Entropy and information in flagellar axoneme cybernetics: a radial spokes integrative function

Complexity Change in Cardiovascular Disease

With the fast development of wearable medical device in recent years, it becomes critical to conduct research on continuously measured physiological signals. Entropy is a key metric for quantifying the irregularity and/or complexity contained in human physiological signals. In this review, we focus on exploring how entropy changes in various physiological signals in cardiovascular diseases. Our review concludes that the direction of entropy change relies on the physiological signals under investigation. For heart rate variability and pulse index, the entropy of a healthy person is higher than that of a patient with cardiovascular diseases. For diastolic period variability and diastolic heart sound, the direction of entropy change is reversed. Our conclusion should not only give valuable guidance for further research on the application of entropy in cardiovascular diseases but also provide a foundation for using entropy to analyze the irregularity and/or complexity of physiological signals measured by wearable medical device.

The axoneme, a biological template to design a swell energy recovery system

The axonemal micro-machinery, the axial skeleton and actuator of cilia and flagella of eukaryotic cells, is able to bend and twist and generates wave trains. We already demonstrated that it can be the template to construct an active trunk robot (Cibert 2013 Bioinspir. Biomim. 8 026006). The work presented in this paper describes how the axonemal model can also be useful to design worm shaped devices to convert swell energy into usable energy such as electricity. Using dynamic simulation we have designed three models either very close to the biological machinery or being a reasonable interpretation of its functioning principles. Their main advantage as compared with another existing device, Pelamis, is the additional twist degree-of-freedom that gives interesting properties to the system.

Motility of fish spermatozoa: from external signaling to flagella response

For successful fertilization, spermatozoa must access, bind, and penetrate an egg, processes for which activation of spermatozoa motility is a prerequisite. Fish spermatozoa are stored in seminal plasma where they are immotile during transit through the genital tract of most externally fertilizing teleosts and chondrosteans. Under natural conditions, motility is induced immediately following release of spermatozoa from the male genital tract into the aqueous environment. The nature of an external trigger for the initiation of motility is highly dependent on the aquatic environment (fresh or salt water) and the species' reproductive behavior. Triggering signals include osmotic pressure, ionic and gaseous components of external media and, in some cases, egg-derived substances. Extensive study of environmental factors influencing fish spermatozoa motility has led to the proposal of several mechanisms of activation in freshwater and marine fish. However, the signal transduction pathways initiated by these mechanisms remain clear. This review presents the current knowledge with respect to (1) membrane reception of the activation signal and its transduction through the spermatozoa plasma membrane via the external membrane components, ion channels, and aquaporins; (2) cytoplasmic trafficking of the activation signal; (3) final steps of the signaling, including signal transduction to the axonemal machinery, and activation of axonemal dyneins and regulation of their activity; and (4) pathways supplying energy for flagellar motility.

Bending, twisting and beating trunk robot bioinspired from the '3 + 0' axoneme

The axoneme is the skeleton and motor axis of flagella and cilia in eukaryotic organisms. Basically it consists of a series of longitudinal fibers (outer doublets of microtubules) that design a cylinder and whose sliding, due to the coordinated activities of dedicated molecular motors (the dynein arms), is converted into a bending because outer doublets pairs are stabilized by elastic links (the nexine molecules). In spite of these interesting mechanical properties, mechanical and robotics engineers have never considered this amazing molecular machinery as a model. The aim of this paper is to propose the robotic design and the kinematic modeling of the '3 + 0' axoneme that makes motile the flagellum of Diplauxis hatti, the simplest that exists. The model that we propose bends and twists and combines the two movements. It is able to propagate wave trains that could be involved in the development of biomimetic actuators of various mechanisms such as (sub)aquatic robotic propellers as well as robotic trunks.

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.

Geometry drives the ?deviated-bending? of the bi-tubular structures of the 9+2 axoneme in the flagellum

The axoneme "9 + 2" is basically a system constituted of a cylinder of 9 microtubule doublets surrounding a central pair of microtubules. These bi-tubular structures are considered as the support system of the active molecular complexes that generate and regulate the axonemal movement. Schoutens has calculated their moments of inertia [Schoutens, 1994: Journal of Theoretical Biology 171:163-177]. The results obtained allowed us to assume that these bi-tubular systems are endowed with dynamic properties that could be involved in the regulation of the axonemal machinery. For the first time, using the finite elements methods and the resistance of material principles, we have now calculated that the curvature of the axoneme induces the deviated-bending of the bi-tubular structures of the axoneme, because of their geometry only; they behave as beams in a framework. This approach is similar to the one used to measure the deflection of a single microtubule [Kasas et al., 2004: Chem Phys Chem 5:252-257]. These behaviors induce internal movement or constraints of either couples or triplets of doublets within the axonemal cylinder that could be directly involved in a constrained or a spontaneous "convergence/divergence" equilibrium of the cylindrical generatrices that they draw along the axonemal cylinder, which could apparently regulate the activity of the axonemal motors (the dynein arms). These results are discussed here, taking into consideration the dynamic propagation of the wave train along the flagellar axoneme, and the regulated balance between the activities of the two opposite sides of the axoneme during the beat. This study raises a few questions about the architecture-activity duo of the axonemal doublets.