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Günther M, Rockenfeller R, Weihmann T, Haeufle DFB, Götz T, Schmitt S. Rules of nature's Formula Run: Muscle mechanics during late stance is the key to explaining maximum running speed. J Theor Biol 2021; 523:110714. [PMID: 33862096 DOI: 10.1016/j.jtbi.2021.110714] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/04/2020] [Revised: 03/24/2021] [Accepted: 04/08/2021] [Indexed: 10/21/2022]
Abstract
The maximum running speed of legged animals is one evident factor for evolutionary selection-for predators and prey. Therefore, it has been studied across the entire size range of animals, from the smallest mites to the largest elephants, and even beyond to extinct dinosaurs. A recent analysis of the relation between animal mass (size) and maximum running speed showed that there seems to be an optimal range of body masses in which the highest terrestrial running speeds occur. However, the conclusion drawn from that analysis-namely, that maximum speed is limited by the fatigue of white muscle fibres in the acceleration of the body mass to some theoretically possible maximum speed-was based on coarse reasoning on metabolic grounds, which neglected important biomechanical factors and basic muscle-metabolic parameters. Here, we propose a generic biomechanical model to investigate the allometry of the maximum speed of legged running. The model incorporates biomechanically important concepts: the ground reaction force being counteracted by air drag, the leg with its gearing of both a muscle into a leg length change and the muscle into the ground reaction force, as well as the maximum muscle contraction velocity, which includes muscle-tendon dynamics, and the muscle inertia-with all of them scaling with body mass. Put together, these concepts' characteristics and their interactions provide a mechanistic explanation for the allometry of maximum legged running speed. This accompanies the offering of an explanation for the empirically found, overall maximum in speed: In animals bigger than a cheetah or pronghorn, the time that any leg-extending muscle needs to settle, starting from being isometric at about midstance, at the concentric contraction speed required for running at highest speeds becomes too long to be attainable within the time period of a leg moving from midstance to lift-off. Based on our biomechanical model, we, thus, suggest considering the overall speed maximum to indicate muscle inertia being functionally significant in animal locomotion. Furthermore, the model renders possible insights into biological design principles such as differences in the leg concept between cats and spiders, and the relevance of multi-leg (mammals: four, insects: six, spiders: eight) body designs and emerging gaits. Moreover, we expose a completely new consideration regarding the muscles' metabolic energy consumption, both during acceleration to maximum speed and in steady-state locomotion.
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Affiliation(s)
- Michael Günther
- Computational Biophysics and Biorobotics, Institute for Modelling and Simulation of Biomechanical Systems, Universität Stuttgart, Nobelstraße 15, 70569 Stuttgart, Germany; Friedrich-Schiller-Universität, 07737 Jena, Germany.
| | - Robert Rockenfeller
- Mathematisches Institut, Universität Koblenz-Landau, Universitätsstraße 1, 56070 Koblenz, Germany
| | - Tom Weihmann
- Institut für Zoologie, Universität zu Köln, Zülpicher Straße 47b, 50674 Köln, Germany
| | - Daniel F B Haeufle
- Computational Biophysics and Biorobotics, Institute for Modelling and Simulation of Biomechanical Systems, Universität Stuttgart, Nobelstraße 15, 70569 Stuttgart, Germany; Multi-level Modeling in Motor Control and Rehabilitation Robotics, Hertie-Institute for Clinical Brain Research, Eberhard-Karls-Universität, Hoppe-Seyler-Straße 3, 72076 Tübingen, Germany
| | - Thomas Götz
- Mathematisches Institut, Universität Koblenz-Landau, Universitätsstraße 1, 56070 Koblenz, Germany
| | - Syn Schmitt
- Computational Biophysics and Biorobotics, Institute for Modelling and Simulation of Biomechanical Systems, Universität Stuttgart, Nobelstraße 15, 70569 Stuttgart, Germany; Stuttgart Center for Simulation Science (SC SimTech), Universität Stuttgart, Pfaffenwaldring 5a, 70569 Stuttgart, Germany
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Trivedi AK, Rani S, Kumar V. Natural daylight restricted to twilights delays the timing of testicular regression but does not affect the timing of the daily activity rhythm of the house sparrow (Passer domesticus). J Circadian Rhythms 2006; 4:5. [PMID: 16553964 PMCID: PMC1435929 DOI: 10.1186/1740-3391-4-5] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2005] [Accepted: 03/23/2006] [Indexed: 12/02/2022] Open
Abstract
Background A stable and systematic daily change in light levels at dawn and dusk provides the most reliable indicator of the phase of the day. It is likely that organisms have evolved mechanisms to use these twilight transitions as the primary zeitgeber to adjust their circadian phases. In this study, we investigated under natural illumination conditions the effects of daylight exposure restricted to twilights on the timing of testicular regression and locomotor activity of the house sparrow (Passer domesticus), which possesses a strongly self-sustaining circadian system. Methods and results Two experiments were performed on adult male house sparrows. Beginning in the third week of April, the first experiment examined whether exposure to natural daylight only during twilights influenced the timing of testicular regression and concomitant changes in testosterone-dependent beak color of reproductively mature sparrows. Interestingly, there was a significant delay in testicular regression and depigmentation of the beak in sparrows exposed to natural daylight (NDL) only during twilights as compared to those exposed to NDL all day. The second experiment examined twice in the year, around the equinoxes (March and September), the effects of exposure to twilights only on the daily activity rhythm of sparrows kept in an outdoor aviary. Five of 7 birds continued exhibiting entrained activity rhythms when exposed only to twilights (NDL minus day light from sunrise to sunset) in September, but not in March. Both in NDL and twilight conditions, March birds had significantly lower activity counts than September birds. Conclusion Exposure to natural daylight only during twilights delayed the timing of testicular regression and concomitant depigmentation of the beak but did not affect the daily activity rhythm in male sparrows. This suggests that daily twilights can serve as cues for regulation of the circadian activity rhythm but not for the photoperiodic regulation of testicular cycle in the house sparrow.
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Affiliation(s)
- Amit K Trivedi
- Department of Zoology, University of Lucknow, Lucknow 226 007, India
| | - Sangeeta Rani
- Department of Zoology, University of Lucknow, Lucknow 226 007, India
| | - Vinod Kumar
- Department of Zoology, University of Lucknow, Lucknow 226 007, India
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Boulos Z, Macchi M, Terman M. Effects of twilights on circadian entrainment patterns and reentrainment rates in squirrel monkeys. J Comp Physiol A Neuroethol Sens Neural Behav Physiol 1996; 179:687-94. [PMID: 8888579 DOI: 10.1007/bf00216132] [Citation(s) in RCA: 23] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023]
Abstract
Entrainment patterns of the circadian rhythms of body temperature and locomotor activity were compared in 6 squirrel monkeys (Saimiri sciureus) exposed to daily illumination cycles with abrupt transitions between light and darkness (LD-rectangular) or with gradual dawn and dusk transitions simulating natural twilights at the equator (LD-twilight). Daytime light intensity was 500 lux, and the total amount of light emitted per day was the same in the two conditions. Mean daytime body temperature levels were stable in LD-rectangular but increased gradually in LD-twilight, reaching peak levels during the dusk twilight. Locomotor activity showed a similar pattern, but with an additional, secondary peak near the end of dawn. Activity duration was about 0.5 h longer in LD-twilight than in LD-rectangular, but the time of activity midpoint was similar in the two conditions. Reentrainment of the body temperature rhythm was faster following an 8-h advance of the LD cycle than following an 8-h delay, but did not differ significantly between the two LD conditions. These results provide no evidence that the inclusion of twilight transitions affected the strength of the LD zeitgeber, and suggest that the observed differences in the daily patterns reflected direct effects of light intensity on locomotor activity and body temperature rather than an effect of twilights on circadian entrainment mechanisms.
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Affiliation(s)
- Z Boulos
- Institute for Circadian Physiology, Cambridge, MA 02140, USA
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Boulos Z, Macchi M, Houpt TA, Terman M. Photic entrainment in hamsters: effects of simulated twilights and nest box availability. J Biol Rhythms 1996; 11:216-33. [PMID: 8872594 DOI: 10.1177/074873049601100304] [Citation(s) in RCA: 25] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023]
Abstract
Entrainment of wheel-running activity rhythms was compared in hamsters exposed to daily light-dark (LD) cycles with abrupt transitions between 0 and 10 lux or with artificial twilights simulating summer solstice conditions at 41 degrees N latitude but truncated at 10 lux. The photoperiod in LD-rectangular was set at 16.24 h, equating the total light (in lux.min) emitted under the two schedules. The LD cycles were maintained for 35 days and were followed by 14 days of constant darkness (DD). Half the animals in each condition had access to a dark nest box connected to the outer compartment by a tunnel, the remaining animals being confined to a single compartment. Body temperature and locomotor activity inside the nest boxes were recorded by telemetry. Movements between the nest box and the outer compartment were monitored and the data were used to calculate light exposure at different times of the day. In all groups, the phase angle difference between wheel-running onset and dusk was more positive than that between activity offset and dawn. Hamsters with access to nest boxes, however, had later onsets, earlier offsets, and shorter activity durations (alpha s) than those without. These effects could be accounted for by the difference in light exposure between the nest and no-nest animals, particularly light exposure in the morning. The inclusion of twilights also resulted in later onsets and shorter alpha s, but the differences were relatively small and were only observed in the nest animals. The day-to-day variability in activity onset was negatively correlated with onset time and was smaller in the twilight/nest animals than in the other three groups. Most animals showed an expansion of alpha during the first few days of DD, resulting from a rapid advance of activity onsets relative to offsets. The period of the rhythms, determined from the first five activity onsets in DD, was negatively correlated with the balance of evening and morning light exposure. These results are discussed in the context of nonparametric entrainment of compound pacemakers.
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Affiliation(s)
- Z Boulos
- Institute for Circadian Physiology, Cambridge, MA 02140, USA
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Stahlbaum CC, Rovee-Collier C, Fagen JW, Collier G. Twilight activity and antipredator behavior of young fowl housed in artificial or natural light. Physiol Behav 1986; 36:751-8. [PMID: 3714849 DOI: 10.1016/0031-9384(86)90364-1] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
Abstract
Twenty-four-hr patterns of running wheel activity (Experiment 1) and death feigning, an antipredator behavior (Experiment 2), were studied in domestic chicks housed outside, in natural lighting, or indoors, with light onset and offset timed to coincide with the upper limbs of local sunrise and sunset, respectively. Although chicks housed outside were more active and displayed stronger death feigning reactions, the daily patterns of each activity were highly similar in the two groups. Activity peaked during the period corresponding to evening twilight and was negligible during the morning twilight period; in contrast, death feigning peaked during the morning twilight period. Activity measures indicated that chicks on the artificial light schedule had learned to anticipate dark by day 5, and subsequent ontogenetic changes in activity occurred exclusively in the evening twilight phase.
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Kavanau JL, Peters CR. Activity of nocturnal primates: influences of twilight zeitgebers and weather. Science 1976; 191:83-6. [PMID: 813298 DOI: 10.1126/science.813298] [Citation(s) in RCA: 25] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
The time of onset of activity of bush babies (Galago senegalensis), slow lorises (Nycticebus coucang), and an owl monkey (Aotus trivirgatus) living in outdoor enclosures usually fell in certain illuminance ranges of dusk and kept pace with seasonal progressions of sunset time. Influences of cloud cover were variable, but excessive heat and cold were inhibitory. Accurate endogenous timekeeping and reliance on the most stable zeitgeber apparently maintain activities in synchrony with the rhythmically changing environment.
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Kavanau JL, Peters CR. Primate locomotor pattern repetitions, program clocks, and orientation to light. Primates 1974. [DOI: 10.1007/bf01742282] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Kavanau JL, Ramos J, Peters CR. Light preferences of young foxes (Urocyon cinereoargenteus). ZEITSCHRIFT FUR TIERPSYCHOLOGIE 1972; 31:404-9. [PMID: 4650797 DOI: 10.1111/j.1439-0310.1972.tb01776.x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/11/2023]
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