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Each beat of the heart completes the final step in a sequence of events commencing with electrical excitation-triggered release of Ca 2+  from the sarcoplasmic reticulum which, in turn, triggers ATP-hydrolysis-dependent mechanical contraction. Given that  Thermodynamics  is inherently detail-independent, the heart can be thus be viewed as a mechanical pump – the generator of pressure that drives blood through the systemic and pulmonary circulations. The beat-to-beat pressure-volume work (W) of the heart is relatively straightforward to measure experimentally. Given an ability to measure, simultaneously, the accompanying heat production or oxygen consumption, it is trivial to calculate the  mechanical  efficiency: ε = W/ΔH where ΔH is the change of enthalpy: (W + Q),  Q  representing the accompanying production of heat. But it is much less straightforward to measure the thermodynamic efficiency:  η  = W/ΔG  ATP  , where ΔG  ATP   signifies the Gibbs Free Energy of ATP hydrolysis. The difficulty arises because of uncertain quantification of the substrate-dependent yield of ATP - conveniently expressed as the P/O 2  ratio. P/O 2  ratios, originally (“classically”) inferred from thermal studies, have been considerably reduced over the past several decades by re-analysis of the stoichiometric coefficients separating sequential steps in the electron transport system – in particular, dropping the requirement that the coefficients have integer values. Since the early classical values are incompatible with the more recent estimates, we aim to probe this discrepancy with a view to its reconciliation. Our probe consists of a simple, thermodynamically constrained, algebraic model of cardiac mechano-energetics. Our analysis fails to reconcile recent and classical estimates of PO 2  ratios; hence, we are left with a conundrum.

frontiers in physiology

An Equivocal Final Link – Quantitative Determination of the Thermodynamic Efficiency of ATP Hydrolysis – Sullies the Chain of Electric, Ionic, Mechanical and Metabolic Steps Underlying Cardiac Contraction