Exhaustion of Skeletal Muscle Fibers Within Seconds: Incorporating Phosphate Kinetics Into a Hill-Type Model
Initiated by neural impulses and subsequent calcium release, skeletal muscle fibers contract (actively generate force) as a result of repetitive power strokes of acto-myosin cross-bridges. The energy required for performing these cross-bridge cycles is provided by the hydrolysis of adenosine triphos...
| Main Authors: | , , , , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Frontiers Media S.A.
2020-05-01
|
| Series: | Frontiers in Physiology |
| Subjects: | |
| Online Access: | https://www.frontiersin.org/article/10.3389/fphys.2020.00306/full |
| _version_ | 1818034262309339136 |
|---|---|
| author | Robert Rockenfeller Michael Günther Michael Günther Norman Stutzig Daniel F. B. Haeufle Tobias Siebert Syn Schmitt Kay Leichsenring Markus Böl Thomas Götz |
| author_facet | Robert Rockenfeller Michael Günther Michael Günther Norman Stutzig Daniel F. B. Haeufle Tobias Siebert Syn Schmitt Kay Leichsenring Markus Böl Thomas Götz |
| author_sort | Robert Rockenfeller |
| collection | DOAJ |
| description | Initiated by neural impulses and subsequent calcium release, skeletal muscle fibers contract (actively generate force) as a result of repetitive power strokes of acto-myosin cross-bridges. The energy required for performing these cross-bridge cycles is provided by the hydrolysis of adenosine triphosphate (ATP). The reaction products, adenosine diphosphate (ADP) and inorganic phosphate (Pi), are then used—among other reactants, such as creatine phosphate—to refuel the ATP energy storage. However, similar to yeasts that perish at the hands of their own waste, the hydrolysis reaction products diminish the chemical potential of ATP and thus inhibit the muscle's force generation as their concentration rises. We suggest to use the term “exhaustion” for force reduction (fatigue) that is caused by combined Pi and ADP accumulation along with a possible reduction in ATP concentration. On the basis of bio-chemical kinetics, we present a model of muscle fiber exhaustion based on hydrolytic ATP-ADP-Pi dynamics, which are assumed to be length- and calcium activity-dependent. Written in terms of differential-algebraic equations, the new sub-model allows to enhance existing Hill-type excitation-contraction models in a straightforward way. Measured time courses of force decay during isometric contractions of rabbit M. gastrocnemius and M. plantaris were employed for model verification, with the finding that our suggested model enhancement proved eminently promising. We discuss implications of our model approach for enhancing muscle models in general, as well as a few aspects regarding the significance of phosphate kinetics as one contributor to muscle fatigue. |
| first_indexed | 2024-12-10T06:36:22Z |
| format | Article |
| id | doaj.art-3f0fd0d3b61e44ad87f015c646dee451 |
| institution | Directory Open Access Journal |
| issn | 1664-042X |
| language | English |
| last_indexed | 2024-12-10T06:36:22Z |
| publishDate | 2020-05-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Physiology |
| spelling | doaj.art-3f0fd0d3b61e44ad87f015c646dee4512022-12-22T01:58:55ZengFrontiers Media S.A.Frontiers in Physiology1664-042X2020-05-011110.3389/fphys.2020.00306521868Exhaustion of Skeletal Muscle Fibers Within Seconds: Incorporating Phosphate Kinetics Into a Hill-Type ModelRobert Rockenfeller0Michael Günther1Michael Günther2Norman Stutzig3Daniel F. B. Haeufle4Tobias Siebert5Syn Schmitt6Kay Leichsenring7Markus Böl8Thomas Götz9Mathematical Institute, University of Koblenz-Landau, Koblenz, GermanyInstitute for Modelling and Simulation of Biomechanical Systems, Computational Biophysics and Biorobotics, University of Stuttgart, Stuttgart, GermanyFriedrich-Schiller-University, Jena, GermanyDepartment of Motion and Exercise Science, University of Stuttgart, Stuttgart, GermanyHertie-Institute for Clinical Brain Research and Center for Integrative Neuroscience, Eberhard-Karls-University, Tübingen, GermanyDepartment of Motion and Exercise Science, University of Stuttgart, Stuttgart, GermanyInstitute for Modelling and Simulation of Biomechanical Systems, Computational Biophysics and Biorobotics, University of Stuttgart, Stuttgart, GermanyInstitute of Solid Mechanics, Technical University Braunschweig, Braunschweig, GermanyInstitute of Solid Mechanics, Technical University Braunschweig, Braunschweig, GermanyMathematical Institute, University of Koblenz-Landau, Koblenz, GermanyInitiated by neural impulses and subsequent calcium release, skeletal muscle fibers contract (actively generate force) as a result of repetitive power strokes of acto-myosin cross-bridges. The energy required for performing these cross-bridge cycles is provided by the hydrolysis of adenosine triphosphate (ATP). The reaction products, adenosine diphosphate (ADP) and inorganic phosphate (Pi), are then used—among other reactants, such as creatine phosphate—to refuel the ATP energy storage. However, similar to yeasts that perish at the hands of their own waste, the hydrolysis reaction products diminish the chemical potential of ATP and thus inhibit the muscle's force generation as their concentration rises. We suggest to use the term “exhaustion” for force reduction (fatigue) that is caused by combined Pi and ADP accumulation along with a possible reduction in ATP concentration. On the basis of bio-chemical kinetics, we present a model of muscle fiber exhaustion based on hydrolytic ATP-ADP-Pi dynamics, which are assumed to be length- and calcium activity-dependent. Written in terms of differential-algebraic equations, the new sub-model allows to enhance existing Hill-type excitation-contraction models in a straightforward way. Measured time courses of force decay during isometric contractions of rabbit M. gastrocnemius and M. plantaris were employed for model verification, with the finding that our suggested model enhancement proved eminently promising. We discuss implications of our model approach for enhancing muscle models in general, as well as a few aspects regarding the significance of phosphate kinetics as one contributor to muscle fatigue.https://www.frontiersin.org/article/10.3389/fphys.2020.00306/fullfatigueendurance timeparameter estimationoptimizationsensitivity analysisbiomechanics |
| spellingShingle | Robert Rockenfeller Michael Günther Michael Günther Norman Stutzig Daniel F. B. Haeufle Tobias Siebert Syn Schmitt Kay Leichsenring Markus Böl Thomas Götz Exhaustion of Skeletal Muscle Fibers Within Seconds: Incorporating Phosphate Kinetics Into a Hill-Type Model Frontiers in Physiology fatigue endurance time parameter estimation optimization sensitivity analysis biomechanics |
| title | Exhaustion of Skeletal Muscle Fibers Within Seconds: Incorporating Phosphate Kinetics Into a Hill-Type Model |
| title_full | Exhaustion of Skeletal Muscle Fibers Within Seconds: Incorporating Phosphate Kinetics Into a Hill-Type Model |
| title_fullStr | Exhaustion of Skeletal Muscle Fibers Within Seconds: Incorporating Phosphate Kinetics Into a Hill-Type Model |
| title_full_unstemmed | Exhaustion of Skeletal Muscle Fibers Within Seconds: Incorporating Phosphate Kinetics Into a Hill-Type Model |
| title_short | Exhaustion of Skeletal Muscle Fibers Within Seconds: Incorporating Phosphate Kinetics Into a Hill-Type Model |
| title_sort | exhaustion of skeletal muscle fibers within seconds incorporating phosphate kinetics into a hill type model |
| topic | fatigue endurance time parameter estimation optimization sensitivity analysis biomechanics |
| url | https://www.frontiersin.org/article/10.3389/fphys.2020.00306/full |
| work_keys_str_mv | AT robertrockenfeller exhaustionofskeletalmusclefiberswithinsecondsincorporatingphosphatekineticsintoahilltypemodel AT michaelgunther exhaustionofskeletalmusclefiberswithinsecondsincorporatingphosphatekineticsintoahilltypemodel AT michaelgunther exhaustionofskeletalmusclefiberswithinsecondsincorporatingphosphatekineticsintoahilltypemodel AT normanstutzig exhaustionofskeletalmusclefiberswithinsecondsincorporatingphosphatekineticsintoahilltypemodel AT danielfbhaeufle exhaustionofskeletalmusclefiberswithinsecondsincorporatingphosphatekineticsintoahilltypemodel AT tobiassiebert exhaustionofskeletalmusclefiberswithinsecondsincorporatingphosphatekineticsintoahilltypemodel AT synschmitt exhaustionofskeletalmusclefiberswithinsecondsincorporatingphosphatekineticsintoahilltypemodel AT kayleichsenring exhaustionofskeletalmusclefiberswithinsecondsincorporatingphosphatekineticsintoahilltypemodel AT markusbol exhaustionofskeletalmusclefiberswithinsecondsincorporatingphosphatekineticsintoahilltypemodel AT thomasgotz exhaustionofskeletalmusclefiberswithinsecondsincorporatingphosphatekineticsintoahilltypemodel |