Combined in vivo and in silico investigations of activation of glycolysis in contracting skeletal...

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doi: 10.1152/ajpcell.00101.2012304:C180-C193, 2013. First published 31 October 2012;Am J Physiol Cell Physiol

Nicolay, J. J. Prompers, J. A. L. Jeneson and N. A. W. van RielJ. P. J. Schmitz, W. Groenendaal, B. Wessels, R. W. Wiseman, P. A. J. Hilbers, K.of glycolysis in contracting skeletal muscleCombined in vivo and in silico investigations of activation

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Combined in vivo and in silico investigations of activation of glycolysisin contracting skeletal muscle

J. P. J. Schmitz,1,2* W. Groenendaal,1,3* B. Wessels,2 R. W. Wiseman,4,5 P. A. J. Hilbers,1,3 K. Nicolay,2,3

J. J. Prompers,2,3 J. A. L. Jeneson,2,3,6 and N. A. W. van Riel1,3

1Computational Biology, Department of Biomedical Engineering, Eindhoven University of Technology, Eindhoven, TheNetherlands; 2Biomedical NMR, Department of Biomedical Engineering, Eindhoven University of Technology, Eindhoven, TheNetherlands; 3Netherlands Consortium for Systems Biology, Department of Biomedical Engineering, Eindhoven University ofTechnology, Eindhoven, The Netherlands; 4Department of Physiology, Biomedical Imaging Research Center, Michigan StateUniversity, East Lansing, Michigan; 5Department of Radiology, Biomedical Imaging Research Center, Michigan State University,East Lansing, Michigan; and 6Center for Liver, Digestive and Metabolic Disease, Department of Pediatrics, University MedicalCenter Groningen, Groningen, The Netherlands

Submitted 28 March 2012; accepted in final form 26 October 2012

Schmitz JP, Groenendaal W, Wessels B, Wiseman RW,Hilbers PA, Nicolay K, Prompers JJ, Jeneson JA, van Riel NA.Combined in vivo and in silico investigations of activation ofglycolysis in contracting skeletal muscle. Am J Physiol CellPhysiol 304: C180 –C193, 2013. First published October 31, 2012;doi:10.1152/ajpcell.00101.2012.—The hypothesis was tested that thevariation of in vivo glycolytic flux with contraction frequency in skeletalmuscle can be qualitatively and quantitatively explained by calcium-calmodulin activation of phosphofructokinase (PFK-1). Ischemic rattibialis anterior muscle was electrically stimulated at frequenciesbetween 0 and 80 Hz to covary the ATP turnover rate and calciumconcentration in the tissue. Estimates of in vivo glycolytic rates andcellular free energetic states were derived from dynamic changes inintramuscular pH and phosphocreatine content, respectively, deter-mined by phosphorus magnetic resonance spectroscopy (31P-MRS).Computational modeling was applied to relate these empirical obser-vations to understanding of the biochemistry of muscle glycolysis.Hereto, the kinetic model of PFK activity in a previously reportedmathematical model of the glycolytic pathway (Vinnakota KC, RuskJ, Palmer L, Shankland E, Kushmerick MJ. J Physiol 588: 1961–1983,2010) was adapted to contain a calcium-calmodulin binding sensitiv-ity. The two main results were introduction of regulation of PFK-1activity by binding of a calcium-calmodulin complex in combinationwith activation by increased concentrations of AMP and ADP wasessential to qualitatively and quantitatively explain the experimentalobservations. Secondly, the model predicted that shutdown of glyco-lytic ATP production flux in muscle postexercise may lag behinddeactivation of PFK-1 (timescales: 5–10 s vs. 100–200 ms, respec-tively) as a result of accumulation of glycolytic intermediates down-stream of PFK during contractions.

glycolysis; skeletal muscle; calcium regulation; 31P-MRS; computa-tional modeling; systems biology

GLYCOLYSIS PLAYS A CENTRAL role in catabolism and anabolismfor all cell types (20; 44). Identification of regulatory mecha-nisms has been important to many areas of biomedical re-search, ranging from basic understanding of the biochemistryof carbohydrate utilization to applications in biotechnology(48) and drug development for cancer therapies (39). In mam-malian cells, skeletal muscle has been a key experimental

model to study the regulation of glycolysis and glycogenolysis.It can increase the glycogenolytic ATP production flux by twoorders of magnitude during rest to work transitions on atimescale of seconds (56). This exceptionally broad and dy-namic operational range of glyco(genol)ytic flux puts a highduty cycle upon the control mechanism(s) of this pathway.

Several approaches have been used to elucidate the under-lying regulatory mechanisms including physical isolation andin vitro kinetic characterization of individual enzymes fromskeletal muscle providing a wealth of information on theindividual components of this pathway (3). The application ofnoninvasive, nondestructive investigative techniques such as invivo nuclear magnetic resonance spectroscopy (MRS) havesince allowed studying the behavior of the intact pathway inmuscle (8). For example, it has been demonstrated that glyco-lytic flux rapidly shuts down in the absence of muscle contrac-tion (6, 12, 14, 15, 43). More recently, computational modelingapproaches have been used to integrate the accumulatedknowledge base at the molecular level including quantitativeformulation of hypotheses on regulatory mechanisms with invivo flux measurements to test this knowledge base againstempirical data (3).

The precise biochemical mechanisms underlying the rapidshutdown of glycolysis in muscle upon termination of mus-cle contraction have remained poorly understood (3, 47).We have previously shown that reproducing this particularpathway characteristic solely on the basis of known in vitroenzymes kinetics is not possible (47). Specifically, silencingof glycolysis in noncontracting muscle requires rapid deac-tivation of the key crossover enzymes phosphofructokinase(PFK-1) and pyruvate kinase (PYK) in the pathway (47).The regulation at the level of PFK-1 was predicted to havea dominant role in glycolytic flux control, while in contrastthe regulation of PYK was found to be more relevant toglycolytic metabolite concentration control particularly withrespect to intermediate metabolites downstream of PFK-1. Amechanism that may explain the wanting additional regula-tion at the level of PFK-1 is calcium-calmodulin-mediatedactivation of this enzyme by binding of PFK-1 to, e.g.,cytoskeleton and the contractile proteins (34, 36, 37).Whether or not this mechanism is qualitatively and quanti-tatively sufficient to reconcile the observed characteristicsin vivo remains to be tested.

* J. P. J. Schmitz and W. Groenendaal contributed equally to this work.Address for reprint requests and other correspondence: J. P. J. Schmitz, P.O.

Box 513, 5600 MB, Eindhoven, The Netherlands (e-mail: J.P.J.Schmitz@tue.nl.).

Am J Physiol Cell Physiol 304: C180–C193, 2013.First published October 31, 2012; doi:10.1152/ajpcell.00101.2012.

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Here, this question was further investigated. Testing of thePFK-1 calcium activation hypothesis is, however, not straight-forward for practical reasons. On the one hand, the 1) com-plexity of muscle cell structure (e.g., cytoskeletonal localiza-tion), and 2) ancillary processes (e.g., fast calcium release anduptake and calcium-calmodulin signaling) are difficult to in-clude in an in vitro experimental system. On the other hand, invivo experiments likewise suffer from practical limitations.These include the fact that 1) the pathway can only be studiedas an integrated system, 2) few biochemical indicators areavailable to evaluate glycolytic output (for example interme-diate metabolite concentrations are often unknown), 3) there isonly limited control of individual variables [metabolite levelsoften covary with changes in flux (12, 14)], and 4) pathwayflux may change with negligible variations in steady statemetabolite concentrations.

To overcome these limitations, the present investigation ofcalcium regulation of PFK-1 activity in skeletal muscle viaPFK-1-calmodulin interaction has employed an integrativeapproach of combining in vivo measurements of pathwaybehavior and the extensive database of known enzyme kineticsembedded in a computational model. The in vivo readoutswere acquired in the rat using 31P-MRS of the ischemic tibialisanterior (TA) evoking contractions at different duty cycles,thereby inducing varying conditions of myocellular calciumconcentration and glycolytic flux. The objective of the model-ing studies was to reproduce both metabolite and pH dynamicsfor these different electrically induced contraction protocolsand test whether pathway regulation proposed within the com-putational model was consistent with the measured physiologicbehavior. It is shown that introduction of regulation of PFK-1activity by binding of a calcium-calmodulin complex in com-bination with classic AMP and ADP activation was quantita-tively necessary and sufficient for model predictions to beconsistent with in vivo behavior.

METHODS

Study Design

The principal aim of this study was to investigate the regulation ofglycolysis in muscle in vivo through the use of an integrated approachof experiments and computational modeling. The experimental workinvolved 31P-MRS of the exercising rat TA muscle. To preventcomplications from oxidative ATP production, all experiments wereperformed under conditions of ischemia. Different metabolic work-loads and levels of calcium were applied by varying the frequency ofmuscle excitation. From these data, measures for the metabolic statusof the muscle (PCr concentration) and the glycolytic rate (deducedfrom pH dynamics) was determined. The aim of the modeling effortwas to test if addition of calcium-calmodulin activation of PFK-1allowed the model to reproduce both metabolic state of the muscle(PCr concentration) and glycolytic rate (pH dynamics). The recordeddynamics of the sugar phosphates were used as input signal of themodel (for detailed description see Pathway supply flux). Thereforethe model for glycogenolysis does not contain a kinetic description ofglycogen phosphorylase (GP). The dynamics of GP activity, includingthe activation of GP by calcium (7), were included in the experimen-tally determined input flux.

Experimental Methods

Animals. Adult male Wistar rats (385 � 22 g, 15-wk-old, n � 28;Charles River Laboratories) were housed in groups at 20°C and 50%humidity on a 12-h light-dark cycle with ad libitum access to water

and chow. The principles of laboratory animal care were followed,and all experimental procedures were approved by the Animal EthicsCommittee of Maastricht University (Maastricht, The Netherlands).During preparatory surgical procedures and MRS experiments, ani-mals were anesthetized using 0.8–1.2% isoflurane (Forene; Abbot,Wiesbaden, Germany) administered via a face mask with medical airand oxygen (0.2 and 0.1 l/min, respectively). Temgesic was used asanalgesic [0.3 mg/ml Temgesic in saline solution (1:10), 0.10 mg/kg;Schering-Plough]. Body temperature was maintained at 37 � 1°Cusing heat pads and monitored by a custom-built monitoring system.In the MR scanner, respiration was monitored using a pressure sensorregistering thorax movement (Rapid Biomedical, Rimpar, Germany).Ischemia was applied by means of a silicone vessel loop (Identi LoopsSupermaxi Blue; Dispo Medical), which was applied around the thighto restrict blood flow in the leg.

Contractions were induced by using electrical stimuli applied viaacute, subcutaneously implanted platinum electrodes positioned alongthe distal nerve trajectory of the n. peroneus communis. Excitation ofthis nerve induced contraction in the TA, extensor digitorum longus(EDL), peroneus longus, and brevis in the anterior compartment of therat hindlimb (16, 17). Stimulation voltage ranged between 6 and 7 V,and pulse length was 1 ms. Contractile duty cycles were varied overa range of frequencies (5, 10, 40, and 80 Hz) and pulse train lengthssummarized in Table 1. For each group, four to five successfulmeasurements were obtained in different animals. All experimentswere conducted under ischemic conditions. Successful occlusion ofoxygen supply to the muscle was verified by the absence of any PCrand pH recovery in the 10 min after exercise.

31P-NMR acquisition parameters. All MRS measurements wereperformed on a 6.3-T horizontal Bruker magnetic resonance spec-trometer (Bruker, Ettlingen, Germany). 31P-MRS was performed byusing a two-coil configuration. A circular 1H surface coil (40 mm) wasused to adjust the magnetic field homogeneity using the availableproton signal from water, while a smaller elliptical surface coil (10/18mm) was positioned over the TA to acquire phosphorus data. 31P-spectra were acquired applying an adiabatic excitation pulse with aflip angle of 90°. A fully relaxed spectrum (TR � 20 s, 32 averages)was measured at rest. A time series of spectra (TR � 5 s, 2 averages)before, during, and after electrical stimulation of ischemic TA. A timeseries consisted of a 2-min rest, 8-min stimulation, and 10 min afterstimulation. An exception was the experiment without stimulation(group 1, Table 1), which had a duration of 120 min.

Coil sensitivity profile. The sensitivity profile of the 31P coil wascalculated from a two-dimensional (2D) chemical shift imaging (CSI)data set recorded in rest conditions with blood supply intact. 2D CSIacquisition parameters were as follows: field of view, 25 � 25 mm2;matrix size, 16 � 16 (reconstruction 32 � 32); TR � 5,000 ms;hamming weighted acquisition and postprocessing with 1,800 scans intotal, and adiabatic excitation pulse with a flip angle of 90° (identicalto the time series experiments). The intensity of the PCr peak wascalculated for each voxel. The intensity of the PCr peak was integrated

Table 1. Summary experimental groups

GroupStimulation

Frequency, Hz

Pulse TrainLength, no.of pulses

Pulse TrainLength, s

Duration of theExperiment,

Group 1 (rest) No stimulation 120 minGroup 2 1 5 5 20 min*Group 3 5 10 2 20 min*Group 4 10 10 1 20 min*Group 5 40 10 0.25 20 min*Group 6 40 20 0.5 20 min*Group 7 80 10 0.125 20 min*

*Protocol consisted out of 2-min rest, 8-min electrical stimulation, and10-min rest.

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over the voxels of the muscle in which contractions were induced(TA, EDL, and peroneus longus � brevis), and the voxels in which nocontractions were induced. These calculations indicated that 75% ofthe signal detected by the surface coil, originated from contractingmuscle. The residual signal (25%) was received from the noncontract-ing muscle.

Data processing. 31P-MR spectra were fitted in the time domain byusing nonlinear least squares algorithm in the jMRUI software pack-age (53). The PCr peak was fitted to a Lorentzian line shape. Theinorganic phosphate (Pi) and phosphor-monoester (PME) peaks and�- and �-ATP peaks were fitted to Gaussian line shapes. The �- and�-ATP peaks were fitted with equal peak areas. The �-ATP was notquantified because of concerns for the limited bandwidth of theexcitation pulse. Absolute concentrations were calculated after cor-rection for partial saturation with the assumption that the ATP con-centration is 8.2 mM at rest (50, 54). Intracellular pH was calculatedfrom the chemical shift difference between the Pi and PCr resonances(�; measured in part per million), according to Eq. 1 (51).

pH � 6.75 � log�� 3.27

5.63 � �� (1)

The 31P-coil received signal from both contracting muscle (75%) andnoncontracting muscle (25%; see Coil sensitivity profile). The metabolitedynamics in the contracting muscle were derived from the measureddynamics according to the following calculations. The signal received bythe 31P-MRS coil is described by Eq. 2.

Xobserved(t) � Xcontraction(t) * Fcontraction

� Xnoncontracting(t) * Fnoncontracting

where, Xobserved, Xcontraction, Xnoncontracting, Fcontraction, and Fnoncontracting

denote the measured metabolite concentration, the metabolite concen-tration in contracting muscle, metabolite concentration in the noncon-tracting muscle, the fraction of the signal originating from contractingmuscle and the fraction of the signal originating from noncontractingmuscle, respectively. Fcontraction and Fnoncontracting were set accordingto the values determined from the 2D-CSI data set: 0.75 and 0.25,respectively. Xnoncontracting(t) was determined from the ischemia ex-periment without electrical muscle stimulation. According to this dataset ATPnoncontraction(t) could be assumed constant during the first 30 min at8.2 mM. PCrnoncontracting(t), Pinoncontracting(t), and PMEnoncontracting(t)during the first 30 min are well described by the equations:PCrnoncontracting(t) � PCrrest ATPaserest·t, Pinoncontracting(t) �Pirest � ATPaserest·t and PMEnoncontracting(t) � .092 � 0.000564·t,with PCrrest, Pirest, and ATPaserest set to 33.5 mM, 6.2 mM, and0.01 mM/s, respectively. By addition of this information to Eq. 2,the equations for calculation of metabolite dynamics in the con-tracting muscle compartment become:

PCrcontracting(t) �PCrobserved(t) � (33.5 � 0.01 · t) · 0.25

Picontracting(t) �Piobserved(t) � (6.2 � 0.01 · t) · 0.25

ATPcontracting(t) �ATPobserved(t) � 8.2 · 0.25

PMEcontracting(t) �PMEobserved(t) � (0.92 � 0.000564 · t) · 0.25

Selection of data included in computational analysis. The ATPhydrolysis rate was modeled by mass action kinetics (Eq. 4). Becausethe ATP concentration is well buffered by creatine kinase at valuesclose to 8.2 mM, effectively the ATP hydrolysis rate is assumedconstant during exercise. The experimental data included in thenumerical analyses were therefore limited to the part of the data set for

which it was verified that this assumption was not violated by theonset of fatigue. The ATP hydrolysis flux during the experiment wascalculated as the sum of the PCr breakdown rate and the glycolyticATP production. Estimation of glycolytic ATP production rate wasperformed by application of a phenomenological model described byConley et al. (9). From these calculations, it followed that theassumption of constant ATP hydrolysis rate was not violated forconditions of pH 6.5. Therefore, model simulations were run untilpH dropped below 6.5.

Computational Methods

Modeling glycolysis in skeletal muscle. A previously developeddetailed kinetic model of glycolysis in muscle was used as a basis ofthe computational analyses (55). A schematic overview of the modelis shown in Fig. 1. The model includes flux descriptions of theglycolytic enzymes: GP, phosphoglucomutase (PGLM), phospho-

Fig. 1. Schematic overview of the computational model. PGLM, phosphoglu-comutase; PGI, phosphoglucoisomerase; PFK-1, phosphofructokinase; ALD,aldolase; TPI, triose phosphate isomerase; GAPDH, glyceraldehydes-3-phos-phate dehydrogeanse; G3PDH, glycerol-3-phosphate dehydrogenase; PGK,phosphoglycerate kinase; PGM, phosphoglyceromutase; EN, enolase; PYK,pyruvate kinase; LDH, lactate dehydrogenase; CK, creatine kinase; AK,adenylate kinase; ATPase, ATP hydrolysis; G1P, glucose-1-phosphate; G6P,glucose-6-phosphate; F6P, fructose-6-phosphate; F1,6P2, fructose-1,6-bi-phophate; DHAP, dihydroxyacetone-phosphate; G3P, glycerol-3-phosphate;GAP, glyceraldehydes-3-phosphate; 13BPG, 1,3-biphosphoglycerate; 3PG,3-phosphoglycerate; 2PG, 2-phosphoglycerate; PEP, phosphoenolpyruvate;PYR, pyruvate; LAC, lactate; PCr, phosphocreatine; Cr, creatine; ADP, aden-osine-diphospate; ATP, adenosine-triphosphate; Ca2CaM, calcium-calmodulincomplex; AMP, adenosine-monophosphate; Pi, inorganic phosphate; HX,protons bound to cellular proton buffer.

C182 REGULATION OF GLYCOLYSIS IN MUSCLE

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gluco-isomerase (PGI), phosphofructokinase (PFK-1), aldolase andtriose phosphate isomerase (ALD and TPI), glycerol-3-phosphatedehydrogenase (G3PDH), glyceraldehyde-3-phosphate dehydroge-nase (GAPDH), phosphoglycerate kinase (PGK), phosphoglyceromu-tase and enolase (PGM and EN), pyruvate kinase (PYK), and lactatedehydrogenase (LDH). In addition, the model contained detailedreaction kinetics of cellular ATP buffering processes: creatine kinase(CK) and adenylate kinase (AK). ATP hydrolysis was described bymass action kinetics (Eq. 4).

fluxATP_Hydr � kATP_Hydr[ATP] (4)

During actual experimental conditions, large acidifications in cy-tosolic pH were observed (7.2–6.2). The effects of varying protonconcentration on enzyme kinetics, pH dependency of enzyme Vmax

and equilibrium constants were included when known. Furthermore,proton buffering by metabolites and proteins and other cell structureswas modeled by assuming a constant cellular buffer capacity (pro-teins) and dynamical buffer capacity that was calculated from metab-olite concentrations. The stoichiometry of proton production andconsumption was included for all modeled reactions to predict cellularproton accumulation. For further details on flux equations and kineticparameter values we refer to the original work published by Vinnakota etal. (55). Ordinary differential equations (ODEs) were numerically solvedusing ODE15s, Matlab 7.5.0 (The Mathworks, Natick, MA).

Several changes to the Vinnakota model were made: first, thetemperature for the model simulations was set to 35°C. Since theoriginal framework by Vinnakota et al. used Vmax parameters deter-mined at 25°C, all Vmax parameters were updated according to valuesdetermined at 37°C reported by Eagle and Scopes (18). Second, ATPsynthesis flux by oxidative phosphorylation was removed because thecurrent experiments were conducted under ischemic conditions.Third, the model for pathway supply of phosphorylated glucose waschanged, and fourth, the kinetic model description of PFK-1 wassubstituted by a new rate equation. In the following sections, thechanges for the model for pathway supply flux and rate equations ofPFK will be described in detail.

Pathway supply flux. The original model described by Vinnakota etal. (55) included GP to account for the pathway supply flux. However,model simulations revealed that the dynamic range of the GP modelwas insufficient to predict a realistic flux through this pathway (datanot shown). This model behavior was probably due to lack ofallosteric interactions of glucose-6-phosphate (G6P) in the flux de-scriptions and enzyme phosphorylation dynamics. At the moment, nobetter validated, detailed model of GP is available. Therefore, it waschosen to deduce pathway influx from our own experimental data. Forconditions of constant ATP, it was assumed that the PME resonancerepresented the summed concentration of glucose-1-phosphate (G1P),G6P, and fructose-6-phosphate (F6P), which is in accordance withreports from other investigators (15, 56). The PME dynamics werewell described by a linear function (data not shown). The derivative ofthis linear function was used to model the G1P input flux. Thecoefficients of the linear relation are provided in Table 2. It wasassumed that all pathway influx was due to glycogen breakdown. Thecontribution of hexokinase was assumed negligible due to the com-

plete occlusion of muscle blood flow blocking glucose supply to themuscles.

Calcium-calmodulin mediated activation of PFK-1. The PFK-1model was substituted by the pseudorandom order, statistical inhibi-tion model originally developed by Waser et al. (57) and adapted byConnett (10). In this section, the adaptations of this model aredescribed. For the full set of equations governing this model, thereader is referred to in the APPENDIX. Connett reported this model to besuperior in terms of reproducing in vitro enzyme kinetics comparedwith the PFK-1 description used by Vinnakota et al. (55). It does notinclude regulation by citrate or fructose-2,6 biphosphate, both ofwhich are strong allosteric modulators of PFK in vitro (38). Therationale for not including them in the kinetic model was that formammals the dynamic range of these modulators in skeletal muscle issmall, and therefore their contribution to the control of the enzyme invivo is very limited (31, 41).

The model proposed by Connett featured an ADP- and AMP-dependent term to account for competitive binding of ADP and AMPto the ATP inhibition site. This term will hereafter be referred to as the“deinhibition” term. The definition of this term is:

deinhibition � 1 �AMP

KAMP�

KADP(5)

where KAMP and KADP are the AMP and ADP competitive bindingconstants, respectively, and AMP and ADP the AMP and ADPconcentrations. Effectively, an increase of the deinhibition term as aresult of elevated AMP and ADP levels relieves part of the ATPinhibition thereby activating PFK-1 flux. At physiological concentra-tions (�8 mM), ATP inhibition results in a nearly full deactivation ofthe enzyme (95%; Ref. 36). Therefore, reversing this inhibition willresult in a significant increase of the enzymes catalytic activity.

In the present investigation, three different configurations of thePFK-1 model were evaluated (Fig. 2). The first configuration (modelconfiguration i) represents conditions in which no calcium-calmodulinmediated activation of PFK-1 is present (Fig. 2A). This model in-cludes the PFK-1 flux equation proposed by Connett (10). Theparameter values of KAMP and KADP were estimated from the PCr andpH time course data as described in Parameter estimation.

The second configuration (configuration ii) included calcium-calm-odulin activation of PFK-1 (Fig. 2B). Two forms of PFK-1 weredefined: an inactive (PFKinactive) and an active (PFKactive) form (36,37). The inactive PFK-1 was described by the model proposed byConnett (10). Upon binding of two calcium-calmodulin complexes theenzymes switches from the inactive to the active isoform (36).Activation of the enzyme was suggested to occur via reversing theinhibitory effect of ATP (36). To account for this regulatory effect thedeinhibition term of the active PFK-1 enzyme was modified to aconstant (kdeinhib_Act; Eq. 6):

deinhibitionactivePFK � kdeinhib_Act (6)

The value of kdeinhib_Act was estimated from the PCr and pH timecourse data as described in Parameter estimation. Effectively, thevalue of the deinhibition term of the active PFK enzyme was largercompared with the inactive PFK-1 enzyme. Consequently, switchingfrom inactive to active form stimulates overall PFK-1 flux. Thefractions of PFK-1 in active and inactive form were described bydifferential Eqs. 7 and 8. Switching of the enzyme from inactive toactive form was stimulated by elevated cellular calcium-calmodulinconcentrations, which is in accordance with observations by (7, 34,36, 37). The values of kon and koff were estimated from the PCr and pHtime course data as described in Parameter estimation.

dPFKactive

dt� konCa2CaM2 · (1 � PFKactive) � kof fPFKactive (7)

PFKinactive � 1 � PFKactive (8)

Table 2. Linear fit to observed PME dynamics

Group [PME] t � 0, mM Slope, mM/s

Group 1 (rest) 0.9 0.00056Group 2 (1 Hz) 1.5 0.010Group 3 (5 Hz) 1.5 0.022Group 4 (10 Hz) 1.5 0.023Group 5 (40 Hz) 1.5 0.019Group 6 (40 Hz) 1.5 0.019Group 7 (80 Hz) 1.5 0.015

[PME], phosphor-monoester concentration.

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The deinhibition term of configuration ii (Eq. 6) was independentfrom cellular ADP and AMP levels. There are, however, indicationsthat the flux through the activated PFK-1 enzyme is dependent on bothcellular calcium levels and ADP and AMP levels (12). This particularregulatory scheme was represented by model configuration iii. To thisend, the deinhibition term of the activated enzyme was modeled as afunction of ADP and AMP concentrations, albeit with differentcompetitive binding constants (KAMP

act and KADPact ; Eq. 9).

deinhibitionactivePFK � 1 �AMP

KAMPact �

KADPact (9)

The values of KAMPact and KADP

act were estimated from the PCr and pHtime course data as described in Parameter estimation. Comparedwith the inactive enzyme, the values of the competitive bindingconstants KAMP

act and KADPact were lower. Consequently, the flux through

the active PFK-1 enzyme is already increased at low AMP and ADPconcentrations (compared to the inactive enzyme). The calcium-calmodulin fraction of PFK-1 in active and inactive form was mod-eled identical to model configuration ii: i.e., according to differentialEqs. 7 and 8.

For the full set of equations governing the PFK-1 model, the readeris referred to the APPENDIX.

Calcium-calmodulin dynamics in muscle. The differential equa-tions of PFK-1 (de)activation are modeled as a function of Ca2CaM(Eqs. 7 and 8). As a consequence, the PFK-1 (de)activation kineticsare determined by the particular reaction kinetics of calcium-calmo-dulin binding and unbinding, respectively. The latter were derivedfrom a previously developed temperature dependent spatiotemporalmodel of skeletal muscle calcium handling (4, 26). The calciumhandling model was extended by calcium-calmodulin reaction kinet-ics based on mass action kinetics. The values for the koff and Kd wereset to 100 s1 and 3.8 �M, and 5,000 s1 and 28.9 �M for theformation of Ca2CaM and Ca4CaM, respectively (2, 21, 29, 46). Thespatially averaged calcium-calmodulin signal (Ca2CaM) was calcu-lated for 35°C and used as an input of the glycolysis model.

Parameter estimation. The model contained several parametersfor which an accurate value was either not available from anyliterature or were previously estimated in a computational studyand likewise had no solid experimental basis (Table 3). Theseparameters were (re-)estimated from the newly recorded PCr and pHtime-course data using a non linear least squares optimization algo-rithm (lsqnonlin, Matlab 7.5.0; The Mathworks, Natick, MA). Thephysiological meaning of each of the parameters included in theparameter estimation procedure is listed in Table 3. The algorithmadjusted parameter values during a series of model evaluations withthe aim of minimizing the error (SSE) between model predictions andPCr and pH time-course data defined by Eq. 10. Because PCr and pHdata are expressed in different units, a weighting parameter is requiredto balance the contribution of PCr and pH time-course data to the SSE.

Instead of applying arbitrary defined weighting parameters, the accu-racy of the measurement data (quantified by the SD of each data point)was used as weighting value. The confidence interval of the estimatedparameter values was determined using Matlab routine nlparci, whichexploited the Fisher information matrix to estimate the confidenceintervals for each parameter.

The entire data set was divided into two groups: i.e., 1) data forparameterization, and 2) data for verification. The parameterizationdata [at 0, 5, 10, 40 (1 pulse train per 5 s, 10 pulses per pulse train),and 80 Hz] was used to estimate model parameter values. Theseparameters, initial conditions and the optimal values are given inTable 3. As indicated in Table 3, the initial parameter values werecalculated from the MRS data or taken from other studies. An initialguess for the values of the PFK-1, calcium-calmodulin binding con-stant, i.e., kon and koff was however, not available. Therefore, theinitial values for these parameters were randomly taken from uniformdistributions with ranges as indicated in Table 3 using a multistartoptimization approach (500 runs).

Model predictions were next tested against independent data (i.e,data not used in the parameter estimation procedure): 5 pulses per 5 s(1 Hz) and 1 pulse train per 5 s, 20 pulses per pulse train (40 Hz). Forthese simulations all parameters were left unchanged, except for theATP hydrolysis rate constant kATP_Hydr. The resulting estimatedvalues of these rate constants are provided in Table 3.

Quantification of model fit. The goodness of fit of the differentmodel configurations to the experimental data was quantified by thesum of squared errors (SSE). The SSE was summed over all data usedfor parameter estimation. Data points were weighted by the SD of theexperimental data (n � 4–5; Eq. 10).

SSE � �j�1

�i�1

N �mean�PCrobserved(i)� � PCrpredicted(i)

SD�PCrobservd(i)� �2

� �i�1

N �mean�pHobserved(i)� � pHpredicted(i)

SD�pHobservd(i)� �2(10)

In this equation PCrobserved(i) represents the mean PCr concentra-tion ([PCr]; across-animal) at time point i; PCrpredicted(i) representsthe predicted [PCr] at time point i; pHobserved(i) represents the meanpH (across-animal) at time point i; pHpredicted(i) represents the pre-dicted pH at time point i; SD[PCrobserved(i)] represents the across-animal SD of the [PCr] at time point i; SD[pHobserved(i)] representsthe across-animal SD of the pH at time point i; j denotes a specificexperimental groups (e.g., 0, 5, 10, 40, and 80 Hz).

Akaike information criterion. The Akaike information criterion(AIC; Ref. 1) was calculated for each model configuration toinvestigate if any improvement in SSE was merely the results ofadditional degrees of freedom of the model. AIC was calculatedaccording to Eq. 11:

Fig. 2. Schematic representation of the regulation of PFK-1 as modeled in each model configuration. Model configuration i (A) represented the hypothesis inwhich no regulation of PFK-1 by calcium-calmodulin signaling is present. Model configuration ii (B) represented the hypothesis in which binding ofcalcium-calmodulin complexes to PFK-1 partly reliefs ATP inhibition of the enzyme independent of the levels of ADP and AMP. Model configuration iii (C)represented the hypothesis in which binding of calcium-calmodulin complexes partly reliefs ATP inhibition by enhancing the competititve binding of AMP andADP to the inhibitory ATP site.

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AIC � n * ln(SSE ⁄ n) � 2 * K (11)

In this equation, n denotes the number of datapoints (422) and Krepresents the number of estimated parameters (9, 12, and 13, forconfigurations i, ii, and iii, respectively). The AIC provides a means toselect the preferred model (lowest AIC) taking into account the reductionof SSE while penalizing the additional degrees of freedom (K).

RESULTS

31P-MRS: Characterization of Pathway Dynamics

The dynamics of cellular metabolites: ATP, PCr, Pi, andPME as well as intracellular pH were monitored by 31P-MRSin ischemic rat TA muscle, under varying muscle stimulationfrequencies (0–80 Hz). Figure 3A shows a stack plot of thespectra recorded during the 10-Hz stimulation protocol. Thesespectra were obtained by averaging 12 free-induction decaysand processed with 5-Hz line broadening. In response tomuscle contraction and corresponding elevated cellular ATPdemand flux, the cellular ATP buffer PCr is consumed tobalance energy demand and supply. PCr depletion coincideswith the production of Pi, a product of ATP hydrolysis. Inaddition, during stimulation an increasing PME resonance wasobserved which was in the absence of any ATP depletion,attributed to the accumulation of sugar-phosphates (G1P, G6P,and F6P; Refs. 15, 56). Figure 3, B and C, shows an example(10 Hz) of the PCr and pH dynamics used for model testing(data expressed as mean � SE). The part of the data used formodel testing is indicated in Fig. 3. Any PCr and/or pHrecovery was not observed during the period after stimulation.This observation validated the successful occlusion of bloodcirculation and obstruction of O2 delivery to the muscle cells.

Model Simulations vs. Experimental Data

Model simulations according to the three different model con-figurations were compared with the experimental data (Fig. 4).Figure 4, A–E, shows the PCr dynamics for all three modelconfigurations; Fig. 4, F–J, shows the pH dynamics for allthree model configurations. The goodness of fit was used to testthe hypothesis represented by each model configuration. Modelconfiguration i (red lines) represented conditions lacking anycalcium activation of PFK, whereas configurations ii (greenlines) and iii (blue lines) both include calcium activation ofPFK, albeit according to a different kinetic mechanism. Bothmodel configurations i and ii failed in reproducing the exper-imental data. In contrast, model configuration iii could suc-cessfully reproduce both the energetic state of the muscle (PCr)as well as the glycolytic flux (pH dynamics) simultaneously.Compared with the model configurations i and ii, the sum ofsquared errors was reduced more than eightfold (386.7 and354.6 vs. 44.8, respectively). The calculated AIC for modelconfigurations i, ii, and iii were 8.1, 49.4, and 920.5respectively. The large reduction in AIC for model configura-tion iii compared with configurations i and ii indicates that theimprovement in the model fit (reduction in SSE) was muchlarger than could be expected from the additional number ofestimated parameters. Based on these results, it was concludedthat model configurations i and ii could not explain the in vivosampled pathway dynamics. In contrast, these results providedevidence that calcium-calmodulin-mediated activation ofPFK-1 in combination with activation of the enzyme by in-T

(�3.

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(�6.

(�10

(�3.

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76(�

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31(�

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einhib

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creased concentrations of AMP and ADP (model configurationiii) can explain the recorded dynamics of glycolytic flux inskeletal muscle in vivo.

Figure 4, K–O, shows the predicted ATP supply flux by PCrhydrolysis (grey lines) and glycolysis (black lines) and ATPdemand flux (blue lines), compared with values derived fromthe experimental data by using the phenomenological model

described by Conley et al. (9). For clarity of presentation,these predictions are only showed for the model configura-tion iii. These results demonstrate that the fluxes predictedby the mechanistic model and the phenomenological modelare consistent with one another. In retrospect, the predic-tions of the model configuration iii were also consistent withthe calculations used to identify the part of the data at which

Fig. 3. Characterization of in vivo pathwaydynamics. Typical result of the experimentaldata obtained to characterize in vivo pathwaybehavior. A: stack plot of spectra obtained at10-Hz stimulation. These spectra were obtainedby averaging 12 free-induction decays and pro-cessed with 5-Hz line broadening. PME, Pi,phosphocreatine, PCr, and ATP resonances areindicated. Pooled PCr (B) and pH (C) dynamicsat 10-Hz stimulation (n � 5). Error bars indi-cate SE. The part of the data analyzed by thecomputational model is indicated by a blackarrow.

Fig. 4. Quantitative hypotheses testing; experimental data vs. model simulations. Experimental data are indicated in black. Error bars indicate SE (n � 4–5).Simulation results according to model configuration i (without calcium activation of PFK-1, red lines) and model configuration ii and iii (with calcium activationof PFK-1, green and blue, respectively) are shown. Optimized model parameter values listed in Table 3 were obtained by fitting model stimulations to these data.A–E: PCr. F–J: pH. K–O: predictions according to model configuration iii (solid lines) of ATP supply flux by PCr hydrolysis (grey lines) and glycolysis (blacklines) and ATP demand flux (blue lines), compared with values derived from the experimental data by using the phenomenological model (dots) described byConley et al. (9). Calculations with the phenomenological model were performed using the estimated value of the static proton buffer capacity as listed in Table3. As a result of the fast (de)activation kinetics of PFK-1 (see Fig. 7) the net glycolytic ATP synthesis flux was also pulsatile. For clarity of presentation, theglycolytic flux (black lines) indicated represents the net flux averaged over epochs of 5 s.

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the model assumption of constant ATP hydrolyses rateswere not violated. The model predictions show that forconditions of pH 6.5 the sum of PCr breakdown rate (PCrdynamics) and glycolytic ATP production (pH dynamics)remain constant while being consistent with the experimen-tal data.

Model verification: model testing against independent data.The veracity of the model was increased by using thealgorithm on independent data sets. Experimental data ofgroups with a different number of excitation pulses per 5 s(compared with the data used for parameter estimation) wasused: i.e., 1-Hz continuous stimulation (5 pulses/5 s) and 40Hz (1 pulse train per 5 s, 20 pulses per pulse train).Experimental data vs. model predictions are shown in Fig. 5.These results show that the model can describe the behaviorof the pathway for conditions of varying number of muscleexcitation pulses. Model simulations are shown for thedifferent configurations. The results show that only model

configuration iii (blue lines) can reproduce the data. Theseresults therefore act as validation of model configuration iiiand they falsify model configurations i and ii. Figure 5, Eand F, shows the predicted ATP supply flux by PCr hydro-lysis (grey lines) and, glycolysis (black lines) and ATPdemand flux (blue lines), compared with values derivedfrom the experimental data by using the phenomenologicalmodel described by Conley et al. (9). For clarity of presen-tation, these predictions are only showed for the modelconfiguration iii.

Model Predictions: Deactivation of Glycolysis Postexercise

It has been well documented that glycolysis is rapidlysilenced after termination of muscle contraction (6, 12, 14,15, 43). We tested if adding calcium regulation of PFK tothe model could indeed explain this pathway characteristic.

Fig. 6. Model predictions of the silencing of glycolysis in noncontractingmuscle. Simulations of exercise (5-Hz continuous muscle excitation, 60s)-recovery protocol. The dotted line indicates the end of exercise (time � 60s). At the onset of recovery a small PCr resynthesis is observed (A). The PCrdynamics reflects the glycolytic ATP production at the beginning of recovery.B: model simulations of the summed concentration of glycolytic intermediatesdownstream of PFK-1 (F1,6P2 � DHAP � G3P � GAP � 13BPG � 3PG �2PG � PEP). C: PFK-1 flux (grey) and the PGK � PYK flux (black). PGK andPYK are the ATP generating steps of the pathway. These predictions show thatalthough PFK flux is quickly deactivated postexercise, ATP production flux(PGK � PYK flux) is deactivated at a slower timescale.

Fig. 5. Model verification: comparison of model simulations and independentdata for other stimulation frequencies than used for parameterization. Modelsimulations according to configurations i, ii, and iii are indicated in red, greenand blue, respectively. Experimental data are indicated in black and correspondto muscle stimulation protocols of 1 Hz continues stimulation (A and C) and 40Hz (1 pulse train per 5 s, 20 pulses per pulse train; B and D). Error bars indicateSE (n � 4–5). E and F: predictions according to model configuration iii (solidlines) of ATP supply flux by PCr hydrolysis (grey lines) and glycolysis (blacklines) and ATP demand flux (blue lines), compared with values derived fromthe experimental data by using the phenomenological model (dots) describedby Conley et al. (9). Calculations with the phenomenological model wereperformed using the estimated value of the static proton buffer capacity aslisted in Table 3. As a result of the fast (de)activation kinetics of PFK-1 (seeFig. 7) the net glycolytic ATP synthesis flux was also pulsatile. For clarity ofpresentation, the glycolytic flux (black lines) indicated represents the net fluxaveraged over epochs of 5 s.

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Figure 6 shows model predictions of a rest-exercise (60-s,10-Hz continuous muscle stimulation)-recovery protocol.The ATP synthesis by the pathway postexercise is reflectedin the PCr dynamics. Figure 6A, inset, shows a small PCrresynthesis and thus glycolytic ATP production, postexer-cise. The time constant of the PCr resynthesis is between 5and 10 s, and the ATP produced by the pathway during thisperiod is �1 mM. These predictions are in excellent accor-dance with the time constant and magnitude of the PCrrecovery due to glycolytic ATP production reported byForbes et al. (19) and Crowther et al. (14). This resultshowed that the model can reproduce transients observed inother independent data sets, providing addition model ver-ification. Results of simulations were explored to determinethe origin of this small glycolytic ATP production in the firstfew seconds of recovery. It was concluded that these dy-namics were caused by accumulation of pathway interme-diates downstream of PFK-1 (Fig. 6B). Recovery of theseintermediates to baseline levels occurred in 5–10 s, therebyyielding �1 mM ATP. Figure 6C shows PFK-1 flux, whichclosely tracked the rapid pulsatile Ca2� release and reuptakeduring exercise. As a result, PFK-1 flux was quickly deac-tivated postexercise. In addition, the sum of the fluxesthrough the ATP producing steps in the pathway (PGK �PYK) is shown. These simulation results provided furtherevidence that, although PFK-1 flux is quickly silenced(100 –200 ms), ATP production by glycolysis lags behind by5–10 s.

Model Predictions: PFK Activation Dynamics

The time constant of activation and deactivation of calcium-calmodulin binding to PFK-1 have to this date remainedunknown. This process was included in the model and valuesof kinetic kon and koff parameters were inferred from the in vivoexperimental data. Simulations with the parameterized modelwere performed to investigate the (de)activation kinetics ofPFK-1 for two stimulation frequencies, 10 and 40 Hz (Fig. 7,A and B). In addition, kinetics of calcium-calmodulin (redlines) and calcium (blue lines) are shown that were used asinput of the model and drive the (de)activation of PFK-1 areshown. For illustrative purposes, the concentrations of thesetwo molecules were scaled to the same order of magnitude asthe fraction activated PFK. For calcium-calmodulin, 1 unit

corresponds to 0.040 �M and for calcium 1 unit corresponds to30 �M.

DISCUSSION

The principal result of this investigation was that incorpo-ration of calcium-calmodulin mediated modulation of PFK-1activity combined with activation of the enzyme by increasedlevels of AMP and ADP into a kinetic model of glycolysis inskeletal muscle significantly improved prediction of in vivoglycolytic flux in ischemic skeletal muscle. This main result, itsimplications, as well as several methodological considerationswill be discussed.

Methodological Considerations: Computational Modeling

The modeling framework developed by Vinnakota et al. (55)was selected as basis for this investigation. A unique propertyof this specific model of glycolysis in muscle is that it includesa detailed description of proton buffering by metabolites andpH dependency of the different reactions. Modeling theseaspects of the pathway in detail was essential because pHdynamics were used as reporter of glycolytic flux. Moreover,during the experiments large changes in pH were observed(7.2–6.2), which strongly influences glycolytic flux (see e.g.,Refs. 22, 52).

In this study, the explanatory power of incorporation ofcalcium regulation of glycolytic flux at the level of PFK-1 wasinvestigated in detail. It is, however, well known that calciumstimulates GP flux via enzyme phosphorylation (7). This pro-cess was not explicitly modeled, but instead the dynamics ofGP activity were implicitly taken into account by using therecorded dynamics of the sugar phosphates as input signal ofthe model. This methodology allowed simplifying the analyseswhile still taking the calcium changes of GP activity intoaccount. For the modeling of the calcium-calmodulin dynam-ics, a similar strategy was applied. These dynamics weresampled from a previously developed model of calcium han-dling in fast twitch skeletal muscle. Fast twitch is also thedominant (95%) fiber type of rat TA muscle (35). Thiscalcium handling model was shown to have excellent perfor-mance in reproducing calcium-dye dynamical data for excita-tion frequencies ranging from 1 to 80 Hz (25, 26) and wastherefore considered a good representation of this aspect ofmuscle physiology.

Fig. 7. Calcium, calcium-calmodulin, and PFK-1(de)activation kinetics. Predictions of (de)activa-tion kinetics of PFK-1 (black), calcium-calmodu-lin kinetics (red) and calcium kinetics (bue) for 10Hz (A) and 40 Hz (B). For illustrative purposes theconcentrations of calcium-calmodulin and calciumwere scaled to the same order of magnitude as thefraction activated PFK-1. For calcium-calmodulin1 unit corresponds to 0.040 �M and for calcium 1unit corresponds to 30 �M.

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In the model, the effect of, e.g., fructose-2,6-biphosphate orcitrate on PFK-1 flux was not taken into account. The rationalefor not including these interactions in the kinetic model wasthat for mammals the dynamic range of these modulators inskeletal muscle is small ,and therefore, their contribution to thecontrol of the enzyme in vivo is expected to be rather limited(31, 41). However, there is also some evidence indicating thatfructose-2,6-biphosphate concentration can change under somespecific experimental conditions (45). It can therefore not beruled out that during ischemia dynamics of this metabolite orothers [e.g., citrate (38), glucose-1,6-biphosphate (31), or lac-tate (11)] exert some control on enzyme flux. Nevertheless, thesimulation results indicated that it was not necessary to includethese interactions in the model to explain the experimental datarecorded in this study.

The proton buffer capacity (BuffCapFixed) of the musclecells was previously estimated by Vinnakota and et al. (55)at 0.016 M. In this study, this parameter value was reesti-mated. It was verified that this choice did not affect the mainoutcome of the study: i.e., simulations showed that if thevalue of BuffCapFixed was not optimized but fixed at 0.016M, model configuration iii could still reproduce the exper-imental data.

The simulation results shown for model configuration iand ii represent the best model fit to the data. These modelconfigurations could not reproduce the PCr and pH dynam-ics simultaneously. Specifically, PCr dropped to fast andglycolytic flux increased too little. One could propose thatthis problem could be solved by increasing the Vmax ofPFK-1. This possibility was investigated by manually in-creasing the Vmax of PFK-1. This parameter adaptationresulted in significantly worse fits for PCr and pH timecourse data recorded in ischemic muscle at rest (0-Hzstimulation): to whit, the predicted fall in pH became toofast and the decline in PCr too slow. Moreover, additionalsimulations indicated this problem could not be solved byjust changing other estimated model parameters. Thus, evenif Vmax of PFK-1 was set to a higher activity the fit of modelconfiguration iii was still superior and did not vitiate ourconclusions.

The fits presented in Fig. 4 were obtained by minimizing theerror (SSE) between model predictions and experimental data,according to the cost function (Eq. 10). Apparently, for con-figuration i and ii the error was minimal when the modelreproduced the pH dynamics but failed to describe the PCrtime-course data. It is important to realize this is the outcomeof a mathematical optimization procedure. The observationthat these (falsified) model configurations only reproduced pHdata and failed to predict PCr data provided therefore nofurther physiological insights other than the conclusion thatmodel configuration i and ii could not explain the experimentaldata. Indeed, the verification tests (Fig. 5) demonstrated thatwhen no parameters were optimized except the ATPase rateconstant (kATP_Hydr) model configurations i and ii indeed failedin reproducing both the PCr kinetics (Fig. 5A) and pH kinetics(Fig. 5D).

The confidence intervals for the estimated parameters werecalculated using Matlab routine nlparci and were listed inTable 3. These results indicate that for model configuration iand iii all parameters could be estimated with relative highaccuracy. In contrast, for model configuration ii, the confidence

interval of parameters kdeinhib_Act and koff was very large (seeTable 3). This is probably a result of a strong correlationbetween these parameters. Because model configuration ii wasalready falsified by the results shown in Figs. 4 and 5, thisobservation was not analyzed in more detail.

Methodological Considerations: In Vivo 31P-MRSMeasurements in Ischemic Rat Muscle

Electrical stimulation along the distal nerve trajectory of then. peroneus communis-induced contractions in the TA, EDL,peroneus longus, and brevis, which was previously validatedby functional MRI recordings (16, 17). Analysis of the sensi-tivity profile of the 31P coil by CSI indicated that 25% of therecorded signal originated from nonactivated muscle. Thisproblem is not unique for this specific study. For example, it iswell known that MRS recordings during voluntary exercise inhumans often represent the lumped dynamics of both activatedand non-activated motor units (13, 27, 28). Nevertheless, toimprove the quality of the analysis this partial volume problemwas taken into account and corrected for by a data postpro-cessing step described in METHODS. The percentage of signaloriginating from the noncontracting muscle is an influentialparameter in these calculations. It was therefore verified thatoutcome of the study was not sensitive to the specific value ofthis parameter. Specifically, all simulations (parameter optimi-zations and model predictions) were performed assuming thesignal originating from noncontracting muscle to be 20 or 30%.The results of these simulations (data not shown) indicated thatreported conclusions were indeed not sensitive to the specificvalue of this parameter.

Calcium Modulation of PFK Activity

Past failure of model predictions lacking any regulation bycalcium previously illustrated additional regulation must bepresent in vivo (47). Numerical analysis indicated PFK-1 asmost likely site for the additional control (47). In addition,based on evidence provided by experimental studies (5, 36,37), it was hypothesized that calcium-calmodulin activation ofPFK-1 has a dominant role in controlling the response ofpathway dynamics for varying muscle stimulation frequencies.This specific mechanism was therefore tested in the computa-tional analysis. The effects of calcium-calmodulin on PFK-1activity were reported to occur in a biphasic manner (37): atphysiological Ca2� concentrations PFK-1 is activated, how-ever, if the Ca2� concentration in the cells rises to pathologicallevels, PFK-1 is deactivated again. In the model, only theactivation of PFK-1 was included. The rationale for this choicewas that the analysis was restricted to the part of the data inwhich ATPase rate remained constant (pH 6.5). For theseconditions, it was not expected Ca2� concentrations rise topathological conditions.

The kinetic model of calcium-calmodulin mediated PFK-1(de)activation was constructed using available information inthe literature. Activation of PFK-1 is thought to occur viabinding of two calcium-calmodulin complexes to a PFK-dimer(36). This binding reduces the inhibition of the enzyme by ATP(36). At physiological concentrations (�8 mM) ATP inhibitionresults in a nearly full deactivation of the enzyme (95%; Ref.36). Therefore, reversing this inhibition will result in a signif-icant increase of the enzymes catalytic activity. By competitive

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binding to the inhibition site, AMP and ADP are able to reversethe ATP inhibition of the inactive form of PFK-1 (10). Itremains unknown whether for the activated form of the enzymedeinhibition is likewise mediated by competitive binding ofADP and AMP, albeit with a lower binding constant, oralternatively, if it is independent of ADP and AMP levels.Irrespectively, both scenarios were evaluated using the com-putational model (model configurations ii and iii, respectively).A detailed analysis showed that only a model containingdeinhibition mediated by competitive binding of ADP andAMP could reproduce the experimental data. A possible con-cern could be that comparison of the three models was biasedbecause each model had a different number of degrees offreedom; in general, models with a greater number of freeparameters tend to fit data better. This concern was quantita-tively addressed using the Akaike test. A large reduction in thevalue of AIC indicated that improvement of the fit of modelconfiguration iii was larger than could be expected from thefew additional degrees of freedom, suggesting a biologicalcomponent responsible. Although kinetic data for validation ofthis prediction are unavailable, it is consistent with resultsreported by Crowther et al. (12), that both elevated calciumlevels and increased ADP and AMP levels were required toincrease flux downstream of glycogen phoshorylase (12). Fur-ther confidence in the validity of the computational model wasprovided by verification against data not used for parameterestimation (see Fig. 5). Finally, a corollary of the particularkinetic model for calcium control of PFK-1 that was developedand used here is that the kinetics of PFK-1 activation anddeactivation were almost exclusively (but see Eq. 9) deter-mined by the reaction kinetics of calcium-calmodulin interac-tion. Empirical studies have shown that the latter are extremelyrapid (Kd 100 s1 or faster; see METHODS). As a result, PFK-1(de)activation in the model was equally rapid. No data wereavailable in the literature to verify that this model corollary isaccurate, and it remains to be tested.

Silencing of Glycolysis in Noncontracting Muscle

It has been well documented that glycolysis is quicklysilenced after termination of muscle contraction (9, 12, 14,15, 43). In the present investigation, these observations werereproduced by the absence of PCr resynthesis in the periodafter stimulation. Two independent studies reported a deac-tivation of the pathway in the order of 10 - 20 s (14, 19).This timescale is slow compared with the rapid deactivationof PFK-1 (100 –200 ms; see Fig. 6). However, simulationsrevealed that after intense muscle contractions the deacti-vation of the pathway is delayed as a result of accumulationof intermediates downstream of PFK-1. In addition, simula-tions indicated that glycolytic ATP production during the firstseconds of recovery is dependent on the intensity of the precedingexercise (data not shown) and may explain the experimentalobservations that a complete absence of glycolytic flux at theonset of recovery occurs (6, 43). These findings may haveimportant implications for the analyses of PCr recovery kinet-ics. PCr recovery kinetics are believed to predominantly reflectoxidative ATP production rate, and this rate of PCr recovery isfrequently used as a measure of in vivo oxidative capacityand/or mitochondrial function (42). Two experimental studiesalready suggested that the first 10 s of recovery may be

contaminated by glycolytic ATP production. The current sim-ulation study provided additional support for this contention.These results therefore imply that to obtain PCr kinetics thattruly reflect the oxidative ATP synthesis it is advisable toexclude the first 10 s of recovery from the data analyses.

Parallel Activation of ATP Consumption and Glycolytic ATPProduction

The results of this study indicate that to meet energeticdemands parallel activation of glycolytic ATP supply fluxand muscle contraction by the same signaling event, i.e.,calcium release in the myoplasm, is necessary. The effect ofvarying calcium stimulation frequency on parallel activationof these pathways has only been addressed in relatively fewstudies. Conley et al. (9) used 31P-MRS to determine theeffect of varying muscle excitation at low frequencies(0.5–3 Hz) and concluded that at these low stimulationfrequencies glycolytic flux scales linearly with contractionfrequency. A similar conclusion was inferred from themodel simulations. PFK-1 (de)activation kinetics remainedpulsatile for muscle excitation frequencies 10 Hz. For thisrange of stimulation frequencies, PFK-1 activation waslinearly related to muscle excitation. These simulationsyield results with much broader implications for glycolyticflux than previously suggested in part because reproducingthese characteristics also reported by Crowther et al. alsopermits model predictions for much higher frequencies.Remarkably, at these frequencies, the fusing of individualPFK-1 activation pulses was qualitatively similar to forcedynamics of fast twitch muscle. These predictions alsosuggest that for these stimulation frequencies (10 Hz)activation of PFK-1 remains closely linked to muscle ATPdemand flux. We speculate that the regulation of glycolysisin skeletal muscle is optimized to facilitate this parallelactivation throughout the wide dynamical range of muscleexcitation frequencies.

Future Outlook

Recently, Vinnakota et al. (55) used the previous version ofthis computational model of glycolysis in skeletal muscle toanalyze metabolite and pH dynamics in resting mouse EDLand soleus muscle. Although their model simulations repro-duced these dynamics fairly well, the simulations failed todescribe recorded dynamics during muscle excitation. A pos-sible explanation for this model limitation was the lack of feedforward regulation downstream of glycogen phosphorylase,activated during mechanical work. This study has found thatadding regulation by calcium mediated activation of PFK-1improves the consistency of model predictions and experimen-tal data over a wide operational range of muscle excitationfrequencies (0–80 Hz). We therefore concluded that the pro-posed model does provide an improved basis for modelingenergy metabolism in skeletal muscle. In this context, relevantquestions or model limitations open for future study will bediscussed below.

The predictions of the current model were tested for condi-tions of ischemia. It will be interesting to investigate if thesepredictions are also accurate for conditions of normoxia. Thisrequires adding a description of ATP production by oxidativephosphorylation to the computational model and sampling the

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behavior of both mitochondrial and glycolytic pathway exper-imentally under normoxic conditions. In the present investiga-tion, the experimental readout of the PME resonance allowedto bypass the need for a flux equation of GP. For future studies,it may become relevant to add this flux description. Hereto, animproved model of GP including allosteric regulation by G6Pand the effects of enzyme phosphorylation on kinetic param-eters is probably required. The present analysis was based onthe experimental data in which muscle fatigue had no detect-able effect on cellular ATP hydrolysis rate. Acquiring anexperimental readout and modeling the effects of muscle fa-tigue on ATP hydrolysis rate will be key steps towards com-putational analyses of the remaining of the data. In addition, infuture studies it may become necessary to include the effect ofother metabolites and signaling molecules [e.g., fructose-2,6-BP and glucose-1,6-BP (31), or lactate (11)] on PFK-1. Atthe moment, it is still assumed that the effects of these mole-cules on PFK-1 activity in vivo are negligible. Measuring thedynamics of these metabolites during exercise protocols andextending the PFK-1 rate equation to incorporate the effect ofthese interactions on PFK-1 activity will provide new oppor-tunities to investigate a possible regulatory role of these mol-ecules.

With respect to extending the research on this topic, it mayalso be very interesting to investigate the role of calcium-calmodulin signaling on the flux control of glycolysis in tissuesother than muscle. Based on the current results, it is predictedthat calcium-calmodulin signaling has a very dominant fluxcontrol in skeletal muscle, but there is also evidence indicatingthis signaling mechanism activates glycolytic flux in nervoustissue (30, 33) and also various types of cancerous tissues (23,24, 40, 49). In this view, it will be of particular interest to studyif calcium-calmodulin related alterations in glycolytic fluxobserved for these cell types will also arise from modelpredictions.

In Summary

An integrative experimental and computational modelingapproach was applied to test the hypothesis that calcium-calmodulin-mediated activation of PFK-1 in skeletal muscle isan important signal in flux control underlying in vivo pathwaybehavior. Model simulations revealed that incorporation ofthese mechanisms into a detailed model of skeletal muscleglycolysis was required for model predictions to be consistentwith experimental data, thereby providing quantitative supportfor the hypothesis. Model predictions indicated that the (de-)activation kinetics of PFK-1 in response to different stimula-tion frequencies is very similar to force dynamics in fast twitchmuscle. However, in spite of these very fast PFK-1 deactiva-tion kinetics overall shut down of glycolytic ATP production innoncontracting muscle postexercise may be delayed by 5–10 sas a result of the accumulation of glycolytic intermediatesdownstream of PFK-1.

APPENDIX

Model Configuration i

The PFK rate equation of model configuration i [obtained fromConnett (10); Eq. A1].

Vmax�

E � EA � EAB � EBA

NUM �Q1 ·�1�Q�

c1c2�Q6��Q2 ·�1�

c1c2�Q5�·�1�

c1c2�

E ��1 �Q�

c1c2� Q5� ·�1 �

c1c2� Q6� · (1 � Q7)

EA � Q1 ·�1 �Q�

c1c2� Q6� · Q3 ·�1 �

EB � Q2 ·�1 �Q�

c1c2� Q5� · Q4 ·�1 �

EBA � EAB � NUM�1 �Q

c1c2�

QA �[F6P]

Km1F6P

QB �[MgATP]

Km1MgATP

Q1 � QA�1 �Q7

Q2 � QB�1 �Q7

Q3 ��1 �Q�

c1� ·� Km2

[MgATP]�Q4 ��1 �

c2� ·� Km2

[F6P]�Q5 �� Ki

[F6P]� · (1 � Q�) · Q3 · QA

Q6 �� QiMgATP

[MgATP]� · (1 � Q�) · Q4 · QB

Q7 �[H�]

Ka�1 ��[ATPH]

QiATPH �4

Q�� Q7

�1 �QA

c1�3

·�1 �QB

c2�3

(1 � QA)3 · (1 � QB)3

QiMgATP � Ki

MgATP · deinhibition

QiATPH � Ki

ATPH · deinhibition

deinhibition � 1 �[ADP]

KADP�

All model parameter values are provided in Table A1.

Model Configuration ii:

Model configuration ii contained two PFK-1 forms, an inactivemodeled according to Eq. 11 and an active form for which thedeinhibition term was described by Eq. A2.

deinhibition � kdeinhib_Act (A2)

Activation and deactivation of PFK-1 by binding of calcium-calmodulin was modeled by differential equations Eqs. A3 and A4:

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dPFKactibe

dt� konCa2CaM2 · (1 � PFKactive) � kof fPFKactive(A3)

PFKinactive � 1 � PFKactive (A4)

Parameter values of model configuration ii are listed in Tables 3 and A1.

Model Configuration iii

Model configuration iii contained two PFK-1 forms, an inactivemodeled according to Eq. 11 and an active form for which thedeinhibition term was described by Eq. A5.

deinhibition � 1 �AMP

KAMPact �

KADPact (A5)

Activation and deactivation of PFK-1 by binding of calcium-calmo-dulin was modeled by differential Eqs. A3 and A4. Parameter valuesof model configuration iii are listed in Tables 3 and A1.

ACKNOWLEDGMENTS

We thank Dr. Kalyan Vinnakota for kindly sharing his Matlab code of theglycolysis model and Dr. Sandra Loerakker for the help with the ischemicclamp.

GRANTS

This research was performed within the framework of the Center forTranslational Molecular Medicine (www.ctmm.nl) Project PREDICCt Grant01C-104, supported by The Netherlands Heart Foundation, Dutch DiabetesResearch Foundation, and Dutch Kidney Foundation. It was funded in part bythe National Institutes of Health through a subcontract to Grants HL-072011and DK-095210. This work was carried out within the research programme ofthe Netherlands Consortium for Systems Biology, which is part of TheNetherlands Genomics Initiative/Netherlands Organization for Scientific Re-search.

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the author(s).

AUTHOR CONTRIBUTIONS

Author contributions: J.P.S., W.G., R.W.W., J.J.P., J.A.J., and N.A.v.R.conception and design of research; J.P.S., W.G., B.W., and J.J.P. performedexperiments; J.P.S., W.G., B.W., and J.J.P. analyzed data; J.P.S., W.G., B.W.,R.W.W., P.A.H., K.N., J.J.P., J.A.J., and N.A.v.R. interpreted results ofexperiments; J.P.S. and W.G. prepared figures; J.P.S. and W.G. draftedmanuscript; J.P.S., W.G., R.W.W., P.A.H., K.N., J.J.P., J.A.J., and N.A.v.R.edited and revised manuscript; J.P.S., W.G., B.W., R.W.W., P.A.H., K.N.,J.J.P., J.A.J., and N.A.v.R. approved final version of manuscript.

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Table A1. parameter values PFK-1 model

Parameter Value

Km1F6P 68.49 �M*

Km2F6P 58.70 �M*

Km1MgATP 26.54 �M*

Km2MgATP 37.81 �M*

KiF6P 4.33 �M*

KiMgATP 124.60 �M*

KiATPH 0.649 �M*

Ka 0.0812 �M*k 0.990*c1 19.09*c2 2.63*KADP Estimated (Table 3)KAMP Estimated (Table 3)

F6P, fructose-6-phosphate. *Value obtained from Ref. 10.

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