Unrevealed part of myosin's powerstroke accounts for high efficiency of muscle contraction

BackgroundMyosin II, the motor protein driving muscle contraction, uses energy of ATP hydrolysis to produce movement along actin. The key step of energy transduction is the powerstroke, involving rotation of myosin's lever while myosin is attached to actin. Macroscopic measurements indicated high thermodynamic efficiency for energy conversion. However, single-molecule experiments indicated lower efficiency, provoking a long-standing discrepancy.MethodsBased on the Fluctuation-Dissipation Theorem, we built a sufficiently detailed but low degree-of-freedom model reconstructing the entire mechanoenzymatic cycle.ResultsWe show that a high axial stiffness of the lever during an initial, experimentally yet unrevealed part of the powerstroke results in a short-time, ratchet-like Kramers effect, and is responsible for the missing efficiency. The second part of the powerstroke is an Eyring-like relaxation that dominantly contributes to lever rotation, but produces only a minor part of the work.ConclusionsThe model reveals the structural background of myosin's capability to function as a robust molecular engine and a very precise load sensor as well. Our model also suggests an explanation for the malfunction of myosins harboring mutations that lead to hypertrophic cardiomyopathies with most severe clinical prognosis.General significanceThe model explains how a force-transmitting device within a biological motor can enable high energetic efficiency.     

Elastic lever-arm model for myosin V

We present a mechanochemical model for myosin V, a two-headed processive motor protein. We derive the properties of a dimer from those of an individual head, which we model both with a four-state cycle (detached; attached with ADP.Pi; attached with ADP; and attached without nucleotide) and alternatively with a five-state cycle (where the powerstroke is not tightly coupled to the phosphate release). In each state the lever arm leaves the head at a different, but fixed, angle. The lever arm itself is described as an elastic rod. The chemical cycles of both heads are coordinated exclusively by the mechanical connection between the two lever arms. The model explains head coordination by showing that the lead head only binds to actin after the powerstroke in the trail head and that it only undergoes its powerstroke after the trail head unbinds from actin. Both models (four- and five-state) reproduce the observed hand-over-hand motion and fit the measured force-velocity relations. The main difference between the two models concerns the load dependence of the run length, which is much weaker in the five-state model. We show how systematic processivity measurement under varying conditions could be used to distinguish between both models and to determine the kinetic parameters.     

Ionic Dependence of Reversal Voltage of the Light Response in Limulus Ventral Photoreceptors

The light-induced current as measured using a voltage clamp (holding voltage at resting potential) is attenuated when sodium ions in the bathing solution, Na_o, are replaced by Tris, choline, or Li or when NaCl is replaced by sucrose. After replacement of NaCl by sucrose, the reversal voltage, V_rev, for the light response becomes more negative. In this case, the slope of the V_rev vs. log Na_o near Na_o = 425 mM is approximately 55 mV/decade increase of Na_o (mean for 13 cells). The slope decreases at lower values of Na_o. Choline is not impermeant and partially substitutes for Na; the slope of V_rev vs. log Na_o is 20 mV/decade (mean for three cells). V_rev does not change when Na is replaced by Li. Decreases in the bath concentrations of Ca, Mg, Cl, or K do not affect V_rev. When Na_o = 212 mM, V_rev becomes more positive when K_o is increased. Thus, light induces a change in membrane permeability to Na and probably also to K.     

Single molecule energetics of F1-ATPase motor

Motor proteins are essential in life processes because they convert the free energy of ATP hydrolysis to mechanical work. However, the fundamental question on how they work when different amounts of free energy are released after ATP hydrolysis remains unanswered. To answer this question, it is essential to clarify how the stepping motion of a motor protein reflects the concentrations of ATP, ADP, and P_i in its individual actions at a single molecule level. The F₁ portion of ATP synthase, also called F₁-ATPase, is a rotary molecular motor in which the central γ-subunit rotates against the α₃β₃ cylinder. The motor exhibits clear step motion at low ATP concentrations. The rotary action of this motor is processive and generates a high torque. These features are ideal for exploring the relationship between free energy input and mechanical work output, but there is a serious problem in that this motor is severely inhibited by ADP. In this study, we overcame this problem of ADP inhibition by introducing several mutations while retaining high enzymatic activity. Using a probe of attached beads, stepping rotation against viscous load was examined at a wide range of free energy values by changing the ADP concentration. The results showed that the apparent work of each individual step motion was not affected by the free energy of ATP hydrolysis, but the frequency of each individual step motion depended on the free energy. This is the first study that examined the stepping motion of a molecular motor at a single molecule level with simultaneous systematic control of ΔG_ATP. The results imply that microscopically defined work at a single molecule level cannot be directly compared with macroscopically defined free energy input.     

Influence of water activity on the enzyme biosynthesis and enzyme activities produced by Trichoderma viride TS in solid-state fermentation

Influence of water activity (a_w) on biosynthesis of polygalacturonase, d-xylanase and β-glucosidase in solid culture system of Trichoderma viride TS was studied. It was found that the production of enzymes was strongly affected by water activity of substrate and nature of a_w depressor used. The polygalacturonase and d-xylanase production were maximized at a_w = 0.995 whereas β-glucosidase formation was favored at a_w = 0.96–0.98. The influence of water activity on catalytic effect of enzymes using sodium chloride, glycerol and sorbitol as a_w depressor was also investigated. It was observed that sorbitol improved the thermal stability of polygalacturonase and d-xylanase.     

The ATPase Pathway That Drives the Kinesin-14 Kar3Vik1 Powerstroke

Kar3, a Saccharomyces cerevisiae microtubule minus-end-directed kinesin-14, dimerizes with either Vik1 or Cik1. The C-terminal globular domain of Vik1 exhibits the structure of a kinesin motor domain and binds microtubules independently of Kar3 but lacks a nucleotide binding site. The only known function of Kar3Vik1 is to cross-link parallel microtubules at the spindle poles during mitosis. In contrast, Kar3Cik1 depolymerizes microtubules during mating but cross-links antiparallel microtubules in the spindle overlap zone during mitosis. A recent study showed that Kar3Vik1 binds across adjacent microtubule protofilaments and uses a minus-end-directed powerstroke to drive ATP-dependent motility. The presteady-state experiments presented here extend this study and establish an ATPase model for the powerstroke mechanism. The results incorporated into the model indicate that Kar3Vik1 collides with the microtubule at 2.4 μm⁻¹ s⁻¹ through Vik1, promoting microtubule binding by Kar3 followed by ADP release at 14 s⁻¹. The tight binding of Kar3 to the microtubule destabilizes the Vik1 interaction with the microtubule, positioning Kar3Vik1 for the start of the powerstroke. Rapid ATP binding to Kar3 is associated with rotation of the coiled-coil stalk, and the postpowerstroke ATP hydrolysis at 26 s⁻¹ is independent of Vik1, providing further evidence that Vik1 rotates with the coiled coil during the powerstroke. Detachment of Kar3Vik1 from the microtubule at 6 s⁻¹ completes the cycle and allows the motor to return to its initial conformation. The results also reveal key differences in the ATPase cycles of Kar3Vik1 and Kar3Cik1, supporting the fact that these two motors have distinctive biological functions.     

Elastic deformations of the rotary double motor of single FoF1-ATP synthases detected in real time by Förster resonance energy transfer

Elastic conformational changes of the protein backbone are essential for catalytic activities of enzymes. To follow relative movements within the protein, Förster-type resonance energy transfer (FRET) between two specifically attached fluorophores can be applied. FRET provides a precise ruler between 3 and 8 nm with subnanometer resolution. Corresponding submillisecond time resolution is sufficient to identify conformational changes in FRET time trajectories. Analyzing single enzymes circumvents the need for synchronization of various conformations. F_OF₁-ATP synthase is a rotary double motor which catalyzes the synthesis of adenosine triphosphate (ATP). A proton-driven 10-stepped rotary F_O motor in the Escherichia coli enzyme is connected to a 3-stepped F₁ motor, where ATP is synthesized. To operate the double motor with a mismatch of step sizes smoothly, elastic deformations within the rotor parts have been proposed by W. Junge and coworkers. Here we extend a single-molecule FRET approach to observe both rotary motors simultaneously in individual F_OF₁-ATP synthases at work. We labeled this enzyme with two fluorophores specifically, that is, on the ε- and c-subunits of the two rotors. Alternating laser excitation was used to select the FRET-labeled enzymes. FRET changes indicated associated transient twisting within the rotors of single enzyme molecules during ATP hydrolysis and ATP synthesis. Supported by Monte Carlo simulations of the FRET experiments, these studies reveal that the rotor twisting is greater than 36° and is largely suppressed in the presence of the rotation inhibitor DCCD. This article is part of a Special Issue entitled: 17th European Bioenergetics Conference (EBEC 2012).     

Characterization of the deoxyribonuclease determined by lambda reverse as exonuclease VIII of Escherichia coli.

Gottesman et al. (1974) detected a new DNAase in Escherichia coli infected with λ reverse, a recombination-proficient substitution mutant of phage λ which is deleted for the λ recombination genes. We have purified this enzyme, using the procedure developed for the purification of exonuclease VIII (Kushner et al., 1974), a DNAase produced by E. coli K-12 strains carrying sbcA^? mutations. The λ reverse exonuclease (Exoλrev) is identical to exonuclease VIII by several criteria. The two enzymes elute at similar salt concentrations from DEAE-cellulose and DNA-cellulose; sediment at the same velocity in glycerol gradients, corresponding to a molecular weight of about 1.4 × 10⁵; migrate at the same R_F in sodium dodecyl sulfate/polyacrylamide gels, indicating a polypeptide molecular weight of 1.4 × 10⁵; exhibit maximum activity at 20 mm-Mg²⁺ and pH 8 to 9; and are much more active on double-stranded DNA than on heat-denatured DNA. Both enzymes are rendered sedimentable by antiserum against Exoλrev. This evidence supports the hypothesis that the non-λ DNA substitution in λ reverse includes recE, the structural gene for exonuclease VIII.     

Single-motor mechanics and models of the myosin motor

Recent progress in single-molecule detection techniques is remarkable. These techniques have allowed the accurate determination of myosin-head-induced displacements and how mechanical cycles are coupled to ATP hydrolysis, by measuring individual mechanical events and chemical events of actomyosin directly at the single-molecule level. Here we review our recent work in which we have made detailed measurements of myosin step size and mechanochemical coupling, and propose a model of the myosin motor.     

Screening assay for inhibitors of a recombinant Streptococcus pneumoniae UDP-glucose pyrophosphorylase

The UDP-glucose pyrophosphorylase of Streptococcus pneumoniae (GalU_Spn) is absolutely required for the biosynthesis of capsular polysaccharide, the sine qua non virulence factor of pneumococcus. Since the eukaryotic enzymes are completely unrelated to their prokaryotic counterparts, we propose that the GalU enzyme is a critical target to fight the pneumococcal disease. A recombinant GalU_Spn was overexpressed and purified. An enzymatic assay that is rapid, sensitive and easy to perform was developed. This assay was appropriate for screening chemical libraries for searching GalU inhibitors. This work represents a fundamental step in the exploration of novel antipneumococcal drugs.     

Free energy transduction in a chemical motor model

Motor enzymes catalyse chemical reactions, like the hydrolysis of ATP, and in the process they also perform work. Recent studies indicate that motor enzymes perform work with specific biochemical steps in their catalysed reactions, challenging the classical view that work can only be performed within a biochemical state. To address these studies an alternative class of models, often referred to as chemical motor models, has emerged in which motors perform work with biochemical transitions. In this paper, I develop a novel, self-consistent framework for chemical motor models, which accommodates multiple pathways for free energy transfer, predicts rich behaviors from the simplest multi-motor systems, and provides important new insights into muscle and motor function.     

Unthinned slow-growing ponderosa pine (Pinus ponderosa) trees contain muted isotopic signals in tree rings as compared to thinned trees

Key message

The muted wood isotopic signal in slow-growing trees of unthinned stands indicates lower responsiveness to changing environmental conditions compared to fast-growing trees in thinned stands.

Abstract

To examine the physiological processes associated with higher growth rates after thinning, we analyzed the oxygen isotopic values in wood (δ¹⁸O_w) of 12 ponderosa pine (Pinus ponderosa) trees from control, moderately, and heavily thinned stands and compared them with wood-based estimates of carbon isotope discrimination (?¹³C), basal area increment (BAI), and gas exchange. We found that (heavy) thinning led to shifts and increased inter-annual variability of both stable carbon and oxygen isotope ratios relative to the control throughout the first post-thinning decade. Results of a sensitivity analysis suggested that both an increase in stomatal conductance (g _s) and differences in source water among treatments are equally probable causes of the δ¹⁸O_w shift in heavily thinned stands. We modeled inter-annual changes in δ¹⁸O_w of trees from all treatments using environmental and physiological data and found that the significant increase in δ¹⁸O_w inter-annual variance was related to greater δ¹⁸O_w responsiveness to changing environmental conditions for trees in thinned stands when compared to control stands. Based on model results, the more muted climatic response of wood isotopes in slow-growing control trees is likely to be the consequence of reduced carbon sink strength causing a higher degree of mixing of previously stored and fresh assimilates when compared to faster-growing trees in thinned stands. Alternatively, the muted response of δ¹⁸O_w to climatic variation of trees in the control stand may result from little variation in the control stand in physiological processes (photosynthesis, transpiration) that are known to affect δ¹⁸O_w.     

Covalent binding of proteins and glucose-6-phosphate dehydrogenase to cellulosic carriers activated with s-triazine trichloride

A method was developed for covalently binding proteins and enzymes to cellulosic carriers such that the enzymes retained high specific activity. Optimal conditions for activating the carriers with s-triazine trichloride were found to be: (a) pretreatment of cellulose with 3 m NaOH; and (b) reaction with 5% ($\text{w}\text{w}$) s-triazine trichloride in dioxane-xylene (1:1 $\text{w}\text{w}$) for 30 min at room temperature. All proteins tested bound most readily at pH values below pH 7. Extensive investigation of immobilized glucose-6-phosphate dehydrogenase showed that: (a) over 80% of the specific activity of the enzyme was retained; and (b) the pH optimum and K_m values were not altered significantly from that of the free enzyme. The binding method has been applied successfully to hexokinase, phosphorylase and pronase.     

A biomechanically derived minimum work model of the fish gill lamellar system exhibits its exquisite morphological arrangement and perfusate regulation for oxygen uptake from water

To evaluate the efficiency of oxygen (O₂) uptake from water through the fish gill lamellar system, a cost function (CF) representing mechanical power expenditure for water ventilation and blood circulation through the gill was formulated, by applying steady-state fluid mechanics to a homogeneous lamellar-channel model. This approach allowed us to express CF as the function of inter-lamellar water channel width (w) and to derive an analytical solution of the width (w_min) at the minimum CF. Morphometric and physiological data for rainbow trout in the literature were referred to calculate CF(w) curves and their w_min values at five intensity stages of swimming exercise. Obtained w_min values were evenly distributed around the standard measure of the width (w_s = 24 μm) in this fish. Individual levels of CF(w_min) were also fairly close to the corresponding CF(w_s) values within a 10% deviation, suggesting the reliability of approximating [CF(w_min) = CF(w_s)]. The cost-performance of O₂ uptake through the gill (η_g) was then assessed from reported data of total O₂ uptake/CF(w_s) at each intensity stage. The η_g levels at any swimming stage exceeded 95% of the theoretical maximum value, implying that O₂ uptake is nearly optimally performed in the lamellar-channel system at all swimming speeds. Further analyses of O₂ transport in this fresh water fish revealed that the water ventilation by the buccal/opercular pumping evokes a critical limit of swimming velocity, due to confined O₂ supply to the peripheral skeletal muscles, which is avoided in ram ventilators such as tuna.     

Hydrophobic hydration processes: General thermodynamic model by thermal equivalent dilution determinations

The “hydrophobic hydration processes” can be satisfactorily interpreted on the basis of a common molecular model for water, consisting of two types of clusters, namely W_I and W_II accompanied by free molecules W_III. The principle of thermal equivalent dilution (TED) is the potent tool (Ergodic Hypothesis) employed to monitor the water equilibrium and to determine the number ξ_w of water molecules W_III involved in each process. The hydrophobic hydration processes can be subdivided into two Classes: Class A includes those processes for which the transformation A(−ξ_wW_I → ξ_wW_II + ξ_wW_III + cavity) takes place with the formation of a cavity, by expulsion of ξ_w water molecules W_III whereas Class B includes those processes for which the opposite transformation B(−ξ_wW_II − ξ_wW_III → ξ_wW_I − cavity) takes place with reduction of the cavity, by condensation of ξ_w water molecules W_III. The number ξ_w depends on the size of the reactants and measures the extent of the change in volume of the cavity. Disaggregating the thermodynamic functions ΔH_app and ΔS_app as the functions of T (or lnT) and ξ_w has enabled the separation of the thermodynamic functions into work and thermal components. The work functions ΔG_Work, ΔH_Work and ΔS_Work only refer specifically to the hydrophobic effects of cavity formation or cavity reduction, respectively. The constant self-consistent unitary (ξ_w = 1) work functions obtained from both large and small molecules indicate that the same unitary reaction is taking place, independent from the reactant size. The thermal functions ΔH_Th and ΔS_Th refer exclusively to the passage of state of water W_III.Essential mathematical algorithms are presented in the appendices.     

Influence of the extraction–purification conditions on final properties of alginates obtained from brown algae (Macrocystis pyrifera)

In this work, three methods (ethanol, HCl, and CaCl₂ routes) of sodium alginate extraction–purification from brown seaweeds (Macrocystis pyrifera) were used in order to study the influence of process conditions on final properties of the polymer. In the CaCl₂ route, was found that the precipitation step in presence of calcium ions followed by proton-exchange in acid medium clearly gives alginates with the lowest molecular weight and poor mechanical properties. It is well known that the acid treatment degrade the ether bonds on the polymeric chain. Ethanol route displayed the best performance, where the highest yield and rheological properties were attained with the lowest number of steps. Although the polymer I.1 showed a molar mass and polydispersity index (M_w/M_n) similar to those of commercial sample, its mechanical properties were lower. This performance is related to the higher content of guluronic acid in the commercial alginate, which promotes a more successful calcium chelation. Moreover, the employment of pH 4 in the acid pre-treatment improved the yield of the ethanol route, avoiding the ether linkage hydrolysis. Therefore, samples I.2 and I.3 displayed a higher M_w and a narrower distribution of molecular weights than commercial sample, which gave a higher viscosity and better viscoelastic properties.     

Mechanochemical Symmetry Breaking in Hydra Aggregates

Tissue morphogenesis comprises the self-organized creation of various patterns and shapes. Although detailed underlying mechanisms are still elusive in many cases, an increasing amount of experimental data suggests that chemical morphogen and mechanical processes are strongly coupled. Here, we develop and test a minimal model of the axis-defining step (i.e., symmetry breaking) in aggregates of the Hydra polyp. Based on previous findings, we combine osmotically driven shape oscillations with tissue mechanics and morphogen dynamics. We show that the model incorporating a simple feedback loop between morphogen patterning and tissue stretch reproduces a wide range of experimental data. Finally, we compare different hypothetical morphogen patterning mechanisms (Turing, tissue-curvature, and self-organized criticality). Our results suggest the experimental investigation of bigger (i.e., multiple head) aggregates as a key step for a deeper understanding of mechanochemical symmetry breaking in Hydra.     

Consequential cradle-to-gate carbon footprint of water treatment chemicals using simple and complex marginal technologies for electricity supply

Purpose

Chemicals produced via chlor-alkali electrolysis are widely used throughout the water industry worldwide, with treatment chemicals often the second largest source of environmental impacts from potable water production after electricity use. Population-driven increases in the future demand for potable water will require concomitant increases in the production of water treatment chemicals, with the associated environmental impacts of chemicals production primarily arising from the additional demand for electricity. Due to the dominance of electricity in the environmental performance of chlor-alkali chemicals, assessment of the future environmental impacts of potable water production is largely dependent on proper identification of the marginal source of electricity. In this paper, we present a consequential cradle-to-gate carbon footprint (cCF) for the most widely used chlor-alkali-produced disinfectant (sodium hypochlorite (13 % w/w)) and coagulant (ferric chloride (42 % w/w)) in Australia, with special emphasis placed upon the identification of future marginal electricity supply and the substitution of hydrogen gas and sodium hydroxide during production. While this analysis is presented in an Australian context, commonalities in potable water and chlor-alkali chemical production processes internationally give the findings a broader relevance.

Methods

Consequential models for sodium hypochlorite (13 % w/w) and ferric chloride (42 % w/w) production were developed, and the identification of the marginal source of electricity was modelled using a “simple marginal technology” approach via operationalisation of the Weidema framework and a “complex marginal technology” using a partial equilibrium model. For the simple marginal technology, the levelised cost of electricity was used to select the most competitive energy generation technologies and those most relevant for the Australian market. For the complex marginal technology, the energy sector model was used to simulate the most likely electricity supply mix. Details of the different paths taken in the substitution of hydrogen gas and sodium hydroxide are also presented. To allow for proper incorporation of uncertainties arising from these key factors in the cCF, several scenarios were developed covering fuel and carbon prices for identifying the marginal supply mix of electricity, as well as the likely production routes for sodium carbonate in the context of sodium hydroxide substitution.

Results and discussion

cCF results of sodium hypochlorite (13 % w/w) and ferric chloride (42 % w/w) are presented using simple and complex marginal technologies, and the implications of choosing one marginal technology over the other in the context of water treatment chemicals are presented. For the simple marginal technology approach, the global warming potential (GWP) per megagram of chemical varied from 68 to 429 kg CO₂-eq for sodium hypochlorite (13 % w/w) and 59–1,020 kg CO₂-eq for ferric chloride (42 % w/w). For the complex marginal technology approach, the GWP per megagram of chemical varied from 266 to 332 kg CO₂-eq for sodium hypochlorite (13 % w/w) and 214–629 kg CO₂-eq for ferric chloride (42 % w/w). Insights are given in relation to the impact of the price of fossil fuels, the carbon price, and the different substitution routes.

Conclusions

The use of a partial equilibrium model (PEM) has enabled a better understanding of the variability of the results in this study. For example, the use of PEM for the identification of the complex marginal source of electricity shows that, for the case of Australia, any benefit from a carbon price is lost with high prices of natural gas due to the incentive to use cheaper fuels such as black and brown coal. Likewise, the use of explorative scenarios was decisive to manage the inherent uncertainty of the parameters included in the model. In relation to substitution, the case of ferric chloride (42 % w/w) indicated that using only one substitution route was not enough to fully understand the potential continuum of cCF results. The simple marginal approach, where an exclusive marginal source of electricity or substitution route is considered, presents significant risks for the modelling accuracy of the cCF as shown here for sodium hypochlorite (13 % w/w) and ferric chloride (42 % w/w), therefore, it is not recommended.     

Preparation and solution properties of pullulan fractions as standard samples for water-soluble polymers

A series of pullulan fractions with molecular weights in the range 5 × 10³ to 8 × 10⁵ were prepared. The weight-average molecular weight (M_w) of all the samples was determined by sedimentation equilibrium. The hydrodynamic properties of pullulan in aqueous solution were investigated by viscometry and ultracentrifugation. The experimental results indicate that pullulan molecules in water are fairly stable and behave as expanded random coils when M_w is above 2 × 10⁴. The molecular weight distributions of the fractions were measured by gel filtration. The ratio M_w/M_n was close to 1·1, except for a sample with the highest M_w.It is concluded that the pullulan fractions prepared by the present work are well characterized and have a narrow molecular weight distribution. They may be useful as standard samples for studies of water-soluble polymers.