49
views
0
recommends
+1 Recommend
0 collections
    4
    shares
      • Record: found
      • Abstract: found
      • Article: found
      Is Open Access

      A Mathematical Model of Muscle Containing Heterogeneous Half-Sarcomeres Exhibits Residual Force Enhancement

      research-article
      , , *
      PLoS Computational Biology
      Public Library of Science

      Read this article at

      Bookmark
          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          Abstract

          A skeletal muscle fiber that is stimulated to contract and then stretched from L 1 to L 2 produces more force after the initial transient decays than if it is stimulated at L 2. This behavior has been well studied experimentally, and is known as residual force enhancement. The underlying mechanism remains controversial. We hypothesized that residual force enhancement could reflect mechanical interactions between heterogeneous half-sarcomeres. To test this hypothesis, we subjected a computational model of interacting heterogeneous half-sarcomeres to the same activation and stretch protocols that produce residual force enhancement in real preparations. Following a transient period of elevated force associated with active stretching, the model predicted a slowly decaying force enhancement lasting >30 seconds after stretch. Enhancement was on the order of 13% above isometric tension at the post-stretch muscle length, which agrees well with experimental measurements. Force enhancement in the model was proportional to stretch magnitude but did not depend strongly on the velocity of stretch, also in agreement with experiments. Even small variability in the strength of half-sarcomeres (2.1% standard deviation, normally distributed) was sufficient to produce a 5% force enhancement over isometric tension. Analysis of the model suggests that heterogeneity in half-sarcomeres leads to residual force enhancement by storing strain energy introduced during active stretch in distributions of bound cross-bridges. Complex interactions between the heterogeneous half-sarcomeres then dissipate this stored energy at a rate much slower than isolated cross-bridges would cycle. Given the variations in half-sarcomere length that have been observed in real muscle preparations and the stochastic variability inherent in all biological systems, half-sarcomere heterogeneity cannot be excluded as a contributing source of residual force enhancement.

          Author Summary

          Textbooks often state that the force produced by a contracting muscle depends on its length. Nearly 60 years ago, it was discovered that this length-tension relationship is violated if the muscle is stretched to a given length while contracting, in which case the muscle produces more force than if it was stretched to the given length prior to contraction. This effect is known as residual force enhancement, and its mechanism remains controversial. Understanding residual force enhancement is important because it potentially affects outcomes of many in vivo and in vitro experiments where contracting muscles or muscle preparations are stretched. In this work, we use a computational model of half-sarcomeres connected in series to show that residual force enhancement is an emergent behavior of the contractile system when the half-sarcomeres are not completely identical. Force enhancement in the model shares several key properties with the phenomenon observed in real muscle, including independence from the rate of stretch and proportionality to stretch magnitude. Enhancement in the model is produced by a previously undescribed mechanism in which complex interactions between the heterogeneous half-sarcomeres dissipate strain-energy from the imposed stretch at very slow rates, creating a long-lasting, enhanced level of force.

          Related collections

          Most cited references32

          • Record: found
          • Abstract: not found
          • Article: not found

          Muscle structure and theories of contraction.

            Bookmark
            • Record: found
            • Abstract: found
            • Article: not found

            Residual force enhancement after stretch of contracting frog single muscle fibers

            Single fibers from the tibialis anterior muscle of Rana temporaria at 0.8-3.8 degrees C were subjected to long tetani lasting up to 8 s. Stretch of the fiber early in the tetanus caused an enhancement of force above the isometric control level which decayed only slowly and stayed higher throughout the contraction. This residual enhancement was uninfluenced by velocity of stretch and occurred only on the descending limb of the length-tension curve. The absolute magnitude of the effect increased with sarcomere length to a maximum at approximately 2.9 micrometers and then declined. The phenomenon was further characterized by its dependence on the amplitude of stretch. The final force level reached after stretch was usually higher than the isometric force level corresponding to the starting length of the stretch. The possibility that the phenomenon was caused by nonuniformity of sarcomere length along the fiber was examined by (a) laser diffraction studies that showed sarcomere stretch at all locations and (b) studies of 9-10 segments of approximately 0.6-0.7 mm along the entire fiber, which all elongated during stretch. Length-clamped segments showed residual force enhancement after stretch when compared with the tetanus produced by the same segment held at the short length as well as at the long length. It is concluded that residual force enhancement after stretch is a property shown by all individual segments along the fiber.
              Bookmark
              • Record: found
              • Abstract: not found
              • Article: not found

              The force exerted by active striated muscle during and after change of length.

                Bookmark

                Author and article information

                Contributors
                Role: Editor
                Journal
                PLoS Comput Biol
                plos
                ploscomp
                PLoS Computational Biology
                Public Library of Science (San Francisco, USA )
                1553-734X
                1553-7358
                September 2011
                September 2011
                29 September 2011
                : 7
                : 9
                : e1002156
                Affiliations
                [1]Department of Physiology and the Center for Muscle Biology, University of Kentucky, Lexington, Kentucky, United States of America
                University of Calgary, Canada
                Author notes

                Conceived and designed the experiments: SGC KSC. Performed the experiments: SGC PCH. Analyzed the data: SGC. Contributed reagents/materials/analysis tools: SGC PCH KSC. Wrote the paper: SGC KSC.

                Article
                PCOMPBIOL-D-11-00502
                10.1371/journal.pcbi.1002156
                3182863
                21980268
                b09a13df-c9d5-4f0f-88d0-db7363a72e63
                Campbell et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
                History
                : 11 April 2011
                : 20 June 2011
                Page count
                Pages: 11
                Categories
                Research Article
                Biology
                Biophysics
                Biomechanics
                Biophysics Simulations
                Computational Biology
                Biophysic Al Simulations

                Quantitative & Systems biology
                Quantitative & Systems biology

                Comments

                Comment on this article