Rotary protein motors

The cluster model of energy transduction in biological systems

The central problem in transduction is to explain how the energy caught from sunlight by chloroplasts becomes biological work. Or to express it in different terms: how does the energy remain trapped in the biological network and not get lost through thermalization into the environment? The pathway consists of an immensely large number of steps crossing hierarchical levels - some upwards, to larger assemblies, others downwards into energy rich molecules - before fuelling an action potential or a contracting cell. Accepting the assumption that steps are executed by protein domains, we expect that transduction mechanisms are the result of conformational changes, which in turn involve rearrangements of the bonds responsible for the protein fold. But why are these essential changes so difficult to detect? In this presentation, the metabolic pathway is viewed as equivalent to an energy conduit composed of equally sized units - the protein domains - rather than a row of catalysts. The flow of energy through them occurs by the same mechanism as through the cytoplasmic medium (water). This mechanism is based on the cluster-wave model of water structure, which successfully explains the transfer of energy through the liquid medium responsible for the build up of osmotic pressure. The analogy to the line of balls called "Newton's cradle" provides a useful comparison, since there the transfer is also invisible to us because the intermediate balls are motionless. It is further proposed that the spatial arrangements of the H-bonds of the α and β secondary structures support wave motion, with the linear and lateral forms of the groups of bonds belonging to the helices and sheets executing the longitudinal and transverse modes, respectively.

Inertialess gyrating engines

A typical model for a gyrating engine consists of an inertial wheel powered by an energy source that generates an angle-dependent torque. Examples of such engines include a pendulum with an externally applied torque, Stirling engines, and the Brownian gyrating engine. Variations in the torque are averaged out by the inertia of the system to produce limit cycle oscillations. While torque generating mechanisms are also ubiquitous in the biological world, where they typically feed on chemical gradients, inertia is not a property that one naturally associates with such processes. In the present work, seeking ways to dispense of the need for inertial effects, we study an inertia-less concept where the combined effect of coupled torque-producing components averages out variations in the ambient potential and helps overcome dissipative forces to allow sustained operation for vanishingly small inertia. We exemplify this inertia-less concept through analysis of two of the aforementioned engines, the Stirling engine, and the Brownian gyrating engine. An analogous principle may be sought in biomolecular processes as well as in modern-day technological engines, where for the latter, the coupled torque-producing components reduce vibrations that stem from the variability of the generated torque.

ARP2/3 Regulates Fatty Acid Synthesis by Modulating Lipid Droplets' Motility

The breakdown of lipid droplets (LDs) provides energy and contributes to the proliferation and migration of cancer cells. Recent studies have suggested that motility plays a key role in LD breakdown. However, the molecular mechanisms underlying LD motility were poorly characterized. In this study, we examined the function of microfilament-associated proteins 2 and 3 (ARP2 and ARP3) in regulating LDs’ motility in Hela cells. ARP2/3 mediated the LDs’ physical contact with F-actin and promoted the recruitment of Myosin Heavy Chain 9 (MYH9). MYH9 regulated the LD content by binding with LDs and ARP2/3. The number of LDs and TG content was increased after MYH9 interfered. The genes related to FA-related genes and neutral lipid synthesis-related genes were significantly increased (p < 0.05) when ARP2 and ARP3 were overexpressed. Bioinformatic analysis indicated that the high expression of ARP2/3 was associated with a poorer prognosis in cervical squamous cell carcinoma (CSCC). This study showed the effect of cytoskeletal filaments on LD metabolism in cancer cells.

Charge transfer across biomembranes: A solution to the conundrum of high desolvation free energy penalty in ion transport

Charge transfer across membranes is an important problem in a wide variety of fundamental physicochemical and biological processes. Since Mitchell's concept of the ion well advanced in 1968, several models of ion translocation across biomembranes, for instance through the membrane-bound F_O portion of ATP synthase have been proposed. None of these models has considered the large desolvation free energy penalty of ~500 meV incurred in transferring a protonic charge from the aqueous phase into the membrane that hinders such charge transfer processes. The difficulty has been pointed out repeatedly. However, the problem of how the adverse ∆G_desolvation barrier is overcome in order to enable rapid ion translocation in biomembranes has not been satisfactorily resolved. Hence the fact that the self-energy of the charges has been overlooked can be regarded as a main source of confusion in the field of bioenergetics. Further, in order to consider charges of a finite size (and not just point charges), the free energy of transferring the ions from water into a membrane phase of lower dielectric ε_m needs to be evaluated. Here a solution to the longstanding conundrum has been proposed by including the bound anion - the second ion in Nath's two-ion theory of energy coupling and ATP synthesis - in the free energy calculations. The mechanistic importance of the H⁺ - A^- charge pair in causing rotation and ATP synthesis by ion-protein interactions is highlighted. The ∆G calculations have been performed by using the Kirkwood-Tanford-Warshel (KTW) theory that takes into account the self-energies of the ions. The results show that the adverse ∆G_desolvation can be almost exactly compensated by the sum of the electrostatic free energy of the charge-charge interactions and the dipole solvation energy for long-range ion pairs. Results of free energy compensation using the KTW theory have been compared with experimental data on the ∆G of ion pairs and shown to be in reasonable agreement. A general thermodynamic cycle for coupled ion transfer has been constructed to further elucidate facilitated ion permeation between water and membrane phases. Molecular interpretations of the results and their implications for various mechanisms of energy transduction have been discussed. We firmly believe that use of electrostatic theories such as the KTW theory that properly include the desolvation free energy penalty arising from the self-energy of the relevant ions are crucial for quantifying charge transfer processes in bioenergetics. Finally, the clear-cut implication is that proton-only and single-ion theories of ATP synthesis, such as the chemiosmotic theory, are grossly inadequate to comprehend energy storage and transduction in biological processes.

Biomolecular Basis of Cellular Consciousness via Subcellular Nanobrains

Cells emerged at the very beginning of life on Earth and, in fact, are coterminous with life. They are enclosed within an excitable plasma membrane, which defines the outside and inside domains via their specific biophysical properties. Unicellular organisms, such as diverse protists and algae, still live a cellular life. However, fungi, plants, and animals evolved a multicellular existence. Recently, we have developed the cellular basis of consciousness (CBC) model, which proposes that all biological awareness, sentience and consciousness are grounded in general cell biology. Here we discuss the biomolecular structures and processes that allow for and maintain this cellular consciousness from an evolutionary perspective.

Nanozymes as Enzyme Inhibitors

Nanozyme is a type of nanomaterial with intrinsic enzyme-like activity. Following the discovery of nanozymes in 2007, nanozyme technology has become an emerging field bridging nanotechnology and biology, attracting research from multi-disciplinary areas focused on the design and synthesis of catalytically active nanozymes. However, various types of enzymes can be mimicked by nanomaterials, and our current understanding of nanozymes as enzyme inhibitors is limited. Here, we provide a brief overview of the utility of nanozymes as inhibitors of enzymes, such as R-chymotrypsin (ChT), β-galactosidase (β-Gal), β-lactamase, and mitochondrial F0F1-ATPase, and the mechanisms underlying inhibitory activity. The advantages, challenges and future research directions of nanozymes as enzyme inhibitors for biomedical research are further discussed.

How to Build a Biological Machine Using Engineering Materials and Methods

We present work in 3D printing electric motors from basic materials as the key to building a self-replicating machine to colonise the Moon. First, we explore the nature of the biological realm to ascertain its essence, particularly in relation to the origin of life when the inanimate became animate. We take an expansive view of this to ascertain parallels between the biological and the manufactured worlds. Life must have emerged from the available raw material on Earth and, similarly, a self-replicating machine must exploit and leverage the available resources on the Moon. We then examine these lessons to explore the construction of a self-replicating machine using a universal constructor. It is through the universal constructor that the actuator emerges as critical. We propose that 3D printing constitutes an analogue of the biological ribosome and that 3D printing may constitute a universal construction mechanism. Following a description of our progress in 3D printing motors, we suggest that this engineering effort can inform biology, that motors are a key facet of living organisms and illustrate the importance of motors in biology viewed from the perspective of engineering (in the Feynman spirit of “what I cannot create, I cannot understand”).

A solid-state NMR tool box for the investigation of ATP-fueled protein engines

Motor proteins are involved in a variety of cellular processes. Their main purpose is to convert the chemical energy released during adenosine triphosphate (ATP) hydrolysis into mechanical work. In this review, solid-state Nuclear Magnetic Resonance (NMR) approaches are discussed allowing studies of structures, conformational events and dynamic features of motor proteins during a variety of enzymatic reactions. Solid-state NMR benefits from straightforward sample preparation based on sedimentation of the proteins directly into the Magic-Angle Spinning (MAS) rotor. Protein resonance assignment is the crucial and often time-limiting step in interpreting the wealth of information encoded in the NMR spectra. Herein, potentials, challenges and limitations in resonance assignment for large motor proteins are presented, focussing on both biochemical and spectroscopic approaches. This work highlights NMR tools available to study the action of the motor domain and its coupling to functional processes, as well as to identify protein-nucleotide interactions during events such as DNA replication. Arrested protein states of reaction coordinates such as ATP hydrolysis can be trapped for NMR studies by using stable, non-hydrolysable ATP analogues that mimic the physiological relevant states as accurately as possible. Recent advances in solid-state NMR techniques ranging from Dynamic Nuclear Polarization (DNP), ³¹P-based heteronuclear correlation experiments, ¹H-detected spectra at fast MAS frequencies >100 kHz to paramagnetic NMR are summarized and their applications to the bacterial DnaB helicase from Helicobacter pylori are discussed.

A Chaperone for the Stator Units of a Bacterial Flagellum

The bacterial flagellum is a reversible rotating motor powered by ion transport through stator units, which also exert torque on the rotor component to turn the flagellum for motility. Species-specific adaptations to flagellar motors impact stator function to meet the demands of each species to sufficiently power flagellar rotation. We identified another evolutionary adaptation by discovering that FlgX of Campylobacter jejuni preserves the integrity of stator units by functioning as a chaperone to protect stator proteins from degradation by the FtsH protease complex due to the physiology of the bacterium. FlgX is required to maintain a level of stator units sufficient to power the naturally high-torque flagellar motor of C. jejuni for motility in intestinal mucosal layers to colonize hosts. Our work continues to identify an increasing number of adaptations to flagellar motors across bacterial species that provide the mechanics necessary for producing an effective rotating nanomachine for motility.

The stator units of the flagellum supply power to the flagellar motor via ion transport across the cytoplasmic membrane and generate torque on the rotor for rotation. Flagellar motors across bacterial species have evolved adaptations that impact and enhance stator function to meet the demands of each species, including producing stator units using different fuel types or various stator units for different motility modalities. Campylobacter jejuni produces one of the most complex and powerful flagellar motors by positioning 17 stator units at a greater radial distance than in most other bacteria to increase power and torque for high velocity of motility. We report another evolutionary adaptation impacting flagellar stators by identifying FlgX as a chaperone for C. jejuni stator units to ensure sufficient power and torque for flagellar rotation and motility. We discovered that FlgX maintains MotA and MotB stator protein integrity likely through a direct interaction with MotA that prevents their degradation. Suppressor analysis suggested that the physiology of C. jejuni drives the requirement for FlgX to protect stator units from proteolysis by the FtsH protease complex. C. jejuni ΔflgX was strongly attenuated for colonization of the natural avian host, but colonization capacity was greatly restored by a single mutation in MotA. These findings suggest that the likely sole function of FlgX is to preserve stator unit integrity for the motility required for host interactions. Our findings demonstrate another evolved adaptation in motile bacteria to ensure the equipment of the flagellar motor with sufficient power to generate torque for motility.

Multiple CheY Homologs Control Swimming Reversals and Transient Pauses in Azospirillum brasilense

Chemotaxis, together with motility, helps bacteria foraging in their habitat. Motile bacteria exhibit a variety of motility patterns, often controlled by chemotaxis, to promote dispersal. Motility in many bacteria is powered by a bidirectional flagellar motor. The flagellar motor has been known to briefly pause during rotation because of incomplete reversals or stator detachment. Transient pauses were previously observed in bacterial strains lacking CheY, and these events could not be explained by incomplete motor reversals or stator detachment. Here, we systematically analyzed swimming trajectories of various chemotaxis mutants of the monotrichous soil bacterium, Azospirillum brasilense. Like other polar flagellated bacterium, the main swimming pattern in A. brasilense is run and reverse. A. brasilense also uses run-pauses and putative run-reverse-flick-like swimming patterns, although these are rare events. A. brasilense mutant derivatives lacking the chemotaxis master histidine kinase, CheA4, or the central response regulator, CheY7, also showed transient pauses. Strikingly, the frequency of transient pauses increased dramatically in the absence of CheY4. Our findings collectively suggest that reversals and pauses are controlled through signaling by distinct CheY homologs, and thus are likely to be functionally important in the lifestyle of this soil organism.

Systems biology approach to late-onset Alzheimer's disease genome-wide association study identifies novel candidate genes validated using brain expression data and Caenorhabditis elegans experiments

INTRODUCTION

We sought to determine whether a systems biology approach may identify novel late-onset Alzheimer's disease (LOAD) loci.

METHODS

We performed gene-wide association analyses and integrated results with human protein-protein interaction data using network analyses. We performed functional validation on novel genes using a transgenic Caenorhabditis elegans Aβ proteotoxicity model and evaluated novel genes using brain expression data from people with LOAD and other neurodegenerative conditions.

RESULTS

We identified 13 novel candidate LOAD genes outside chromosome 19. Of those, RNA interference knockdowns of the C. elegans orthologs of UBC, NDUFS3, EGR1, and ATP5H were associated with Aβ toxicity, and NDUFS3, SLC25A11, ATP5H, and APP were differentially expressed in the temporal cortex.

DISCUSSION

Network analyses identified novel LOAD candidate genes. We demonstrated a functional role for four of these in a C. elegans model and found enrichment of differentially expressed genes in the temporal cortex.

Dissecting the peripheral stalk of the mitochondrial ATP synthase of chlorophycean algae

The algae Chlamydomonas reinhardtii and Polytomella sp., a green and a colorless member of the chlorophycean lineage respectively, exhibit a highly-stable dimeric mitochondrial F1Fo-ATP synthase (complex V), with a molecular mass of 1600 kDa. Polytomella, lacking both chloroplasts and a cell wall, has greatly facilitated the purification of the algal ATP-synthase. Each monomer of the enzyme has 17 polypeptides, eight of which are the conserved, main functional components, and nine polypeptides (Asa1 to Asa9) unique to chlorophycean algae. These atypical subunits form the two robust peripheral stalks observed in the highly-stable dimer of the algal ATP synthase in several electron-microscopy studies. The topological disposition of the components of the enzyme has been addressed with cross-linking experiments in the isolated complex; generation of subcomplexes by limited dissociation of complex V; detection of subunit-subunit interactions using recombinant subunits; in vitro reconstitution of subcomplexes; silencing of the expression of Asa subunits; and modeling of the overall structural features of the complex by EM image reconstruction. Here, we report that the amphipathic polymer Amphipol A8-35 partially dissociates the enzyme, giving rise to two discrete dimeric subcomplexes, whose compositions were characterized. An updated model for the topological disposition of the 17 polypeptides that constitute the algal enzyme is suggested. This article is part of a Special Issue entitled 'EBEC 2016: 19th European Bioenergetics Conference, Riva del Garda, Italy, July 2-6, 2016', edited by Prof. Paolo Bernardi.

The divide-and-conquer second-order proton propagator method based on nuclear orbital plus molecular orbital theory for the efficient computation of proton binding energies

An efficient computational method to evaluate the binding energies of many protons in large systems was developed.

A robust and efficient method for estimating enzyme complex abundance and metabolic flux from expression data

A major theme in constraint-based modeling is unifying experimental data, such as biochemical information about the reactions that can occur in a system or the composition and localization of enzyme complexes, with high-throughput data including expression data, metabolomics, or DNA sequencing. The desired result is to increase predictive capability and improve our understanding of metabolism. The approach typically employed when only gene (or protein) intensities are available is the creation of tissue-specific models, which reduces the available reactions in an organism model, and does not provide an objective function for the estimation of fluxes. We develop a method, flux assignment with LAD (least absolute deviation) convex objectives and normalization (FALCON), that employs metabolic network reconstructions along with expression data to estimate fluxes. In order to use such a method, accurate measures of enzyme complex abundance are needed, so we first present an algorithm that addresses quantification of complex abundance. Our extensions to prior techniques include the capability to work with large models and significantly improved run-time performance even for smaller models, an improved analysis of enzyme complex formation, the ability to handle large enzyme complex rules that may incorporate multiple isoforms, and either maintained or significantly improved correlation with experimentally measured fluxes. FALCON has been implemented in MATLAB and ATS, and can be downloaded from: https://github.com/bbarker/FALCON. ATS is not required to compile the software, as intermediate C source code is available. FALCON requires use of the COBRA Toolbox, also implemented in MATLAB.

Molecular machines - a new dimension of biological sciences

Biological systems are characterized by directional and precisely controlled flow of matter and information along with the maintenance of their structural patterns. This is possible thanks to sequential transformations of information, energy and structure carried out by molecular machines. The new perception of biological systems, including their mechanical aspects, requires the implementation of tools and approaches previously developed for engineering sciences. In this review paper, a biological system is presented in a new perspective as an ensemble of coordinated molecular devices functioning in the limited space confined by the biological membrane. The working of a molecular machine is presented using the example of F0F1 ATPase, and the general conditions necessary for the coordination of a large number of functional units are described.

Modeling stochastic kinetics of molecular machines at multiple levels: from molecules to modules

A molecular machine is either a single macromolecule or a macromolecular complex. In spite of the striking superficial similarities between these natural nanomachines and their man-made macroscopic counterparts, there are crucial differences. Molecular machines in a living cell operate stochastically in an isothermal environment far from thermodynamic equilibrium. In this mini-review we present a catalog of the molecular machines and an inventory of the essential toolbox for theoretically modeling these machines. The tool kits include 1), nonequilibrium statistical-physics techniques for modeling machines and machine-driven processes; and 2), statistical-inference methods for reverse engineering a functional machine from the empirical data. The cell is often likened to a microfactory in which the machineries are organized in modular fashion; each module consists of strongly coupled multiple machines, but different modules interact weakly with each other. This microfactory has its own automated supply chain and delivery system. Buoyed by the success achieved in modeling individual molecular machines, we advocate integration of these models in the near future to develop models of functional modules. A system-level description of the cell from the perspective of molecular machinery (the mechanome) is likely to emerge from further integrations that we envisage here.

Motor proteins and molecular motors: how to operate machines at the nanoscale

Several classes of biological molecules that transform chemical energy into mechanical work are known as motor proteins or molecular motors. These nanometer-sized machines operate in noisy stochastic isothermal environments, strongly supporting fundamental cellular processes such as the transfer of genetic information, transport, organization and functioning. In the past two decades motor proteins have become a subject of intense research efforts, aimed at uncovering the fundamental principles and mechanisms of molecular motor dynamics. In this review, we critically discuss recent progress in experimental and theoretical studies on motor proteins. Our focus is on analyzing fundamental concepts and ideas that have been utilized to explain the non-equilibrium nature and mechanisms of molecular motors.

pH-dependent regulation of electron transport and ATP synthesis in chloroplasts

This review is focused on pH-dependent mechanisms of regulation of photosynthetic electron transport and ATP synthesis in chloroplasts. The light-induced acidification of the thylakoid lumen is known to decelerate the plastoquinol oxidation by the cytochrome b 6 f complex, thus impeding the electron flow between photosystem II and photosystem I. Acidification of the lumen also triggers the dissipation of excess energy in the light-harvesting antenna of photosystem II, thereby protecting the photosynthetic apparatus against a solar stress. After brief description of structural and functional organization of the chloroplast electron transport chain, our attention is focused on the nature of the rate-limiting step of electron transfer between photosystem II and photosystem I. In the context of pH-dependent mechanism of photosynthetic control in chloroplasts, the mechanisms of plastoquinol oxidation by the cytochrome b 6 f complex have been considered. The light-induced alkalization of stroma is another factor of pH-dependent regulation of electron transport in chloroplasts. Alkalization of stroma induces activation of the Bassham-Benson-Calvin cycle reactions, thereby promoting efflux of electrons from photosystem I to NADP(+). The mechanisms of the light-induced activation of ATP synthase are briefly considered.

Molecular mechanisms for generating transmembrane proton gradients

Membrane proteins use the energy of light or high energy substrates to build a transmembrane proton gradient through a series of reactions leading to proton release into the lower pH compartment (P-side) and proton uptake from the higher pH compartment (N-side). This review considers how the proton affinity of the substrates, cofactors and amino acids are modified in four proteins to drive proton transfers. Bacterial reaction centers (RCs) and photosystem II (PSII) carry out redox chemistry with the species to be oxidized on the P-side while reduction occurs on the N-side of the membrane. Terminal redox cofactors are used which have pKas that are strongly dependent on their redox state, so that protons are lost on oxidation and gained on reduction. Bacteriorhodopsin is a true proton pump. Light activation triggers trans to cis isomerization of a bound retinal. Strong electrostatic interactions within clusters of amino acids are modified by the conformational changes initiated by retinal motion leading to changes in proton affinity, driving transmembrane proton transfer. Cytochrome c oxidase (CcO) catalyzes the reduction of O2 to water. The protons needed for chemistry are bound from the N-side. The reduction chemistry also drives proton pumping from N- to P-side. Overall, in CcO the uptake of 4 electrons to reduce O2 transports 8 charges across the membrane, with each reduction fully coupled to removal of two protons from the N-side, the delivery of one for chemistry and transport of the other to the P-side.

Torque measurement at the single-molecule level

Methods for exerting and measuring forces on single molecules have revolutionized the study of the physics of biology. However, it is often the case that biological processes involve rotation or torque generation, and these parameters have been more difficult to access experimentally. Recent advances in the single-molecule field have led to the development of techniques that add the capability of torque measurement. By combining force, displacement, torque, and rotational data, a more comprehensive description of the mechanics of a biomolecule can be achieved. In this review, we highlight a number of biological processes for which torque plays a key mechanical role. We describe the various techniques that have been developed to directly probe the torque experienced by a single molecule, and detail a variety of measurements made to date using these new technologies. We conclude by discussing a number of open questions and propose systems of study that would be well suited for analysis with torsional measurement techniques.

Kinetic mechanism of translocation and dNTP binding in individual DNA polymerase complexes

Complexes formed between phi29 DNA polymerase (DNAP) and DNA fluctuate discretely between the pre-translocation and post-translocation states on the millisecond time scale. The translocation fluctuations can be observed in ionic current traces when individual complexes are captured atop the α-hemolysin nanopore in an electric field. The presence of complementary 2'-deoxynucleoside triphosphate (dNTP) shifts the equilibrium across the translocation step toward the post-translocation state. Here we have determined quantitatively the kinetic relationship between the phi29 DNAP translocation step and dNTP binding. We demonstrate that dNTP binds to phi29 DNAP-DNA complexes only after the transition from the pre-translocation state to the post-translocation state; dNTP binding rectifies the translocation but it does not directly drive the translocation. Based on the measured time traces of current amplitude, we developed a method for determining the forward and reverse translocation rates and the dNTP association and dissociation rates, individually at each dNTP concentration and each voltage. The translocation rates, and their response to force, match those determined for phi29 DNAP-DNA binary complexes and are unaffected by dNTP. The dNTP association and dissociation rates do not vary as a function of voltage, indicating that force does not distort the polymerase active site and that dNTP binding does not directly involve a displacement in the translocation direction. This combined experimental and theoretical approach and the results obtained provide a framework for separately evaluating the effects of biological variables on the translocation transitions and their effects on dNTP binding.

Step detection in single-molecule real time trajectories embedded in correlated noise

Single-molecule real time trajectories are embedded in high noise. To extract kinetic or dynamic information of the molecules from these trajectories often requires idealization of the data in steps and dwells. One major premise behind the existing single-molecule data analysis algorithms is the gaussian 'white' noise, which displays no correlation in time and whose amplitude is independent on data sampling frequency. This so-called 'white' noise is widely assumed but its validity has not been critically evaluated. We show that correlated noise exists in single-molecule real time trajectories collected from optical tweezers. The assumption of white noise during analysis of these data can lead to serious over- or underestimation of the number of steps depending on the algorithms employed. We present a statistical method that quantitatively evaluates the structure of the underlying noise, takes the noise structure into account, and identifies steps and dwells in a single-molecule trajectory. Unlike existing data analysis algorithms, this method uses Generalized Least Squares (GLS) to detect steps and dwells. Under the GLS framework, the optimal number of steps is chosen using model selection criteria such as Bayesian Information Criterion (BIC). Comparison with existing step detection algorithms showed that this GLS method can detect step locations with highest accuracy in the presence of correlated noise. Because this method is automated, and directly works with high bandwidth data without pre-filtering or assumption of gaussian noise, it may be broadly useful for analysis of single-molecule real time trajectories.

The nonlinear chemo-mechanic coupled dynamics of the F 1 -ATPase molecular motor

The ATP synthase consists of two opposing rotary motors, F0 and F1, coupled to each other. When the F1 motor is not coupled to the F0 motor, it can work in the direction hydrolyzing ATP, as a nanomotor called F1-ATPase. It has been reported that the stiffness of the protein varies nonlinearly with increasing load. The nonlinearity has an important effect on the rotating rate of the F1-ATPase. Here, considering the nonlinearity of the γ shaft stiffness for the F1-ATPase, a nonlinear chemo-mechanical coupled dynamic model of F1 motor is proposed. Nonlinear vibration frequencies of the γ shaft and their changes along with the system parameters are investigated. The nonlinear stochastic response of the elastic γ shaft to thermal excitation is analyzed. The results show that the stiffness nonlinearity of the γ shaft causes an increase of the vibration frequency for the F1 motor, which increases the motor's rotation rate. When the concentration of ATP is relatively high and the load torque is small, the effects of the stiffness nonlinearity on the rotating rates of the F1 motor are obvious and should be considered. These results are useful for improving calculation of the rotating rate for the F1 motor and provide insight about the stochastic wave mechanics of F1-ATPase.

Currents in defective coupled ratchets

Transport phenomena in a one-dimensional system of interacting particles is studied. This system is embedded in a periodic and left-right asymmetric potential driven by a force periodic in time and space. When the density (number of particles per site) is an integer, directional current of the particles is collective; that is, it involves the whole system since all the sites are equivalents. On the other hand, when the system has a defect, a new localized or noncollective current appears due to the migration of defects from one site to another. We show here how this "defective" (defects generated) current can be controlled by white noise.

Single-molecule studies of viral DNA packaging

Many double-stranded DNA bacteriophages and viruses use specialized ATP-driven molecular machines to package their genomes into tightly confined procapsid shells. Over the last decade, single-molecule approaches - and in particular, optical tweezers - have made key contributions to our understanding of this remarkable process. In this chapter, we review these advances and the insights they have provided on the packaging mechanisms of three bacteriophages: φ 29, λ, and T4.

Molecular motors in conservative and dissipative regimes

We present a theoretical study of a rotatory molecular motor under a conservative torque regime. We show that conservative and dissipative regimes present a different observable phenomenology. Our approach starts with a preliminary deterministic calculation of the motor cycle, which is complemented with stochastic simulations of a Langevin equation under a flashing ratchet potential. Finally, by using parameter values obtained from independent experimental information, our theoretical predictions are compared with experimental data of the F(1)-ATPase motor of the Bacillus PS3.

Torque generation and utilization in motor enzyme F0F1-ATP synthase: half-torque F1 with short-sized pushrod helix and reduced ATP Synthesis by half-torque F0F1

ATP synthase (F(0)F(1)) is made of two motors, a proton-driven motor (F(0)) and an ATP-driven motor (F(1)), connected by a common rotary shaft, and catalyzes proton flow-driven ATP synthesis and ATP-driven proton pumping. In F(1), the central γ subunit rotates inside the α(3)β(3) ring. Here we report structural features of F(1) responsible for torque generation and the catalytic ability of the low-torque F(0)F(1). (i) Deletion of one or two turns in the α-helix in the C-terminal domain of catalytic β subunit at the rotor/stator contact region generates mutant F(1)s, termed F(1)(1/2)s, that rotate with about half of the normal torque. This helix would support the helix-loop-helix structure acting as a solid "pushrod" to push the rotor γ subunit, but the short helix in F(1)(1/2)s would fail to accomplish this task. (ii) Three different half-torque F(0)F(1)(1/2)s were purified and reconstituted into proteoliposomes. They carry out ATP-driven proton pumping and build up the same small transmembrane ΔpH, indicating that the final ΔpH is directly related to the amount of torque. (iii) The half-torque F(0)F(1)(1/2)s can catalyze ATP synthesis, although slowly. The rate of synthesis varies widely among the three F(0)F(1)(1/2)s, which suggests that the rate reflects subtle conformational variations of individual mutants.

Rotation and structure of FoF1-ATP synthase

F(o)F(1)-ATP synthase is one of the most ubiquitous enzymes; it is found widely in the biological world, including the plasma membrane of bacteria, inner membrane of mitochondria and thylakoid membrane of chloroplasts. However, this enzyme has a unique mechanism of action: it is composed of two mechanical rotary motors, each driven by ATP hydrolysis or proton flux down the membrane potential of protons. The two molecular motors interconvert the chemical energy of ATP hydrolysis and proton electrochemical potential via the mechanical rotation of the rotary shaft. This unique energy transmission mechanism is not found in other biological systems. Although there are other similar man-made systems like hydroelectric generators, F(o)F(1)-ATP synthase operates on the nanometre scale and works with extremely high efficiency. Therefore, this enzyme has attracted significant attention in a wide variety of fields from bioenergetics and biophysics to chemistry, physics and nanoscience. This review summarizes the latest findings about the two motors of F(o)F(1)-ATP synthase as well as a brief historical background.

Directed transport with real-time steering and drifts along predesigned paths using a Brownian motor

We have realized real-time steering of the directed transport in a Brownian motor based on cold atoms in optical lattices and demonstrate drifts along predesigned paths. The transport is induced by spatiotemporal asymmetries in the system, where we can control the spatial part, and we show that the response to changes in asymmetry is very fast. In addition to directional steering, a real-time control of the magnitude of the average drift velocity and an on-off switching of the motor are also demonstrated. We use a noninvasive real-time detection of the transport, enabling feedback control of the system.

Theoretical analysis of the F(1)-ATPase experimental data

F(1)-ATPase is a rotatory molecular motor fueled by ATP nucleotides. Different loads can be attached to the motor axis to show that it rotates in main discrete steps of 120 degrees with substeps of approximately 80 degrees and 40 degrees . Experimental data show the dependence on the mean rotational velocity omega with respect to the external control parameters: the nucleotide concentration [ATP] and the friction of the load gamma(L). In this work we present a theoretical analysis of the experimental data whose main results are: 1), A derivation of a simple analytical formula for omega([ATP], gamma(L)) that compares favorably with experiments; 2), The introduction of a two-state flashing ratchet model that exhibits experimental phenomenology of a greater specificity than has been, to our knowledge, previously available; 3), The derivation of an argument to obtain the values of the substep sizes; 4), An analysis of the energy constraints of the model; and 5), The theoretical analysis of the coupling ratio between the ATP consumed and the success of a forward step. We also discuss the compatibility of our approach with recent experimental observations.

Analytical model of ion transport and conversion of light energy in chloroplasts

An analytical model, which describes the stationary transformation of light energy to the energy of pigment electronic excitation, has been constructed. A proton pump of the thylakoid membrane has been considered as a two-level conformon. The difference between the energies of the excited and ground states of both the pigment and the protein complex is assumed to be the energy of an absorbed photon. It has been found how the concentration of ions in a lumen and the potential across the thylakoid membrane depend on the concentration of ions in the stroma and the brightness temperature of absorbed radiation. Conditions for the maximum efficiency of the photosynthesis process have been analyzed. This model has been used to determine the electric potential (phi approximately 6.7mV) at the chloroplast thylakoid membrane. The calculated value of the electric potential is in good agreement with the experimental data. A limitation on the stoichiometric coefficient of the proton transport through ATP-synthase, m>3, has been found theoretically.

Multiscale approaches for studying energy transduction in dynein

Cytoplasmic dynein is an important motor that drives all minus-end directed movement along microtubules. Dynein is a complex motor whose processive motion is driven by ATP-hydrolysis. Dynein's run length has been measured to be several millimetres with typical velocities in the order of a few nanometres per second. Therefore, the average time between steps is a fraction of a second. When this time scale is compared with typical time scales for protein side chain and backbone movements (approximately 10(-9) s and approximately 10(-5) s, respectively), it becomes clear that a multi-timescale modelling approach is required to understand energy transduction in this protein. Here, we review recent efforts to use computational and mathematical modelling to understand various aspects of dynein's chemomechanical cycle. First, we describe a structural model of dynein's motor unit showing a heptameric organization of the motor subunits. Second, we describe our molecular dynamics simulations of the motor unit that are used to investigate the dynamics of the various motor domains. Third, we present a kinetic model of the coordination between the two dynein heads. Lastly, we investigate the various potential geometries of the dimer during its hydrolytic and stepping cycle.

Electrodynamic ratchet motor

Brownian ratchets produce directed motion through rectification of thermal fluctuations and have been used for separation processes and colloidal transport. We propose a flashing ratchet motor that enables the transduction of electrical energy into rotary micromechanical work. This is achieved through torque generation provided by boundary shaping of equipotential surfaces. The present device contrasts to previous implementations that focus on translational motion. Stochastic simulations elucidate the performance characteristics of this device as a function of its geometry. Miniaturization to nanoscale dimensions yields rotational speeds in excess of 1 kHz, which is comparable to biomolecular motors of similar size.

The bacteriophage DNA packaging motor

An ATP-powered DNA translocation machine encapsidates the viral genome in the large dsDNA bacteriophages. The essential components include the empty shell, prohead, and the packaging enzyme, terminase. During translocation, terminase is docked on the prohead's portal protein. The translocation ATPase and the concatemer-cutting endonuclease reside in terminase. Remarkably, terminases, portal proteins, and shells of tailed bacteriophages and herpes viruses show conserved features. These DNA viruses may have descended from a common ancestor. Terminase's ATPase consists of a classic nucleotide binding fold, most closely resembling that of monomeric helicases. Intriguing models have been proposed for the mechanism of dsDNA translocation, invoking ATP hydrolysis-driven conformational changes of portal or terminase powering DNA motion. Single-molecule studies show that the packaging motor is fast and powerful. Recent advances permit experiments that can critically test the packaging models. The viral genome translocation mechanism is of general interest, given the parallels between terminases, helicases, and other motor proteins.

Dynamics and efficiency of Brownian rotors

Brownian rotors play an important role in biological systems and in future nanotechnological applications. However the mechanisms determining their dynamics, efficiency, and performance remain to be characterized. Here the F0 portion of the F-ATP synthase is considered as a paradigm of the Brownian rotor. In a generic analytical model we analyze the stochastic rotation of F0-like motors as a function of the driving free energy difference and of the free energy profile the rotor is subjected to. The latter is composed of the rotor interaction with its surroundings, of the free energy of chemical transitions, and of the workload. The dynamics and mechanical efficiency of the rotor depend on the magnitude of its stochastic motion driven by the free energy difference and its rectification on the reaction-diffusion path. We analyze which free energy profiles provide maximum flow and how their arrangement on the underlying reaction-diffusion path affects rectification and--by this--the efficiency.

The coupled chemomechanics of the F(1)-ATPase molecular motor

The enzyme F(1)-ATPase is a rotary nanomotor in which the central gamma subunit rotates inside the cavity made of alpha(3)beta(3) subunits. The experiments showed that the rotation proceeds in steps of 120 degrees and each 120 degrees step consists of 80 degrees and 40 degrees substeps. Here the Author proposes a stochastic wave mechanics of the F(1)-ATPase motor and combines it with the structure-based kinetics of the F(1)-ATPase to form a chemomechanic coupled model. The model can reproduce quantitatively and explain the experimental observations about the F(1) motor. Using the model, several rate-limited situations about gamma subunit rotation are proposed, the effects of the friction and the load on the substeps are investigated and the chemomechanic coupled time during ATP hydrolysis cycle is determined.

Proton transport and torque generation in rotary biomotors

We analyze the dynamics of rotary biomotors within a simple nanoelectromechanical model, consisting of a stator part and a ring-shaped rotor having 12 proton-binding sites. This model is closely related to the membrane-embedded F0 motor of adenosine triphosphate (ATP) synthase, which converts the energy of the transmembrane electrochemical gradient of protons into mechanical motion of the rotor. It is shown that the Coulomb coupling between the negative charge of the empty rotor site and the positive stator charge, located near the periplasmic proton-conducting channel (proton source), plays a dominant role in the torque-generating process. When approaching the source outlet, the rotor site has a proton energy level higher than the energy level of the site, located near the cytoplasmic channel (proton drain). In the first stage of this torque-generating process, the energy of the electrochemical potential is converted into potential energy of the proton-binding sites on the rotor. Afterwards, the tangential component of the Coulomb force produces a mechanical torque. We demonstrate that, at low temperatures, the loaded motor works in the shuttling regime where the energy of the electrochemical potential is consumed without producing any unidirectional rotation. The motor switches to the torque-generating regime at high temperatures, when the Brownian ratchet mechanism turns on. In the presence of a significant external torque, created by ATP hydrolysis, the system operates as a proton pump, which translocates protons against the transmembrane potential gradient. Here we focus on the F0 motor, even though our analysis is applicable to the bacterial flagellar motor.

Nanomechanical function from self-organizable dendronized helical polyphenylacetylenes

Self-organizable dendronized helical polymers provide a suitable architecture for constructing molecular nanomachines capable of expressing their motions at macroscopic length scales. Nanomechanical function is demonstrated by a library of self-organized helical dendronized cis-transoidal polyphenylacetylenes ( cis-PPAs) that possess a first-order phase transition from a hexagonal columnar lattice with internal order (varphi h (io)) to a hexagonal columnar liquid crystal phase (varphi h). These polymers can function as nanomechanical actuators. When extruded as fibers, the self-organizable dendronized helical cis-PPAs form oriented bundles. Such fibers have been shown capable of work by displacing objects up to 250-times their mass. The helical cis-PPA backbone undergoes reversible extension and contraction on a single molecule length scale resulting from cisoid-to-transoid conformational isomerization of the cis-PPA. Furthermore, we clarify supramolecular structural properties necessary for the observed nanomechanical function.