In , Hill described the relation between force (P=load) and initial velocity of when a muscle fiber generating the maximum isometric force Po is first made slack, Figure Schematic drawing of experimental arrangement to apply quick. and P0 is the force exerted at zero speed, i.e. in an isometric contraction. He called this with a curved force-velocity relationship similar to that in frog's muscle. The However, there is at presentno other evidence for this view than super-. The force velocity relationship is the observation that muscle force and Hill's original formula includes two constants in addition to a measure of maximum isometric force and describes a hyperbolic relationship View More on Instagram.
From Edman [ 5 ]. Thus, they obtained P-V relations at various times during the course of isometric force development as shown in Figure 5B.
The value of Vmax was found to remain unchanged irrespective of the time during the development of isometric tension. This result can easily be accounted for on the basis of the Huxley contraction model, since Vmax results from the balance between positive and negative forces at both sides of the equilibrium position 0, and therefore independent of the number of A-M links Figure 3C.
Meanwhile, Cecchi et al. P-V relations obtained at various times during the course of isometric force development. A Records showing length upper traces and force lower traces changes when the fiber was subjected to ramp-shaped releases with solid line or without broken line at 75 ms ams band ms c after the beginning of stimulus. B P-V relations obtained at 75 ms ams band ms c after the beginning of stimulus. They obtained P-V relations under various auxotonic loads Figure 6.
The shape of the auxotonic P-V relation was convex upwards, reflecting the extremely slow velocity when the fiber starts shortening under auxotonic loads. This seems to suggest that the kinetics of actin-myosin interaction might be more or less similar during both isotonic shortening and auxotonic shortening in the high force region. P-V relations under various auxotonic loads in maximally stimulated single frog muscle fibers. Broken line indicates the double hyperbolic P-V relation obtained from isotonic shortening experiments.
Force-Velocity Relation: Its Implications about Molecular Mechanism of Muscle Contraction
Inset shows length upper traces and force lower traces changes when a muscle fiber generating the maximum isometric force Po is first made slack, and then subjected to auxotonic loads with different compliance values. Dotted lines in both length and force records show the development of isometric force when the fiber length is kept at the slackened length.
Note that, after being made to slack, the fiber starts shortening against auxotonic load with extremely small velocities compared to the velocity of subsequent shortening. P-V relation during auxotonic shortening after normalization of forces P during auxotonic shortening. A Diagram showing method of normalization of P relative to Piso during isomeric force development at the same time t after the beginning of auxotonic shortening and force development.
Isotonic Velocity Transients and Its Explanation in Terms of Attached Myosin Head Distribution Experiments with whole frog muscle are inadequate to record time course of muscle shortening at its early phase, because of mechanical vibrations when muscle starts shortening against a massive load [ 8 ]. To make this point clear, Civan and Podolsky [ 9 ] performed experiments, in which the early phase of isotonic shortening of isolated single frog muscle fibers was recorded.
To avoid mechanical vibrations at the beginning of shortening, they used a steel spring with a length much longer than the distance of fiber shortening, so that the fibers shortened by pulling the long spring, so that the fiber shortening took place under practically constant load.
By this method, they could successfully record the early phase of isotonic fiber shortening. They found that, at the beginning of isotonic shortening, the fiber first showed non steady shortening resembling damped sine waves.
As can be seen in Figure 8, the fiber shortens initially at a velocity higher than the subsequent constant velocity.
The velocity then slows down and again increase until it reaches a constant value. Upper and lower records show fiber shortening and step changes in load, respectively. The magnitude of step changes in load is given as fractions of Po. As the Huxley contraction model Figure 3 only describes distribution of myosin head attached to actin filament during constant velocity shortening, Podolsky and Nolan [ 10 ] proposed another contraction model to account for the isotonic velocity transients Figure 9.Force velocity relationship
In contrast with the Huxley contraction model, the Podolsky-Nolan model assumes large values of f and a very small value of g in the positive x region, so that all myosin heads passing through this region form A-M links irrespective the velocity of filament sliding.
In the negative x region, g remains to be very small over a distance from the equilibrium position 0 and then increases to a large value Figure 9. As the result, the mode of distribution of A-M link under various loads is markedly different from that in the Huxley contraction model Figure By some additional assumptions, the Podolsky-Nolan model can explain not only the isotonic velocity transients, but also other muscle contraction characteristics and also heat measurement results.
Podolsky-Nolan contraction model constructed to explain the isotonic velocity transient. Upper and middle panel show f and g, i.
CV Physiology: Force-Velocity Relationship
Lower panel shows dependence of elastic constant k of A-M link on x. Values of P are given at the left of diagrams. In each diagram, A-M link distribution immediately after quick changes in load is given by shaded area, while the subsequent steady A-M link distribution is given by solid line.
Schematic drawing of experimental arrangement to apply quick changes in load in two arbitrary steps.
A single fiber P is mounted between force transducer T and lever L with clips C1 and C2, and stimulated maximally with Pt wire electrodes.
Lever L is pivoted at A and loaded by spring F1, which is hooked to lever L and another lever K, so that the length of F1 can be changed by micromanipulator G1 carrying K. Long arms of L and K are restrained by pairs of electromagnetically controlled stops S1 and S2 and S3 and S4, respectively.
Short arm of L serves as a vane interrupting light bean C directed towards photodiode not shown to serve as displacement transducer recording fiber length changes. With a pair of additional springs F2 and F3, whose lengths are adjusted by microman3 ipulators G2 and G3, the length of F1 can be changed quickly when S3 and S4 are removed to produce movement of K.
Oscillation of K is damped with Y shaped dashpot device H. After the fiber develops the maximum isometric force Po, stops restraining lever motion are removed in various sequences, so that the amount of load on the fiber can be changed in two arbitrary steps, as shown in Figure 12 and 13 From ref.
The early time course of isotonic shortening was similar to the isotonic velocity transients reported by Civan and Podolsky [ 9 ], while the early time course of isotonic lengthening was variable. The values of P are expressed relative to Po on the left of each record. Records of experiments, in which the load on the fiber was increased quickly after a period of isotonic shortening under a load of 0. Note marked oscillatory length changes with alternate lengthening and shortening.
To account for the marked fiber length oscillations with alternate fibre lengthening and shortening shown in Figure 13, Sugi and Tsuchiya [ 11 ] constructed a contraction model shown in Figure The dependence of the values of f and g, i.
Sugi-Tsuchiya contraction model constructed to explain the marked oscillatory fiber length changes following quick increases in load. The values of rate constants f and g for the formation and the breaking of A-M links, respectively, are shown as functions of distance from the myosin head equilibrium position 0.
As described above, no definite conclusion can be reached about what is actually taking place in muscle, though various contraction models have been presented to explain mechanical responses of muscle fibers in terms of changes in the A-M link distribution. Much more experimental work is needed for the full understanding of contraction mechanism.
Force-Velocity Relation in Single Skinned Muscle Fibers To obtain information about the molecular mechanism of muscle contraction, the use of intact muscle fibers has serious limitations resulting from difficulties in precisely control chemical and ionic conditions around the myofilaments. The difficulties can be overcome by the use of skinned muscle fibers, from with surface membrane is removed by mechanical or chemical means. To eliminate the gap between contraction characteristic of intact muscle or muscle fibers and biochemical studies on actomyosin ATPase reaction steps in solution, where the three-dimensional myofilament lattice is destroyed, skinned fibers are widely used and their characteristics including the force-pCa relation and MgATP concentration dependence of force development and shortening velocity have been obtained [ 1213 ].
Force velocity relationship | S&C Research
Another great advantage in the use of skinned fibers is that the rate of ATP hydrolysis by the contractile system can be measured simultaneously with mechanical experiments by measuring the rate of ADP production by NADH fluorescence [ 14 ]. Due to structural instability of skinned fibers, however, it is difficult to obtain enough data points to obtain P-V relations, since fiber deterioration slowly proceeds in each contraction-relaxation cycle by the application of contracting and relaxing solutions [ 12 ].
Until the early s, it was necessary for us to use hand-made mechanical or electronic elements to construct such an experimental setup such as shown in Figure 9, with enormous technical skill and patience, because the performance of commercially available electronic devices at that time were not satisfactory for our purpose.
Fortunately, it is now possible to perform sophisticated mechanical experiments including multi-step load changes and ramp decreases in force with instruments commercially available Aurora Scientific Inc. They found that, in the presence of the antibody 1.
In response to ramp decreases in force, skinned fibers shortened with velocities increasing with decreasing force, reaching a maximum at zero force. The P-V relations thus obtained are presented in Figure Despite the decreased steady isometric force, the value of Vmax remained unchanged Figure 16Aand when the P-V curves were found to be identical if they were normalized with respect to the maximum steady force attained Figure 16B.
These results indicate that the decrease in isomeric force by the antibody results from decrease in the number of myosin heads involved in force generation, while all myosin heads hydrolyze ATP irrespective of whether they generate force or do not generate force; in other words, individual myosin molecules in myosin filaments no longer generate force if the antibody attach to their subfragment-2 region, while their ATPase activity remains unchanged Figures 17 and Effect of antibody to myosin subfragment-2 on the isometric force development and the MgATPase activity in skinned muscle fibers.
The records were obtained before application Aand after min B and min C after application of antibody to myosin subfragment-2 1. Times of application of contracting and relaxing solutions are indicated by upward and downward arrows, respectively.
This relationship is altered by changes in both preload and inotropy. The former shares some similarities with skeletal muscle; the latter, however, is unique to cardiac muscle. How Preload Affects the Force-Velocity Relationship If preload is increased, cardiac muscle fibers will have a greater velocity of shortening at a given afterload see figure. Conversely, if preload decreases, the velocity of shortening decreases at a given afterload. This occurs because the length-tension relationship dictates that as the preload is increased, there is an increase in active tension development.
Once the fiber begins to shorten, the increased tension generating capability at the increased preload results in a greater velocity of shortening.
In other words, increasing the preload enables to muscle to contract faster against a given afterload. Note that increasing preload increases the maximal isometric force Fmaxas well as increases the shortening velocity at a given afterload, but does not alter not alter Vmax.
If the inotropic state of the cardiac fiber is increased, there is a parallel shift in the force-velocity curve such that there is an increase in both Vmax and in maximal isometric force Fmax figure 3. The increase in Vmax is particularly noteworthy because Vmax represents the intrinsic capability of a muscle fiber to generate force independent of load.
Therefore, Vmax is sometimes used in experiments as an index or measure of inotropy for a muscle fiber.