M.Sc Thesis

M.Sc StudentVatury Nisim
SubjectCharacterization of the Action-Reaction Law of the Muscle:
Testing the Prevailing Models
DepartmentDepartment of Biomedical Engineering
Supervisor ASSOCIATE PROF. Amir Landesberg


The study characterizes the `action-reaction law` of the muscle. It integrates our knowledge from isolated fiber studies and theoretical models, and relates it to the immediate response of the human muscle to imposed perturbations. The muscle force-response to fast perturbations is of great importance in daily life activities. However, the dominant underlying mechanism is vague, although muscle functions were investigated for more than a century. The prevailing theories suggest that the force-response is mediated by the stretch reflex, the viscoelastic properties of the tendons and viscoelastic proteins (collagen or titin), and by the actomyosin cross-bridges (XBs), the molecular motors of the muscles. The research tests three models to scrutinize this enigma: Hill’s model, Huxley’s model of XB attachment-detachment and our model of the sarcomeric control of contraction (SCC). The three models yield different predictions, that were tested experimentally. The SCC suggests that the force-response (macro) is dominated by XB dynamics (nano) and the force-response to ramp extension is determined by the product of the initial force, perturbation velocity and duration. 

The study was approved by the institutional Helsinki committee. The volunteers (n=15) placed the tip of the index finger on the lever arm of a computer-controlled motor. The controller imposed various ramps at three velocities (50, 100, 150 mm/s), for three durations (20,40,60 msec), and from three different initial isometric tetanic forces (5,10,15 N). The controller provides high resolutions of time (0.2 msec) position (1 µm) and force (4 mN) measurements. The study investigated the functions of the flexor-digitorum superficialis, but relates to the striated muscle “action-reaction” in general.

The main characteristics of the `action reaction` are: (1) The “reaction” is instantaneous and independent of the stretch-reflex. (2) The force-response rate is huge and proportional to the initial isometric force level. The rate is about 350 % of the baseline force per second, for relative slow ramp velocity of 50 mm/s. (3) The response is determined by the product of the initial force, perturbation velocity and duration:


The dependence of the force-response on the product of the initial force and the displacement negates Hill’s model prediction. Refuting Hill’s model suggests that the XBs play the dominant role in the observed responses. The prolong and consistent increase in the force negates Huxley’s model that predicts attenuation of the force-response due to the increase in the XB detachment rate.

The increase in the force during lengthening is due to the increase in number of XBs. It is achieved by decreasing XB weakening rate. According to the SCC model the sarcomere velocity affects the rate of XB weakening, and lengthening decreases the XB weakening rate. Interestingly, the coefficient G* in the above equation is in the expected order of what was found in isolated muscle fibers. It strengthens the notion that the nano dictates the whole muscle response.

Beyond the scientific significance the study may have practical merits for sport (stretch-shortening cycle), sport medicine (prevention of injuries), and preservation of muscle function in the elderly.