Thermodynamic Aspects of Flagellar Activity

1. The frequencies of the beat of cilia and flagella from various organisms have been determined at temperatures in the range 5-35°C. 2. Values of the activation enthalpy (ΔH{ddagger}, kcal./mole) and activation entropy (ΔS{ddagger}, e.u.) derived from the thermal dependence of frequency show a linear correlation of the form, ΔS{ddagger} = 3.25 ΔH{ddagger}-50.75. 3. The corresponding isokinetic activation free energy is 15.6 kcal./mole. 4. The results support a hypothesis that the breakdown of an ATP-ATPase complex could be the common rate-limiting reaction for flagellar activity. 5. Values of ΔH{ddagger} and ΔS{ddagger} for the decay of length or tension in striated muscles also fall on the same regression line but some smooth muscles show deviations

Swimming dynamics of a micro-organism in a couple stress fluid : a rheological model of embryological hydrodynamic propulsion

Mathematical simulations of embryological fluid dynamics are fundamental to improving clinical understanding of the intricate mechanisms underlying sperm locomotion. The strongly rheological nature of reproductive fluids has been established for a number of decades. Complimentary to clinical studies, mathematical models of reproductive hydrodynamics provide a deeper understanding of the intricate mechanisms involved in spermatozoa locomotion which can be of immense benefit in clarifying fertilization processes. Although numerous non-Newtonian studies of spermatozoa swimming dynamics in non-Newtonian media have been communicated, very few have addressed the micro-structural characteristics of embryological media. This family of micro-continuum models include Eringen’s micro-stretch theory, Eringen’s microfluid and micropolar constructs and V.K. Stokes’ couple-stress fluid model, all developed in the 1960s. In the present paper we implement the last of these models to examine the problem of micro-organism (spermatozoa) swimming at low Reynolds number in a homogenous embryological fluid medium with couple stress effects. The micro-organism is modeled as with Taylor’s classical approach, as an infinite flexible sheet on whose surface waves of lateral displacement are propagated. The swimming speed of the sheet and rate of work done by it are determined as function of the parameters of orbit and the couple stress fluid parameter (α). The perturbation solutions are validated with a Nakamura finite difference algorithm. The perturbation solutions reveal that the normal beat pattern is effective for both couple stress and Newtonian fluids only when the amplitude of stretching wave is small. The swimming speed is observed to decrease with couple stress fluid parameter tending to its Newtonian limit as alpha tends to infinity. However the rate of work done by the sheet decreases with α and approaches asymptotically to its Newtonian value. The present solutions also provide a good benchmark for more advanced numerical simulations of micro-organism swimming in couple-stress rheological biofluids

Excess resistivity in graphene superlattices caused by umklapp electron–electron scattering

In electronic transport, umklapp processes play a fundamental role as the only intrinsic mechanism that allows electrons to transfer momentum to the crystal lattice and, therefore, provide a finite electrical resistance in pure metals1,2. However, umklapp scattering is difficult to demonstrate in experiment, as it is easily obscured by other dissipation mechanisms1–6. Here we show that electron–electron umklapp scattering dominates the transport properties of graphene-on-boron-nitride superlattices over a wide range of temperature and carrier density. The umklapp processes cause giant excess resistivity that rapidly increases with increasing superlattice period and are responsible for deterioration of the room-temperature mobility by more than an order of magnitude as compared to standard, non-superlattice graphene devices. The umklapp scattering exhibits a quadratic temperature dependence accompanied by a pronounced electron–hole asymmetry with the effect being much stronger for holes than electrons. In addition to being of fundamental interest, our results have direct implications for design of possible electronic devices based on heterostructures featuring superlattices. © 2018, The Author(s), under exclusive licence to Springer Nature Limited

A physical model of microtubule sliding in ciliary axonemes.

Ciliary movement is caused by coordinated sliding interactions between the peripheral doublet microtubules of the axoneme. In demembranated organelles treated with trypsin and ATP, this sliding can be visualized during progressive disintegration. In this paper, microtubule sliding behavior resulting from various patterns of dynein arm activity and elastic link breakage is determined using a simplified model of the axoneme. The model consists of a cylindrical array of microtubules joined, initially, by elastic links, with the possibility of dynein arm interaction between microtubules. If no elastic links are broken, sliding can produce stable distortion of the model, which finds application to straight sections of a motile cilium. If some elastic links break, the model predicts a variety of sliding patterns, some of which match, qualitatively, the observed disintegration behavior of real axonemes. Splitting of the axoneme is most likely to occur between two doublets N and N + 1 when either the arms on doublet N + 1 are active and arms on doublet N are inactive or arms on doublet N - 1 are active while arms on doublet N are inactive. The analysis suggests further experimental studies which, in conjunction with the model, will lead to a more detailed understanding of the sliding mechanism, and will allow the mechanical properties of some axonemal components to be evaluated

A Mechanochemical Model of Flagellar Activity

A theory is presented which quantitatively links the physical properties of a flagellum with parameters which characterize the chemical reactions responsible for deforming the flagellum. Realistic values for the wave parameters are predicted when order-of-magnitude values for the appropriate constants are used. The model may be useful in other fields where mechanochemical coupling occurs

Mechanochemical aspects of axonemal dynein activity studied by in vitro microtubule translocation.

We have determined the relationship between microtubule length and translocation velocity from recordings of bovine brain microtubules translocating over a Paramecium 22S dynein substratum in an in vitro assay chamber. For comparison with untreated samples, the 22S dynein has been subjected to detergent and/or to pretreatments that induce phosphorylation of an associated 29 kDa light chain. Control and treated dyneins have been used at the same densities in the translocation assays. In any given condition, translocation velocity (v) shows an initial increase with microtubule length (L) and then reaches a plateau. This situation may be represented by a hyperbola of the general form v = aL/(L+b), which is formally analogous to the Briggs-Haldane relationship, which we have used to interpret our data. The results indicate that the maximum translocation velocity Vo(= a) is increased by pretreatment, whereas the length constant KL(= b), which corresponds to Km, does not change with pretreatment, implying that the mechanochemical properties of the pretreated dyneins differ from those of control dyneins. The conclusion that KL is constant for defined in vitro assays rules out the possibility that the velocity changes seen are caused by changes in geometry in the translocation assays or by the numbers of dyneins or dynein heads needed to produce maximal translocational velocity. From our analysis, we determine that f, the fraction of cycle time during which the dynein is in the force-generating state, is small--roughly 0.01, comparable to the f determined previously for heavy meromyosin. The practical limits of these mechanochemical changes imply that the maximum possible ciliary beat frequency is about 120 Hz, and that in the physiological range of 5-60 Hz, beat frequency could be controlled by varying the numbers of phosphorylated outer arm dyneins along an axonemal microtubule