Energetic Bias Research Articles

Decomposition driven interface evolution for layers of binary mixtures. III. Two-dimensional steady films with flat and modulated surfaces

We study two-dimensional steady concentration and film thickness profiles for isothermal free surface films of a binary liquid mixture on a solid substrate employing model-H that couples the diffusive transport of the components of the mixture (convective Cahn-Hilliard equation) and the transport of momentum (Navier-Stokes-Korteweg equations). The analysis is based on minimising the underlying free energy equivalent to solving the static limit of model-H. Additionally, the linear stability (in time) of relevant layered films is analyzed. This allows for a comparison of the position of certain branching points in the bifurcation diagrams of steady solutions with the value predicted as onset of a linear instability. Results are presented for the cases of (i) a flat film without energetic bias at the free surface, (ii) a flat film with energetic bias, (iii) a height-modulated film without energetic bias, and (iv) a height-modulated film with energetic bias. In all cases we discuss symmetries of the various steady solutions allowing us to order them and to infer properties of solution branches and relations between them.

Fluorescence Triple Correlation Spectroscopy Resolves Ten Intermediates Along Different Parallel Ribosome Assembly Pathways

Efficient self-assembly of the bacterial 30S ribosomal subunit depends on the interplay of a large number of sequential RNA folding and protein binding events. In many cases the order of these events is not rigidly defined, giving rise to an assembly landscape crossed by parallel assembly pathways. The biological and biophysical implications of parallel assembly are unclear, and seem to contradict the current understanding of the ways large RNAs avoid kinetic traps. There has been very little direct characterization of the degree of parallel assembly in ribosomes because current biophysical techniques have difficulty resolving intermediates, especially with a large macromolecule (>500kDa) that requires high concentrations (100-1000nM) to assemble.To quantitate 30S intermediates, Fluorescence Correlation Spectroscopy (FCS) was extended to create Fluorescence Triple Correlation Spectroscopy (F3CS). By correlating three signals, F3CS can study complex stoichiometric systems, kinetic processes and irreversible reactions. Theory, numerical correlation strategies, and experimental practices were established and a two-photon excitation, three-color detection microscope was built to perform the first F3CS measurements. The technique is implemented as a suite of software, Triple Correlation Toolbox, to enable triple correlation experiments with existing microscopes.F3CS simultaneously identified intermediates both on and off the ribosome assembly pathways that were predicted by classic assembly maps. A weak energetic bias favors one assembly pathway over the others, but the bias energy is not strong enough to prevent the formation of intermediates off of the favored pathway. The interaction energies of ribosomal proteins S7, S9 and S19 are initially weak, which in principle reduces the potential for kinetic traps. F3CS has broad applications for identifying the subunit composition of non-ribosomal macromolecular complexes, non-destructively and in real time, and for identifying time-reversal asymmetries.

Design, synthesis and binding studies of a novel quadruple ADDA hydrogen-bond array

The design and synthesis of a novel ADDA hydrogen-bond array is described. The ureidodiimidazole motif (UDIM) 2 engages in interactions with complementary diamidonaphthyridine (DAN) 3 motifs with an association constant K(a) = 825 ± 16 M(-1) in chloroform. (1)H NMR and molecular modelling studies were carried out in order to explain the unexpected behaviour of this new supramolecular motif. These revealed that a combination of effects including; an energetic bias for the folded conformer, subtle differences in shape complementarity between the two components and the potential for self-association of UDIM 2 disfavour higher affinity interactions between the two components.

Decomposition driven interface evolution for layers of binary mixtures. II. Influence of convective transport on linear stability

We study the linear stability with respect to lateral perturbations of free surface films of polymer mixtures on solid substrates. The study focuses on the stability properties of the stratified and homogeneous steady film states studied in Part I [U. Thiele, S. Madruga, and L. Frastia, Phys. Fluids 19, 122106 (2007)]. To this aim, the linearized bulk equations and boundary equations are solved using continuation techniques for several different cases of energetic bias at the surfaces corresponding to linear and quadratic solutal Marangoni effects. For purely diffusive transport, an increase in the film thickness either exponentially decreases the lateral instability or entirely stabilizes the film. Including convective transport leads to a further destabilization as compared to the purely diffusive case. In some cases the inclusion of convective transport and the related widening of the range of available film configurations (it is then able to change its surface profile) change the stability behavior qualitatively. We furthermore present results regarding the dependence of the instability on several other parameters, namely, the Reynolds number, the surface tension number, and the ratio of the typical velocities of convective and diffusive transport.

Calculation of Proteins’ Total Side-Chain Torsional Entropy and Its Influence on Protein–Ligand Interactions

Despite the high density within a typical protein fold, the ensemble of sterically permissible side-chain repackings is vast. Here, we examine the extent of this variability that survives energetic biases due to van der Waals interactions, hydrogen bonding, salt bridges, and solvation. Monte Carlo simulations of an atomistic model exhibit thermal fluctuations among a diverse set of side-chain arrangements, even with the peptide backbone fixed in its crystallographic conformation. We have quantified the torsional entropy of this native-state ensemble, relative to that of a noninteracting reference system, for 12 small proteins. The reduction in entropy per rotatable bond due to each kind of interaction is remarkably consistent across this set of molecules. To assess the biophysical importance of these fluctuations, we have estimated side-chain entropy contributions to the binding affinity of several peptide ligands with calmodulin. Calculations for our fixed-backbone model correlate very well with experimentally determined binding entropies over a range spanning more than 80 kJ/(mol·308 K).

The Rop-Dimer: A Folded Protein Living Between Two Alternate Structures

A central assumption in protein folding is that a protein's native state is unique and stable. The Rop-dimer (Repressor Of Primer) shows strong changes in its folding kinetics and binding ability to RNA upon mutation of its hydrophobic core. Computer simulations investigated the possibility of two competing conformations to explain these results. Given an equivalent energetic bias, both conformations show different kinetic accessibilities in these simulations. Thus Rop's mutational behavior was explained by a preference of the kinetically less favored Wild-Type conformation for slow (un)folding mutants. Faster (un)folding mutants should prefer the kinetically favored conformation. For specific mutants it was suggested that the protein's native state is constituted by two competing conformations. Inspired by these simulations, single-molecule FRET-measurements verified the suggestion of two competing conformations constituting the native ensemble. Despite the need of a large-scale conformational change to get from the one conformation to the other, it shows that for a specific mutant the same dimer can adopt both conformations over time without disassociation of its monomers or changes in environmental conditions.

T7 RNA Polymerase Studied by Force Measurements Varying Cofactor Concentration

RNA polymerases carry out the synthesis of an RNA copy from a DNA template. They move along DNA, incorporate nucleotide triphosphate (NTP) at the end of the growing RNA chain, and consume chemical energy. In a single-molecule assay using the T7 RNA polymerase, we study how a mechanical force opposing the forward motion of the enzyme along DNA affects the translocation rate. We also study the influence of nucleotide and magnesium concentration on this process. The experiment shows that the opposing mechanical force is a competitive inhibitor of nucleotide binding. Also, the single-molecule data suggest that magnesium ions are involved in a step that does not depend on the external load force. These kinetic results associated with known biochemical and mutagenic data, along with the static information obtained from crystallographic structures, shape a very coherent view of the catalytic cycle of the enzyme: translocation does not take place upon NTP binding nor upon NTP cleavage, but rather occurs after PPi release and before the next nucleotide binding event. Furthermore, the energetic bias associated with the forward motion of the enzyme is close to kT and represents only a small fraction of the free energy of nucleotide incorporation and pyrophosphate hydrolysis.

Virial Scaling of Massive Dark Matter Halos: Why Clusters Prefer a High Normalization Cosmology

We present a precise estimate of the bulk virial scaling relation of halos formed via hierarchical clustering in an ensemble of simulated cold dark matter cosmologies. The result is insensitive to cosmological parameters; the presence of a trace, dissipationless gas component; and numerical resolution down to a limit of ~1000 particles. The dark matter velocity dispersion scales with total mass as log [σDM(M,z)] = = log(1082.9 ± 4.0 km s−1) + (0.3361 ± 0.0026)log[h(z)M200/1015 M☉], with h(z) being the dimensionless Hubble parameter. At fixed mass, the velocity dispersion likelihood is nearly lognormal, with scatter σln σ = 0.0426 ± 0.015, except for a tail with higher dispersions containing 10% of the population that are merger transients. We combine this relation with the halo mass function in ΛCDM models and show that a low normalization condition, S8 = σ8(Ωm/0.3)0.35 = 0.69, favored by recent WMAP and SDSS analysis requires that galaxy and gas-specific energies in rich clusters be 50% larger than that of the underlying dark matter. Such large energetic biases are in conflict with the current generation of direct simulations of cluster formation. A higher normalization, S8 = 0.80, alleviates this tension and implies that the hot gas fraction within r500 is , a value consistent with recent Sunyaev-Zel'dovich observations.

Mutations as trapdoors to two competing native conformations of the Rop-dimer.

Conformational transitions play a central role in regulating protein function. Structure-based models with multiple basins have been used to understand the mechanisms governing these transitions. A model able to accommodate multiple folding basins is proposed to explore the mutational effects in the folding of the Rop-dimer (Rop). In experiments, Rop mutants show unusually strong increases in folding rates with marginal effects on stability. We investigate the possibility of two competing conformations representing a parallel (P) and the wild-type antiparallel (AP) arrangement of the monomers as possible native conformations. We observe occupation of both distinct states and characterize the transition pathways. An interesting observation from the simulations is that, for equivalent energetic bias, the transition to the P basin (non-wild-type basin) shows a lower free-energy barrier. Thus, the rapid kinetics observed in experiments appear to be the result of two competing states with different kinetic behavior, triggered upon mutation by the opening of a trapdoor arising from Rop's symmetric structure. The general concept of having competing conformations for the native state goes beyond explaining Rop's mutational behaviors and can be applied to other systems. A switch between competing native structures might be triggered by external factors to allow, for example, allosteric control or signaling.

Exploring the relationship between funneled energy landscapes and two‐state protein folding

It should take an astronomical time span for unfolded protein chains to find their native state based on an unguided conformational random search. The experimental observation that folding is fast can be rationalized by assuming that protein energy landscapes are sloped towards the native state minimum, such that rapid folding can proceed from virtually any point in conformational space. Folding transitions often exhibit two-state behavior, involving extensively disordered and highly structured conformers as the only two observable kinetic species. This study employs a simple Brownian dynamics model of "protein particles" moving in a spherically symmetrical potential. As expected, the presence of an overall slope towards the native state minimum is an effective means to speed up folding. However, the two-state nature of the transition is eradicated if a significant energetic bias extends too far into the non-native conformational space. The breakdown of two-state cooperativity under these conditions is caused by a continuous conformational drift of the unfolded proteins. Ideal two-state behavior can only be maintained on surfaces exhibiting large regions that are energetically flat, a result that is supported by other recent data in the literature (Kaya and Chan, Proteins: Struct Funct Genet 2003;52:510-523). Rapid two-state folding requires energy landscapes exhibiting the following features: (i) A large region in conformational space that is energetically flat, thus allowing for a significant degree of random sampling, such that unfolded proteins can retain a random coil structure; (ii) a trapping area that is strongly sloped towards the native state minimum.

The Transition State for Folding of a Peripheral Subunit-binding Domain Contains Robust and Ionic-strength Dependent Characteristics

The denaturant dependencies of the folding and unfolding kinetics were used to characterize the structure of the transition state for folding of E3BD, a peripheral subunit-binding domain. For the majority of E3BD mutants, the Phi-values calculated at 298 K from the analysis of chevron plots were in good agreement with those previously determined at 325 K using Arrhenius analysis. This agreement further demonstrates the general robustness of Phi-value analyses, since different experiments, methods of denaturation and thermodynamic assumptions were used to determine each set of Phi(F) values. The structure of the transition state for folding was grossly conserved at 298 K and 325 K, with residues in Helix I playing a lesser role in folding than those located in the 3(10) helix, disordered loop and Helix II. However, the energetic contributions of a cluster of basic residues close to the N-terminus and Helix I, which are an integral part of the ligand-binding site, were susceptible to ionic strength effects because of electrostatic strain in native and transition states of E3BD at low ionic strength. We found no evidence of the downhill folding previously proposed for E3BD, even though the conditions employed in this study significantly increased the energetic bias towards the native state.

Bridge-Mediated Two-Electron Transfer via Delocalized Bridge Orbitals

Bridge mediated two-electron transfer (TET) in a donor-acceptor (D-A) complex is studied theoretically. A type of bridge is considered where the intersite coupling in the bridge becomes so large that the TET proceeds along delocalized bridge states but against the background of fast vibrational transitions within and between these states. The assumption of fast vibrational relaxations allows us to follow our earlier approach (Petrov; et al. J. Phys. Chem. B 2002, 106, 3092) and to derive kinetic equations governing the populations of the states involved in the TET reaction. The conditions are explained in detail at which a reduction to distant D-A TET can be carried out. Moreover, an analytic expression for the overall D-A TET rate is given for the case of a regular bridge as well as for a bridge perturbed by an intersite energetic bias. The stepwise and the concerted route of the D-A TET is analyzed in dependence on the bridge length. It is shown that the stepwise route follows from a thermal activation of a specific intermediate state. Its contribution to the overall transfer rate is determined by two single-electron transfer steps each of them related to two single-electron pathways through the bridge. The first pathway requires a population of the extended bridge state by thermal activation and thus can be termed the thermally activated pathway. The second pathway utilizes the bridging states as virtual intermediate states and thus is termed the single-electron superexchange pathway. The concerted D-A TET mechanism uses the extended bridge states as well as the mentioned intermediate state as virtual states. Therefore, it can be understood as a two-electron unistep superexchange transition between the D and the A. This transition can take place even at zero temperature. The perturbation of a regular arrangement of bridge levels by an energetic bias favors the stepwise route because it includes thermal activation of the intermediate state. This fact also explains that the efficiency of the concerted two-electron superexchange route is larger than that of the thermally activated stepwise route if low temperatures and short bridges (one or two units) are considered.

Interactions among glucose, lactate and adenosine regulate energy substrate utilization in hippocampal cultures

Glucose is the major energy source during normal adult brain activity. However, it appears that glial-derived lactate is preferred as an energy substrate by neurons following hypoxia–ischemia. We examined factors influencing this switch in energetic bias from glucose to lactate in cultured hippocampal neurons, focusing on the effects of the physiological changes in lactate, glucose and adenosine concentrations seen during hypoxia–ischemia. We show that with typical basal concentrations of lactate and glucose, lactate had no effect on glucose uptake. However, at the concentrations of these metabolites found after hypoxia–ischemia, lactate inhibited glucose uptake. Reciprocally, glucose had no effect on lactate utilization regardless of glucose and lactate concentrations. Furthermore, we find that under hypoglycemic conditions adenosine had a small, but significant, inhibitory effect on glucose uptake. Additionally, adenosine increased lactate utilization. Thus, the relative concentrations of glucose, lactate and adenosine, which are indicative of the energy status of the hippocampus, influence which energy substrates are used. These results support the idea that after hypoxia–ischemia, neurons are biased in the direction of lactate rather than glucose utilization and this is accomplished through a number of regulatory steps.

On the role of conformational geometry in protein folding

Using a lattice model of protein folding, we find that once certain native contacts have been formed, folding to the native state is inevitable, even if the only energetic bias in the system is nonspecific, homopolymeric attraction to a collapsed state. These conformations can be quite geometrically unrelated to the native state (with as low as only 53% of the native contacts formed). We demonstrate these results by examining the Monte Carlo kinetics of both heteropolymers under Go interactions and homopolymers, with the folding of both types of polymers to the native state of the heteropolymer. Although we only consider a 48-mer lattice model, our findings shed light on the effects of geometrical restrictions, including those of chain connectivity and steric excluded volume, on protein folding. These effects play a complementary role to that of the rugged energy landscape. In addition, the results of this work can aid in the interpretation of experiments and computer simulations of protein folding performed at elevated temperatures.

Voltammetric studies of bidirectional catalytic electron transport in Escherichia coli succinate dehydrogenase: comparison with the enzyme from beef heart mitochondria

The succinate dehydrogenases (SDH: soluble, membrane-extrinsic subunits of succinate:quinone oxidoreductases) from Escherichia coli and beef heart mitochondria each adsorb at a pyrolytic graphite ‘edge’ electrode and catalyse the interconversion of succinate and fumarate according to the electrochemical potential that is applied. E. coli and beef heart mitochondrial SDH share only ca. 50% homology, yet the steady-state catalytic activities, when measured over a continuous potential range, display very similar catalytic operating potentials and energetic biases (the relative ability to catalyse succinate oxidation vs. fumarate reduction). Importantly, E. coli SDH also exhibits the interesting ‘tunnel-diode’ behaviour previously reported for the mitochondrial enzyme. Thus as the potential is lowered below ca. −60 mV (pH 7, 38°C) the rate of catalytic fumarate reduction decreases abruptly despite an increase in driving force. Since the homology relates primarily to residues associated with active site regions, the marked similarity in the voltammetry reaffirms our previous conclusions that the tunnel-diode behaviour is a characteristic property of the enzyme active site. Thus, succinate dehydrogenase is an excellent fumarate reductase, but its activity in this direction is limited to a very specific range of potential.

Linear model of nitrogen balance and examination of the nature of true metabolisable energy and its nitrogen corrected form

1. The nature of nitrogen (N) corrected true metabolisable energy (TMEN) was derived using a linear model of N balance, constructed from the relationship between excreted and ingested N. 2. TME was described in terms of a regression line, formed from 'fed' points relating energy voided to energy ingested (GE), as GE- (afed + bGE)+afast. On assignment of theoretical excreta and ingested energy components, a deviation from conceptual metabolisable energy (MEc), equal to the difference between afed and afast, was established and attributed to metabolic urinary energy (UmE). 3. The N balance model is based on the form of relationship between N excreted and N ingested (Nl) that exhibits a linear deviation at 'initial' rates of N ingestion. The model postulates the following: The deviation is the result of a sparing effect of ingested N on the N component of UmE, viz. metabolic urinary N (UmN); The magnitude of UmN, through 'initial' values of fed N, is described by an intercept component, a a slope quantity, -(bnr-bna) Nl, where bNna and bnr are respectively the slopes of N excretion through 'initial' and 'subsequent' rates of ingested food N; The magnitude of the deviation from zero nitrogen balance (ZNB) through 'initial' and 'subsequent' rates of ingested N is the sum of the previous terms and aNm -(1-bNr) Nl, where aNm is the intercept component representing maintenance losses of N at fasting and (1- bNr) NI is the quantity of fed N retained to replace maintenance N loss. 4. Application of the appropriate energetic forms of UmN and aNm, viz. Et aNp -Et (bNr-bNna) NI and EuaNm, to the expression for obtaining TME, demonstrated that TME exceeded MEc by the quantities Et (bNr-bNna) NI and EtaNp, for test food intakes resulting in 'initial' and 'subsequent' rates of food N, respectively. 5. Application of appropriate energetic components of the model to simulate correction of TME to ZNB, demonstrated TMEZNB to be a biased quantity, deviating from MEc by the amount -Eu (1-bnr) NI or expressed as an excreta energy slope component, bEu(1-bNrNI/GE)GE where Eu is an appropriate energy coefficient. An alternative perspective is that ZNB correction removes the energetic form of UmN as a source of bias, but introduces one related to EuaNm. Its nature may be perceived by regarding TME as a function of a regression line relating energy excreted (EE) to energy ingested that has been corrected for UmN energetic bias and is pivoting on a fulcrum vertically aligned with the position of ZNB on the GE (x) axis. The regression line rotates anti-clockwise in response to ZNB correction by an amount equal to the magnitude of EuaNm measured on the EE (y) axis from the point of interception. 6. The study identified processes that may be employed to remove bias and improve precision of TME.

Characterization of foldable protein models: Thermodynamics, folding kinetics and force field

We propose three analytical models that describe the characteristics of proteins that can be folded into unique native structures. Model I is characterized by a mean-field single-residue energy which favors the native state and has a large energy gap between the native and non-native states; Model II involves mean-field cooperative interactions among the residues in the native states, and Model III is characterized by the mean-field single-residue energy at a low degree of folding and by the cooperative interactions among native residues at a high degree of folding. The thermodynamics of all three protein models exhibit two-state transition behavior, in which the non-native state is dominated by large entropy while the native state is determined by low energy. The folding kinetics of the models are studied by means of the master equation method. While the kinetics of folding of all three models are driven by the energetic biases of individual residues which favor the native state, the different interaction modes lead to different folding rates. It is found that the models with long-range cooperativity (i.e., Models II and III) fold several orders of magnitude faster than the model with only localized interactions (Model I). The intramolecular interactions that are responsible for the different properties of these models are examined, and the ways that these models may be used for developing the force fields for realistic proteins are discussed.

Correlation corrected periodic Hartree–Fock study of the interactions between water and the (001) magnesium oxide surface

A theoretical study of water adsorption on the surface of a three-layer (001) magnesium oxide film has been performed using periodic Hartree–Fock (PHF) theory with density-functional-based correlation corrections. The calculations treated two water molecules per MgO unit cell (one on each side of the film), and for most of the calculations, the size of the unit cell was chosen such that the ratio of water molecules to surface magnesium ions was 1:4. In these configurations the water dipoles were aligned parallel and the water–water spacing was 5.95 Å between molecules in neighboring cells. Nine geometries were examined, three of which were found to be strongly bound to the surface. The binding energies for the three bound configurations range from 4.1 to 8.9 kcal/mol at the PHF level of theory and 6.3 to 12.5 kcal/mol when correlation effects were included. For the two cases where the geometry of the bound water molecule was allowed to relax at the equilibrium water–film distance, the H–O–H angle increased 1–3° from the 6-31G* free molecule value of 105.6° and the O–H bond distance did not change. The six remaining geometries did not show significant binding to the surface. Additional calculations were performed in which the dipoles of the water molecules were aligned antiparallel. These calculations indicate that as the coverage increases the water molecules will tend to form islands on the magnesium oxide surface rather than wet the surface. The formation of a fully hydroxylated surface (one hydroxyl group added to every surface magnesium ion and one hydrogen atom to every surface oxygen ion) was also examined, but was found to be energetically unfavorable. The energetic bias against dissociative chemistry on the clean MgO (001) surface, consisting of fully five coordinated ions, is in agreement with previously published ultraviolet photoemission spectroscopy, x-ray photoemission spectroscopy, and IR studies.

Montecarlo Simulation of Charge Collection Time in Closed Ended HP Ge Gamma Detectors

Charge collection dynamics for gamma radiation in closed ended HP Ge detectors is numerically computed by means of a Montecarlo simulation. The resulting collection time spectra for different bias voltages are then compared with the ones obtained for true coaxial detectors. The geometrical shape of closed ended detectors affects charge collection times mainly for weakly energetic gamma rays and low bias voltages, adding both a slow and a fast tail to time spectra.