The legacy of A. V. Hill's Nobel Prize winning work on muscle energetics

Figures

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  Figure 1. A. V. Hill's Nobel medal Photo: N. A. Curtin, personal collection. Used with permission from the Nobel Foundation.

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  Figure 2. A. V. Hill (centre) and other physiologists aboard the SS Minnekahda on the voyage to the first International Physiological Congress to be held in North America in 1929 From the Physiological Society's Photographic Collection with permission.

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  Figure 3. Among many other roles during World War 2, Hill served as Member of Parliament for Cambridge University and visited India on behalf of the Royal Society to research and prepare recommendations for the future of science and medical education A, A. V. Hill entering Parliament in 1940. Used with permission from the Churchill Archives Centre, The Papers of Professor A. V. Hill, AVHL II 5/123. B, Hill during his Indian visit in 1944 with Dr S. S. Bhatnagar FRS, the first Director‐General of the Indian Board of Scientific and Industrial Research. Used with permission from the Churchill Archives Centre, The Papers of Professor A. V. Hill, AVHL II 5/119.

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  Figure 4. A, improvements in the speed of thermopile response Records showing time course of thermopile output in response to a brief heating pulse. A, 1920 (lower time scale); B, 1933; C, 1933, D, 1937; E, 1938. Reproduced from Hill (1939b ), used with permission from IOP Publishing. B, the first heat records from a single frog muscle fibre. Top left: thermopile output in response to single stimulus pulses, showing the all‐or‐none response (4 V, no response; 5 and 6 V, same amplitude response) at 15°C. Top right: thermopile output during 5 s stimulation at 3°C. Lower records show signals adjusted to account for heat lost during recording and converted to temperature units for twitch (left) and tetanus (right). Fibre dimensions: length, 4.3 mm; diameter, 150 μm; mass, 80 μg. From Curtin et al. (1981) used with permission from John Wiley & Sons.

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  Figure 5. Thermopiles for measuring muscle heat production A, diagram of chamber and thermopile used by Fenn (1923). A pair of sartorius muscles (only one shown, labelled ‘M’) lie along each surface of a thermopile (therm), over the active thermocouples. The thermocouples were composed of constantan‐silver created by electroplating (Wilson & Epps, 1919). The thermopile is held between two paraffin‐filled glass tubes; these serve to keep the reference thermocouples at a constant temperature. The muscle is stimulated via fine platinum wires (e1 and e2). The thermopile and muscle are enclosed in a glass chamber that allows the apparatus to be immersed in an isothermal water bath. Figure from Fenn (1923) used with permission from John Wiley & Sons. B, a contemporary thermopile (Barclay, 2015), consisting of antimony–bismuth thermocouples created using vacuum deposition (Mulieri et al. 1977). The reference thermocouples are clamped in a gold‐plated brass frame (F). A muscle fibre bundle (M; from a mouse soleus, length, ∼10 mm) lies along one surface of the thermopile (therm) over the active thermocouples. The muscle is connected, using aluminium T‐clips (C), at one end to the frame and at the…

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  Figure 6. Use of Hill's equation to describe the relationship between fibre force output and Ca2+ concentration The examples are from skinned single fibres of human vastus lateralis and show examples of a slow‐twitch fibre (A) and a fast‐twitch fibre (B). [Ca2+] is expressed in logarithmic form, where pCa = −log10([Ca2+]). The values of the two parameters of the Hill equation are shown in each panel. The curve for slow fibres is less steep (lower n) but reaches 50% of maximum force at a similar [Ca2+] as for fast fibres. From Linari et al. (2004), used with permission from John Wiley & Sons.

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  Figure 7. Nobel Prize winners A. V. Hill (left) and Otto Meyerhof photographed in Highgate, London, where the Hill family lived during his time at University College London Image used with permission from the Churchill Archives Centre, The Papers of Professor A. V. Hill, AVHL II 5/119.

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  Figure 8. Energy balance during a 15 s isometric tetanus of frog muscle at 0°C showing some characteristics of its time course A, solid symbols show the observed heat + work (h + w) output, open symbols show the h + w explained by the observed chemical reactions. In A, the area between the curves is the unexplained h + w. B, the time course of unexplained h + w; it is produced at a high rate at the start of contraction and then the rate progressively slows over 5–10 s. Beyond that time, no further unexplained h + w is produced. Dashed line is the time course of the labile heat. C, representative record of tension produced during the contraction. Figure from Curtin & Woledge (1979) used with permission from John Wiley & Sons.

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  Figure 9. Time courses of heat output from Ca2+‐related reactions A mathematical model of Ca2+ movements within a fibre in response to stimulation was used to calculate the heat produced by Ca2+ binding to troponin‐C (labelled ‘qTn’) and parvalbumin (qPv) and by the Ca2+ pump that returns Ca2+ to the sarcoplasmic reticulum (qSR). The sum of the heat from these sources is the line labelled ∑q, usually referred to as the activation heat. Ca2+ binds rapidly to TnC and relatively slowly to parvalbumin. Inset: calculated time courses of force and initial heat output (from cross‐bridge cycling and Ca2+‐related reactions). Mouse extensor digitorum longus muscle at 20°C. From Barclay & Launikonis (2021), used with permission from Springer Nature.

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  Figure 10. Fenn's demonstration that performance of work is accompanied by an increase in heat production Energy output, as work or heat, is shown on the y‐axis and the load lifted on the x‐axis. The heat is shown as the amount in excess of that produced in an isometric contraction (which was 193 × 102 ergs). The work and heat were the totals produced in an afterloaded isotonic twitch of a frog muscle at 0°C. Correction for a calibration error (Hill & Woledge 1962) would require the heat values to be 0.65 of the values shown. Figure from Fenn (1923) used with permission from John Wiley & Sons.

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  Figure 11. Example of a biomechanical model used to simulate human knee extensions from Tsianos & MacFadden (2016) Top panel: schematic diagram of the dynamic model of human knee extension. Middle panel: comparison between model prediction (filled black symbols) and experimental data for the rate of O2 uptake at different work rates by knee extensors for five human subjects (grey symbols connected by broken lines). The predicted values take account of resting metabolism, energy use by cycling cross‐bridges, activation costs and the dynamics of the oxidative recovery system. The experimental data are from Andersen & Saltin (1985) (used with permission of John Wiley & Sons) and the model prediction and figures are reproduced from Tsianos & MacFadden (2016), © 2016 Tsianos, MacFadden under the Creative Commons Attribution 4.0 International licence.

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  Figure 12. A, efficiency depends on the velocity of shortening The figure shows data for cross‐bridge thermodynamic efficiency of fast‐twitch extensor digitorum longus muscle (open symbols) and slow‐twitch soleus muscle (filled symbols) of the mouse. For fast muscle, the peak efficiency is lower than that for slow muscle but remains close to its maximum over a broader range of shortening velocities than that for the slow muscle. Inset: the same curves drawn as a function of the load opposing shortening (S, soleus; E, extensor digitorum longus); load and shortening velocity are related according to the muscles’ force–velocity curves. B, the series arrangement of the processes of ATP consumption and regeneration. In the diagram the box on the left represents the conversion of a fraction (ηI; initial thermodynamic efficiency) of the free energy from ATP hydrolysis (ΔG ATP) into mechanical work; the remainder of the free energy is converted into heat. ADP produced in that reaction is rephosphorylated (box on the right) using free energy extracted from metabolic substrates (ΔG Substrate) (ηR; recovery thermodynamic efficiency). The overall efficiency, ηO, is ηI×ηR. Both figures from Barclay…