An approach to measuring change in muscular tissue contraction

In this paper the authors consider a histological muscular component from the point of view of systems theory. Of the smooth and striated types of muscular fibres, the latter have a structural component that permits them to contract. Unlike the visceral striated and cardiac fibres, movements in the skeletal striated fibres are predominantly voluntary. An overlapping of certain fibre components--specifically a sliding movement of the filaments of which the fibre is composed--causes a variation in the overall size of the fibre and therefore of the muscle. The distances covered, whether in contraction or lengthening, vary according to the type of fibre from 1.8 to 3.8 microm, but depend only on the capacity of some filaments to slide over other filaments, with filament size itself remaining unchanged. Our objective is to obtain a metric of this system that will permit us to obtain some idea of the degree of variation in these distances. In future projects it will be possible to extend this theory to other involuntary muscular tissue movements (myocardial tissue, e.g.), in an endeavour to develop a mathematical approach to the study of myocardial processes damaged by electrical conduction problems.     

On the mechanism of muscular contraction.

A thermodynamic analysis is presented for the energy conversion by muscle contraction. During the cyclic processes the major change in energy of the myosin-actin system is due to bond formation between myosin heads and actin. To account for the high efficiency of a working muscle the work done is connected directly to the formation of myosin-actin bond. It is suggested that successively stronger bonds are formed by a stepwise movement of myosin heads over an interval between two troponin molecules on the actin filament. At the end of the interval, where the bond has maximum strength, energy is supplied to break the bond. Here the work is not primarily connected to the 45 degrees rotation of myosin heads as is commonly done. A way of separating the different kinds of energy losses is presented.     

Autonomic energy conversion. I. The input relation: phenomenological and mechanistic considerations

The differences between completely and incompletely coupled linear energy converters are discussed using suitable electrochemical cells as examples. The output relation for the canonically simplest class of self-regulated incompletely coupled linear energy converters has been shown to be identical to the Hill force-velocity characteristic for muscle. The corresponding input relation (the “inverse” Hill equation) is now derived by two independent methods. The first method is a direct transformation of the output relation through the phenomenological equations of the converter; Onsager symmetry has no influence on the result. The second method makes use of a model system, a hydroelectric device with a regulator mechanism which depends only on the operational limits of the converter (an electro-osmosis cell operated in reverse) and on the load. The inverse Hill equation is shown to be the simplest solution of the regulator equation. An interesting and testable series of relations between input and output parameters arises from the two forms of the Hill equation. For optimal regulation the input should not be greatly different in the two limiting stationary states (level flow and static head). The output power will then be nearly maximal over a considerable range of load resistance, peak output being obtained at close to peak efficiency.     

An electrodynamic (moving field) theory of muscular contraction

It is proposed that muscular contraction is the result of electrostatic attraction between oppositely charged areas on actin and myosin filaments. On the latter charged areas are assumed to be moving, always a step ahead of stationary charged areas on actin filaments, the moving charges pulling the stationary charges, hence the actin filaments, with them. It may be noted that electric motors in human technology work on a similar moving field principle. On myosin filaments minute charged areas are assumed to spiral along the surface of the filament on 2 or 3-start helical paths, probably the latter, thus engaging with adjacent actin filaments in a screw-like fashion. The spiralling charges follow each other like peristaltic waves, engaging with an increasing number of static fields on actin filaments as interdigitation proceeds. The source of the electrostatic charges are assumed to be minute voltaic cells, one associated with every myosin head. It is suggested that they could be calcium-magnesium cells, calcium adsorbed by troponin complexes on actin filaments constituting one electrode, and magnesium complexed with ATP on myosin filaments the other. The potential difference that has to exist between actin and myosin filaments, if muscles are to be capable of developing a maximum force of 20 N per cm2, is calculated at about 50 mV.     

Relative intensity of muscular contraction during shivering.

The intensity of cold-induced shivering, quantified by surface electromyography (EMG) and then expressed as a function of the maximal myoelectrical activity (integrated EMG) obtained during a maximum voluntary contraction (MVC), was examined in this study in individuals classified by body fat. In addition, the relationship between shivering and metabolic rate (MR) and the relative contribution of various muscle groups to total heat production were studied. Ten seminude male volunteers, 5 LEAN (less than 11% body fat) and 5 NORM (greater than 15% body fat) were exposed to 10 degrees C air for 2 h. EMG of six muscle groups (pectoralis major, rectus abdominis, rectus femoris, gastrocnemius, biceps brachii, and brachioradialis) was measured and compared with the EMG of each muscle's MVC. A whole body index of shivering, determined from the mass-weighted intensity of shivering of each muscle group, was correlated with MR. After the initial few minutes of exposure, only the pectoralis major, rectus femoris, and biceps brachii continued to increase their intensity of shivering. Shivering intensity was higher in the central muscles, ranging from 5 to 16% of MVC compared with that in the peripheral muscles, which ranged from 1 to 4% of MVC. Shivering intensities were similar in the peripheral muscles for the LEAN and NORM groups, whereas differences occurred in the trunk muscles for the pectoralis major and rectus abdominis. The whole body index of shivering correlated significantly with each individual's increase in MR (r = 0.63-0.97).(ABSTRACT TRUNCATED AT 250 WORDS)     

Structural fluctuations in the steady state of muscular contraction.

Recent studies of the intensity fluctuation spectra of coherent light scattered from striated muscle have demonstrated the existence of large scale fluctuations in position and polarizability at the level of the myofibrillar sarcomere and its major structural subunits during the steady state of contraction. The existence of these fluctuations implies a fluctuating driving force. Various possible fluctuating motions of the thick and thin filaments, A and I bands, and entire sarcomeres are described. The magnitude of the fluctuating forces associated with the making and breaking of cross bridges is estimated. A mechanical model is proposed for coupling structural elements of a single sarcomere to one another and for coupling myofibrillar sarcomeres to one another. It is shown that the fluctuating force generated by the spontaneous making and breaking of cross bridges in conjunction with the model accounts for some of the features of the observed intensity fluctuation spectra.     

Theory of muscle contraction II. Isotonic contraction

The theory of muscle contraction developed in Part I is extended to non-isometric cases. The basic feature of the approach is the strong viscous coupling of the movement of the counterionic (K⁺) layer with the movement of I-filaments. The surface conductance of the K⁺ layer governs the flux of H⁺ along the I-filaments which in turns regulates the rate of ATP hydrolysis. The energy output of the muscle becomes the function of its mechanical activity. By assuming linear dependence of the K⁺ layer's surface conductance on the velocity of shortening Hill's equation has been derived. With a set of reasonably chosen values of the basic parameters of the theory the values of Hill's constants have been computed. The theory has been also shown to provide the observed dependence of the isometric tension on the degree of the myofilamental overlap.     

Caudal ventrolateral medullary cells responsive to muscular contraction

The pressor reflex evoked by muscular contraction (exercise pressor reflex) is held to be an important mechanism in producing the cardiovascular adjustments to static exercise. Recent experiments using lesioning and metabolic labeling methods have indicated that the caudal ventrolateral medulla may be a key integrative site for the reflex evoked by muscular contraction induced by ventral root stimulation. Therefore, we sought to determine whether cells in this region could be associated with the cardiovascular reflex accompanying muscular contraction through analysis of their discharge characteristics. Eighty cells were characterized as to their response to ventral root stimulus-induced static muscular contraction, intra-arterial capsaicin (selective groups III and IV stimulus), and mechanical probing. The cells' receptive fields were also determined by mechanical probing. The receptive fields were usually large, often including all four limbs and the trunk. Four response patterns were observed to static contractions: a brisk initial discharge followed by a gradual return toward control levels (slowly adapting), a brief onset and cessation response, a brief inhibition followed by a slowly adapting discharge, and inhibition alone. Virtually all cells tested were responsive to capsaicin. Histological analysis verified the position of the recorded cells. It is suggested that the cells most likely to participate in the pressor response to muscular contraction were those cells in the general region of the lateral reticular nucleus which responded with an initial and sustained discharge and the cells that were inhibited in the region of the nucleus ambiguus (possible inhibition of vagal outflow).     

An enzymological approach to mitochondrial energy transduction

An approach to the problem of mitochondrial energy transduction is outlined. The approach is based on the fundamental assumption that there is an intimate relation between the mechanisms of enzyme catalysis and energy transduction. The implications of this assumption for the coupling of two chemical reactions and the coupling of a chemical reaction to an ion flux are discussed.