State-to-state reaction probabilities within the quantum transition state framework

Rigorous quantum dynamics calculations of reaction rates and initial state-selected reaction probabilities of polyatomic reactions can be efficiently performed within the quantum transition state concept employing flux correlation functions and wave packet propagation utilizing the multi-configurational time-dependent Hartree approach. Here, analytical formulas and a numerical scheme extending this approach to the calculation of state-to-state reaction probabilities are presented. The formulas derived facilitate the use of three different dividing surfaces: two dividing surfaces located in the product and reactant asymptotic region facilitate full state resolution while a third dividing surface placed in the transition state region can be used to define an additional flux operator. The eigenstates of the corresponding thermal flux operator then correspond to vibrational states of the activated complex. Transforming these states to reactant and product coordinates and propagating them into the respective asymptotic region, the full scattering matrix can be obtained. To illustrate the new approach, test calculations study the D + H2(ν, j) → HD(ν′, j′) + H reaction for J = 0.

Electrochemical study and dependence of 'transition state' in Co(II) and Ni(II) complexes with some antibiotics and cephalothin

Electrode kinetics and study of 'transition state' with applied potential in case of [M - antibiotics - cephalothin] system were reported at pH = 7.30 ± 0.01 at suitable supporting electrolyte at 25.0ºC. The M = Co or Ni and antibiotics were doxycycline, chlortetracycline, oxytetracycline, tetracycline, minocycline, amoxicillin and chloramphenicol used as primary ligands and cephalothin as secondary ligand. Kinetic parameters viz. transfer coefficient (a), degree of irreversibility (l), diffusion coefficient (D) and rate constant (k) were determined. The values of a and k varied from 0.41 to 0.59 and 2.60 X 10-3 cm s-1 to 9.67 X 10-3 cm s-1 in case of [Co - antibiotics - cephalothin] system. In case of [Ni - antibiotics - cephalothin], a and k varied from 0.41 to 0.58 and 2.34 X 10-3 cm s-1 to 9.19 X 10-3 cm s-1 respectively confirmed that transition state behaves between oxidant and reductant response to applied potential and it adjusts it self in such a way that the same is located midway between dropping mercury electrode and solution interface. The values of rate constant confirmed the quasireversible nature of electrode processes. The stability constants (logb) of complexes were also determined.

Synthesis of unsaturated aminopyranosides as possible transition state mimics for glycosidases

Four unsaturated aminopyranosides have been prepared as possible transition-state mimics targeted towards carbohydrate processing enzymes. The conformations of the protonated aminosugars have been investigated by molecular modelling and their ability to inhibit alpha- and beta-glucosidases and an a-mannosidase have been probed. Two targets proved moderate inhibitors of alpha-glucosidases from Brewer's yeast and Bacillus stearothennophilus.

Mode-specificity and transition state-specific energy redistribution in the chemisorption of CH4 on Ni{100}

We have investigated methane (CH4) dissociative chemisorption on the Ni{100} surface by first-principles molecular dynamics (MD) simulations. Our results show that this reaction is mode-specific, with the n1 state being the most strongly coupled to efficient energy flow into the reaction coordinate when the molecule reaches the transition state. By performing MD simulations for two different transition state (TS) structures we provide evidence of TS structure-specific energy redistribution in methane chemisorption. Our results are compared with recently reported state-resolved measurement of methane adsorption probability on nickel surfaces, and we find that a strong correlation exists between the highest vibrational efficacy measured on Ni{100} for the n1 state and the calculated highest fractional vibrational energy content in this mode.

Configuration-dependent diffusion can shift the kinetic transition state and barrier height of protein folding

We show that diffusion can play an important role in protein-folding kinetics. We explicitly calculate the diffusion coefficient of protein folding in a lattice model. We found that diffusion typically is configuration- or reaction coordinate-dependent. The diffusion coefficient is found to be decreasing with respect to the progression of folding toward the native state, which is caused by the collapse to a compact state constraining the configurational space for exploration. The configuration- or position-dependent diffusion coefficient has a significant contribution to the kinetics in addition to the thermodynamic free-energy barrier. It effectively changes (increases in this case) the kinetic barrier height as well as the position of the corresponding transition state and therefore modifies the folding kinetic rates as well as the kinetic routes. The resulting folding time, by considering both kinetic diffusion and the thermodynamic folding free-energy profile, thus is slower than the estimation from the thermodynamic free-energy barrier with constant diffusion but is consistent with the results from kinetic simulations. The configuration- or coordinate-dependent diffusion is especially important with respect to fast folding, when there is a small or no free-energy barrier and kinetics is controlled by diffusion. Including the configurational dependence will challenge the transition state theory of protein folding. The classical transition state theory will have to be modified to be consistent. The more detailed folding mechanistic studies involving phi value analysis based on the classical transition state theory also will have to be modified quantitatively.

Comparison of Experimental and Theoretical Structures of a Transition State Analogue Used for the Induction of Anti-Cocaine Catalytic Antibodies

Comparison of the crystal structure of a transition state analogue that was used to raise catalytic antibodies for the benzoyl ester hydrolysis of cocaine with structures calculated by ab initio, semiempirical, and solvation semiempirical methods reveals that modeling of solvation is crucial for replicating the crystal structure geometry. Both SM3 and SM2 calculations, starting from the crystal structure TSA I, converged on structures similar to the crystal structure. The 3-21G(*)/HF, 6-31G*/HF, PM3, and AM1 calculations converged on structures similar to each other, but these gas-phase structures were significantly extended relative to the condensed phase structures. Two transition states for the hydrolysis of the benzoyl ester of cocaine were located with the SM3 method. The gas phase calculations failed to locate reasonable transition state structures for this reaction. These results imply that accurate modeling of the potential energy surfaces for the hydrolysis of cocaine requires solvation methods.

A Semiempirical Transition State Structure for the First Step in the Alkaline Hydrolysis of Cocaine. Comparison between the Transition State Structure, the Phosphonate Monoester Transition State Analog, and a Newly Designed Thiophosphonate Transition State Analog

Semiempirical molecular orbital calculations have been performed for the first step in the alkaline hydrolysis of the neutral benzoylester of cocaine. Successes, failures, and limitations of these calculations are reviewed. A PM3 calculated transition state structure is compared with the PM3 calculated structure for the hapten used to induce catalytic antibodies for the hydrolysis of cocaine. Implications of these calculations for the computer–aided design of transition state analogs for the induction of catalytic antibodies are discussed.

Communication: Transition State Theory for dissipative systems without a dividing surface

Transition state theory is a central cornerstone in reaction dynamics. Its key step is the identification of a dividing surface that is crossed only once by all reactive trajectories. This assumption is often badly violated, especially when the reactive system is coupled to an environment. The calculations made in this way then overestimate the reaction rate and the results depend critically on the choice of the dividing surface. In this Communication, we study the phase space of a stochastically driven system close to an energetic barrier in order to identify the geometric structure unambiguously determining the reactive trajectories, which is then incorporated in a simple rate formula for reactions in condensed phase that is both independent of the dividing surface and exact.

Non-enzymatic and enzymatic hydrolysis of alkyl halides: A haloalkane dehalogenation enzyme evolved to stabilize the gas-phase transition state of an SN2 displacement reaction

The semiempirical PM3 method, calibrated against ab initio HF/6–31+G(d) theory, has been used to elucidate the reaction of 1,2-dichloroethane (DCE) with the carboxylate of Asp-124 at the active site of haloalkane dehalogenase of Xanthobacter autothropicus. Asp-124 and 13 other amino acid side chains that make up the active site cavity (Glu-56, Trp-125, Phe-128, Phe-172, Trp-175, Leu-179, Val-219, Phe-222, Pro-223, Val-226, Leu-262, Leu-263, and His-289) were included in the calculations. The three most significant observations of the present study are that: (i) the DCE substrate and Asp-124 carboxylate, in the reactive ES complex, are present as an ion-molecule complex with a structure similar to that seen in the gas-phase reaction of AcO− with DCE; (ii) the structures of the transition states in the gas-phase and enzymatic reaction are much the same where the structure formed at the active site is somewhat exploded; and (iii) the enthalpies in going from ground states to transition states in the enzymatic and gas-phase reactions differ by only a couple kcal/mol. The dehalogenase derives its catalytic power from: (i) bringing the electrophile and nucleophile together in a low-dielectric environment in an orientation that allows the reaction to occur without much structural reorganization; (ii) desolvation; and (iii) stabilizing the leaving chloride anion by Trp-125 and Trp-175 through hydrogen bonding.

Phage display of a catalytic antibody to optimize affinity for transition-state analog binding

Catalytic antibodies have shown great promise for catalyzing a tremendously diverse set of natural and unnatural chemical transformations. However, few catalytic antibodies have efficiencies that approach those of natural enzymes. In principle, random mutagenesis procedures such as phage display could be used to improve the catalytic activities of existing antibodies; however, these studies have been hampered by difficulties in the recombinant expression of antibodies. Here, we have grafted the antigen binding loops from a murine-derived catalytic antibody, 17E8, onto a human antibody framework in an effort to overcome difficulties associated with recombinant expression and phage display of this antibody. “Humanized” 17E8 retained similar catalytic and hapten binding properties as the murine antibody while levels of functional Fab displayed on phage were 200-fold higher than for a murine variable region/human constant region chimeric Fab. This construct was used to prepare combinatorial libraries. Affinity panning of these resulted in the selection of variants with 2- to 8-fold improvements in binding affinity for a phosphonate transition-state analog. Surprisingly, none of the affinity-matured variants was more catalytically active than the parent antibody and some were significantly less active. By contrast, a weaker binding variant was identified with 2-fold greater catalytic activity and incorporation of a single substitution (Tyr-100aH → Asn) from this variant into the parent antibody led to a 5-fold increase in catalytic efficiency. Thus, phage display methods can be readily used to optimize binding of catalytic antibodies to transition-state analogs, and when used in conjunction with limited screening for catalysis can identify variants with higher catalytic efficiencies.

Transition-state structure as a unifying basis in protein-folding mechanisms: Contact order, chain topology, stability, and the extended nucleus mechanism

I attempt to reconcile apparently conflicting factors and mechanisms that have been proposed to determine the rate constant for two-state folding of small proteins, on the basis of general features of the structures of transition states. Φ-Value analysis implies a transition state for folding that resembles an expanded and distorted native structure, which is built around an extended nucleus. The nucleus is composed predominantly of elements of partly or well-formed native secondary structure that are stabilized by local and long-range tertiary interactions. These long-range interactions give rise to connecting loops, frequently containing the native loops that are poorly structured. I derive an equation that relates differences in the contact order of a protein to changes in the length of linking loops, which, in turn, is directly related to the unfavorable free energy of the loops in the transition state. Kinetic data on loop extension mutants of CI2 and α-spectrin SH3 domain fit the equation qualitatively. The rate of folding depends primarily on the interactions that directly stabilize the nucleus, especially those in native-like secondary structure and those resulting from the entropy loss from the connecting loops, which vary with contact order. This partitioning of energy accounts for the success of some algorithms that predict folding rates, because they use these principles either explicitly or implicitly. The extended nucleus model thus unifies the observations of rate depending on both stability and topology.

Denaturant-induced movement of the transition state of protein folding revealed by high-pressure stopped-flow measurements

The small all-β protein tendamistat folds and unfolds with two-state kinetics. We determined the volume changes associated with the folding process by performing kinetic and equilibrium measurements at variable pressure between 0.1 and 100 MPa (1 to 1,000 bar). GdmCl-induced equilibrium unfolding transitions reveal that the volume of the native state is increased by 41.4 ± 2.0 cm3/mol relative to the unfolded state. This value is virtually independent of denaturant concentration. The use of a high-pressure stopped-flow instrument enabled us to measure the activation volumes for the refolding (ΔVf0‡) and unfolding reaction (ΔVu0‡) over a broad range of GdmCl concentrations. The volume of the transition state is 60% native-like (ΔVf0‡ = 25.0 ± 1.2 cm3/mol) in the absence of denaturant, indicating partial solvent accessibility of the core residues. The volume of the transition state increases linearly with denaturant concentration and exceeds the volume of the native state above 6 M GdmCl. This result argues for a largely desolvated transition state with packing deficiencies at high denaturant concentrations and shows that the structure of the transition state depends strongly on the experimental conditions.

A specific transition state for S-peptide combining with folded S-protein and then refolding

We measured the folding and unfolding kinetics of mutants for a simple protein folding reaction to characterize the structure of the transition state. Fluorescently labeled S-peptide analogues combine with S-protein to form ribonuclease S analogues: initially, S-peptide is disordered whereas S-protein is folded. The fluorescent probe provides a convenient spectroscopic probe for the reaction. The association rate constant, kon, and the dissociation rate constant, koff, were both determined for two sets of mutants. The dissociation rate constant is measured by adding an excess of unlabeled S-peptide analogue to a labeled complex (RNaseS*). This strategy allows kon and koff to be measured under identical conditions so that microscopic reversibility applies and the transition state is the same for unfolding and refolding. The first set of mutants tests the role of the α-helix in the transition state. Solvent-exposed residues Ala-6 and Gln-11 in the α-helix of native RNaseS were replaced by the helix destabilizing residues glycine or proline. A plot of log kon vs. log Kd for this series of mutants is linear over a very wide range, with a slope of −0.3, indicating that almost all of the molecules fold via a transition state involving the helix. A second set of mutants tests the role of side chains in the transition state. Three side chains were investigated: Phe-8, His-12, and Met-13, which are known to be important for binding S-peptide to S-protein and which also contribute strongly to the stability of RNaseS*. Only the side chain of Phe-8 contributes significantly, however, to the stability of the transition state. The results provide a remarkably clear description of a folding transition state.

Trapping the transition state of an ATP-binding cassette transporter: Evidence for a concerted mechanism of maltose transport

High-affinity uptake into bacterial cells is mediated by a large class of periplasmic binding protein-dependent transport systems, members of the ATP-binding cassette superfamily. In the maltose transport system of Escherichia coli, the periplasmic maltose-binding protein binds its substrate maltose with high affinity and, in addition, stimulates the ATPase activity of the membrane-associated transporter when maltose is present. Vanadate inhibits maltose transport by trapping ADP in one of the two nucleotide-binding sites of the membrane transporter immediately after ATP hydrolysis, consistent with its ability to mimic the transition state of the γ-phosphate of ATP during hydrolysis. Here we report that the maltose-binding protein becomes tightly associated with the membrane transporter in the presence of vanadate and simultaneously loses its high affinity for maltose. These results suggest a general model explaining how ATP hydrolysis is coupled to substrate transport in which a binding protein stimulates the ATPase activity of its cognate transporter by stabilizing the transition state.