The principles of cascading power limits in small, fast biological and engineered systems

Ilton, Mark; Bhamla, M. Saad; Ma, Xinyan; Cox, S. M.; Fitchett, Leah L.; Kim, Yongjin; Koh, Je‐Sung; Krishnamurthy, Deepak; Kuo, Chi‐Yun; Temel, Fatma Zeynep; Crosby, Alfred J.; Prakash, Manu; Sutton, Gregory P.; Wood, Robert J.; Azizi, Emanuel; Bergbreiter, Sarah; Patek, S. N.

doi:10.1126/science.aao1082

Cited by 223 publications

(305 citation statements)

References 143 publications

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“…Elastic energy exchange is a common theme in biology, yet animals do not possess ideal springs [44,2]. Instead, spring-like behavior arises from physical interactions across many length scales.…”

Section: Strain Coupling Improves Energy Exchange Performancementioning

confidence: 99%

“…For instance, Manduca sexta benefits from the nonlinear summation of P return . Beyond insect flight, elastic energy exchange in exoskeletal structures is a key component of power amplified behavior [48,49,50,2]. Like other biological structures with complex geometry, the performance of spring-like structures in the thorax may be highly dependent on their integration with the global system and cannot be characterized in isolation [51,18].…”

Section: Strain Coupling Improves Energy Exchange Performancementioning

confidence: 99%

“…Unlike traditional skeletal muscle, the power muscles in many species indirectly generate wing movements by deforming a continuous exoskeleton surrounding the thorax [1]. Like the complex interactions between power limited muscles, non-ideal latches, and imperfect springs in power amplified biological systems, the introduction of the deformable exoskeleton could have significant consequences on flight mechanics [2]. For instance, the thorax's frequency response may cause some wingbeat frequencies to be energetically favorable, thereby encouraging flight within a narrow band as seen in Manduca sexta [3].…”

Section: Introductionmentioning

confidence: 99%

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Indirect actuation reduces flight power requirements inManduca sextavia elastic energy exchange

Gau

Gravish

Sponberg

2019

Preprint

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In the vast majority of flying insects, wing movements are generated indirectly via the deformations of the exoskeleton. Indirect measurements of inertial and aerodynamic power requirements suggest that elastic energy exchange in spring-like structures may reduce the high power requirements of flight by recovering energy from one wingstroke to the next. We directly measured deformation mechanics and elastic energy storage in a hawkmoth Manduca sexta thorax by recording the force required to deform the thorax over a frequency range encompassing typical wingbeat frequencies. We found that a structural damping model, not a viscoelastic model, accurately describes the thorax's linear spring-like properties and frequency independent dissipation. The energy recovered from thorax deformations is sufficient to minimize flight power requirements. By removing the passive musculature, we find that the exoskeleton determines thorax mechanics. To assess the factors that determine the exoskeleton's spring-like properties, we isolated functional thorax regions, disrupted strain in an otherwise intact thorax, and compared results to a homogeneous hemisphere. We found that mechanical coupling between spatially separated thorax regions improves energy exchange performance. Furthermore, local mechanical properties depend on global strain patterns. Finally, the addition of scutum deformations via indirect actuation provides additional energy recovery without added dissipation.

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Section: Strain Coupling Improves Energy Exchange Performancementioning

confidence: 99%

Section: Strain Coupling Improves Energy Exchange Performancementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Indirect actuation reduces flight power requirements inManduca sextavia elastic energy exchange

Gau

Gravish

Sponberg

2019

Preprint

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“…Ultrafast motility occurs at many length scales in nature, from large multicellular organisms such as a mantis shrimp and trap-jaw ants [1,2] to microscopic single cells such as Vorticella and nematocysts of jellyfish [3][4][5][6][7]. Mechanistic understanding how organisms achieve repeatable rapid motion, especially at small scales is an emerging area of interdisciplinary research with potential to advance our understanding of the biophysics of cellular actuators and motors, as well as inspire design of smallscale robots [8]. In this work, our goal is to develop a biophysical understanding of the ultrafast contraction of the unicellular protozoan Spirostomum ambiguum, which upon an a stimulus can contract its 4 mm long cigarshaped body to 1/4 th of its original length in less than 5 milliseconds, followed by a slow elongation mechanism (∼ 1 s) back to its elongated length (Fig 1a,b, SI Movie 1) [9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Biophysical mechanism of ultrafast helical twisting contraction in the giant unicellular ciliate Spirostomum ambiguum

Bhamla

2019

Preprint

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The biophysical mechanism of cytoskeletal structures has been fundamental to understanding of cellular dynamics. Here, we present a mechanism for the ultrafast contraction exhibited by the unicellular ciliate Spirostomum ambiguum. Powered by a Ca 2+ binding myoneme mesh architecture, Spirostomum is able to twist its two ends in the same direction and fully contract to 75% of its body length within five milliseconds, followed by a slow elongation mechanism driven by the uncoiling of the microtubules. To elucidate the principles of this rapid contraction and slow elongation cycle, we used high-speed imaging to examine the same-direction coiling of the two ends of the cell and immunofluorescence techniques to visualize and quantify the structural changes in the myoneme mesh, microtubule arrays, and the cell membrane. Lastly, we provide support for our hypotheses using a simple physical model that captures key features of Spirostomum's ultrafast twisting contraction. SIGNIFICANCEUltrafast movements are ubiquitous in nature, and some of the most fascinating ultrafast biophysical systems are found on the cellular level. Quantitative studies and models are key to understand the biophysics of these fast movements. In this work, we study Spirostomum's ultrafast contraction by using high-speed imaging, labeling relevant cytoskeletal structures, and building a physical model to provide a biophysical mechanism especially of the helical same direction twisting of this extremely large single cell organism. Deeper understanding of how single cells can execute extreme shape changes hold potential for advancing basic cell biophysics and also inspire new cellular inspired actuators for engineering applications.

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“…Mechanical systems are defined by their force-velocity relationship, which relates the magnitude of the work performed and the rate at which it is delivered. The inherent tradeoff between force and velocity holds true on scales ranging from man-made machines down to single molecule actuators and determines the peak power that can be delivered by a mechanical system (Ilton et al, 2018;Mahadevan and Matsudaira, 2000). In biological organisms, the magnitude of the mechanical power delivered determines the timescales on which it can respond to its environment, for example to evade a predator or to capture a prey.…”

Section: Introductionmentioning

confidence: 99%

The Mechanical Power of Protein Folding

Eckels

Haldar

Tapia‐Rojo³

et al. 2018

Preprint

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The delivery of mechanical power, a crucial component of animal motion, is constrained by the universal compromise between force and velocity of its constituent molecular systems. Here we demonstrate a switchable power amplifier in an Ig domain of the massive muscle protein titin.Titin is composed of many tandem repeats of individually foldable Ig domains, which unfold and extend during muscle stretch and readily refold when the force on titin is quenched during a contraction. Cryptic cysteine residues are common in elastic proteins like titin where they can oxidize to form intra-domain disulfide bonds, limiting the extensibility of an unfolding domain.However, the functional significance of disulfide-bonds in titin Ig domains remains unknown and may be fundamental to muscle mechanics. Here we use ultra-stable magnetic tweezers force spectroscopy to study the elasticity of a disulfide bonded modular titin protein operating in the physiological range, with the ability to control the oxidation state of the protein in real time using both organic reagents and oxidoreductase enzymes. We show that presence of an oxidized disulfide bond allows the parent Ig domain to fold at much higher forces, shifting the midpoint folding probability from 4.0 pN to 12.8 pN after formation. The presence of disulfide bonds in titin regulates the power output of protein folding in an all-or-none manner, providing for example at 6.0 pN, a boost from 0 to 6,000 zeptowatts upon oxidation. At this same force, single molecular motors such as myosin are typically stalled and perform little to no work. We further demonstrate that protein disulfide isomerase (PDI) readily reintroduces disulfide bonds into unfolded titin Ig domains, an important mechanism for titin which operates under a resting force of several pN in vivo. Our results demonstrate, for the first time, the functional significance of disulfide bonds as potent power amplifiers in titin and provide evidence that protein folding can generate substantial amounts of power to supplement the myosin motors during a contraction.

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The principles of cascading power limits in small, fast biological and engineered systems

Cited by 223 publications

References 143 publications

Indirect actuation reduces flight power requirements inManduca sextavia elastic energy exchange

Indirect actuation reduces flight power requirements inManduca sextavia elastic energy exchange

Biophysical mechanism of ultrafast helical twisting contraction in the giant unicellular ciliate Spirostomum ambiguum

The Mechanical Power of Protein Folding

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