Understanding altered contractile properties in advanced age: insights from a systematic muscle modelling approach

Figures

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  Fig. 1. Muscle model properties. a Activator concentration (lower trace) and activation level during a twitch (dashed) and 1 s stimulation train at 10 Hz. b Activation-activator relationship. c Activation-pCa relationship. d CE and PEE force–length relationships. Shaded region represents range of optimal CE lengths. e CE force–velocity relationship. f SEE force-strain relationship

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  Fig. 2. Hill-type muscle model optimisation. Experimental plantar flexion twitch torque and simulated twitch force for young (Y) adult humans. Inset, twitch contraction time (CT) and half-relaxation time (HRT) for experimental (filled) and simulated (open) data were identical following parameter optimization (CT: 125 ms; HRT: 102.5 ms). Agreement was achieved between twitch torque measured with the ankle at 0° and the knee extended and twitch force simulated at an initial CE length of 1.0 L0

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  Fig. 3. Effect of calcium concentration on submaximal and maximal force generation. a Activator concentration and b active force during a twitch at 1.23 L0 with varying levels of instantaneous Ca2+ concentration (con.). Instantaneous Ca2+ concentration was reduced by 30 and 50% relative to the control condition. Inset, twitch contraction time and half-relaxation time. c Activator concentration and d active force during sustained 10 Hz stimulation at 1.23 L0. e Force-frequency relationships at 1.23 L0. Active force expressed relative to P0 of control condition. f Activation-pCa relationships. In e and f, solid squares denote 10 Hz stimulation and small and large solid circles denote 100 and 200 Hz stimulation, respectively. In f, shaded regions represent the Ca2+ concentration range between 100 and 200 Hz

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  Fig. 4. Effect of calcium uptake rate on force generation at submaximal calcium. a Activator concentration and b active force during a twitch at 1.23 L0 with varying rates of Ca2+ removal (rem.). The rate constant of Ca2+ removal was reduced by 30 and 50% relative to the control condition, representing increases in the time constant of Ca2+ removal, τ2, of 43 and 100%, respectively. Inset, twitch contraction time and half-relaxation time. c Activator concentration and d active force during sustained 10 Hz stimulation at 1.23 L0. e Force-frequency relationships at 1.23 L0. Active force expressed relative to P0 of control condition. Inset, activation-pCa relationship. Solid squares denote the activator concentration and activation level during sustained stimulation at 10 Hz

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  Fig. 5. Effect of calcium sensitivity and cooperativity on force at submaximal and maximal calcium concentrations. a Activation-pCa relationships with varying Ca2+ sensitivities and e cooperativities. Ca2+ sensitivity of force was reduced by 0.05 and 0.10 pCa units relative to the control condition. Cooperativity was decreased from 3 to 2 and increased to 4. a Inset, corresponding activation-activator relationships. Small and large black circles denote 100 and 200 Hz stimulation, respectively. b, f Twitch force at 1.23 L0. Inset, twitch contraction time and half-relaxation time. c, g Force-frequency relationships at 1.23 L0. Active force expressed relative to P0 of control condition. d, h Active force plotted as a function of activator concentration for a 50 ms, 100 Hz train (i.e., 6 pulses) at 1.23 L0. Inset, force summation; the ratio of tetanic (50 ms, 100 Hz) force-to-twitch force

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  Fig. 6. Effect of reducing calcium concentration and Ca2+ sensitivity in concert on maximal force generation. a Activation-pCa relationships with varying Ca2+ sensitivities. Ca2+ sensitivity was reduced by 0.05 and 0.10 pCa units relative to the control condition (5.99). b, c Force-frequency relationships at 1.23 L0 for concomitant reduction in Ca2+ concentration and Ca2+ sensitivity. Force expressed relative to P0 of control condition. Instantaneous activator concentration was reduced by 30% in b and 50% in c. Inset, activator-frequency relationships for control and reduced Ca2+ concentration (dashed) conditions. d Activation-pCa relationships illustrating Ca2+ concentration and activation level for 100 (small circle) and 200 Hz (large circle) stimulation. Data are shown for a 50% reduction in instantaneous activator concentration. The two overlapping shaded regions represent the Ca2+ concentration range between the control and 50% reduction conditions for 100 and 200 Hz stimulation. Inset, activator-frequency relationships

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  Fig. 7. Effect of reducing Ca2+ release and Ca2+ uptake rate, or Ca2+ sensitivity and Ca2+ uptake rate in concert. a, d Activator concentration and b, e force during a twitch and sustained 10 Hz stimulation at 1.23 L0. In a, Ca2+ release was reduced by 30%, but the rate constant of Ca2+ uptake was also reduced by 40% (67% increase in τ2) relative to the control condition. In d, the rate constant of Ca2+ uptake was reduced by 30% (43% increase in τ2), but the Ca2+ sensitivity of force (e inset) was reduced by 0.10 pCa units relative to the control condition. c, f Force-frequency relationships at 1.23 L0. Force expressed relative to P0 of control condition

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  Fig. 8. Effect of intrinsic shortening speed and SEE stiffness on force development. a Force–velocity relationships with varying values of Vmax and a/P0. Vmax was reduced by 30 and 50% relative to the control condition, and a/P0 was increased by 0.05 for illustrative purposes only. d SEE force–length relationships with varying stiffnesses. Deformation expressed as percentage of CE L0. Average SEE stiffness normalised to P0 and CE L0 (kSEE, inset) was reduced by 30% and increased by 50% relative to the control condition. Dotted line indicates passive force at optimal initial CE length of 1.23 L0. b, e Twitch force at an initial CE length of 1.0 and 1.23 L0, respectively. Inset, twitch contraction time and half-relaxation time. c, f Force during a brief tetanic contraction (50 ms, 100 Hz) at an initial CE length of 1.0 and 1.23 L0, respectively. Inset, CE length as a function of time in c and force in f; the dotted lines indicate total force. Solid bar underneath force and CE length traces at contraction onset represents duration of stimulation

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  Fig. 9. Effect of SEE stiffness on modulation of force development by Vmax. a CE force–velocity relationships for control condition and 50% reduction in Vmax (dashed). Inset, SEE force–length relationships with varying stiffnesses. Normalised stiffness (kSEE) was reduced by 30% (14 P0·L0−1) and increased by 50% (30 P0·L0−1) relative to a reference kSEE of 20 P0·L0−1, which gives a normalised SEE deformation value of 5%. b Twitch force at an initial CE length of 1.02 L0. c Force as a function of instantaneous CE length during a twitch. CE length was constrained to the plateau region of the CE force–length relationship

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  Fig. 10. Effect of type I fibre fractional area. a Activator concentration during a twitch, b activation-pCa relationship, and c force–velocity relationship for varying fractions of muscle cross-sectional area (CSA) occupied by type I fibres (i.e., type I MHC content). Control values for Ca2+ removal (rem.) rate, pCa50 and nH, and Vmax were adjusted after back-calculation of the fibre type specific value from a defined fibre type-related difference and a weighting factor proportional to the fractional area of type I fibres. The fractional area of type I fibres was increased by 0.10 and 0.20 from a control value of 0.60 (i.e., 60%). d Twitch force at an initial CE length of 1.23 L0. Inset, twitch contraction time and half-relaxation time. e Force during sustained 10 Hz stimulation at 1.23 L0. f Force-frequency relationship at 1.23 L0. Active force expressed relative to P0 of control condition. Solid squares denote the force for 10 Hz stimulation

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  Fig. 11. Model optimization to simulate time course and relative amplitude of plantar flexion twitch of old men. a Measured plantar flexion twitch torque of young (Y) and older (O) men. b Plantar flexion twitch torque of older men and simulated twitch force after parameter optimisation. Twitch contraction time and half-relaxation time for experimental and simulated data were identical following optimization (CT: 154 ms; HRT: 134.5 ms). c Simulated twitch force for young and old muscle. The relative deficit in twitch amplitude owing to ageing was 18% for simulated and experimental conditions. Inset, force-frequency relationships, where force is expressed relative to the respective P0 of each muscle