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PubMed1983

Enthalpy, entropy and heat capacity changes induced by binding of calcium ions to cardiac troponin C.

Microcalorimetric titrations have been used to study the binding of Ca2+ to cardiac troponin C. Measurements were made both in the presence and in the absence of Mg2+, and at temperatures of 5 degrees, 15 degrees and 25 degrees C. Changes in enthalpy, entropy and heat capacity of troponin C associated with Ca binding have been determined. Cardiac troponin C exhibited a decrease in enthalpy and an increase in entropy associated with Ca binding. Enthalpy changes increased linearly with temperature, indicating that the Ca binding causes negative changes in the heat capacity of troponin C. These results show that the Ca binding causes a strong hydrophobic effect and a tightening of the molecular structure of cardiac troponin C.

Animals↗

PubMed1987

Pf1 Inovirus. Electron density distribution calculated by a maximum entropy algorithm from native fibre diffraction data to 3 A resolution and single isomorphous replacement data to 5 A resolution.

We have calculated the electron density distribution of the Pf1 strain of filamentous bacteriophage by a maximum entropy method. In the calculation we included native X-ray fibre diffraction data extending to 3 A resolution in the meridional direction on 60 layerlines that are resolved to 4 A in the equatorial direction, and lower resolution data from a single isomorphous derivative iodinated on the Tyr25 residue. The electron density map indicates that the 46-residue protein subunit is a single, gently curved stretch of alpha-helix with its axis at an angle of about 20 degrees to the axis of the virion. The alpha-helix subunit curves around the virion axis by about 1/6 turn, and decreases from about 27 A radius to about 13 A radius in the virion as the amino acid sequence of the subunit runs from the N terminus to the C terminus. Nearest-neighbour alpha-helical subunits are about 10 A apart along their length, and the axis of each subunit makes an unexpected negative angle with its nearest neighbours in the virion. To confirm the validity of the maximum entropy calculation, we have varied the constraints on the calculation. All variations result in either a map that is close to the original map or a map that cannot be interpreted in terms of secondary structure: we find only one map that makes structural sense.

Algorithms↗

PubMed1990

Fractal structure and conformational entropy of protein chain.

The structures of 25 proteins arbitrarily chosen are investigated by fractal geometry, and their fractal dimensions (Df) and conformational entropies S(NO) are calculated by Havlin-Ben Avraham and Monte Carlo method, respectively. Comparison of the Df and S(NO) give the relation: Df = 1.532 - 3.00 x 10(-4) S(NO). The entropy data obtained by Monte Carlo method for the chain of random self-avoiding walks confirm the prediction of renormalization group: S(NO) = 1.544NO + 0.1667 In NO + 0.1570 where NO is the number of residues in a protein chain. Both the Df and S(NO) reflect the conformational properties of a protein molecular chain. The idea resulting from the present communication suggests that the thermodynamic behaviours of proteins may be related to multifractals.

Mathematics↗

PubMed1992

Quantal analysis using maximum entropy noise deconvolution.

When applying quantal analysis to synaptic transmission it is often unclear how much of the measured postsynaptic signal fluctuation arises from random sampling and noise rather than from the probabilistic transmitter release process. Unconstrained noise deconvolution methods do not overcome this because they tend to overfit the data, often giving a misleading picture of the underlying process. Instead, maximum entropy deconvolution provides a solution which is the smoothest, or most featureless, distribution that is still compatible with the data, taking noise and sample size into account. A simple way of achieving this is described, together with results of Monte Carlo simulations which show that the features present in the maximum entropy solution usually reflect the process underlying the data and not random sampling or noise.

Algorithms↗

PubMed1994

Enthalpy-entropy compensation in the thermodynamics of hydrophobicity.

Using Widom's potential distribution theory (J. Chem. Phys. 39 (1963) 2808; J. Phys. Chem. 86 (1982) 869), a general and a special theorems are derived, by means of which one can judge whether a particular sub-process of an overall process will produce compensating changes in enthalpy and entropy. The enthalpy-entropy compensation phenomena that are observed in the transfer process of a hydrophobic molecule from a non-aqueous phase to water are examined in the light of these theorems. It is concluded that most sub-processes involved in the hydrophobic transfer process are compensating except one, that of inserting a cavity corresponding to the solute molecule in the liquid. The reason that this process is non-compensating, and therefore most responsible for the hydrophobicity, is traced to the hard core overlap between solvent and the solute molecules.

Chemical Phenomena↗

PubMed1996

In vitro RNA folding: the principle of sequential minimization of entropy loss at work.

We introduce the principle of sequential minimization of entropy loss (SMEL) in the context of biopolymer folding in vitro. This principle asserts that at each stage in the dominant folding pathway, the conformational entropy loss, denoted DeltaS loop, associated with loop closure is minimized while the number n of effective contacts is maximized to the extent that at each stage the chosen event is the one that minimizes the number Q = n-1 exp(-DeltaS loop/R). This principle is compatible with thermodynamic control exerted sequentially, that is, at every stage of the folding process. Moreover, the validity of the SMEL will be shown to be tantamount to assume kinetic control whenever folding is subject to time constraints. Because of the exponential dependence, the applicability of the SMEL principle is contingent upon a rigorous and reliable derivation of the contribution DeltaS loop. This derivation is carried out in this work for RNA by taking into account the orientational restrictions associated to the self energy of charged phosphate moieties within a loop. The predictive potential of the principle thus derived is tested by showing that the theory reproduces the consensus biologically competent secondary structures of specific ribozymes and explains how the structures emerge.

Animals↗

PubMed1975

Problems with entropy in biology.

Entropy has been widely referred to as a measure of biological order. The validity of this notion is discussed in conjunction with it's relation to the spontaneous creation of order. Information theory offers a quantitative method for characterization of order, however, it is not fundamentally connected to formalisms of irreversible thermodynamics, and it is severely limited because the meaning and value of the information is neglected. A completely general notation is proposed for including measures of order of a biological system in the entropy balance equation of irreversible thermodynamics. Problems of assigning energetic equivalents to measures of order are indicated, with a final focus on the problem of meaning and value.

Calorimetry↗

PubMed1989

The application of the maximum entropy method to electron microscopic tomography.

The maximum entropy method has been applied to single axis tilt electron microscopic tomography. Its application requires that the problem be correctly formulated and that the model for the noise in electron micrographs be developed. A suitable noise model was determined empirically. The maximum entropy method was applied to a reconstruction of a test object from projections to which noise had been added. These reconstructions were superior to those obtained by reciprocal space weighted back protection. The method was also robust towards the incorrect specification of the noise, the penalty being an increase in the time required for convergence rather than degradation of the quality of the reconstructed image. In the reconstruction of negatively stained chromatin fibres it was possible to obtain satisfactory images utilizing all the information in the projections, in contrast to conventional methods in which high resolution data are removed by the application of Fourier space filters.

Algorithms↗

PubMed1990

EELS elemental mapping with unconventional methods. I. Theoretical basis: image analysis with multivariate statistics and entropy concepts.

Electron energy loss filtered images recorded within a transmission analytical electron microscope are now widely used for the mapping of the elemental distribution of a given atomic species in a specimen prepared as a thin film. Such an image processing may produce both valuable results and artifacts if a careful inspection of all the hypotheses needed by the calculation is not carried out. This paper presents some general statistical methods for a contrast information analysis of a noisy image data set. After a brief introduction of different concepts such as contrast, variance, information and entropy, two unconventional approaches for image analysis are explained: the relative entropy computed with respect to a pure random and signal-free image and the factorial analysis of correspondence (a branch of multivariate statistics). In the companion article (part II), these concepts are applied to real experiments and the results compared with those obtained with a conventional method. Although electron energy loss spectroscopy is the only technique considered here, these methods for image analysis can be applied to a wide variety of noisy data sets (spectra, images, ...) recorded from various sources (electrons, photons, ...).

Algorithms↗

PubMed1986

Aging as entropy.

Like the weather, many people talk about aging, but no one seems able to do anything about it. This implacability derives, at least in part, from our inability to provide a conceptual base from which analytic insight might derive. The emerging field of nonlinear thermodynamics presents a new view of the universe. It relates matter and energy in the framework of time. Entropy, "time's arrow," gives direction. Energy, rendered coherent through the metabolism of biology, acts to retard dissipation as entropy. For physicians, particularly those interested in geriatrics, this provides the challenge to understand how these forces are inscribed onto the human condition. The homeostatic controls which order our existence are energy dependent. As energies diminish, homeostasis as order deteriorates, aging proceeds and life is threatened. It seems to follow that if we are to diminish the entropic declines of aging our clinical strategies should emphasize actions which might retard the disruption of ordering processes. Homeostasis is at risk to the ravages of disease. This has been the standard business of medicine. But homeostasis is manifestly determined by the ordering effects of an energy flow. Either too little energy flow as disuse, or too much, as stress, lends further major burden to homeostatic controls. Every body system, at every level of organization, is beholden to this mandate. As our wisdom stretches to encompass the notion that aging and illness have other dimensions than just disease our view of ourselves will become more whole and in enlarging consonance with universal law.

Adenosine Triphosphate↗

PubMed2005

Entropy minimization and spectral dissimilarity curve resolution technique applied to nuclear magnetic resonance data sets.

The use of entropy minimization and spectral dissimilarity is applied to three nuclear magnetic resonance (NMR) data sets. The data sets contain 2, 2, and 3 observables each. It was found that without any a priori information the sets of pure component spectra underlying the NMR spectroscopic observations could be extracted. These successful spectral resolutions suggest that a combined entropy minimization and spectral dissimilarity approach can be further developed for even larger NMR data sets containing a larger number of observables. Brief comparison to DECRA and PMF curve resolution results is also presented.

Journal Article↗

PubMed2004

A further discussion on the peculiarity of maximum entropy image deconvolution in HREM.

Some important features observed in the maximum entropy image deconvolution in HREM were studied and demonstrated as a supplement to previous publications in Ultramicroscopy 35 (1991) 339 and 62 (1996) 141. It has been shown that in the process of image deconvolution how the errors of assigned electron-optical parameters can be compensated and the effect of crystal thickness can be corrected. The 'negative-potential problem' has been solved more perfectly than before via the normalization of sum total entropy.

Journal Article↗

PubMed1987

Configurational entropy of native proteins.

Simulations of the residual configurational entropy of a protein in the native state suggest that it is nearly an order of magnitude larger than the entropy of denaturation. The implications of this result are discussed.

Mathematics↗

PubMed1993

Thermodynamic entropy of two conformational transitions of single Na+ channel molecules.

Single cardiac Na+ channel currents were recorded with improved resolution (bandwidth up to 20 kHz) at two temperatures, 10 and 25 degrees C. The mean open time was determined at voltages between -50 and 0 mV by evaluation of the distribution of the event-related gaps in the center of the baseline noise. Fit of the voltage-dependent reciprocal mean open times at both temperatures allowed even for a single channel molecule to separate an entropic from an enthalpic part of activation energy for both deactivation and inactivation. Both entropies are positive and the entropy of deactivation exceeds that of inactivation by more than twice.

Animals↗

PubMed2003

Comparison of the differential isosteric adsorption enthalpies and entropies calculated from chromatographic data.

The differential isosteric enthalpies, -deltaH(ads), and entropies, -deltaS(ads), of adsorption were calculated taking the retention times of the peak maxima and the centres of gravity of peaks into account and compared with the results obtained from the adsorption second virial coefficients. A mathematical link between the -deltaH(ads) and -deltaS(ads) magnitudes and experimental data was derived through the Antoine-type equation which enables the -deltaH(ads) and -deltaS(ads) magnitudes to be found from adsorption second virial coefficients, B2S, calculated on the basis of chromatographically determined adsorption isotherm data. The virial coefficients were calculated employing the values of the Tóth and Unilan equation parameters. There are no significant differences to be found between the isosteric enthalpies obtained, whereas the values of the adsorption entropies were the highest for the centre of peak gravity data.

Adsorption↗

PubMed1990

RecA protein self-assembly. II. Analytical equilibrium ultracentrifugation studies of the entropy-driven self-association of RecA.

We have investigated the self-association of RecA protein from Escherichia coli by equilibrium ultracentrifugation. Monomeric RecA (Mr = 37,842) was observed in reversible equilibrium with trimers, hexamers and dodecamers in the presence of 1.5 M-KCl, 5 mM-Hepes, 1 mM-EDTA, 2 mM-ATP (pH 7.0) at 1 degrees C. The equilibrium was strongly temperature-dependent, with polymerization being favored as the temperature was raised from 1 degrees C 21 degrees C, and was reversible with respect to temperature. The values of both the standard enthalpy and entropy of self-association were positive, indicating that it is an entropy-driven process under these conditions. In the absence of KCl, in 50 mM-citrate, 5 mM-ATP, 5% (v/v) glycerol (pH 6.0) at 4 degrees C, only small amounts of RecA monomer could be detected, while in 10 mM-Tris-acetate, 10% glycerol (pH 7.5) at 4 degrees C, the smallest species present in significant concentration appeared to be the trimer. The majority of the species observed had molecular weights between 228,000 and 456,000, suggesting dominant stoichiometries of six to 12 monomers per oligomer. At pH 6.0, in the absence of ATP, much larger oligomers containing at least 24 monomers also appeared to be present. The data are consistent with an equilibrium mixture of monomers, trimers, hexamers, dodecamers, 24-mers and higher oligomers, with the distribution of oligomers being dependent on solution conditions. Thermodynamic analysis indicates that these oligomeric species are in reversible equilibrium with each other. It is not certain whether trimers assemble directly into hexamers, or whether disassembly into monomers is a prerequisite for the formation of higher oligomers. The possible role of higher-order RecA oligomers in the formation of RecA nucleoprotein filaments is discussed.

Adenosine Triphosphate↗

PubMed1991

Reconstruction of the antibody affinity distribution from experimental binding data by a minimum cross-entropy procedure.

A new solution is presented for the reconstruction of the distribution of association constants of antigen-antibody binding from a finite number of noisy experimental binding data. This ill-posed problem is solved by utilizing an information-theoretic method based on the principle of minimum cross-entropy (MCE) to select, as the solution, that unique antibody binding distribution which minimizes the cross entropy relative to some prior distribution subject to the constraints imposed by the given measurements. The prior distribution is selected to properly encode all the a priori information on the affinity distribution before the measurement of the experimental binding data. The utility of the method is demonstrated by application to synthetic binding data.

Antibody Affinity↗

PubMed1984

Energy transformation and entropy production in living systems I. Applications to embryonic growth.

Generalized material and energy balances are presented for biological systems that experience negligible kinetic, elastic, and potential energy changes. The balances are used to characterize the mass changes and energy transformations that occur in the developing avian embryo, using as an example a consistent set of data for the chicken egg. It is shown that the rate of total chemical energy turnover by the embryo is a quantity of interest and that this rate is not necessarily equivalent to the metabolic rate that is predicted from heat transfer measurements or oxygen consumption rates. The energy required for evaporative water loss is accounted for in the overall energy balance. Using the results of the energy calculations and a generalized expression for the rates of internal and total entropy production, the Prigogine-Wiame hypothesis is examined for the developing embryo with two different assumptions regarding the efficiency of biomass conversion. An order of magnitude analysis of the internal heat-conduction term is performed to show that the chemical reaction term dominates the entropy production relation. The constant efficiency case is shown to be in agreement with the Prigogine-Wiame hypothesis for the data used in the analysis.

Animals↗