A lower bound to the survival probability and an approximate first passage time distribution for Markovian and non-Markovian dynamics in phase space

We derive a very general expression of the survival probability and the first passage time distribution for a particle executing Brownian motion in full phase space with an absorbing boundary condition at a point in the position space, which is valid irrespective of the statistical nature of the dynamics. The expression, together with the Jensen's inequality, naturally leads to a lower bound to the actual survival probability and an approximate first passage time distribution. These are expressed in terms of the position-position, velocity-velocity, and position-velocity variances. Knowledge of these variances enables one to compute a lower bound to the survival probability and consequently the first passage distribution function. As examples, we compute these for a Gaussian Markovian process and, in the case of non-Markovian process, with an exponentially decaying friction kernel and also with a power law friction kernel. Our analysis shows that the survival probability decays exponentially at the long time irrespective of the nature of the dynamics with an exponent equal to the transition state rate constant.

Kinetics and the Mechanism of Interaction of the Endoplasmic Reticulum Chaperone, Calreticulin, with Monoglucosylated (Glc1Man9GlcNAc2) Substrate

Calreticulin is a lectin-like molecular chaperone of the endoplasmic reticulum in eukaryotes. Its interaction with N-glycosylated polypeptides is mediated by the glycan, Glc(1)Man(9)GlcNAc(2), present on the target glycoproteins. In this work, binding of monoglucosyl IgG (chicken) substrate to calreticulin has been studied using real time association kinetics of the interaction with the biosensor based on surface plasmon resonance (SPR). By SPR, accurate association and dissociation rate constants were determined, and these yielded a micromolar association constant. The nature of reaction was unaffected by immobilization of either of the reactants. The Scatchard analysis values for K-a agreed web crith the one obtained by the ratio k(1)/k(-1). The interaction was completely inhibited by free oligosaccharide, Glc(1)Man(9)GlcNAc(2), whereas Man(9)GlcNAc(2) did not bind to the calreticulin-substrate complex, attesting to the exquisite specificity of this interaction. The binding of calreticulin to IgG was used for the development of immunoassay and the relative affinity of the lectin-substrate association was indirectly measured. The values are in agreement with those obtained with SPR. Although the reactions are several orders of magnitude slower than the diffusion controlled processes, the data are qualitatively and quantitatively consistent with single-step bimolecular association and dissociation reaction. Analyses of the activation parameters indicate that reaction is enthalpically driven and does not involve a highly ordered transition state. Based on these data, the mechanism of its chaperone activity is briefly discussed.

Stereoselectivity in the addition of hydrogen chloride to cyclohex-1-enecarbonitrile: Possible role of chlorine lone pair-nitrile π-orbital pseudoallylic A1, 3 interaction

The (overall trans) addition of hydrogen chloride to cyclohex-1- enecarbonitrile in anhydrous alcoholic media proceeds to give cis-2-chlorocyclohexanecarboxylate (together with some cis-2- chlorocyclohexanecarboxamide): no corresponding products with the trans-configuration are detectable. In anhydrous ether the addition proceeds to give a single isomer, presumably cis-, of 2-chlorocyclohexanecarbonitrile, indicating that the configuration of the products may not be equilibrium-controlled in alcoholic media. An examination of the steric factors indicates that the transition state for protonation of the presumed intermediate, 2-chlorocyclohexylidenemethylideneimine, leading to cis-product is favoured if interaction between the lateral π-orbital of the C-N double bond and the lone-pairs on the chlorine atom at the 2-position is large. Consideration of interactions in the transition states meets Zimmerman's criticism that invoking A1, 3 interaction existing in ground states to explain product configuration takes insufficient account of the Curtin-Hammett principle.

Kinetics and the mechanism of interaction of the endoplasmic reticulum chaperone, calreticulin, with monoglucosylated (Glc(1)Man(9)GlcNAc(2)) substrate

Calreticulin is a lectin-like molecular chaperone of the endoplasmic reticulum in eukaryotes. Its interaction with N-glycosylated polypeptides is mediated by the glycan, Glc(1)Man(9)GlcNAc(2), present on the target glycoproteins. In this work, binding of monoglucosyl IgG (chicken) substrate to calreticulin has been studied using real time association kinetics of the interaction with the biosensor based on surface plasmon resonance (SPR). By SPR, accurate association and dissociation rate constants were determined, and these yielded a micromolar association constant. The nature of reaction was unaffected by immobilization of either of the reactants. The Scatchard analysis values for K-a agreed web crith the one obtained by the ratio k(1)/k(-1). The interaction was completely inhibited by free oligosaccharide, Glc(1)Man(9)GlcNAc(2), whereas Man(9)GlcNAc(2) did not bind to the calreticulin-substrate complex, attesting to the exquisite specificity of this interaction. The binding of calreticulin to IgG was used for the development of immunoassay and the relative affinity of the lectin-substrate association was indirectly measured. The values are in agreement with those obtained with SPR. Although the reactions are several orders of magnitude slower than the diffusion controlled processes, the data are qualitatively and quantitatively consistent with single-step bimolecular association and dissociation reaction. Analyses of the activation parameters indicate that reaction is enthalpically driven and does not involve a highly ordered transition state. Based on these data, the mechanism of its chaperone activity is briefly discussed.

Asynchronous behaviour in some three-atom linear concerted radical-exchange reactions

A few simple three-atom thermoneutral radical exchange reactions (i.e. A + BC --> AB + C) are examined by ab initio SCF methods. Emphasis is laid on the detailed analysis of density matrices rather than on energetics. Results reveal that the sum of the bond orders of the breaking and forming bonds is not conserved to unity, due to development of free valence on the migrating atom 'B' in the transition state. Bond orders, free valence and spin densities on the atoms are calculated. The present analysis shows that the bond-cleavage process is always more advanced than the bond-formation process in the transition state. Further analysis shows a development of the negative spin density on the migrating atom 'B' in the transition state. The depletion of the alpha-spin density on the radical site "A" in the reactant during the reaction lags behind the growth of the alpha-spin density on the terminal atom "C" of the reactant bond, 'B-C' in the transition state. But all these processes are completed simultaneously at the end of the reaction. Hence, the reactions are asynchronous but kinetically concerted in most cases.

Computer modelling studies on the mechanism of action of ribonuclease T1

The mechanism of action of ribonuclease (RNase) T1 is still a matter of considerable debate as the results of x-ray, 2-D nmr and site-directed mutagenesis studies disagree regarding the role of the catalytically important residues. Hence computer modelling studies were carried out by energy minimisation of the complexes of RNase T1 and some of its mutants (His40Ala, His40Lys, and Glu58Ala) with the substrate guanyl cytosine (GpC), and of native RNase T1 with the reaction intermediate guanosine 2',3'-cyclic phosphate (G greater than p). The puckering of the guanosine ribose moiety in the minimum energy conformer of the RNase T1-GpC (substrate) complex was found to be O4'-endo and not C3'-endo as in the RNase T1-3'-guanylic acid (inhibitor/product) complex. A possible scheme for the mechanism of action of RNase T1 has been proposed on the basis of the arrangement of the catalytically important amino acid residues His40, Glu58, Arg77, and His92 around the guanosine ribose and the phosphate moiety in the RNase T1-GpC and RNase T1-G greater than p complexes. In this scheme, Glu58 serves as the general base group and His92 as the general acid group in the transphosphorylation step. His40 may be essential for stabilising the negatively charged phosphate moiety in the enzyme-transition state complex.

The Mechanism Of The Hydrogen Abstraction Process By Photo-Excited Ketones

Qualitative potential energy surfaces for hydrogen abstraction from alkanes containing primary, secondary and tertiary C-H bonds by a photo-excited ketone have been reported, The results suggest that the activation barriers for these processes decrease in the order primary > secondary > tertiary in agreement with the observed trend in the rate constants. The analysis of the electronic structure of the transition-state reveal that electron-transfer from hydrocarbon to ketone and formation of a new bond are almost synchronous in the hydrogen transfer process. The tunneling of hydrogen is not important in the normal temperature region even though the barriers are small.

pi.-Facial selectivities in cycloadditions to norbornyl- and norbornenyl-fused p-benzoquinones

The stereochemistry of the Diels-Alder cycloaddition of several dienes to the facially perturbed dienophiles 2,3-norbornenobenzoquinone (3) and 2,3-norbornanobenzoquinone (4) has been examined. Unambiguous structural proof for the adducts formed has been obtained from complementary 'H and I3C NMR spectral data and in two cases through X-ray crystal structure determination. While 1,3-~yclopentadiene1, ,3-~yclohexadienea, nd cyclooctatetraene exhibit preference for addition to 3 from the bottom side, the stereochemical outcome is reversed in their response to 4.1,3-DiphenyIisobenzofuran and 1,2,3,4-tetrachloro-5,5-dimethoxycyclopentadieenneg aged 3 from the top side with marked selectivity, which is further enhanced in their reaction with 4. The observed stereoselectivities seem to be essentially controlled by steric interactons at the transition state. Model calculations provide support for this interpretation.

A simple computational model for predicting .pi.-facial selectivity in reductions of sterically unbiased ketones. Relative importance of electrostatic and orbital interactions

Various factore controlling the preferred facial selectivity in the reductions of a number of sterically unbiased ketones have been evaluated using a semiempirical MO procedure. MNDO optimized geometries do not reveal any significant ground-state distortions which can be correlated with the observed face selectivities. Electrostatic effecta due to an approaching reagent were modeled by placing a test negative charge at a fixed distance from the carbonyl carbon on each of the two faces. A second series of calculations was carried out using the hydride ion as a test nucleophile. The latter calculations effectively include orbital interactions involving the u and u* orbitals of the newly formed bond in the reaction. The computed energy differences with the charge model are generally much larger compared to those with the hydride ion. However, both models lead to predictions which are qualitatively consistent with the experimentally determined facial preferences for most of the systems. Thus, electrostatic interactions between the nucleophile and the substrate seem to effectively determine the face selectivities in these molecules. However, there are a few exceptions in which orbital interactions are found to contribute significantly and occasionally reverse the preference dictated by electrostatic effecta. The remarkable succew of the hydride model calculations, in spite of retaining the unperturbed geometries of the substrates, points to the unimportance of torsional effeds and orbital distortions associated with the pyramidalized carbonyl unit in the transition state in most of the substrates considered. Additional experimental results are reported which provide useful calibration for the present computational approach.

Aromatic claisen rearrangements in carbohydrates: stereocontrol of rearrangement rates in unsaturated sugar substrates

A remarkable difference is observed in the rates of [3,3]-sigmatropic rearrangement of aryl 4,6-di-O-acetyl-2,3-dideoxy-D-erythro-hex-2-enopyranosides 1 and 2; the slower reactivity of the alpha-isomers is consistent with AM1 calculated transition state energetics of model systems.

Effects of Ultrafast Solvation on the Rate of Adiabatic Outer-Sphere Electron Transfer Reactions

Recent studies have demonstrated that solvation dynamics in many common dipolar liquids contain an initial, ultrafast Gaussian component which may contribute even more than 60% to the total solvation energy. It is also known that adiabatic electron transfer reactions often probe the high-frequency components of the relevant solvent friction (Hynes, J. T. J. Phys. Chem. 1986, 90, 3701). In this paper, we present a theoretical study of the effects of the ultrafast solvent polar modes on the adiabatic electron transfer reactions by using the formalism of Hynes. Calculations have been carried out for a model system and also for water and acetonitrile. It is found that, in general, the ultrafast modes can greatly enhance the rate of electron transfer, even by more than an order of magnitude, over the rate obtained by using only the slow overdamped modes usually considered. For water, this acceleration of the rate can be attributed to the high-frequency intermolecular vibrational and librational modes. For a weakly adiabatic reaction, the rate is virtually indistinguishable from the rate predicted by the Marcus transition state theory. Another important result is that even in this case of ultrafast underdamped solvation, energy diffusion appears to be efficient so that electron transfer reaction in water is controlled essentially by the barrier crossing dynamics. This is because the reactant well frequency is-directly proportional to the rate of the initial Gaussian decay of the solvation time correlation function. As a result, the value of the friction at the reactant well frequency rarely falls below the value required for the Kramers turnover except when the polarizability of the water molecules may be neglected. On the other hand, in acetonitrile, the rate of electron transfer reaction is found to be controlled by the energy diffusion dynamics, although a significant contribution to the rate comes also from the barrier crossing rate. Therefore, the present study calls for a need to understand the relaxation of the high-frequency modes in dipolar liquids.

Ab initio studies of the structure and vibrational spectra of methyl isocyanide-borane and acetonitrile-borane

The SCF/DZP and MP2/DZP methods of ab initio quantum chemistry have been utilized to study the structure, vibrational spectra, binding energy, and barrier to internal rotation of methyl isocyanide-borane and acetonitrile-borane adducts. The eclipsed conformation of the complexes was predicted to be a minimum, and the staggered form is a transition state with a barrier height of about 10 cal/mol. The vibrational analyses of CH3NC-BH3 and CH3CN-BH3 and several of their isotopomers have been carried out by the GF matrix method. Computations have also been carried out for free CH3NC and CH3CN in order to investigate the changes in CH3NC and CH3CN as a result of their complex formation with BH3. To obtain an acceptable set of force constants, a recently proposed procedure ''RECOVES'' has been utilized. The increase in the N=C/C=N stretching force constant of CH3NC/CH3CN on adduct formation is interpreted with the help of Parr and Borkman's model. The binding energies for the two adducts have been determined taking basis set superposition error (BSSE) into consideration. The effect of the BSSE on structure, dipole moment, and vibrational frequencies of CH3CN and CH3NC is also evaluated. The predicted infrared band intensities for the two complexes are in good agreement with the experimentally observed features, and they have been utilized in the assignment of vibrational frequencies.

Role of free valences and spin densities on the migrating atom in location of saddle points in radical-exchange reactions

The principle of the conservation of bond orders during radical-exchange reactions is examined using Mayer's definition of bond orders. This simple intuitive approximation is not valid in a quantitative sense. Ab initio results reveal that free valences (or spin densities) develop on the migrating atom during reactions. For several examples of hydrogen-transfer reactions, the sum of the reaction coordinate bond orders in the transition state was found to be 0.92 +/- 0.04 instead of the theoretical 1.00 because free valences (or spin densities) develop on the migrating atom during reactions. It is shown that free valence is almost equal to the square of the spin density on the migrating hydrogen atom and the maxima in the free valence (or spin density) profiles coincide (or nearly coincide) with the saddle points in the corresponding energy profiles.

The structural theory and physical organic chemistry

Woolley's revolutionary proposal that quantum mechanics does not sanction the concept of ''molecular structure'' - which is but only a ''metaphor'' - has fundamental implications for physical organic chemistry. On the one hand, the Uncertainty Principle limits the precision with which transition state structures may be defined; on the other, extension of the structure concept to the transition state may be unviable. Attempts to define transition states have indeed caused controversy. Consequences for molecular recognition, and a mechanistic classification, are also discussed.

Isomerization dynamics in viscous liquids: Microscopic investigation of the coupling and decoupling of the rate to and from solvent viscosity and dependence on the intermolecular potential

A detailed investigation of viscosity dependence of the isomerization rate is carried out for continuous potentials by using a fully microscopic, self-consistent mode-coupling theory calculation of both the friction on the reactant and the viscosity of the medium. In this calculation we avoid approximating the short time response by the Enskog limit, which overestimates the friction at high frequencies. The isomerization rate is obtained by using the Grote-Hynes formula. The viscosity dependence of the rate has been investigated for a large number of thermodynamic state points. Since the activated barrier crossing dynamics probes the high-frequency frictional response of the liquid, the barrier crossing rate is found to be sensitive to the nature of the reactant-solvent interaction potential. When the solute-solvent interaction is modeled by a 6-12 Lennard-Jones potential, we find that over a large variation of viscosity (eta), the rate (k) can indeed be fitted very well to a fractional viscosity dependence: (k similar to eta(-alpha)), with the exponent alpha in the range 1 greater than or equal to alpha >0. The calculated values of the exponent appear to be in very good agreement with many experimental results. In particular, the theory, for the first time, explains the experimentally observed high value of alpha even at the barrier frequency, omega(b). similar or equal to 9 X 10(12) s(-1) for the isomerization reaction of 2-(2'-propenyl)anthracene in liquid eta-alkanes. The present study can also explain the reason for the very low value of vb observed in another study for the isomerization reaction of trans-stilbene in liquid n-alkanes. For omega(b) greater than or equal to 2.0 X 10(13) s(-1), we obtain alpha similar or equal to 0, which implies that the barrier crossing rate becomes identical to the transition-state theory predictions. A careful analysis of isomerization reaction dynamics involving large amplitude motion suggests that the barrier crossing dynamics itself may become irrelevant in highly viscous liquids and the rate might again be coupled directly to the viscosity. This crossover is predicted to be strongly temperature dependent and could be studied by changing the solvent viscosity by the application of pressure. (C) 1999 American Institute of Physics. [S0021-9606(9950514-X].