Shannon entropy as a predictor of avoided crossing in confined atoms

Avoided crossing is one of the unique spectroscopic features of a confined atomic system. Shannon information entropy of the ground state and some of the excited states of confined H atom as a predictor of avoided crossing is studied in this work. This is accomplished by varying the strength of the confinement and examining structure properties like ionization energy and Shannon information entropy. Along with the energy level repulsion at the avoided crossing, Shannon information entropy is also exchanged between the involved states. This work also addresses a question: In addition to that regarding localization, what other property of the system can be extracted from Shannon entropy? Insightful connection is discovered between Shannon entropy and the average value of confinement potential, Coulomb potential, and kinetic energy.     

Photosynthetic models with maximum entropy production in irreversible charge transfer steps

Steady-state bacterial photosynthesis is modelled as cyclic chemical reaction and is examined with respect to overall efficiency, power transfer efficiency, and entropy production. A nonlinear flux–force relationship is assumed. The simplest two-state kinetic model bears complete analogy with the performance of an ideal (zero ohmic resistance of the P–N junction) solar cell. In both cases power transfer to external load is much higher than the 50% allowed by the impedance matching theorem for the linear flux–force relationship. When maximum entropy production is required in the transition with a load, one obtains high optimal photochemical yield of 97% and power transfer efficiency of 91%. In more complex photosynthetic models, entropy production is maximized in all irreversible electron/proton (non-slip) transitions in an iterative procedure. The resulting steady-state is stable with respect to an extremely wide range of initial values for forward rate constants. Optimal proton current increases proportionally to light intensity and decreases with an increase in the proton-motive force (the backpressure effect). Optimal affinity transfer efficiency is very high and nearly perfectly constant for different light absorption rates and for different electrochemical proton gradients. Optimal overall efficiency (of solar into proton-motive power) ranges from 10% (bacteriorhodopsin) to 19% (chlorophyll-based bacterial photosynthesis). Optimal time constants in a photocycle span a wide range from nanoseconds to milliseconds, just as corresponding experimental constants do. We conclude that photosynthetic proton pumps operate close to the maximum entropy production mode, connecting biological to thermodynamic evolution in a coupled self-amplifying process.     

Conformational Dynamics of Human ALKBH2 Dioxygenase in the Course of DNA Repair as Revealed by Stopped-Flow Fluorescence Spectroscopy

Elucidation of physicochemical mechanisms of enzymatic processes is one of the main tasks of modern biology. High efficiency and selectivity of enzymatic catalysis are mostly ensured by conformational dynamics of enzymes and substrates. Here, we applied a stopped-flow kinetic analysis based on fluorescent spectroscopy to investigate mechanisms of conformational transformations during the removal of alkylated bases from DNA by ALKBH2, a human homolog of Escherichia coli AlkB dioxygenase. This enzyme protects genomic DNA against various alkyl lesions through a sophisticated catalytic mechanism supported by a cofactor (Fe(II)), a cosubstrate (2-oxoglutarate), and O₂. We present here a comparative study of conformational dynamics in complexes of the ALKBH2 protein with double-stranded DNA substrates containing N1-methyladenine, N3-methylcytosine, or 1,N6-ethenoadenine. By means of fluorescent labels of different types, simultaneous detection of conformational transitions in the protein globule and DNA substrate molecule was performed. Fitting of the kinetic curves by a nonlinear-regression method yielded a molecular mechanism and rate constants of its individual steps. The results shed light on overall conformational dynamics of ALKBH2 and damaged DNA during the catalytic cycle.     

Minimizing the Entropy Penalty for Ligand Binding: Lessons from the Molecular Recognition of the Histo Blood‐Group Antigens by Human Galectin‐3

Ligand conformational entropy plays an important role in carbohydrate recognition events. Glycans are characterized by intrinsic flexibility around the glycosidic linkages, thus in most cases, loss of conformational entropy of the sugar upon complex formation strongly affects the entropy of the binding process. By employing a multidisciplinary approach combining structural, conformational, binding energy, and kinetic information, we investigated the role of conformational entropy in the recognition of the histo blood‐group antigens A and B by human galectin‐3, a lectin of biomedical interest. We show that these rigid natural antigens are pre‐organized ligands for hGal‐3, and that restriction of the conformational flexibility by the branched fucose (Fuc) residue modulates the thermodynamics and kinetics of the binding process. These results highlight the importance of glycan flexibility and provide inspiration for the design of high‐affinity ligands as antagonists for lectins.     

Benchmark values of Shannon entropy for spherically confined hydrogen atom

The information‐theoretic measure of confined hydrogen atom has been investigated extensively in the literature. However, most of them were focused on the ground state and accurate values of information entropies, such as Shannon entropy, for confined hydrogen are still not determined. In this work, we establish the benchmark results of the Shannon entropy for confined hydrogen atom in a spherical impenetrable sphere, in both position and momentum spaces. This is done by examining the bound state energies, the normalization of wave functions, and the scaling property with respect to isoelectronic hydrogenic ions. The angular and radial parts of Shannon entropy in two conjugate spaces are provided in detail for both free and confined hydrogen atom in ground and several excited states. The entropies in position space decrease logarithmically with decreasing the size of confinement, while those in momentum space increase logarithmically. The Shannon entropy sum, however, approaches to finite values when the confinement radius closes to zero. It is also found that the Shannon entropy sum shares same trend for states with similar density distributions. Variations of entropy for nodeless bound states are significantly distinct form those owning nodes when changing the confinement radius.     

Mechanism and kinetics of the enzymatic hydrolysis of polyester nanoparticles by lipases

The degradation of several aliphatic and aromatic polyesters with lipases from Candida cylindracea (CcL) and Pseudomonas species (PsL) was investigated applying nanoparticles of the polymers. Nanoparticles (diameters 50 nm to 250 nm) of a particle concentration up to 6 mg/ml could be prepared by a precipitation technique without adding any stabilizing agents in the aqueous solutions. Using a titration system to monitor ester cleavage, enzymatic degradation experiments could be performed in the time scale of some minutes. A kinetic model is proposed which is based on a surface erosion process dependent on molar ester bond density and enzyme loading. Experimental evidence provided that degradation of the particles occurs uniformly at the surface after a Langmuir type adsorption of the enzyme. Rate constants and the maximal enzyme loadings of enzyme were estimated from the kinetic model for different polyesters and the rate constants correlate well with the length of the diacid component of the polyester. Comparison of degradation rates of polyester films and nanoparticles revealed that nanoparticles of aliphatic polyesters are in the amorphous state. Hence, differences of the rate constants reflect the direct influence of the polymer structure on the enzymatic hydrolysis not overlaid by effects of crystallinity.     

Wild-type and molten globular chorismate mutase achieve comparable catalytic rates using very different enthalpy/entropy compensations

The origin of the catalytic power of enzymes with a meta-stable native state,e.g.molten globular state,is an unsolved challenging issue in biochemistry.To help understand the possible differences between this special class of enzymes and the typical ones,we report here computer simulations of the catalysis of both the well-folded wild-type and the molten globular mutant of chorismate mutase.Using the ab initio quantum mechanical/molecular mechanical minimum free-energy path method,we determined the height of reaction barriers that are in good agreement with experimental measurements.Enzyme-substrate interactions were analyzed in detail to identify factors contributing to catalysis.Computed angular order parameters of backbone N–H bonds and side-chain methyl groups suggested site-specific,non-uniform rigidity changes of the enzymes during catalysis.The change of conformational entropy from the ground state to the transition state revealed distinctly contrasting entropy/enthalpy compensations in the dimeric wild-type enzyme and its molten globular monomeric variant.A unique catalytic strategy was suggested for enzymes that are natively molten globules:some may possess large conformational flexibility to provide strong electrostatic interactions to stabilize the transition state of the substrate and compensate for the entropy loss in the transition state.The equilibrium conformational dynamics in the reactant state were analyzed to quantify their contributions to the structural transitions enzymes needed to reach the transition states.The results suggest that large-scale conformational dynamics make important catalytic contributions to sampling conformational regions in favor of binding the transition state of substrate.     

Significant kinetic solvent isotope effects in folding of the catalytic RNA from the hepatitis delta virus

The exchange of deuterium for hydrogen in water often produces solvent kinetic isotope effects (KSIEs) on the rate constants associated with enzyme reactions, including those catalyzed by RNA. Recently, KSIEs have been used to show that proton transfer occurs in the rate-limiting step of cleavage by the hepatitis delta virus (HDV) ribozyme and other catalytic RNAs. To test the underlying assumption that KSIEs are related to the chemistry step of ribozyme-mediated cleavage reactions, we developed fluorescence resonance energy transfer assays to measure KSIEs on the rate constants of conformational changes associated with substrate binding and dissociation by a trans-acting HDV ribozyme. We observe comparable KSIEs ( approximately 2-2.5-fold) of rate constants of conformational change and cleavage, while proton inventory experiments are consistent with a shift in the ensemble of transition states upon increase of D2O in the solvent. Taken together, these results challenge the common assumption that pL profiles of RNA-catalyzed reactions yielding a pKa and KSIE necessarily provide evidence for an ionization (chemistry) step to be rate-limiting. They also suggest that an unusual proton inventory may provide a signature for a conformational change contributing to the rate-limiting step.     

Single-molecule enzyme kinetics in the presence of inhibitors

Recent studies in single-molecule enzyme kinetics reveal that the turnover statistics of a single enzyme is governed by the waiting time distribution that decays as mono-exponential at low substrate concentration and multi-exponential at high substrate concentration. The multi-exponentiality arises due to protein conformational fluctuations, which act on the time scale longer than or comparable to the catalytic reaction step, thereby inducing temporal fluctuations in the catalytic rate resulting in dynamic disorder. In this work, we study the turnover statistics of a single enzyme in the presence of inhibitors to show that the multi-exponentiality in the waiting time distribution can arise even when protein conformational fluctuations do not influence the catalytic rate. From the Michaelis-Menten mechanism of inhibited enzymes, we derive exact expressions for the waiting time distribution for competitive, uncompetitive, and mixed inhibitions to quantitatively show that the presence of inhibitors can induce dynamic disorder in all three modes of inhibitions resulting in temporal fluctuations in the reaction rate. In the presence of inhibitors, dynamic disorder arises due to transitions between active and inhibited states of enzymes, which occur on time scale longer than or comparable to the catalytic step. In this limit, the randomness parameter (dimensionless variance) is greater than unity indicating the presence of dynamic disorder in all three modes of inhibitions. In the opposite limit, when the time scale of the catalytic step is longer than the time scale of transitions between active and inhibited enzymatic states, the randomness parameter is unity, implying no dynamic disorder in the reaction pathway.     

Surface enzyme kinetics for biopolymer microarrays: a combination of Langmuir and Michaelis-Menten concepts

Real-time surface plasmon resonance (SPR) imaging measurements of surface enzymatic reactions on DNA microarrays are analyzed using a kinetics model that couples the contributions of both enzyme adsorption and surface enzyme reaction kinetics. For the case of a 1:1 binding of an enzyme molecule (E) to a surface-immobilized substrate (S), the overall enzymatic reaction can be described in terms of classical Langmuir adsorption and Michaelis-Menten concepts and three rate constants: enzyme adsorption (k(a)), enzyme desorption (k(d)) and enzyme catalysis (k(cat)). In contrast to solution enzyme kinetics, the amount of enzyme in solution is in excess as compared to the amount of substrate on the surface. Moreover, the surface concentration of the intermediary enzyme-substrate complex (ES) is not constant with time, but goes to zero as the reaction is completed. However, kinetic simulations show that the fractional surface coverage of ES on the remaining unreacted sites does reach a steady-state value throughout the course of the surface reaction. This steady-state value approaches the Langmuir equilibrium value for cases where k(a)[E] > k(cat). Experiments using the 3' --> 5' exodeoxyribonuclease activity of Exonuclease III on double-stranded DNA microarrays as a function of temperature and enzyme concentration are used to demonstrate how this model can be applied to quantitatively analyze the SPR imaging data.     

Photometric and fluorimetric assay of alkaline phosphatase with new coumarin-derived substrates

Summary Two new coumarin-derived synthetic substrates for use in the direct and continuous kinetic assay of alkaline phosphatase are presented. They have been studied with respect to optimum pH (9.5) and rate of enzymatic hydrolysis (1.5–1.8 nmol/min at pH 9.5) by alkaline phosphatase from calf intestine. Detection limits were 0.0005 units/ml for the photometric assay, and 0.00001 units/ml for the fluorimetric one. The relatively longwave shifted absorption and emission maxima of the new substrates in addition to the large Stoke's shifts allow the determination of enzyme activities in a spectral range distinctly outside the intrinsic fluorescence of biological matter such as serum.     

Activation enthalpies and entropies for the microscopic rate constants of acetate-catalyzed isomerization of 5-androstene-3,17-dione

Both acetic acid and acetate catalyze the isomerization of 5-androstene-3,17-dione (1) to its conjugated isomer, 4-androstene-3,17-dione (3), through a dienol(ate) intermediate. The temperature dependence of the overall isomerization rate constants and of the microscopic rate constants for this isomerization was determined, and the Arrhenius plots give the activation enthalpy and entropy for each step. The source of the activation energy for the overall isomerization and for each of the individual steps is predominantly enthalpic, with a moderate to low entropic penalty. Additionally, the entropy and enthalpy for the keto-enol equilibrium of 1 and dienol were determined; this equilibrium is entirely controlled by enthalpy with no entropic contribution. The relevance of these results to the mechanism of the isomerization of 1 catalyzed by the enzyme 3-oxo-Delta(5)-steroid isomerase is discussed.     

Structure, Stability, and Activity of Adsorbed Enzymes

A proteolytic enzyme, α-chymotrypsin, and a lipolytic enzyme, cutinase, were adsorbed from aqueous solution onto a hydrophobic Teflon surface and a hydrophilic silica surface. We investigated the influence of adsorption on the structure, the structure thermal stability and the activity of these enzymes. Probing the protein structure by circular dichroism spectroscopy indicates that Teflon promotes the formation of helical structure in α-chymotrypsin, but the reverse effect is found with cutinase. The perturbed protein structures on Teflon are remarkably stable, showing no heat-induced structural transitions up to 100°C, as monitored by differential scanning calorimetry. Contact with the hydrophilic silica surface leads to a loss in the helix content of both proteins. Differential scanning calorimetry points to a heterogeneous population of adsorbed protein molecules with respect to their conformational states. The fraction of the native-like conformation in the adsorbed layer increases with increasing coverage of the silica surface by the proteins. The specific enzymatic activity in the adsorbed state qualitatively correlates with the fraction of proteins in the native-like conformation.     

Temperature effects on the catalytic activity of the D38E mutant of 3-oxo-Delta5-steroid isomerase: favorable enthalpies and entropies of activation relative to the nonenzymatic reaction catalyzed by acetate ion

3-oxo-Delta5-steroid isomerase (ketosteroid isomerase, KSI) catalyzes the isomerization of 5-androstene-3,17-dione (1) to 4-androstene-3,17-dione (3) via a dienolate intermediate (2-). KSI catalyzes this conversion about 13 orders of magnitude faster than the corresponding reaction catalyzed by acetate ion, a difference in activation energy (DeltaG) of approximately 18 kcal/mol. To evaluate whether the decrease in DeltaG by KSI is due to enthalpic or entropic effects, the activation parameters for the isomerization of 1 catalyzed by the D38E mutant of KSI were determined. A linear Arrhenius plot of kcat/KM versus 1/T gives the activation enthalpy (DeltaH = 5.9 kcal/mol) and activation entropy (TDeltaS = -2.6 kcal/mol). Relative to catalysis by acetate, D38E reduces DeltaH by approximately 10 kcal/mol and increases TDeltaS by approximately 5 kcal/mol. The activation parameters for the microscopic rate constants for D38E catalysis were also determined and compared to those for the acetate ion-catalyzed reaction. Enthalpic stabilization of 2- and favorable entropic effects in both chemical transition states by D38E result in an overall energetically more favorable enzymatic reaction relative to that catalyzed by acetate ion.     

CENCALC: A computational tool for conformational entropy calculations from molecular simulations

We present the CENCALC software that has been designed to estimate the conformational entropy of single molecules from extended Molecular Dynamics (MD) simulations in the gas‐phase or in solution. CENCALC uses both trajectory coordinates and topology information in order to characterize the conformational states of the molecule of interest by discretizing the time evolution of internal rotations. The implemented entropy methods are based on the mutual information expansion, which is built upon the converged probability density functions of the individual torsion angles, pairs of torsions, triads, and so on. Particularly, the correlation‐corrected multibody local approximation selects an optimum cutoff in order to retrieve the maximum amount of genuine correlation from a given MD trajectory. We illustrate these capabilities by carrying out conformational entropy calculations for a decapeptide molecule either in its unbound form or in complex with a metalloprotease enzyme. CENCALC is distributed under the GNU public license at http://sourceforge.net/projects/cencalc/ .     

Two-state irreversible thermal denaturation of anionic peanut (Arachis hypogaea L.) peroxidase

Detailed differential scanning calorimetry (DSC), steady-state tryptophan fluorescence and far-UV circular dichroism (CD) studies, together with enzymatic assays, were carried out to monitor the thermal stability of anionic peanut peroxidase (aPrx) at pH 3.0. The spectral parameters were seen to be good complements to the highly sensitive but integral method of DSC. Thus, changes in far-UV CD corresponded to changes in the overall secondary structure of the enzyme, while changes in intrinsic tryptophan fluorescence emission corresponded to changes in the tertiary structure of the enzyme. The results, supported with data concerning changes in enzymatic activity with temperature, show that thermally induced transitions for aPrx are irreversible and strongly dependent upon the scan rate, suggesting that denaturation is under kinetic control. It is shown that the process of aPrx denaturation can be interpreted with sufficient accuracy in terms of the simple kinetic scheme, , where k is a first-order kinetic constant that changes with temperature, as given by the Arrhenius equation; N is the native state, and D is the denatured state. On the basis of this model, the parameters of the Arrhenius equation were calculated.