Introduction

Progressive loss is one of the major characteristics of intervertebral disc (IVD) degeneration [1]. As the primary component of the extracellular matrix (ECM), the PGs produced by IVD cells are capable of entrapping water which gives the IVD the necessary shock-absorbing ability to transmit mechanical loads in conjunction with the rigid collagen network [2]. Therefore, loss of PGs contributes to compromised IVD structure and mechanical function.

PG biosynthesis is an ATP-driven process [3, 4] in which ATP not only serves as an energy source but also a building block [4]. Furthermore, ATP is constantly released by IVD cells, and the release is promoted by mechanical loading [5,6,7]. Extracellular ATP is well-known as a signaling molecule which can bind with purinergic P2 receptors expressed on the cell membrane and mediate biological cascades in response to various physiological and pathophysiological stimuli [8,9,10,11,12]. A high level of extracellular ATP was found in the PG-rich region of avascular IVD [6], which could be due to the inhibitive effect of glycosaminoglycan side chain of PGs on ATP hydrolysis [13]. Our study further showed that extracellular ATP could enhance in IVD cells’ ability to produce ECM protein [14]. Stimulated cell proliferation and ECM biosynthesis by ATP treatment were also reported in cartilage tissue [10, 15]. Furthermore, ATP has been demonstrated to be a potent agent to inhibit inflammation in many cell types [16,17,18], which can be potentially beneficial to the IVD since inflammation is associated with disc degeneration [16,17,18].

In vivo, extracellular ATP is progressively dephosphorylated by the widespread families of transmembrane ecto-nucleotidases [19,20,21,22], resulting in the formation of purine derivatives (i.e. ADP, AMP and adenosine) as well as inorganic pyrophosphate (PPi) and phosphate ions (Pi). It has been demonstrated that mechanical loading reduces extracellular ATP content in the IVD [6], indicating that hydrolysis of extracellular ATP may be promoted in the IVD under mechanical loading. Adenosine as the primary hydrolytic product represents another ubiquitous means of cell-cell communication which produces several regulatory functions in the human body via activation of membrane-bound G-protein coupled receptors [23,24,25,26]. Adenosine can be transported back into cells and potentiate a series of biological responses [27]. Similar to ATP, extracellular adenosine was also found to be capable of promoting the PG production of IVD cells by increasing intracellular ATP levels via adenosine uptake [28]. On the other hand, extracellular PPi and Pi are reported to differentially regulate the formation of phosphate calcium minerals while a high Pi/PPi ratio is a determinant factor for pathological tissue calcification [29, 30]. In the IVD, endplate calcification is associated with disc degeneration due to its adverse impact on the transport of nutrients to disc cells. In particular, the calcification potential of the IVD was suggested to be directly linked to the level of Pi [31]. Therefore, extracellular ATP level may have a significant influence on IVD health.

Given the potential biological impacts of extracellular ATP and its metabolic products on the IVD, it is imperative to analyze the level of extracellular ATP in the disc. However, in-vivo experimental measurements have always been challenging due to biological interferences [32] and repeated insertion of testing probes into IVD may introduce irreversible tissue damage. In view of the technical difficulties, numerical simulation offers a practical alternative. Finite element modelling of the IVD based on mechano-electrochemical mixture theory have long been established and developed over the years, taking into account the disc geometry, tissue deformation and the transport of nutrients, interstitial fluid and ions within the IVD [33,34,35]. The theoretical framework has also been extended to describe the metabolism and distribution of tissue components [36,37,38] and key nutrients [39] as well as drug delivery [40,41,42]. Therefore, the objective of this study was to develop a 3D finite element model to predict extracellular ATP distribution in the IVD and evaluate the impact of degeneration on extracellular ATP distribution. To achieve this, ATP release and breakdown by IVD cells and ATP-PG binding kinetics were measured and coupled into the disc model. The model was first validated with experimental results. Then, extracellular ATP profiles in non-degenerated and degenerated human discs were analyzed.

Materials and Methods

Isolation of IVD Tissue and Cell Culture

IVD tissues were harvested from spines of Yorkshire pig cadavers (Male, 14–16 weeks, 80–100 lbs.) within 2 h of sacrifice (Institutional Animal Care and Use Committee approved). The pig source was provided through Tissue Sharing program in Department of Veterinary Resource of University of Miami (Miami, FL). Tissue samples from NP and AF regions were separately digested in high glucose (25 mM) Dulbecco’s Modified Eagle Medium (DMEM; Thermos Fisher Scientific Corp., Waltham, MA) containing 1% antibiotic-antimycotic (Lonza, Walkersville, MD), 1 mg/mL type II collagenase (Worthington Biochemical Corp., Lakewood, NJ) and 0.6 mg/mL protease (Sigma Chemical, St. Louis, MO) for 24 h at a standard culture condition (21% O2, 5% CO2, 37 °C). After enzymatic digestion, the cell-enzyme solutions were filtered using a 70 μm strainer (BD Biosciences, San Jose, CA) and centrifuged to collect IVD cells. The cells were seeded into three-dimensional (3D) agarose constructs (8 mm in diameter and 2 mm in thickness) at a density of 10 million cells/mL [28, 43, 44]. The 3D agarose gel system was selected because of its ability to retain phenotypes of IVD cells [45,46,47]. Agarose constructs were cultured in high glucose DMEM supplemented with 10% fetal bovine serum (FBS; VWR, Radnor, PA) and 1% antibiotic-antimycotic for 48 h.

Determination of ATP Hydrolysis Rates of Porcine NP and AF Cells

Each agarose gel sample was cut into small pieces and transferred into a custom-made chamber filled with 600 µL of 10 µM ATP solution made of serum-free high glucose DMEM and incubated under the standard culture condition for 4 h with continuous magnetic stirring. At 0.5 h intervals, a small aliquot (5 µL) was removed from the chamber and mixed with in 95 µL serum-free DMEM (20-fold dilution). The small sample volume was expected to cause negligible effects on the change of total medium volume (600 µL) throughout the experiment. The diluted samples (100 µL) were mixed with an equal volume of 3 mM ethylenediaminetetraacetic acid (EDTA) and boiled for 2 min to prevent ATP hydrolysis. All collected samples were stored at − 80 °C until the ATP content was measured using an ATP Bioluminescent Assay Kit (Sigma-Aldrich, St. Louis, Mo) according to manufacturer's instruction. Briefly, fifty microliters of sample were mixed with assay reagent at 1:1 volume ratio. The resulting luminescence was read immediately by a microplate reader (DTX880, Beckman Coulter, Brea, CA). Serum-free DMEM mixed with EDTA solution was used as blank.

Michaelis-Menten equation was applied to delineate the kinetics of enzyme-catalyzed ATP hydrolysis by IVD cells [48]:

$$\frac{{{\text{d}}c_{{{\text{ATP}}}} }}{{{\text{d}}t}} = - \frac{{V_{{{\text{max}}}} c_{{{\text{ATP}}}} }}{{K_{{\text{m}}} + C_{{{\text{ATP}}}} }}\rho^{{{\text{cell}}}},$$
(1)

where t is the time, CATP is the concentration of ATP, Vmax is the maximum reaction rate, Km is the Michaelis–Menten constant, and ρcell is the cell density in the chamber.

The analytical solution to Eq. (1) is derived as [44]:

$$t = \frac{{K_{{\text{m}}} }}{{V_{{{\text{max}}}} \rho }}\ln \left( {\frac{{c_{{{\text{ATP}}}}^{I} }}{{C_{{{\text{ATP}}}} }}} \right) + \frac{{c_{{{\text{ATP}}}}^{I} - C_{{{\text{ATP}}}} }}{{V_{{{\text{max}}}} \rho }} + t_{0},$$
(2)

where \(c_{{{\text{ATP}}}}^{I}\) is the initial concentration of ATP and t0 is the time at the beginning of the experiment (\(t_{0}\) = 0). Vmax and Km of NP and AF cells were obtained by curve-fitting data of \(c_{{{\text{ATP}}}}\) and \(t\) to Eq. (2) in MATLAB (R2018b, MathWorks, Natick, MA).

Measurement of ATP Release Rate of Porcine NP and AF Cells

Following an initial culture in standard condition, the ATP release rate of porcine NP and AF cells was separately measured under hypoxia, which was reported to affect cellular ATP release pattern [49]. In a separate study, the oxygen distribution within the whole disc sample was determined under the culture condition reported in Chong et al.’s study [6] and found that the O2 level decreased from 10% at the periphery to 5% in the center. Therefore, 5% O2 level was selected for the measurement of ATP release rate to match the experimental condition and make comparison. Cell-agarose constructs were maintained in 6 mL serum-free DMEM (5 mM glucose) with under hypoxia for 3 d until a steady state was reached. On day 3, each sample was transferred into a custom-made chamber and incubated in 600 µL of freshly prepared media (no ATP initially) for an additional 4 h. ATP concentration in the medium at 4 h (\(c_{{{\text{ATP}}\_4h}}\)) was measured using the ATP Bioluminescent assay as described above. The experimental procedure was simulated using the built-in time-dependent diffusion model in COMSOL software (COMSOL 5.3, COMSOL, Inc., Burlington, MA), incorporating the geometry of the chamber and kinetics of ATP hydrolysis as measured above. Using a relationship between ATP release rates \((R^{{{\text{ATP}}}} )\) and \(c_{{{\text{ATP}}\_4h}}\) obtained from the COMSOL simulations, \(R^{{{\text{ATP}}}}\) was determined for the ATP release experiment based on the measurement of \(c_{{{\text{ATP}}\_4h}}\).

Measurement of Water Content of Porcine IVD Tissue

The water content (\(\phi_{0}^{w}\)) of porcine NP and AF tissue was examined as water volume fraction. Specimens were weighed in air (\(W_{t}\)) followed by lyophilization (LABCONCO, Kansas City, MO) to obtain dry weight (Wd). \(\phi_{0}^{w}\) was calculated from:

$$\phi_{0}^{w} = \frac{{V_{w} }}{{V_{t} }} = \frac{{(W_{t} - W_{d}) }}{{W_{t} }} \cdot \frac{{\rho_{t} }}{{\rho_{w} }},$$
(3)

where \(V_{w}\) and \(V_{t}\) are volume of water and tissue, respectively, \(\rho_{t}\) and \(\rho_{w}\) are the mass densities of tissue (\(\rho_{{{\text{NP}}}}\) = 1.02 g/cm3, \(\rho_{{{\text{AF}}}}\) = 1.11 g/cm3 according to our previous study [50]) and water, respectively.

Tissue Preparation for ATP Association Binding Experiment

Fresh-frozen NP and AF tissue samples obtained from the abovementioned source were weighed. AF tissue samples were chopped into small pieces to facilitate processing. All tissue samples underwent 3 cycles of freezing and thawing that were completed by 5 min of rapid freezing in liquid nitrogen followed by 10 min of thawing at room temperature for each cycle to break down cell membrane and remove DNA [51,52,53]. After that, each sample was decellularized by immersion in 500 µL formic acid (FA) (> 95%, Sigma-Aldrich, St. Louis, MO) for 2 h to remove cellular debris while retaining major ECM components, namely PGs and collagen. The acid treatment was selected for its advantages in preserving PG content over traditional decellularization reagents, such as Triton X-100 and sodium dodecyl sulfate (SDS) [54,55,56]. In order to evaluate ATP binding with collagen, some FA-treated AF samples were incubated in an additional 500 µL of trypsin-hyaluronidase (TH) digestion solution which contains 2.5 mg/mL of trypsin (Sigma-Aldrich, St. Louis, MO) and 3 mg/mL hyaluronidase (Worthington Biochemical Corp., Lakewood, NJ) under sonication for 18 h at the standard culture condition [57] to remove PG content. After the chemical treatment, samples were centrifuged at 14,000 rpm for 10 min and the supernatant was discarded. The precipitated tissue pellets were washed with 500 µL PBS 3 times to completely remove FA. During the last wash cycle, the tissue pellets were homogenized (PowerMax AHS200, VWR, Radnor, PA) at a speed of 20,000 rpm for 30 s for NP samples and 2 min for AF samples. The resulting homogenates were centrifuged at 14,000 rpm again for 10 min to collect tissue particles for the experiment.

Microstructure of Tissue Particles in ATP Association Binding Experiment

The size and morphology of NP and AF tissue particles after FA treatment and homogenization were examined using a scanning electron microscopy (SEM; JSM-6010PLUS/LA, JEOL, Peabody, MA). Specimens were prepared by placing a small drop of tissue homogenates onto an adhesive carbon tab on the top of an aluminium stub. The samples were then air-dried and sputter-coated with gold before SEM observation.

ECM Content of Tissue Particles in ATP Association Binding Experiment

The PG and collagen contents of the natural and treated tissue samples were quantified to evaluate the tissue loss during preparation. Samples were digested in 500 µL PBS buffer solution containing 250 µg/mL of papain and 10 mM of EDTA at 60 °C for 16 h [50, 58]. The resulting solution was diluted 15-folds with PBS and assayed with dimethylmethylene blue (DMMB) staining for PG content [59] in which 20 µL aliquot of the diluted tissue digest was rapidly mixed with 200 µL of the dye solution. The absorbance of the resulting mixture was read at 525 nm. A series of chondroitin sulphate (from bovine trachea, Sigma-Aldrich, St. Louis, Mo) solution made of the same papain buffer were used as the standards. Meanwhile, total collagen content in the tissue samples were determined by hydroxyproline (HYP) [60]. Briefly, 150 µL of the above undiluted papain digest was hydrolyzed with 1 mL 6 N hydrochloric acid at 105 °C for additional 16 h to produce HYP, which was further oxidized by 7% (w/v) chloramine-T. The absorbance of the final solution was read at 558 nm [60]. L-HYP solutions made in PBS were mixed with 6 N HCl at 1:6 volume ratio and used as the standards. The results of PG and collagen content were normalized by sample weight (50 mg).

Measurement of ATP Binding to IVD Tissue

The measurements of ATP binding with IVD tissue were performed by adding 500 µL PBS solution containing various concentrations of ATP (100 µM, 200 µM, 400 µM, 500 µM) to tissue particles in a 24-well plate. The resulting suspension was centrifuged at 3700 rpm for 10 min to form a thin layer of tissue particles at the bottom of each well. Samples were then incubated for a period of 6 h. At 1 h interval, two microliters of aliquots from the incubating solution were sampled and mixed with 98 µL of PBS (50-fold dilution) before being stored at − 80 °C. Samples at all time points were assayed together for ATP content.

Determination of Binding Rate Constants and Concentration of Binding Protein

In the ATP binding experiment, free ATP molecules in the incubating PBS solution were assumed to bind with immobile binding protein (BP) present in the ECM of IVD tissue, forming an immobile bound complex (BC) which could be reversibly dissociated. The procedure is described by an one-site Langmuir binding model [61] in which one ligand binds to one binding protein molecule:

$${\text{ATP}} + {\text{BP}}\underset{{k_{{{\text{off}}}} }}{\overset{{k_{{{\text{on}}}} }}{\rightleftarrows}}{\text{BC}}$$
(4)

where \(k_{{{\text{on}}}}\) and \(k_{{{\text{off}}}}\) are the association and dissociation binding rate constants, respectively.

Based on the kinetic model of mass action, the rate of change of the concentration of each entity presented in above relationship can be expressed as:

$$\frac{{{\text{d}}c^{{{\text{ATP}}}} }}{{{\text{d}}t}} = - k_{{{\text{on}}}} c^{{{\text{ATP}}}} c^{{{\text{BP}}}} + k_{{{\text{off}}}} c^{{{\text{BC}}}}$$
(5)
$$\frac{{{\text{d}}c^{{{\text{BP}}}} }}{{{\text{d}}t}} = - k_{{{\text{on}}}} c^{{{\text{ATP}}}} c^{{{\text{BP}}}} + k_{{{\text{off}}}} c^{{{\text{BC}}}}$$
(6)
$$\frac{{{\text{d}}c^{{{\text{BC}}}} }}{{{\text{d}}t}} = k_{{{\text{on}}}} c^{{{\text{ATP}}}} c^{{{\text{BP}}}} - k_{{{\text{off}}}} c^{{{\text{BC}}}}$$
(7)

where \(c^{{{\text{ATP}}}}\),\(c^{{{\text{BP}}}}\) and \(c^{{{\text{BC}}}}\) represent the time-dependent concentrations of free ATP, unoccupied binding proteins and bound complex in the incubating PBS solution, respectively.

At any time, the law of conservation of mass is obeyed:

$$c^{{{\text{ATP}}}} + c^{{{\text{BC}}}} = c_{{\text{T}}}^{{{\text{ATP}}}}$$
(8)
$$c^{{{\text{BP}}}} + c^{{{\text{BC}}}} = c_{{\text{T}}}^{{{\text{BP}}}}$$
(9)

where \(c_{{\text{T}}}^{{{\text{ATP}}}}\) and \(c_{{\text{T}}}^{{{\text{BP}}}}\) represent the total concentrations of ATP and binding protein in the incubating PBS solution, respectively. Incorporating Eq. (8, 9) into Eq. (5, 6), the amended form of rate of change of \(c^{{{\text{BC}}}}\) is:

$$\frac{{{\text{d}}c^{{{\text{BC}}}} }}{{{\text{d}}t}} = k_{{{\text{on}}}} \left( {c_{{\text{T}}}^{{{\text{ATP}}}} - c^{{{\text{BC}}}} } \right)\left( {c_{{\text{T}}}^{{{\text{BP}}}} - c^{{{\text{BC}}}} } \right) - k_{{{\text{off}}}} c^{{{\text{BC}}}}$$
(10)

Integrating Eq. (10) with initial value (t = 0, \(c^{{{\text{BC}}}}\) = 0), the analytical solution is

$$c^{{{\text{BC}}}} = \frac{{c_{{\text{T}}}^{{{\text{ATP}}}} c_{{\text{T}}}^{{{\text{BP}}}} c_{{{\text{eq}}}}^{{{\text{BC}}}} \left( {1 - e^{{k_{{{\text{on}}}} \left( {c_{{{\text{eq}}}}^{{{\text{BC}}}} - \frac{{c_{{\text{T}}}^{{{\text{ATP}}}} c_{{\text{T}}}^{{{\text{BP}}}} }}{{c_{{{\text{eq}}}}^{{{\text{BC}}}} }}} \right)t}} } \right)}}{{c_{{\text{T}}}^{{{\text{ATP}}}} c_{{\text{T}}}^{{{\text{BP}}}} - c_{{{\text{eq}}}}^{{{\text{BC}}^{2} }} e^{{k_{{{\text{on}}}} \left( {c_{{{\text{eq}}}}^{{{\text{BC}}}} - \frac{{c_{{\text{T}}}^{{{\text{ATP}}}} c_{{\text{T}}}^{{{\text{BP}}}} }}{{c_{{{\text{eq}}}}^{{{\text{BC}}}} }}} \right)t}} }},$$
(11)

where \(c_{{{\text{eq}}}}^{{{\text{BC}}}}\) is \(c^{{{\text{BC}}}}\) at equilibrium \(\left( {i.e. \frac{{{\text{d}}c^{{{\text{BC}}}} }}{{{\text{d}}t}} = 0 {\text{in Eq}}.{ }7} \right)\) and expressed as [61]:

$$c_{{{\text{eq}}}}^{{{\text{BC}}}} = \frac{{\left( {c_{{\text{T}}}^{{{\text{BP}}}} + { }c_{{\text{T}}}^{{{\text{ATP}}}} + { }\frac{{k_{{{\text{off}}}} }}{{k_{{{\text{on}}}} }}} \right) - \sqrt {\left( {c_{{\text{T}}}^{{{\text{BP}}}} + { }c_{{\text{T}}}^{{{\text{ATP}}}} + { }\frac{{k_{{{\text{off}}}} }}{{k_{{{\text{on}}}} }}} \right)^{2} - 4c_{{\text{T}}}^{{{\text{ATP}}}} c_{{\text{T}}}^{{{\text{BP}}}} } }}{2}$$
(12)

In the ATP binding experiment as described above, four different levels of \(c_{{\text{T}}}^{{{\text{ATP}}}}\) were chosen: 100 µM, 200 µM, 400 µM and 500 µM. For each group, data of \(c^{{{\text{BC}}}}\) versus time were obtained by subtracting the measurement of ATP content in the incubating media at each time point from corresponding \(c_{{\text{T}}}^{{{\text{ATP}}}}\) according to Eq. (8,6b). The average values of \(c^{{{\text{BC}}}}\) over time from all four groups were curve-fitted together to Eq. (11) to determine kon, koff and \(c_{{\text{T}}}^{{{\text{BP}}}}\) using MATLAB (R2018b, MathWorks Inc., Natick, MA). The resulting \(c_{{\text{T}}}^{{{\text{BP}}}}\) was multiplied by the volume of incubating media (500 µL) to estimate the amount of BP in the samples as denoted by \(T_{{{\text{BP}}}}\). Values of \(T_{{{\text{BP}}}}\) were plotted against the PG content in samples of each tissue type and the data were curve-fitted to examine the correlation between the two. In this study, it is hypothesized that the amount of binding protein in IVD tissue is proportional to its PG content. Therefore, \(c_{{\text{T}}}^{{{\text{BP}}}}\) in human IVD tissue can be determined when its PG content is known.

Measurement of Adenine Derivatives

To rule out the possibility that reduction of ATP in the ATP binding experiment was caused by ATP hydrolysis over time, the concentrations of ADP and AMP were measured using a modified version of protocol published in literature [62]. Briefly, three portions of 100 µL incubating supernatant were sampled after the binding experiment. One portion was tested with ATP Bioluminescent assay directly and the other two portions were mixed with 10 µL freshly prepared ADP and AMP assays separately followed by an incubation on ice for 2 h before tested with ATP Bioluminescent assay. The ADP and AMP assays were used to enzymatically convert ADP and AMP to ATP, respectively. The ADP assay contained 50 mM phosphoenolpyruvate, 100 mM Tris-Cl (pH 7.4), 35 mM KCl, 6 mM MgCl2 and 150 IU/mL pyruvate kinase. The AMP assay contained the same chemical components as ADP assay with the addition of myokinase (100 IU/mL) and 0.02 µM of GTP solution. ATP, AMP, ADP solutions made of PBS were used as standards. All assays were simultaneously conducted to detect different purine products.

Theoretical Models

The theoretical models developed in this study were based on the previously published mechano-electrochemical continuum mixture theory [39, 63]. IVD tissue was considered as a mixture of 3 phases: an intrinsically incompressible, porous, negatively charged solid phase with ATP binding proteins (s), interstitial fluid phase (w), charged and uncharged solute phases. Sodium ion (Na+) and chloride ion (Cl−) were considered as charged ions to balance the fixed negative charges on the solid phase. The metabolic rates of sodium and chloride ions were assumed to be zero. Furthermore, the free ATPs in the interstitial fluid were assumed to be reversibly bound to proteins in the solid matrix to form a bound complex. The mass balance equations for free ATP and the immobile bound complex in the mechano-electrochemical mixture model were derived according to Eqs. (1), (8, 9) and (10), and written as:

$$\frac{{{ }\partial { }\left( {\phi^{w} c^{{{\text{ATP}}*}} } \right)}}{\partial t} + \nabla \cdot ( {\varvec{J}}^{{{\text{ATP}}}} + \phi^{w} c^{{{\text{ATP}}}} *{\mathbf{v}}^{s} ) = \left( {R^{{{\text{ATP}}}} - \frac{{V_{{{\text{max}}}} c^{{{\text{ATP}}*}} }}{{K_{{\text{m}}} + c^{{{\text{ATP}}*}} }}} \right)\rho^{{{\text{cell}}*}} - \phi^{w} Q^{{{\text{Bind}}}}$$
(13)
$$\frac{{{ }\partial { }\left( {\phi^{w} c^{{{\text{BC}}*}} } \right)}}{\partial t} + \nabla \cdot ( \phi^{w} c^{{{\text{ATP}}}} {\mathbf{v}}^{s} ) = \phi^{w} Q^{{{\text{Bind}}}}$$
(14)
$$Q^{{{\text{Bind}}}} = k_{{{\text{on}}}} \left( {c_{{\text{T}}}^{{{\text{BP}}*}} - c^{{{\text{BC}}*}} } \right)c^{{{\text{ATP}}*}} - k_{{{\text{off}}}} c^{{{\text{BC}}*}}$$
(15)

where \(c^{{{\text{ATP}}*}}\) and \(c^{{{\text{BC}}*}}\) are the molar concentrations of free ATP and bound complex per unit interstitial water volume, \({\mathbf{v}}^{s}\) is the velocity of the solid matrix, \({\varvec{J}}^{{{\text{ATP}}}}\) are the molar flux of ATP relative to the solid phase, \(\phi^{w}\) is the water content in the tissue (\(\phi^{w}\) = \({ }\frac{{\phi_{0}^{w} + e}}{1 + e}\) , where e is the tissue dilatation), \(R^{{{\text{ATP}}}}\) is the ATP release rate per cell, \(\rho^{{{\text{cell}}*}}\) is cell density of the tissue, \(Q^{{{\text{Bind}}}}\) is the sink in Eq. (13), resulting from binding reaction (Eq. 15), and \(c_{{\text{T}}}^{{{\text{BP}}*}}\) is the concentration of total ATP binding proteins per unit interstitial water volume in the tissue matrix which is dependent on tissue deformation:

$$c_{{\text{T}}}^{{{\text{BP}}*}} = \frac{{c_{{{\text{T}}0}}^{{{\text{BP}}*}} }}{{1 + \frac{e}{{\phi^{w} }}}},$$
(16)

where \(c_{{{\text{T}}0}}^{{{\text{BP}}*}}\) is the total concentration of binding proteins at reference configuration.

Finite Element Analysis

The 3D porcine disc geometry was taken from the lumbar IVD of mature pigs with a size of 30 mm anterior-posteriorly, 40 mm laterally, and 3.6 mm in height. Only NP and AF regions were considered in the model (Fig. 1a). The human IVD was also modeled as an inhomogeneous tissue consisting of NP and AF region based on the geometry as described previously [36, 64, 65]. The same disc geometry was used for both non-degenerated and degenerated human IVD (Fig. 1b). Due to symmetry about the mid-transverse and mid-sagittal planes, only the upper-right quarter of all models was analyzed. The porcine, non-degenerated human and degenerated IVDs were meshed with 17550, 9186 and 8556 quadratic tetrahedral Lagrange elements, respectively [36, 40,41,42, 64, 65]. All models were discretized by weak form finite element method based on the work published in [39, 63] and implemented in COMSOL software (COMSOL 5.3, COMSOL, Inc., Burlington, MA).

Fig. 1
figure 1

Schematic view of upper quarter of a porcine IVD. b human IVD with meshes

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The porcine IVD model was validated by using experimental results from our previous study [6]. The tissue properties and boundary conditions used in the porcine model were summarized in Tables 1 and 2. Some tissue properties were measured in this study and listed in the result session.

Table 1 Tissue properties used in the numerical analyses.
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Table 2 Boundary conditions used in the numerical analyses
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After the validation, extracellular ATP distribution in non-degenerated and degenerated human IVD cases were simulated. Human discs of Thompson Grade 1 and 4 were used to represent non-degendered and degenerated disc status, respectively. Due to the lack of experimental data, in-vivo ATP release rates of human IVD cells were assumed to be the same as those of porcine IVD cells. The tissue properties and boundary conditions were adopted from previous studies [36, 39, 65] and summarized in Tables 1 and 2.

Statistical Analysis

A total of 6 agarose gel samples were used for ATP hydrolysis experiment for both NP and AF cells. The Michaelis–Menten constants were determined by individually curve-fitting data generated from each sample and the results from the two cell types were compared by unpaired two-tailed student’s t test to analyze the significant differences. A total of 9 agarose gel samples were used in each group for the ATP release experiment. For each cell type, unpaired two-tailed student’s t test was used to compare ATP release between two groups with different oxygen levels at the same glucose level or with different glucose levels at the same oxygen level. For ATP binding experiment, the measurements of PG and collagen content in IVD tissue were obtained from a total of 9 samples. Two-tailed student’s t test was used to determine if results were significantly affected by tissue preparation. The binding rate constants and the concentration of binding protein were determined from a total of 18 samples (6 independent experiments with 3 samples per group in each experiment. Unpaired two-tailed Student’s t test was performed to examine significant difference between NP and AF tissue. Statistical significance was considered with p value < 0.05 in all analysis. The coefficient of determination R2 was used as an index for the quality of all curve fitting. All results were presented as mean ± standard deviation.

Results

Rates of ATP Hydrolysis by IVD Cells

A typical curve fitting of hydrolysis of 10 µM extracellular ATP by IVD cells is shown in Fig. 2. The results of \(V_{{{\text{max}}}}\) and \(K_{{\text{m}}}\) are listed in Table 3. AF cells were shown to hydrolyze ATP much faster than that of NP cells with exhibiting greater \(V_{{{\text{max}}}}\) and \(K_{{\text{m}}}\) (p = 0.0026 and 0.0064, respectively).

Fig. 2
figure 2

Typical curve fitting of hydrolysis of extracellular ATP (10 µM) by IVD cells

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Table 3 Summary of parameters of ATP release and hydrolysis by porcine IVD cells.
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Rates of ATP Release by IVD Cells

A strong linear relationship (R2 > 0.99) was demonstrated between ATP release rate and ATP concentration in the medium at 4-h incubation for both NP and AF cells (Fig. 3). The ATP concentrations in the media of NP and AF cell culture at 4-h incubation were measured as 0.539 ± 0.121 µM and 0.017 ± 0.003 µM, respectively. The average values of \(c_{{{\text{ATP}}\_4h}}\) were used to calculate corresponding RATP based on the linear regression equations as shown in Fig. 3. The results of RATP were shown in Table 3.

Fig. 3
figure 3

Correlation between values of RATP and \(c_{{{\text{ATP}}\_4h}}\) for a NP cells and b AF cells in the ATP release experiment

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Microstructure of Tissue Particles in ATP Binding Experiment

The typical particle sizes of NP and AF tissue after FA treatment plus homogenization were in the range of 10–20 μm in length with a roughly elliptical to spherical shape (Fig. 4a, b).

Fig. 4
figure 4

Typical SEM images of homogenized a NP, b AF tissue particles after decellularization by FA and homogenization. The c PG and d collagen content in natural and treated porcine IVD tissue (n = 9). The *Symbol indicates significant differences compared to the control group (p < 0.05)

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PG and Collagen Content of Tissue Particles in ATP Binding Experiment

The PG content in the NP particles after FA treatment and homogenization reduced to about one third of that in natural tissue (Fig. 4c) while the collagen content was almost depleted (Fig. 4d). The same treatment preserved about 80% of the PG content and collagen content in treated AF tissue while the additional TH treatment completely removed PG without significantly affecting the collagen content (Fig. 4).

ATP Binding to IVD Tissue

Typical curve-fit plots of ATP binding to NP and AF tissues are shown in Fig. 5. There was very good agreement between the experimental data and theoretical curve fitting for both types of tissue (R2 > 0.99). NP and AF tissue particles with similar PG content (Fig. 4c) exhibited similar ATP binding profiles (Fig. 5), whereas AF tissue homogenates with PG removed by additional TH treatment were tested in the binding experiment with the highest concentration of ATP (500 uM) and did not show any binding with ATP over the course of 6 h (data not shown), suggesting the binding effect solely existed between ATP and PG.

Fig. 5
figure 5

Typical curve fitting of ATP binding to FA-treated porcine a NP and b AF tissue homogenates incubated in PBS with different ATP concentrations. Data points represent the mean of 3 measurements per group in one independent experiment. The curves represent the global fits of data of all groups in one experiment to Eq. (13)

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The values of kon, and koff derived by theoretical curve fitting of data from NP and AF tissue are summarized in Table 4. There was no significant difference between the average of kon, and koff derived from NP and AF tissue (p = 0.6178 and 0.1054, respectively) which indicates the kinetics of binding reaction is not tissue specific. Meanwhile, the linear curve-fit with the constraint of passing through the origin showed a strong correlation between \(T_{{{\text{BP}}}}\) and PG content in both types of treated tissue particles (R2 = 0.79) (Fig. 6), which confirmed the speculation of this study that binding capacity of IVD tissue is only PG-dependent. The quantitative relationship is represented by the slope of the curve-fitted line in Fig. 6 with an extrapolated value of 6.058 × 10−5 µmole BP per µg PG. The number was used to calculate \(c_{{{\text{T}}0}}^{{{\text{BP}}*}}\) for porcine IVD tissue using the mean value of PG content in the tissue as shown in Fig. 5a. The results of \(c_{{{\text{T}}0}}^{{{\text{BP}}*}}\) for porcine NP and AF tissue were listed in Table 4. For non-degenerated and degenerated human NP tissue, PG content was chosen to be 500 µg/mg dry tissue weight and 150 µg/mg dry tissue weight, respectively according to [66]. For degenerated and non-degenerated human AF tissue, PG content was considered to be 120 µg/mg dry tissue weight and 100 µg/mg dry tissue weight, respectively according to [67]. The values of \(c_{{{\text{T}}0}}^{{{\text{BP}}*}}\) for non-degenerated and degenerated human NP tissue were calculated to be 4410 and 2058 µM respectively. For non-degenerated and degenerated human AF tissue, the values were 1890 and 1939 µM, respectively.

Table 4 Parameters of ATP binding to porcine IVD tissue
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Fig. 6
figure 6

Correlation between the amount of ATP binding protein (TBP) and average amount of PGs in FA-treated IVD tissue particles. Data points of Tbp represent the estimated values from 6 independent ATP binding experiments with 3 samples in each group in one experiment. Two specific clusters represented NP and AF tissue. The linear curve-fit which was forced to pass through the origin showed a strong correlation between the two

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Furthermore, ADP and AMP were not detected in the PBS solution after the binding experiment, suggesting the reduction in ATP concentration was due to the binding between ATP with PGs in IVD tissue, not due to ATP hydrolysis.

Additional Porcine Tissue Properties for the Numerical Analysis

The results of measurements of the water content and fixed charge density for porcine AF and NP tissue are shown in Table 5.

Table 5 Additional porcine tissue properties used in the numerical analyses
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Extracellular ATP Concentration Predicted by IVD Models

The majority of extracellular ATP were found to be in the form of bound complex and free ATP was maintained at a low level in all cases (Figs. 7, 8). The total extracellular ATP predicted by the porcine model were in the range between 100 and 120 µM in the center of NP and less than 10 µM in AF on average (Fig.7), both of which were comparable to experimental results reported in [6] (Fig. 7). A lower extracellular ATP level was observed in the degenerated human IVD compared to the non-degenerated one (Fig. 8). The extracellular ATP level in the central NP region fell from 120 µM in the non-degenerated disc to about 50 µM in the degenerated disc whereas both cases exhibited an extracellular ATP level less than 10 µM in AF region (Fig. 8).

Fig. 7
figure 7

Distribution of a bound complex and b free ATP in porcine IVD

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Fig. 8
figure 8

Distribution of a, c binding complex and b, d free ATP in non-degenerated and degenerated IVD

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Discussion

This study quantitatively analyzed extracellular ATP distribution in human IVD and its impact on disc degeneration. A novel 3D finite element model was developed by incorporating the rates of ATP release and hydrolysis and the binding reaction between ATP and PG into the established mechano-electrochemical mixture theory for charged hydrated soft tissue. This study demonstrated for the first time that ATP binds with PGs, which influences extracellular ATP distribution in the IVD. The results from the porcine model were consistent with previous experimental measurements, suggesting the model developed by this study is capable of reliably predicting extracellular ATP distribution in the IVD. It was found that the overall extracellular ATP level in the human IVD decreased with degeneration.

This study presents the first evidence that ATP binds to PGs but not to collagen. The ATP binding capacity of PGs could be the reason that a high level of extracellular ATP is observed in the PG-rich NP compared to AF [6]. The ATP binding sites of PGs are located on glycosaminoglycans which exhibit inhibitive effects on ATP hydrolysis through their interactions with ATP [13]. However, the magnitude of the binding rate (i.e. kon and koff) was relatively low compared to values reported in other ligand-receptor binding studies [68,69,70,71,72], indicating the binding reaction is probably weak. Our results also showed that the majority of extracellular ATP in IVD were present in the form ATP-binding complex, rather than free ATP (Figs. 7, 8). It is possible the binding proteins on PG act as energy storage sites, which retain a substantial portion of extracellular ATP within ECM and continuously release a small amount of free ATP in the IVD. Furthermore, in the body, extracellular ATP is inevitably subjected to rapid hydrolysis by ecto-nucleotidases [73, 74]. As the main hydrolytic product of ATP, extracellular adenosine was also shown to increase intracellular ATP level and promote ECM production in IVD cells [13]. Therefore, retention of extracellular ATP and its derivative may help maintain normal ECM metabolism and serve an energy reservoir in the IVD where ECM and energy production are constantly suppressed by limited nutrition supply due to the avascular nature of the IVD.

Our results also indicated that the extracellular ATP content in the IVD decreases with tissue degeneration and the effect is more prominent in the NP. Since the same rates of ATP release and hydrolysis were assumed for both normal and degenerated discs in our simulation, such a reduction could be mainly contributed by a combined effect of reduced tissue cellularity and PG content in the NP, with the latter being a major factor. On the other hand, since the cell density and PG content of AF region were not significantly changed in mature human discs over degeneration [67, 75], it may explain why distribution of extracellular ATP in AF region was maintained at a similar level.

The extracellular ATP level was predicted to be approximately 120 µM and 10 µM in NP and AF region, respectively. Our previous study demonstrated that extracellular ATP treatment at 100 µM can stimulate intracellular ATP production and ECM biosynthesis of NP cells, whereas both productions in AF cells were stimulated by extracellular ATP at a lower level (i.e. 20 μM) [43]. A previous study showed that supplementation of exogenous ATP in a similar range of concentration increased matrix accumulation of cartilage tissue in a dose-dependent manner [76] and suggested that the ATP-mediated upregulation of ECM synthesis could be achieved through purinergic receptor pathway [76]. Therefore, the loss of PGs in degenerated discs, especially in NP region, may have a significant impact on the biological function of disc cells by altering purinergic signaling.

There are limitations in this study. The first one is that the parameters of ATP metabolism and some tissue properties of the porcine IVD were used for simulations in the human IVD cases. However, the majority of young porcine NP cells in this study are of notochordal phenotype [77, 78]. Given notochordal NP cells tend to be more metabolically active than chondrocyte-like AF cells [79, 80] which are largely present in mature adult IVD with a greater proportion in degenerated disc [81, 82], it is possible that ATP release rate of human IVD cells may be overestimated in our model. Secondly, although the ATP release and hydrolysis rates of IVD cells measured in this study are comparable to previous studies [83, 84], they were only measured one oxygen level. However, an oxygen concentration gradient exists in avascular IVD in which O2 concentration can fall from ~ 5% to as low as 1%, depending on the diffusion distance from blood supply at the disc periphery [85]. Since several studies have implicated hypoxia has an impact on the expression and enzymatic activities of ecto-nucleotidases which are responsible for ATP breakdown [86, 87], detailed information regarding ATP hydrolysis and release within the physiological range of oxygen levels is useful for the model to provide more precise predictions.

Conclusion

A mathematical model was developed in this study to quantitively analyze extracellular ATP distribution within the IVD. The new model is capable of providing a realistic prediction of extracellular ATP distribution in the IVD. Due to the capability of PGs to bind ATP, a high retention of extracellular ATP found in the PG-rich NP regulates biological activities in the IVD via purinergic signaling. However, the ATP-PGs binding effect can be diminished due to tissue degeneration, which may have a significant impact on cellular functions in the IVD. This study provides an understanding of metabolism and potential biological influences of extracellular ATP on the IVD and may be useful for developing new therapeutic strategies for IVD degeneration.