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PubMed1985

Effect of dipolar ions on the entropy-driven polymerization of tobacco mosaic virus protein.

The effect of the dipolar ions, glycine, glycylglycine, and glycylglycylglycine on the polymerization of tobacco mosaic virus (TMV) protein has been studied by the methods of light scattering and ultracentrifugation. All three dipolar ions promote polymerization. The major reaction in the early stage is transition from the 4 S to the 20 S state. As in the absence of dipolar ions, the polymerization is enhanced by an increase in temperature; it is endothermic and therefore entropy-driven. The effect of the dipolar ions can be understood in terms of their action as salting-out agents; they increase the activity coefficient of TMV A protein, the 4 S material, and thus shift the equilibrium toward the 20 S state. The salting-out constants, K, for the reaction in 0.10 ionic strength phosphate buffer at pH 6.7 was found by the light scattering method to be 1.6 for glycine, 2.5 for glycylglycine, and 2.5 for glycylglycylglycine. A value of 2.7 was obtained by the ultracentrifugation method for glycylglycine in phosphate buffer at 0.1 ionic strength and pH 6.8 at 10 degrees C. For both glycine and glycylglycine, K increases when the ionic strength of the phosphate buffer is decreased. This result suggests that electrolytes decrease the activity coefficient of the dipolar ions, a salting-in phenomenon. However, the salting-in constants evaluated from these results are substantially higher than those previously determined by solubility measurements. The effect of glycine and glycylglycine on polymerization was studied at pH values between 6.2 and 6.8. The effectiveness of both dipolar ions is approximately 50% greater at pH 6.8 than at pH 6.2. The variation of the extent of polymerization with pH in the presence of the dipolar ions is consistent with the interpretation that approximately one hydrogen ion is bound for half of the polypeptide units in the polymerized A protein.

Capsid Proteins↗

PubMed1989

Binding of plasma membrane glycoproteins to the cytoskeleton during patching and capping is consistent with an entropy-enhancement model.

Concentrations of concanavalin A that induced patching and capping of cell surface receptors on Dictyostelium discoideum also induce binding of the receptors to the cortical cytoskeleton, which was isolated by density-gradient centrifugation. The receptors were solubilized by deoxycholate, purified by affinity chromatography, and used to determine whether the receptors bound directly to the cytoskeletal protein, actin. As the concentration of actin was increased, many of the receptors became bound to purified filamentous rabbit muscle actin, even in the absence of concanavalin A. As in the ligation-induced binding of receptors to the cortical cytoskeleton in cells, concanavalin A induced much stronger binding of the purified receptors to filamentous actin. The results were consistent with a previously stated hypothesis that induction of receptor binding to the cytoskeleton during their patching and capping is driven by clustering the receptors, which reduces their translational entropy and by doing so enhances their avidity for the cytoskeleton.

Actins↗

PubMed1994

Probing of active site structure of lipoprotein lipase: contribution of activation entropy in the catalysis.

In this study, I have utilized the chromogenic short-chain esters of p-nitrophenol as substrates for probing the active site structure of lipoprotein lipase (LPL). The results indicated that there is a consistent trend in the decrease of the Michaelis-Menten constant with increase of the acyl-chain length. Therefore, it was concluded that the decrease of reactivity with increased chain length is probably not a consequence of a lower affinity of the substrate for the enzyme. The fact that butyrate ester has the optimum acyl-chain length to be a substrate of LPL can be attributed to its chain length being long enough for optimum interaction with the active site His-Ser-Asp triad in forming the transition state complex; yet it is short enough to provide freedom for optimum positioning of the ester bond for transition state complex formation. It is likely that, because of the structural features of the enzyme active site, the increase of the acyl-chain of the substrate from C4 to C5 initiates the contact between the hydrocarbon tail of the acyl-chain and the hydrophobic surface of the active site pocket. Such an interaction, although it causes the stabilization of the ground state enzyme-substrate complex, also causes a large increase in negative activation entropy because of the restricted random motion of the bound substrate. The latter effect is also the likely cause for the progressively lower reactivity of the enzyme with the increase of acyl-chain length above C4, as seen in the LPL-catalyzed lipolysis of monoacid triacylglycerols.

Amino Acid Sequence↗

PubMed1984

Thermodynamic properties of the cholesterol transfer reaction from liposomes to cytochrome P450scc: an enthalpy-entropy compensation effect.

We have investigated the thermodynamic properties of the cholesterol transfer reaction from various types of liposomes to purified steroid-free cytochrome P450scc. From the results of temperature effect on the reaction, we obtained delta G+, delta H+, and delta S+ values for the reaction with various phosphatidylcholine vesicles containing different fatty acyl chains. The plots of delta H+ against delta S+, and delta G+ against delta H+ both reveal that an enthalpy-entropy compensation effect was seen in a series of phospholipid and micellar media of cholesterol. Our beta-value of 420 degrees K is unusually high among reported values for biochemical reactions.

Adrenal Cortex↗

PubMed1996

Temperature-nearly-independent binding constant in several biochemical systems. The underlying entropy-driven binding mechanism and its practical significance.

Arguments are presented in this commentary to show that the model of temperature-nearly-independent binding that we proposed to rationalize the binding characteristics of beta-adrenergic antagonists (Miklavc et al., Biochem Pharmacol 40: 663-669, 1990) in fact provides a consistent interpretation of the temperature-nearly-independent binding constant in all other systems that have been reported in the literature: in the binding of coenzyme NADH to horse liver alcohol dehydrogenase and to octopine dehydrogenase and in the binding of an inhibitor to acetylcholinesterase No such consistent interpretation has been given thus far for any of these systems. It is characteristic of them that the binding takes place in a hydrophobic, sterically constrained environment. One can assume, therefore, that the underlying entropy-driven binding mechanism would reflect the existence and the properties of the steric bottleneck surrounding the binding pocket. We also explain why the temperature effects characteristic of hydrophobic interactions are not found experimentally in these systems, whereas in other, sometimes even structurally similar, systems such temperature effects are clearly present. Further work in necessary to establish more firmly the key features of the temperature-nearly-independent binding mechanism that has been disclosed through our analysis. The binding mechanism in question not only appears in important biochemical systems, but also has the interesting property of being relative unaffected by smaller structural changes.

Acetylcholinesterase↗

PubMed1996

Polymerized cyclomaltoheptaose (beta-cyclodextrin, beta-CDn) inclusion complex formation with chlorogenic acid: solvent effects on thermochemistry and enthalpy-entropy compensation.

The inclusion of chlorogenic acid (CA) by epichlorohydrin-polymerized cyclomaltoheptaose (beta-cyclodextrin, beta-CDn) was studied with regard to temperature, solvent, and water activity aH2O approximately mole fraction = XH2O = 0.8-1 using MeOH as the diluent; 0.1 M sodium phosphate buffer). We discovered that the extreme convex curvature in K (the apparent stability constant) as a function of temperature was nearly eliminated at the lowest XH2O. The latter finding argues that this unusual CD behavior in aqueous media was due to perturbations in beta-CD's spatial organization in the polymeric matrix with temperature. Related to this we found, from the dependence of K on XH2O (K = K'XzH2O), that the beta-CDn.CA complex's stoichiometric coefficient, z, for water, varied between 5 and 8, depending on the temperature of the solution (K' = 400-800 M-1; T approximately 295-315 K). Our determinations of z were similar to those reported previously for beta-CD.(+)-limonene (z approximately 7), soluble beta-CD.CA (z approximately 6) or obtained by molecular dynamics calculations for beta-CD.CA reported herein (z approximately 5). However, beta-CDn.CA's z values did show a significant positive correlation with temperature not evident in equivalent solution experiments. Calculations of delta H and delta S at various XH2O values show linear enthalpy-entropy compensation (delta H plotted against delta S) but with a slope (Tc = theta delta H/theta delta S approximately 228 K) significantly less than Tc values determined from either standard aqueous thermodynamic experiments (Tc approximately 305 K on either beta-CD or beta-CDn) or variable XH2O (Tc approximately 272 K) experiments. To the best of our knowledge, this is the smallest Tc value detected in a multitude of CD.guest studies. This evident solvent effect on Tc strongly argues that the chemical part process of inclusion complex formation involves changes in the solvation of the beta-CDn's binding site.

Carbohydrate Conformation↗

PubMed1992

Activation energy and entropy for intramolecular excimer formation in a dipyrenylphosphatidylcholine probe in lamellar and hexagonal lipid phases.

Intramolecular excimer formation in pyrene-labeled phosphatidylcholine was used as a tool to determine thermodynamic characteristics of the lamellar to hexagonal phase transitions in a binary lipid system dilinoleoylphosphatidylethanolamine (DLPE)/palmitoyloleoylphosphatidylcholine (POPC). Upon an L alpha/HII phase transition, the activation energy Ea for excimer formation increased from 5.6 +/- 0.2 kcal/mol to 6.3 +/- 0.2 kcal/mol, while the activation entropy delta S decreased from -40.0 +/- 0.8 cal/K.mol to -38.4 +/- 0.8 cal/K.mol. The results are consistent with the idea of molecular splaying of the acyl chains in the hexagonal phase. It is estimated that the molecular area at the terminal carbon of the lipid acyl chains increases by a factor of 2.2 upon the L alpha HII transition in DLPE/POPC.

Lipids↗

PubMed1982

Classification of somatic evoked potentials through maximum entropy spectral analysis.

Maximum entropy (ME) spectra are currently considered to be superior to spectra calculated by means of Fast Fourier Transforms (FFT) because the former offer higher resolution. However, in terms of classification of somatic evoked potentials (SEPs), FFT spectra are found to be better than ME spectra. An even better set of parameters for discriminating SEPs is the set of reflection coefficients derived in the process of calculating the ME spectra. They permit separation of SEPs obtained from monkeys with dorsal column lesion from SEPs obtained from normal monkeys, as well as distinguishing between SEPs obtained from large nerve fiber stimulation and SEPs from stimulation of all nerve fibers.

Animals↗

PubMed1992

Abnormality of background EEG determined by the entropy of power spectra in epileptic patients.

Relationships between epileptiform discharges and background activity were examined by power spectral entropy (PSE), measuring a degree of EEG irregularity. The EEGs were recorded from 10 electrodes placed at F3, F4, C3, C4, T3, T4, P3, P4, O1 and O2 in 11 epileptic patients with widespread lateralized spike and wave complexes (SWCs). Bipolar records were also made from the antero-posterior derivations. The locations of the maximum PSE coincided with those of the maximum amplitude of SWC in most of the patients. Bipolar derivations with the maximum PSE always included the locations with the maximum PSE obtained from a linked ears reference. Pearson's correlation coefficient between PSE and SWC amplitude was 0.62 +/- 0.14 (mean +/- S.D.) in 11 patients, thus indicating that the scalp distribution of PSE was closely related to that of the amplitude of SWC. These findings suggest that the background EEG is disorganized in or near the epileptogenic focus. A focal background abnormality can therefore be estimated by PSE.

Adolescent↗

PubMedDate not supplied

Application of the entropy theory of perception to auditory intensity discrimination.

The entropy theory of perception has been developed from principles of information theory and predicts both psychophysical data and firing rates of sensory receptors or primary afferents. It has demonstrated how mathematical relationships subsist among many previously unrelated phenomena, such as adaptation processes, reaction times and subjective magnitudes and can be applied to most modalities of perception. The current study demonstrates how the theory can be applied to intensity discrimination of auditory pure tones. A psychophysical experiment of intensity discrimination was carried out under computer control in three practiced normal hearing listeners. Three different derivations for the entropic description of intensity discrimination were applied to the data and analyzed in terms of computer generated best-fitting parameters. The physiological meaning of these parameters is discussed.

Audiometry, Pure-Tone↗

PubMed1995

An expectation maximization reconstruction algorithm for emission tomography with non-uniform entropy prior.

A Bayesian image reconstruction algorithm is proposed for emission tomography. It incorporates the Poisson nature of the noise in the projection data and uses a non-uniform entropy as an a priori probability distribution of the image in a maximum a posteriori (MAP) approach. The expectation maximization (EM) method was applied to find the MAP estimator. The Newton-Raphson numerical method whose convergence and positive solutions are proven, was used to solve the EM problem. The prior mean at iteration k was determined by smoothing the image obtained at iteration k-1. Comparisons between the ML and the MAP algorithm were carried out with a numerical phantom that contains a narrow valley region. The ML solution after 50 iterations was chosen as the initial solution for the MAP algorithm, since the global performance of the ML algorithm deteriorates with increasing number of iterations while its local performance in the valley region is always improving. The resulting algorithm is a compromise between ML who has the best local performance in the valley region and the MAP who has the best global performance.

Algorithms↗

PubMed1992

Aging as a multi-step process characterized by a lowering of entropy production leading the cell to a sequence of defined stages. II. Testing some predictions on aging human fibroblasts in culture.

The concepts of irreversible thermodynamics have been used in order to develop a theory of aging considered as a multi-step process leading the cell through a sequence of defined stages characterized by a lower level of entropy production and finally to a critical level of errors involving cell death (Toussaint et al., 1991). One of the predictions of this model is that external stresses which can be considered as fluctuations would accelerate the evolution of the cell from one state to the other according to the intensity of the stress. Seven morphotypes have been observed in the serially cultivated human fibroblasts, cells passing progressively from one morphotype to the other. In this paper, we experimentally tested the effect of two different molecules, tert-butylhydroperoxide and ethanol, in order to determine their influence on the shift from one morphotype to the other. When applied for a single period of time on cultivated cells, both molecules effectively showed a modification in the pattern of the different morphotypes which was dependent on the stress intensity: a decreased proportion of the early morphotypes and an increased proportion of the late and post-mitotic morphotypes were observed within three days after the stresses. Similar results were obtained when successive stresses were performed at every subculture. The results also indicated that all stages are not equally stable with morphotypes III and IV being the most stable. The positive effect on the increased shift of these cells from one morphotype to the other by two different stresses firms one of the prediction of the thermodynamic model which states that cellular aging can be considered as a multi-step process which can be speeded up by various external modifications.

Cell Division↗

PubMed1994

Deriving non-homogeneous DNA Markov chain models by cluster analysis algorithm minimizing multiple alignment entropy.

Non-homogeneous Markov chain models can represent biologically important regions of DNA sequences. The statistical pattern that is described by these models is usually weak and was found primarily because of strong biological indications. The general method for extracting similar patterns is presented in the current paper. The algorithm incorporates cluster analysis, multiple alignment and entropy minimization. The method was first tested using the set of DNA sequences produced by Markov chain generators. It was shown that artificial gene sequences, which initially have been randomly set up along the multiple alignment panels, are aligned according to the hidden triplet phase. Then the method was applied to real protein-coding sequences and the resulting alignment clearly indicated the triplet phase and produced the parameters of the optimal 3-periodic non-homogeneous Markov chain model. These Markov models were already employed in the GeneMark gene prediction algorithm, which is used in genome sequencing projects. The algorithm can also handle the case in which the sequences to be aligned reveal different statistical patterns, such as Escherichia coli protein-coding sequences belonging to Class II and Class III. The algorithm accepts a random mix of sequences from different classes, and is able to separate them into two groups (clusters), align each cluster separately, and define a non-homogeneous Markov chain model for each sequence cluster.

Algorithms↗

PubMed1987

Enthalpy and entropy of hippuraldehyde hydration and binding to papain.

In aqueous solution hippuraldehyde, PhCONHCH2CHO, is approx. 10-times more extensively hydrated than simple aliphatic aldehydes. Studies of the temperature dependence of the NMR spectrum of hippuraldehyde and its hydrate in 2H2O indicate that the dehydration is endothermic (delta H = 3.9 +/- 0.9 kcal/mol), but entropically favored (delta S = 7.9 +/- 1.9 cal/mol per deg). For simple aliphatic aldehydes the corresponding dehydration is slightly more endothermic, but somewhat more favorable entropically. Fluorescence titration studies show that Kd for the hemithioacetal adduct of hippuraldehyde with papain-SH (1.2 microM at 298 K) is approx. 3000-times smaller than that estimated for simple thiols. Dissociation of hippuraldehyde from papain is endothermic by 18.1 kcal/mol, and this is only partly offset by the favorable entropy change of 33.7 cal/mol per deg. Thus, at least in thermodynamic terms, the binding of this putative 'transition-state analog' to papain is not unlike the binding of other small ligands to the active site of chymotrypsin.

Hippurates↗

PubMed1995

Detection of regularities in heart rate variations by linear and non-linear analysis: power spectrum versus approximate entropy.

Regularity or complexity characteristics of RR interval variations have attained importance in the evaluation of a variety of pathological conditions. Regular periodic fluctuations in heart rate are considered indicators of loss of control in the cardiovascular system and of disturbances in pulmonary function. Methods to detect such loss of cardiopulmonary function have been developed mainly through linear and non-linear system analysis. Both approaches were tested in the present study. MBW, which is the ratio between maximal power spectrum (PS) amplitude and its 3-db bandwidth (BW) in the 0-0.1 Hz frequency range, was calculated and compared for different examples derived from 24 h Holter recordings and for sinusoidal function mixed with varying degrees of noise. Approximate entropy (ApEn), a measure derived from non-linear system analysis has been tested for the same data and compared with the MBW ratio. The results show that MBW effectively differentiates regular and non-regular epochs while ApEn differentiates them in a less optimal manner especially in cases where higher degrees of noise are present but regularity is still observed visually.

Artifacts↗

PubMed1983

Entropy effects on the ion-diffusion rate in transmembrane protein channels.

We treat the transport of univalent cations through pore-like protein channels in biological membranes analytically, using two models (A + B) for the channel and the ion-channel interaction. A Lennard-Jones-type repulsion between the ions and the pore wall is introduced. We also include Van der Waals- and coulomb-type interactions between polar ligands of the pore-forming protein (e.g., carbonyl groups directed towards the axis of the channel) and the migrating particles. In model A, the polar groups are assumed to occur in pairs of dipoles pointing in opposite directions (as in the gramicidin A channel), while in model B the channel is treated as a pore with a radially isotropic charge distribution. In both models the ion-channel interaction leads to the occurrence of periodic potentials, corresponding to quasi-equilibrium and transition state sites of the ion in the pore. The diffusion rate can be calculated employing rate-theoretical concepts on the basis of microscopic parameters. It is demonstrated that the anomaly (inversion of the normal mass effect) for the transport rates of different ions can be related to differences in the activation entropy. The latter quantity is estimated analytically for both models. As a test, we performed numerical calculations with parameters based on the gramicidin A model. The results are in good agreement with experimental data and data from computer simulations. This shows that simple analytic expressions are well suited for predicting trends in the ionic conductivity of protein channels on the basis of microscopic interactions.

Diffusion↗

PubMed1987

Origin of calcium-induced minimum in bulk compressional modulus of lipid membranes. Configurational entropy of adsorbed Ca2+.

Addition of Ca2+ to a dipalmitoylphosphatidylcholine lamellar system decreases the bulk compressional modulus (increases compressibility) of the membrane (S. Aruga, R. Kataoka and S. Mitaku, Biophys. Chem. 21 (1985) 265). The bulk modulus was reported to show a minimum value at 10 mM Ca2+ within the temperature range 20-45 degrees C. In the present report, the occurrence of this minimum in the bulk modulus is explained quantitatively as a result of fluctuation in the number of Ca2+ adsorbed onto the lipid bilayer surface. From this theory, the change in apparent molal volume of Ca2+ upon surface adsorption is estimated to be 5.7 cm3 mol-1, which appears to be a reasonable value. The number of adsorbed Ca2+ at the concentration where the bulk modulus assumes the minimum value is half of the number of allowable adsorption sites on lipid membranes. The configurational entropy of the adsorbed Ca2+ attains a maximum at the minimum point.

1,2-Dipalmitoylphosphatidylcholine↗

PubMed2006

Modeling a syphilis outbreak through space and time using the Bayesian maximum entropy approach.

PURPOSE: The aim of the study is to describe changes in the spatial distribution of syphilis before, during, and after an outbreak in Baltimore, MD, by using Bayesian maximum entropy (BME), a modern geostatistical technique for space-time analysis and mapping. METHODS: BME was used to conduct simple and composite space-time analyses of the density of syphilis infection based on primary, secondary and early latent syphilis cases reported to the Baltimore City Health Department between January 1, 1994, and December 31, 2002. RESULTS: Spatiotemporal covariance plots indicated that the distribution of the density of syphilis cases showed both spatial and temporal dependence. Temporally dependent disease maps suggested that syphilis increased within two geographic core areas of infection and spread outward. A new core area of infection was established to the northwest. As the outbreak waned, density diminished and receded in all core areas. Morbidity remained elevated in the two original central and new northwestern core areas after the outbreak. CONCLUSIONS: Density of syphilis infection was a simple informative measure easily compared across years. The BME approach was useful for quantitatively and qualitatively describing the spatial development and spread of syphilis. Our results are specific to Baltimore; however, the BME approach is generalizable to other settings and diseases.

Baltimore↗