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PubMed2007

Quantitative CARS spectroscopy using the maximum entropy method: the main lipid phase transition.

The maximum entropy method for phase retrieval of multiplex coherent anti-Stokes Raman scattering (CARS) spectra is described in detail and applied to the time-resolved measurement of the main lipid phase transition of small, unilamellar 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) vesicles subject to a 3 min temperature sweep. Since the--thus derived--imaginary part of the third-order CARS susceptibility can be directly related to the linear vibrational spectrum, the multiplex CARS spectral data can be analyzed quantitatively and without prior knowledge of the sample. It is shown that the maximum entropy model provides an exact description of the original data, including the noise, if all available autocorrelation functions are used. Our findings confirm the acyl-chain order-disorder phase-transition behavior of small, unilamellar lipid vesicles.

Computer Simulation↗

PubMed2005

Phase-space overlap measures. I. Fail-safe bias detection in free energies calculated by molecular simulation.

We consider ways to quantify the overlap of the parts of phase space important to two systems, labeled A and B. Of interest is how much of the A-important phase space lies in that important to B, and how much of B lies in A. Two measures are proposed. The first considers four total-energy distributions, formed from all combinations made by tabulating either the A-system or the B-system energy when sampling either the A or B system. Measures for A in B and B in A are given by two overlap integrals defined on pairs of these distributions. The second measure is based on information theory, and defines two relative entropies which are conveniently expressed in terms of the dissipated work for free-energy perturbation (FEP) calculations in the A-->B and B-->A directions, respectively. Phase-space overlap is an important consideration in the performance of free-energy calculations. To demonstrate this connection, we examine bias in FEP calculations applied to a system of independent particles in a harmonic potential. Systems are selected to represent a range of overlap situations, including extreme subset, subset, partial overlap, and nonoverlap. The magnitude and symmetry of the bias (A-->B vs B-->A) are shown to correlate well with the overlap, and consequently with the overlap measures. The relative entropies are used to scale the amount of sampling to obtain a universal bias curve. This result leads to develop a simple heuristic that can be applied to determine whether a work-based free-energy measurement is free of bias. The heuristic is based in part on the measured free energy, but we argue that it is fail-safe inasmuch as any bias in the measurement will not promote a false indication of accuracy.

Algorithms↗

PubMed2000

Comparisons of pressure and temperature activation parameters for amide hydrogen exchange in T4 lysozyme.

Activation enthalpies and entropies are reported for proton-deuteron exchange at 42 amide sites in T4 lysozyme and compared with activation volumes for the same residues obtained earlier [Hitchens, T. K., and Bryant, R. G. (1998) Biochemistry 37, 5878-5887]. There is no correlation found between activation volume and activation entropy or activation enthalpy. The activation enthalpy is linearly related to the activation entropy in part as a consequence of a relatively narrow sampling window for the rate constants that corresponds to a narrow range of activation free energy. A consequence of the entropy-enthalpy compensation is preservation of rank order of proton exchange. Variations in DeltaH, DeltaS, and DeltaV for residues that are structurally close together in the folded protein suggest that there may be a variety of energetically distinct pathways for the access of solvent to these structurally related exchange sites.

Bacteriophage T4↗

PubMed2004

A simulation method for calculating the absolute entropy and free energy of fluids: application to liquid argon and water.

The hypothetical scanning (HS) method is a general approach for calculating the absolute entropy and free energy by analyzing Boltzmann samples obtained by Monte Carlo (MC) or molecular dynamics techniques. With HS applied to a fluid, each configuration i of the sample is reconstructed by adding its atoms gradually to the initially empty volume, i.e., by placing them in their positions at i using transition probabilities (TPs). At each step of the process, the volume is divided into two parts, the already visited part (the "past") and the "future" part, where obtaining the TP requires calculating partition functions over the future part in the presence of the frozen past. In recent publications, the TPs were calculated approximately by taking into account only partial future. Here we present a "complete HSMC" procedure, where the TPs are calculated from MC simulations carried out over the complete future. The complete HSMC method is applied to systems of liquid argon and the TIP3P model of water, and very good results for the free energy are obtained, as compared with results obtained by thermodynamic integration.

Argon↗

PubMed2006

Computer simulation of the distribution of hexane in a lipid bilayer: spatially resolved free energy, entropy, and enthalpy profiles.

The partitioning behavior of small molecules in lipid bilayers is important in a variety of areas including membrane protein folding and pharmacology. However, the inhomogeneous nature of lipid bilayers on a nanometer length scale complicates experimental studies of membrane partitioning. To gain more insight in the partitioning of a small molecule into the lipid bilayer, we have carried out atomistic computer simulations of hexane in a dioleoyl phosphatidylcholine model membrane. We have been able to obtain spatially resolved free energy, entropy, enthalpy, and heat capacity profiles based on umbrella sampling calculations at three different temperatures. In agreement with experiment, hexane partitions preferentially to the center of the bilayer. This process is driven almost entirely by a favorable entropy change, consistent with the hydrophobic effect. In contrast, partitioning to the densest region of the acyl chains is dominated by a favorable enthalpy change with a small entropy change, which is consistent with the "nonclassical" hydrophobic effect or "bilayer" effect. We explain the features of the entropy and enthalpy profiles in terms of density and free volume in the system.

Computer Simulation↗

PubMed1999

[Study of ultrasonographic image textures with second-order statistical methods].

BACKGROUND: We report the sonographic image texture of the neonatal heart in different stages of development by calculating numerical parameters extracted from the gray scale cooccurrence matrix. To show pixel values differences and enhance texture structure, images were equalized, and then the gray level range was reduced to 16 to allow for sufficiently high occupancy frequency of the cooccurrence matrix. MATERIALS AND METHODS: We measured B-mode US images, all acquired with the same unit, using the same setup (gain, frequency, constant TGC). For each case measurements were made on 3 diastolic images by selecting a 32 x 64 pixel on the interventricular septum ROI. This procedure was applied to 3 different examinations made at birth, at 3 days, and after a month of life. For each 8 bit image we obtained a coocurrence matrix by sampling adjacent pixels at 0 degree, from which we calculated entropy; then the images were equalized and converted to 4 bit format; on these processed images we calculated 4 gray scale coocurrence matrix samplings adjacent pixels at angles of 0 degree, 45 degrees, 90 degrees, and 180 degrees. Parameters obtained from different angles cooccurrence matrix were averaged to get a numerical parameter independent of sampling angles. RESULTS: The one-way analysis of variance and Student's "t"-test were performed on the parameters obtained from 3 different examinations and the differences among different developmental stages are 95% significant. No significance was obtained comparing images at birth with those at 3 days. CONCLUSIONS: Differences are so little significant that they may be due to different factors affecting image texture and the variability introduced by manual ROI positioning; therefore no definitive conclusions can be drawn as to considering this kind of analysis capable of discriminating different stages of myocardial development. To apply this analysis to routine US examinations, different correction factors for range, azimuth, and focal dependence of texture must be considered.

Mathematics↗

PubMed1997

A pentapeptide model for an early folding step in the refolding of staphylococcal nuclease: the role of its turn propensity.

Recently the folding of a staphylococcal nuclease (P117G) variant was examined with the hydrogen-deuterium (H-D) exchange technique. Many of the residues that showed significant protection are located in beta-sheet regions. About half the residues protected belong to an antiparallel beta-hairpin structure (residues 21-35) in the native structure. The beta-hairpin structure is formed by strands 2 and 3 of sheet 2 connected by the sequence 27Y KGQP31 in a type 1' reverse turn conformation with a 4-->1 hydrogen bonding between Q30 NH and Y27 C = O. We have targeted the conformational characterization of the peptide model Ac-YKGQP-NH2 with 1H two-dimensional nmr techniques in aqueous solution with a view to assessing its propensity to sample turn conformational forms and thus initiate the formation of beta-hairpin structure. Based upon the observed d alpha n (i, i + 1), d alpha n (i, i + 3), and dnn (i, i + 1) nuclear Overhauser effect connectivities, temperature coefficients for amide protons and conformational analysis with quantum mechanical perturbative configuration interaction over localized orbitals method, we conclude that the model peptide samples turn conformational forms with reduced conformational entropy. We suggest that the turn can nucleate the formation of the beta-hairpin structure in the refolding of nuclease. Observation of turn propensity for this sequence is consistent with the folding mechanism of the Greek key motif (present in Staphylococcal nuclease) proposed in the literature.

Micrococcal Nuclease↗

PubMed2002

Estimating probabilities from experimental frequencies.

Estimating the probability distribution q governing the behavior of a certain variable by sampling its value a finite number of times most typically involves an error. Successive measurements allow the construction of a histogram, or frequency count f, of each of the possible outcomes. In this work, the probability that the true distribution be q, given that the frequency count f was sampled, is studied. Such a probability may be written as a Gibbs distribution. A thermodynamic potential, which allows an easy evaluation of the mean Kullback-Leibler divergence between the true and measured distribution, is defined. For a large number of samples, the expectation value of any function of q is expanded in powers of the inverse number of samples. As an example, the moments, the entropy, and the mutual information are analyzed.

Journal Article↗

PubMed1977

Vapor phase adsorption of water on hydroxyapatite.

Water vapor adsorption isotherms were determined gravimetrically on three hydroxyapatite sampel differing in preparation and with surface areas of 70.4, 22.5, and 3.0 M2/gm, respectively. Heats of adsorption for the first layer of water were found to be 13.3, 13.2, and 13.9 kcal/mole on these hydroxypatites. From repeated thermal desorption and adsorption cycles of water, stepwise adsorption was observed which diminished with each outgassing cycle until it disappeared after the fourth cycle. Cross-sectional area of adsorbed water molecule on hydroxyapatite surface was estimated at 11.5 A2. Standard free energies, isosteric heats, changes in enthalpy, and entropy of adsorption of water on HAP samples outgassed at 300 C were determined.

Adsorption↗

PubMed2006

Non-uniformly sampled double-TROSY hNcaNH experiments for NMR sequential assignments of large proteins.

The initial step of protein NMR resonance assignments typically identifies the sequence positions of 1H-15N HSQC cross-peaks. This is usually achieved by tediously comparing strips of multiple triple-resonance experiments. More conveniently, this could be obtained directly with hNcaNH and hNcocaNH-type experiments. However, in large proteins and at very high fields, rapid transverse relaxation severely limits the sensitivity of these experiments, and the limited spectral resolution obtainable in conventionally recorded experiments leaves many assignments ambiguous. We have developed alternative hNcaNH experiments that overcome most of these limitations. The TROSY technique was implemented for semiconstant time evolutions in both indirect dimensions, which results in remarkable sensitivity and resolution enhancements. Non-uniform sampling in both indirect dimensions combined with Maximum Entropy (MaxEnt) reconstruction enables such dramatic resolution enhancement while maintaining short measuring times. Experiments are presented that provide either bidirectional or unidirectional connectivities. The experiments do not involve carbonyl coherences and thus do not suffer from fast chemical shift anisotropy-mediated relaxation otherwise encountered at very high fields. The method was applied to a 300 microM sample of a 37 kDa fragment of the E. coli enterobactin synthetase module EntF, for which high-resolution spectra with an excellent signal-to-noise ratio were obtained within 4 days each.

Chromatography, Gel↗

PubMed2001

Four-dimensional dielectric property image obtained from electron spectroscopic imaging series.

We have demonstrated a new quantitative method to characterize two-dimensional distributions of energy-dependent dielectric function of materials from low loss electron spectroscopic image (ESI) series. Two problems associated with extracted image-spectrum from the low-loss image series, under-sampling and loss of energy resolution, were overcome by using fast Fourier transformation (FFT) interpolation and maximum entropy deconvolution method. In this study, Black Diamond/Si3N4/SiO2/Si-substrate dielectric layer designed for copper metallization was used as the sample. We show that the reconstructed (FFT interpolated and maximum entropy deconvoluted) image-spectrum obtained from ESI series images can be quantified with the same accuracy as conventional electron energy-loss spectroscopy spectra. Since the analysis of the dielectric function is sensitive to the local thickness of the specimen using Kramers-Kronig analysis, we also developed a new method to quantitatively determine the dielectric constant for low-k materials. We have determined the thickness of the Black Diamond using the extrapolated thickness method from the materials of known dielectric constants. Using Kramers-Kronig formula, the dielectric function map can be deduced from two-dimensional reconstructed single scattering spectra with providing the information of thickness. We proposed a four-dimensional data presentation for revealing the uniformity of the energy dependent property. The accuracy of our methods depends on the thickness determination and on the quality of the reconstructed spectra from the image series.

Journal Article↗

PubMed2003

Robust biased Brownian dynamics for rate constant calculation.

A reaction probability is required to calculate the rate constant of a diffusion-dominated reaction. Due to the complicated geometry and potentially high dimension of the reaction probability problem, it is usually solved by a Brownian dynamics simulation, also known as a random walk or path integral method, instead of solving the equivalent partial differential equation by a discretization method. Building on earlier work, this article completes the development of a robust importance sampling algorithm for Brownian dynamics-i.e., biased Brownian dynamics with weight control-to overcome the high energy and entropy barriers in biomolecular association reactions. The biased Brownian dynamics steers sampling by a bias force, and the weight control algorithm controls sampling by a target weight. This algorithm is optimal if the bias force and the target weight are constructed from the solution of the reaction probability problem. In reality, an approximate reaction probability has to be used to construct the bias force and the target weight. Thus, the performance of the algorithm depends on the quality of the approximation. Given here is a method to calculate a good approximation, which is based on the selection of a reaction coordinate and the variational formulation of the reaction probability problem. The numerically approximated reaction probability is shown by computer experiments to give a factor-of-two speedup over the use of a purely heuristic approximation. Also, the fully developed method is compared to unbiased Brownian dynamics. The tests for human superoxide dismutase, Escherichia coli superoxide dismutase, and antisweetener antibody NC6.8, show speedups of 17, 35, and 39, respectively. The test for reactions between two model proteins with orientations shows speedups of 2578 for one set of configurations and 3341 for another set of configurations.

Antigen-Antibody Complex↗

PubMed2004

Entropy calculation of HIV-1 Env gp120, its receptor CD4, and their complex: an analysis of configurational entropy changes upon complexation.

The HIV-1 gp120/CD4 interaction shows a large, unprecedented entropy/enthalpy compensation, with the capacity to fine-tune recognition over a broad range of affinity. The intermolecular interaction involves stable hydrophobic contacts with a unique protruding CD4-Phe43 structure surrounded by an intermolecular hydrogen-bond network that covers the hemisphere of the CD4 D1 domain. We have applied a heuristic formula based on the covariance matrix of atom-positional fluctuations to assess the configurational entropy of the gp120/CD4 complex at different levels. The system was dissected into various subsets of atoms to evaluate the entropic contributions of different functional elements. By combining the trajectories of the free and complex forms, further insight into the conformational sampling was extracted. Despite the limited sampling time of 10 ns, the theoretically derived changes in configurational entropy are in fair agreement with the experimentally determined data. The simultaneous evaluation of different interaction modes through a decomposition approach is only feasible with the knowledge of the atomic trajectory of the system. The configurational entropy analysis in terms of combined trajectories presented here shall potentially provide accurate estimations of thermodynamic properties of biomolecules given sufficient sampling of conformational space.

Biophysics↗

PubMed1997

Differential scanning calorimetric studies on the thermotropic phase transitions of dry and hydrated forms of N-acylethanolamines of even chainlengths.

N-acylethanolamines (NAEs) have attracted the attention of researchers in the last two decades due to their occurrence in biological membranes under conditions of stress as well as under normal conditions. Differential scanning calorimetric studies have been carried out on dry and hydrated samples of a homologous series of N-acylethanolamines containing saturated acyl chains of even number of carbon atoms (n = 8-20). In both cases a major sharp endothermic transition was observed which occurs at the melting point for the dry NAEs whereas for the hydrated samples it occurs at considerably lower temperatures. The enthalpies and entropies corresponding to this transition could be fitted, in each case, to a straight line suggesting that the transition enthalpy and transition entropy consist of a fixed component from the polar head group and the terminal methyl group, whereas the contribution of the methylene groups, (CH2)n, is linearly proportional to the number of carbon atoms in it. The contributions of each methylene unit to the transition enthalpy and transition entropy of NAEs were found to be deltaH(inc) = 0.82 (+/-0.02) and 0.96 (+/-0.06) kcal mol(-1), and deltaS(inc) = 2.01 (+/- 0.06) and 2.37 (+/-0.17) cal mol(-1) K(-1), respectively, for the dry and hydrated samples of NAEs, whereas the end contributions arising from the head group and the terminal methyl group were determined to be deltaH(o) = -0.10 (+/-0.26) and -0.52 (+/-0.82) kcal mol(-1) and deltaS(o) = 2.12 (+/-0.71) and 3.1 (+/-2.3) cal mol(-1) K(-1), respectively, for the dry and hydrated samples of NAEs. These results are relevant to an understanding of the thermodynamics of the phase properties of NAEs in membranes.

Acylation↗

PubMed2005

Investigating entropy changes during gas adsorption in ETS-4.

Energetic heterogeneity has been investigated for Engelhard titanium silicate Na-ETS-4 adsorbent and its Sr-exchanged variant, Sr-ETS-4. Na-ETS-4 was nearly homogeneous, while Sr exchange seemed to induce some degree of energetic heterogeneity in the sample, which diminished upon dehydration at higher temperature. Analysis of the entropy change during adsorption showed that the adsorbate molecules at low as well as moderate loading possess entropy greater than that predicted by the 2-D mobile film model, the excess being attributed to vibrational freedom. The wavelength of this vibration decreased with increasing coverage, as expected. For oxygen, the observed entropy drops in Na-ETS-4 and in Sr-ETS-4 are comparable, whereas, for nitrogen and methane, Sr exchange resulted in a greater entropy drop than in Na-ETS-4, suggesting greater restriction to movement in the Sr-exchanged sample. This study presents a simplistic yet effective understanding of the energetic behavior of the adsorbed molecules in ETS-4 adsorbent. This is vital to a thorough energetic characterization and study of the adsorption phenomenon in these new, promising adsorbents.

Journal Article↗

PubMed2005

Thermodynamic theory of light-induced material transport in amorphous azobenzene polymer films.

It was discovered 10 years ago that the exposure of an initially flat layer of an azobenzene-containing polymer to an inhomogeneous light pattern leads to the formation of surface relief structures, accompanied by a mass transport over several micrometers. However, the driving force of this process is still unclear. We propose a new thermodynamic approach that explains a number of experimental findings including the light-induced deformation of free-standing films and the formation of surface relief gratings for main inscription geometries. Our basic assumption is that under homogeneous illumination, an initially isotropic sample should stretch itself along the polarization direction to compensate the entropy decrease produced by the photoinduced reorientation of azobenzene chromophores. The magnitude of the elastic stress, estimated by taking the derivative of the free energy over the sample deformation, is shown to be sufficient to induce plastic deformation of the polymer film. Orientational distributions of chromophores predicted by our model are compared with those deduced from Raman intensity measurements.

Journal Article↗

PubMed2002

Intensive direct cavernous sinus sampling identifies high-frequency, nearly random patterns of FSH secretion in ovariectomized ewes: combined appraisal by RIA and bioassay.

Analyses of FSH secretion suggest pulsatile, nonpulsatile, or compositely pulsatile and nonpulsatile release modes. This may reflect the reduced signal-to-noise ratio inherent in FSH pulse estimation procedures and/or immunological-biological assay inconsistencies. To address these issues, we sampled cavernous sinus and jugular venous blood concomitantly from ovariectomized sheep at either 5-min or 1-min intervals. Samples from the former were assayed by RIA, and those from the latter by RIA and bioassay. Waveform-independent peak detection revealed FSH pulses occurring at high frequency. Pulsatile FSH secretion accounted for 28% of total secretion. Approximate entropy analysis showed that FSH secretion was nearly random. There was synchronous release of LH and FSH, but most FSH secretion was not associated with LH release; 13% of discrete FSH and LH pulses were concordant. We infer that FSH secretion exhibits pulsatile and basal/nonpulsatile features, with high-entropy features. Linear and nonlinear statistical measures revealed joint sample-by-sample synchrony of FSH and LH release, indicating pattern coordination despite sparse synchrony of pulses. We postulate that pattern synchrony of FSH and LH release is effected at the level of the gonadotrope. Concordant FSH and LH pulses probably result from pulsatile GnRH input, but other mechanisms could account for independent FSH pulses.

Animals↗

PubMed2006

Phonons and thermodynamics of unmixed and disordered Li0.6FePO4.

The lithium-storage material Li(0.6)FePO(4) was studied by inelastic neutron scattering and differential scanning calorimetry. Li(0.6)FePO(4) undergoes a transformation from a two-phase mixture (heterosite and triphylite) to a disordered solid-solution at 200 degrees C. Phonon densities of states (DOS) obtained from the inelastic neutron scattering were similar for the two-phase sample measured at 180 degrees C and the disordered sample measured at 220 degrees C. The vibrational entropy of transformation is 1.8 +/-0.9 J/(K mol), which is smaller than the configurational entropy difference of approximately 3.1 J/(K mol). The measured enthalpy of the disordering transition was estimated as 2.5 kJ/mol. The phonon data show a small change in lattice dynamics upon disordering.

Journal Article↗