Global Fitting Procedure Research Articles

Accurate global fit of the H4 potential energy surface

A global potential energy surface (PES) for the adiabatic ground state of the H4 system which fit published ab initio data [Boothroyd, et al. J. Chem. Phys. 95, 4331 (1991)] at a quantitative level has been obtained (root-mean-square error about 2 mhartree or 1–2 kcal/mol), and without any quantity of ad hoc character, preserving the accuracy of the ab initio points. The global fitting procedure used here is an extension of the corresponding procedure for triatomic systems including the functional form previously proposed by the authors. The global H4 PES obtained here is totally symmetric with respect to permutations of the hydrogen atoms and satisfies the criteria needed to be used in scattering calculations.

Time-resolved optical absorption studies of intramolecular electron transfer in cytochrome c oxidase.

Intramolecular electron transfer and conformational changes in cytochrome c oxidase were studied at room temperature following the photodissociation of CO bound to mixed-valence enzyme (cytochrome a3(2+)-CO CuB+ cytochrome a3+ CuA2+) and fully reduced enzyme. Time-resolved optical absorption difference spectra were collected in the Soret region on time scales of nanoseconds to milliseconds using a gated optical spectrometric multichannel analyzer. A global exponential fitting procedure combined with a singular value decomposition method was used to analyze the transient difference spectra at various times following CO photolysis. The analysis shows that at least two processes, with apparent lifetimes of 1.4 microseconds and 11.1 ms, are present following the photodissociation of CO bound to the fully reduced enzyme. These are attributed to a conformational change and CO recombination at the cytochrome a3 site, respectively. Global analysis of the mixed-valence CO complex transient difference spectra showed the presence of five intermediates with apparent lifetimes of 1.0 microseconds, 5.2 microseconds, 83.7 microseconds, 10.5 ms, and 25.3 ms. The data on a microsecond time scale are consistent with a mechanism involving a conformational change at cytochrome a3, followed by electron transfer from cytochrome a3 to cytochrome a with subsequent electron transfer to CuA. One of the two processes on a millisecond time scale is attributed to CO recombination and the other to a structural rearrangement or heme-heme electron transfer. On the basis of this mechanism, the kinetics and the absorption spectra of the intermediates involved in the conformational and electron transfer dynamics of the mixed-valence enzyme were determined.

Thermodynamic study of complex formation by hydrogen bonding in halogenoalkane–oxygenated solvent mixtures: halothane with acetone, methyl acetate, tetrahydrofuran and methyl tert-butyl ether

Complex-formation equilibria in binary mixtures of 2-bromo-2-chloro-1,1,1-trifluoroethane (halothane) with acetone (AC), methyl acetate (MA), tetrahydrofuran (THF) and methyl tert-butyl ether (MBE) have been analysed in detail using several association models. Previously reported vapour–liquid equilibria, limiting activity coefficients, excess enthalpy and excess heat capacity data for these mixtures have been correlated using a multiproperty global fitting procedure. The thermodynamic properties for halothane–AC and –MA are best correlated using the ideal association model while for halothane–THF and –MBE the best model is an athermal solvation model where the Flory–Huggins expression for the species activity coefficients is considered. In halothane–THF and –MBE mixtures there are only 1 : 1 H-bonded complexes while for halothane–AC and –MA the 2 : 1 complexes are also present. An explanation at the molecular-level for this behaviour is given by PC MODEL calculations which indicated that the oxygen surface area available for H-bonding is twice as large in AC and MA than in THF and MBE. The model parameters, i.e. the equilibrium constants, enthalpies and heat capacities of complexation, were found to be reliable, truly representing the halothane–oxygenated solvent H-bonded complexes. Using quantum-mechanical methods, enthalpies of complexation for the present mixtures were calculated and found to be in excellent agreement with those obtained thermodynamically. Other models, where the physical contributions to the excess properties of the present systems are given by the properties of (halothane–homomorph-of-solvent) and (homomorph-of-halothane–oxygenated solvent) mixtures, have been tested. These extensions of the ideal association model do not represent improvements of the simple models.

A new functional form to obtain analytical potentials of triatomic molecules

A new way of fitting ab initio values of the potential energy of triatomic molecules is discussed. The new functional form proposed for the potential energy function satisfies several criteria for use in scattering calculations and it is so stable that, when increasing the number of parameters in the fit, it maintains a good behavior at short, intermediate, and long range of the whole potential. Applications of the fitting technique to obtain the potential energy functions for the ground states of H3, H2He+, and LiHF are presented. For the H3 system, we fit all 267 of Liu and Siegbahn’s ab initio points. With one nonlinear parameter and 23 linear parameters, the root-mean-square error was 1.21 kcal/mol and the maximum absolute deviation 7.94 kcal/mol; these values are lower than previous global fittings with a similar number of parameters except for the Truhlar and Horowitz fit of the Liu and Siegbahn data, LSTH potential, but when the number of linear parameters was increased to 71, the root-mean-square error was reduced to 0.07 kcal/mol and the maximum absolute deviation to 0.25 kcal/mol (approximately one half the corresponding values of the LSTH ones). The new global fitting procedure is then applied to obtain potential energy functions for the H2He+ and the LiHF systems within the chemical accuracy of 1 kcal/mol.

KINETIC ANALYSIS OF TIME‐RESOLVED INFRARED DIFFERENCE SPECTRA OF THE L and M INTERMEDIATES OF BACTERIORHODOPSIN*

Abstract– Infrared difference spectra with 4 cm−1 spectral resolution and 10‐u.s temporal resolution, obtained previously with a stroboscopic Fourier‐transform difference technique (Braiman et al., 1991, Proc. Natl. Acad. Sci. USA 88, 2388), were analyzed by means of a global exponential fitting procedure based on singular value decomposition. Using a simple linear kinetic model K → L → M for the bacteriorhodopsin (bR) photocycle in the time range10–1000 μ.s at 16.5°C, it was possible to generate bR → L and bR → M difference spectra with signal/noise ratios comparable to those obtainable with low temperature difference spectroscopy. The resulting time‐resolved bR → L and bR‐→ M difference spectra are both very similar to the corresponding static FTIR difference spectra obtained at 175 K and 250 K, respectively. In the bR → L spectrum, however, there are interesting differences that may indicate a greater degree of deprotonation of Asp‐96 when L is formed at physiological temperatures than when it is observed in a low‐temperature steady state.

Global parameter optimization for cardiac potassium channel gating models

Quantitative ion channel model evaluation requires the estimation of voltage dependent rate constants. We have tested whether a unique set of rate constants can be reliably extracted from nonstationary macroscopic voltage clamp potassium current data. For many models, the rate constants derived independently at different membrane potentials are not unique. Therefore, our approach has been to use the exponential voltage dependence predicted from reaction rate theory (Stevens, C. F. 1978. Biophys. J. 22:295-306; Eyring, H., S. H. Lin, and S. M. Lin. 1980. Basic Chemical Kinetics. Wiley and Sons, New York) to couple the rate constants derived at different membrane potentials. This constrained the solution set of rate constants to only those that also obeyed this additional set of equations, which was sufficient to obtain a unique solution. We have tested this approach with data obtained from macroscopic delayed rectifier potassium channel currents in voltage-clamped guinea pig ventricular myocyte membranes. This potassium channel has relatively simple kinetics without an inactivation process and provided a convenient system to determine a globally optimized set of voltage-dependent rate constants for a Markov kinetic model. The ability of the fitting algorithm to extract rate constants from the macroscopic current data was tested using "data" synthesized from known rate constants. The simulated data sets were analyzed with the global fitting procedure and the fitted rate constants were compared with the rate constants used to generate the data. Monte Carlo methods were used to examine the accuracy of the estimated kinetic parameters. This global fitting approach provided a useful and convenient method for reliably extracting Markov rate constants from macroscopic voltage clamp data over a broad range of membrane potentials. The limitations of the method and the dependence on initial guesses are described.

Transition dipole orientations in the early photolysis intermediates of rhodopsin

The linear dichroism spectrum of rhodopsin in sonicated bovine disk membranes was measured 30, 60, 170, and 600 ns after room temperature photolysis with a linearly polarized, 7-ns laser pulse (lambda = 355 or 477 nm). A global exponential fitting procedure based on singular value decomposition was used to fit the linear dichroism data to two exponential processes which differed spectrally from one another and whose lifetimes were 42 +/- 7 ns and 225 +/- 40 ns. These results are interpreted in terms of a sequential model where bathorhodopsin (BATHO, lambda max = 543 nm) decays toward equilibrium with a blue shifted intermediate (BSI, lambda max = 478 nm). BSI then decays to lumirhodopsin (LUMI, lambda max = 492 nm). It has been suggested that two bathorhodopsins decay in parallel to their products. However, a Monte Carlo simulation of partial photolysis of solid-state visual pigment samples shows that one mechanism which creates populations of BATHO having different photolysis rates at 77 K may not be responsible for the two decay rates reported here at room temperature. The angle between the cis band and 498-nm band transition dipoles of rhodopsin is determined to be 38 degrees. The angles between both these transition dipoles and those of the long-wave-length bands of BATHO, BSI, and LUMI are also determined. It is shown that when BATHO is formed its transition dipole moves away from the original cis band transition dipole direction. The transition dipole then moves roughly twice as much towards the original cis band direction when BSI appears. Production of LUMI is associated with return of the transition dipole almost to the original orientation relative to the cis band, but with some displacement normal to the plane which contains the previous motions. The correlation between the lambda max of an intermediate and its transition dipole direction is discussed.

A method for writing enzyme rate equations: application to the estimation of the number and size of key proton families

We develop a method to derive the rate equation for enzyme models that include pH-dependent activation. Our presentation is based on a kinetic model recently described for sucrase, the three-key-proton model of Vasseur and coworkers, which considers the existence, in the acid ionization reaction, of two functionally distinct prototropic groups, respectively responsible for either V-type or K-type kinetic effects. In contrast, as concerns the basic ionization reaction, the model conforms to classical concepts of pH-dependent activation, whereby a single proton participates in either V-type or K-type effects but not in both at the same time. Enzymes with more than three key protons have been described, indicating that, rather than isolated protons, groups of protons should be considered, and therefore the model can be better described as a three-proton-family model, where a proton family is defined as one or several protons that are gained or lost as a block and perform the same kinetic function. The resulting model is treated here as a useful framework upon which other models can be built. To facilitate the writing of the rate equations, we define two new entities: (1) intralevel coefficients, which describe the various combinations of the enzyme with either the substrate(s), the allosteric effector(s), or both at a given protonation level, and (2) interlevel coefficients, which describe the interplay between the various protonation levels. The resulting rate equation can be used in a global fit procedure permitting in a single computer run the estimation of (1) the entire set of dissociation and microscopic ionization constants of the model, (2) the number and kinetic function of proton families characterizing the enzyme under consideration, and (3) the number of key protons constituting each family, which is derived from the derivatives of the kinetic parameters, V m/K m, V m , and K m .

A new bond-order functional form for triatomic molecules

A generalization to the triatomic systems of a Bond Order approach developed in the preceding paper for the diatomic molecules is discussed. The new global fitting procedure is first tested against other methods for the H3 molecule and then applied to the BeHF system.

Diffraction of He at the reconstructed Si(100) surface

We present a study of the Si(100) surface using thermal-energy-He diffraction. We find that the clean surface reconstructs with a primary (2 \ifmmode\times\else\texttimes\fi{} 1) two-domain periodicity and with substantial additional intensity indicating a secondary reconstruction. We are unable to order the latter using several annealing procedures and consistently obtain diffuse streaks extending across the reciprocal net at the half-order positions. We interpret this reciprocal net in terms of a disordered $c(2\ifmmode\times\else\texttimes\fi{}4)$ structure which in addition contains $p(2\ifmmode\times\else\texttimes\fi{}2)$ and possible $c(2\ifmmode\times\else\texttimes\fi{}2)$ regions. The half- and integer-order intensities vary with incident angle and wavelength in a manner qualitatively describable by semiclassical rainbow scattering. The differential cross section for incoherent scattering has structure similar in angle to the coherent intensities suggesting weak energy losses or surface disorder. Specular intensity scans indicate that the surface is extremely rough on the scale of the He wavelength, with large phase shifts, significant shadowing, and a breakdown of the uniform-attractive-well approximation. The extreme roughness makes a simple global fitting procedure unlikely and the lack of an ordered surface suggests that it will be difficult to fit calculations with a model structure.