Evaluation of the sliding distance in shortening muscles and in polymerizing actin from Hill's force-velocity equation.

The relationship derived earlier between the sliding distance, Deltal(m), and a/P(0), the characteristic parameter of Hill's force-velocity equation for muscle contraction, was re-formulated in order to get a more general relationship which can be applied also to other biological mechano-chemical energy converters: alpha x Deltal(m)=phi (0)(a/P(0))Deltal(m)=-Deltag where Deltag is the free energy change accompanying the hydrolysis of one ATP molecule while alpha and phi (0) are, respectively, the average forces developed by a myosin head-actin complex which are responsible for shortening and for isometric tension generation. These two molecular forces are different in magnitude and in nature and it is demonstrated that alpha , not phi (0), is the true contractile force. The values of alpha and of phi (0) have been calculated for three muscles.

The simultaneous collapse of both the swinging crossbridge theory of muscle contraction and the in vitro motility essays.

In the early seventies we discovered that isolated, active, myosin fragments can induce movement and tension generation by actin filaments in both in vitro and in vivo systems, employing a variety of techniques. It was not in line with the domineering swinging crossbridge theory of muscle contraction. We then proposed an hydrodynamic mechanism which explained our results and was applied to muscle contraction and to other biological engines.

A new outlook on the energetics of muscle contraction.

Analysis of experimental data on two muscles demonstrates that, in contracting striated muscle, the total rate of ATP splitting, nu(t) (number of ATP molecules split per active myosin head per second), comprises of three separate components: nu(p), which is required for the generation of the contractile force P which is equal to the external load; nu(v) which is devoted to the development of the velocity of shortening V; and nu(w), which is responsible for the production of the mechanical power (PV). Nu(p) is proportional to P and nu(v) to V, which means that the sliding distance is independent of P. The mechanical power was found to be equal to the free energy change associated with the hydrolysis of nu(w), which means that the thermodynamic efficiency of the power-producing component is practically 100%.

Do the bacterial flagellar motor and ATP synthase operate as water turbines?

Despite much progress in the study of the rotary motors ATP synthase (F0F1) and the bacterial flagellar motor, we still cannot answer the most basic and simple question, how the random thermal movement of H+ (or Na+) ions down a pH (or Na+) gradient spins the rotors. I suggest consideration of the possibility that the motors operate like water turbines, i.e.

Are rotors at the heart of all biological motors?

Biological motors are generally divided into two classes: 1) rotary motors. These include ATP synthase (F0-F1) and the bacterial flagellar motor which are driven by proton and Na+ gradients., 2) linear motors.