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.

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The hydrodynamics of swimming microorganisms

We have developed video microscopy methods to visualize the assembly and disassembly of individual microtubules at 33-ms intervals. Porcine brain tubulin, free of microtubule-associated proteins, was assembled onto axoneme fragments at 37 degrees C, and the dynamic behavior of the plus and minus ends of microtubules was analyzed for tubulin concentrations between 7 and 15.5 microM. Elongation and rapid shortening were distinctly different phases. At each end, the elongation phase was characterized by a second order association and a substantial first order dissociation reaction. Association rate constants were 8.9 and 4.3 microM-1 s-1 for the plus and minus ends, respectively; and the corresponding dissociation rate constants were 44 and 23 s-1. For both ends, the rate of tubulin dissociation equaled the rate of tubulin association at 5 microM. The rate of rapid shortening was similar at the two ends (plus = 733 s-1; minus = 915 s-1), and did not vary with tubulin concentration. Transitions between phases were abrupt and stochastic. As the tubulin concentration was increased, catastrophe frequency decreased at both ends, and rescue frequency increased dramatically at the minus end. This resulted in fewer rapid shortening phases at higher tubulin concentrations for both ends and shorter rapid shortening phases at the minus end. At each concentration, the frequency of catastrophe was slightly greater at the plus end, and the frequency of rescue was greater at the minus end. Our data demonstrate that microtubules assembled from pure tubulin undergo dynamic instability over a twofold range of tubulin concentrations, and that the dynamic instability of the plus and minus ends of microtubules can be significantly different. Our analysis indicates that this difference could produce treadmilling, and establishes general limits on the effectiveness of length redistribution as a measure of dynamic instability. Our results are consistent with the existence of a GTP cap during elongation, but are not consistent with existing GTP cap models.

https://rupress.org/jcb/article-pdf/107/4/1437/1056860/1437.pdf

Dynamic Instability of Individual Microtubules Analyzed by Video Light Microscopy: Rate Constants and Transition Frequencies

Contraction of smooth muscle is regulated by the cytosolic Ca2+ level ([Ca2+]i)b, and the sensitivity to Ca2+ of the contractile elements in response to changes in the environment surrounding the cell. The first sequence of events in regulation includes the binding of endogenous substances, such as

/pdf/calcium-movements-distribution-and-functions-in-smooth-3zozpe9uj6.pdf

Calcium Movements, Distribution, and Functions in Smooth Muscle

Cells generate distinct microtubule subtypes by expressing different tubulin isotypes and through tubulin post-translational modifications, such as detyrosination, acetylation, polyglutamylation and polyglycylation The recent discovery of enzymes responsible for many of these modifications has shown how they may regulate microtubule functions

Post-translational regulation of the microtubule cytoskeleton: mechanisms and functions

Protamines are the major nuclear sperm proteins. The human sperm nucleus contains two types of protamine: protamine 1 (P1) encoded by a single-copy gene and the family of protamine 2 (P2) proteins (P2, P3 and P4), all also encoded by a single gene that is transcribed and translated into a precursor protein. The protamines were discovered more than a century ago, but their function is not yet fully understood. In fact, different hypotheses have been proposed: condensation of the sperm nucleus into a compact hydrodynamic shape, protection of the genetic message delivered by the spermatozoa, involvement in the processes maintaining the integrity and repair of DNA during or after the nucleohistone-nucleoprotamine transition and involvement in the epigenetic imprinting of the spermatozoa. Protamines are also one of the most variable proteins found in nature, with data supporting a positive Darwinian selection. Changes in the expression of P1 and P2 protamines have been found to be associated with infertility in man. Mutations in the protamine genes have also been found in some infertile patients. Transgenic mice defective in the expression of protamines also present several structural defects in the sperm nucleus and have variable degrees of infertility. There is also evidence that altered levels of protamines may result in an increased susceptibility to injury in the spermatozoan DNA causing infertility or poor outcomes in assisted reproduction. The present work reviews the articles published to date on the relationship between protamines and infertility.

/pdf/protamines-and-male-infertility-2zxvclca2k.pdf

Protamines and male infertility.

PHYSICOCHEMICAL characterization of components of flagella and cilia is essential for an understanding of the mechanisms underlying flagellar and ciliary movement. The so-called “9 + 2” fibres (microtubules) are one of the chief ultrastructures in both flagella and cilia, and can be isolated with minimum contamination of other components1,2.

Amino-acid Composition of “Tubulin” constituting Microtubules of Sperm Flagella

Flagellar movement of human spermatozoa held by their heads with a micropipette was recorded by means of a video-strobe system. Spermatozoa were studied in normal Hanks' solution, Hanks' solution with increased viscosity, cervical mucus, and hyaluronic acid.

When flagellar movement in normal Hanks' solution was observed from the direction parallel to the beating plane, segments of the flagellum in focus did not lie on a straight line but on two diverging dashed lines. The distance between the two dashed lines was about 20% of the bend amplitude in the major beating plane. These observations indicate that flagellar beating of human spermatozoa in normal Hanks' solution is not planar. In contrast, segments of the flagellum in focus lay on a straight line when the spermatozoa were observed in Hanks' solution with increased viscosity, cervical mucus, or hyaluronic acid. In normal Hanks' solution, free swimming spermatozoa rotated constantly around their longitudinal axes with a frequency similar to the beat frequency, whereas little or no rotation of spermatozoa occurred in Hanks' solution with increased viscosity, in cervical mucus, or in hyaluronic acid.

We conclude that human spermatozoa in normal Hanks' solution beat with a conical helical waveform having an elliptical cross section, the semiaxes of which have a ratio of 0.2. The three-dimensional geometry of the flagellar movement is responsible for the rotation of the sperm around their longitudinal axes.

Flagellar movement of human spermatozoa

Studies on flagellar ATPase from sea urchin spermatozoa. I. Purification and some properties of the enzyme.

Human X- and Y-bearing sperm differ in cell surface sialic acid content.

Caudal epididymal spermatozoa of golden hamsters were incubated in capacitation medium. Their movement patterns changed as they became hyperactivated and underwent the acrosome reaction. To understand the basic mechanism by which changes in movement pattern are brought about, digital image analysis was carried out on the flagellar movements recorded with a video system. The degree of flagellar bending increased with incubation time, especially in the proximal midpiece. The hyperactivated spermatozoa had remarkably asymmetrical flagellar waves of large amplitude because either the bends in the same direction as the hook of the head (referred as the “pro-hook bend”) or the bends in the opposite direction to the hook of the head (referred as the “anti-hook bend”) extremely increased their curvature; whereas, the acrosome-reacted spermatozoa had relatively symmetrical flagellar waves of large amplitude because both the pro- and anti-hook bends remarkably increased their curvature. Beat frequency significantly decreased while wavelength of flagellar waves increased after hyperactivation and further after the acrosome reaction. These results suggest that both extreme pro- and anti-hook bends are essential in the acrosome-reacted spermatozoa even though beat frequency decreased markedly.Mol. Reprod. Dev. 61: 376–384, 2002. © 2002 Wiley-Liss, Inc.

Hideo Mohri

Papers

Amino-acid Composition of “Tubulin” constituting Microtubules of Sperm Flagella

Flagellar movement of human spermatozoa

Studies on flagellar ATPase from sea urchin spermatozoa. I. Purification and some properties of the enzyme.

Human X- and Y-bearing sperm differ in cell surface sialic acid content.

Quantitative analysis of flagellar movement in hyperactivated and acrosome-reacted golden hamster spermatozoa.