Integrated model validation

Model verification

Simulation of dynamic responses at metabolic level induced by incremental test and high-intensity intermittent exercises

To validate the model we investigated a dynamic behaviour of the system in response to diverse single-bout aerobic exercises and compared them with published experimental data. Initially, we quantitatively estimated biochemical responses of essential metabolic variables (ATP, ADP, PCr, lactate concentrations and pH in muscle fibers type I and II) in the incremental ramp test which is a commonly used approach to evaluate aerobic capacity. In our simulation, muscle fibres type I are recruited after the beginning of exercise, while fibre type II - only at power over 24% of VO2max (6 min after exercise onset, Fig. 1A). Increasing the power during the test effects on various physiological variables like the volume of muscle containing fibre type I and/or II, blood flow as well as of transport and metabolic fluxes in both fibre types (Fig. 1). The model simulations reasonably well correspond to experimental measurements (Roussel et al., 2003; Greiner et al., 2007; Cannon et al., 2013)[1][2][3] obtained in studies with the exercise mode (Fig. 2). However, it is worth to note that the current version of the model does not take into account an effect of the muscle exhaustion during the incremental ramp test which is physiologically observed and provides a direction for the model improvements.

Figure 1. Simulation results for incremental ramp exercise till exhaustion. (A) Exercise power and fibers recruitment pattern: total power, W (orange), power generated by type I (red) and II (blue) fibers; (B) ATP concentrations in type I (red, dotted) and II (blue, dotted) fibers and in the muscle tissue, mmol/kg ww (orange, solid); (C) ADP concentrations in type I (red, dotted) and II (blue, dotted) fibers and in the muscle tissue, mmol/kg ww (orange, solid); (D) PCr concentrations in type I (red, dotted) and II (blue, dotted) fibers and in the muscle tissue, mmol/kg ww (orange, solid); (E) Lactate concentrations in type I (red, dotted) and II (blue, dotted) fibers and in the muscle tissue, mmol/kg ww (orange, solid); (F) pH changes in type I (red, dotted) and II (blue, dotted) fibers and in the muscle tissue, mmol/kg ww (orange, solid).

Figure 2. Model validation. The model simulations were compared to experimental data collected from incremental ramp and low intensity, moderate intensity exercises. (A) Model-predicted dynamic changes of PCr concentration in muscle tissue cells during incremental (blue line), low intensity(green line) and moderate intensity (red line) exercises (axis X - time of the exercise in minutes) and experimental measurements of PCr concentration changes during incremental (blue dots, Greiner et al., 2007)[2], low-intensity (dark red dots (Krustrup et al., 2004)[4], green dots (Barker et al., 2008)[5], pink dots (Cannon et al., 2014)[6]) and high-intensity (dark pink dots (Cannon et al., 2014)[6] exercises; (B) Model-predicted dynamic changes of lactate concentration in muscle tissue cells during incremental (blue line), low intensity(green line) and moderate intensity (red line) exercises (axis X - time of the exercise in minutes) and experimental measurements of lactate concentration changes during low-intensity (dark red dots (Krustrup et al., 2004)[4]) exercise; (C) Model-predicted dynamic changes of ATP concentration in muscle tissue cells during incremental (blue line), low intensity(green line) and moderate intensity (red line) exercises (axis X - time of the exercise in minutes) and experimental measurements of ATP concentration changes during low-intensity (dark red dots (Krustrup et al., 2004)[4]) and all-out intensity (red dots (Bartlett et al., 2020)[7]) exercises; (D) Model-predicted dynamic changes of pH in muscle tissue cells during incremental (blue line), low intensity(green line) and moderate intensity (red line) exercises (axis X - time of the exercise in minutes) and experimental measurements of ATP concentration changes during low-intensity (dark red dots (means ± SD) (Krustrup et al., 2004)[4]) exercise.

For additional verification of the model, we simulated responses to an alternative exercise mode that is a high-intensity intermittent exercise (Fig. 3, 4). As a result, the model qualitatively reproduces dynamic changes in PCr concentration during high-intensity intermittent exercise with different work:recovery durations.

Figure 3. Simulation results for high-intensity intermittent exercise with different work:recovery durations (initial - 16:32 s; intermediate - 32:64 s; final - 64:128 s) (Davies et al., 2017)[8]. (A) Exercise power and fibers recruitment pattern: total power (Wmax=250), W (orange), power generated by type I (red, Wmax=125) and II (blue, Wmax=125) fibers; (B) PCr concentration (mmol/kg ww) in Type I (red) and Type II fibers (blue).

The first scenario to reproduce experimental PCr measurements in Kappenstein with coathours study (Kappenstein et al., 2013)[9] used the external power which is equal to 250, while the parameter value was doubled in the second simulated scenario. The maximal value of the parameter was unchangeable on each bout of 30-s exercise separated by 20-s recovery. Whereas the external power was gradually decreased after the fifth bout (Fig. 4E) due to physical exhaustion of the volunteered subject. It has been predicted that gradual exhaustion or reduction in the external power after a certain exercise bout much better reproduces experimental measurements on phosphocreatine dynamics in skeletal muscle than simulations with constant maximal power value on each bout (Kappenstein et al., 2013)[9].

Figure 4. Simulation results for high-intensity intermittent exercise (Kappenstein et al., 2013)[9]. (A, C, E) Exercise power and fibers recruitment pattern: total power (A: Wmax=250; C: Wmax=500; E: Wmax=500), W (orange), power generated by type I (red, A-C: Wmax=125) and II (blue, A: Wmax=125; C: Wmax=375; E: Wmax=375 and successive decline) fibers; (B) PCr concentration (mmol/kg ww) in Type I (red) and Type II fibers (blue) with total power at Wmax=250; (D) PCr concentration (mmol/kg ww) in Type I (red) and Type II fibers (blue) with total power at Wmax=500; (F) PCr concentration (mmol/kg ww) in Type I (red) and Type II fibers (blue) with total power at Wmax=500 and successive decline of the power on each bout of 30-s exercise.

Simulation of dynamic responses at metabolic and gene regulatory levels induced by low- and moderate intensity exercises

At the next step of the model validation, we predicted dynamic changes of the same biochemical variables, an activation of both signaling molecules (AMPK and Ca2+-dependent proteins) and transcription factor (CREB1), as well as expression of genes (NR4A3, NR4A2, PPARGC1A) in response to low (50% VO2max) and moderate intensity (70% VO2max) continuous exercises. During this type of the exercise mode metabolic fluxes varied by means of recruitment of both muscle fibers type I, and type II. Comparison of the model simulations with experimental data (Krustrup et al., 2004; Barker et al., 2008; Cannon et al., 2014; Fiedler et al., 2016; Bartlett et al., 2020)[4][5][6][10][7] has shown that the model reasonably well reproduces dynamic behaviour of the muscle metabolism during the exercise (Fig. 2 and 5).

Figure 5. Simulation results for low (50% VO2max, A-F) and moderate intensity (70% VO2max, G-L) continuous exercises. (A,G) Exercise power and fibers recruitment pattern: total power, W (orange), power generated by type I (red) and II (blue) fibers; (B,H) ATP concentrations in type I (red, dotted) and II (blue, dotted) fibers and in the muscle tissue, mmol/kg ww (orange, solid); (C,I) ADP concentrations in type I (red, dotted) and II (blue, dotted) fibers and in the muscle tissue, mmol/kg ww (orange, solid); (D,J) PCr concentrations in type I (red, dotted) and II (blue, dotted) fibers and in the muscle tissue, mmol/kg ww (orange, solid); (E,K) Lactate concentrations in type I (red, dotted) and II (blue, dotted) fibers and in the muscle tissue, mmol/kg ww (orange, solid); (F,L) pH changes in type I (red, dotted) and II (blue, dotted) fibers and in the muscle tissue, mmol/kg ww (orange, solid).

Development of the integrated model incorporating signaling and gene expression modules enables to simulate expression dynamics of early and delayed response genes on mRNA levels (Fig. 6). Numerical analysis of the model enabled to reveal crucial steps in this signal transduction pathway for the adaptation and demonstrated the necessity of consideration of additional transcription factors modulating transcription of genes with delayed response in order to adequately reproduce gene expression data that were taken in human vastus lateralis muscle during and after acute cycling exercise (Fig. 6C-D). Bioinformatics analysis of the original transcriptomics data, in turn, proposed that CREB-like proteins from FOS and JUN families forming heterodimer complexes with transcription factor CREB1 are indeed these intermediate regulators of genes with delayed response (Akberdin et al., 2020)[11].

Figure 6. Simulation results for moderate intensity (70% VO2max) continuous exercises without (A-B) and with (C-D) intermediate X factor regulating expression of PPARGC1A gene. Expression of (A,C) NR4A3 (solid), NR4A2 (dashed), PPARGC1A (dot-dashed) in Type I fibers, (B,D) the same indexes in type II fibers (in Fold changes).

Discussion

The Integrated modular model comprises three hierarchical levels (metabolic, signaling pathways and regulation of gene expression)

We have previously developed a multi-compartmental mathematical model describing the dynamics of intracellular species concentrations and fluxes in human muscle at rest and intracellular metabolic rearrangements in exercising skeletal muscles during an aerobic exercise on a cycle ergometer (Kiselev et al., 2019)[12]. As an initial model for this study, we have used a more complex model of energy metabolism in the human skeletal muscle developed by Li and coauthors and considered two types of the muscle fibers (Li et al., 2012)[13]. We have proposed a modular representation of the complex model using BioUML platform (Kolpakov et al., 2019)[14]. The modular representation provides the possibility of rapid expansion and modification of the model compartments to account for the complex organization of muscle cells and the limitations of the rate of diffusion of metabolites between intracellular compartments. This feature allowed us to integrate modules of signalling pathways modulating downstream regulatory processes of early response and genes with delayed response during the exercise and recovery. The parametric fitting of the modular model to published experimental data (Krustrup et al., 2004; Greiner et al., 2007; Barker et al., 2008; Cannon et al., 2014; Bartlett et al., 2020)[4][2][5][6][7] showed the validity of the modular modeling approach implemented in BioUML. Furthermore, the integrated modular model provides an absolutely novel in silico platform to predict molecular responses of the human skeletal muscle cells to diverse modes of the exercise on levels of metabolic, signaling pathways and gene expression regulation experimental precise measurements of which are currently methodologically limited or even remain elusive.

Model constraints and further ways for the development

GS activity is regulated through multiple mechanisms, including feedbacks mediated by glycogen, blood glucose concentration,rate of glucose uptake, insulin, epinephrine and GS phosphorylation state (Jensen & Lai, 2009; Prats et al., 2009; Jensen et al., 2012b; Palm et al., 2013)[15][16][17][18]. However, in the current model GS activity depends on glycogen content only. In our model, the post-exercise glycogen synthesis is lower than estimated in the majority of studies (Casey et al., 1995; Jentjens & Jeukendrup, 2003; Burke et al., 2017)[19][20][21] because many factors are omitted, such as feeding and associated rises in blood glucose concentration, rate of glucose uptake, sensitivity to and changes in insulin, etc. At the same time, glycogen synthesis is higher than observed during exercise recovery in a fasted state (Maehlum & Hermansen, 1978)[22].

References

1. Roussel M, Mattei JP, Le Fur Y, Ghattas B, Cozzone PJ, and Bendahan D. Metabolic determinants of the onset of acidosis in exercising human muscle: a 31P-MRS study. J Appl Physiol (1985). 2003 Mar;94(3):1145-52. DOI:10.1152/japplphysiol.01024.2000 |
2. Greiner A, Esterhammer R, Bammer D, Messner H, Kremser C, Jaschke WR, Fraedrich G, and Schocke MF. High-energy phosphate metabolism in the calf muscle of healthy humans during incremental calf exercise with and without moderate cuff stenosis. Eur J Appl Physiol. 2007 Mar;99(5):519-31. DOI:10.1007/s00421-006-0379-2 |
3. pmid=PMC3764623
4. Krustrup P, Söderlund K, Mohr M, and Bangsbo J. Slow-twitch fiber glycogen depletion elevates moderate-exercise fast-twitch fiber activity and O2 uptake. Med Sci Sports Exerc. 2004 Jun;36(6):973-82. DOI:10.1249/01.mss.0000128246.20242.8b |
5. Barker AR, Welsman JR, Fulford J, Welford D, and Armstrong N. Muscle phosphocreatine kinetics in children and adults at the onset and offset of moderate-intensity exercise. J Appl Physiol (1985). 2008 Aug;105(2):446-56. DOI:10.1152/japplphysiol.00819.2007 |
6. Cannon DT, Bimson WE, Hampson SA, Bowen TS, Murgatroyd SR, Marwood S, Kemp GJ, and Rossiter HB. Skeletal muscle ATP turnover by 31P magnetic resonance spectroscopy during moderate and heavy bilateral knee extension. J Physiol. 2014 Dec 1;592(23):5287-300. DOI:10.1113/jphysiol.2014.279174 |
7. Bartlett MF, Fitzgerald LF, Nagarajan R, Hiroi Y, and Kent JA. Oxidative ATP synthesis in human quadriceps declines during 4 minutes of maximal contractions. J Physiol. 2020 May;598(10):1847-1863. DOI:10.1113/JP279339 |
8. Davies MJ, Benson AP, Cannon DT, Marwood S, Kemp GJ, Rossiter HB, and Ferguson C. Dissociating external power from intramuscular exercise intensity during intermittent bilateral knee-extension in humans. J Physiol. 2017 Nov 1;595(21):6673-6686. DOI:10.1113/JP274589 |
9. Kappenstein J, Ferrauti A, Runkel B, Fernandez-Fernandez J, Müller K, and Zange J. Changes in phosphocreatine concentration of skeletal muscle during high-intensity intermittent exercise in children and adults. Eur J Appl Physiol. 2013 Nov;113(11):2769-79. DOI:10.1007/s00421-013-2712-x |
10. Fiedler GB, Schmid AI, Goluch S, Schewzow K, Laistler E, Niess F, Unger E, Wolzt M, Mirzahosseini A, Kemp GJ, Moser E, and Meyerspeer M. Skeletal muscle ATP synthesis and cellular H(+) handling measured by localized (31)P-MRS during exercise and recovery. Sci Rep. 2016 Aug 26;6:32037. DOI:10.1038/srep32037 |
11. https://doi.org/10.17537/2020.15.20
12. https://doi.org/10.17537/2019.14.373
13. Li Y, Lai N, Kirwan JP, and Saidel GM. Computational Model of Cellular Metabolic Dynamics in Skeletal Muscle Fibers during Moderate Intensity Exercise. Cell Mol Bioeng. 2012 Mar;5(1):92-112. DOI:10.1007/s12195-011-0210-y |
14. Kolpakov F, Akberdin I, Kashapov T, Kiselev L, Kolmykov S, Kondrakhin Y, Kutumova E, Mandrik N, Pintus S, Ryabova A, Sharipov R, Yevshin I, and Kel A. BioUML: an integrated environment for systems biology and collaborative analysis of biomedical data. Nucleic Acids Res. 2019 Jul 2;47(W1):W225-W233. DOI:10.1093/nar/gkz440 |
15. Jensen J and Lai YC. Regulation of muscle glycogen synthase phosphorylation and kinetic properties by insulin, exercise, adrenaline and role in insulin resistance. Arch Physiol Biochem. 2009 Feb;115(1):13-21. DOI:10.1080/13813450902778171 |
16. Prats C, Helge JW, Nordby P, Qvortrup K, Ploug T, Dela F, and Wojtaszewski JF. Dual regulation of muscle glycogen synthase during exercise by activation and compartmentalization. J Biol Chem. 2009 Jun 5;284(23):15692-700. DOI:10.1074/jbc.M900845200 |
17. Jensen J, Tantiwong P, Stuenæs JT, Molina-Carrion M, DeFronzo RA, Sakamoto K, and Musi N. Effect of acute exercise on glycogen synthase in muscle from obese and diabetic subjects. Am J Physiol Endocrinol Metab. 2012 Jul 1;303(1):E82-9. DOI:10.1152/ajpendo.00658.2011 |
18. Palm DC, Rohwer JM, and Hofmeyr JH. Regulation of glycogen synthase from mammalian skeletal muscle--a unifying view of allosteric and covalent regulation. FEBS J. 2013 Jan;280(1):2-27. DOI:10.1111/febs.12059 |
19. Casey A, Short AH, Hultman E, and Greenhaff PL. Glycogen resynthesis in human muscle fibre types following exercise-induced glycogen depletion. J Physiol. 1995 Feb 15;483 ( Pt 1)(Pt 1):265-71. DOI:10.1113/jphysiol.1995.sp020583 |
20. Jentjens R and Jeukendrup A. Determinants of post-exercise glycogen synthesis during short-term recovery. Sports Med. 2003;33(2):117-44. DOI:10.2165/00007256-200333020-00004 |
21. Burke LM, van Loon LJC, and Hawley JA. Postexercise muscle glycogen resynthesis in humans. J Appl Physiol (1985). 2017 May 1;122(5):1055-1067. DOI:10.1152/japplphysiol.00860.2016 |
22. Maehlum S and Hermansen L. Muscle glycogen concentration during recovery after prolonged severe exercise in fasting subjects. Scand J Clin Lab Invest. 1978 Oct;38(6):557-60. DOI:10.1080/00365517809108819 |