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PubMed2004

Markov entropy backbone electrostatic descriptors for predicting proteins biological activity.

The spherical truncation of electrostatic interactions between aminoacids makes it possible to break down long-range spatial electrostatic interactions, resulting in short-range interactions. As a result, a Markov Chain model may be used to calculate the probabilities with which the effect of a given interaction reaches aminoacids at different distances within the backbone. The entropies of a Markov Chain model of this type may then be used to codify information about the spatial distribution of charges in the protein used in this study exploring the structure-activity relationship. In this paper, a linear discriminant analysis is reported, which correctly classified 92.3% of 26 under investigation in training and leave-one-out cross validation, purely for illustrative purposes. Classification was carried out for three possible activities: lysozymes, dihydrofolate reductases, and alcohol dehydrogenases. The discriminant analysis equations were contracted into two canonical roots. These simple canonical roots have high regression coefficients (R(c1)=0.903 and R(c2)=0.70). Root1 explains the biological activity of alcohol dehydrogenases while Root2 discriminates between lysozymes and dihydrofolate reductases. It was possible to profile the effect of core, middle, and surface aminoacids on biological activity. In contrast, a model considering classic physicochemical parameters such as: polarizability, refractivity, and partition coefficient classify correctly only the 80.8% of the proteins.

Alcohol Dehydrogenase↗

PubMed2003

Cooperativity, partially bound states, and enthalpy-entropy compensation.

Efforts to develop a quantitative understanding of molecular recognition rely on the additivity of individual intermolecular interactions, and cooperativity represents one of the major potential stumbling blocks. A chemical double-mutant cycle has been used to experimentally measure cooperativity between functional group interactions within a complex framework. The interaction between two aromatic groups varies by 0.2 +/- 0.4 kJ mol(-1) in synthetic H-bonded complexes that differ by 8-13 kJ mol(-1) in overall stability. In these systems, the free energies associated with individual intermolecular interactions can therefore be reliably treated in an additive fashion. The results suggest that alternative explanations should be considered for cooperative phenomena observed in other systems, and a rationale based on the population of partially bound states in flexible molecules is proposed to account for the enthalpic chelate effect and enthalpy-entropy compensation.

Magnetic Resonance Spectroscopy↗

PubMed2005

Calculation of the Entropy of Lattice Polymer Models from Monte Carlo Trajectories.

While lattice models are used extensively for macromolecules (synthetic polymers proteins, etc), calculation of the absolute entropy, S, and the free energy, F, from a given Monte Carlo (MC) trajectory is not straightforward. Recently we have developed the hypothetical scanning MC (HSMC) method for calculating S and F of fluids. Here we extend HSMC to self-avoiding walks on a square lattice and discuss its wide applicability to complex polymer lattice models. HSMC is independent of existing techniques and thus constitutes an independent research tool; it provides rigorous upper and lower bounds for F, which can be obtained from a very small sample and even from a single chain conformation.

Journal Article↗

PubMed2004

Accelerated acquisition of high resolution triple-resonance spectra using non-uniform sampling and maximum entropy reconstruction.

Non-uniform sampling is shown to provide significant time savings in the acquisition of a suite of three-dimensional NMR experiments utilized for obtaining backbone assignments of H, N, C', CA, and CB nuclei in proteins : HNCO, HN(CA)CO, HNCA, HN(CO)CA, HNCACB, and HN(CO)CACB. Non-uniform sampling means that data were collected for only a subset of all incremented evolution periods, according to a user-specified sampling schedule. When the suite of six 3D experiments was acquired in a uniform fashion for an 11 kDa cytoplasmic domain of a membrane protein at 1.5 mM concentration, a total of 146 h was consumed. With non-uniform sampling, the same experiments were acquired in 32 h and, through subsequent maximum entropy reconstruction, yielded spectra of similar quality to those obtained by conventional Fourier transform of the uniformly acquired data. The experimental time saved with this methodology can significantly accelerate protein structure determination by NMR, particularly when combined with the use of automated assignment software, and enable the study of samples with poor stability at room temperature. Since it is also possible to use the time savings to acquire a greater numbers of scans to increase sensitivity while maintaining high resolution, this methodology will help extend the size limit of proteins accessible to NMR studies, and open the way to studies of samples that suffer from solubility problems.

Carbon Isotopes↗

PubMed2006

Spectral reconstruction methods in fast NMR: reduced dimensionality, random sampling and maximum entropy.

The need to reduce data acquisition times of multidimensional NMR experiments has fostered considerable interest in novel data acquisition schemes. A recurring theme is that of reduced dimensionality experiments, in which time evolutions in the indirect dimensions are incremented together, rather than independently. Spectral analysis of such data is carried out using methods such as filtered back-projection, GFT, or parametric signal modeling. By using Maximum Entropy reconstruction of reduced-dimensionality data, we show that the artifacts that arise in reduced dimensionality experiments are intrinsic to the data sampling, and are not, in general, the result of the methods used to compute spectra. Our results illustrate that reduced dimensionality is a special case of non-uniform sampling in the time domain. We show that MaxEnt reconstruction yields more accurate spectra for reduced dimensionality data than back-projection reconstruction and that randomly choosing time increments based on an exponentially weighted distribution is more efficient, with fewer artifacts, than the systematic coupling of time increments used in most reduced dimensionality approaches.

Artifacts↗

PubMed2005

Maximum entropy image deconvolution applied to structure determination for crystal Nd1.85Ce0.15CuO4-delta.

Eight [100] images from a through-focus series of tetragonal crystal Nd1.85Ce0.15CuO4-delta were transformed separately into the structure images by means of maximum entropy image deconvolution. The constructed projected structure model based on the deconvoluted image is confirmed by image simulation. It is demonstrated that the image deconvolution is still successful even when some reflections fall in the vicinity of zero cross of contrast transfer function. The effectiveness and advantages of the technique are discussed.

Journal Article↗

PubMed2005

An expanded approach to noise reduction from high-resolution STEM images based on the maximum entropy method.

An expanded use of the maximum entropy method (MEM) is suggested to reduce noise from an experimental high-angle annular dark-field (HAADF) scanning transmission electron microscope (STEM) image. The MEM is combined with an estimate of the standard deviation of noise from an experimental HAADF STEM image and low-pass filtering using the information limit for an incoherent STEM image. Consequently, the present method has just one parameter of a Lagrange multiplier. It is demonstrated that the present method can reduce noise efficiently in high-resolution HAADF STEM images.

Journal Article↗

PubMed2003

Role of side-chain conformational entropy in transmembrane helix dimerization of glycophorin A.

Dimerization of the transmembrane domain of glycophorin A is mediated by a seven residue motif LIxxGVxxGVxxT through a combination of van der Waals and hydrogen bonding interactions. One of the unusual features of the motif is the large number of beta-branched amino acids that may limit the entropic cost of dimerization by restricting side-chain motion in the monomeric transmembrane helix. Deuterium NMR spectroscopy is used to characterize the dynamics of fully deuterated Val80 and Val84, two essential amino acids of the dimerization motif. Deuterium spectra of the glycophorin A transmembrane dimer were obtained using synthetic peptides corresponding to the transmembrane sequence containing either perdeuterated Val80 or Val84. These data were compared with spectra of monomeric glycophorin A peptides deuterated at Val84. In all cases, the deuterium line shapes are characterized by fast methyl group rotation with virtually no motion about the C(alpha)-C(beta) bond. This is consistent with restriction of the side chain in both the monomer and dimer due to intrahelical packing interactions involving the beta-methyl groups, and indicates that there is no energy cost associated with dimerization due to loss of conformational entropy. In contrast, deuterium NMR spectra of Met81 and Val82, in the lipid interface, reflected greater motional averaging and fast exchange between different side-chain conformers.

Computer Simulation↗

PubMed1981

The role of subunit entropy in cooperative assembly. Nucleation of microtubules and other two-dimensional polymers.

The self-assembly and nucleation of two-dimensional polymers is described by a theory based on a model of rigid subunits and bonds and simple principles of thermodynamics. The key point in the theory is to separate as an explicit parameter the free energy, primarily attributed to the entropy of the free subunit, that is required to immobilize a subunit in the polymer. Quantitative relations for the association of a subunit forming a longitudinal bond, a lateral bone, or both together are obtained, which demonstrate the basis and magnitude of cooperativity. The same formalism leads to a quantitative estimate for th concentration of the small polymers that are important intermediates in nucleation. It is shown that, if the concentration of free subunits is below a certain "critical supersaturation," the concentration of some essential intermediates is too low to support any significant assembly and nucleation is blocked. If the subunit concentration is above the critical supersaturation, all of the small intermediates are sufficiently stable to form and grow spontaneously. The theory predicts a critical supersaturation of 3.5 to 7 (the ratio of subunit concentration to the equilibrium solubility) for parameters appropriate to assembly of the microtubule wall. Experimentally, nucleation and assembly of microtubules is obtained at somewhat lower concentrations, 1.5 to 3 times the equilibrium solubility. Special mechanisms that could stabilize small polymers and facilitate nucleation of microtubule assembly are suggested.

Animals↗

PubMed2001

Creating discrete joint densities from continuous ones: the moment matching-maximum entropy approach.

An approach for converting continuous densities into discrete ones with a pre-assigned set of support points is developed. The algorithm performs this conversion in a most skeptical, least-informative way, by finding the discrete distribution with the maximum entropy that satisfies a set of moment constraints derived from the stated continuous distribution, such as means and variances. Individualized drug therapies based on multiple model control rely on the availability of discrete distributions to generate the underlying model set. The methods developed herein are especially compatible with individualized drug therapies based on multiple model control that rely on the availability of discrete densities to generate the model set.

Absorption↗

PubMed1987

Transport, space, entropy, diffusion and flow. Elements underlying separation by electrophoresis, chromatography, field-flow fractionation and related methods.

We describe here some elements common among separation methods, including the requirement for separative transport, the sensitive utilization of space, and the dissipative (band broadening) roles of entropy, diffusion, and flow. We focus on the need to carefully manage the unceasing competition between separative and dissipative transport in all high resolution methods. We then examine the more specific roles these elements play in influencing separation in several important analytical separation techniques. We begin with electrophoresis and sedimentation, which are conceptually among the simplest of systems because they require no flow and only a single dimension of space. The conflict between separative and dissipative transport is examined closely for these systems and it is shown that the outcome is a theoretical plate number which can be expressed as a ratio of two energies: a structuring energy--delta mu ext, which organizes the separation, and thermal energy RT, which is responsible for its dissipation. It is explained why optimal separation is most often achieved in thin layers or in capillary tubes. Chromatography and field-flow fractionation are then described as two closely related methods in which flow is powerfully coupled with a simple enrichment process occurring at right angles to flow. Unlike electrophoresis, these systems are intrinsically two-dimensional. It is shown how flow and diffusion processes both assume two diametrically opposite roles: those of aiding separation and simultaneously causing its dissipation. With a few equations it is demonstrated that the dissipative role is best contained by reducing the thickness (diameter) of the system or of certain elements within the system.

Chemical Fractionation↗

PubMed1990

Characterization of nucleotidic sequences using maximum entropy techniques.

A statistical method for characterizing nucleotidic sequences based on maximum entropy techniques is presented. The method uses only codon usage tables and takes into account the length of sequences, and preserves the information contained in each codon by a punctual index. We present the methodological aspects of the analysis, showing an application relative to nucleotidic sequences of eukaryotes.

Animals↗

PubMed1984

Cell membrane entropy as regulator of receptor submergence.

An entropic mechanism, previously worked out to explain the low adhesiveness of fluid phospholipid, also seems to explain some effects of membrane fluidity on the "embedding" of receptor proteins. Water, at the phospholipid interface, has to compete with protein for the available area but is impeded in its Brownian motion by hydrogen bonding to the slow-moving phosphatide. Hence, any increase in phosphatide mobility (e.g. by lipid melting) is entropically favourable to water, which spreads by displacing receptor particles from the interface into the hydrocarbon phase. This reconciles the kinetic viewpoint of Shintzky (experimental correlation of submergence with microviscosity) with the thermodynamic theory of Gerson (submergence increases with phospholipid hydrophilicity). Because Brownian motion increases water entropy, it follows that a more fluid interface must have a more negative free energy i.e. become more hydrophilic.

Cell Membrane↗

PubMed2002

Improved QSPR analysis of standard entropy of acyclic and aromatic compounds using optimized correlation weights of linear graph invariants.

Entropy is calculated for a representative set of acyclic and aromatic compounds within the realm of QSAR/QSPR theory. Flexible topological molecular indices are chosen as independent variables in the fitting equations. The comparison with results derived from quantum mechanical calculations shows that the present approach gives better predictions. Some possible future extensions are pointed out.

Journal Article↗

PubMed1998

Entropy-driven binding/partition of amino acids/dipeptides to stratum corneum lipid vesicles.

This study employed large unilamillar vesicles composed of purchased stratum corneum lipids to investigate the binding/partition of amino acids/dipeptides to stratum corneum lipid vesicles. The partition coefficients of amino acids/dipeptides between the stratum corneum lipid vesicles and the acetate buffer were determined by HPLC. In addition, the binding/partition enthalpy of amino acids/dipeptides with the stratum corneum lipid vesicles was derived by directly measuring the binding/partition heat with isothermal titration calorimetry. According to the binding/petition Gibbs free energy and the binding/partition enthalpy, all the binding/partition of amino acids/dipeptides with the stratum corneum lipid vesicles is endothermic, implying an entropy-driven binding/partition. Also, the equilibrium binding/partition results demonstrate that the partition coefficients of amino acids/dipeptides do not correlate with the transdermal permeability. This finding suggests that either the interaction between the penetrants and the lipid bilayer between corneocytes may not be a determining step or that the paracellular path is not a dominant route of transdermal penetration.

Amino Acids↗

PubMed2001

Thermodynamics of the hydrophobic effect. II. Calorimetric measurement of enthalpy, entropy, and heat capacity of aggregation of alkylamines and long aliphatic chains.

The thermodynamics of long aliphatic chain alkylamine aggregation in aqueous solution was studied by isothermal titration calorimetry (ITC). Protonated alkylammonium cations with linear aliphatic chains of 10-14 carbon atoms were fully soluble in aqueous solution at the beginning of titration, but practically insoluble after deprotonation by titrating with sodium hydroxide. The alkylamines aggregated and precipitated during the reaction, enabling direct measurement of the enthalpy of aggregation. The enthalpy of aggregation became increasingly exothermic upon increasing the chain length. Hydrophobic aggregation was enthalpy-driven and entropy-opposed for alkylamines with 12-14 carbon atoms at room temperature. Direct observation of hydrophobic aggregation by ITC at constant temperature and pressure provided more accurate thermodynamic parameters than obtainable from van't Hoff analysis. Aggregation into liquid or solid phases could be distinguished by ITC, but not by van't Hoff analysis of alkylamine solubility data.

Alkanes↗

PubMed1998

Photophysics of ethidium bromide complexed to ct-DNA: a maximum entropy study.

Time-integrated and time-resolved fluorescence spectroscopies have been used to probe the photophysical properties of ethidium bromide (Eb) complexed to calf thymus DNA (ct-DNA). Fluorescence decay profiles are obtained using the technique of time-correlated single photon counting (TCSPC), and subsequently analysed using conventional sum-of-exponential (SOE) routines and also the maximum entropy method (MEM). Through use of these methods and simulated decay data, it is demonstrated that the kinetics of Eb in the presence of ds-DNA are best described by a generic model consisting of three exponential terms. At all DNA:Eb ratios and NaCl concentrations studied, free Eb is detected. Furthermore, Eb is found to interact with ds-DNA through two mechanisms, each distinguishable by its fluorescence decay time. Eb is shown to interact with DNA through classic intercalation, and also through binding at secondary sites. The component decay times are shown to be a function of NaCl concentration but independent of DNA:Eb molar ratio.

Journal Article↗

PubMed1997

Non-linear analysis of emotion EEG: calculation of Kolmogorov entropy and the principal Lyapunov exponent.

For 76 healthy subjects, two non-linear measures, capturing the dynamical properties of the system orbiting within the attractor (i.e. Kolmogorov entropy, K2 and principal Lyapunov exponent, L1), were calculated from EEG segments, corresponding to different states of brain activity, induced by emotionally valenced (i.e. neutral, affective positive and negative) video stimuli. Significantly elevated values of EEG K2 and L1 in response to both positive and negative film categories as compared to neutral one were evidenced. Relying on the obtained findings, it is suggested that increased cortical dynamics, up to a certain level, are probably necessary for emotion functioning.

Adolescent↗