Modelling of the SDF-1/CXCR4 regulated in vivo homing of therapeutic mesenchymal stem/stromal cells in mice

Hepatic ischemia-reperfusion (I/R) injury model

All animal procedures are approved by the Animal Ethics Committee of the University of Queensland (MED/493/15/NHMRC) and are carried out in accordance with Australian Code for the Care and Use of Animals for Scientific Purposes 8th edition. Healthy mice (Male 20-week-old BALB/c nude) are anaesthetized initially by an intraperitoneally injection of ketamine hydrochloride (80 mg/kg) and xylazine (10 mg/kg). Body temperature is controlled by placing mice on a heating pad set to 37 °C. Hepatic I/R injury is induced by clamping the portal vein and hepatic artery supplying the median and left lobes using a microvascular clamp. After 45 min of partial ischemia, the clamp is removed to allow reperfusion in the liver.

Hypoxia-precondition of human MSCs

Bone marrow aspirates are collected from fully informed healthy human volunteer donors who provided written consent. The healthy volunteer donors are recruited from Mater Private Hospital, Brisbane, Australia. Ethical approval is granted through the Mater Health Services Human Research Ethics Committee and ratified by the Queensland University of Technology Human Ethics Committee (number: 1000000938). Human MSCs are isolated from bone marrow aspirates, cultured and characterized as we previously described (Parekkadan & Milwid, 2010; Squillaro, Peluso & Galderisi, 2016). All cells are cultured in monolayer using expansion media formulated from low glucose DMEM (ThermoFischer) supplemented with 10% fetal bovine serum (FBS; Thermo Fisher, Waltham, MA, USA) and 10 ng/mL FGF-1 (Peprotech). All experiments involving MSCs are performed at passage 4-8, tested negative for mycoplasma contamination, and <80% confluence. MSCs are cultured in a hypoxia chamber incubator (catalog No. 27310; StemCell Technologies, Vancouver, BC, Canada) at 37 °C in 3% O₂, 5% CO₂ and 92% N₂ for 24 h, and these MSCs are named as hypoxia-preconditioned MSCs. MSCs cultured for 24 h in 95% air and 5% CO₂ are used as a control.

In vivo transplantation of MSCs

Male 20-week-old BALB/c nude mice are purchased from the Animal Resource Centre (Perth, Western Australia). 150 µl of a suspension of 5 × 10⁵ or 1. 5 × 10⁶ MSCs is injected with a 27-gauge needle through the tail vein of the control mice or mice with hepatic I/R injury at the time of reperfusion. Prior to injection, the MSCs are maintained at 4 °C, and the cells are gently resuspended with a pipette to ensure no aggregation before injection. Animals (n = 3) are sacrificed at designated times (30 min, 4, 15, 24, and 48 h post-injection). Here n indicates the number of mice used, following the guidelines for the welfare and use of animals in pharmacokinetic studies (Workman et al., 2010). Blood is obtained by cardiac puncture. The normal liver and the liver with I/R injury are removed for analysis.

Droplet digital PCR assays for Alu sequences

Genomic DNA (gDNA) of the blood and liver are isolated using DNA Mini Kit (Qiagen, Valencia, CA, USA). Droplet digital PCR (ddPCR) is performed in reaction consisting of gDNA, primer sets (Alu forward: GCCTGTAATCCCAGCACTTT; Alu reverse: CACTACGCCCGGCTAATTT) (Zhao et al., 2011), H₂O and ddPCR EvaGreen Supermix (BioRad, USA). ddPCR is performed according to manufacturer’s manual. Briefly, 20 µL of ddPCR reaction mix is separated into droplets with QX200 Droplet Generator (BioRad, USA). The droplets are transferred into a 96-well PCR plate, sealed and incubated at following cycling conditions: one cycle of 95 °C for 5 min, 45 cycles of 95 °C for 30 s, 55 °C for 1 min and one cycle of 4 °C for 5 min, 90 °C for 5 min and an infinite hold of 12 °C. After thermal cycling, the PCR plate is transferred in QX200 Droplet Reader (read) and read in FAM channel using QuantaSoft version 1.7.

Quantitative ELISA analysis

Liver samples are weighed and immediately placed in 10 volumes (wt/vol) of a protease inhibitor cocktail containing 10 nmol/l EDTA, 2 mmol/l PMSF, 0.1 mg/ml soybean trypsin inhibitor, 1.0 mg/ml bovine serum albumin, and 0.002% sodium azide in isotonic PBS, pH 7.0. Tissues are disrupted with a tissue homogenizer, and lysates are incubated at 4 °C for 2 h. Samples are clarified by two rounds of centrifugation at 12,500 g for 10 min at 4 °C. SDF-1 concentrations in blood and liver are assessed by enzyme-linked immunosorbent assay (CUSABIO, TX, USA). CXCR4 concentration in human MSCs are assessed by ELISA (CUSABIO, TX, USA).

Immunohistochemistry for SDF-1 and CXCR4 expression

Liver tissues and human MSCs are fixed in 10% neutral-buffered formalin, processed, and then embedded in paraffin for light microscopy. Immunohistochemistry is performed following the standard avidin/streptavidin-biotin peroxidase methods. All slides (4 µM) are deparaffinized, rehydrated and boiled for antigen retrieval (30 m at 98 °C in citrate buffer pH 6.0). Primary antibodies against SDF-1 (1:200) and CXCR4 (1:400) proteins (Abcam, USA) are used on the sections of the tumor tissue. After being incubated overnight at 4 °C, the slides are incubated with biotinylated anti-rabbit immunoglobulin for 30 min and then with horseradish peroxidase-jugated streptavidin for 30 min. Negative control experiments include omission of either the primary or secondary antibody with 1% BSA-PBS. Jurkat cells are used as a positive control of SDF-1 expression, and HeLa cells are used as a positive control of CXCR4 expression according to the manufacturer’s instructions. Each step is followed by a washing with PBS. Staining is revealed by 3,3′-diaminobenzidine and counterstained with hematoxylin.

Model formulation

The population-level mathematical model includes the descriptions of MSC and SDF-1 kinetics in the blood and liver. After intravenous injection, MSCs are arrested in the liver from blood by both passive homing (via blood flow) and active homing (via the liver SDF-1 attracting CXCR4 in MSCs) (Karp & Teo, 2009). The number of MSCs in the liver can decrease due to a series of mechanisms including release back to the blood circulation and depletion. Here we refer to depletion as the loss of cell functionality and viability caused by various mechanisms (Oh, Lee & Wagers, 2014; Wang et al., 2016). Therefore, the governing differential equation describing MSCs in the liver is as follows: (1)${\displaystyle \frac{\mathrm{d}{M}_{\mathrm{L}}\left(t\right)}{\mathrm{d}t}=\stackrel{\text{Passive homing}\left(\text{via blood flow}\right)}{\overbrace{\alpha M_{\mathrm{B}}\left(t\right)}}+\stackrel{\text{Active homing}\left(\text{via SDF}-1∕\text{CXCR}4\right)}{\overbrace{\beta S_{\mathrm{L}}\left(t\right)\left(1-\frac{M_{\mathrm{L}}\left(t\right)}{K}\right)}}-\stackrel{\text{Loss due to release and depletion}}{\overbrace{\gamma M_{\mathrm{L}}\left(t\right)}}}$ where M_L(t) (cell/kg) is the dose of MSCs in the liver, M_B(t) (cell/kg) is the dose of MSCs in the blood, S_L(t) (pg/mL) is the concentration of SDF-1 in the liver, t (h) is time, α (h⁻¹) is the MSC arrest rate associated with blood flow, β (cell mL/(kg h pg)) is the MSC arrest rate associated with SDF-1/CXCR4 attraction, K (cell/kg) is the attraction capacity of MSCs expressing CXCR4 attracted by SDF-1 in the liver, and γ (h⁻¹) is the MSC loss rate in the liver including release and depletion.

For MSCs in the blood, a relatively fast dose-decrease at early time, known as the distribution phase, is followed by a slower decrease at later time, known as the elimination phase. These processes can be modelled using a biexponential decay model (Armitage, Dick & Bourne, 2003): (2)${\displaystyle M_{\mathrm{B}}\left(t\right)=\stackrel{\text{Distribution phase}}{\overbrace{C_1{\mathrm{e}}^{-{\lambda }_{1}t}}}+\stackrel{\text{Elimination phase}}{\overbrace{C_2{\mathrm{e}}^{-{\lambda }_{2}t}}}}$ where C₁ (cell/kg) and C₂ (cell/kg) are the intercepts for the distribution and elimination phases of MSCs, and λ₁ (h⁻¹) and λ₂ (h⁻¹) are the decay rates for the distribution and elimination phases of MSCs, respectively.

In normal mice, the SDF-1 concentration in the blood remains approximately constant. For SDF-1 in the blood with an injured liver, the initial concentration is the same as that of normal uninjured mice and increases at early reperfusion followed by a relatively slower decrease at later time. Therefore, the SDF-1 in the blood with an injured organ is modelled using the function form associated with modified-biexponential decay (Wilson et al., 2015): (3)${\displaystyle S_{\mathrm{B}}\left(t\right)=\stackrel{\text{Initial SDF}-1\text{concentration}}{\overbrace{S_{\mathrm{B}}\left(0\right)}}+\stackrel{\text{Kinetics of SDF}-1}{\overbrace{a_{\mathrm{B}}{\mathrm{e}}^{-b_{\mathrm{B}}t}\left(1-{\mathrm{e}}^{-c_{\mathrm{B}}t}\right)}}}$ where S_B(0) (pg/mL) is the initial concentration of SDF-1 in the blood of mice with injured liver, a_B (pg/mL) is the amplitude of SDF-1 concentration change, b_B (h⁻¹) is the SDF-1 decay rate, and c_B (h⁻¹) is the control factor of SDF-1 kinetics.

In normal mice, the SDF-1 concentration in the liver remains approximately constant. SDF-1 concentration in the injured liver has the same function form as in the blood: (4)${\displaystyle S_{\mathrm{L}}\left(t\right)=S_{\mathrm{L}}\left(0\right)+a_{\mathrm{L}}{\mathrm{e}}^{-b_{\mathrm{L}}t}\left(1-{\mathrm{e}}^{-c_{\mathrm{L}}t}\right)}$ where S_L (0), a_L= a_B/η₁, b_L= b_B/η₂, and c_L = c_B/η₃ are the corresponding parameters in the liver that have the same physiological meanings as described in the model for SDF-1 kinetics in the blood. To develop the model on the basis of clinically accessible variables, the parameters for the SDF-1 in the liver are presented in terms of their relations with the corresponding parameters in the blood by association coefficients η₁, η₂, and η₃.

Model calibration

The calibration of the model is performed using MATLAB’s nonlinear curve-fitting function, lsqcurvefit (MathWorks, 2018). Both models for SDF-1 and MSCs in the blood are calibrated with experimental data. The association coefficients η₁, η₂, and η₃ are then determined by comparing the calibrated models for SDF-1 in the blood and liver, and are validated by predicting the SDF-1 concentration in the liver based on the calibrated model for the SDF-1 concentration in the blood using published independent external data (Wilson et al., 2015). Details of the validation of the association coefficients are shown in the Supplemental Information. The calibrated models for SDF-1 in the liver and MSCs in the blood are then inputted into the model for MSCs in the liver, to estimate the parameters in normal and injured livers, respectively.

Experimental results

Previous studies show that SDF-1 expression increases in the liver with ischemia/reperfusion (I/R) injury (Lentsch et al., 1999; Wilson et al., 2015). Our immunohistochemistry for SDF-1 in the mouse liver with ischemia/reperfusion (I/R) injury also reveals a significantly higher SDF-1 level in the I/R injured liver than the control (Figs. 2A and 2C). It has been reported that SDF-1 can activate two chemokine receptors, CXCR4 and CXCR7, with different downstream signaling pathways during liver injury (Lentsch et al., 1999; Wilson et al., 2015). To elucidate the SDF-1/CXCR4 regulated in vivo homing of human MSCs, we use droplet digital PCR assays for human-specific Alu sequences to quantify the numbers MSCs in the blood and liver of normal and hepatic I/R injured mice (Figs. 2D and 2E). Indeed, a higher MSC concentration is found in the I/R injured liver (Fig. 2E).

In conjunction with Figs. 2A, 2B shows the overexpression of CXCR4 in hypoxia-preconditioned MSCs, which is consistent with previous experimental observations (Cencioni, Capogrossi & Napolitano, 2012; Liu et al., 2012). Comparing with the normal MSCs, the CXCR4 expression in 24 h hypoxia-preconditioned MSCs is about 4-fold higher. Previous studies find that the hypoxia preconditioned MSCs also become more active in terms of both cell motility and proliferation (Ali et al., 2016; Beegle et al., 2015; Liu et al., 2012). Aligning with these experimental findings, our ddPCR results show an increased number of hypoxia-preconditioned MSCs in the I/R injured liver comparing to the normal MSCs in the same liver condition. However, at this stage how the hypoxia-preconditioning facilitates in vivo homing of MSCs remains unclear. For example, it is unclear whether the hypoxic preconditioning enhances MSC homing through: (i) the SDF-1/CXCR4 chemotaxis (active homing); or (ii) the transportation via blood flow (passive homing); or (iii) a combination of effects from (i) and (ii). We now attempt to distinguish between these two possibilities by calibrating our mathematical model to the experimental data.

Modelling results

The mathematical model for in vivo human bone marrow-derived MSC homing is developed based on the published intravital imaging details of administered MSCs (Toma et al., 2009; Wang et al., 2016) and SDF-1/CXCR4 chemotaxis of MSCs (Fig. 1A) (Dar et al., 2005; Ji et al., 2004). Following intravenous injection, MSCs are arrested in organs by both passive homing (via blood flow) and active homing (via the organ SDF-1 attracting CXCR4 expressing MSCs) (Karp & Teo, 2009). MSC release and depletion in organs are described by a single loss term in our model. Differentiation is not included in the model as differentiation is slow relative to the time scale of the experiment and hence would have a small impact on the MSC distribution at the organ level over the observation period (Hass et al., 2011; Schmidt et al., 2006). As shown in Fig. 1B, this model has two compartments: blood and injured organ (liver). All MSCs are assumed to act independently with no obligatory connections or intercellular feedback loops. In summary, we assume the in vivo kinetics of MSCs are governed by two processes: (i) transport to the organ (liver) via blood flow and the SDF-1/CXCR4 chemotaxis; and (ii) loss in the organ by release and depletion. Variables included in the model are time t (h), SDF-1 concentration in blood S_B(t) (pg/mL) and liver S_L(t) (pg/mL), and MSC dose in blood M_B(t) (cell/kg) and liver M_L(t) (cell/kg).

Previous modelling of the in vivo homing of MSCs in organs neglects SDF-1/CXCR4 chemotaxis (Wang et al., 2016), while the biological evidence suggests that this mechanism plays an important role in the MSC homing (Abbott et al., 2004; Hu et al., 2013; Lentsch et al., 1999; Wilson et al., 2015). With the SDF-1/CXCR4 chemotaxis incorporated in our model, we calibrate the model system (Eqs. 1–4) to the experimental data, as shown in Figs. 2C–2E. The model captures key features of the observed time evolution of MSC dose in the mouse liver with a high goodness-of-fit, with R²=0.987 (Fig. S1). The SDF-1 profiles in Fig. 2C show that the SDF-1levels in the liver and blood are maximally increased after approximately 12 h of reperfusion, which correlates with maximal liver injury after hepatic I/R injury reported in previous studies (Lentsch et al., 1999; Wilson et al., 2015). Following intravenous injection, the MSC dose in the liver increases until 4 h after injection, and then slowly declined. The area under the curve (AUC_0−48hr) of MSCs in the liver indicates that organ loading of MSCs (Fig. 2E) increases by 1.52 times following hepatic I/R injury (from 2.00 × 10⁹cells h/kg to 3.05 × 10⁹ cells h/kg), and the organ loading of hypoxia-preconditioned MSCs (Fig. 2E) increases by 1.71 times (3.43 × 10⁸ cells h/kg). The increased organ loading suggests that the injured liver is an effective attractant for both normal and hypoxia-preconditioned MSCs.

The parameter estimates obtained by calibrating the model to match the experimental data are listed in Table 1. These parameter estimates reveal three important features:

1. Estimates of α, which represents the MSC arrest rate associated with blood flow, are approximately the same for all liver and MSC conditions. The small change (about 10%) in α estimates suggests that neither the liver nor MSC conditions have significant impact on the passive homing,

2. The highest SDF-1/CXCR4 attraction capacity and MSC arrest rate associated with SDF-1/CXCR4 attraction are obtained for the hypoxia-preconditioned MSCs in I/R injured livers. Both the SDF-1/CXCR4 attraction capacity and the corresponding MSC arrest rate significantly increase (over 100%) compared to those obtained for the normal MSCs in normal livers, indicating that SDF-1 in organs is an effective in vivo attractant for MSCs expressing CXCR4,

3. The MSC depletion rate is lower for the hypoxia-preconditioned MSCs than for the untreated MSCs, which is consistent with results from previous studies that hypoxic preconditioning enhances the MSC survival in vivo (Beegle et al., 2015; Liu et al., 2012). Based on our modelling results, we suggest that the hypoxic preconditioning enhances in vivo homing of MSCs though active homing and the survival of MSCs in the organ, whereas its impact on passive homing is small.

To further validate the model, simulations of SDF-1 levels in mouse blood and livers are compared with published data (Wilson et al., 2015). All parameters are obtained using the same approach described in the Methods section. As shown in Fig. S2, there is a high goodness-of-fit with R²=0.986, between model predictions and the independent data, indicating that the model is suitable to characterize the in vivo kinetics of SDF-1. Our model is then used to predict the in vivo homing of the MSCs administered at a different initial dose (1.5 × 10⁶ cells/animal). All parameters in the model are maintained the same as shown in Table 1, and we find that the model adequately predicts the MSC doses in both normal and injured livers, again with a high goodness-of-fit with R² close to unity (Fig. 3). The good agreement between the model predictions and experimental data confirms that this model can be readily applied to different MSC dose regimens. There is substantial evidence that administered MSCs would accumulate within sites of disease or injury (Hu et al., 2013; Ji et al., 2004; Kitaori et al., 2009; Liu et al., 2012). However, previously published cytokinetic models often underestimate the therapeutic cell concentration in diseased organs such as the heart with myocardial infarction or fibrotic liver (Wang et al., 2016; Zhu et al., 1996). As our model includes the important SDF-1/CXCR4 axis which regulates the in vivo homing of stem cells to sites of injury, it is able to account for the effect of tissue injury on MSC distribution.