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PubMed2003

Elimination of 13Calpha splitting in protein NMR spectra by deconvolution with maximum entropy reconstruction.

Homonuclear 13C-13C couplings can significantly reduce the sensitivity and resolution of multidimensional NMR experiments. The most important of these couplings is the 13Calpha-13Cbeta coupling, and several different methods have been developed to eliminate its effect from spectra used for backbone assignment, including short or constant-time evolution periods, selectively labeled amino acids, and multiple-band decoupling sequences. In this communication we show that postacquisition deconvolution of the spectra with a maximum entropy algorithm can be superior to experimental decoupling. The method is very robust, does not introduce shifts of the resonance positions, and simplifies the measurement of the most important NMR experiments for protein backbone assignment.

Carbon Isotopes↗

PubMed2005

Temperature dependence of three-body hydrophobic interactions: potential of mean force, enthalpy, entropy, heat capacity, and nonadditivity.

Temperature-dependent three-body hydrophobic interactions are investigated by extensive constant-pressure simulations of methane-like nonpolar solutes in TIP4P model water at six temperatures. A multiple-body hydrophobic interaction is considered to be (i) additive, (ii) cooperative, or (iii) anti-cooperative if its potential of mean force (PMF) is (i) equal to, (ii) smaller than, or (iii) larger than the corresponding pairwise sum of two-methane PMFs. We found that three-methane hydrophobic interactions at the desolvation barrier are anti-cooperative at low to intermediate T, and vary from essentially additive to slightly cooperative at high T. Interactions at the contact minimum are slightly anti-cooperative over a wider temperature range. Enthalpy, entropy, and heat capacity are estimated from the computed PMFs. Contrary to the common expectation that burial of solvent-accessible nonpolar surface area always leads to a decrease in heat capacity, the present results show that the change in heat capacity upon three-methane association is significantly positive at the desolvation barrier and slightly positive at the contact minimum. This suggests that the heat capacity signature of a hydrophobic polymer need not vary uniformly nor monotonically with conformational compactness. Ramifications for protein folding are discussed.

Entropy↗

PubMed2004

Hydration free energies and entropies for water in protein interiors.

Free energy calculations for the transfer of a water molecule from the pure liquid to an interior cavity site in a protein are presented. Two different protein cavities, in bovine pancreatic trypsin inhibitor (BPTI) and in the I76A mutant of barnase, represent very different environments for the water molecule: one which is polar, forming four water-protein hydrogen bonds, and one which is more hydrophobic, forming only one water-protein hydrogen bond. The calculations give very different free energies for the different cavities, with only the polar BPTI cavity predicted to be hydrated. The corresponding entropies for the transfer to the interior cavities are calculated as well and show that the transfer to the polar cavity is significantly entropically unfavorable while the transfer to the nonpolar cavity is entropically favorable. For both proteins an analysis of the fluctuations in the positions of the protein atoms shows that the addition of a water molecule makes the protein more flexible. This increased flexibility appears to be due to an increased length and weakened strength of protein-protein hydrogen bonds near the cavity.

Animals↗

PubMed2005

The bilayer-vesicle transition is entropy driven.

Self-assembled bilayer membranes have a remarkable inclination to form closed shells or vesicles. This bilayer-vesicle transition has been shown experimentally and by various kinds of computer simulation techniques. Here we study this transition using coarse-grained molecular dynamics. The advantage of this simulation technique is that it allows for a detailed analysis of the transition, such as changes of the internal energy. Generally it is assumed that the bilayer-vesicle transition is driven by minimization of the edge energy. However, our simulations, which include solvent particles, show an increase in the potential energy of the system during the transition, implicating that the transition is not energy but entropy driven.

Computer Simulation↗

PubMed2006

Combination of polarized TIRF and ATR spectroscopies for determination of the second and fourth order parameters of molecular orientation in thin films and construction of an orientation distribution based on the maximum entropy method.

This article describes two mathematical formalisms for the determination of the second and fourth order parameters of molecular films using optical spectroscopy. Method A uses polarized total internal reflection fluorescence (TIRF) to calculate the second and fourth order parameters, {P2(cos theta)} and {P4(cos theta)}, using an independently determined value for the angle between the absorption and emission dipoles, gamma. Method B uses {P2(cos theta)} obtained from attenuated total reflectance (ATR) data, along with polarized TIRF measurements to calculate {P4(cos theta)} and {cos2 gamma}. The choice of a specific method should rely on experimental considerations. We also present a method to separate the contributions of substrate surface roughness and dipole orientation with respect to the molecular axis from the spectroscopically determined second and fourth order parameters. Finally, a maximum entropy approach for construction of an orientation distribution from order parameters is compared with the commonly used delta and Gaussian distributions.

Entropy↗

PubMed2006

Two-dimensional lipid mixing entropy regulates the formation of multicomponent lipoplexes.

The mechanism of formation of multicomponent lipoplexes was investigated by means of synchrotron Small-Angle X-ray Diffraction (SAXD). Mixed lipid dispersions were prepared by mixing different populations of binary cationic liposomes. When adding DNA to mixed lipid dispersions, multicomponent lipoplexes spontaneously formed exhibiting structural properties, i.e., membrane thickness, surface charge density, and one-dimensional DNA packing density, intermediate between those of binary lipoplexes. These results suggested that DNA lets liposomes come into contact and fuse and that a complete lipid mixing at the molecular level occurs. The equilibrium structure of multicomponent lipoplexes was found to be unique and did not depend on the number and kind of populations composing lipid dispersion but only on the lipid species involved and on their relative molar ratio. According to recent theoretical models we identified two-dimensional lipid mixing entropy as the key factor regulating the existence of only multicomponent lipoplexes with ideally mixed lipid species.

Entropy↗

PubMed2006

Photoinduced electron transfer from tetrasulfonated porphyrin to benzoquinone revisited. The structural volume-normalized entropy change correlates with marcus reorganization energy.

Time-resolved laser-induced optoacoustic spectroscopy was used for the determination of the enthalpy, DeltaTH, and structural volume changes, DeltaTV, concomitant with triplet state formation upon excitation of meso-tetrakis(4-sulfonatophenyl)porphyrin, TSPP(4-), as well as with the triplet state electron-transfer (ET) quenching by benzoquinone, BQ (DeltaRH and DeltaRV). The values of DeltaTH and DeltaTV for (3)TSPP(4-) formation in the presence of different cations (Li+, Na+, K+, NH4+, and Cs+) correlated with each other and afforded a value of DeltaTG = 140 +/- 20 kJ mol(-1), equal to the value of E+ at 77 K, but much larger than the DeltaTH values in solution at room temperature, due to the large entropic factor in solution. The influence of the cations on DeltaTH and DeltaTV (a contraction ranging from 5.4 to 3.8 cm3 mol(-1)) is attributed to changing chromophore-water interactions in the ground and triplet states. Upon quenching of 3TSPP(4-) by BQ, the quantum yield of free radical formation, PhiR = 0.66 +/- 0.04, is the same in the solutions of the five cations. The values of DeltaRH and DeltaRV are small and have a large error. The energy level of the free radicals formed is thus very similar to that of 3TSPP(4-). TDeltaRS and X = TDeltaRS/DeltaRV, i.e., the structural volume change-normalized entropy change for free radicals formation, were derived using average values of DeltaRH and DeltaRV together with the calculated DeltaRG degrees . The measured Marcus reorganization energy, lambda, and X fall into the lambda vs X linear dependence we previously found for the radical formation upon ET quenching of triplet flavins (3FMN and 3FAD) by amines and amino acids. Thus, X = TDeltaRS/DeltaRV in aqueous solutions is a property of the particular donor-acceptor pair linearly correlated to the corresponding Marcus reorganization energy. The value of X is much larger than the predicted value applying the electrostriction concepts in view of the noncontinuum nature of the aqueous solutions.

Benzoquinones↗

PubMed2006

Judging on host-guest binding mode uniqueness: association entropy as an indicator in enantioselection.

[reaction: see text] Supramolecular enantiodifferentiation was studied by isothermal titration calorimetry in an effort to address the order-disorder distinction in the diastereomeric complexes formed from a chiral macrocyclic host and enantiomeric carboxylates. As a result, the association entropy component TDeltaS emerged as an indicator in the enantioselection of tartrate 14 and aspartate 15 by the macrocycle 13 containing two guanidinium anchor groups connected to each other by four urea units. The parent monotopic guanidinium compounds 1 or 2 did not show any enantioselection for chiral carboxylates.

Binding Sites↗

PubMed1999

Maximum entropy approach to the determination of solution conformation of flexible polypeptides by global conformational analysis and NMR spectroscopy--application to DNS1-c-[D-A2,bu2,Trp4,Leu5]enkephalin and DNS1-c-[D-A2bu2,Trp4,D-Leu5]enkephalin.

A method is proposed to determine the conformational equilibrium of flexible polypeptides in solution, using the data provided by NMR spectroscopy and theoretical conformational calculations. The algorithm consists of the following three steps: (i) search of the conformational space in order to find conformations with reasonably low energy; (ii) simulation of the NOE spectrum and vicinal coupling constants for each of the low energy conformations; and (iii) determining the statistical weights of the conformations, by means of the maximum-entropy method, in order to obtain the best fit of the averaged NOE intensities and coupling constants to the experimental quantities. The method has been applied to two cyclic enkephalin analogs: DNS1-c-[D-A2bu2,Trp4,Leu5]enkephalin (ENKL) and DNS1-c-[D-A2bu2,Trp4,D-Leu5]enkephalin (ENKD). NMR measurements were carried out in deuterated dimethyl sulfoxide. Two techniques were used in conformational search: the electrostatically driven Monte Carlo method (EDMC), which results in extensive search of the conformational space, but gives only energy minima, and the molecular dynamics method (MD), which results in a more accurate, but also more confined search. In the case of EDMC calculations, conformational energy was evaluated using the ECEPP/3 force field augmented with the SRFOPT solvation-shell model, while in the case of MD the AMBER force field was used with explicit solvent molecules. Both searches and subsequent fitting of conformational weights to NMR data resulted in similar conformations of the cyclic part of the peptides studied. For both ENKL and ENKD a common feature of the low-energy solution conformations is the presence of a type II' or type IV beta-turn at residues 3 and 4; the ECEPP/3 force field also gives a remarkable content of type III beta-turn. These beta-turns are tighter in the case of ENKL, which is reflected in different distributions of the D-A2bu(N gamma H)...D-A2bu(CO) and D-A2bu(N gamma H)...Gly3(CO) hydrogen-bonding distances, indicating that the D-A2bu(N gamma H) amide proton is more shielded from the solvent than in the case of ENKD. This finding conforms with the results of temperature coefficient data of the D-A2bu(N gamma H) proton. It has also been found that direct (MD) or Boltzmann (EDMC) averages of the observables do not exactly conform with the measured values, even when explicit solvent molecules are included. This suggests that improving force-field parameters might be necessary in order to obtain reliable conformational ensembles in computer simulations, without the aid of experimental data.

Algorithms↗

PubMed2001

Very empirical treatment of solvation and entropy: a force field derived from log Po/w.

A non-covalent interaction force field model derived from the partition coefficient of 1-octanol/water solubility is described. This model, HINT for Hydropathic INTeractions, is shown to include, in very empirical and approximate terms, all components of biomolecular associations, including hydrogen bonding, Coulombic interactions, hydrophobic interactions, entropy and solvation/desolvation. Particular emphasis is placed on: (1) demonstrating the relationship between the total empirical HINT score and free energy of association, deltaGinteraction; (2) showing that the HINT hydrophobic-polar interaction sub-score represents the energy cost of desolvation upon binding for interacting biomolecules; and (3) a new methodology for treating constrained water molecules as discrete independent small ligands. An example calculation is reported for dihydrofolate reductase (DHFR) bound with methotrexate (MTX). In that case the observed very tight binding, deltaGinteraction < or = -13.6 kcal mol(-1), is largely due to ten hydrogen bonds between the ligand and enzyme with estimated strength ranging between -0.4 and -2.3 kcal mol(-1). Four water molecules bridging between DHFR and MTX contribute an additional -1.7 kcal mol(-1) stability to the complex. The HINT estimate of the cost of desolvation is +13.9 kcal mol(-1).

1-Octanol↗

PubMed2002

Maximum-entropy calculation of free energy distributions for two forms of myoglobin.

The temperature dependence of the heat capacity of myoglobin depends dramatically on pH. At low pH (near 4.5), there are two weak maxima in the heat capacity at low and intermediate temperatures, respectively, whereas at high pH (near 10.7), there is one strong maximum at high temperature. Using literature data for the low-pH form (Hallerbach and Hinz, 1999) and for the high-pH form (Makhatadze and Privalov, 1995), we applied a recently developed technique (Poland, 2001d) to calculate the free energy distributions for the two forms of the protein. In this method, the temperature dependence of the heat capacity is used to calculate moments of the protein enthalpy distribution function, which in turn, using the maximum-entropy method, are used to construct the actual distribution function. The enthalpy distribution function for a protein gives the fraction of protein molecules in solution having a given value of the enthalpy, which can be interpreted as the probability that a molecule picked at random has a given enthalpy value. Given the enthalpy distribution functions at several temperatures, one can then construct a master free energy function from which the probability distributions at all temperatures can be calculated. For the high-pH form of myoglobin, the enthalpy distribution function that is obtained exhibits bimodal behavior at the temperature corresponding to the maximum in the heat capacity (Poland, 2001a), reflecting the presence of two populations of molecules (native and unfolded). For this form of myoglobin, the temperature evolution of the relative probabilities of the two populations can be obtained in detail from the master free energy function. In contrast, the enthalpy distribution function for the low-pH form of myoglobin does not show any special structure at any temperature. In this form of myoglobin the enthalpy distribution function simply exhibits a single maximum at all temperatures, with the position of the maximum increasing to higher enthalpy values as the temperature is increased, indicating that in this case there is a continuous evolution of species rather than a shift between two distinct population of molecules.

Calorimetry↗

PubMedDate not supplied

Noise, not stimulus entropy, determines neural information rate.

In the quest for deciphering the neural code, theoretical advances were made which allow for the determination of the information rate inherent in the spike trains of nerve cells. However, up to now, the dependence of the information rate on stimulus parameters has not been studied in any neuron in a systematic way. Here, I investigate the information carried by the spike trains of H1, a motion-sensitive visual interneuron of the blowfly (Calliphora vicina) using a moving grating as a stimulus. Stimulus parameters fall in two classes: those that have only a minor effect on the information rate like increasing the frequency bandwidth or the maximum amplitude of the stimulus velocity, and those which dramatically affect the neural information rate, like varying the spatial size or the contrast of the visual pattern being moved. It appears that, for a broad range of complex stimuli, the neuron covers the stimulus with its whole response repertoire regardless of the stimulus entropy, with the information rate being limited by the noise of the stimulus and the neural hardware.

Animals↗

PubMed1997

Entropy detection by pigeons: response to mixed visual displays after same-different discrimination training.

Pigeons were trained to peck 2 different buttons in response to 16-icon Same versus Different arrays. In Same arrays, the icons were identical to one another, whereas in Different arrays, the icons were different from one another. In Experiment 1, pigeons discriminated Same from Different arrays and transferred their discriminative responding to arrays of novel icons. In Experiments 2-4, pigeons exhibited sensitivity to the degree of display variability when shown intermediate Mixture arrays. Entropy, an information theoretic measure, systematically described these results while outperforming rival accounts.

Animals↗

PubMed2001

Same-different conceptualization by baboons (Papio papio): the role of entropy.

The authors trained 6 baboons (Papio papio) to make 1 of 2 report responses to 16-icon same arrays versus 16-icon different arrays. In the same arrays, the icons were all the same as one another, whereas in the different arrays the icons were all different from one another. In Experiment 1, the baboons discriminated the same arrays from the different arrays, and they transferred their discriminative responding to arrays of novel icons. In Experiments 2 and 3, the baboons exhibited strong sensitivity to the degree of display variability when they were shown mixed arrays that comprised some same and some different items. The information theoretic measure "entropy" systematically described these results and outperformed several rival metrics. Finally, in Experiments 4 and 5, the baboons' responses to displays that contained jittered and blurred icons suggested that their same-different conceptual behavior was not based on the spatial orderliness of the visual arrays.

Animals↗

PubMed1999

Increased protein backbone conformational entropy upon hydrophobic ligand binding.

For complexes between proteins and very small hydrophobic ligands, hydrophobic effects alone may be insufficient to outweigh the unfavorable entropic terms resulting from bimolecular association. NMR relaxation experiments indicate that the backbone flexibility of mouse major urinary protein increases upon binding the hydrophobic mouse pheromone 2-sec-butyl-4,5-dihydrothiazole. The associated increase in backbone conformational entropy of the protein appears to make a substantial contribution toward stabilization of the protein-pheromone complex. This term is likely comparable in magnitude to other important free energy contributions to binding and may represent a general mechanism to promote binding of very small ligands to macromolecules.

Animals↗

PubMed2000

Retrospective shading correction based on entropy minimization.

Shading is a prominent phenomenon in microscopy, manifesting itself via spurious intensity variations not present in the original scene. The elimination of shading effects is frequently necessary for subsequent image processing tasks, especially if quantitative analysis is the final goal. While most of the shading effects may be minimized by setting up the image acquisition conditions carefully and capturing additional calibration images, object-dependent shading calls for retrospective correction. In this paper a novel method for retrospective shading correction is proposed. Firstly, the image formation process and the corresponding shading effects are described by a linear image formation model, which consists of an additive and a multiplicative parametric component. Secondly, shading correction is performed by the inverse of the image formation model, whose shading components are estimated retrospectively by minimizing the entropy of the acquired images. A number of tests, performed on artificial and real microscopical images, show that this approach is efficient for a variety of differently structured images and as such may have applications in and beyond the field of microscopical imaging.

Alloys↗

PubMed1999

Analysis of rapid eye movement periodicity in narcoleptics based on maximum entropy method.

We examined REM sleep periodicity in typical narcoleptics and patients who had shown signs of a narcoleptic tetrad without HLA-DRB1*1501/DQB1*0602 or DR2 antigens, using spectral analysis based on the maximum entropy method. The REM sleep period of typical narcoleptics showed two peaks, one at 70-90 min and one at 110-130 min at night, and a single peak at around 70-90 min during the daytime. The nocturnal REM sleep period of typical narcoleptics may be composed of several different periods, one of which corresponds to that of their daytime REM sleep.

Adult↗

PubMed2004

Kolmogorov-Sinai entropy for the A+B-->P reaction in transitional flows.

We study global decay of the bimolecular reaction A+B-->P as c(t) approximately t(-alpha) in a nonlinear transitional flow. A relationship is established between the decay exponent alpha, and a modified Kolmogorov-Sinai entropy, hr. We find that for dynamic conditions which induce relatively strong mixing, the decay exponent is alpha is proportional to ln psi(-Bhr) with B being a characteristic reactive mix-down time for the system, and psi is a space-time scaling parameter. Dynamic conditions which imply weak mixing lead to a degenerate dependence of alpha on hr. The proposed relationship between alpha on hr should be a useful link between the dynamical evolution of the flow field and reaction kinetics in vortex dominated flows.

Entropy↗