Global Nonlinear Least-squares Research Articles

Domino Tunneling.

Matrix-isolation experiments near 3 K and state-of-the-art quantum chemical computations demonstrate that oxalic acid [1, (COOH)2] exhibits a sequential quantum mechanical tunneling phenomenon not previously observed. Intensities of numerous infrared (IR) bands were used to monitor the temporal evolution of the lowest-energy O-H rotamers (1cTc, 1cTt, 1tTt) of oxalic acid for up to 19 days following near-infrared irradiation of the matrix. The relative energies of these rotamers are 0.0 (1cTc), 2.6 (1cTt), and 4.0 (1tTt) kcal mol(-1). A 1tTt → 1cTt → 1cTc isomerization cascade was observed with half-lives (t1/2) in different matrix sites ranging from 30 to 360 h, even though the sequential barriers of 9.7 and 10.4 kcal mol(-1) are much too high to be surmounted thermally under cryogenic conditions. A general mathematical model was developed for the complex kinetics of a reaction cascade with species in distinct matrix sites. With this model, a precise, global nonlinear least-squares fit was achieved simultaneously on the temporal profiles of nine IR bands of the 1cTc, 1cTt, and 1tTt rotamers. Classes of both fast (t(1/2) = 30-50 h) and slow (t(1/2) > 250 h) matrix sites were revealed, with the decay rate of the former in close agreement with first-principles computations for the conformational tunneling rates of the corresponding isolated molecules. Rigorous kinetic and theoretical analyses thus show that a "domino" tunneling mechanism is at work in these oxalic acid transformations.

Populated Intermediates in the Thermal Unfolding of the Human Telomeric Quadruplex

Thermal denaturation profiles of several model oligonucleotides of the human telomere DNA sequence including d[A(GGGTTA)(3)GGG] (Tel22) were determined using circular dichroism (CD), fluorescence of adenine → 2-aminopurine analogs, and fluorescence resonance energy transfer (FRET) to monitor the unfolding process at specific locations within the quadruplex. The resulting optical spectra vs temperature data matrices were analyzed by singular value decomposition (SVD) to ascertain the minimum number of species required to reproduce the unfolding spectral profiles. Global nonlinear least-squares fitting of the SVD amplitude vectors was used to estimate thermodynamic parameters and optical spectra of all species for a series of unfolding mechanisms that included one-, two-, and three-step sequential pathways F ⇌ I(n) ⇌ U, n = 0, 1, or 2) as well as two mechanisms with spectroscopically distinct starting structures (F(1) and F(2)). The CD and FRET data for Tel22 unfolding between 4 and 94 °C in 25 mM KCl were best described by a sequential unfolding model with two intermediates, while the 2-aminopurine analogs required one intermediate. The higher melting intermediate I(2) had a transition midpoint temperature (T(m)) of 61 °C and a CD spectrum with a maximum and minimum at ~265 and ~245 nm, respectively. The fluorescence emission spectra of the 2-aminopurine and FRET derivatives suggest greater solvent exposure of the 5'-AGGGTTA- segment in the intermediate compared to the folded state. The spectroscopic properties of the 61 °C intermediate suggest that it may be a triple helical structure.

Identification of continuous-time systems with multiple unknown time delays by global nonlinear least-squares and instrumental variable methods

This paper considers the identification problem of multiple input single output (MISO) continuous-time systems with unknown time delays of the inputs, from sampled input–output data. An iterative global separable nonlinear least-squares (GSEPNLS) method which estimates the time delays and transfer function parameters separably is derived to significantly reduce the possibility of convergence to a local minimum, by using the stochastic global-optimization techniques. Furthermore, the GSEPNLS method is modified to a novel global separable nonlinear instrumental variable (GSEPNIV) method to remove the biases of the estimates in the presence of high measurement noise. Simulation results show that the proposed algorithms work quite well.

Experimental determination of spin–orbital coupling states of O2(−)

Electron affinities, Ea, E1 and A1 are reported for the 12 primary X, A–K (27 spin) states of O2(−): KeqT3/2 = (SanQan)(2πmek/h2)3/2exp(Ea/RT); k1 = A1T−1/2exp(−E1/RT). These are obtained from pulsed discharge electron capture detector data by rigorously including literature values and uncertainties in a global non-linear least-squares adjustment. Simple molecular orbital theory predicts 27 bonding and 27 anti-bonding low-lying spin states. For the first time, the positive Ea for the 27 bonding states are reported. The partition function ratios of the negative ion and neutral (SanQan), the A1(X–E) and the spin separations are from fundamental constants. The Ea (in eV) are as follows (with the spin states in brackets): [1.050, 1.070]; [0.915, 0.935]; [0.698, 0.718, 0.746, 0.782]; [0.734, 0.754]; [0.559, 0.587]; 0.518; [0.430, 0.450]; 0.380; 0.354; [0.286, 0.298, 0.318, 0.346]; [0.232, 0.252]; [0.172, 0.184, 0.204, 0.232]. The activation energies (in eV) are as follows: E1(X–C) 1.0; E1(D,E) 1.0, 0.8, 0.6; E1(F–K) 0.12–0.08. The Ea and E1 are used to calculate bonding Herschbach ionic Morse–Person empirical curves.

Assessing Degradation Rates of Chlorinated Ethylenes in Column Experiments with Commercial Iron Materials Used in Permeable Reactive Barriers

Multiple column experiments were performed using two commercial iron materials to evaluate the necessity and usefulness of preliminary investigations in permeable reactive barrier (PRB) design for chlorinated organics. Experiments were performed with contaminated groundwater and involved fresh iron granules or altered iron material excavated from PRBs. The determination of first-order rate coefficients by global nonlinear least-squares fittings indicated a variability in rate coefficients on 1 or 2 orders of magnitude. Geometric mean values of surface area normalized rate coefficients (in 10(-5) L m(-2) h(-1)) for fresh gray cast iron and iron sponge, respectively, are: tetrachloroethene (4.5, 2.6), trichloroethene (8.1, 3.3), cis-1,2-dichloroethene (3.1, 2.9), trans-1,2-dichloroethene (9.5, 5.3), 1,1-dichloroethene (4.0, 4.4), and vinyl chloride (1.6, 6.1). The increasing rate coefficients with decreasing grade of chlorination, which characterize degradation at iron sponge are linearly related to diffusion coefficients in water, suggesting diffusion limitation in the degradation process for this particular material, possibly due to a high inner surface. The variability in rate coefficients seems to be too high to use mean rate coefficients from published studies in the design procedure of PRBs, and variabilities cannot be related to groundwater characteristics, waterflow through the reactive cells, or secondary corrosion reactions.

ATP-dependent Translocation of Proteins along Single-stranded DNA: Models and Methods of Analysis of Pre-steady State Kinetics

Processive DNA helicases are able to translocate along single-stranded DNA (ssDNA) with biased directionality in a nucleoside triphosphate-dependent reaction, although translocation is not generally sufficient for helicase activity. An understanding of the mechanism of protein translocation along ssDNA requires pre-steady state transient kinetic experiments. Although ensemble experimental approaches have been developed recently for the study of translocation of proteins along DNA, quantitative analysis of the complete time-courses from these experiments, which is needed to obtain quantitative estimates of translocation kinetic parameters (rate constants, processivity, step sizes and ATP coupling) has been lacking. We discuss three ensemble transient kinetic experiments that can be used to study protein translocation along ssDNA, along with the advantages and limitations of each approach. We further describe methods to analyze the complete kinetic time-courses obtained from such experiments performed with a series of ssDNA lengths under "single-round" conditions (i.e. in the absence of re-binding of dissociated protein to DNA). These analysis methods utilize a sequential "n-step" model for protein translocation along ssDNA and enable quantitative determinations of the rate constant, processivity and step size for translocation through global non-linear least-squares fitting of the full time-courses.

Identification of continuous-time systems with unknown time delays by global nonlinear least-squares method

This paper considers the identification problem of continuous-time systems with unknown time delays from sampled input-output data. By using a digital prefilter, an approximated discrete-time estimation model is first derived, in which the system parameters remain in their original form and the time delays need not be an integral multiple of sampling period. Then an iterative separable nonlinear least-squares (SEPNLS) method which estimates the time delays and transfer function parameters separably is derived. Futhermore, we propose an iterative global SEPNLS method to avoid convergence to a local minimum of the SEPNLS method by using of stochastic global-optimization techniques. Simulational results show that the global SEPNLS method is able to converge to global estimate.

Activation of striated muscle: nearest-neighbor regulatory-unit and cross-bridge influence on myofilament kinetics.

We have formulated a three-compartment model of muscle activation that includes both strong cross-bridge (XB) and Ca(2+)-activated regulatory-unit (RU) mediated nearest-neighbor cooperative influences. The model is based on the tight coupling premise--that XB retain activating Ca(2+) on the thin filament. Using global non-linear least-squares, the model produced excellent fits to experimental steady-state force-pCa and ATPase-pCa data from skinned rat soleus fibers. In terms of the model, nearest-neighbor influences over the range of Ca(2+) required for activation cause the Ca(2+) dissociation rate from regulatory-units (k(off)) to decrease and the cross-bridge association rate (f) to increase each more than ten-fold. Moreover, the rate variations occur in separate Ca(2+) regimes. The energy of activation governing f is strongly influenced by both neighboring RU and XB. In contrast, the energy of activation governing k(off) is less affected by neighboring XB than by neighboring RU. Nearest-neighbor cooperative influences provide both an overall sensitization to Ca(2+) and the well-known steep response of force to free Ca(2+). The apparent sensitivity for Ca(2+)-activation of force and ATPase is a function of cross-bridge kinetic rates. The model and derived parameter set produce simulated behavior in qualitative agreement with steady-state experiments reported in the literature for partial TnC replacement, increased [P(i)], increased [ADP], and MalNEt-S1 addition. The model is an initial attempt to construct a general theory of striated muscle activation-one that can be consistently used to interpret data from various types of muscle manipulation experiments.

Surface-tension studies of inclusion complexes of hexanediols with cyclodextrins in aqueous solutions

A surface-tension method developed previously was used to investigate the formation of an inclusion compound between hexanediols (HDs) and cyclodextrins (CDs) in an aqueous solution. A global nonlinear least-squares fit of surface tension data was applied to estimate binding constants for complexes between HD and CD, 1,2-HD forms a 1:1 complex (HD/CD) with CD while 1,6-HD and 2,5-HD form predominantly a 2:1 complex (2HDs/CD) with CD. Binding effects are discussed in relation to the different positioning of the hydroxyl groups of HDs.

High-resolution Fourier transform spectroscopy of the Meinel system of OH

The infrared spectrum of the hydroxyl radical OH, between 1850 and 9000/cm has been measured with a Fourier transform spectrometer. The source, a hydrogen-ozone diffusion flame, was designed to study the excitation of rotation-vibration levels of the OH Meinel bands under conditions similar to those in the upper atmosphere which produce the nighttime OH airglow emission. Twenty-three bands were observed: nine bands in the Delta upsilon = 1 sequence, nine bands in the Delta upsilon = 2 sequence, and five bands in the Delta upsilon = 3 sequence. A global nonlinear least-squares fit of 1696 lines yielded molecular parameters with a standard deviation of 0.003/cm. Term values are computed, and transition frequencies in the Delta upsilon = 3, 4, 5, 6 sequences in the near-infrared are predicted.

High-Resolution Fourier Transform Spectroscopy of the Vibration-Rotation Spectrum of the OD Radical

The infrared spectrum of the deuterated hydroxyl radical OD has been measured with a Fourier transform spectrometer between 1850 and 9000 cm−1. The source, a deuterium atom ozone diffusion flame, was designed to study the chemiluminescent excitation of the vibration-rotation energy levels of the OD radical. Twenty-one bands were observed, 6 bands in the Δv = 1 sequence, 9 bands in the Δv = 2 sequence, and 6 bands in the Δv = 3 sequence. A global nonlinear least-squares fit, utilizing the unique perturber approximation, of 2112 lines to 76 molecular parameters yielded a standard deviation of 0.007 cm−1 including 35 parameters for the previously unobserved v = 6-10 vibrational states.

Linkage between cooperative oxygenation and subunit assembly of cobaltous human hemoglobin

The thermodynamic linkage between cooperative oxygenation and dimer-tetramer subunit assembly has been determined for cobaltous human hemoglobin in which iron(II) protoporphyrin IX is replaced by cobalt(II) protoporphyrin IX. The equilibrium parameters of the linkage system were determined by global nonlinear least-squares regression of oxygenation isotherms measured over a range of hemoglobin concentrations together with the deoxygenated dimer-tetramer assembly free energy determined independently from forward and reverse reaction rates. The total cooperative free energy of tetrameric cobalt hemoglobin (over all four binding steps) is found to be 1.84 (+/- 0.13) kcal, compared with the native ferrous hemoglobin value of 6.30 (+/- 0.14) kcal. Detailed investigation of stepwise cooperativity effects shows the following: (1) The largest change occurs at the first ligation step and is determined on model-independent grounds by knowledge of the intermediate subunit assembly free energies. (2) Cooperativity in the shape of the tetrameric isotherm occurs mainly during the middle two steps and is concomitant with the release of quaternary constraints. (3) Although evaluation of the pure tetrameric isotherm portrays identical binding affinity between the last two steps, this apparent noncooperativity is the result of a "hidden" oxygen affinity enhancement at the last step of 0.48 (+/- 0.12) kcal. This quaternary enhancement energy is revealed by the difference in subunit assembly free energies of the triply and fully ligated species and is manifested visually by the oxygenation isotherms at high versus low hemoglobin concentration. (4) Cobaltous hemoglobin dimers exhibit apparent anticooperativity of 0.49 (+/- 0.16) kcal (presumed to arise from heterogeneity of subunit affinities).(ABSTRACT TRUNCATED AT 250 WORDS)

Highly excited rotational states of the Meinel system of OH

view Abstract Citations (12) References (16) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Highly Excited Rotational States of the Meinel System of OH Abrams, Mark C. ; Davis, Sumner P. ; Rao, M. L. P. ; Engleman, Rolf, Jr. Abstract The OH infrared spectrum, produced in an inductively coupled plasma discharge, has been measured with a Fourier transform spectrometer between 1850 and 5768/cm. This source was chosen in order to study the high-rotational quantum number levels of the OH Meinel bands. Two bands in the Delta-v = 1 sequence were observed, and extended to high J values: the P branch of the 1-0 band was observed up to J - 27.5 and the R branch to 13.5. The P branch of the 2-1 band was observed up to J = 25.5 and the R branch to 12. 5. Nonperturbative rotational crossings were observed in both the 1-0 and 2-1 bands. A global nonlinear least-squares fit of the 1-0 and 2-1 bands yielded equilibrium molecular parameters with a standard deviation of 0.0024/cm. Publication: The Astrophysical Journal Pub Date: November 1990 DOI: 10.1086/169346 Bibcode: 1990ApJ...363..326A Keywords: Atmospheric Chemistry; Hydroxyl Radicals; Molecular Excitation; Molecular Rotation; Fourier Transformation; Infrared Spectra; Molecular Spectra; Atomic and Molecular Physics; LABORATORY SPECTRA; MOLECULAR PROCESSES full text sources ADS |