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PubMed1996

Quantifying biological specificity: the statistical mechanics of molecular recognition.

The Random Energy Model of statistical physics is applied to the problem of the specificity of recognition between two biological (macro)molecules forming a non-covalent complex. In this model, the native mode of association is separated by an energy gap from a large body of non-native modes. Whereas the native mode is unique, the non-native modes form an energy spectrum which is approximated by a gaussian distribution. Specificity can then be estimated by writing the partition function and calculating the ratio r of non-native to native modes at thermodynamic equilibrium. We examine three situations: (i) recognition in the absence of a competitor; (ii) recognition in the presence of a competing ligand; (iii) recognition in a heterogeneous mixture. We derive the dependence of the ratio r on temperature and on the concentration of competing ligands, and we estimate the effect of a local perturbation such as can result from a point mutation. Cases (i) and (iii) are modeled by docking experiments in the computer. In case (iii), which is representative of a wide variety of biological situations, we show that increasing the heterogeneity of a mixture affects the specificity of recognition, even when the concentration of competing species is kept constant.

Binding Sites↗
PubMed1986

Quantification of scalp hair--a computer-aided methodology.

A method for obtaining a quantitative assessment of hair density is described. First, a photographic image of the scalp is digitized onto a high-resolution computer graphics screen. Second, the frequency of each of 256 gray levels (one for each of 500 vertical X 500 horizontal = 250,000 locations on the screen) is obtained and the frequency histogram of gray levels is displayed. Third, a statistical procedure, gaussian mixture analysis, is used to resolve the frequency distribution into two normally distributed component distributions. The first component distribution describes the range of gray levels that are typically associated with hair. The second component distribution describes shades of gray that are typically associated with scalp. The statistical model provides a precise measure of the proportion of the head that exhibits gray levels in each of the two component distributions (hair or scalp). The proportion of the first component distribution is a scale-independent measure of hair density. The difference in this quantity before and after treatment provides an accurate quantitative determination of the change in hair density and hence of the efficacy of treatment.

Alopecia Areata↗
PubMed2006

Subclass discriminant analysis.

Over the years, many Discriminant Analysis (DA) algorithms have been proposed for the study of high-dimensional data in a large variety of problems. Each of these algorithms is tuned to a specific type of data distribution (that which best models the problem at hand). Unfortunately, in most problems the form of each class pdf is a priori unknown, and the selection of the DA algorithm that best fits our data is done over trial-and-error. Ideally, one would like to have a single formulation which can be used for most distribution types. This can be achieved by approximating the underlying distribution of each class with a mixture of Gaussians. In this approach, the major problem to be addressed is that of determining the optimal number of Gaussians per class, i.e., the number of subclasses. In this paper, two criteria able to find the most convenient division of each class into a set of subclasses are derived. Extensive experimental results are shown using five databases. Comparisons are given against Linear Discriminant Analysis (LDA), Direct LDA (DLDA), Heteroscedastic LDA (HLDA), Nonparametric DA (NDA), and Kernel-Based LDA (K-LDA). We show that our method is always the best or comparable to the best.

Algorithms↗
PubMed2003

Fourier transform infrared attenuated total reflection and transmission spectra studied by dispersion analysis.

Fourier transform infrared transmission (FT-IR) and attenuated total reflection (ATR) spectra of water-ethanol mixtures are recorded and reconstructed thanks to a causal dispersion analysis technique. As expected, the Beer's law technique is an empirical approximate method that cannot account for complex spectral features. On the other hand, a rigorous analysis performed by using the theoretical optical paths for both experimental techniques and Gaussian dispersion analysis (GDA) allows the dielectric functions of the pure liquids to be calculated. Simulations of the whole mid-infrared spectra in the range 500-4000 cm(-1) match the experimental data very well, whatever the water-ethanol mixtures. This method is a powerful tool to quantify such model mixtures and more generally could be the first step toward software for assistance to the FT-IR spectrum analysis.

Algorithms↗
PubMed1983

Temperature dependence of the electronic spin-lattice relaxation time in a 2-iron-2-sulphur model complex.

The complex [Fe2S2(S2-o-xylyl)2]2- in DMF (dimethylformamide), DMSO (dimethylsulphoxide) or a 1:1 DMF/DMSO mixture, a model for the chromophore in the 2Fe-2S proteins (ferredoxins), has been reduced and studied by conventional EPR over a temperature range. The low-field feature of the spectrum, Hz, has been computer simulated in order to analyse the lineshape in terms of a convolution product of Lorentzian and Gaussian distributions. The Gaussian contribution to the linewidth and a fixed part of the Lorentzian contribution, which is a function of the solvent and the way it freezes, were measured at a low temperature (less than or equal to 100 K) and subtracted from the linewidths in the higher-temperature range (130-200 K). The variable Lorentzian contribution thus obtained was related to spin-lattice relaxation times. The spin-lattice relaxation times of the sample having 1:1 DMSO/DMF solvent were measured in the range 6 to 11 K by the saturating pulse technique and in the range 10 to 65 K by continuous saturation methods. Up to 65 K the results follow the law 1/T1 alpha T4.5, a relationship which is not readily interpreted in terms of a simple Debye model. At higher temperatures the results may be interpreted in terms either of a dominant Orbach mechanism involving excited states at approx. 900 +/- 50 cm-1 (DMSO, DMF) or 770 +/- 50 cm-1 (1:1 DMSO/DMF), or of a Raman process in which 1/T1 alpha T7.5. The former is compatible with the two-phonon process already described in some ferredoxins, especially those with little anisotropy (gy - gx approximately 0.0) which have characteristically high [J] values.

Dimethyl Sulfoxide↗
PubMed2005

Ultrafast molecular dynamics of liquid aromatic molecules and the mixtures with CCl4.

The ultrafast molecular dynamics of liquid aromatic molecules, benzene, toluene, ethylbenzene, cumene, and 1,3-diphenylpropane, and the mixtures with CCl(4) have been investigated by means of femtosecond optical heterodyne-detected Raman-induced Kerr effect spectroscopy. The picosecond Kerr transients of benzene, toluene, ethylbenzene, and cumene and the mixtures with CCl(4) show a biexponential feature. 1,3-Diphenylpropane and the mixtures with CCl(4) show triexponential picosecond Kerr transients. The slow relaxation time constants of the aromatic molecules and the mixtures with CCl(4) are qualitatively described by the Stoke-Einstein-Debye hydrodynamic model. The ultrafast dynamics have been discussed based on the Kerr spectra in the frequency range of 0-800 cm(-1) obtained by the Fourier transform analysis of the Kerr transients. The line shapes of the low-frequency intermolecular spectra located at 0-180 cm(-1) frequency range have been analyzed by two Brownian oscillators ( approximately 11 cm(-1) and approximately 45 cm(-1) peaks) and an antisymmetric Gaussian function ( approximately 65 cm(-1) peak). The spectrum shape of 1,3-diphenylpropane is quite different from the spectrum shapes of the other aromatic molecules for the low magnitude of the low-frequency mode of 1,3-diphenylpropane and/or an intramolecular vibration. Although the concentration dependences of the low- and intermediate-frequency intermolecular modes (Brownian oscillators) do not show a significant trend, the width of high-frequency intermolecular mode (antisymmetric Gaussian) becomes narrower with the higher CCl(4) concentration for all the aromatics mixtures with CCl(4). The result indicates that the inhomogeneity of the intermolecular vibrational mode in aromatics/CCl(4) mixtures is decreasing with the lower concentration of aromatics. The intramolecular vibrational modes of the aromatic molecules observed in the Kerr spectra are also shown with the calculation results based on the density functional theory.

Journal Article↗
PubMed1999

Sensitivity to modulations of luminance and contrast in visual white noise: separate mechanisms with similar behaviour.

Human vision can detect spatiotemporal information conveyed by first-order modulations of luminance and by second-order, non-Fourier modulations of image contrast. Models for second-order motion have suggested two filtering stages separated by a rectifying nonlinearity. We explore here the encoding of stationary first-order and second-order gratings, and their interaction. Stimuli consisted of 2-D binary, broad-band, static, visual noise sinusoidally modulated in luminance (LM, first-order) or contrast (CM, second-order). Modulation thresholds were measured in a two-interval forced-choice staircase procedure. Sensitivity curves for LM and CM had similar shape as a function of spatial frequency, and as a function of the size of a circular Gaussian blob of modulation. Weak background gratings present in both intervals produced order-specific facilitation: LM background facilitated LM detection (the dipper function) and CM facilitated CM detection. LM did not facilitate CM, nor vice-versa, neither in-phase nor out-of-phase, and this is strong evidence that LM and CM are detected via separate mechanisms. This conclusion was further supported by an experiment on the detection of LM/CM mixtures. From a general mathematical model and a specific computer simulation we conclude that a single mechanism sensitive to both LM and CM cannot predict the pattern of results for mixtures, while a model containing separate pathways for LM and CM, followed by energy summation, does so successfully and is quantitatively consistent with the finding of order-specific facilitation.

Contrast Sensitivity↗
PubMed2005

Progressive thermal desorption of vapor mixtures from a preconcentrator with a porous metal foam internal architecture and variable thermal ramp rates.

A vapor preconcentrator has been designed with the porous polymer (Tenax) packed into a highly porous metal foam to facilitate thermal conductivity and temperature uniformity throughout the bed of the preconcentrator during heating. Vapors were desorbed using linear temperature programming from room temperature to a maximum temperature of 170 or 200 degrees C; the programmed duration of the thermal ramp was varied from 10 to 180 s. The partial separation of vapor mixtures that are thermally desorbed from the preconcentrator has been examined in terms of a metric for resolution, using methyl ethyl ketone, toluene, and dimethyl methylphosphonate as a test mixture. Vapors desorbed as a sequence of partially separated overlapping peaks, as observed with a polymer-coated flexural plate wave sensor. It was shown that vapor mixture resolution improved as the total time of the thermal ramp was extended from 30 to 120 s. In this way, the preconcentrator serves to act as a preseparator in addition to its usual functions for sampling, signal modulation, and improving sensitivity. Overlapping peaks were modeled, and peak areas were extracted using an exponentially modified Gaussian model. Peak areas were independent of the thermal ramp rate. Uses of such preconcentrators with multivariate detectors, such as sensor arrays, are discussed.

Journal Article↗
PubMed2007

A nonlinear latent class model for joint analysis of multivariate longitudinal data and a binary outcome.

We consider a joint model for exploring association between several correlated longitudinal markers and a clinical event. A nonlinear growth mixture model exhibits the different latent classes of evolution of the latent quantity underlying the correlated longitudinal markers and a logistic regression models the probability of occurence of the clinical event according to the latent classes. By introducing a flexible nonlinear transformation including parameters to be estimated between each marker and the latent process, the model also deals with non-Gaussian continuous markers. Through an application on cognitive ageing, the two advantages of the model are underlined: (1) the latent profiles of evolution associated with the clinical event are described including covariate effects in the longitudinal model but also in the probability of class membership and in the probability of occurence of the event, and (2) a diagnostic and a prognostic tools are derived from the model for early detection of the clinical event using any available information about the longitudinal markers.

Data Interpretation, Statistical↗
PubMed1989

Decay time distribution analysis of Yt-base in benzene-methanol mixtures.

Frequency-domain fluorometry was used to measure intensity decays of synthetic Yt-base in mixtures of benzene-methanol at 20 degrees C. Multiexponential analysis shows that the decay of Yt-base fluorescence in benzene and methanol can be well fitted to a single-exponential model with tau = 9.67 ns and 6.25 ns respectively. In mixtures of benzene-methanol the decays became heterogeneous, and the maximum of heterogeneity observed was in a mixture containing 6% methanol. Since we expected a distribution of Yt-base solvation states in the solvent mixtures, and because the decay times of Yt-base are sensitive to solvent, we analyzed the data in terms of decay time distributions. The goodness-of-fit for the unimodal distribution model which has two floating parameters was equivalent to that found using the double exponential model with three floating parameters. The Lorentzian distribution model appears to provide a slightly superior fit relative to the Gaussian distribution model. These results suggest that the intensity decays of solvent-sensitive fluorophores in mixed solvents are described by a distribution of decay times.

Benzene↗
PubMed1988

The molecular mobility of alpha-actinin and actin in a reconstituted model of gelation.

Dictyostelium discoideum alpha-actinin (D.d. alpha-actinin) is a calcium and pH-regulated actin-binding protein that can cross-link F-actin into a gel at a submicromolar free calcium concentration and a pH less than 7 [Fechheimer, et al., 1982]. We examined mixtures of actin and D.d. alpha-actinin at four pH and calcium concentrations that exhibited various degrees of gelation or solation. The macroscopic viscosities of these mixtures were measured by falling ball viscometry (FBV) and compared to the translational diffusion coefficients measured by gaussian spot and periodic-pattern fluorescence photobleaching recovery (FPR) of both the actin filaments and D.d. alpha-actinin. A homogeneous, macroscopic gel was not composed of a static actin network. Instead, the filament diffusion coefficient decreased to approximately 65% of the control value. If the D.d. alpha-actinin concentration was increased, the solution became inhomogeneous, consisting of domains of higher actin concentration. These domains were often composed of a static actin network. The mobility of D.d. alpha-actinin consisted of a major fraction that freely diffused and a minor fraction that appeared immobile under the conditions employed. This suggested that D.d. alpha-actinin binding to the actin filaments was static over the time course of measurement (approximately 5 sec). Under solation conditions, there was no apparent interaction of actin with D.d. alpha-actinin. These results demonstrate that 1) actin filaments need not be cross-linked into an immobile, static array in order to have macroscopic properties of a gel; 2) interpretation of the rheological properties of actin:alpha-actinin gels are complicated by spatial heterogeneity of the filament concentration and mobility; and 3) a fraction of D.d. alpha-actinin binds statically to actin in undisturbed gels. The implications of these results are discussed in relation to cytoplasmic structure and contractility.

Actinin↗
PubMed2004

Q-ball imaging.

Magnetic resonance diffusion tensor imaging (DTI) provides a powerful tool for mapping neural histoarchitecture in vivo. However, DTI can only resolve a single fiber orientation within each imaging voxel due to the constraints of the tensor model. For example, DTI cannot resolve fibers crossing, bending, or twisting within an individual voxel. Intravoxel fiber crossing can be resolved using q-space diffusion imaging, but q-space imaging requires large pulsed field gradients and time-intensive sampling. It is also possible to resolve intravoxel fiber crossing using mixture model decomposition of the high angular resolution diffusion imaging (HARDI) signal, but mixture modeling requires a model of the underlying diffusion process.Recently, it has been shown that the HARDI signal can be reconstructed model-independently using a spherical tomographic inversion called the Funk-Radon transform, also known as the spherical Radon transform. The resulting imaging method, termed q-ball imaging, can resolve multiple intravoxel fiber orientations and does not require any assumptions on the diffusion process such as Gaussianity or multi-Gaussianity. The present paper reviews the theory of q-ball imaging and describes a simple linear matrix formulation for the q-ball reconstruction based on spherical radial basis function interpolation. Open aspects of the q-ball reconstruction algorithm are discussed.

Algorithms↗
PubMed2002

Parabolic-Lorentzian modified Gaussian model for describing and deconvolving chromatographic peaks.

A new mathematical model for characterising skewed chromatographic peaks, which improves the previously reported polynomially modified Gaussian (PMG) model, is proposed. The model is a Gaussian based equation whose variance is a combined parabolic-Lorentzian function. The parabola accounts for the non-Gaussian shaped peak, whereas the Lorentzian function cancels the variance growth out of the elution region, which gives rise to a problematic baseline increase in the PMG model. The proposed parabolic-Lorentzian modified Gaussian (PLMG) model makes a correct description of peaks showing a wide range of asymmetry with positive and/or negative skewness. The new model is shown to give better fittings than other models as the Li, log-normal or Pap-Pápai models, which have a different mathematical basis. The model parameters are also related to peak properties as the skewness and kurtosis. The PLMG model is applied to the deconvolution of peaks in binary mixtures of structurally related compounds that are highly overlapped (retention times in min): oxytetracycline (9.00)--tetracycline (10.20), sulfathiazole (3.67)--sulfachloropyridazine (3.93), and sulfisoxazole (5.14)--sulfapyridine (5.24). The use of non-linear least-squares calibration in combination with the PLMG model gave superior results than the classical multiple linear least-squares and partial least-squares regressions. The proposed method takes into account run to run changes in retention time that occur along the injection of standards and samples, and the possible interactions that exist between the coeluting compounds. This decreases significantly the quantitation errors.

Chromatography↗
PubMed2003

Soft learning vector quantization.

Learning vector quantization (LVQ) is a popular class of adaptive nearest prototype classifiers for multiclass classification, but learning algorithms from this family have so far been proposed on heuristic grounds. Here, we take a more principled approach and derive two variants of LVQ using a gaussian mixture ansatz. We propose an objective function based on a likelihood ratio and derive a learning rule using gradient descent. The new approach provides a way to extend the algorithms of the LVQ family to different distance measure and allows for the design of "soft" LVQ algorithms. Benchmark results show that the new methods lead to better classification performance than LVQ 2.1. An additional benefit of the new method is that model assumptions are made explicit, so that the method can be adapted more easily to different kinds of problems.

Costs and Cost Analysis↗
PubMed1996

A technique for measuring epidemiologically useful features of birthweight distributions.

Birthweight distributions have been conceptualized as a predominant Gaussian distribution contaminated in the tails by an unspecified 'residual' distribution. Acknowledging this idea, we propose a technique for measuring certain features of birthweight distributions useful to epidemiologists: the mean and variance of the predominant distribution; the proportions of births in the low- and high-birthweight residual distributions, and the boundaries of support for these residual distributions. Our technique, based on an underlying multinomial sampling distribution, involves estimating parameters in a mixture model for the multinomial bin probabilities after having chosen the support of the residual distribution with a model selection criterion. A modest simulation study and experience with a few actual datasets indicate that use of a Bayesian information criterion (BIC) as model selection criterion is superior to use of Akaike's information criterion (AIC) in this application.

Analysis of Variance↗
PubMed2005

Nonmonotonic composition dependence of vibrational phase relaxation rate in binary mixtures.

We present here isothermal-isobaric N-P-T ensemble molecular dynamics simulations of vibrational phase relaxation in a model system to explore the unusual features arising due to concentration fluctuations which are absent in one component systems. The model studied consider strong attractive interaction between the dissimilar species to discourage phase separation. The model reproduces the experimentally observed nonmonotonic, nearly symmetric, composition dependence of the dephasing rate. In addition, several other experimentally observed features, such as the maximum of the frequency modulation correlation time tau(c) at mole fraction near 0.5 and the maximum rate enhancement by a factor of about 3 above the pure component value, are also reproduced. The product of mean square frequency modulation [ ] with tau(c) indicates that the present model is in the intermediate regime of inhomogeneous broadening. The nonmonotonic composition chi(A) dependence of the dephasing time tau(v) is found to be primarily due to the nonmonotonic chi dependence of tau(c), rather than due to a similar dependence in the amplitude of Delta omega(2)(0). The probability distribution of Delta omega shows a markedly non-Gaussian behavior at intermediate composition (chi(A) approximately =0.5). We have also calculated the composition dependence of the viscosity in order to explore the correlation between the composition dependence of viscosity eta(*) with that of tau(v) and tau(c). It is found that both the correlation time essentially follow the composition dependence of the viscosity. A mode coupling theory is presented to include the effects of composition fluctuations in binary mixture.

Journal Article↗
PubMed1999

Monitoring epidemiologic surveillance data using hidden Markov models.

The analysis of routinely collected surveillance data is an important challenge in public health practice. We present a method based on a hidden Markov model for monitoring such time series. The model characterizes the sequence of measurements by assuming that its probability density function depends on the state of an underlying Markov chain. The parameter vector includes distribution parameters and transition probabilities between the states. Maximum likelihood estimates are obtained with a modified EM algorithm. Extensions are provided to take into account trend and seasonality in the data. The method is demonstrated on two examples: the first seeks to characterize influenza-like illness incidence rates with a mixture of Gaussian distributions, and the other, poliomyelitis counts with mixture of Poisson distributions. The results justify a wider use of this method for analysing surveillance data.

Disease Outbreaks↗
PubMed2004

Infrared spectra of H(2)16O, H(2)18O and D(2)O in the liquid phase by single-pass attenuated total internal reflection spectroscopy.

Mid-infrared attenuated total internal reflection (ATR) spectra of H(2)16O, H(2)18O and D(2)16O in the liquid state were obtained and normal coordinate analysis was performed based on the potential energy surface obtained from density functional theory (DFT) calculations. Fits of the spectra to multiple Gaussians showed a consistent fit of three bands for the bending region and five bands for the stretching region for three isotopomers, H(2)16O, H(2)18O and D(2)16O. The results are consistent with previous work and build on earlier studies by the inclusion of three isotopomers and mixtures using the advantage of single-pass ATR to obtain high quality spectra of the water stretching bands. DFT calculation of the vibrational spectrum of liquid water was conducted on seven model systems, two systems with periodic boundary conditions (PBC) consisting of four and nine H(2)16O molecules, and five water clusters consisting of 4, 9, 19, 27 and 32 H(2)16O molecules. The PBC and cluster models were used to obtain a representation of bulk water for comparison with experiment. The nine-water PBC model was found to give a good fit to the experimental line shapes. A difference is observed in the broadening of the water bending and stretching vibrations indicative of a difference in the rate of pure dephasing. The nine-water PBC calculation was also used to calculate the wavenumber shifts observed in the water isotopomers.

Deuterium Oxide↗