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PubMed2006

Diffusivity, excess entropy, and the potential-energy landscape of monatomic liquids.

The connection between thermodynamic, transport, and potential-energy landscape features is studied for liquids with Lennard-Jones-type pair interactions using both microcanonical molecular-dynamics and isothermal-isobaric ensemble Monte Carlo simulations. Instantaneous normal-mode and saddle-point analyses of two variants of the monatomic Lennard-Jones liquid have been performed. The diffusivity is shown to depend linearly on several key properties of instantaneous and saddle configurations-the energy, the fraction of negative curvature directions, and the mean, maximum, and minimum eigenvalues of the Hessian. Since the Dzugutov scaling relationship also holds for such systems [Nature (London) 381, 137 (1996)], the exponential of the excess entropy, within the two-particle approximation, displays the same linear dependence on energy landscape properties as the diffusivity.

Journal Article↗

PubMed2006

Dynamical noise filter and conditional entropy analysis in chaos synchronization.

It is shown that, in a chaotic synchronization system whose driving signal is exposed to channel noise, the estimation of the drive system states can be greatly improved by applying the dynamical noise filtering to the response system states. If the noise is bounded in a certain range, the estimation errors, i.e., the difference between the filtered responding states and the driving states, can be made arbitrarily small. This property can be used in designing an alternative digital communication scheme. An analysis based on the conditional entropy justifies the application of dynamical noise filtering in generating quality synchronization.

Journal Article↗

PubMed2006

Observation of hydrogen in deuterated methane hydrate by maximum entropy method with neutron powder diffraction.

The crystal structure of deuterated methane hydrate (structure I, space group: Pm(-)3n) was investigated by neutron powder diffraction at temperatures of 7.7-185 K. The scattering amplitude density distribution was examined by a combination of Rietveld method and maximum entropy method (MEM). The distribution of the D atoms in both D(2)O and CD(4) molecules was clarified from three-dimensional graphic images of the scattering amplitude density. The MEM results showed that there were low-density sites for the D atom of D(2)O in a particular location within the D(2)O cage at low temperatures. The MEM provided more reasonable results because of the decrease in the R factor that is attainable by this method. Accordingly, the low-density sites for the D atom of D(2)O probably exist within the D(2)O cage. This suggests that a spatial disorder of the D atom of D(2)O occurs at these sites and that hydrogen bonds between D(2)O molecules become partially weakened. With regard to the CD(4) molecules, there were high-density sites for the D atom of CD(4), and the density distribution of the C and D atoms was observed separately in the scattering amplitude density image. Consequently, the C-D bonds of CD(4) were not observed clearly because the CD(4) molecules had an orientational disorder. The D atoms of CD(4) were displaced from the line between the C and O atoms, and were located near the face center of the polygon in the cage. Accordingly, the D atoms of CD(4) were not bonded to specific O atoms. This result is consistent with the hydrophobicity of the CD(4) molecule. We also report the difference between the small and the large cages in the density distribution map and the temperature dependence of the scattering amplitude density.

Journal Article↗

PubMed2006

Information entropies for eigendensities of homogeneous potentials.

For homogeneous potentials, the sum S(T), of position and momentum Shannon information entropies Sr and Sp is shown to be independent of the coupling strength scaling. The other commonly used uncertainty like products also follow similar behavior. The ramifications of this scaling property in the cases of hydrogenlike, harmonic oscillator, Morse, and Poeschl-Teller potentials are discussed with the example of S(T).

Journal Article↗

PubMed1971

Postulational basis of the law of increase of entropy.

The law increase of entropy is shown to be a consequence of the central assumption, in the manner of Gibbs, for the construction of the ensemble that represents the physical system. It is no longer necessary to make two separate assumptions in the Gibbs-Tolman development of the bases of statistical mechanics.

Journal Article↗

PubMed1973

Temperature adaptation of enzymes: roles of the free energy, the enthalpy, and the entropy of activation.

The enzymic reactions of ectothermic (cold-blooded) species differ from those of avian and mammalian species in terms of the magnitudes of the three thermodynamic activation parameters, the free energy of activation (DeltaG()), the enthalpy of activation (DeltaH()), and the entropy of activation (DeltaS()). Ectothermic enzymes are more efficient than the homologous enzymes of birds and mammals in reducing the DeltaG() "energy barrier" to a chemical reaction. Moreover, the relative importance of the enthalpic and entropic contributions to DeltaG() differs between these two broad classes of organisms.

Acclimatization↗

PubMed1976

Free energy levels and entropy production associated with biochemical kinetic diagrams.

"Basic" and "gross" free energy levels are defined for the discrete states of a macromolecular biochemical kinetic system such as a free energy transducing enzyme (e.g., myosin or Na,K-ATPase). Basic free energy level differences are related to the first-order rate constants for transitions between states while gross free energy differences, along with the corresponding fluxes, determine the rate of entropy production in the system. In muscle contraction the analysis is complicated by the possibility of the system doing external mechanical work. The question of the sign of the flux or of the gross free energy level change in a given transition is examined for both single-cycle and multi-cycle models. More definite statements can be made in single-cycle cases. Some numerical examples are included. The more complicated cases are reserved for a subsequent paper.

Adenosine Triphosphatases↗

PubMed1977

Heat capacity and entropy changes in processes involving proteins.

Six possible sources of the large heat capacity and entropy changes frequently observed for processes involving proteins are identified. Of these the conformational, hydrophobic, and vibrational effects seem likely to be of greatest importance. A method is proposed for estimating the magnitudes of the hydrophobic and vibrational contributions. Application of this method to several protein processes appears to achieve significant clarification of previously confusing and apparently contradictory data.

Calorimetry↗

PubMed1979

The rate of access to the organic ligand-binding region of serum albumin is entropy controlled.

The technique of real time dielectric relaxation measurement coupled with a conventional stopped-flow device has made it possible to measure the rates of association and dissociation of the complex of human serum albumin with its most prevalent ligands, the long-chain fatty acids. This association was previously shown to proceed in two steps: a fast, probably diffusion-controlled, nonspecific association, followed by a slower (approximately 3 sec--1) rearrangement of the intermediate protein--ligand configuration, whose kinetics is first order. By use of the Arrhenius relation and standard theory of rate processes it is determined that there is virtually no activation enthalpy in the forward binding reaction and that the rate of access to the interior hydrophobic binding region of serum albumin is controlled by a negative entropy of activation, reflecting a high degree of ordering in the transition state. A complete thermodynamic and kinetic profile of the association reaction is given.

Binding Sites↗

PubMed1980

The "excess entropy" around nonequilibrium steady states, (deltaS)(ss), is not a Liapunov function.

In a response to my recent paper [Fox, R. F. (1979) Proc. Natl. Acad. Sci. USA 76, 2114-2117], Nicolis and Prigogine [Nicolis, G. & Prigogine, I. (1979) Proc. Natl. Acad. Sci. USA 76, 6060-6061] reasserted that the "excess entropy" around nonequilibrium steady states, (delta(2)S)(ss), is a Liapunov function. A simple, explicit counterexample which invalidates this claim is presented. The existence of an alternative theory possessing a proper Liapunov function for steady states is reviewed.

Journal Article↗

PubMed1983

Maximum-entropy calculation of the electron density at 4 A resolution of Pf1 filamentous bacteriophage.

A 4 A electron-density map of Pf1 filamentous bacterial virus has been calculated from x-ray fiber diffraction data by using the maximum-entropy method. This method produces a map that is free of features due to noise in the data and enables incomplete isomorphous-derivative phase information to be supplemented by information about the nature of the solution. The map shows gently curved (banana-shaped) rods of density about 70 A long, oriented roughly parallel to the virion axis but slewing by about 1/6th turn while running from a radius of 28 A to one of 13 A. Within these rods, there is a helical periodicity with a pitch of 5 to 6 A. We interpret these rods to be the helical subunits of the virion. The position of strongly diffracted intensity on the x-ray fiber pattern shows that the basic helix of the virion is right handed and that neighboring nearly parallel protein helices cross one another in an unusual negative sense.

Bacteriophages↗

PubMed1987

Enhanced protein thermostability from site-directed mutations that decrease the entropy of unfolding.

It is proposed that the stability of a protein can be increased by selected amino acid substitutions that decrease the configurational entropy of unfolding. Two such substitutions, one of the form Xaa----Pro and the other of the form Gly----Xaa, were constructed in bacteriophage T4 lysozyme at sites consistent with the known three-dimensional structure. Both substitutions stabilize the protein toward reversible and irreversible thermal denaturation at physiological pH. The substitutions have no effect on enzymatic activity. High-resolution crystallographic analysis of the proline-containing mutant protein (Ala-82----Pro) shows that its three-dimensional structure is essentially identical with the wild-type enzyme. The overall structure of the other mutant enzyme (Gly-77----Ala) is also very similar to wild-type lysozyme, although there are localized conformational adjustments in the vicinity of the altered amino acid. The combination of a number of such amino acid replacements, each of which is expected to contribute approximately 1 kcal/mol (1 cal = 4.184 J) to the free energy of folding, may provide a general strategy for substantial improvement in the stability of a protein.

Calorimetry↗

PubMed1991

Approximate entropy as a measure of system complexity.

Techniques to determine changing system complexity from data are evaluated. Convergence of a frequently used correlation dimension algorithm to a finite value does not necessarily imply an underlying deterministic model or chaos. Analysis of a recently developed family of formulas and statistics, approximate entropy (ApEn), suggests that ApEn can classify complex systems, given at least 1000 data values in diverse settings that include both deterministic chaotic and stochastic processes. The capability to discern changing complexity from such a relatively small amount of data holds promise for applications of ApEn in a variety of contexts.

Journal Article↗

PubMed2000

Free entropy and property T factors.

We show that a large class of finite factors has free entropy dimension less than or equal to one. This class includes all prime factors and many property T factors.

Journal Article↗

PubMed1995

Enthalpy and entropy of hydration of bovine crystallins.

Transparency of the lens of the eye is the result of a short range order in the packing of crystallin molecules within the fiber cells. Short range order depends on crystallin-crystallin as well as water-crystallin interactions. Light scattering measurements can provide information on the hydration of crystallins. Light scattering intensities were obtained as a function of scattering angle, concentration, and temperature on dilute solutions of beta H, beta L, and gamma fractions of bovine lens crystallins. The temperature dependence of the second virial coefficient was negative for the beta crystallin fractions and positive for the gamma fraction as well as that for alpha crystallin (Wang, X., and Bettelheim, F. A. (1989) Proteins Struct. Funct. Genet. 5, 166-169). The partial molar enthalpy values of the solutions were negative for the beta crystallin fractions, indicating a tendency for homo- and heterodimer and -oligomer association. The enthalpy values were positive for the alpha and gamma fractions. The negative values of the enthalpy of solutions differentiate the beta crystallins from the other crystallins. The partial molar entropy values of solutions of beta L and gamma fractions were identical, those of the oligomeric beta H fraction were higher, whereas those of alpha crystallin were a magnitude larger than those of the smaller crystallin molecules.

Animals↗

PubMed1996

The multi-hemoglobin system of the hydrothermal vent tube worm Riftia pachyptila. II. Complete polypeptide chain composition investigated by maximum entropy analysis of mass spectra.

The deep-sea tube worm Riftia pachyptila Jones possesses a complex of three extracellular Hbs: two in the vascular compartment, V1 (approximately 3500 kDa) and V2 (approximately 400 kDa), and one in the coelomic cavity, C1 (approximately 400 kDa). These native Hbs, their dissociation products and derivatives were subjected to electrospray ionization mass spectrometry (ESI-MS). The data were analyzed by the maximum entropy deconvolution system. We identified three groups of peaks for V1 Hb, at approximately 16, 23 27, and 30 kDa, corresponding to (i) two monomeric globin chains, b (Mr 16,133.5) and c (Mr 16,805.9); (ii) four linker subunits, L1 L4 (Mr 23,505.2, 23,851.4, 26,342.4, and 27,425.8, respectively); and (iii) one disulfide-bonded dimer D1 (Mr 31,720.7) composed of globin chains d (Mr 15,578.5) and e (Mr 16, 148.3). V2 and C1 Hbs had no linkers and contained a glycosylated monomeric globin chain, a (Mr 15,933.4) and a second dimer D2 (Mr 32,511.7) composed of chains e and f (Mr 16,368.1). The dimer D1 was absent from C1 Hb, clearly differentiating V2 and C1 Hbs. These Hbs were also subjected to SDS-PAGE analysis for comparative purposes. The following models are proposed ((cD1)(bD1)3) for the one-twelfth protomer of V1 Hb, ((cD)(bD)6(aD)) (D corresponding to either D1 or D2) for V2 and C1 Hbs. HBL V1 Hb would be composed of 180 polypeptide chains with 144 globin chains and 36 linker chains, each twelfth being in contact with three linker subunits, providing a total molecular mass = 3285 kDa. V2 and C1 would be composed of 24 globin chains providing a total molecular mass = 403 kDa and 406 kDa, respectively. These results are in excellent agreement with experimental Mr determined by STEM mass mapping and MALLS.

Animals↗

PubMed1988

On the possibility of obtaining non-diffused proximity functions from cloud-chamber data: II. Maximum entropy and Bayesian methods.

Maximum entropy and Bayesian methods are applied to an inversion problem which consists of unfolding diffusion from proximity functions calculated from cloud-chamber data. The solution appears to be relatively insensitive to statistical errors in the data (an important feature) given the limited number of tracks normally available from cloud-chamber measurements. It is the first time, to our knowledge, that such methods are applied to microdosimetry.

Bayes Theorem↗

PubMed1988

The enhancement of radiographic images from a multiwire camera using a maximum entropy algorithm.

The multiwire camera (MWC) produces high speed, quantitative autoradiography of radiolabelled substances in two-dimensional systems. While greatly superior to film-based systems in respect of speed and quantitativity the MWC has significantly poorer spatial resolution (particularly for high energy beta-emitting radiolabels) and the performance is ultimately limited by the noise induced in the images by Poisson statistics and counter background. Processing the MWC images with a maximum entropy algorithm significantly improves the performance of the system in these respects. The algorithm has been tested using one-dimensional data taken from images of known tritium, 14C and 125I distributions. Processed images are visually more acceptable with improved quantitative accuracy and spatial resolution. Quantitative accuracy, calculated as the root mean square deviation between an image and the known sample activities, is 10-40% lower for processed images compared with original camera images. Spatial resolution, calculated from slopes in the images representing edges of activity in the sources, is improved by 20-40% for the processed images. The algorithm is used to improve a two-dimensional image from a biological study. The source distribution consisted of a set of circular dots of varying activity. The dots with lowest activity were barely discernible in the raw MWC image but are clearly resolved after processing. The algorithm used is simple and effective and executes acceptably quickly on a personal computer. It should prove useful in any context where the imaging performance of a system is limited by Poisson statistics.

Algorithms↗