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The target article by Dr. Prilutsky is based on three incorrectly derived mathematical rules concerning force-sharing among synergistic muscles associated with a cost function that minimizes the sum of the cubed muscle stresses. Since these derived rules govern all aspects of Dr. Prilutsky's discussion and conclusion and form the basis for his proposed theory of coordination between one-and two-joint muscles, most of what is said in the target article is confusing or misleading at best or factually wrong at worst. The aim of our commentary is to sort right from wrong in Dr. Prilutsky's article within space limitations that do not allow for detailed descriptions of mathematical proofs and explicit discussions of the relevant experimental literature.

Linear and nonlinear optimal designs have been used abundantly to predict the forces exerted by individual muscles for everyday movements such as walking. Individual muscle force predictions for athletic movements, those involving large ranges of motion and fast velocities of muscle contractions, are almost nonexistent. The purpose of this paper is to illustrate some of the design characteristics that must be considered for predicting individual muscle forces in athletic movements. To do this, the load sharing between two muscles, derived from nonlinear optimal designs, is considered in two ways: (a) in hypothetical experiments of muscle contractions, and (b) in real experiments of knee extension movements performed by one subject. The results suggested that additional design considerations must be made when predicting forces in athletic movements compared to everyday movements.

In this response, the major criticisms of the target article are addressed. Terminology from the target article that may have caused some confusion is clarified. In particular, the tasks that have the basic features of muscle coordination, as identified in the target article, have been limited in scope. Anew metabolic optimization criterion suggested by Alexander (2000) is examined for its ability to predict muscle coordination in walking. Issues concerning the validation of muscle force predictions, the rules of muscle coordination, and the role of directional constraints in coordination of two-joint muscles are discussed. It is shown in particular that even in one-joint systems, the forces predicted by the criterion of Crowninshield and Brand (1981) depend upon the muscle moment arms and the physiological cross-sectional areas in much more complex ways than either previously assumed in the target article, or incorrectly derived by Herzog and Ait-Haddou (2000). It is concluded that the criterion of Crowninshield and Brand qualitatively predicts the basic coordination features of the major one- and two-joint muscles in a number of highly skilled, repetitive motor tasks performed by humans under predictable conditions and little demands on stability and accuracy. A possible functional significance of such muscle coordination may be the minimization of perceived effort, muscle fatigue, and/or energy expenditure.