Mathematical modeling of white adipocyte exocytosis predicts adiponectin secretion and quantifies the rates of vesicle exo- and endocytosis

Abstract

Adiponectin is a hormone secreted from white adipocytes and takes part in the regulation of several metabolic processes. Although the pathophysiological importance of adiponectin has been thoroughly investigated, the mechanisms controlling its release are only partly understood. We have recently shown that adiponectin is secreted via regulated exocytosis of adiponectin-containing vesicles, that adiponectin exocytosis is stimulated by cAMP-dependent mechanisms, and that Ca²⁺ and ATP augment the cAMP-triggered secretion. However, much remains to be discovered regarding the molecular and cellular regulation of adiponectin release. Here, we have used mathematical modeling to extract detailed information contained within our previously obtained high-resolution patch-clamp time-resolved capacitance recordings to produce the first model of adiponectin exocytosis/secretion that combines all mechanistic knowledge deduced from electrophysiological experimental series. This model demonstrates that our previous understanding of the role of intracellular ATP in the control of adiponectin exocytosis needs to be revised to include an additional ATP-dependent step. Validation of the model by introduction of data of secreted adiponectin yielded a very close resemblance between the simulations and experimental results. Moreover, we could show that Ca²⁺-dependent adiponectin endocytosis contributes to the measured capacitance signal, and we were able to predict the contribution of endocytosis to the measured exocytotic rate under different experimental conditions. In conclusion, using mathematical modeling of published and newly generated data, we have obtained estimates of adiponectin exo- and endocytosis rates, and we have predicted adiponectin secretion. We believe that our model should have multiple applications in the study of metabolic processes and hormonal control thereof.

Keywords: adipocyte; adipokine; adiponectin; electrophysiology; endocytosis; exocytosis; mathematical modeling.

Figure 1.

Biological insights formally tested using mathematical modeling. A, biological insights adapted from Ref. . In brief, adiponectin vesicle exocytosis is triggered by cAMP alone but is augmented by the combined presence of ATP and Ca²⁺. Moreover, Ca²⁺-dependent mechanisms recruit vesicles to a functional pool from where they can be released (vesicles become release competent). B, developed original mathematical model with 11 free parameters. Large arrows represent transitions between the different vesicle states and smaller arrows indicate model inputs. The rate of exocytosis in the model is compared with the experimentally measured rate of capacitance change.

Figure 2.

Vesicle recruitment to the releasable pool must be ATP-dependent. Exocytotic rates (ΔC/Δt) were measured at indicated time points, as described in Ref. . Simulations of the original model are shown as gray lines, and the refined model with ATP dependence is indicated by dashed blue lines. A–D, model simulations and capacitance recordings from Ref. (black circles ± S.E.) in fully differentiated 3T3-L1 adipocytes infused with pipette solutions containing or lacking 0.1 mm cAMP, 3 mm ATP, or 1.5 μm Ca²⁺, as indicated. C and D, absolute intracellular Ca²⁺-free conditions were ascertained by inclusion of 10 mm of the Ca²⁺ chelator BAPTA in the pipette solution. E and F, model simulations of the remaining vesicles in the releasable pool after addition of cAMP, Ca²⁺, and ATP (E) or cAMP and Ca²⁺ without ATP (F). G, structure of the refined model with ATP dependence (dashed blue arrow), including 12 free parameters.

Figure 3.

Contribution of Ca²⁺-dependent endocytosis to the capacitance measurements improves the model. A, structure of the endocytosis model with 15 free parameters. The difference between the rate of exocytosis and endocytosis in the model is compared with the experimentally measured rate of capacitance change. B, ΔC/Δt in cells infused with a solution containing ≥10 μm free Ca²⁺ together with 3 mm ATP and 0.1 mm cAMP. The average exocytotic rate (ΔC/Δt) was quantified at the indicated time points. Results are an average from 11 recordings. C, data from Ref. with a pipette solution lacking cAMP (1.5 μm Ca²⁺ and 3 mm ATP included). The average ΔC/Δt was quantified at the designated time points. D–G, data from Ref. ; see Fig. 2, A–D, for details.

Figure 4.

Exocytosis induced by extracellular forskolin together with IBMX resembles that stimulated by intracellular cAMP. Representative trace displaying the effect of 10 μm forskolin together with 200 μm IBMX (FSK/IBMX; added as indicated by the arrow) on 3T3-L1 adipocyte membrane capacitance as well as histogram showing the average exocytotic rate (ΔC/Δt). The trace is representative of eight individual experiments.

Figure 5.

Developed model can predict adiponectin release levels at different time points. A, time-resolved predictions with uncertainties from simulations of the final model structure and the found acceptable parameters. In the simulated predictions, levels of cAMP, ATP, and Ca²⁺ were varied to reflect the experimentally added FSK/IBMX (left), FSK/IBMX in cells pre-treated with BAPTA (middle), and a combination of FSK/IBMX and ionomycin (Iono) (right). B, summary of the predicted adiponectin release intervals at time point 30 min in A. C, experimental data from Ref. showing adiponectin release under the same conditions as simulated in B. D, time-resolved predicted adiponectin release after FSK/IBMX addition. E, experimental adiponectin release at the indicated time points (cf. simulations in D). Included concentrations were: 10 μm forskolin, 200 μm IBMX, and 1 μm ionomycin. Ca²⁺-chelated cells were pre-treated with 50 μm BAPTA during 30 min. *, p < 0.05; **, p < 0.01; ***, p < 0.001.

Figure 6.

Ca²⁺-dependent endocytosis contributes to the capacitance measurements. A, illustrative figure and equation showing how intervals of the endocytosis contribution to the measured capacitance signal were calculated. B, calculated endocytosis contribution under indicated different intracellular conditions (cAMP and ATP present at 100 μm and 3 mm, respectively).

Figure 7.

Final model including endocytosis and back-translation to interaction graph. The developed model with ATP/endocytosis included and back-translation to an interaction graph, including the cell physiological insights from this work. In agreement with the original model (Fig. 1A), adiponectin exocytosis is triggered by cAMP alone and augmented by the combination of ATP and Ca²⁺. As revealed by this study, ATP is also required in combination with Ca²⁺ in order for adiponectin-containing vesicles to attain release competence (in our model, to be transferred from the reserve pool to the releasable pool). In addition to stimulating exocytosis, Ca²⁺ also induces membrane retrieval (endocytosis). The Ca²⁺-triggered endocytosis needs to be preceded by cAMP-triggered exocytosis (cf. Fig. 3C). The contribution of Ca²⁺-dependent endocytosis to the measured signal is substantial at unphysiologically high intracellular Ca²⁺ concentrations (see text for more details).

Figure 8.

CARS and MPEF microscopy. Fully differentiated 3T3-L1 adipocytes imaged using CARS and MPEF. CARS signal is in red, and CellTracker^TM Red is shown in blue.