Uphill Steps Research Articles

Undulating Free Energy Landscapes Buffer Redox Chains from Environmental Fluctuations.

Roller-coaster or undulating free energy landscapes, with alternating high and low potential cofactors, occur frequently in biological redox chains. Yet, there is little understanding of the possible advantages created by these landscapes. We examined the tetraheme subunit associated with Blastochloris viridis reaction centers, comparing the dynamics of the native protein and of hypothetical (in silico) mutants. We computed the variation in the total number of electrons in wild type (WT) and mutant tetrahemes connected to an electron reservoir in the presence of a time-varying potential, as a model for a fluctuating redox environment. We found that roller-coaster free energy landscapes buffer the redox cofactor populations from these fluctuations. The WT roller-coaster landscape slows forward and backward electron transfer in the face of fluctuations, and may offer the advantage of sustaining the reduction of essential cofactors, such as the chlorophyll special pair in photosynthesis, even though an undulating landscape introduces thermodynamically uphill steps in multistep redox chains.

Formate dehydrogenase activity by a Cu(II)-based molecular catalyst and deciphering the mechanism using DFT studies.

Due to the requirement to establish renewable energy sources, formic acid (FA), one of the most probable liquid organic hydrogen carriers (LOHCs), has received great attention. Catalytic formic acid dehydrogenation in an effective and environmentally friendly manner is still a challenge. The N3Q3 ligand (N3Q3 = N,N-bis(quinolin-8-ylmethyl)quinolin-8-amine) and the square pyramidal [Cu(N3Q3)Cl]Cl complex have been synthesised in this work and characterised using several techniques, such as NMR spectroscopy, mass spectrometry, EPR spectroscopy, cyclic voltammetry, X-ray diffraction and DFT calculations. This work investigates the dehydrogenation of formic acid using a molecular and homogeneous catalyst [Cu(N3Q3)Cl]Cl in the presence of HCOONa. The mononuclear copper complex exhibits catalytic activity towards the dehydrogenation of formic acid in H2O with the evolution of a 1 : 1 CO2 and H2 mixture. The activation energy of formic acid dehydrogenation was calculated to be Ea = 86 kJ mol-1, based on experiments carried out at various temperatures. The Gibbs free energy was found to be 82 kJ at 298 K for the decomposition of HCOOH. The DFT studies reveal that [Cu(N3Q3)(HCOO-)]+ undergoes an uphill process of rearrangement followed by decarboxylation to generate [Cu(N3Q3)(H-)]+. The initial uphill step for forming a transition state is the rate-determining step. The [Cu(N3Q3)(H-)]+ follows an activated state in the presence of HCOOH to liberate H2 and generate the [Cu(N3Q3)(OH2)]2+.

Unexpected Heme Redox Potential Values Implicate an Uphill Step in Cytochrome b6f.

Cytochromes bc, key enzymes of respiration and photosynthesis, contain a highly conserved two-heme motif supporting cross-membrane electron transport (ET) that connects the two catalytic quinone-binding sites (Qn and Qp). Typically, this ET occurs from the low- to high-potential heme b, but in photosynthetic cytochrome b6f, the redox midpoint potentials (Ems) of these hemes remain uncertain. Our systematic redox titration analysis based on three independent and comprehensive low-temperature spectroscopies (continuous wave and pulse electron paramagnetic resonance (EPR) and optical spectroscopies) allowed for unambiguous assignment of spectral components of hemes in cytochrome b6f and revealed that Em of heme bn is unexpectedly low. Consequently, the cross-membrane ET occurs from the high- to low-potential heme introducing an uphill step in the energy landscape for the catalytic reaction. This slows down the ET through a low-potential chain, which can influence the mechanisms of reactions taking place at both Qp and Qn sites and modulate the efficiency of cyclic and linear ET in photosynthesis.

Making the second generation of molecular motors operate unidirectionally in response to electricity

Electricity is an attractive energy input to operate molecular motors. We found that anionization using constant potential could make the 2nd generation molecular motors operate under ground state unidirectionally, persistently, and free from ultraviolet light. In this approach, the original energetically uphill step with large energy barrier driven by ultraviolet could be replaced by a combination of an anionization step followed by an energetically downhill anionic isomerization and a neutralization step. Anionization decreases the energy barrier of the first isomerization step significantly, while the barrier of the second isomerization step still keeps high level, which ensures nearly 100% perfect unidirectionality kinetically. The free energy of the anionic intermediate isomer is lower enough than that of the original isomer, which makes the isomerization could be driven thermodynamically and ensures the nearly 100% perfect unidirectionality. We hope that our investigations could provide a new strategy for constructing electronic stimuli-responsive nanosystems based on the 2nd generation molecular motors.

An uncharacteristically low-potential flavin governs the energy landscape of electron bifurcation

Electron bifurcation, an energy-conserving process utilized extensively throughout all domains of life, represents an elegant means of generating high-energy products from substrates with less reducing potential. The coordinated coupling of exergonic and endergonic reactions has been shown to operate over an electrochemical potential of ∼1.3 V through the activity of a unique flavin cofactor in the enzyme NADH-dependent ferredoxin-NADP+ oxidoreductase I. The inferred energy landscape has features unprecedented in biochemistry and presents novel energetic challenges, the most intriguing being a large thermodynamically uphill step for the first electron transfer of the bifurcation reaction. However, ambiguities in the energy landscape at the bifurcating site deriving from overlapping flavin spectral signatures have impeded a comprehensive understanding of the specific mechanistic contributions afforded by thermodynamic and kinetic factors. Here, we elucidate an uncharacteristically low two-electron potential of the bifurcating flavin, resolving the energetic challenge of the first bifurcation event.

Electron flow in multiheme bacterial cytochromes is a balancing act between heme electronic interaction and redox potentials.

The naturally widespread process of electron transfer from metal reducing bacteria to extracellular solid metal oxides entails unique biomolecular machinery optimized for long-range electron transport. To perform this function efficiently, microorganisms have adapted multiheme c-type cytochromes to arrange heme cofactors into wires that cooperatively span the cellular envelope, transmitting electrons along distances greater than 100 Å. Implications and opportunities for bionanotechnological device design are self-evident. However, at the molecular level, how these proteins shuttle electrons along their heme wires, navigating intraprotein intersections and interprotein interfaces efficiently, remains a mystery thus far inaccessible to experiment. To shed light on this critical topic, we carried out extensive quantum mechanics/molecular mechanics simulations to calculate stepwise heme-to-heme electron transfer rates in the recently crystallized outer membrane deca-heme cytochrome MtrF. By solving a master equation for electron hopping, we estimate an intrinsic, maximum possible electron flux through solvated MtrF of 10(4)-10(5) s(-1), consistent with recently measured rates for the related multiheme protein complex MtrCAB. Intriguingly, our calculations show that the rapid electron transport through MtrF is the result of a clear correlation between heme redox potential and the strength of electronic coupling along the wire: thermodynamically uphill steps occur only between electronically well-connected stacked heme pairs. This observation suggests that the protein evolved to harbor low-potential hemes without slowing down electron flow. These findings are particularly profound in light of the apparently well-conserved staggered cross-heme wire structural motif in functionally related outer membrane proteins.

A First-Principles Study of the Role of Quaternary-N Doping on the Oxygen Reduction Reaction Activity and Selectivity of Graphene Edge Sites

Density functional theory (DFT) was used to investigate O2 chemisorption on the edge sites of graphene doped with quaternary nitrogen (N-graphene). The location of the doped quaternary N within the graphene cluster was systematically varied to determine the effect of interior versus edge doping on the reactivity of the edge graphene sites. Model 1b, where a quaternary-N atom is at the zigzag edge of the graphene cluster, is found to be the most favored structure and strongly adsorbs O2 molecule via a “two feet” geometry. For this most stable O2 binding configuration, the potential-dependent free energy of reaction for the subsequent oxygen reduction reaction (ORR) steps was evaluated. The favored four electron-proton transfer mechanism passes through a dissociative O*+OH* state instead of an OOH* intermediate, followed by a series of reduction steps to produce water. At the equilibrium potential for ORR of 1.23 V-NHE, the protonation of O* and OH* both show uphill steps, but the production of O* is facile with a small overpotential. An applied potential of −0.15 V-NHE is required to facilitate the protonation of OH* to water, a larger overpotential than observed experimentally. While solvent effects may reduce this overpotential, our results suggest that the edge of the N-graphene is very active towards activation of O2 and production of O* and OH* but because of strong binding of the oxygen atom, the subsequent steps of the ORR reaction will be hindered. Mechanisms that have OH* formed at the edge site and then move to adjacent sites for more facile protonation will have to be explored in the future.

Stair Ramp Leg Power Validation Study

The performance of daily tasks, such as stair climbing or lifting an object, requires both muscle strength and power. Age-associated reductions in strength and power can affect an older adult's ability to complete daily tasks such as standing up from a chair or lifting a grandchild (Miszko et al., 2003) and may decrease independence and increase falls. Currently, there are few tests for people over the age of 50 that can assess lower body power and quantify power accurately (Signorile et al., 2007). PURPOSE: The purpose of this study was to validate a new lower body power field test and compare this to a valid field test known as the Margaria-Kalamen stair climbing test using younger adults to initially prove the validity of the new test. METHODS: A one shot case study design was selected for this study. Subject (n = 9) characteristics (mean ± SD) included age (20-40 ± 2.7 yrs), gender (6 female/3 male), height (63.5 ± 1.3 in.), and weight (140 ± 4.5 lbs). A newly designed uphill step ramp method vs. regular stairs was utilized to determine power (force × distance/time). College students were used to reduce the risk of injury during this beta test. All subjects were weighed on a calibrated healthometer scale to determine accurate body weight before a 5 minute specific neuromuscular warm-up began. Once a neuromuscular warm up was performed, participants lined up 3 meters from the first step and sprinted up the stair ramp at full effort. Each subject was given 3 trial attempts, with 2-3 minutes of rest in-between to restore ATP-PC levels. The subjects performed the Margaria-Kalamen stair climbing test within an hour and obtained 3 power scores in watts (W), resting 2-5 minutes between each attempt. RESULTS: An intra-class correlation was selected to determine any variation between subjects' times during their 3 trials. Based on the results, the step ramp method is a reliable test to assess lower body power (r =.995). A Pearson Product Moment Correlation (r =.861) was conducted to determine differences in the best trial power (W) score (mean ± SD) between the Margaria-Kalamen Stair Test (618 ± 119 W) and the modified stair-ramp test (634 ± 119 W). CONCLUSION: Based upon this beta test, the step ramp power test -seems to be a reliable and reasonably good method for determining lower body power in young adults.

Molecular Basis for Directional Electron Transfer

Biological macromolecules involved in electron transfer reactions display chains of closely packed redox cofactors when long distances must be bridged. This is a consequence of the need to maintain a rate of transfer compatible with metabolic activity in the framework of the exponential decay of electron tunneling with distance. In this work intermolecular electron transfer was studied in kinetic experiments performed with the small tetraheme cytochrome from Shewanella oneidensis MR-1 and from Shewanella frigidimarina NCIMB400 using non-physiological redox partners. This choice allowed the effect of specific recognition and docking to be eliminated from the measured rates. The results were analyzed with a kinetic model that uses the extensive thermodynamic characterization of these proteins reported in the literature to discriminate the kinetic contribution of each heme to the overall rate of electron transfer. This analysis shows that, in this redox chain that spans 23 A, the kinetic properties of the individual hemes establish a functional specificity for each redox center. This functional specificity combined with the thermodynamic properties of these soluble proteins ensures directional electron flow within the cytochrome even outside of the context of a functioning respiratory chain.

Computational Mapping of the Conformational Transitions in Agonist Selective Pathways of a G-Protein Coupled Receptor

The active state conformation of a G-protein coupled receptor (GPCR) is influenced by the chemical structure and the efficacy of the bound ligand. Insight into the active state conformation as well as the activation pathway for ligands with different efficacies is critical in designing functionally specific drugs for GPCRs. Starting from the crystal structure of the beta2-adrenergic receptor, we have used coarse grain computational methods to understand the modulation of the potential energy landscape of the receptor by two full agonists, two partial agonists, and an inverse agonist. Our coarse grain method involves a systematic conformational spanning of the receptor transmembrane helices followed by an energy minimization and ligand redocking in each sampled conformation. We have derived the activation pathways for several agonists and partial agonists, using a Monte Carlo algorithm, and these are in agreement with fluorescence spectroscopy measurements. The calculated pathways for the full agonists start with an energy downhill step leading to a stable intermediate followed by a barrier crossing leading to the active state. We find that the barrier crossing involves breaking of an interhelical hydrogen bond between helix5 and helix6, and polarization of the binding site residues by water facilitates the barrier crossing. The uphill step in the partial agonist salbutamol induced activation is distinct from full agonist norepinephrine, and originates from steric hindrance with the aromatic residues on helix6. Virtual ligand screening with the salbutamol-stabilized conformation shows enrichment of noncatechol agonists over the norepinephrine-stabilized conformation. Our computational method provides an unprecedented opportunity to derive hypotheses for experiments and also understand activation mechanisms in GPCRs.

Surface mass diffusion and step stiffness on V(011)

By step fluctuation experiments on V(011) thin films grown on (112¯0) α-Al2O3, using low energy electron microscopy, we determine the coefficient of surface mass diffusion Ds in the temperature range of 1170K<T<1560K, centered near 0.6Tm, with the melting temperature Tm=2183K for V. As is common to annealed V, Nb, and Ta in UHV, submonolayer coverages of O were present on the otherwise clean and well-defined surface. We obtain Ds=0.8exp (−1.43eV∕kBT)cm2∕s for this temperature interval. Compared to Nb(011), the step stiffness obtained from the measurements is relatively small and isotropic at ∼60meV∕nm. Sublimation is made visible by uphill step flow above 1460K, with a temperature dependence consistent with the known cohesive energy.

Kinetic Performance and Energy Profile in a Roller Coaster Electron Transfer Chain: A Study of Modified Tetraheme-Reaction Center Constructs

In many electron-transfer proteins, the arrangement of cofactors implies a succession of uphill and downhill steps. The kinetic implications of such arrangements are examined in the present work, based on a study of chimeric photosynthetic reaction centers obtained by expressing the tetraheme subunit from Blastochloris viridis in another purple bacterium, Rubrivivax gelatinosus. Site-directed mutations of the environment of heme c559, which is the immediate electron donor to the primary donor P, induced modifications of this heme's midpoint potential over a range of 400 mV. This resulted in shifts of the apparent midpoint potentials of the neighboring carriers, yielding estimates of the interactions between redox centers. At both extremities of the explored range, the energy profile of the electron-transfer chain presented an additional uphill step, either downstream or upstream from c559. These modifications caused conspicuous changes of the electron-transfer rate across the tetraheme subunit, which became approximately 100-fold slower in the mutants where the midpoint potential of c559 was lowest. A theoretical analysis of the kinetics is presented, predicting a displacement of the rate-limiting step when lowering the potential of c559. A reasonable agreement with the data was obtained when combining this treatment with the rates predicted by electron transfer theory for the individual rate constants.

Gender Differences In The 3000 Meter Steeplechase Water Jump

The 3000m steeplechase has been competed among women in the United States since 1996 and among men since the 1800's. While conditioning is of great importance to steeplechase athletes, technique through 35 barriers, seven of them with a 3.66m water pit following the barrier, plays a major role in how successful an athlete may be. The barriers have heights of 0.914m and 0.762m for men and women respectively. With the slower running speeds of women and the differences in barrier heights, it is expected that the movement patterns of each gender will vary over barrier with a water pit following it. PURPOSE This study investigated the differences between men and women in 3000m steeplechase water-jump technique. METHODS Eighteen men and twelve women were filmed at three major track and field meets during the 2004 season. A two-dimensional analysis was used to determine horizontal velocities throughout the jump, the distance from takeoff to the barrier, knee extension at pushoff from the barrier, and the distance from the barrier to landing in the water. Analysis of variance was used to determine technique differences between genders. RESULTS Race pace, horizontal velocity approaching the barrier, and horizontal velocity leaving the water were all significantly greater for men (p<0.001). Horizontal velocity divided by race pace was greater for men compared with women (0.90 and 0.86 respectively, p=0.003). This may be due to a greater horizontal velocity approaching the barrier and a greater landing distance for men (p=0.003). The approach was also different for men than women. Men had a greater hip angle at takeoff to the barrier which approached significance (p=0.052) and a greater distance from takeoff to the barrier (p<0.001). This may be due to the higher barrier for men and the greater approach velocity. CONCLUSION Women may need to be coached differently in technique for the water jump. With the lower approach velocity for women, there is a need to takeoff closer to the barrier. The lower approach velocity also appears to lead to a shorter jump and as consequence, results with an uphill step out of the water pit following landing. Thus, women's race paces are affected more by the water jump than men.

Electron Transfer and Catalytic Control by the Iron−Sulfur Clusters in a Respiratory Enzyme,E.coliFumarate Reductase

Factors governing the efficacy of long-range electron relays in enzymes have been examined using protein film voltammetry in conjunction with site-directed mutagenesis. Investigations of the fumarate reductase from Escherichia coli, in which three Fe-S clusters relay electrons over more than 30 A, lead to the conclusion that varying the medial [4Fe-4S] cluster potential over a 100 mV range does not have a significant effect on the inherent kinetics of electron transfer to and from the active-site flavin. The results support a proposal that the reduction potential of an individual electron relay site in a multicentered enzyme is not a strong determinant of activity; instead, as deduced from the potential dependence of catalytic electron transfer, electron flow through the intramolecular relay is rapid and reversible, and even uphill steps do not limit the catalytic rate.

Kinetic and Thermodynamic Aspects of NAD-Related Enzyme-Linked Mediated Bioelectrocatalysis

The diaphorase-catalyzed electrochemical oxidation of NADH with the aid of quinones (MAP) or ferrocene derivatives (FMCA) as electron transfer mediators was studied by cyclic voltammetry under variable conditions of concentration polarization of NADH near the electrode surface. The suppression of this polarization was obtained by the redox L-lactate dehydrogenase-catalyzed reaction between L-lactate and NAD+. The addition of pyruvate inhibits the formation of NADH owing to the thermodynamically unfavorable (uphill) electron transfer from L-lactate to NAD+. The role played by the uphill/downhill character of the last step of the catalytic chain was illustrated by regenerating NADH using the redox couple gluconolactone/glucose with glucose dehydrogenase as catalyst. The influence on the catalytic wave of the presence of a downhill or uphill step between diaphorase and NAD+/NADH couple was also rationalized via the digital simulation technique using experimental data reported in the literature.

Determination of step-edge orientation by helium atom scattering

Helium atom scattering (HAS) has been used to determine the step-edge orientation on a Rh(311) surface, whose close-packed rows are separated by alternating (100) and (111) microfacets. The measurements were performed on a surface in which the step density was previously increased by sputtering. Intense additional peaks were observed at $\ensuremath{\sim}48\ifmmode^\circ\else\textdegree\fi{}$ and $\ensuremath{\sim}56\ifmmode^\circ\else\textdegree\fi{}$ from the specular beam when the incident He beam was impinging on the (100) or (111) microfacets, respectively. The same behavior was observed at different He energies and angles of incidence, demonstrating that the observed peaks are caused by specular diffraction at uphill step edges. The step height could also be determined from the appearance of additional maxima at higher He energies. These results allow us to determine the in-plane scattering geometry in HAS studies of stepped surfaces in a very simple way.

Classification by ordering a (sparse) matrix: a “simulated annealing” approach

A technique is described, due to Gourlay, for classifying similarity/interaction data in the form of a sparse matrix. Element weights in the matrix are drawn closer to the leading diagonal, thereby packing related items together. Some undersirable properties of the original algorithm are noted and modifications are suggested, principally the use of circularly connected matrices and the permitting of uphill steps in order to avoid local minima as the algorithm traverses the cost-function landscape. The controlled use of uphill steps is known as simulated annealing, by analogy with the slow cooling of liquids in thermodynamics. Methods of identifying subsystem structure in the reordered matrix are examined. The techniques described in this paper and their relation to previous work are illustrated by applying them to a classic study on the confusion of consonants. Diverse uses of the generalised reordering algorithm are described, including a representation of the travelling salesman problem whose runtime cost is approximately linear with N, allowing very large problems to be tackled.

Solving Quadratic Assignment Problems by ‘Simulated Annealing’

Abstract Recently, an interesting analogy between problems in combinatorial optimization and statistical mechanics has been developed and has proven useful in solving certain traditional optimization problems such as computer design, partitioning, component placement, wiring, and traveling salesman problems. The analogy has resulted in a methodology, termed “simulated annealing,” which, in the process of iterating to an optimum, uses Monte Carlo sampling to occasionally accept solutions to discrete optimization problems which increase rather than decrease the objective function value. This process is counter to the normal ‘steepest-descent’ algorithmic approach. However, it is argued in the analogy that by taking such controlled uphill steps, the optimizing algorithm need not get “stuck” on inferior solutions. This paper presents an application of the simulated annealing method to solve the quadratic assignment problem (QAP). Performance is tested on a set of “standard” problems, as well as some newly gen...

Using simulated annealing to solve routing and location problems

AbstractIn recent papers by Kirkpatrick et al., an analogy between the statistical mechanics of large multivariate physical systems and combinatorial optimization has been presented and used to develop a general strategy for solving discrete optimization problems. The method relies on probabilistically accepting intermediate increases in the objective function through a set of user‐controlled parameters. It is argued that by taking such controlled uphill steps, from time to time, a high quality solution can eventually be found in a moderate amount of computer time. In this paper, we implement this idea, apply it to the traveling salesman problem and the p‐median location problem, and test the approach extensively.

Layer assignment by simulated annealing

A linear heuristic method for the via minimization problem for 2 layers, which is similar to the simulation of the process of cristallization, is introduced. The idea of this method is starting from an initial configuration, not only to accept rearrangements that lower the cost function but to allow also controlled uphill steps.