrocytes may further reveal their roles in osteoarthritis development and be worth future research efforts.

Limitations

Because the theoretical model provides new insights about the initiation mechanism and features of spontaneous calcium signaling of chondrocytes, certain limitations of the model should be emphasized. First, the spontaneous calcium model proposed in this study was based on a few assumptions and was built mainly to understand the general temporal features of the calcium peaks. Simplified mathematical formulas were proposed to describe the calcium peaks, and many physiochemical factors (such as influence from the multiplicative and mutually interactive pathways or channels) were not considered. These could limit the curve-fitting capability of the model, although it is feasible to add extra terms and controlling parameters in the [Ca²⁺]_i intensity function in future. In addition, the fluorescent intensity change in calcium images may not reflect the actual fold change of the [Ca²⁺]_i concentration. Second, the curve-fitting using the theoretical model only took the deterministic term into account, by assuming the stochastic terms to be negligibly small. Third, the concentrations of the pharmacological reagents were justified in previous calcium signaling studies. It is important to note that most agonists or antagonists are not specific to a single pathway or channel. Off-target effects on several other pathways often exist. For example, the HBSS used for the calcium-free condition lacks nutrient and supplementary components compared with the regular DMEM, which may also affect the spontaneous calcium signaling of chondrocytes. A thorough understanding of a specific pathway in the spontaneous calcium signaling of chondrocytes may require extensive efforts with multiple different techniques rather than a single agonist-antagonist test. Therefore, the present experiments using pathway antagonists, despite their common usage in pathway studies, can only provide limited information about the related pathways.

CONCLUSIONS

This work proved the presence of spontaneous calcium signaling in cartilage cells. Each cell has a fingerprint-like spatiotemporal pattern in its spontaneous [Ca²⁺]_i peaks. A multistage biophysical model was developed to understand the initiation mechanism and spatiotemporal features of the calcium peaks. The new model can successfully predict the evolution of a spontaneous [Ca²⁺]_i signaling event in a single chondrocyte, and explain the lognormal distribution of the temporal parameters of the [Ca²⁺]_i peaks. To initiate a spontaneous [Ca²⁺]_i peak, extracellular Ca²⁺ is required. Both the intracellular ER calcium store and purinoceptors on the plasma membrane play key roles in spontaneous calcium signaling. Physical stimulation–activated calcium channels, such as mechanosensitive and TRPV4 channels, are also critical for the initiation of spontaneous [Ca²⁺]_i peaks. According to our stochastic-deterministic hybrid model, inhibition of these channels could increase the threshold for the stochastic Ca²⁺ puffs to induce a cellular-level calcium signaling event.

Supplementary Material

This article includes supplemental data. Please visit http://www.fasebj.org to obtain this information.

Glossary

18α-GA

18α-glycyrrhetinic acid

[Ca²⁺]_i

intracellular calcium

ECM

extracellular matrix

ER

endoplasmic reticulum

GdCl₃

gadolinium chloride

IP₃

inositol 1,4,5-trisphosphate

PIEZO

piezo-type mechanosensitive ion channel component

PPADS

pyridoxal-phosphate-6-azophenyl-2′,4′-disulfonate

TRPV4

transient receptor potential vanilloid 4

VGCC

voltage-gated calcium channel

AUTHOR CONTRIBUTIONS

Y. Zhou, M. Lv, and X. L. Lu designed the research; Y. Zhou, T. Li, R. Duncan, L. Wang, and X. L. Lu wrote and/or helped edit the manuscript; Y. Zhou and T. Zhang performed the experiments; and Y. Zhou, M. Lv, and T. Zhang analyzed the experimental data.