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PubMed2000

Probability calculus for quantitative HREM. Part II: entropy and likelihood concepts.

The technique of extracting atomic coordinates from HREM images by R-factor refinement via iterative simulation and global optimisation is described in the context of probability density estimations for unknown parameters. In the second part of this two-part paper we discuss in comparison maximum likelihood and maximum entropy techniques with respect to their suitability of application within HREM. We outline practical difficulties of likelihood estimation and present a synthesis of two point-cloud techniques as a recommendable solution. This R-factor refinement with independent Monte-Carlo error calibration is a highly versatile method which allows adaptation to the special needs of HREM. Unlike simple text-book estimation methods, there is no requirement here on the noise being additive, uncorrelated, or Gaussian. It also becomes possible to account for a subset of systematic errors.

Journal Article↗
PubMed2002

A correction algorithm for undersampled images using dynamic segmentation and entropy based focus criterion.

A post-processing technique is presented for correcting images undersampled in k-space. The method works by taking advantage of the image's background zeros (dynamically segmented through the application of a threshold) to extrapolate the missing k-space samples. The algorithm can produce good quality images from a small set of k-space frequencies with only a few iterations of simple matrix operations, using the image entropy as the focus criterion. It does not require any special patient preparation, extra pulse sequences, complex gradient programming or specialized hardware. This makes it a good candidate for any application that requires short scan times or where only few frequencies can be sampled.

Algorithms↗
PubMed2003

Weighted two-band target entropy minimization for the reconstruction of pure component mass spectra: simulation studies and the application to real systems.

A method is proposed, on the basis of a recently developed algorithm--Band Target Entropy Minimization (BTEM)--to reconstruct mass spectra of pure components from mixture spectra. This method is particular useful in dealing with spectral data with discrete features (like mass spectra). Compared to the original BTEM, which has been applied to differentiable spectroscopies such as Fourier-transfer infrared spectroscopy (FTIR), ultraviolet (UV), Raman, and nuclear magnetic resonance (NMR), the latest modifications were obtained through: (1) Reformulating the objective function using the peak heights instead of their derivatives; (2) weighting the abstract vector VT to reduce the effect of noise; (3) using a two-peak targeting strategy (tBTEM) to deal with strongly overlapping peaks; and (4) using exhaustive search to locate all the component spectra. A set of 50 multi-component mass spectra was generated from ten reference experimental pure component spectra. Many of the compounds chosen have common MS fragments and therefore, many of the pure component spectra have considerable intensity in same data channels. In addition, a set of MS spectra from a real system with four components was used to examine the newly developed algorithm. Successful reconstruction of the ten component spectra of the simulated system and the four component spectra of the real system was rapidly achieved using the new tBTEM algorithm. The advantages of the new algorithm and its implication for rapid system identification of unknown mixtures are readily apparent.

Journal Article↗
PubMed1991

Pure absorption-mode spectra from Bayesian maximum entropy analysis of ion cyclotron resonance time-domain signals.

Fourier transform ion cyclotron resonance (FT/ICR) mass spectra are normally reported in the (phase-independent) magnitude-mode format. In principle, the absorption-mode format offers spectral resolution enhanced by a factor ranging from square root of 3 to 2 over the corresponding magnitude-mode spectrum obtained by discrete FT of the same unapodized time-domain data. However, an absorption-mode display is generally unsuitable in practice because of the auxiliary spectral peaks (Gibbs oscillations) resulting from the relatively long time delay between excitation and detection. Although the resulting large phase variation (up to 100 pi rad or more across the Nyquist spectral bandwidth) can be corrected exactly for a continuous time-domain signal, phase correction of a discrete time-domain signal results in Gibbs oscillations even for a perfectly phased absorption-mode spectrum. In this paper, we show that a Bayesian "maximum-entropy" analysis of simulated and experimental ion cyclotron resonance time-domain noisy signals can recover a precisely phased absorption-mode frequency-domain spectrum that is devoid of Gibbs oscillations, is less sensitive to noise, and offers improved mass accuracy over that obtained from a conventional magnitude-mode discrete fast Fourier transform (FFT) spectrum.

Fourier Analysis↗
PubMed2000

A study of the enthalpy and entropy contributions of the stationary phase in reversed-phase liquid chromatography.

The goal of this study was to elucidate the roles played by the stationary and mobile phases in retention in reversed-phase liquid chromatography (RPLC) in terms of their individual enthalpic and entropic contribution to the Gibbs free energy of retention. The experimental approach involved measuring standard enthalpies of transfer of alkylbenzenes from typical mobile phases used in RPLC (methanol/water and acetonitrile/water mixtures), as well as from n-hexadecane (a simple analogue of the stationary phase) to the gas phase, using high-precision headspace gas chromatography. By combining the measured enthalpies with independently measured free energies of transfer, the entropies of transfer were obtained. This allowed us to examine more fully the contribution that each phase makes to the overall retention. It was found that the standard enthalpy of retention in RPLC (i.e., solute transfer from the mobile phase to the stationary phase) is favorable, due to the large and favorable stationary-phase contribution, which actually overcomes an unfavorable mobile-phase contribution to the enthalpy of retention. Further, the net free energy of retention is favorable due to the favorable enthalpic contribution to retention, which arises from the net interactions in the stationary phase. Entropic contributions to retention are not controlling. Therefore, to a great extent, retention is due to enthalpically dominated lipophilic interaction of nonpolar solutes with the stationary phase and not from solvophobic processes in the mobile phase. Further, our enthalpy data support a "partition-like" mechanism of retention rather than an "adsorption-like" mechanism. These results indicate that the stationary phase plays a very significant role in the overall retention process. Our conclusions are in direct contrast to the solvophobic model that has been used extensively to interpret retention in RPLC.

Journal Article↗
PubMed2005

Development of 2D band-target entropy minimization and application to the deconvolution of multicomponent 2D nuclear magnetic resonance spectra.

Spectral reconstruction from multicomponent spectroscopic data is the frequent primary goal in chemical system identification and exploratory chemometric studies. Various methods and techniques have been reported in the literature. However, few algorithms/methods have been devised for spectral recovery without the use of any a priori information. In the present studies, a higher dimensional entropy minimization method based on the BTEM algorithm (Widjaja, E.; Li, C.; Garland, M. Organometallics 2002, 21, 1991-1997.) and related techniques were extended to large-scale arrays, namely, 2D NMR spectroscopy. The performance of this novel method had been successfully verified on various real experimental mixture spectra from a series of randomized 2D NMR mixtures (COSY NMR and HSQC NMR). With the new algorithm and raw multicomponent NMR alone, it was possible to reconstruct the pure spectroscopic patterns and calculate the relative concentration of each species without recourse to any libraries or any other a priori information. The potential advantages of this novel algorithm and its implications for general chemical system identification of unknown mixtures are discussed.

Journal Article↗
PubMed2001

Why is it so difficult to simulate entropies, free energies, and their differences?

The classical 19th century thermodynamic inequalities of Clausius and Helmholtz are applied to the calculation of entropy and free energy changes by computer simulation. The irreversibility of finite-time thermodynamic paths is exploited to obtain upper and lower bounds on these quantities. Schrödinger's microscopic interpretation of heat and work provides the basis for a literal implementation of the key historical concepts on the computer using the Monte Carlo algorithm of Metropolis. Coupling schemes, paths, and reference states are variationally optimized to improve the convergence of the simulated properties, and a newly introduced variational flexibility, metric scaling, is overviewed. Reasons for expecting limiting power laws for the convergence are outlined.

Chemistry↗
PubMed1995

Thermodynamic and activation parameters for binding of a pyrene-labeled substrate by the Tetrahymena ribozyme: docking is not diffusion-controlled and is driven by a favorable entropy change.

Association and dissociation rates for the pyrene-(pyr)-labeled oligoribonucleotide substrate pyrCUCU binding to the L-21 ScaI group I ribozyme are reported as a function of temperature. Combined with thermodynamic parameters for binding of pyrCUCU to rGGAGAA, the results allow calculation of the activation and thermodynamic parameters for docking of pyrCUCU into the catalytic core of the ribozyme. The activation enthalpy for docking is 22 kcal/mol, much larger than the approximately 4 kcal/mol expected for a diffusion-controlled process. Thus, docking is not diffusion-controlled. The activation and equilibrium entropies for docking are favorable at 21 and 37 eu, respectively. The results suggest the rate-limiting step and the driving force for docking may involve desolvation of RNA functional groups or of Mg2+ ions.

Animals↗
PubMed1994

Influence of substrates and MgADP on the time-resolved intrinsic fluorescence of phosphofructokinase from Escherichia coli. Correlation of tryptophan dynamics to coupling entropy.

The influence of that MgADP and the substrate ligands MgATP and fructose 6-phosphate (Fru-6-P) have on the structure of E. coli phosphofructokinase (PFK) in the vicinity of the single tryptophan that exists in each subunit has been examined by employing both steady-state and time-resolved measurements of the tryptophan fluorescence. The accessibility of the tryptophan to iodide quenching is over 1 order of magnitude less than experienced by N-acetyltryptophanamide in solution but varies nonetheless with the state of ligation. Most, but not all, of these changes correlate with changes in the degree of local motion available to the tryptophan side chain as determined by steady-state and time-resolved polarization measurements. When the data obtained from differential polarization experiments are fit to a model in which the motion of the tryptophan side chain is able to move with high frequency within a cone of limited amplitude as part of an otherwise slowly tumbling spherical protein, it was found that ligands primarily affect the amplitude of the available local motion. By interpreting these effects with reference to the disproportionation equilibria which define the negative coupling free energy between MgADP and Fru-6-P and the positive coupling free energy between MgADP and MgATP, it is apparent that changes in the local motion amplitudes correlate with the sign of the component coupling entropy previously determined from van't Hoff analyses (Johnson & Reinhart, 1994).(ABSTRACT TRUNCATED AT 250 WORDS)

Adenosine Diphosphate↗
PubMed1988

Stability mutants of staphylococcal nuclease: large compensating enthalpy-entropy changes for the reversible denaturation reaction.

By use of intrinsic fluorescence to determine the apparent equilibrium constant Kapp as a function of temperature, the midpoint temperature Tm and apparent enthalpy change delta Happ on reversible thermal denaturation have been determined over a range of pH values for wild-type staphylococcal nuclease and six mutant forms. For wild-type nuclease at pH 7.0, a Tm of 53.3 +/- 0.2 degrees C and a delta Happ of 86.8 +/- 1.4 kcal/mol were obtained, in reasonable agreement with values determined calorimetrically, 52.8 degrees C and 96 +/- 2 kcal/mol. The heat capacity change on denaturation delta Cp was estimated at 1.8 kcal/(mol K) versus the calorimetric value of 2.2 kcal/(mol K). When values of delta Happ and delta Sapp for a series of mutant nucleases that exhibit markedly altered denaturation behavior with guanidine hydrochloride and urea were compared at the same temperature, compensating changes in enthalpy and entropy were observed that greatly reduce the overall effect of the mutations on the free energy of denaturation. In addition, a correlation was found between the estimated delta Cp for the mutant proteins and the d(delta Gapp)/dC for guanidine hydrochloride denaturation. It is proposed that both the enthalpy/entropy compensation and this correlation between two seemingly unrelated denaturation parameters are consequences of large changes in the solvation of the denatured state that result from the mutant amino acid substitutions.

Kinetics↗
PubMed1990

Time-resolved fluorescence of the single tryptophan residue in rat alpha-fetoprotein and rat serum albumin: analysis by the maximum-entropy method.

The time-resolved fluorescence emissions of the lone tryptophan residues in rat alpha-fetoprotein (RFP) and rat serum albumin (RSA) were studied. The total fluorescence intensity decays in both proteins were multiexponential. Analysis of the data by nonlinear least squares as a sum of discrete exponentials showed that four exponentials were needed for a satisfactory fit for both proteins. Analysis by the maximum entropy method using 150 logarithmically equally spaced exponentials yielded four well-resolved excited-state lifetime classes with barycenters and relative amplitudes values (ci) that corresponded to those obtained from the nonlinear least-squares method. Changing the temperature affected the relative amplitudes of the lifetime classes but had little effect on the lifetime values themselves. This suggests that the four classes reflect local conformational substates that exchange slowly with respect to the time window of observation defined by the longest lifetime. The internal rotational dynamics of the tryptophan in each protein was monitored by fluorescence anisotropy decay measurements. The mobility of the tryptophan appeared to be larger and faster in RFP than in RSA. The nonlinear least-squares analysis suggests the existence of three rotational correlation times of 0.1, 3, and 55 ns for this protein. As a function of temperature, the long correlation time did not follow the Perrin's law expected for a rigid rotating body. This suggests that this correlation time may reflect not only the Brownian rotation of the whole protein but also the flexibilities of domains in the protein. For RSA a two-component model with correlation times of 0.4 and 31 ns was sufficient to describe the data.(ABSTRACT TRUNCATED AT 250 WORDS)

Animals↗
PubMedDate not supplied

The estimation of melting points and fusion enthalpies using experimental solubilities, estimated total phase change entropies, and mobile order and disorder theory.

Melting points and fusion enthalpies are predicted for a series of 81 compounds by combining experimental solubilities in a variety of solvents and analyzed according to the theory of mobile order and disorder (MOD) and using the total phase change entropy estimated by a group additivity method. The error associated in predicting melting points is dependent on the magnitude of the temperature predicted. An error of +/- 12 K (+/- 1 sigma) was obtained for compounds melting between ambient temperature and 350 K (24 entries). This error increased to +/- 23 K when the temperature range was expanded to 400 K (46 entries) and +/- 39 K for the temperature range 298-555 K (79 entries). Fusion enthalpies were predicted within +/- 2sigma of the experimental values (+/- 6.4 kJ mol(-1)) for 79 entries. The uncertainty in the fusion enthalpy did not appear dependent on the magnitude of the melting point. Two outliers, adamantane and camphor, have significant phase transitions that occur below room temperature. Estimates of melting temperature and fusion enthalpy for these compounds were characterized by significantly larger errors.

Journal Article↗
PubMedDate not supplied

Inferring lifetime distributions from kinetics by maximizing entropy using a bootstrapped model.

A bootstrapped model is used to improve the lifetime distribution recovered using the maximum entropy method from kinetics that involves overlapping exponential and distributed phases. The model defaulted to in the limit of low signal-to-noise is iteratively derived from the data to counter the tendency of regularization methods to over-smooth sharp features while under-smoothing broad ones. Upon each revision, some of the lifetime distribution is focused and the rest is blurred. This differential blurring can produce distributions that are virtually free of artifacts. The change in the result obtained upon a reasonable change in the default model provides a useful measure of the uncertainty in the lifetime distribution. In particular, the widths of peaks may not be well determined.

Journal Article↗
PubMedDate not supplied

Novel scoring functions comprising QXP, SASA, and protein side-chain entropy terms.

Novel scoring functions that predict the affinity of a ligand for its receptor have been developed. They were built with several statistical tools (partial least squares, genetic algorithms, neural networks) and trained on a data set of 100 crystal structures of receptor-ligand complexes, with affinities spanning 10 log units. The new scoring functions contain both descriptors generated by the QXP docking program and new descriptors that were developed in-house. These new descriptors are based on solvent accessible surface areas and account for conformational entropy changes and desolvation effects of both ligand and receptor upon binding. The predictive r(2) values for a test set of 24 complexes are in the 0.712-0.741 range and RMS prediction errors in the 1.09-1.16 log K(d) range. Inclusion of the new descriptors led to significant improvements in affinity prediction, compared to scoring functions based on QXP descriptors alone. However, the QXP descriptors by themselves perform better in binding mode prediction. The performance of the linear models is comparable to that of the neural networks. The new functions perform very well, but they still need to be validated as universal tools for the prediction of binding affinity.

Algorithms↗
PubMed2002

Dependence of the rate of an interfacial Diels-Alder reaction on the steric environment of the immobilized dienophile: an example of enthalpy-entropy compensation.

This paper describes a physical organic study of the relationship between the rate for an interfacial Diels-Alder reaction and the steric environment around the reacting molecules. The study used as a model reaction the cycloaddition of cyclopentadiene with a self-assembled monolayer (SAM) presenting benzoquinone groups surrounded by hydroxyl-terminated alkanethiolates. The accessibility of the quinone was varied by preparing monolayers from hydroquinone-terminated alkanethiols of different lengths [HS(CH(2))(n)-HQ, n = 6-14] and a hydroxyl-terminated alkanethiol [HS(CH(2))(11)-OH] of constant length. Cyclic voltammetry was used to measure the rate of the reaction by monitoring the decay of the redox-active quinone. The second-order rate constant showed a modest change as the position of quinone was varied relative to the hydroxyl groups of the monolayer. For monolayers wherein the quinone groups were extended from the interface, the rate constants oscillated near 0.20 M(-1) s(-1) with an even-odd dependence on the length of the alkanethiol. For monolayers that positioned the quinone groups below the surrounding hydroxyl groups, the rate constants decreased by approximately 8-fold. Examination of the activation parameters revealed that the quinone groups that were positioned below the interface (and in a crowded environment) reacted with an enthalpy of activation that was 4 kcal/mol greater than did the quinones that were accessible at the interface. The reaction of the buried quinone, however, proceeded with an entropy of activation that was more favorable by 13 eu, and therefore with a similar free energy of activation. The combination of SAMs for preparing model interfaces and cyclic voltammetry for measuring rates provides a new opportunity for physical organic studies of interfacial reactions.

Journal Article↗
PubMed2002

Modern spectrum analysis in multidimensional NMR spectroscopy: comparison of linear-prediction extrapolation and maximum-entropy reconstruction.

NMR spectroscopy is an inherently insensitive technique, and many challenging applications such as biomolecular studies operate at the very limits of sensitivity and resolution. Advances in superconducting magnet, cryogenic probe, and pulse sequence technologies have resulted in dramatic improvements in both sensitivity and resolution in the past decade. Conversely, the signal-processing method used most widely in NMR spectroscopy, extrapolation of the time domain signal by linear prediction (LP) followed by discrete Fourier transformation (DFT), was developed in the early 1980s and has not been subjected to detailed scrutiny for its impact on sensitivity and resolution. Here we report the first systematic investigation of the accuracy and precision of spectra obtained by LP extrapolation followed by DFT. We compare the results to spectra obtained by maximum-entropy (MaxEnt) reconstruction, which was developed contemporaneously to LP extrapolation but is not widely employed in NMR spectroscopy. Although it reduces truncation artifacts and increases the amplitudes of strong peaks, we find that LP extrapolation generates false-positive peaks and introduces frequency errors. These defects of LP extrapolation become less pronounced for longer data records and higher signal-to-noise ratio. MaxEnt generally yields more detectable peaks for a given number of data samples, more accurate peak frequencies, and fewer false-positive peaks than LP extrapolation. MaxEnt also permits the use of nonlinear sampling, which can give dramatic improvements in resolution. These results show that the use of MaxEnt together with nonlinear sampling, rather than LP extrapolation, could reduce the amount of instrument time required for adequate sensitivity and resolution by a factor of 2 or more.

Fourier Analysis↗
PubMed2003

The glass transition time scale and configurational entropy in polymers: an experimental molecular view.

We report direct experimental observation of local conformational dynamics in a polymer chain at the calorimetric glass transition temperature Tg. Variable-temperature two-dimensional (2D) solid-state exchange NMR, at natural abundance, reveals segmental dynamics in pure polyisobutylene (PIB) occurring on a time scale of several seconds over the Tg range observed by DSC (203-208 K). To our knowledge, this is the first direct observation of molecular-level conformer interchange (trans-trans/trans-gauche/gauche-gauche) at the caloric glass transition temperature. Our results provide a chronologically accurate and pedagogically advantageous demonstration of molecular processes during a polymer phase transition, relative to traditional bulk mechanical and calorimetric techniques. More importantly, we use a miscible blend to demonstrate a general strategy for quantitative evaluation of configurational entropy changes via combination of temperature-dependent 2D exchange NMR and Adams-Gibbs theory. Our results on the Tg time scale are directly relevant to fundamental understanding of the Tg length scale, i.e., the dimension of cooperatively rearranging regions.

Journal Article↗