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Mechanical and Metabolic Design of the Muscular System in Vertebrates

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Abstract

The sections in this article are:

1 An Integrative and Absolute Approach to Adaptation and Design
1.1 Caveats and Potential Limitations of the Approach
1.2 Science and Semantics of Adaptation and Design
1.3 Organization of the Chapter
2 Components of the Mechanical System
2.1 Molecular Level
2.2 Cellular Level
2.3 Organ Level/Anatomical Level
3 Design Constraints of the Mechanical System
3.1 Design Constraint 1: Myofilament Overlap
3.2 Design Constraint 2: V/Vmax for Maximum Power Production
3.3 Design Constraint 3: Setting of Kinetics of Force Generation and Muscle Relaxation
3.4 Final Considerations about Mechanical Design Constraints
4 Components of the Metabolic System
4.1 Molecular/Enzyme Level
4.2 Cellular Level
4.3 Organ Level
4.4 System Level
5 Emergent Design Principles of the Metabolic System
5.1 Molecular/Enzyme Level—Design Constraint 1: ATP Demand Is a Function of Contractile Speed
5.2 Cellular Level—Design Constraint 2: Maximum Oxygen Uptake of Skeletal Muscle Mitochondria Is a Constant Function of Mitochondrial Inner‐Membrane Surface Area
5.3 Organ Level—Design Constraint 3: Oxygen Conductance through the Tissue Must Be Set to Meet the ATP Demand
5.4 System Level—Design Constraint 4: The Capacities of the Most Phenotypically Plastic Structures Will Be “Just Adequate” to Match the Maximum Oxidative Requirements of the Muscles
5.5 Final Considerations about Metabolic Design Constraints
6 Mechanical and Metabolic Design of the Muscular System
6.1 Design for Power Generation
6.2 Design for Steady Terrestrial Locomotion
6.3 Design for Sound Production
6.4 Design for Heat Production
7 Conclusion: Principles of Design
Figure 1. Figure 1.

For two types of design considerations, important design parameters (muscle properties that can be varied during evolution) and potential design constraints are shown (system values that are kept constant). Empirical studies suggest that myofilament overlap and V/Vmax are important design constraints; that is, the values of design parameters are set so that muscle operates only over the shaded portion of the curves, where force, power, and efficiency (Effic) are maximal.

Figure 2. Figure 2.

Relative force, power, rate of energy utilization, efficiency, and economy of force generation as a function of relative shortening velocity for a muscle with a high Vmax (dashed curves) and a muscle with a low Vmax (solid curves). Respective Vmax values are shown on velocity axis. V1 and V2 are arbitrarily chosen examples of low and high shortening velocities. Values for curves are derived from heat, oxygen, and mechanics measurements on frog muscle .

Figure 3. Figure 3.

Longitudinal view (a), dorsal view (b), and cross section (c) of carp. Red muscle represents a thin sheet of muscle just under the skin which extends to a depth of only 10% of the distance to the backbone (cross section of the red muscle is exaggerated for illustrative purposes). Because the red fibers run parallel to the body axis, SL excursion depends on both curvature of the spine and distance from the spine. The trajectories of the white muscle fibers shown in a and b are based on Alexander's description. The white fibers lie closer to the median plane than the red ones, and they run helically rather than parallel to the long axis of the body. Consequently, they shorten by only about a quarter as much as the red ones for a given curvature change of the body (see text). Placement of electromyography (EMG) electrodes used to determine the activity of the red and white muscles are shown in c.

From Rome et al
Figure 4. Figure 4.

Shortening deactivation during cyclical length changes allows muscle to relax more rapidly. Whereas during isometric contractions (A), scup red muscle doesn't relax between tetani, when given the same stimulus (40 ms, 50 pps, 7.5 times/s) while undergoing ±5% length changes (B), muscle relaxes almost completely between tetani. Note that scup can swim with a tail beat frequency of 7.5 Hz.

Figure 5. Figure 5.

Hypothetical work loops for muscles driven under high‐frequency length changes. A: Muscle with sufficiently fast activation and relaxation rates that the processes are completed in a small portion of the cycle, and hence appear instantaneous. B: Muscle with a slow relaxation rate driven under the same conditions. Note that with the same long stimulation duration, the muscle does not relax between contractions. C: Slow‐relaxing muscle driven under the same length charges in which stimulation conditions have been optimized for work production. This involves shortening the duration and shifting the stimulus to precede shortening.

Figure 6. Figure 6.

Simple model demonstrating the relative mechanical response and energetic cost of a muscle with a high Ca2+ pumping rate and one with a low Ca2+ pumping rate. For didactic purposes, it is assumed that (1) rate of relaxation is set by rate of calcium pumping, (2) calcium is pumped at a constant rate, rather than at a rate proportional to the exponential drop in [Ca2+], and (3) 1 arbitrary unit of ATP is used to pump 1 arbitrary unit of Ca2+. Muscles which pump Ca2+ faster can relax much faster, but this entails a proportionally greater energetic cost.

Figure 7. Figure 7.

A: Sarcomere length (SL) changes and electromyograms (EMG) of red muscle of fish during steady swimming at 50 cm/s (note that synchronization of EMG with SL is only approximate). Six of the seven parameters that define the length change and stimulation pattern can be readily measured. Note that shape refers to the shape of the SL change, which can be a ramp, sinusoid, or an arbitrary waveform in between. B: The next step, imposing the seven defining parameters on an isolated muscle and measuring the resultant force production. Note in this case a ramp is used for shape and the stim rate was chosen to give a fused tetanus. Work production is calculated from resultant force–length loops as illustrated in Figure . Note that (B) is not meant to try to reproduce the results in (A).

Figure 8. Figure 8.

Balancing ATP supply to contractile and sarcoplasmic reticulum (SR) demand within the muscle fiber. A: Linking of supply to demand is a two‐step process. The first step involves ATP needs of myosin and the ion pumps during muscle contraction, which are met, in temporal order, (1) by the ATP stores within the muscle fiber; (2) by utilizing the high‐energy phosphate (∼P) buffer in the phosphocreatine (PCr); when this source is depleted, (3) by anaerobic catabolism of glycogen contained within the cell; and finally, if the demand persists, (4) the aerobic synthesis of ATP by the mitochondria. Creatine kinase (CK) is the enzyme that catalyzes the exchange of phosphate (PCr). When muscle remains active over prolonged periods, this energy supply‐and‐demand balance is possible only when oxygen supply by the cardiovascular system via the capillaries is sufficient to meet the oxidative demands of the mitochondria. Any constraint in the uptake or supply of oxygen or in the capacity of the contractile use of ATP will limit the ability of the muscle to sustain power output or contractions. B shows that for ATP to be supplied by oxidative phosphorylation, the demand at the muscle must be supplied by the coordinated activities of the entire respiratory system. This schematic diagram of the mammalian respiratory system was first conceived by Dejours and later elaborated by Weibel and Taylor . We have chosen to rotate the figure 180 degrees (onto its lung), because ultimately the demand for oxygen is set not by the lung, but by the aerobic energetics of active muscle. To meet that demand, sufficient oxygen must be pumped by ventilation into the lung, move by diffusion into the blood, be pumped to the muscle tissue by the heart, and finally move by diffusion to the mitochondrial inner membranes. Collectively, function and capacity of those structures through which oxygen flows on its journey to the mitochondria must be subservient to the demand for oxygen set by the muscle.

Figure A courtesy of Dr. Kevin Conley
Figure 9. Figure 9.

Relationship between maximal speed of muscle shortening and actin‐activated myosin ATPase activity of skeletal muscles from various species of vertebrates. We have plotted the data provided by Bárány for a variety of skeletal muscles.

Figure 10. Figure 10.

When maximum O2 uptake () is plotted against mean mitochondrial volume density, there is an apparent linear relationship between and mitochondrial volume density among mammals. This relationship spans over four orders of magnitude in body mass and nearly one order of magnitude in aerobic capacity. On average, the skeletal muscle mitochondria are consuming a maximum of about 4.7 ml O2 · cm−3 of mitochondrial volume · min−1 equal to 70,000 O2 molecules per square micron of inner mitochondrial membrane per second in mammals.

Redrawn from
Figure 11. Figure 11.

Maximum mitochondrial oxygen uptake per unit of inner mitochondrial membrane in a number of vertebrate species. Because these muscles may operate over a broad range of temperatures, we have normalized all the measurements to 30 °C by using a Q10 of 2.2 . Despite great differences in absolute oxygen uptake, maximum mitochondrial oxygen uptake is similar across species, suggesting a fundamental energetic “design element” of vertebrate skeletal muscle.

From Schaeffer, Conley, and Lindstedt
Figure 12. Figure 12.

If is examined in a man as a dependent function of O2 delivery, there are two critical observations. First, extraction never exceeds 90% (dashed line) in these studies. However, in examining these linked studies (i.e., manipulation of delivery), in nearly every case the highest extraction occurs with the lowest oxygen delivery. While artificially boosting O2 delivery may result in a slight increase in O2 uptake, the increase is not proportional. The only apparent way to increase by this manner is at the expense of decreased O2 extraction. While the system may be driven at artificially high O2 availability, the consequence is an apparent decrease in “structural efficiency.” This pattern is more pronounced in elite athletes (filled symbols) than in nonathletes (open symbols). In addition to infusion and withdrawal of blood, this figure includes carbon monoxide inhalation (triangles) and hyperoxia (squares). As extraction in these studies never exceeded 90%, it would appear that in the unmanipulated state O2 delivery meets the muscles' O2 demand at this level of extraction.

From Lindstedt et al.
Figure 13. Figure 13.

Pronghorn antelope and domestic goats are similarly sized ruminants that may be closely related, though maximum oxygen uptake is roughly five times higher in pronghorn than in a group of goats living at the same facility. This histogram presents goat functional and structural data (stippled bars) relative to that of a single pronghorn (hatched bars). The difference we measured in performance () is quantitatively consistent with structural differences in (1) lung volume and the structural diffusing capacity of the lung for O2, (Dlo2) a measure of the lung's ability to transport O2 from the air into the blood; (2) cardiac output (CO) and hemoglobin concentration (Hb), a measure of the potential delivery of oxygen; and (3) muscle mass and total oxidative capacity (total mitochondrial volume), a measure of the muscles' potential oxygen use.

Reprinted by permission from Nature 353:748–753, copyright © 1991 Macmillan Magazines Ltd
Figure 14. Figure 14.

Muscle function during jumping in frogs. A and B show the length‐change and stimulation pattern the semimembranosus muscle undergoes during a maximal jump. C and D show an isolated muscle bundle driven through the in vivo length‐change and stimulation pattern, and E shows the resulting force production of the muscle. Isolated muscle bundles were stimulated at either 200 or 120 pps, but this had only a minor effect on the results. Stimulation duration was determined from the EMG. The phase of the stimulus with respect to the length change was determined in the following fashion: Initiation of shortening was determined by extrapolating the constant velocity portion of the length record back to zero length (B). Lag between the stimulus and shortening was defined as time between onset of EMG and initiation of shortening. Because during jumping, the early portion of the length record was curved, digital smoothing was used to obtain the correct shape of the computer‐generated length change (D). Dashed line (E) is isometric force; dotted line is the steady‐state force generated by the same muscle at the same V during a force–velocity experiment

see Fig. ). The jump shown in A–B is the longest measured (distance = 0.8 m, V = 3.78 ML/s), and this was reproduced in C‐E. From Lutz and Rome
Figure 15. Figure 15.

Where does the semimembranosus muscle operate on its SL–tension and force–velocity curves? A: Open symbols represent results from one experiment; solid symbols represent results from the other. SL–tension relationship was not studied at SL >2.35, because frogs do not use these during jumping and because of well‐known experimental problems associated with “fixed‐end” contractions at long SLs . Muscle shortens from an SL of 2.34 to about 1.83 μm at takeoff. Note that during jumps force and power fell rapidly prior to takeoff so that the most power was generated at somewhat longer SL. Even at 1.83 μm, however, the muscle still generated over 90% tension. B shows typical force–velocity and power–velocity curves. Power curve was simply calculated from the force–velocity fit. At the V used during jumping, the muscle operates over the portion of the power curve where at least 99% of maximum power is generated.

From Lutz and Rome
Figure 16. Figure 16.

Typical record showing changes in sarcomere length in anterior, middle, and posterior positions of a carp swimming at 25 cm/s and 40 cm/s. Five frames (A) separated by 0.1 s are shown; numbers on the photographs correspond to data points in the 25 cm/s graphs (B). For comparison, corresponding sarcomere length–time graph is shown for the same fish swimming at 40 cm/s (C). Note the reduction in noise and increased sarcomere length excursion in the anterior sections of the fish at the higher speed. Sarcomere length excursion (average difference between shortest and longest lengths measured in a sequence) was calculated from the amplitude of the graph. Muscle velocity was calculated from the slope of the graph.

From Rome, Funke, and Alexander
Figure 17. Figure 17.

Design constraint 1—myofilament overlap. During all movements, muscle is used at nearly optimal myofilament overlap. During steady swimming (A), carp uses red muscle over an SL of 1.91–2.23 μm, where no less than 96% maximal tension is generated. If the red muscle had to power the more extreme escape response (B), it would have to shorten to 1.4 μm, at which it generates little tension and can be damaged. Instead, the white muscle, which has a four times greater gear ratio, is used. In the posterior region of the fish, the white muscle shortens to only 1.75 μm, at which at least 85% maximal tension is generated. In the rest of the fish the excursion is smaller and the force higher.

From Rome and Sosnicki
Figure 18. Figure 18.

The startle response of a carp. A resting carp received a 100 ms, 150 Hz sound pulse through an underwater speaker in the aquarium about 30 cm from the fish. The response was filmed at 200 frames per second and six consecutive frames (separated by 5 ms) are numbered and shown on the left. The SL excursions of the white muscle in the anterior, middle, and posterior positions are shown on the right (solid symbols). The SL excursion of the white muscle is greatest in the posterior, because here the backbone undergoes its largest curvature. Note that the open symbols show how far the red muscle would have to shorten if it were powering the movement. The red fibers do not actually shorten to the SL shown because they can't shorten fast enough.

Adapted from Rome et al. and Rome and Sosnicki
Figure 19. Figure 19.

Sarcomere length (SL) distribution in steaks from the three positions along the carp. The cross sections of the anterior, middle, and posterior regions of a bent fish are shown, as well as the SL at different pioints in the steak. Unlike the red muscle, the white muscle SL excursion did not depend on distance from the backbone. There was little variation in SL of the white muscle in a given steak and there was no consistent pattern to the variation, suggesting that the white muscle operates as a unit. At all three positions, however, the SL of the red muscle is very different from the white.

From Rome and Sosnicki
Figure 20. Figure 20.

Design constraint 2—V/Vmax in carp. During slow movements and fast ones, active fibers always shorten at a V/Vmax of 0.17–0.38, at which maximum power and efficiency are generated. During steady swimming (red muscle), the fibers are used at a V/Vmax if 0.17–0.36 (top). The red fibers cannot power the escape response because they would have to shorten at 20 ML/s, or four times their Vmax. Escape response is powered by the white muscle, which needs to shorten at only 5 ML/s (V/Vmax = 0.38) because of its four times higher gear ratio (bottom). The white muscle would not be well suited to power slow swimming movements, as it would have to shorten at a V/Vmax of 0.01–0.03, where power and efficiency are low. Thus fast movements are obtained with fibers with a high Vmax and a large gear ratio.

Figure 21. Figure 21.

Influence of temperature on mechanical properties of carp red muscle and on their use during swimming. Shown are the average force–velocity and power–velocity curves of carp red muscle at 10 °C and 20 °C based on the results of . As muscle‐shortening velocity during steady swimming was independent of temperature, the swimming speed axis has been placed on the graph as well. Thus during steady swimming, the curves provide the power, force, and muscle shortening velocity as a function of swimming speed. Shaded regions represent the V during steady swimming with red muscle. Dotted vertical lines at each temperature represent transition swimming speeds. At slower swimming speeds than that of the leftmost line, the carp uses “burst and coast” swimming with red muscle. At higher swimming speeds than that of the rightmost line, the white muscle is recruited and the carp uses “burst and coast” swimming. For each temperature, the V/Vmax at the transition points is given. Note that V/Vmax over which the red muscle is used is the same at both temperatures.

From Rome, Funke, and Alexander
Figure 22. Figure 22.

V/Vmax of the fast‐swimming scup and slow‐swimming carp. The force–velocity and power–velocity curves are shown for the red muscle of both species at 20 °C. Although scup can swim to 80 cm/s with the red muscle while carp can only swim to about 45 cm/s, their Vmax s are nearly the same. At the maximum swimming speed at which the red muscle is used (80 cm/s in scup and 45 cm/s in carp), it shortens at the same V (about 2.04 ML/s). Hence both species use their red muscle over the same range of V/Vmax, but this occurs at higher swimming speeds (and higher tail beat frequencies) in the scup.

Constructed with data from
Figure 23. Figure 23.

Length changes, stimulation pattern, force production, and work output of red muscle of scup during swimming. Step 1 was to measure in a swimming (80 cm/s) fish the EMGs (A) and length changes (B) for the red muscle at four places along the length of the fish. Step 2 was to impose on muscle bundles isolated from these four positions the length changes (D) and stimulation pattern (C) that were observed during swimming. Step 3 was to measure in the isolated muscle the resulting force production (E) and work production (F). Note that the reason for the apparent discrepancy between traces A–B and C–D is that A–B represent records from one of the fish (tail beat frequency = 6 Hz) while C–D represent the record for a muscle driven through the average swimming values (i.e., tail beat frequency = 6.4 Hz). Traces A–E are all functions of time. Trace F is a plot of force produced against length changes, where the area of the enclosed loop is the work produced during a tail beat cycle. This value is much larger in the POST than in the ANT‐1 position.

From Rome, Swank, and Corda
Figure 24. Figure 24.

Mechanical properties of ANT‐1 and POST muscles. Columns I and II show a POST and an ANT‐1 muscle bundle driven through respective length changes and stimulation pattern that the muscles undergo during swimming. By contrast, column III shows a POST muscle undergoing the stimulation pattern and length changes that are encountered by the ANT‐1 muscle during swimming. Trace A shows the isometric twitch of the muscles in question. Traces B and C show the imposed stimulation pattern and length changes determined during swimming experiments. (Note the phase of the stimulus is defined with respect to maximum length.) The resulting force is shown in trace D and the resulting work (area enclosed by loop) in E. A–D are functions of time, whereas E is force as a function of length. Note the large strain in the POST compared to the ANT‐1 and the much larger work produced in that muscle. Note also that relaxation is much faster in muscle undergoing shortening (D, caused by shortening deactivation) than that being held isometrically (A). Finally note that relaxation is much faster in ANT‐1 muscle than POST(A). This permits the ANT‐1 muscle (HE) to perform work under conditions where the POST muscle cannot (IIIE).

Adapted from Rome, Swank, and Corda
Figure 25. Figure 25.

Work loops performed by scup red muscle during oscillatory contractions at 1 and 10 H2 and in vivo conditions. Heavy lines on the work loops correspond to where the stimulus is on. Note that at 1 Hz (A), the stimulus is turned on just prior to shortening and is turned off just prior to the end of shortening. Hence activation and relaxation can be viewed as instantaneous and have little effect on muscle performance. At 10 Hz (B), however the stimulus is started well before shortening begins and it ends before shortening even begins. Thus if scup swam at this frequency, the kinetics of activation and relaxation would impinge significantly on muscle performance, and hence we would conclude that evolution had set the activation and relaxation rates to be slow. During actual locomotion (swimming at 80 cm/s with a tail beat frequency of 6.4 Hz), the activation and relaxation processes have a large influence on power production, and thus we conclude that evolution sets these processes to be relatively slow.

Figure 26. Figure 26.

Curves representing the average of three strides each for the EKE, tot (thin bottom lines). ECM,tot (middle dashed lines) and the instant‐by‐instant sum of the two, Etot (thick top lines). Curves shown are for one stride of a 60 g chipmunk galloping at 1.2 m · s−1 (upper left); a 90 g chipmunk galloping at 1.6 m · s−1 (lower left); a 5.0 kg dog galloping; at 3.7 m · s−1; one stride (two steps) of a 45 g quail running at 038 m · s−1 (upper right); and one stride of the small quail running at 1.52 m · s−1. Shaded areas represent the aerial phases of the strides. Arrows pointing down are labeled f, b, r, or l for foot‐down for the front, back (quadrupeds), or right or left (bipeds) feet, respectively. Arrows pointing up are for foot‐up. Dashes in the ECMtot curve are at 50 evenly spread intervals during the stride and show the 50 divisions into which each stride was divided.

From Heglund et al.
Figure 27. Figure 27.

Left: mass‐specific metabolic energy input. Emetab/Mb is plotted as a function of running speed for the following animals: a, 43 g painted quail; b, 107 g chipmunk; c, 5.0 kg dog; d, 6.4 kg turkey; e, 70 kg human. Steady‐state oxygen consumption per gram body mass of running animals increases nearly linearly with speed and decreases dramatically with increasing body size. Right: total mass‐specific mechanical power required to maintain the oscillations in kinetic and potential energy of body as animals run at a constant average speed. Etot/Mb, is plotted as a function of speed. Although there is a fair amount of scatter in the data, the total power output does not appear to be size dependent; the dotted line (f) shows the average total mechanical power output calculated by adding the general equations for E'KE,tot/Mb and ECM,tot/Mb determined for a greater diversity of animals. Etot/Mb increases curvilinearly with speed and is independent of size.

From Heglund et al.
Figure 28. Figure 28.

Muscular efficiency, calculated as the ratio of total mechanical work production to metabolic energy input (as a percentage), as a function of running velocity for: a, 43 g painted quail; b, 107 g chipmunk; c, 5.0 kg dog; d, 6.4 kg turkey; e, 70 kg human. Efficiency increases with running speed and decreases with decreasing body size.

From Heglund et al.
Figure 29. Figure 29.

Scaling of stride frequency and Vmax with body size. (A) Stride frequency at the trot‐gallop transition scales with . Graph is drawn from data in Heglund and Taylor . (B) Vmax determined in skinned fibers at 15 °C using the slack test is plotted as a function of full adult body mass. When plotted on log scales, there is a linear (r2 = 0.99) relationship for both Type IIB and Type I fibers. The rat data are from , and the rabbit data are from . The rat IIA data is from .

From Rome, Sosnicki, and Goble
Figure 30. Figure 30.

How compression of recruitment order in small animals influences scaling of the energetics of locomotion. (A) is a schematic representation of recruitment of different fiber types (open symbols, SO; closed symbols, FOG) as a function of running speed in the rat and the horse. Vmax for each fiber type (data from ) has been measured from skinned fibers at 15 °C except for the rat FOG, which is calculated from the Vmax of rat FG data. Five points are demonstrated. First, at physiological equivalent speeds, the animals use the same fiber types. Thus at the maximum sustainable galloping speed (3.1 m/s in rats, 11 m/s in horses), all aerobic (SO and FOG) fibers are recruited. Second, the physiologically equivalent speed occurs at a much higher running speed in large animals than small ones (e.g., maximum sustainable galloping speeds are 11 m/s and 3.1 m/s for the horse and rat, respectively; calculated from ]. Third, the recruitment order is therefore compressed into a slower range of running speeds in the small animal. Fourth, at an absolute running speed, the small animal will be recruiting faster fiber types. For instance at 3.1 m/s, the horse is likely using only slow fibers (SO), as this is close to its minimal trotting speed . Fifth, Vmax increases more rapidly with running speed in the small animal than the large, in a similar fashion to the way 1/tc does. (B) shows how Vmax of SO and FOG fibers scale with Mb. If one measures at physiologically equivalent speeds (i.e., maximum sustainable galloping speed), then the animals would be using the same fiber types. Hence the Vmax and the cost of generating force in the fibers being utilized would scale the same as Vmax of the FOG fibers (). This agrees with how of animals running at physiological equivalent speeds scale. If is measured at an absolute speed such as 3.1 m/s, then the rat would be using both its FOG and SO fibers, but the horse at this speed will be using only its SO fibers. Thus we would be comparing the mechanics and energetics of the FOG fibers in the rat to that of SO fibers in the large animals. This would give an equivalent scaling exponent of for the cost of generating force and Vmax of the recruited fibers, which is close to the scaling exponent for at absolute running speeds.

From Rome
Figure 31. Figure 31.

Double logarithmic plot of body mass against frequency for maximum power output (fopt) for all preparations. Open circle, mouse; solid circle, rat; open triangle, rabbit. Solid line was fitted by least‐squares regression. Dashed line is the relationship between stride frequency at the trot‐gallop transition and body size, determined by Heglund and Taylor , from Altringham and Young .

Figure 32. Figure 32.

(A) Relationship between body size and blood oxygen affinity determined at the body temperature for each species. The PO2 at 50% hemoglobin saturation (P50) was shown by Dhindsa, Hoverland, and Metcalfe to vary systematically with body size and, hence, apparently aerobic capacity. Note the two nonconforming species both have low aerobic capacities. (B) Bohr shift of hemoglobin in relation to body size. Hemoglobin of small mammals has a greater Bohr shift (i.e., is more acid sensitive) than the hemoglobin of large mammals and, therefore, can release more oxygen at a given PO2 .

From Dhindsa, Hoverland, and Metcalfe and Riggs
Figure 33. Figure 33.

Proportion of skeletal muscle mitochondria that are packed beneath the sarcolemma is shown as a function of body mass in mammalian diaphragm muscles. Not only do small animals have a greater density of mitochondria, but these are distributed much closer to the cell membrane, apparently facilitating diffusion in smaller, more aerobic mammals.

Figure 34. Figure 34.

Twitch tension (upper) and calcium transients (lower) of three fiber types from toadfish at 16 °C (A), and of sonic fibers at 16 °C–35°C (B). In each case, the force and the calcium transient have been normalized to their maximum value. (A) The twitch and calcium transient become briefer going from the slow‐twitch red fiber (r), to the fast‐twitch white fiber (w), to the superfast‐twitch swimbladder fiber (s). (B) Records from rattlesnake shaker fibers (RS; dotted) at 16 °C and 35 °C and swimbladder fibers (s; solid) at 16 °C and 25 °C. Note that the time scale is expanded about 30 times in (B). The same traces from the swimbladder at 16 °C are shown in both (A) and (B).

Adapted from Rome et al.
Figure 35. Figure 35.

Calcium transients and force production during repetitive stimuli. (A) Slow‐twitch red fiber stimulated at 3.5 Hz. Dotted line, threshold [Ca2+] for force generation (derived from Fig. ). (B) Swimbladder stimulated at 67 Hz. Note that the threshold is much higher for the swimbladder than for the red fiber. Note also the large magnitude of the first swimbladder Ca2+ transient compared to subsequent ones and the different calibration for the ordinate. Both toadfish fiber experiments were performed at 16 °C. (C) Rattlesnake shakers fibers at 16 °C stimulated at 30 Hz. (D) Shaker fibers at 35 °C stimulated at 100 Hz. Calcium thresholds are not shown for shaker fibers.

From Rome et al.
Figure 36. Figure 36.

Force–pCa relationship of toadfish red, white, and swimbladder fibers. The force–pCa curve for fast‐twitch fibers of the frog Rana temporaria was also measured for comparison. For each fiber type an individual force–pCa data set is shown along with a curve fitted using the equation:Note that the force from swimbladder fibers rose much more sharply than the fitted curve at forces below 50% and more gradually than the fitted curve at forces above 80%.

From Rome et al.
Figure 37. Figure 37.

Calcium transient and modeled troponin occupancy for a swimbladder fiber, based on two different values of Koff for calcium binding to troponin. A fiber was stimulated at 67 Hz (as in Fig. B), and the measured Ca2+ transient is shown (trace d). Because it is thought that troponin has two binding sites and that both binding sites must have calcium bound in order to produce force, the calculated traces (b,c) represent the square of the single‐site troponin occupancy, corresponding to the fraction of troponin sites in an uninhibited state. For Koff to be consistent with the force record in trace a, the occupancy trace must decline faster than the force record, as a delay associated with crossbridge kinetics is also expected. The fact that the force (trace a) declines more completely than the occupancy when Koff =115 · s−1 (trace b, derived from frog) shows that this Koff is likely not fast enough. By contrast, if a Koff of three times this value (345 · s−1; based on changes in force–pCa) is used (trace c), the drop in occupancy is faster than that of tension, making this Koff consistent with the rate of relaxation of the muscle.

From Rome et al.
Figure 38. Figure 38.

Force–velocity curves of toadfish and rattlesnake fibers. For each fiber type an individual force–velocity data set is shown. The corresponding unconstrained Hill equation is fitted up to 80% isometric force (solid line for toadfish; dashed line for rattlesnake), beyond which the curve is approximated with a spline fit (dotted). The force‐velocity curves are shown for the red (r), white (w), and swimbladder (s) fibers of toadfish, and the rattlesnake fibers (rs) at 16° and 35°C. All toadfish fibers were measured at 16° C.

From Rome et al.


Figure 1.

For two types of design considerations, important design parameters (muscle properties that can be varied during evolution) and potential design constraints are shown (system values that are kept constant). Empirical studies suggest that myofilament overlap and V/Vmax are important design constraints; that is, the values of design parameters are set so that muscle operates only over the shaded portion of the curves, where force, power, and efficiency (Effic) are maximal.



Figure 2.

Relative force, power, rate of energy utilization, efficiency, and economy of force generation as a function of relative shortening velocity for a muscle with a high Vmax (dashed curves) and a muscle with a low Vmax (solid curves). Respective Vmax values are shown on velocity axis. V1 and V2 are arbitrarily chosen examples of low and high shortening velocities. Values for curves are derived from heat, oxygen, and mechanics measurements on frog muscle .



Figure 3.

Longitudinal view (a), dorsal view (b), and cross section (c) of carp. Red muscle represents a thin sheet of muscle just under the skin which extends to a depth of only 10% of the distance to the backbone (cross section of the red muscle is exaggerated for illustrative purposes). Because the red fibers run parallel to the body axis, SL excursion depends on both curvature of the spine and distance from the spine. The trajectories of the white muscle fibers shown in a and b are based on Alexander's description. The white fibers lie closer to the median plane than the red ones, and they run helically rather than parallel to the long axis of the body. Consequently, they shorten by only about a quarter as much as the red ones for a given curvature change of the body (see text). Placement of electromyography (EMG) electrodes used to determine the activity of the red and white muscles are shown in c.

From Rome et al


Figure 4.

Shortening deactivation during cyclical length changes allows muscle to relax more rapidly. Whereas during isometric contractions (A), scup red muscle doesn't relax between tetani, when given the same stimulus (40 ms, 50 pps, 7.5 times/s) while undergoing ±5% length changes (B), muscle relaxes almost completely between tetani. Note that scup can swim with a tail beat frequency of 7.5 Hz.



Figure 5.

Hypothetical work loops for muscles driven under high‐frequency length changes. A: Muscle with sufficiently fast activation and relaxation rates that the processes are completed in a small portion of the cycle, and hence appear instantaneous. B: Muscle with a slow relaxation rate driven under the same conditions. Note that with the same long stimulation duration, the muscle does not relax between contractions. C: Slow‐relaxing muscle driven under the same length charges in which stimulation conditions have been optimized for work production. This involves shortening the duration and shifting the stimulus to precede shortening.



Figure 6.

Simple model demonstrating the relative mechanical response and energetic cost of a muscle with a high Ca2+ pumping rate and one with a low Ca2+ pumping rate. For didactic purposes, it is assumed that (1) rate of relaxation is set by rate of calcium pumping, (2) calcium is pumped at a constant rate, rather than at a rate proportional to the exponential drop in [Ca2+], and (3) 1 arbitrary unit of ATP is used to pump 1 arbitrary unit of Ca2+. Muscles which pump Ca2+ faster can relax much faster, but this entails a proportionally greater energetic cost.



Figure 7.

A: Sarcomere length (SL) changes and electromyograms (EMG) of red muscle of fish during steady swimming at 50 cm/s (note that synchronization of EMG with SL is only approximate). Six of the seven parameters that define the length change and stimulation pattern can be readily measured. Note that shape refers to the shape of the SL change, which can be a ramp, sinusoid, or an arbitrary waveform in between. B: The next step, imposing the seven defining parameters on an isolated muscle and measuring the resultant force production. Note in this case a ramp is used for shape and the stim rate was chosen to give a fused tetanus. Work production is calculated from resultant force–length loops as illustrated in Figure . Note that (B) is not meant to try to reproduce the results in (A).



Figure 8.

Balancing ATP supply to contractile and sarcoplasmic reticulum (SR) demand within the muscle fiber. A: Linking of supply to demand is a two‐step process. The first step involves ATP needs of myosin and the ion pumps during muscle contraction, which are met, in temporal order, (1) by the ATP stores within the muscle fiber; (2) by utilizing the high‐energy phosphate (∼P) buffer in the phosphocreatine (PCr); when this source is depleted, (3) by anaerobic catabolism of glycogen contained within the cell; and finally, if the demand persists, (4) the aerobic synthesis of ATP by the mitochondria. Creatine kinase (CK) is the enzyme that catalyzes the exchange of phosphate (PCr). When muscle remains active over prolonged periods, this energy supply‐and‐demand balance is possible only when oxygen supply by the cardiovascular system via the capillaries is sufficient to meet the oxidative demands of the mitochondria. Any constraint in the uptake or supply of oxygen or in the capacity of the contractile use of ATP will limit the ability of the muscle to sustain power output or contractions. B shows that for ATP to be supplied by oxidative phosphorylation, the demand at the muscle must be supplied by the coordinated activities of the entire respiratory system. This schematic diagram of the mammalian respiratory system was first conceived by Dejours and later elaborated by Weibel and Taylor . We have chosen to rotate the figure 180 degrees (onto its lung), because ultimately the demand for oxygen is set not by the lung, but by the aerobic energetics of active muscle. To meet that demand, sufficient oxygen must be pumped by ventilation into the lung, move by diffusion into the blood, be pumped to the muscle tissue by the heart, and finally move by diffusion to the mitochondrial inner membranes. Collectively, function and capacity of those structures through which oxygen flows on its journey to the mitochondria must be subservient to the demand for oxygen set by the muscle.

Figure A courtesy of Dr. Kevin Conley


Figure 9.

Relationship between maximal speed of muscle shortening and actin‐activated myosin ATPase activity of skeletal muscles from various species of vertebrates. We have plotted the data provided by Bárány for a variety of skeletal muscles.



Figure 10.

When maximum O2 uptake () is plotted against mean mitochondrial volume density, there is an apparent linear relationship between and mitochondrial volume density among mammals. This relationship spans over four orders of magnitude in body mass and nearly one order of magnitude in aerobic capacity. On average, the skeletal muscle mitochondria are consuming a maximum of about 4.7 ml O2 · cm−3 of mitochondrial volume · min−1 equal to 70,000 O2 molecules per square micron of inner mitochondrial membrane per second in mammals.

Redrawn from


Figure 11.

Maximum mitochondrial oxygen uptake per unit of inner mitochondrial membrane in a number of vertebrate species. Because these muscles may operate over a broad range of temperatures, we have normalized all the measurements to 30 °C by using a Q10 of 2.2 . Despite great differences in absolute oxygen uptake, maximum mitochondrial oxygen uptake is similar across species, suggesting a fundamental energetic “design element” of vertebrate skeletal muscle.

From Schaeffer, Conley, and Lindstedt


Figure 12.

If is examined in a man as a dependent function of O2 delivery, there are two critical observations. First, extraction never exceeds 90% (dashed line) in these studies. However, in examining these linked studies (i.e., manipulation of delivery), in nearly every case the highest extraction occurs with the lowest oxygen delivery. While artificially boosting O2 delivery may result in a slight increase in O2 uptake, the increase is not proportional. The only apparent way to increase by this manner is at the expense of decreased O2 extraction. While the system may be driven at artificially high O2 availability, the consequence is an apparent decrease in “structural efficiency.” This pattern is more pronounced in elite athletes (filled symbols) than in nonathletes (open symbols). In addition to infusion and withdrawal of blood, this figure includes carbon monoxide inhalation (triangles) and hyperoxia (squares). As extraction in these studies never exceeded 90%, it would appear that in the unmanipulated state O2 delivery meets the muscles' O2 demand at this level of extraction.

From Lindstedt et al.


Figure 13.

Pronghorn antelope and domestic goats are similarly sized ruminants that may be closely related, though maximum oxygen uptake is roughly five times higher in pronghorn than in a group of goats living at the same facility. This histogram presents goat functional and structural data (stippled bars) relative to that of a single pronghorn (hatched bars). The difference we measured in performance () is quantitatively consistent with structural differences in (1) lung volume and the structural diffusing capacity of the lung for O2, (Dlo2) a measure of the lung's ability to transport O2 from the air into the blood; (2) cardiac output (CO) and hemoglobin concentration (Hb), a measure of the potential delivery of oxygen; and (3) muscle mass and total oxidative capacity (total mitochondrial volume), a measure of the muscles' potential oxygen use.

Reprinted by permission from Nature 353:748–753, copyright © 1991 Macmillan Magazines Ltd


Figure 14.

Muscle function during jumping in frogs. A and B show the length‐change and stimulation pattern the semimembranosus muscle undergoes during a maximal jump. C and D show an isolated muscle bundle driven through the in vivo length‐change and stimulation pattern, and E shows the resulting force production of the muscle. Isolated muscle bundles were stimulated at either 200 or 120 pps, but this had only a minor effect on the results. Stimulation duration was determined from the EMG. The phase of the stimulus with respect to the length change was determined in the following fashion: Initiation of shortening was determined by extrapolating the constant velocity portion of the length record back to zero length (B). Lag between the stimulus and shortening was defined as time between onset of EMG and initiation of shortening. Because during jumping, the early portion of the length record was curved, digital smoothing was used to obtain the correct shape of the computer‐generated length change (D). Dashed line (E) is isometric force; dotted line is the steady‐state force generated by the same muscle at the same V during a force–velocity experiment

see Fig. ). The jump shown in A–B is the longest measured (distance = 0.8 m, V = 3.78 ML/s), and this was reproduced in C‐E. From Lutz and Rome


Figure 15.

Where does the semimembranosus muscle operate on its SL–tension and force–velocity curves? A: Open symbols represent results from one experiment; solid symbols represent results from the other. SL–tension relationship was not studied at SL >2.35, because frogs do not use these during jumping and because of well‐known experimental problems associated with “fixed‐end” contractions at long SLs . Muscle shortens from an SL of 2.34 to about 1.83 μm at takeoff. Note that during jumps force and power fell rapidly prior to takeoff so that the most power was generated at somewhat longer SL. Even at 1.83 μm, however, the muscle still generated over 90% tension. B shows typical force–velocity and power–velocity curves. Power curve was simply calculated from the force–velocity fit. At the V used during jumping, the muscle operates over the portion of the power curve where at least 99% of maximum power is generated.

From Lutz and Rome


Figure 16.

Typical record showing changes in sarcomere length in anterior, middle, and posterior positions of a carp swimming at 25 cm/s and 40 cm/s. Five frames (A) separated by 0.1 s are shown; numbers on the photographs correspond to data points in the 25 cm/s graphs (B). For comparison, corresponding sarcomere length–time graph is shown for the same fish swimming at 40 cm/s (C). Note the reduction in noise and increased sarcomere length excursion in the anterior sections of the fish at the higher speed. Sarcomere length excursion (average difference between shortest and longest lengths measured in a sequence) was calculated from the amplitude of the graph. Muscle velocity was calculated from the slope of the graph.

From Rome, Funke, and Alexander


Figure 17.

Design constraint 1—myofilament overlap. During all movements, muscle is used at nearly optimal myofilament overlap. During steady swimming (A), carp uses red muscle over an SL of 1.91–2.23 μm, where no less than 96% maximal tension is generated. If the red muscle had to power the more extreme escape response (B), it would have to shorten to 1.4 μm, at which it generates little tension and can be damaged. Instead, the white muscle, which has a four times greater gear ratio, is used. In the posterior region of the fish, the white muscle shortens to only 1.75 μm, at which at least 85% maximal tension is generated. In the rest of the fish the excursion is smaller and the force higher.

From Rome and Sosnicki


Figure 18.

The startle response of a carp. A resting carp received a 100 ms, 150 Hz sound pulse through an underwater speaker in the aquarium about 30 cm from the fish. The response was filmed at 200 frames per second and six consecutive frames (separated by 5 ms) are numbered and shown on the left. The SL excursions of the white muscle in the anterior, middle, and posterior positions are shown on the right (solid symbols). The SL excursion of the white muscle is greatest in the posterior, because here the backbone undergoes its largest curvature. Note that the open symbols show how far the red muscle would have to shorten if it were powering the movement. The red fibers do not actually shorten to the SL shown because they can't shorten fast enough.

Adapted from Rome et al. and Rome and Sosnicki


Figure 19.

Sarcomere length (SL) distribution in steaks from the three positions along the carp. The cross sections of the anterior, middle, and posterior regions of a bent fish are shown, as well as the SL at different pioints in the steak. Unlike the red muscle, the white muscle SL excursion did not depend on distance from the backbone. There was little variation in SL of the white muscle in a given steak and there was no consistent pattern to the variation, suggesting that the white muscle operates as a unit. At all three positions, however, the SL of the red muscle is very different from the white.

From Rome and Sosnicki


Figure 20.

Design constraint 2—V/Vmax in carp. During slow movements and fast ones, active fibers always shorten at a V/Vmax of 0.17–0.38, at which maximum power and efficiency are generated. During steady swimming (red muscle), the fibers are used at a V/Vmax if 0.17–0.36 (top). The red fibers cannot power the escape response because they would have to shorten at 20 ML/s, or four times their Vmax. Escape response is powered by the white muscle, which needs to shorten at only 5 ML/s (V/Vmax = 0.38) because of its four times higher gear ratio (bottom). The white muscle would not be well suited to power slow swimming movements, as it would have to shorten at a V/Vmax of 0.01–0.03, where power and efficiency are low. Thus fast movements are obtained with fibers with a high Vmax and a large gear ratio.



Figure 21.

Influence of temperature on mechanical properties of carp red muscle and on their use during swimming. Shown are the average force–velocity and power–velocity curves of carp red muscle at 10 °C and 20 °C based on the results of . As muscle‐shortening velocity during steady swimming was independent of temperature, the swimming speed axis has been placed on the graph as well. Thus during steady swimming, the curves provide the power, force, and muscle shortening velocity as a function of swimming speed. Shaded regions represent the V during steady swimming with red muscle. Dotted vertical lines at each temperature represent transition swimming speeds. At slower swimming speeds than that of the leftmost line, the carp uses “burst and coast” swimming with red muscle. At higher swimming speeds than that of the rightmost line, the white muscle is recruited and the carp uses “burst and coast” swimming. For each temperature, the V/Vmax at the transition points is given. Note that V/Vmax over which the red muscle is used is the same at both temperatures.

From Rome, Funke, and Alexander


Figure 22.

V/Vmax of the fast‐swimming scup and slow‐swimming carp. The force–velocity and power–velocity curves are shown for the red muscle of both species at 20 °C. Although scup can swim to 80 cm/s with the red muscle while carp can only swim to about 45 cm/s, their Vmax s are nearly the same. At the maximum swimming speed at which the red muscle is used (80 cm/s in scup and 45 cm/s in carp), it shortens at the same V (about 2.04 ML/s). Hence both species use their red muscle over the same range of V/Vmax, but this occurs at higher swimming speeds (and higher tail beat frequencies) in the scup.

Constructed with data from


Figure 23.

Length changes, stimulation pattern, force production, and work output of red muscle of scup during swimming. Step 1 was to measure in a swimming (80 cm/s) fish the EMGs (A) and length changes (B) for the red muscle at four places along the length of the fish. Step 2 was to impose on muscle bundles isolated from these four positions the length changes (D) and stimulation pattern (C) that were observed during swimming. Step 3 was to measure in the isolated muscle the resulting force production (E) and work production (F). Note that the reason for the apparent discrepancy between traces A–B and C–D is that A–B represent records from one of the fish (tail beat frequency = 6 Hz) while C–D represent the record for a muscle driven through the average swimming values (i.e., tail beat frequency = 6.4 Hz). Traces A–E are all functions of time. Trace F is a plot of force produced against length changes, where the area of the enclosed loop is the work produced during a tail beat cycle. This value is much larger in the POST than in the ANT‐1 position.

From Rome, Swank, and Corda


Figure 24.

Mechanical properties of ANT‐1 and POST muscles. Columns I and II show a POST and an ANT‐1 muscle bundle driven through respective length changes and stimulation pattern that the muscles undergo during swimming. By contrast, column III shows a POST muscle undergoing the stimulation pattern and length changes that are encountered by the ANT‐1 muscle during swimming. Trace A shows the isometric twitch of the muscles in question. Traces B and C show the imposed stimulation pattern and length changes determined during swimming experiments. (Note the phase of the stimulus is defined with respect to maximum length.) The resulting force is shown in trace D and the resulting work (area enclosed by loop) in E. A–D are functions of time, whereas E is force as a function of length. Note the large strain in the POST compared to the ANT‐1 and the much larger work produced in that muscle. Note also that relaxation is much faster in muscle undergoing shortening (D, caused by shortening deactivation) than that being held isometrically (A). Finally note that relaxation is much faster in ANT‐1 muscle than POST(A). This permits the ANT‐1 muscle (HE) to perform work under conditions where the POST muscle cannot (IIIE).

Adapted from Rome, Swank, and Corda


Figure 25.

Work loops performed by scup red muscle during oscillatory contractions at 1 and 10 H2 and in vivo conditions. Heavy lines on the work loops correspond to where the stimulus is on. Note that at 1 Hz (A), the stimulus is turned on just prior to shortening and is turned off just prior to the end of shortening. Hence activation and relaxation can be viewed as instantaneous and have little effect on muscle performance. At 10 Hz (B), however the stimulus is started well before shortening begins and it ends before shortening even begins. Thus if scup swam at this frequency, the kinetics of activation and relaxation would impinge significantly on muscle performance, and hence we would conclude that evolution had set the activation and relaxation rates to be slow. During actual locomotion (swimming at 80 cm/s with a tail beat frequency of 6.4 Hz), the activation and relaxation processes have a large influence on power production, and thus we conclude that evolution sets these processes to be relatively slow.



Figure 26.

Curves representing the average of three strides each for the EKE, tot (thin bottom lines). ECM,tot (middle dashed lines) and the instant‐by‐instant sum of the two, Etot (thick top lines). Curves shown are for one stride of a 60 g chipmunk galloping at 1.2 m · s−1 (upper left); a 90 g chipmunk galloping at 1.6 m · s−1 (lower left); a 5.0 kg dog galloping; at 3.7 m · s−1; one stride (two steps) of a 45 g quail running at 038 m · s−1 (upper right); and one stride of the small quail running at 1.52 m · s−1. Shaded areas represent the aerial phases of the strides. Arrows pointing down are labeled f, b, r, or l for foot‐down for the front, back (quadrupeds), or right or left (bipeds) feet, respectively. Arrows pointing up are for foot‐up. Dashes in the ECMtot curve are at 50 evenly spread intervals during the stride and show the 50 divisions into which each stride was divided.

From Heglund et al.


Figure 27.

Left: mass‐specific metabolic energy input. Emetab/Mb is plotted as a function of running speed for the following animals: a, 43 g painted quail; b, 107 g chipmunk; c, 5.0 kg dog; d, 6.4 kg turkey; e, 70 kg human. Steady‐state oxygen consumption per gram body mass of running animals increases nearly linearly with speed and decreases dramatically with increasing body size. Right: total mass‐specific mechanical power required to maintain the oscillations in kinetic and potential energy of body as animals run at a constant average speed. Etot/Mb, is plotted as a function of speed. Although there is a fair amount of scatter in the data, the total power output does not appear to be size dependent; the dotted line (f) shows the average total mechanical power output calculated by adding the general equations for E'KE,tot/Mb and ECM,tot/Mb determined for a greater diversity of animals. Etot/Mb increases curvilinearly with speed and is independent of size.

From Heglund et al.


Figure 28.

Muscular efficiency, calculated as the ratio of total mechanical work production to metabolic energy input (as a percentage), as a function of running velocity for: a, 43 g painted quail; b, 107 g chipmunk; c, 5.0 kg dog; d, 6.4 kg turkey; e, 70 kg human. Efficiency increases with running speed and decreases with decreasing body size.

From Heglund et al.


Figure 29.

Scaling of stride frequency and Vmax with body size. (A) Stride frequency at the trot‐gallop transition scales with . Graph is drawn from data in Heglund and Taylor . (B) Vmax determined in skinned fibers at 15 °C using the slack test is plotted as a function of full adult body mass. When plotted on log scales, there is a linear (r2 = 0.99) relationship for both Type IIB and Type I fibers. The rat data are from , and the rabbit data are from . The rat IIA data is from .

From Rome, Sosnicki, and Goble


Figure 30.

How compression of recruitment order in small animals influences scaling of the energetics of locomotion. (A) is a schematic representation of recruitment of different fiber types (open symbols, SO; closed symbols, FOG) as a function of running speed in the rat and the horse. Vmax for each fiber type (data from ) has been measured from skinned fibers at 15 °C except for the rat FOG, which is calculated from the Vmax of rat FG data. Five points are demonstrated. First, at physiological equivalent speeds, the animals use the same fiber types. Thus at the maximum sustainable galloping speed (3.1 m/s in rats, 11 m/s in horses), all aerobic (SO and FOG) fibers are recruited. Second, the physiologically equivalent speed occurs at a much higher running speed in large animals than small ones (e.g., maximum sustainable galloping speeds are 11 m/s and 3.1 m/s for the horse and rat, respectively; calculated from ]. Third, the recruitment order is therefore compressed into a slower range of running speeds in the small animal. Fourth, at an absolute running speed, the small animal will be recruiting faster fiber types. For instance at 3.1 m/s, the horse is likely using only slow fibers (SO), as this is close to its minimal trotting speed . Fifth, Vmax increases more rapidly with running speed in the small animal than the large, in a similar fashion to the way 1/tc does. (B) shows how Vmax of SO and FOG fibers scale with Mb. If one measures at physiologically equivalent speeds (i.e., maximum sustainable galloping speed), then the animals would be using the same fiber types. Hence the Vmax and the cost of generating force in the fibers being utilized would scale the same as Vmax of the FOG fibers (). This agrees with how of animals running at physiological equivalent speeds scale. If is measured at an absolute speed such as 3.1 m/s, then the rat would be using both its FOG and SO fibers, but the horse at this speed will be using only its SO fibers. Thus we would be comparing the mechanics and energetics of the FOG fibers in the rat to that of SO fibers in the large animals. This would give an equivalent scaling exponent of for the cost of generating force and Vmax of the recruited fibers, which is close to the scaling exponent for at absolute running speeds.

From Rome


Figure 31.

Double logarithmic plot of body mass against frequency for maximum power output (fopt) for all preparations. Open circle, mouse; solid circle, rat; open triangle, rabbit. Solid line was fitted by least‐squares regression. Dashed line is the relationship between stride frequency at the trot‐gallop transition and body size, determined by Heglund and Taylor , from Altringham and Young .



Figure 32.

(A) Relationship between body size and blood oxygen affinity determined at the body temperature for each species. The PO2 at 50% hemoglobin saturation (P50) was shown by Dhindsa, Hoverland, and Metcalfe to vary systematically with body size and, hence, apparently aerobic capacity. Note the two nonconforming species both have low aerobic capacities. (B) Bohr shift of hemoglobin in relation to body size. Hemoglobin of small mammals has a greater Bohr shift (i.e., is more acid sensitive) than the hemoglobin of large mammals and, therefore, can release more oxygen at a given PO2 .

From Dhindsa, Hoverland, and Metcalfe and Riggs


Figure 33.

Proportion of skeletal muscle mitochondria that are packed beneath the sarcolemma is shown as a function of body mass in mammalian diaphragm muscles. Not only do small animals have a greater density of mitochondria, but these are distributed much closer to the cell membrane, apparently facilitating diffusion in smaller, more aerobic mammals.



Figure 34.

Twitch tension (upper) and calcium transients (lower) of three fiber types from toadfish at 16 °C (A), and of sonic fibers at 16 °C–35°C (B). In each case, the force and the calcium transient have been normalized to their maximum value. (A) The twitch and calcium transient become briefer going from the slow‐twitch red fiber (r), to the fast‐twitch white fiber (w), to the superfast‐twitch swimbladder fiber (s). (B) Records from rattlesnake shaker fibers (RS; dotted) at 16 °C and 35 °C and swimbladder fibers (s; solid) at 16 °C and 25 °C. Note that the time scale is expanded about 30 times in (B). The same traces from the swimbladder at 16 °C are shown in both (A) and (B).

Adapted from Rome et al.


Figure 35.

Calcium transients and force production during repetitive stimuli. (A) Slow‐twitch red fiber stimulated at 3.5 Hz. Dotted line, threshold [Ca2+] for force generation (derived from Fig. ). (B) Swimbladder stimulated at 67 Hz. Note that the threshold is much higher for the swimbladder than for the red fiber. Note also the large magnitude of the first swimbladder Ca2+ transient compared to subsequent ones and the different calibration for the ordinate. Both toadfish fiber experiments were performed at 16 °C. (C) Rattlesnake shakers fibers at 16 °C stimulated at 30 Hz. (D) Shaker fibers at 35 °C stimulated at 100 Hz. Calcium thresholds are not shown for shaker fibers.

From Rome et al.


Figure 36.

Force–pCa relationship of toadfish red, white, and swimbladder fibers. The force–pCa curve for fast‐twitch fibers of the frog Rana temporaria was also measured for comparison. For each fiber type an individual force–pCa data set is shown along with a curve fitted using the equation:Note that the force from swimbladder fibers rose much more sharply than the fitted curve at forces below 50% and more gradually than the fitted curve at forces above 80%.

From Rome et al.


Figure 37.

Calcium transient and modeled troponin occupancy for a swimbladder fiber, based on two different values of Koff for calcium binding to troponin. A fiber was stimulated at 67 Hz (as in Fig. B), and the measured Ca2+ transient is shown (trace d). Because it is thought that troponin has two binding sites and that both binding sites must have calcium bound in order to produce force, the calculated traces (b,c) represent the square of the single‐site troponin occupancy, corresponding to the fraction of troponin sites in an uninhibited state. For Koff to be consistent with the force record in trace a, the occupancy trace must decline faster than the force record, as a delay associated with crossbridge kinetics is also expected. The fact that the force (trace a) declines more completely than the occupancy when Koff =115 · s−1 (trace b, derived from frog) shows that this Koff is likely not fast enough. By contrast, if a Koff of three times this value (345 · s−1; based on changes in force–pCa) is used (trace c), the drop in occupancy is faster than that of tension, making this Koff consistent with the rate of relaxation of the muscle.

From Rome et al.


Figure 38.

Force–velocity curves of toadfish and rattlesnake fibers. For each fiber type an individual force–velocity data set is shown. The corresponding unconstrained Hill equation is fitted up to 80% isometric force (solid line for toadfish; dashed line for rattlesnake), beyond which the curve is approximated with a spline fit (dotted). The force‐velocity curves are shown for the red (r), white (w), and swimbladder (s) fibers of toadfish, and the rattlesnake fibers (rs) at 16° and 35°C. All toadfish fibers were measured at 16° C.

From Rome et al.
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Lawrence C. Rome, Stan L. Lindstedt. Mechanical and Metabolic Design of the Muscular System in Vertebrates. Compr Physiol 2011, Supplement 30: Handbook of Physiology, Comparative Physiology: 1587-1651. First published in print 1997. doi: 10.1002/cphy.cp130223