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Although the raison d'etre of the brain is the survival of the body, there are relatively few theoretical studies of closed-loop rhythmic motor control systems. In this paper we provide a unified framework, based on variational analysis, for investigating the dual goals of performance and robustness in powerstroke–recovery systems. To demonstrate our variational method, we augment two previously published closed-loop motor control models by equipping each model with a performance measure based on the rate of progress of the system relative to a spatially extended external substrate—such as a long strip of seaweed for a feeding task, or progress relative to the ground for a locomotor task. The sensitivity measure quantifies the ability of the system to maintain performance in response to external perturbations, such as an applied load. Motivated by a search for optimal design principles for feedback control achieving the complementary requirements of efficiency and robustness, we discuss the performance–sensitivity patterns of the systems featuring different sensory feedback architectures. In a paradigmatic half-center oscillator-motor system, we observe that the excitation–inhibition property of feedback mechanisms determines the sensitivity pattern while the activation–inactivation property determines the performance pattern. Moreover, we show that the nonlinearity of the sigmoid activation of feedback signals allows the existence of optimal combinations of performance and sensitivity. In a detailed hindlimb locomotor system, we find that a force-dependent feedback can simultaneously optimize both performance and robustness, while length-dependent feedback variations result in significant performance-versus-sensitivity tradeoffs. Thus, this work provides an analytical framework for studying feedback control of oscillations in nonlinear dynamical systems, leading to several insights that have the potential to inform the design of control or rehabilitation systems. [ABSTRACT FROM AUTHOR]

Scientists have long been fascinated by the biomolecular machines in living systems that process energy and information to sustain life. The first synthetic molecular rotor capable of performing repeated 360° rotations due to a combination of photo‐ and thermally activated processes was reported in 1999. The progress in designing different molecular machines in the intervening years has been remarkable, with several outstanding examples appearing in the last few years. Despite the synthetic accomplishments, there remains confusion regarding the fundamental design principles by which the motions of molecules can be controlled, with significant intellectual tension between mechanical and chemical ways of thinking about and describing molecular machines. A thermodynamically consistent analysis of the kinetics of several molecular rotors and pumps shows that while light driven rotors operate by a power‐stroke mechanism, kinetic asymmetry—the relative heights of energy barriers—is the sole determinant of the directionality of catalysis driven machines. Power‐strokes—the relative depths of energy wells—play no role whatsoever in determining the sign of the directionality. These results, elaborated using trajectory thermodynamics and the nonequilibrium pump equality, show that kinetic asymmetry governs the response of many non‐equilibrium chemical phenomena. [ABSTRACT FROM AUTHOR]

The power stroke mechanism for ribosome translocation is evaluated through calculations of basic aspects of the mechanics, hydrodynamics, and elasticity involved in such a process. The results show that reported power stroke magnitudes would generate several physical problems for ribosome translocation: unwanted or disproportionate displacements of the ribosome and mRNA, destabilizing competing forces and high tension on the mRNA in the ribosome tunnel. All these issues can be related to the ribosome losing its correct reading frame during mRNA translation. To improve ribosome translocation models, the suggestion is to change the focus from tRNA–mRNA forced displacement to ribosome motion along the mRNA. Also, to consider that the mRNA is essentially different from cytoskeleton fibers and that the ribosome does not work alone during mRNA translation. [ABSTRACT FROM AUTHOR]

Axonemal outer dynein arm (ODA) motors generate force for ciliary beating. We analyzed three states of the ODA during the power stroke cycle using in situ cryo‐electron tomography, subtomogram averaging, and classification. These states of force generation depict the prepower stroke, postpower stroke, and intermediate state conformations. Comparison of these conformations to published in vitro atomic structures of cytoplasmic dynein, ODA, and the Shulin–ODA complex revealed differences in the orientation and position of the dynein head. Our analysis shows that in the absence of ATP, all dynein linkers interact with the AAA3/AAA4 domains, indicating that interactions with the adjacent microtubule doublet B‐tubule direct dynein orientation. For the prepower stroke conformation, there were changes in the tail that is anchored on the A‐tubule. We built models starting with available high‐resolution structures to generate a best‐fitting model structure for the in situ pre‐ and postpower stroke ODA conformations, thereby showing that ODA in a complex with Shulin adopts a similar conformation as the active prepower stroke ODA in the axoneme. Synopsis: Outer dynein arms in the ciliary axoneme generate force for ciliary beating. Here, cryo‐electron tomography study of the outer dynein arm from the unicellular alga C. reinhardtii revealed structures of multiple intermediate and prepower stroke states in the presence of ATP, as well as structural differences between in situ and in vitro complexes. The in situ structure of the axonemal outer dynein arm differs from the structures obtained by single‐particle analysis from split axonemes.In situ, in the absence of nucleotides, all three heavy chains adopt a Post‐2 conformation.In the presence of ATP, multiple outer dynein arm states exist, including a prepower stroke conformation and various intermediate states.Modeling of the prepower stroke outer dynein arm enables a more detailed description of the differences between the pre‐ and postpower stroke state. [ABSTRACT FROM AUTHOR]

During protein synthesis, ribosome moves along mRNA to decode one codon after the other. Ribosome translocation is induced by a universally conserved protein, elongation factor G (EF-G) in bacteria and elongation factor 2 (EF-2) in eukaryotes. EF-G-induced translocation results in unwinding of the intramolecular secondary structures of mRNA by three base pairs at a time that renders the translating ribosome a processive helicase. Professor Alexander Sergeevich Spirin has made numerous seminal contributions to understanding the molecular mechanism of translocation. Here, we review Spirin's insights into the ribosomal translocation and recent advances in the field that stemmed from Spirin's pioneering work. We also discuss key remaining challenges in studies of translocase and helicase activities of the ribosome. [ABSTRACT FROM AUTHOR]

[Display omitted] • Anthrax toxin translocates cytotoxic enzyme factors across membranes into host cells. • Protective antigen moiety forms a large oligomeric translocase channel. • Channel contains three peptide-clamp active sites that catalyze translocation. • Channel translocates β-sheet sequences via an extended-chain Brownian ratchet. • Channel translocates α-helical sequences via a helix-compression mechanism. Dedicated translocase channels are nanomachines that often, but not always, unfold and translocate proteins through narrow pores across the membrane. Generally, these molecular machines utilize external sources of free energy to drive these reactions, since folded proteins are thermodynamically stable, and once unfolded they contain immense diffusive configurational entropy. To catalyze unfolding and translocate the unfolded state at appreciable timescales, translocase channels often utilize analogous peptide-clamp active sites. Here we describe how anthrax toxin has been used as a biophysical model system to study protein translocation. The tripartite bacterial toxin is composed of an oligomeric translocase channel, protective antigen (PA), and two enzymes, edema factor (EF) and lethal factor (LF), which are translocated by PA into mammalian host cells. Unfolding and translocation are powered by the endosomal proton gradient and are catalyzed by three peptide-clamp sites in the PA channel: the α clamp, the ϕ clamp, and the charge clamp. These clamp sites interact nonspecifically with the chemically complex translocating chain, serve to minimize unfolded state configurational entropy, and work cooperatively to promote translocation. Two models of proton gradient driven translocation have been proposed: (i) an extended-chain Brownian ratchet mechanism and (ii) a proton-driven helix-compression mechanism. These models are not mutually exclusive; instead the extended-chain Brownian ratchet likely operates on β-sheet sequences and the helix-compression mechanism likely operates on α-helical sequences. Finally, we compare and contrast anthrax toxin with other related and unrelated translocase channels. [ABSTRACT FROM AUTHOR]

Two mechanisms have been proposed for the function of motor proteins: The power stroke and the Brownian ratchet. The former refers to generation of a large downhill free energy gradient over which the motor protein moves nearly irreversibly in making a step, whereas the latter refers to biasing or rectifying the diffusive motion of the motor. Both mechanisms require input of free energy, which generally involves the processing of an ATP (adenosine 5'-triphosphate) molecule. Recent advances in experiments that reveal the details of the stepping motion of motor proteins, together with computer simulations of atomistic structures, have provided greater insights into the mechanisms. Here, we compare the various models of the power stroke and the Brownian ratchet that have been proposed. The 2 mechanisms are not mutually exclusive, and various motor proteins employ them to different extents to perform their biological function. As examples, we discuss linear motor proteins Kinesin-1 and myosin-V, and the rotary motor F1-ATPase, all of which involve a power stroke as the essential element of their stepping mechanism. [ABSTRACT FROM AUTHOR]

We propose a chemical–mechanical model of myosin heads in sarcomeres, within the classical description of rigid sliding filaments. In our case, myosin heads have two mechanical degrees-of-freedom (dofs)—one of which associated with the so-called power stroke—and two possible chemical states, i.e., bound to an actin site or not. Our major motivations are twofold: (1) to derive a multiscale coupled chemical–mechanical model and (2) to thus account—at the macroscopic scale—for mechanical phenomena that are out of reach for classical muscle models. This model is first written in the form of Langevin stochastic equations, and we are then able to obtain the corresponding Fokker–Planck partial differential equations governing the probability density functions associated with the mechanical dofs and chemical states. This second form is important, as it allows to monitor muscle energetics and also to compare our model with classical ones, such as the Huxley'57 model to which our equations are shown to reduce under two different types of simplifying assumptions. This provides insight and gives a Langevin form for Huxley'57. We then show how we can calibrate our model based on experimental data—taken here for skeletal muscles—and numerical simulations demonstrate the adequacy of the model to represent complex physiological phenomena, in particular the fast isometric transients in which the power stroke is known to have a crucial role, thus circumventing a limitation of many classical models. [ABSTRACT FROM AUTHOR]

During the early evolution of Equoidea, two families co-existed, Equidae and Palaeotheriidae. Both groups show a similar ancestral molar morphology and evolved from bunodont to lophodont or selenolophodont (lophodont with crescent-shaped cutting edge in some form) respectively, with a clearly pronounced ectoloph. Fossils of the here studied brachydont equids and palaeotheriids are known from the early Eocene to the middle Miocene in North America and Eurasia. Due to the rich fossil record, dental evolution and related functional shifts can be investigated in detail in each family. In this study, we focused on changes in the different masticatory paths, identified different functions within the power stroke and evaluated the efficiency of the different modes in mastication to correlate tooth morphology to the potential palaeodiets. The analysis is based on three-dimensional (3D) polygonal surface scans, allowing the detailed investigation of morphological features. The results show that primitive equoids possess well-developed cutting and shearing structures, despite being generally referred to as simply bunodont. These structures enable the primitive forms to break down structural plant parts more efficiently than for example Phenacodus ('condylarth' outgroup), showing simple rounded cusps, and therefore representing a more primitive type of bunodont dentition. It is general consensus that the diet of the more derived early equoids shifts to a higher percentage of tough plant parts and they adopt different strategies to efficiently comminute those parts. Equids emphasise cutting and shearing both buccally and lingually, trending towards a one-phase power stroke, a pattern resembling that of modern hypsodont Equidae. Our results suggest that the derived brachydont equids specialised to consume leaves rather than grasses. In comparison, derived palaeotheriids mainly emphasise shearing and cutting function buccally and a distinct grinding function in a two-phase power stroke. The combination of different functions suggest a broader diet different from only leaves, likely including twigs or hard fruits. [ABSTRACT FROM AUTHOR]

The precise 3-nucleotide movement of mRNA is critical for translation fidelity. One mRNA translocation error propagates to all of the following codons, which is detrimental to the cell. However, none of the current methods can reveal the mRNA dynamics near the ribosome entry site, which limits the understanding of this important issue. We have developed an assay of dual DNA rulers that provides such capability. By uniquely probing both the 3ʹ- and 5ʹ-ends of mRNA, we observed an antibiotic-trapped intermediate state that is consistent with a ribosomal conformation containing mRNA asymmetric partial displacements at its entry and exit sites. Based on the available ribosome structures and computational simulations, we proposed a 'looped' mRNA conformation, which suggested a stepwise 'inchworm' mechanism for ribosomal translocation. The same 'looped' intermediate state identified with the dual rulers persists with a '-1' frameshifting motif, indicating that the branching point of normal and frameshifting translocations occurs at a later stage of translocation. [ABSTRACT FROM AUTHOR]