Analysis of the Swimming of Microscopic Organisms
22 Nov 1951-Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences (The Royal Society)-Vol. 209, Iss: 1099, pp 447-461
TL;DR: In this article, it was shown that if the waves down neighbouring tails are in phase, very much less energy is dissipated in the fluid between them than when the waves are in opposite phase.
Abstract: Large objects which propel themselves in air or water make use of inertia in the surrounding fluid. The propulsive organ pushes the fluid backwards, while the resistance of the body gives the fluid a forward momentum. The forward and backward momenta exactly balance, but the propulsive organ and the resistance can be thought about as acting separately. This conception cannot be transferred to problems of propulsion in microscopic bodies for which the stresses due to viscosity may be many thousands of times as great as those due to inertia. No case of self-propulsion in a viscous fluid due to purely viscous forces seems to have been discussed. The motion of a fluid near a sheet down which waves of lateral displacement are propagated is described. It is found that the sheet moves forwards at a rate 2π 2 b 2 /λ 2 times the velocity of propagation of the waves. Here b is the amplitude and λ the wave-length. This analysis seems to explain how a propulsive tail can move a body through a viscous fluid without relying on reaction due to inertia. The energy dissipation and stress in the tail are also calculated. The work is extended to explore the reaction between the tails of two neighbouring small organisms with propulsive tails. It is found that if the waves down neighbouring tails are in phase very much less energy is dissipated in the fluid between them than when the waves are in opposite phase. It is also found that when the phase of the wave in one tail lags behind that in the other there is a strong reaction, due to the viscous stress in the fluid between them, which tends to force the two wave trains into phase. It is in fact observed that the tails of spermatozoa wave in unison when they are close to one another and pointing the same way.
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TL;DR: The exciting successes in taming molecular-level movement thus far are outlined, the underlying principles that all experimental designs must follow, and the early progress made towards utilizing synthetic molecular structures to perform tasks using mechanical motion are highlighted.
Abstract: The widespread use of controlled molecular-level motion in key natural processes suggests that great rewards could come from bridging the gap between the present generation of synthetic molecular systems, which by and large rely upon electronic and chemical effects to carry out their functions, and the machines of the macroscopic world, which utilize the synchronized movements of smaller parts to perform specific tasks. This is a scientific area of great contemporary interest and extraordinary recent growth, yet the notion of molecular-level machines dates back to a time when the ideas surrounding the statistical nature of matter and the laws of thermodynamics were first being formulated. Here we outline the exciting successes in taming molecular-level movement thus far, the underlying principles that all experimental designs must follow, and the early progress made towards utilizing synthetic molecular structures to perform tasks using mechanical motion. We also highlight some of the issues and challenges that still need to be overcome.
2,301 citations
TL;DR: The biophysical and mechanical principles of locomotion at the small scales relevant to cell swimming, tens of micrometers and below are reviewed, with emphasis on the simple physical picture and fundamental flow physics phenomena in this regime.
Abstract: Cell motility in viscous fluids is ubiquitous and affects many biological processes, including reproduction, infection and the marine life ecosystem. Here we review the biophysical and mechanical principles of locomotion at the small scales relevant to cell swimming, tens of micrometers and below. At this scale, inertia is unimportant and the Reynolds number is small. Our emphasis is on the simple physical picture and fundamental flow physics phenomena in this regime. We first give a brief overview of the mechanisms for swimming motility, and of the basic properties of flows at low Reynolds number, paying special attention to aspects most relevant for swimming such as resistance matrices for solid bodies, flow singularities and kinematic requirements for net translation. Then we review classical theoretical work on cell motility, in particular early calculations of swimming kinematics with prescribed stroke and the application of resistive force theory and slender-body theory to flagellar locomotion. After examining the physical means by which flagella are actuated, we outline areas of active research, including hydrodynamic interactions, biological locomotion in complex fluids, the design of small-scale artificial swimmers and the optimization of locomotion strategies. (Some figures in this article are in colour only in the electronic version) This article was invited by Christoph Schmidt.
2,274 citations
Cites background or methods from "Analysis of the Swimming of Microsc..."
...In this subsection, we review Taylor’s calculation [29]....
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...Taylor asked how a microorganism could propel itself using viscous forces alone, rather than imparting momentum to the surrounding fluid as fish do [29]....
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...The first historical evidence of important hydrodynamic effects between nearby eukaryotic flagella were observations by James Gray of in-phase beating of spermatozoa flagella, later reproduced by Taylor [29]....
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...We then discuss the classic contributions of Taylor [29], Hancock [30] and Gray [31], who all but started the field more than 50 years ago (§5); we also outline many of the subsequent works that followed....
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TL;DR: It is shown that a linear chain of colloidal magnetic particles linked by DNA and attached to a red blood cell can act as a flexible artificial flagellum, which induces a beating pattern that propels the structure, and that the external fields can be adjusted to control the velocity and the direction of motion.
Abstract: Microorganisms such as bacteria and many eukaryotic cells propel themselves with hair-like structures known as flagella, which can exhibit a variety of structures and movement patterns. For example, bacterial flagella are helically shaped and driven at their bases by a reversible rotary engine, which rotates the attached flagellum to give a motion similar to that of a corkscrew. In contrast, eukaryotic cells use flagella that resemble elastic rods and exhibit a beating motion: internally generated stresses give rise to a series of bends that propagate towards the tip. In contrast to this variety of swimming strategies encountered in nature, a controlled swimming motion of artificial micrometre-sized structures has not yet been realized. Here we show that a linear chain of colloidal magnetic particles linked by DNA and attached to a red blood cell can act as a flexible artificial flagellum. The filament aligns with an external uniform magnetic field and is readily actuated by oscillating a transverse field. We find that the actuation induces a beating pattern that propels the structure, and that the external fields can be adjusted to control the velocity and the direction of motion.
1,700 citations
TL;DR: The latest generations of sophisticated synthetic molecular machine systems in which the controlled motion of subcomponents is used to perform complex tasks are discussed, paving the way to applications and the realization of a new era of “molecular nanotechnology”.
Abstract: The widespread use of molecular machines in biology has long suggested that great rewards could come from bridging the gap between synthetic molecular systems and the machines of the macroscopic world. In the last two decades, it has proved possible to design synthetic molecular systems with architectures where triggered large amplitude positional changes of submolecular components occur. Perhaps the best way to appreciate the technological potential of controlled molecular-level motion is to recognize that nanomotors and molecular-level machines lie at the heart of every significant biological process. Over billions of years of evolution, nature has not repeatedly chosen this solution for performing complex tasks without good reason. When mankind learns how to build artificial structures that can control and exploit molecular level motion and interface their effects directly with other molecular-level substructures and the outside world, it will potentially impact on every aspect of functional molecule and materials design. An improved understanding of physics and biology will surely follow.
The first steps on the long path to the invention of artificial molecular machines were arguably taken in 1827 when the Scottish botanist Robert Brown observed the haphazard motion of tiny particles under his microscope.1,2 The explanation for Brownian motion, that it is caused by bombardment of the particles by molecules as a consequence of the kinetic theory of matter, was later provided by Einstein, followed by experimental verification by Perrin.3,4 The random thermal motion of molecules and its implications for the laws of thermodynamics in turn inspired Gedankenexperiments (“thought experiments”) that explored the interplay (and apparent paradoxes) of Brownian motion and the Second Law of Thermodynamics. Richard Feynman’s famous 1959 lecture “There’s plenty of room at the bottom” outlined some of the promise that manmade molecular machines might hold.5,6 However, Feynman’s talk came at a time before chemists had the necessary synthetic and analytical tools to make molecular machines. While interest among synthetic chemists began to grow in the 1970s and 1980s, progress accelerated in the 1990s, particularly with the invention of methods to make mechanically interlocked molecular systems (catenanes and rotaxanes) and control and switch the relative positions of their components.7−24
Here, we review triggered large-amplitude motions in molecular structures and the changes in properties these can produce. We concentrate on conformational and configurational changes in wholly covalently bonded molecules and on catenanes and rotaxanes in which switching is brought about by various stimuli (light, electrochemistry, pH, heat, solvent polarity, cation or anion binding, allosteric effects, temperature, reversible covalent bond formation, etc.). Finally, we discuss the latest generations of sophisticated synthetic molecular machine systems in which the controlled motion of subcomponents is used to perform complex tasks, paving the way to applications and the realization of a new era of “molecular nanotechnology”.
1.1. The Language Used To Describe Molecular Machines
Terminology needs to be properly and appropriately defined and these meanings used consistently to effectively convey scientific concepts. Nowhere is the need for accurate scientific language more apparent than in the field of molecular machines. Much of the terminology used to describe molecular-level machines has its origins in observations made by biologists and physicists, and their findings and descriptions have often been misinterpreted and misunderstood by chemists. In 2007 we formalized definitions of some common terms used in the field (e.g., “machine”, “switch”, “motor”, “ratchet”, etc.) so that chemists could use them in a manner consistent with the meanings understood by biologists and physicists who study molecular-level machines.14
The word “machine” implies a mechanical movement that accomplishes a useful task. This Review concentrates on systems where a stimulus triggers the controlled, relatively large amplitude (or directional) motion of one molecular or submolecular component relative to another that can potentially result in a net task being performed. Molecular machines can be further categorized into various classes such as “motors” and “switches” whose behavior differs significantly.14 For example, in a rotaxane-based “switch”, the change in position of a macrocycle on the thread of the rotaxane influences the system only as a function of state. Returning the components of a molecular switch to their original position undoes any work done, and so a switch cannot be used repetitively and progressively to do work. A “motor”, on the other hand, influences a system as a function of trajectory, meaning that when the components of a molecular motor return to their original positions, for example, after a 360° directional rotation, any work that has been done is not undone unless the motor is subsequently rotated by 360° in the reverse direction. This difference in behavior is significant; no “switch-based” molecular machine can be used to progressively perform work in the way that biological motors can, such as those from the kinesin, myosin, and dynein superfamilies, unless the switch is part of a larger ratchet mechanism.14
1,434 citations
TL;DR: In this paper, the authors demonstrate magneto-elastic soft millimetre-scale robots that can swim inside and on the surface of liquids, climb liquid menisci, roll and walk on solid surfaces, jump over obstacles, and crawl within narrow tunnels.
Abstract: Untethered small-scale (from several millimetres down to a few micrometres in all dimensions) robots that can non-invasively access confined, enclosed spaces may enable applications in microfactories such as the construction of tissue scaffolds by robotic assembly, in bioengineering such as single-cell manipulation and biosensing, and in healthcare such as targeted drug delivery and minimally invasive surgery. Existing small-scale robots, however, have very limited mobility because they are unable to negotiate obstacles and changes in texture or material in unstructured environments. Of these small-scale robots, soft robots have greater potential to realize high mobility via multimodal locomotion, because such machines have higher degrees of freedom than their rigid counterparts. Here we demonstrate magneto-elastic soft millimetre-scale robots that can swim inside and on the surface of liquids, climb liquid menisci, roll and walk on solid surfaces, jump over obstacles, and crawl within narrow tunnels. These robots can transit reversibly between different liquid and solid terrains, as well as switch between locomotive modes. They can additionally execute pick-and-place and cargo-release tasks. We also present theoretical models to explain how the robots move. Like the large-scale robots that can be used to study locomotion, these soft small-scale robots could be used to study soft-bodied locomotion produced by small organisms.
1,326 citations
References
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TL;DR: The head of the sea‐urchin spermatozoon is pear‐shaped and axially symmetrical, and the tail, which terminates in an axial fibre, probably contains spiral or coiled structures, as in mammalian spermatozoa.
Abstract: Summary
i. The head of the sea-urchin spermatozoon is pear-shaped and axially symmetrical. The sub-microscopic morphology of the middle piece has not been investigated, but the tail, which terminates in an axial fibre, probably contains spiral or coiled structures, as in mammalian spermatozoa.
2. Spermatozoa of Psammechinus miliaris swim in spirals (frequency, 30–40 per sec), at an average translatory speed of 200/x/sec. at 18o C. This figure applies to very dilute suspensions. The spermatozoa of Echinus esculentus do not always swim in spirals.
3. The evidence in favour of sea-urchin spermatozoa being attracted by egg secretions is not conclusive. Experiments to settle this controversial question could be done without great difficulty.
4. Little is known about the metabolism of sea-urchin spermatozoa. The most important features are:
(a)No movement in absence of oxygen.
(b)Negligible acid production in presence or absence of oxygen.
(c)Over certain limits, oxygen consumption per spermatozoon an inverse function of sperm concentration.
(d)Cytochromes a, b, c, e and a3, succinic dehydrogenase, cocarboxylase, and catalase (in significant quantities) present.
(e)Endogenous substrate unknown, though possibly carbohydrate.
(f) Respiration inhibited by cyanide, and photo-reversibly by carbon monoxide.
A large number of substances, of widely different types, are said to stimulate or maintain the oxygen consumption of semen or spermatozoa. Among these are succinate, malonate, iodoacetate, copper, zinc, calcium, albumin and seminal plasma. The mode of action of these substances is in general obscure.
5. Sea-urchin spermatozoa contain a proteolytic enzyme which decreases the viscosity of gelatine, and desoxyribonuclease.
6. Sea-urchin spermatozoa contain or secrete three substances with characteristic chemical and biological properties. These substances and their principal characteristics are:
(a)Androgamone I. Not a protein. Inhibits sperm movement in certain circumstances.
(b)Androgamone II. Protein. Dissolves or precipitates egg jelly. Also called Antifertilizin.
(c)Androgamone III. Not a protein. Liquefies egg cortex. Sometimes called Sperm Lysin.
7. The spontaneously reversible agglutination of sea-urchin spermatozoa in the presence of egg secretions, and in particular of Gynogamone II, has a number of characteristics in common with serological reactions. In recent years this subject has been extensively studied and reviewed by Tyler (1948). Some of the more important conclusions are:
(a)Spermatozoa and G. II are multivalent with respect to their complementary combining groups, a condition which is responsible for the agglutination of spermatozoa in G. II.
(b)Multivalent G. II can be converted into a univalent form in which it reacts with homologous spermatozoa, but without causing agglutination.
(c)The sperm-G. II reaction exhibits the zone phenomenon (maximum agglutination when the two reactants are present in particular proportions).
(d)The sperm-G. II reaction causes a reduction in the fertilizing capacity of agglutinated spermatozoa.
52 citations