The mechanics of cilia and flagella: What we know and what we need to know

In this review, we provide a condensed overview of what is currently known about the mechanical functioning of the flagellar/ciliary axoneme. We also present a list of 10 specific areas where our current knowledge is incomplete and explain the benefits of further experimental investigation. Many of the physical parameters of the axoneme and its component parts have not been determined. This limits our ability to understand how the axoneme structure contributes to its functioning in several regards. It restricts our ability to understand how the mechanics of the structure contribute to the regulation of motor function. It also confines our ability to understand the three-dimensional workings of the axoneme and how various beating modes are accomplished. Lastly, it prevents accurate computational modeling of the axoneme in three-dimensions.

Identification of functional candidate variants and genes for feed efficiency in Holstein and Jersey cattle breeds using RNA-sequencing

The identification of functional genetic variants and associated candidate genes linked to feed efficiency may help improve selection for feed efficiency in dairy cattle, providing economic and environmental benefits for the dairy industry. This study used RNA-sequencing data obtained from liver tissue from 9 Holstein cows [n = 5 low residual feed intake (RFI), n = 4 high RFI] and 10 Jersey cows (n = 5 low RFI, n = 5 high RFI), which were selected from a single population of 200 animals. Using RNA-sequencing, 3 analyses were performed to identify: (1) variants within low or high RFI Holstein cattle; (2) variants within low or high RFI Jersey cattle; and (3) variants within low or high RFI groups, which are common across both Holstein and Jersey cattle breeds. From each analysis, all variants were filtered for moderate, modifier, or high functional effect, and co-localized quantitative trait loci (QTL) classes, enriched biological processes, and co-localized genes related to these variants, were identified. The overlapping of the resulting genes co-localized with functional SNP from each analysis in both breeds for low or high RFI groups were compared. For the first two analyses, the total number of candidate genes associated with moderate, modifier, or high functional effect variants fixed within low or high RFI groups were 2,810 and 3,390 for Holstein and Jersey breeds, respectively. The major QTL classes co-localized with these variants included milk and reproduction QTL for the Holstein breed, and milk, production, and reproduction QTL for the Jersey breed. For the third analysis, the common variants across both Holstein and Jersey breeds, uniquely fixed within low or high RFI groups were identified, revealing a total of 86,209 and 111,126 functional variants in low and high RFI groups, respectively. Across all 3 analyses for low and high RFI cattle, 12 and 31 co-localized genes were overlapping, respectively. Among the overlapping genes across breeds, 9 were commonly detected in both the low and high RFI groups (INSRR, CSK, DYNC1H1, GAB1, KAT2B, RXRA, SHC1, TRRAP, PIK3CB), which are known to play a key role in the regulation of biological processes that have high metabolic demand and are related to cell growth and regeneration, metabolism, and immune function. The genes identified and their associated functional variants may serve as candidate genetic markers and can be implemented into breeding programs to help improve the selection for feed efficiency in dairy cattle.

Emergence of flagellar beating from the collective behavior of individual ATP-powered dyneins

Flagella are hair-like projections from the surface of eukaryotic cells, and they play an important role in many cellular functions, such as cell-motility. The beating of flagella is enabled by their internal architecture, the axoneme, and is powered by a dense distribution of motor proteins, dyneins. The dyneins deliver the required mechanical work through the hydrolysis of ATP. Although the dynein-ATP cycle, the axoneme microstructure, and the flagellar-beating kinematics are well studied, their integration into a coherent picture of ATP-powered flagellar beating is still lacking. Here we show that a time-delayed negative-work-based switching mechanism is able to convert the individual sliding action of hundreds of dyneins into a regular overall beating pattern leading to propulsion. We developed a computational model based on a minimal representation of the axoneme consisting of two representative doublet microtubules connected by nexin links. The relative sliding of the microtubules is incorporated by modeling two groups of ATP-powered dyneins, each responsible for sliding in opposite directions. A time-delayed switching mechanism is postulated, which is key in converting the local individual sliding action of multiple dyneins into global beating. Our results demonstrate that an overall nonreciprocal beating pattern can emerge with time due to the spatial and temporal coordination of the individual dyneins. These findings provide insights in the fundamental working mechanism of axonemal dyneins and could possibly open new research directions in the field of flagellar motility.

Ensemble velocity of non-processive molecular motors with multiple chemical states

We study the ensemble velocity of non-processive motor proteins, described with multiple chemical states. In particular, we discuss the velocity as a function of ATP concentration. Even a simple model which neglects the strain dependence of transition rates, reverse transition rates and nonlinearities in the elasticity can show interesting functional dependencies, which deviate significantly from the frequently assumed Michaelis-Menten form. We discuss how the order of events in the duty cycle can be inferred from the measured dependence. The model also predicts the possibility of velocity reversal at a certain ATP concentration if the duty cycle contains several conformational changes of opposite directionalities.

Human airway ciliary dynamics

Airway cilia depend on precise changes in shape to transport the mucus gel overlying mucosal surfaces. The ciliary motion can be recorded in several planes using video microscopy. However, cilia are densely packed, and automated computerized systems are not available to convert these ciliary shape changes into forms that are useful for testing theoretical models of ciliary function. We developed a system for converting planar ciliary motions recorded by video microscopy into an empirical quantitative model, which is easy to use in validating mathematical models, or in examining ciliary function, e.g., in primary ciliary dyskinesia (PCD). The system we developed allows the manipulation of a model cilium superimposed over a video of beating cilia. Data were analyzed to determine shear angles and velocity vectors of points along the cilium. Extracted waveforms were used to construct a composite waveform, which could be used as a standard. Variability was measured as the mean difference in position of points on individual waveforms and the standard. The shapes analyzed were the end-recovery, end-effective, and fastest moving effective and recovery with mean (± SE) differences of 0.31(0.04), 0.25(0.06), 0.50(0.12), 0.50(0.10), μm, respectively. In contrast, the same measures for three different PCD waveforms had values far outside this range.

Bending of the "9+2" axoneme analyzed by the finite element method

Many data demonstrate that the regulation of the bending polarity of the "9+2" axoneme is supported by the curvature itself, making the internal constraints central in this process, adjusting either the physical characteristics of the machinery or the activity of the enzymes involved in different pathways. Among them, the very integrated Geometric Clutch model founds this regulation on the convenient adjustments of the probability of interaction between the dynein arms and the beta-tubulin monomers of the outer doublet pairs on which they walk. Taking into consideration (i) the deviated bending of the outer doublets pairs (Cibert, C., Heck, J.-V., 2004. Cell Motil. Cytoskeleton 59, 153-168), (ii) the internal tensions of the radial spokes and the tangential links (nexin links, dynein arms), (iii) a theoretical 5 microm long proximal segment of the axoneme and (iv) the short proximal segment of the axoneme, we have reevaluated the adjustments of these intervals using a finite element approach. The movements we have calculated within the axonemal cylinder are consistent with the basic hypothesis that found the Geometric Clutch model, except that the axonemal side where the dynein arms are active increases the intervals between the two neighbor outer doublet pairs. This result allows us to propose a mechanism of bending reversion of the axoneme, involving the concerted ignition of the molecular engines along the two opposite sides of the axoneme delineated by the bending plane.

Is the curvature of the flagellum involved in the apparent cooperativity of the dynein arms along the "9+2" axoneme?

In a recent study [Cibert, 2008. Journal of Theoretical Biology 253, 74-89], by assuming that walls of microtubules are involved in cyclic compression/dilation equilibriums as a consequence of cyclic curvature of the axoneme, it was proposed that local adjustments of spatial frequencies of both dynein arms and beta-tubulin monomers facing series create propagation of joint probability waves of interaction (JPI) between these two necessary partners. Modeling the occurrence of these probable interactions along the entire length of an axoneme between each outer doublet pair (without programming any cooperative dialog between molecular complexes) and the cyclic attachment of two facing partners, we show that such constituted active couples are clustered. Along a cluster the dynein arms exhibit a small phase shift with respect to the order according to which they began their cycle after being linked to a beta-tubulin monomer. The number of couples included in these clusters depends on the probability of interaction between the dynein arms and the beta-tubulin, on the location of the outer doublet pairs around the axonemal cylinder, and on the local bending of the axoneme; around the axonemal cylinder, the faster and the larger the sliding, the shorter the clusters. This mechanism could be involved in the apparent cooperativity of molecular motors and the beta-tubulin monomers, since it is partially controlled by local curvature, and the cluster length is inversely proportional to the sliding activity of the outer doublet pairs they link.