Fig 1.
Biochemical reactions are denoted by arrows and are labeled with a reaction number (r1, r2, etc.). Reversible reactions are indicated by double-sided arrows. Orange arrows depict nucleotide-binding reactions, and black arrows depict enzyme-catalyzed synthesis and degradation reactions. Species colored cyan represent unphosphorylated AMPK and species colored red represent phospho-AMPK. To simulate exercise, we changed the rate of the ATPase reaction (r1), which serves as the input to the model. The three modules of the model are distinguished by shading with the bioenergetic module shaded light blue, the AMPK regulatory module medium blue, and the activator module darker blue. The activator module is used to simulate the effects of two activators, ZMP and Compound 991 (C991). When simulating C991, only reactions r22 and r23, which represent reversible binding of C991 to AMPK and phospho-AMPK, are simulated in the activator module. When simulating the effects of ZMP, the module features r22 and r23 as well as r24 and r25, which represents the interconversion of 5-aminoimidazole-4-carboxamide ribonucleoside (AICAR), the precursor molecule, to ZMP (r24) and ZMP degradation (r25). Activator-specific parameter values are used for r22 and r23.
Fig 2.
The model was initially calibrated to data collected from a 30-min submaximal-intensity cycling exercise protocol [5]. For all panels, the measured data are presented as means ± standard error, if available, and the hatched vertical lines indicate the exercise initiation and cessation times. A) Time courses of phosphocreatine (PCr) and inorganic phosphate (Pi) concentrations. The filled circles represent measured PCr concentrations. B) Semi-logarithmic plot showing the time courses of AXP concentrations in response to exercise. The open points, light gray points, and dark gray points represent the measured ATP, ADP, and AMP concentrations, respectively. C) Time courses of the total and phospho-AMPK (p-AMPK) levels. D) Time courses of the simulated kinase activities of each AXP-bound phospho-AMPK (AXP-p-AMPK) complex. Filled circles represent the measured mean relative change in total AMPK activity between rest and exercise.
Fig 3.
The model predictions were compared to data collected from continuous cycling exercise performed by sedentary (panels A-D) or trained human participants (panels E-H) [41] and sprint-interval cycling exercise [6] (panels I-L). The hatched vertical lines indicate the times at which exercise was initiated and ceased. Data points and error bars represent the means ± standard error. A, E, I) Time courses of phosphocreatine (PCr) concentration. The filled circles represent the measured concentration. B, F, J) Semi-logarithmic plot showing the time courses of adenine nucleotide concentrations in response to exercise. The open and grey-filled circles represent the measured ATP and AMP concentrations, respectively. C, G, K) Time courses of total and phospho-AMPK (p-AMPK) levels in response to exercise. The open circles represent measured p-AMPK levels. D, H, L) Time courses of the simulated kinase activities for each AXP-p-AMPK complex. The open circles represent the mean relative change in total AMPK activities between rest and exercise.
Fig 4.
Evaluation of model plausibilities from the α2β2γ3 KD MPSA against data-informed constraints.
A) Workflow of the progressive elimination of implausible models. After partitioning out the simulations into ADP-dominant (left boxes, >80% ADP-frac) or ADP non-dominant cases (right boxes, <80% ADP-frac), we then imposed data-informed constraints on the parameter values and ratios. The labels located in between the workflow boxes represent criteria for identifying models as implausible. B-E) The panels from left to right show the progressive elimination of implausible models from the simulations in the α2β2γ3 KD MPSA in which ADP-p-AMPK contributed less than 0.8 of the time integral of AMPK activity. The panels from left to right correspond to the models featured in the blue-shaded boxes from top to bottom in panel A. Points and curves colored green or blue indicate simulations with fractions of ADP control that tend to either ADP- or AMP-dominant control, respectively. The upper panels display the log10 values of the quantities shown in the top label of each plot for the labelled AMPK complexes below each plot. The green and blue points indicate values from models exhibiting ADP- and AMP-dominant control, respectively. The grey lines indicate implausible relative parameter values between ATP-p-AMPK and ADP-p-AMPK, whereas the black-hatched lines indicate implausible relative parameter values between ATP-p-AMPK and AMP-p-AMPK. which were subsequently eliminated. The lower panels represent the corresponding time courses of p-AMPK. The “Median Integral Ratio” and “Minimum Integral Ratio” correspond to the median and minimum values for the fractions of ADP control for the ensemble of models. B) First pass, simulations in which the Vmax/KM values of the kinase for ADP-AMPK and AMP-AMPK were lower than ATP-AMPK. C) Second pass, simulations in which the Vmax values of the kinase for ADP-AMPK and AMP-AMPK were lower than those for ATP-AMPK. D) Third pass, simulations in which the Vmax/KM of the phosphatase for ADP-p-AMPK and AMP-p-AMPK were higher than ATP-p-AMPK. E) Fourth pass, removing simulations in which the Vmax of the phosphatase for ADP-p-AMPK and AMP-p-AMPK were higher than ATP-p-AMPK.
Fig 5.
AMPK pharmacological activator analysis.
Time courses and dose response of simulated AICAR perfusion, simulated Compound 991 incubation, and moderate intensity exercise (63% ). A) Time courses of concentrations of activators. To simulate perfusion of AICAR, we assumed that its concentration remained unchanged throughout the simulation. The concentration of ZMP was fitted to published data. B) Time courses of phospho-AMPK (p-AMPK) concentrations for each simulation. C) Total AMPK activities for each simulation. The “×” and the “+” markers denote measured AMPK activities in response to Compound 991 and ZMP, respectively. D) Dose response of AMPK activities in response to treatment with Compound 991, ZMP, ADP, and AMP. The model was simulated independent of the bioenergetic module by removing reactions 1–5 and setting the AXP = 0 except if added exogenously, in which case its total concentration was held constant by setting generation and degradation reaction rates to zero. The reactions were simulated for 240 minutes and the steady-state values plotted. The filled portions under each curve indicate the ranges of activator concentrations that are either measured (AMP, ADP) or experimentally applied (ZMP, Compound 991).