Fig 1.
Schematic diagram of Ca2+ dynamics described by the model.
The ER releases Ca2+ to the cytosol and MAM; the fluxes are denoted as JIPR and JnIPR, respectively. The cytosolic Ca2+ is pumped back into the ER lumen via SERCA (JSERCA), and the Ca2+ in MAM are also pumped back into the ER (JnSERCA). Mitochondria uptake Ca2+ from the cytosol (JMCU) and MAM (JnMCU), and mitochondrial Ca2+ is exchanged with Na+ in the cytosol (JNCX) and MAM (JnNCX). Ca2+ can freely diffuse between the cytosol and MAM (Jdiff). The total Ca2+ concentration is regulated by the plasma membrane influx (Jin) and efflux (Jpm).
Table 1.
Parameter values of the model.
The parameters with ★ in the reference column are chosen to reproduce some of experimental data reported by Arruda et al. [9]. The parameters with † in the reference column are modified from the original values proposed by Wacquier et al. [22]. The original values are shown at the bottom of the table.
Fig 2.
Effects of increased MAMs on amplitude of mitochondrial Ca2+ activities.
The model was simulated with a pulse of IP3, Eq 55 with M = 10, t0 = 60, and Δ = 0.2, shown by the inset graph. The blue solid trajectory was simulated with (RS1, RS2) = (0.15, 0.15), while the red dashed spike was generated with the increased MAM surface ratios, (RS1, RS2) = (0.48, 0.48). The black solid curve represents experimentally traced mitochondrial Ca2+ dynamics in control Hepa 1-6 cells, while the black dashed line describes that in the cells expressed with synthetic linkers. The green dashed line indicates the onset of the pulse in the model, and the time at which the cells were treated with 100 μM of ATP in the experiment. The experimental traces were obtained from Arruda et al. [9].
Fig 3.
Evolution of mitochondrial variables.
The model was simulated with two different styles of IP3 dynamics, shown by the inset graph of (A). The resulting behaviors of Ccyt are shown by the blue curves. The black curves show (A) Vm, (B) N, (C) ATPc, and (D) ATPm timeseries concurrent with the Ccyt timeseries.
Fig 4.
Ca2+ oscillations generated from the model exhibit varying orders of magnitude in different compartments.
(A) The model was given continuous stimulation of IP3 with Ps = 0.3 μM. From the top, the panels show Ca2+ oscillations in the ER, the MAM, and the bulk cytosol. (B and C) The magnitudes of IPR Ca2+ fluxes from the ER to the bulk cytosol and the MAM, respectively, during the oscillations shown in (A).
Fig 5.
MAM Ca2+ oscillations generated with varying VnSERCA.
The oscillations were generated with (A) VnSERCA = 12 μM s−1, (B) VnSERCA = 10 μM s−1, and (C) VnSERCA = 8 μM s−1. (D) Zoomed in at the basal level of MAM Ca2+ concentration after a spike, with different values of VnSERCA. The black dashed line indicates the cytosolic Ca2+ concentration right after a spike. For all three simulations, the model was given continuous stimulation of IP3 with Ps = 0.3 μM.
Fig 6.
The first few MAM Ca2+ spikes generated with varying HIPR and the initial condition of hn42.
(A) The oscillations were simulated with HIPR = 0.05 (blue), 0.1 (red), and 0.15 (black). (B) The oscillations were simulated with manually tuned hn42(0) = 2 (blue) and 0 (black). The red trajectory is the control, simulated with the steady state initial condition, hn42(0) = 0.99. (C) and (D) show the corresponding timeseries of hn42 and the fraction of MAM IPRs in the drive mode (Dn), respectively, concurrently simulated with the trajectories shown in (B).
Table 2.
Modified parameters for the obesity model simulations.
Fig 7.
Effects of cellular changes associated with obesity on amplitudes of cytosolic and mitochondrial Ca2+ transients.
The control model and the obesity model was given a pulse of IP3, Eq 55 with M = 10, t0 = 100, and Δ = 0.2, shown by the inset graph in (A). The cytosolic Ca2+ trajectories are shown in (A), while mitochondrial Ca2+ are shown in (B). The blue solid curves are the solutions from the control model, and the red dashed ones are from the obesity model. The green dashed vertical lines indicate the pulsing time. The bottom panels show the quantification of (C) cytosolic and (D) mitochondrial Ca2+ FRET ratio peaks in wild type and ob/ob hepatocytes. The experimental data were obtained from Arruda et al. [9]. * Student’s t-test p-value < 0.05.
Table 3.
Sensitivity of Ccyt and Cmito peaks to a small change in each parameter.
Fig 8.
Effects of the cellular changes associated obesity on Ca2+ oscillations.
Oscillations of (A) cytosolic and (B) mitochondrial Ca2+ concentrations generated from the model with different parameter sets. The blue oscillations were generated from the model with the control parameters. The red dashed oscillations were generated with the modified parameters as in Table 2. The model was given continuous stimulation of IP3 with Ps = 0.3 μM.
Fig 9.
Effects of increased MAMs on Ca2+ oscillations.
Oscillations of (A) cytosolic and (B) mitochondrial Ca2+ concentrations generated from the control model, in blue, and the model with the increased RS’s, in red dashed. The model was given continuous stimulation of IP3 with Ps = 0.3 μM.
Fig 10.
Effects of increased IPR activity on Ca2+ oscillations.
Oscillations of (A) cytosolic and (B) mitochondrial Ca2+ concentrations generated from the control model, in blue, and the model with the increased kIPR and knIPR, in red dashed. The model was given continuous stimulation of IP3 with Ps = 0.3 μM.
Fig 11.
Effects of increased MCU activity on Ca2+ oscillations.
Oscillations of (A) cytosolic, (B) mitochondrial Ca2+ concentrations generated from the control model, in blue, and with the increased VMCU, in red dashed. The corresponding Ca2+ fluxes from the cytosol to mitochondria are shown in (C). The model was given continuous stimulation of IP3 with Ps = 0.3 μM.
Fig 12.
Effects of decreased net SERCA flux on the steady state Ca2+ concentrations and Ca2+ oscillations.
Ca2+ concentrations in (A) the cytosol and (B) the ER at the steady state, Ps = 0 μM, simulated from the control model (in blue) and the model with increased (in red). Oscillations of (C) cytosolic, (D) mitochondrial Ca2+ concentrations generated from the control model, in blue, and with the increased
, in red dashed. The model was given continuous stimulation of IP3 with Ps = 0.3 μM.
Fig 13.
Robustness of Ca2+ oscillations under different model conditions.
We perturbed (A) the control model and (B) the obesity model with gradually increasing stimulation. Initially, Ps was at 0 μM, then was increased to 0.3 μM, 0.6 μM, 0.9 μM, and then to 1.2 μM at t = 500 s, 1500 s, 2500 s, and 3500 s, respectively. The cytosolic Ca2+ concentrations are shown in blue, with the scale on the left y-axis. The green timeseries represent the IP3 concentration, with the scale on the right y-axis.