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, Δlm, and a/P0, 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: α¯⋅Δlm=φ¯0(a/P0)Δlm=−Δg where Δg   is the free energy change accompanying the hydrolysis of one ATP molecule while α¯ and φ¯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 α¯, not φ¯0, is the true contractile   force. The values of α¯ and of φ¯0 have been calculated for three muscles. The equation has been successfully applied to actin polymerization-based motility. The value of Δg in different muscles under different environmental conditions can be easily determined from this equation with the value of Δlm derived experimentally.