Energetics of Contraction

Abstract

Muscles convert energy from ATP into useful work, which can be used to move limbs and to transport ions across membranes. The energy not converted into work appears as heat. At the start of contraction heat is also produced when Ca(2+) binds to troponin-C and to parvalbumin. Muscles use ATP throughout an isometric contraction at a rate that depends on duration of stimulation, muscle type, temperature and muscle length. Between 30% and 40% of the ATP used during isometric contraction fuels the pumping Ca(2+) and Na(+) out of the myoplasm. When shortening, muscles produce less force than in an isometric contraction but use ATP at a higher rate and when lengthening force output is higher than the isometric force but rate of ATP splitting is lower. Efficiency quantifies the fraction of the energy provided by ATP that is converted into external work. Each ATP molecule provides 100 zJ of energy that can potentially be converted into work. The mechanics of the myosin cross-bridge are such that at most 50 zJ of work can be done in one ATP consuming cycle; that is, the maximum efficiency of a cross-bridge is ∼50%. Cross-bridges in tortoise muscle approach this limit, producing over 90% of the possible work per cycle. Other muscles are less efficient but contract more rapidly and produce more power.

A myosin II nanomachine mimicking the striated muscle

“…5b). In this case, the correction for the effect of the random orientation of motors would increase ε to 0.31, similar to muscle values 24 . The reduction of ε for N  < 32 is accounted for by a corresponding reduction in the power delivered per head, ( P max / N  = ) P max,h (Fig.…”

“…As detailed in Methods, the rate functions for the state transitions and their strain-dependence (see Supplementary Fig. 6 and Supplementary Table 1) are first defined to simulate the mechanics and energetics of the fast skeletal muscle of mammals at the same temperature (23 °C) 24–27 and then used to fit the output of the nanomachine.

Fig. 4Model simulation of the mechanical output of the machine.

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“…6b). Detachment from A2 is the rate limiting step in the cycle in isometric conditions, when the rate of ATP splitting is minimum (~11 s −1 per myosin head at room temperature 10,24,27 ) and the fraction of heads attached (the duty ratio) is maximum (~0.3) 23 . With the reduction of the load the rate of ATP splitting increases no more than 3 times 24 , which cannot explain the corresponding increase in power 28 .…”

“…Detachment from A2 is the rate limiting step in the cycle in isometric conditions, when the rate of ATP splitting is minimum (~11 s −1 per myosin head at room temperature 10,24,27 ) and the fraction of heads attached (the duty ratio) is maximum (~0.3) 23 . With the reduction of the load the rate of ATP splitting increases no more than 3 times 24 , which cannot explain the corresponding increase in power 28 . Under these conditions, the maximum power can be predicted only by assuming that, during shortening, the attached myosin heads can rapidly regenerate the working stroke by slipping to the next actin farther from the centre of the sarcomere during the same ATPase cycle 10,28,30–34 (step “slip” in Fig.…”

“…The ratio between P max and the corresponding total ATP split per second is the mechanical energy delivered per ATP, that is (5400 zJ s −1 /480 s −1  = ) 11.2 zJ. Thus, with a free energy of the ATP hydrolysis of 110 zJ 24 , the efficiency of the nanomachine ( ε ) would be (11.2/110 = ) 0.1, at least three times lower than that reported for fast mammalian muscle (0.3–0.4) 24 . Taking into account that the random orientation of the motors reduces the force by 45%, the machine with correctly oriented motors would produce a work per ATP of 20 zJ, with ε still significantly lower than that in the muscle.…”