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Cited by 115Cardiomyopathy and Myosin StudiesAdvanced Thermodynamics and Statistical Mechanicsstochastic dynamics and bifurcation

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From Single Molecule Fluctuations to Muscle Contraction: A Brownian Model of A.F. Huxley's Hypotheses

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Marcucci, Lorenzo, Yanagida, Toshio·2012·PLoS ONE
DOI 10.1371/journal.pone.0040042PMC PMC3397984
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Abstract

Muscular force generation in response to external stimuli is the result of thermally fluctuating, cyclical interactions between myosin and actin, which together form the actomyosin complex. Normally, these fluctuations are modelled using transition rate functions that are based on muscle fiber behaviour, in a phenomenological fashion. However, such a basis reduces the predictive power of these models. As an alternative, we propose a model which uses direct single molecule observations of actomyosin fluctuations reported in the literature. We precisely estimate the actomyosin potential bias and use diffusion theory to obtain a brownian ratchet model that reproduces the complete cross-bridge cycle. The model is validated by simulating several macroscopic experimental conditions, while its interpretation is compatible with two different force-generating scenarios.

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Crossref · 10.1371/journal.pone.0040042

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Figures

Figure 1 Cross-bridge cycle (left) and half-sarcomere model (right). Left side: Four states, two detached (upper) and two attached (lower), are considered. In the force generating step, the actomyosin complex oscillates between stable states either by rotating the lever arm domain (scenario 1) or by sliding the myosin head along the actin filament (scenario 2). Right side: Mechanical representation of the half-sarcomere as many parallel myosin heads. In the detached state, thermal fluctuations by a myosin head are constrained only by an asymmetric elastic element [29]; the absence of other interactions is represented by the flat energy landscape. In the attached state, the head also experiences an actomyosin complex energy landscape, , which has a periodicity of and four minima or stable states (see text). The jump process between attached and detached states is driven by the rate functions and () to generate a flashing Brownian ratchet.
Figure 1 Cross-bridge cycle (left) and half-sarcomere model (right). Left side: Four states, two detached (upper) and two attached (lower), are considered. In the force generating step, the actomyosin complex oscillates between stable states either by rotating the lever arm domain (scenario 1) or by sliding the myosin head along the actin filament (scenario 2). Right side: Mechanical representation of the half-sarcomere as many parallel myosin heads. In the detached state, thermal fluctuations by a myosin head are constrained only by an asymmetric elastic element [29]; the absence of other interactions is represented by the flat energy landscape. In the attached state, the head also experiences an actomyosin complex energy landscape, , which has a periodicity of and four minima or stable states (see text). The jump process between attached and detached states is driven by the rate functions and () to generate a flashing Brownian ratchet.CC BY · PubMed Central
Figure 2 Bias of actomyosin energy. The diffusion of a particle linked to an external micro-needle in a periodic potential tilted by a constant bias, , is simulated, and the ratio of forward, , and backward, , jumps for different is reproduced and compared to the experimental data. Red squares, ; green triangles, ; and blue rumble, . Black dots, experimental data from [15]. Continuous lines are the corresponding exponential fits. Simulations show that a bias higher than corresponds to the observed ratio. A value of is chosen as most probable due to the boundary conditions (see text). Insert: Experimental oscillating sub-steps as expected from [1] during the attached state (see fig. S2). Figure adapted from [15].
Figure 2 Bias of actomyosin energy. The diffusion of a particle linked to an external micro-needle in a periodic potential tilted by a constant bias, , is simulated, and the ratio of forward, , and backward, , jumps for different is reproduced and compared to the experimental data. Red squares, ; green triangles, ; and blue rumble, . Black dots, experimental data from [15]. Continuous lines are the corresponding exponential fits. Simulations show that a bias higher than corresponds to the observed ratio. A value of is chosen as most probable due to the boundary conditions (see text). Insert: Experimental oscillating sub-steps as expected from [1] during the attached state (see fig. S2). Figure adapted from [15].CC BY · PubMed Central
Figure 3 Fast tension recovery. Simulations and experimental data for a small and fast length step, , applied to a muscle fiber in isometric contraction. The simulated tensions after the imposed step, (red triangles), and after actomyosin re-equilibration, (blue triangles), are shown and compared to the experimental results (circles; data from [33]). All tensions are normalized with respect to isometric tension . Simulated Tension vs. Time traces are shown in the insert at different , is estimated by the tangent method [41]. Mean valuesstandard deviation over 11 trials are shown. Where error bars are not visible, errors are smaller than the symbol width.
Figure 3 Fast tension recovery. Simulations and experimental data for a small and fast length step, , applied to a muscle fiber in isometric contraction. The simulated tensions after the imposed step, (red triangles), and after actomyosin re-equilibration, (blue triangles), are shown and compared to the experimental results (circles; data from [33]). All tensions are normalized with respect to isometric tension . Simulated Tension vs. Time traces are shown in the insert at different , is estimated by the tangent method [41]. Mean valuesstandard deviation over 11 trials are shown. Where error bars are not visible, errors are smaller than the symbol width.CC BY · PubMed Central
Figure 4 Velocity of contraction at different external loads. Applied tension is reduced or increased with respect to isometric tension at a given time. Simulated Tension vs. Time traces are shown in the insert. Tensions are normalized to the isometric tension, . For different tensions, velocities are calculated from the linear portion of the shortening traces and normalized to the maximum velocity. The simulated velocities vs. tensions (blue triangles) are compared with experimental data (black dots) from [35]. In the concentric region (), the simulations fit the experimental data well even if the velocity is underestimated in the central part (see text). Experimental data for the eccentric region () are not shown, but a qualitative correspondence can be observed with a plateau region at high tensions. Mean valuesstandard deviation over 11 trials are shown. Where error bars are not visible, errors are smaller than the symbol width.
Figure 4 Velocity of contraction at different external loads. Applied tension is reduced or increased with respect to isometric tension at a given time. Simulated Tension vs. Time traces are shown in the insert. Tensions are normalized to the isometric tension, . For different tensions, velocities are calculated from the linear portion of the shortening traces and normalized to the maximum velocity. The simulated velocities vs. tensions (blue triangles) are compared with experimental data (black dots) from [35]. In the concentric region (), the simulations fit the experimental data well even if the velocity is underestimated in the central part (see text). Experimental data for the eccentric region () are not shown, but a qualitative correspondence can be observed with a plateau region at high tensions. Mean valuesstandard deviation over 11 trials are shown. Where error bars are not visible, errors are smaller than the symbol width.CC BY · PubMed Central
Figure 5 Microscopic behaviour of the model Upper: Simulated mean strain per motor during the steady state phase of isotonic contraction at different external tensions compared with experimental data from [8]. Mean strain is well fitted at high , but overestimated at low , where the low number of attached motors may have compromised the experimental analysis, as observed in [8]. Lower: Relative number of attached motors at different loads during the steady state phase of isotonic contraction. Simulation, triangles; experimental data, circles. Mean valuesstandard deviation over 11 trials are shown. Where error bars are not visible, errors are smaller than the symbol width.
Figure 5 Microscopic behaviour of the model Upper: Simulated mean strain per motor during the steady state phase of isotonic contraction at different external tensions compared with experimental data from [8]. Mean strain is well fitted at high , but overestimated at low , where the low number of attached motors may have compromised the experimental analysis, as observed in [8]. Lower: Relative number of attached motors at different loads during the steady state phase of isotonic contraction. Simulation, triangles; experimental data, circles. Mean valuesstandard deviation over 11 trials are shown. Where error bars are not visible, errors are smaller than the symbol width.CC BY · PubMed Central
Figure 6 Predicted efficiency at different velocities Simulation of the efficiency of contraction, as predicted by the model compared to experimental data (circles from [38], green line). Efficiency is computed as tension times velocity divided by the chemical energy consumed [37] (triangles) and following the method described in [39] (squares). Mean valuesstandard deviation over 11 trials are shown. Where error bars are not visible, errors are smaller than the symbol width.
Figure 6 Predicted efficiency at different velocities Simulation of the efficiency of contraction, as predicted by the model compared to experimental data (circles from [38], green line). Efficiency is computed as tension times velocity divided by the chemical energy consumed [37] (triangles) and following the method described in [39] (squares). Mean valuesstandard deviation over 11 trials are shown. Where error bars are not visible, errors are smaller than the symbol width.CC BY · PubMed Central

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Metadata

Authors
Marcucci, L., & Yanagida, T.
Affiliations
  • The University of Osaka (JP)
  • RIKEN (JP)
Corresponding author
Marcucci, Lorenzo
ORCID
Marcucci, Lorenzo
Venue
PLoS ONE
Publisher
Public Library of Science (PLoS)
Published
2012-07-16
Volume
7
Issue
7
Pages
e40042
ISSN
1932-6203 (ISSN-L)
DOI
10.1371/journal.pone.0040042
PMC
PMC3397984
OpenAlex
W2100332633
Cited by
115
References
44
Citations by year
2025: 1 · 2024: 1 · 2023: 2 · 2021: 21 · 2020: 10 · 2019: 13 · 2018: 10 · 2017: 22 · 2016: 16 · 2015: 8 · 2014: 5 · 2013: 4 · 2012: 2
FWCI
3.91
Type
journal article
Language
en
Open access
Licence
Locations
  • PLoS ONE (publishedVersion, cc-by)
  • Europe PMC (PubMed Central) (publishedVersion, cc-by)
  • PubMed Central (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • Padua Research Archive (University of Padova) (submittedVersion, cc-by)
  • RePEc: Research Papers in Economics (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
  • Figshare (submittedVersion, cc-by)
Funders
Ministry of Education, Culture, Sports, Science and Technology
Topics
  • Health Sciences › Medicine › Cardiology and Cardiovascular Medicine › Cardiomyopathy and Myosin Studies
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › stochastic dynamics and bifurcation
Keywords
muscle contraction, actomyosin, cross-bridge cycling, Huxley model, potential bias, diffusion theory, actin-myosin interaction, muscle force production
MeSH terms
Actomyosin, Diffusion, Models, Biological, Muscle Contraction, Sarcomeres, Temperature, Thermodynamics

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