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.

Immucillin H, a powerful transition-state analog inhibitor of purine nucleoside phosphorylase, selectively inhibits human T lymphocytes

Transition-state theory has led to the design of Immucillin-H (Imm-H), a picomolar inhibitor of purine nucleoside phosphorylase (PNP). In humans, PNP is the only route for degradation of deoxyguanosine, and genetic deficiency of this enzyme leads to profound T cell-mediated immunosuppression. This study reports the biological effects and mechanism of action of Imm-H on malignant T cell lines and on normal activated human peripheral T cells. Imm-H inhibits the growth of malignant T cell leukemia lines with the induction of apoptosis. Imm-H also inhibits activated normal human T cells after antigenic stimulation in vitro. However, Imm-H did not inhibit malignant B cells, colon cancer cell lines, or normal human nonstimulated T cells, demonstrating the selective activity of Imm-H. The effects on leukemia cells were mediated by the cellular phosphorylation of deoxyguanosine and the accumulation of dGTP, an inhibitor of ribonucleotide diphosphate reductase. Cells were protected from the toxic effects of Imm-H when deoxyguanosine was absent or when deoxycytidine was present. Guanosine incorporation into nucleic acids was selectively blocked by Imm-H with no effect on guanine, adenine, adenosine, or deoxycytidine incorporation. Imm-H may have clinical potential for treatment of human T cell leukemia and lymphoma and for other diseases characterized by abnormal activation of T lymphocytes. The design of Imm-H from an enzymatic transition-state analysis exemplifies a powerful approach for developing high-affinity enzyme inhibitors with pharmacologic activity.

The pKa of His-24 in the folding transition state of apomyoglobin

In native apomyoglobin, His-24 cannot be protonated, although at pH 4 the native protein forms a molten globule folding intermediate in which the histidine residues are readily protonated. The inability to protonate His-24 in the native protein dramatically affects the unfolding/refolding kinetics, as demonstrated by simulations for a simple model. Kinetic data for wild type and for a mutant lacking His-24 are analyzed. The pKa values of histidine residues in native apomyoglobin are known from earlier studies, and the average histidine pKa in the molten globule is determined from the pH dependence of the equilibrium between the native and molten globule forms. Analysis of the pH-dependent unfolding/refolding kinetics reveals that the average pKa of the histidine residues, including His-24, is closely similar in the folding transition state to the value found in the molten globule intermediate. Consequently, protonation of His-24 is not a barrier to refolding of the molten globule to the native protein. Instead, the normal pKa of His-24 in the transition state, coupled with its inaccessibility in the native state, promotes fast unfolding at low pH. The analysis of the wild-type results is confirmed and extended by using the wild-type parameters to fit the unfolding kinetics of a mutant lacking His-24.

Partial molar volume, surface area, and hydration changes for equilibrium unfolding and formation of aggregation transition state: High-pressure and cosolute studies on recombinant human IFN-γ

The equilibrium dissociation of recombinant human IFN-γ was monitored as a function of pressure and sucrose concentration. The partial molar volume change for dissociation was −209 ± 13 ml/mol of dimer. The specific molar surface area change for dissociation was 12.7 ± 1.6 nm2/molecule of dimer. The first-order aggregation rate of recombinant human IFN-γ in 0.45 M guanidine hydrochloride was studied as a function of sucrose concentration and pressure. Aggregation proceeded through a transition-state species, N*. Sucrose reduced aggregation rate by shifting the equilibrium between native state (N) and N* toward the more compact N. Pressure increased aggregation rate through increased solvation of the protein, which exposes more surface area, thus shifting the equilibrium away from N toward N*. The changes in partial molar volume and specific molar surface area between the N* and N were −41 ± 9 ml/mol of dimer and 3.5 ± 0.2 nm2/molecule, respectively. Thus, the structural change required for the formation of the transition state for aggregation is small relative to the difference between N and the dissociated state. Changes in waters of hydration were estimated from both specific molar surface area and partial molar volume data. From partial molar volume data, estimates were 25 and 128 mol H2O/mol dimer for formation of the aggregation transition state and for dissociation, respectively. From surface area data, estimates were 27 and 98 mol H2O/mol dimer. Osmotic stress theory yielded values ≈4-fold larger for both transitions.

Visualization of intermediate and transition-state structures in protein-tyrosine phosphatase catalysis.

Engineering site-specific amino acid substitutions into the protein-tyrosine phosphatase (PTPase) PTP1 and the dual-specific vaccinia H1-related phosphatase (VHR), has kinetically isolated the two chemical steps of the reaction and provided a rare opportunity for examining transition states and directly observing the phosphoenzyme intermediate. Changing serine to alanine in the active-site sequence motif HCXXGXXRS shifted the rate-limiting step from intermediate formation to intermediate hydrolysis. Using phosphorus 31P NMR, the covalent thiol-phosphate intermediate was directly observed during catalytic turnover. The importance of the conserved aspartic acid (D92 in VHR and D181 in PTP1) in both chemical steps was established. Kinetic analysis of D92N and D181N mutants indicated that aspartic acid acts as a general acid by protonating the leaving-group phenolic oxygen. Structure-reactivity experiments with native and aspartate mutant enzymes established that proton transfer is concomitant with P-O cleavage, such that no charge develops on the phenolic oxygen. Steady- and presteady-state kinetics, as well as NMR analysis of the double mutant D92N/S131A (VHR), suggested that the conserved aspartic acid functions as a general base during intermediate hydrolysis. As a general base, aspartate would activate a water molecule to facilitate nucleophilic attack. The amino acids involved in transition-state stabilization for cysteinylphosphate hydrolysis were confirmed by the x-ray structure of the Yersinia PTPase complexed with vanadate, a transition-state mimic that binds covalently to the active-site cysteine. Consistent with the NMR, x-ray, biochemical, and kinetic data, a unifying mechanism for catalysis is proposed.

Crystal structure of the complex of a catalytic antibody Fab fragment with a transition state analog: structural similarities in esterase-like catalytic antibodies.

The x-ray structure of the complex of a catalytic antibody Fab fragment with a phosphonate transition-state analog has been determined. The antibody (CNJ206) catalyzes the hydrolysis of p-nitrophenyl esters with significant rate enhancement and substrate specificity. Comparison of this structure with that of the uncomplexed Fab fragment suggests hapten-induced conformational changes: the shape of the combining site changes from a shallow groove in the uncomplexed Fab to a deep pocket where the hapten is buried. Three hydrogen-bond donors appear to stabilize the charged phosphonate group of the hapten: two NH groups of the heavy (H) chain complementarity-determining region 3 (H3 CDR) polypeptide chain and the side-chain of histidine-H35 in the H chain (His-H35) in the H1 CDR. The combining site shows striking structural similarities to that of antibody 17E8, which also has esterase activity. Both catalytic antibody ("abzyme") structures suggest that oxyanion stabilization plays a significant role in their rate acceleration. Additional catalytic groups that improve efficiency are not necessarily induced by the eliciting hapten; these groups may occur because of the variability in the combining sites of different monoclonal antibodies that bind to the same hapten.

Transition-state-theory calculations for reactions of O(3P) with halogenated olefins

The potential energy surfaces for the reactions of atomic oxygen in its ground electronic state, O(P-3), with the olefins: CF2=CCl2 and CF2=CF - CF3, have been characterized using ab initio molecular orbital calculations. Geometry optimization and vibrational frequency calculations were performed for reactants, transition states and products at the MP2 and QCISD levels of theory using the 6-31G(d) basis set. This database was then used to calculate the rate constants by means of Transition-State-Theory. To obtain a better reference and to test the reliability of the activation barriers we have also carried out computations using the CCSD(T)(fc)/6-311Gdagger, MP4(SDQ)(fc)/CBSB4 and MP2(fc)/CBSB3 single point energy calculations at both of the above levels of theory, as well as with the composite CBS-RAD procedure ( P. M. Mayer, C. J. Parkinson, D. M. Smith and L. Radom, J. Chem. Phys., 1998, 108, 604) and a modi. cation of this approach, called: CBS-RAD( MP2, MP2). It was found that the kinetic parameters obtained in this work particularly with the CBS-RAD ( MP2, MP2) procedure are in reasonable agreement with the experimental values. For both reactions it is found that the channels leading to the olefin double-bond addition predominates with respect to any other reaction pathway. However, on account of the different substituents in the alkenes we have located, at all levels of theory, two transition states for each reaction. Moreover, we have found that, for the reactions studied, a correlation exists between the activation energies and the electronic structure of the transition states which can explain the influence of the substituent effect on the reactivity of the halo-olefins.

Quantum transition state theory and solving a first order master equation for complex reactions numerically

The field of chemical kinetics is an exciting and active field. The prevailing theories make a number of simplifying assumptions that do not always hold in actual cases. Another current problem concerns a development of efficient numerical algorithms for solving the master equations that arise in the description of complex reactions. The objective of the present work is to furnish a completely general and exact theory of reaction rates, in a form reminiscent of transition state theory, valid for all fluid phases and also to develop a computer program that can solve complex reactions by finding the concentrations of all participating substances as a function of time. To do so, the full quantum scattering theory is used for deriving the exact rate law, and then the resulting cumulative reaction probability is put into several equivalent forms that take into account all relativistic effects if applicable, including one that is strongly reminiscent of transition state theory, but includes corrections from scattering theory. Then two programs, one for solving complex reactions, the other for solving first order linear kinetic master equations to solve them, have been developed and tested for simple applications.

Investigations into the mechanism of orotidine 5'-monophosphate decarboxylase: Sources of substrate destabilization and transition state stabilization

Orotidine 5′-monophosphate decarboxylase (OMPDC) achieves a rarely paralleled rate acceleration, yet the catalytic basis prompting this enhancement have yet to be fully elucidated. To accomplish decarboxylation, OMPDC must overcome the high energy barrier due to the localized anionic charge of the intermediate. Mechanistic studies employing enzyme mutagenesis and product or intermediate analogues were used to investigate possible transition state stabilization by a carbene resonance structure. Viability of the carbene structure depends upon a key hydrogen bond between O4 of the substrate and the amide backbone of a conserved serine or threonine. Substitution of the conserved residue with Pro resulted in a kcat/KM of 1 M-1s-1; deletion of the FUMP O4 resulted in a product analogue that does not undergo H6 exchange or inhibit decarboxylation. Hence, indirect evidence reveals the O4-backbone interaction plays an important role for binding and catalysis. OMPDC likely has honed multiple mechanisms to attain its remarkable catalysis. The successful crystallizations of OMPDC a decade ago sparked hypotheses that structure and sequence conserved residues induced productive strain on the substrate-enzyme complex. Here, we demonstrate a new source of stress: a hydrophobic pocket adjacent to the OMP carboxylate that exhibits kinetic parameters characteristic of substrate destabilization. Substitution of these residues with hydrophilic side-chains, by providing hydrogen-bonding partners, decreased kcat by 10 to 10^4–fold. The same substitutions display very little change in the rate of product H6 exchange, supporting that this hydrophobic pocket affects the substrate-enzyme complex before the transition state. We also provide evidence that hydrophilic residues can insert water molecules into the pocket with detrimental effects to catalysis.