Fig. 1: A schematic of experimental design.

a Preschoolers and four groups of adults (sedentary, novice, experienced, and elite runners) were studied. EMGs (15 muscles) were collected during over-ground (preschoolers) or treadmill (all adults) running, over 1–3 sessions. b Pre-processed EMGs of every session from each subject were decomposed into time-invariant muscle synergies activated by time-varying coefficients using the non-negative matrix factorization algorithm (NMF). The NMF captures the multivariate structure of variability embedded in EMGs. c Vertical ground reaction force (VGRF) of each running cycle was recorded for deriving, together with body mass and weight (m*g), the acceleration (a), the double integration of which yielded the vertical center-of-mass (CoM) displacement (see Methods for the assumption used for determining the integration constant). A plot of the VGRF against the CoM displacement produced a hysteresis loop, the area within which provided an estimate of the mechanical energy loss during each cycle. Source data for b and c are available as a Source Data file.