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PubMed2001

A physical origin for functional domain structure in nucleic acids as evidenced by cross-linking entropy: II.

In Part I, cross-linking entropy (CLE) was proposed as a mechanism that limits the size of functional domains of RNA. To test this hypothesis, the theory is developed into an RNA secondary structure prediction filter which is applied to nearest-neighbor secondary structure (NNSS) algorithms that utilize a free energy (FE) minimization strategy. (The NNSS strategies are also referred to as the dynamic programming algorithm in the literature.) The cross-linking entropy for RNA is derived from a generalized Gaussian polymer chain model where the entropic contributions caused by the formation of base pairs (stacking) in RNA are analysed globally. Local entropic contributions are associated with the freezing out of degrees of freedom in the links. Both global and local entropic effects are strongly influenced by the persistence length. The cross-linking entropy provides a physical origin for the size of functional domains in long nucleic acid sequences and may go further to explain as to why the majority of the domain regions in typical sequences tend to be less than 600 nucleotides in length. In addition, improvements were observed in the "best guess" predictive capacity over NNSS prediction strategies. The thermodynamic distribution is more representative of the expected structures and is strongly governed by such physical parameters as the persistence length and the excluded volume. The CLE appears to generalize the tabulated penalties used in NNSS algorithms. The principal parameter influencing this entropy is the persistence length. The model is shown to accomodate a variable persistence length and is capable of describing the folding dynamics of RNA. A two-state kinetic model based on the CLE principle is used to help elucidate the folding kinetics of functional domains in the group I introns.

Animals↗

PubMed1997

The role of entropy in the discrimination between CO and O2 in myoglobin.

Using stopped-flow rapid mixing and flash photolysis techniques, the dissociation rate coefficients of horse carbonmonoxy myoglobin (hMbCO) and oxygenated myoglobin (hMbO2) in aqueous solution have been determined as a function of temperature between 274 and 342 K. From the Arrhenius plot, an activation enthalpy for dissociation of 74 kJ/mol was obtained for both ligands. The pronounced kinetic differences arise from markedly different pre-exponentials. We compare the Arrhenius parameters with those of the association reaction, as measured at cryogenic temperatures. In our analysis we conclude that the entropy loss upon binding of O2 is twice as large as that for CO. Taking reasonable estimates for the frequency factor, the transition state entropy in hMbO2 is located roughly half way in between the entropies of the bound and unbound states. By contrast, the entropy of the transition state in hMbCO appears to be identical to that of the bound state. Possible structural reasons for the different behavior are discussed.

Animals↗

PubMed2006

Are organisms committed to lower their rates of entropy production? Possible relevance to evolution of the Prigogine theorem and the ergodic hypothesis.

The physiology at limiting and stress conditions challenges the current view that the overall reaction of metabolic processes is always far from equilibrium and, therefore, that organisms are not committed to lower their rates of entropy production. Plausibly, critical steps of natural selection takes place at limiting conditions, near equilibrium, in the linear range response of entropy production, and consequently the trend to lower the rate of entropy production could be the fitness arrow of biological evolution. The evolutionary relevance of the Prigogine theorem is discussed in connection with the ergodic hypothesis of Boltzmann. The emergence of metabolic strategies to economise carbon/energy resources, of resource-waste systems like active transport and the irreversible increase in the complexity of organisms during evolution may be consequences of a more general trend of metabolic systems to lower the rates of entropy production.

Biological Evolution↗

PubMed2006

Spectral entropy assessment with auditory evoked potential in neuroanesthesia.

OBJECTIVE: The assessment of the level of anesthesia is a very hard task, since no gold standard has stood out in the past three decades. Middle Latency Auditory Evoked Potential (MLAEP) is one of the most popular neurophysiological tools for anesthesia monitoring. Recently, Spectral Entropy (SpEn) has been introduced: it provides two different parameters, State Entropy (SE) and Response Entropy (RE). The aim of this prospective study is to check SpEn end-point, comparing it to MLAEPs in neurosurgical anesthesia. METHODS: Twenty patients submitted to elective supratentorial neurosurgery for removal of a temporal-parietal meningioma were included in the study. SpEn and MLAEPs were simultaneously monitored using the M-entropy module S/5 (GE Health Care, Helsinki, Finland) and Alaris Medical System AEP-ARX index monitor (AAI) (Kidemosevej, Denmark), respectively. RESULTS: Four thousand and sixty four data points of SE, RE and AAI were recorded and ROC curves comparing AAI to RE and SE showed a highly significant (p<0.0001) area under the curve. The RE and SE cut-off values (showing maximal sensitivity with maximal specificity) to discriminate anesthesia from awake or consciousness sedation were 61 and 58, respectively. However, in a group of data points, low AAI was associated to high SpEn (577 data points for RE and 770 for SE) and vice versa (31 data points for RE and 43 for SE). The prediction probability for SE was 0.977 and for RE was 0.968. CONCLUSIONS: Our results suggest that SpEn is as effective as AAI. SIGNIFICANCE: Our results show that SpEn is able to discriminate between the levels of wakefulness and surgical anesthesia. However, the meaning of data showing a discrepancy between AAI and SpEn is not yet clear and calls for further study.

Adolescent↗

PubMed2003

Photosynthetic models with maximum entropy production in irreversible charge transfer steps.

Steady-state bacterial photosynthesis is modelled as cyclic chemical reaction and is examined with respect to overall efficiency, power transfer efficiency, and entropy production. A nonlinear flux-force relationship is assumed. The simplest two-state kinetic model bears complete analogy with the performance of an ideal (zero ohmic resistance of the P-N junction) solar cell. In both cases power transfer to external load is much higher than the 50% allowed by the impedance matching theorem for the linear flux-force relationship. When maximum entropy production is required in the transition with a load, one obtains high optimal photochemical yield of 97% and power transfer efficiency of 91%. In more complex photosynthetic models, entropy production is maximized in all irreversible electron/proton (non-slip) transitions in an iterative procedure. The resulting steady-state is stable with respect to an extremely wide range of initial values for forward rate constants. Optimal proton current increases proportionally to light intensity and decreases with an increase in the proton-motive force (the backpressure effect). Optimal affinity transfer efficiency is very high and nearly perfectly constant for different light absorption rates and for different electrochemical proton gradients. Optimal overall efficiency (of solar into proton-motive power) ranges from 10% (bacteriorhodopsin) to 19% (chlorophyll-based bacterial photosynthesis). Optimal time constants in a photocycle span a wide range from nanoseconds to milliseconds, just as corresponding experimental constants do. We conclude that photosynthetic proton pumps operate close to the maximum entropy production mode, connecting biological to thermodynamic evolution in a coupled self-amplifying process.

Chlorophyll↗

PubMed2005

Proton affinity of beta-oxalylaminoalanine (BOAA): incorporation of direct entropy correction into the single-reference kinetic method.

A new version of the single-reference-extended kinetic method is presented in which direct entropy correction is incorporated. Results of calibration experiments with the monodentate base pyridine and the bidentate base ethylenediamine are presented for which the method provides proton affinities in excellent agreement with published values and reasonable predictions for the protonation entropies. The method is then used to determine the proton affinity and protonation entropy of the non-protein amino acid beta-oxalylaminoalanine (BOAA). The PA of BOAA is found to be 933.1 +/- 7.8 kJ/mol and a prediction for the protonation entropy of -39 J mol(-1) K(-1) is also obtained, indicating a significant degree of intramolecular hydrogen bonding in the protonated form. These results are supported by hybrid density functional theory calculations at the B3LYP/6-311++G**//B3LYP/6-31+G* level. They indicate that the preferred site of protonation is the alpha-nitrogen atom (PA = 935.0 kJ/mol) and that protonated BOAA has a strong hydrogen bond between the hydrogen on the alpha-amino group and one of the carbonyl oxygen atoms on the side chain.

Amino Acids, Diamino↗

PubMed2004

Entropy production mapping on stretched DNA interacted with proteins.

This paper presents an entropy production mapping (EPM) method for detecting a higher-order structure change of a stretched and immobilized DNA molecule on a cover slip through measuring and mapping an increment of the orientational entropy (defined as "entropy production") of the Watson-Crick base pairs by the interaction of biological factors such as proteins; the stretched DNA molecule undergoes a higher-order structure change by the interaction, so that the orientational entropy at the interaction regions increases because the alignment of the base pairs is reduced at the regions. We demonstrated the utility of this "EPM method" by using a histone-lambda DNA system. It is revealed that the histone interaction region is clearly distinguished from no interaction regions on a stretched lambda DNA molecule immobilized on a cover slip.

Algorithms↗

PubMed2005

Loop entropy and cytochrome c stability.

The loop entropy model proposes that loop closure in a protein becomes entropically more costly as the length of the loop increases. A model protein, cytochrome c, is composed of four loops connecting five helices surrounding a heme-containing core. To test the loop entropy model a series of mutant proteins are constructed with (Gly)n or (Thr)n segments (n = 4-20) inserted between Gly23 and Gly24 of omega loop A of a pseudo wild-type reference protein. Scanning calorimetry shows that protein stability decreases as n increases in the (Gly)n or (Thr)n segment. The dependence of stability on loop length is analyzed with the loop entropy model. Fitting to the model gives a quantitative description of stability differences for the mutant proteins, but with a smaller power-dependence of the probability of loop closure (c-value) than expected from polymer theory. A possible explanation for the discrepancy is that thermodynamically unfavorable loop entropy is partially offset by interactions between the inserted homopolymer and flanking heteropolymer portions of the unfolded protein. The interactions may involve molecular crowding that favors coalescence of the heteropolymer at the insert site and thus closure of the homopolymer loops, possibly as an aspect of the folding code. This may allow use of loop insert mutants to assess the strength of the heteropolymer-encoded folding signals that facilitate loop closure at the insert site.

Amino Acid Sequence↗

PubMed2003

Increased backbone mobility in beta-barrel enhances entropy gain driving binding of N-TIMP-1 to MMP-3.

The high-affinity inhibition of stromelysin 1 (MMP-3) by tissue inhibitor of metalloproteinases 1 (TIMP-1) helps control tissue remodeling and tumor development. The interaction of N-TIMP-1 with the catalytic domain of MMP-3 has been investigated by titration calorimetry and 15N NMR. Their unfavorable enthalpy of binding of +6.5 kcal mol(-1) is unusual among protein-protein associations, deviates from structure-based prediction, and is compensated by a net entropy increase providing at least 18 kcal mol(-1) of favorable free energy of binding at a 1M reference state. The small heat capacity of binding agrees well with the heat capacity predicted from 65% of the surface buried on binding being polar, and suggests that the hydrophobic effect can account for only part of the entropy of binding. Using NMR, binding-induced changes in the backbone of N-TIMP-1 were checked as one possible source of conformational entropy changes. MMP binding slightly increases rigidity in some contact sites in TIMP-1 but increases mobility remotely in the otherwise rigid beta-barrel core of N-TIMP-1, increasing 15N relaxation evidence of pico- to nanosecond and micro- to millisecond fluctuations of beta-strands A-F. Residual dipolar couplings suggest dynamic deviations from X-ray coordinates of the complex. These suggest that the beta-barrel has small backbone conformational fluctuations, while segments of strands betaB, betaE and betaF might experience fluctuations only in their backbone environment. This is a distinctive example of affinity between two well-structured proteins being enhanced by increased conformational entropy in the reservoir of a folding core.

Biophysical Phenomena↗

PubMed2000

Calculation of entropy changes in biological processes: folding, binding, and oligomerization.

Changes in configurational entropy represent one of the major contributions to the thermodynamics of folding, binding, and oligomerization. Methods have been developed to estimate changes in the entropy of the backbone and side chains, and for the loss of translational entropy. These methods have been used in combination with empirical methods that provide estimates of the changes in entropy of solvation as well as estimates of the changes of enthalpy. The results of such calculations are in excellent agreement with experimentally observed values.

Entropy↗

PubMed2003

Application of the maximum entropy method to absorption kinetic rate processes.

The maximum entropy method, originally developed for astronomical image restoration, has already been successfully applied to a variety of biophysical problems. Through numerical inverse Laplace transformation, the method determines the lifetime distribution function with the largest informational entropy. Starting from a flat distribution, it results in the consistent selection of a single distribution from the numerous possible ones that correctly fit the data. In this paper, we discuss the application of the method to kinetic processes that have both rise and decay components, and test the algorithm with different signal to noise ratio generated data. It is proved that the mass conservation constraint can be taken into account by reducing the search to a lower dimensional subspace. The effect of noise on the width of lifetime distribution is studied and it is shown that an inherent entropy connected to the underlying kinetics can be separated from the noise generated entropy. The possibility of the application of the method to the photocycle kinetics of bacteriorhodopsin is also shown.

Absorption↗

PubMed2003

Uses of enthalpy-entropy compensation in protein research.

Cooperative systems of proteins and small molecules form most of biology but are so weakly linked that conventional mass-law formalism requiring exact stoichiometry is inapplicable. The weaknesses cannot be eliminated but using selected families of reactions useful fragmentation of those quantities is often possible. Extra-thermodynamic treatments based on linear-free-energy relationships (LFE) are developed to utilize enthalpy, entropy and volume information not otherwise reliable Linkage systems build around mesophilic proteins are well suited to enforced marriage of linear equations and scaled molecule detail because the ratio of substructure sizes on which folded stability depends is independent of total number of amino-acid residues. Conformational changes in physiological function usually no greater than 0.5 A closely scale to linear thermodynamic changes. The formalisms for use of LFE and compensation relationships are modified to eliminate complications that have previously arisen from incorrect inclusion of the thermal parts of enthalpy and entropy changes in free energy changes. The results are used to remove current confusion about the basis of folded stability in proteins and to minimize the quantitative errors arising from classical treatments of denaturation data. The enthalpy to entropy ratio given by the slope of a compensation plot (its 'compensation temperature') is used to characterize protein construction and function so as to extract machine descriptions of protein linkage systems. In this way the 'fragile' nature of the free-energy surfaces of the myoglobin proteins and the 'strong' character of those surfaces of most other mesophiles can be deduced very simply from the Debye-Waller factors obtained in diffraction studies. The major evolutionary achievement in making proteins big is their crystallike phase behavior. That makes entropy exactly as important as enthalpy so the scalar quantities of small-molecule chemistry can be replaced by the vector quantities that appear necessary to make biology possible.

Entropy↗

PubMed1998

An entropy-based algorithm for detecting clusters of cases and controls and its comparison with a method using nearest neighbours.

A new method for detecting disease clustering based on entropy is presented. For this method cases and controls are plotted on a map. The map is divided into regions. The entropy of the space is calculated as the log of the number of possible ways of placing the cases and controls in the various regions given the total number of cases and controls and the number of cases and controls in each region. The power of the entropy technique is tested against the power of the nearest neighbour technique (NNT). The entropy method is shown to be substantially more powerful than the NNT when there is more than one cluster in the space or when the clusters are near the boundary of the space.

Algorithms↗

PubMed2001

An increase in side chain entropy facilitates effector binding: NMR characterization of the side chain methyl group dynamics in Cdc42Hs.

Cdc42Hs is a signal transduction protein that is involved in cytoskeletal growth and organization. We describe here the methyl side chain dynamics of three forms of (2)H,(13)C,(15)N-Cdc42Hs [GDP-bound (inactive), GMPPCP-bound (active), and GMPPCP/PBD46-bound (effector-bound)] from (13)C-(1)H NMR measurements of deuterium T(1) and T(1 rho) relaxation times. A wide variation in flexibility was observed throughout the protein, with methyl axis order parameters (S(2)(axis)) ranging from 0.2 to 0.4 (highly disordered) in regions near the PBD46 binding site to 0.8--1.0 (highly ordered) in some helices. The side chain dynamics of the GDP and GMPPCP forms are similar, with methyl groups on the PBD46 binding surface experiencing significantly greater mobility (lower S(2)(axis)) than those not on the binding surface. Binding of PBD46 results in a significant increase in the disorder and a corresponding increase in entropy for the majority of methyl groups. Many of the methyl groups that experience an increase in mobility are found in residues that are not part of the PBD46 binding interface. This entropy gain represents a favorable contribution to the overall entropy of effector binding and partially offsets unfavorable entropy losses such as those that occur in the backbone.

Amino Acid Sequence↗

PubMed2001

Thermodynamics of electron transfer in oxygenic photosynthetic reaction centers: a pulsed photoacoustic study of electron transfer in photosystem I reveals a similarity to bacterial reaction centers in both volume change and entropy.

The thermodynamic properties of electron transfer in biological systems are far less known in comparison with that of their kinetics. In this paper the enthalpy and entropy of electron transfer in the purified photosystem I trimer complexes from Synechocystis sp. PCC 6803 have been studied, using pulsed time-resolved photoacoustics on the 1 micros time scale. The volume contraction of reaction centers of photosystem I, which results directly from the light-induced charge separation forming P(700+F(A)/F(B-) from the excited-state P700*, is determined to be -26 +/- 2 A3. The enthalpy of the above electron-transfer reaction is found to be -0.39 +/- 0.1 eV. Photoacoustic estimation of the quantum yield of photochemistry in the purified photosystem I trimer complex showed it to be close to unity. Taking the free energy of the above reaction as the difference of their redox potentials in situ allows us to calculate an apparent entropy change (TDeltaS) of +0.35 +/- 0.1 eV. These values of DeltaV and TDeltaS are similar to those of bacterial reaction centers. The unexpected sign of entropy of electron transfer is tentatively assigned, as in the bacterial case, to the escape of counterions from the surface of the particles. The apparent entropy change of electron transfer in biological system is significant and cannot be neglected.

Chlorophyll↗

PubMed2004

Free energy, entropy, and induced fit in host-guest recognition: calculations with the second-generation mining minima algorithm.

This study applies a novel computational method to study molecular recognition for three sets of synthetic hosts: molecular clips, molecular tweezers, and a synthetic barbiturate receptor. The computed standard free energies of binding for the 12 binding reactions agree closely with experiment and provide insight into the roles of configurational entropy, preorganization, and induced fit in the systems studied. The computed changes in configurational entropy are comparable in magnitude to the changes in mean potential plus solvation energy, and they result primarily from changes in the average width of the energy wells upon binding. A strong correlation is observed between the changes in configurational energy and configurational entropy upon binding, resulting in near-linear compensation analogous to classical entropy-enthalpy compensation.

Algorithms↗

PubMed2006

Computer simulation of the distribution of hexane in a lipid bilayer: spatially resolved free energy, entropy, and enthalpy profiles.

The partitioning behavior of small molecules in lipid bilayers is important in a variety of areas including membrane protein folding and pharmacology. However, the inhomogeneous nature of lipid bilayers on a nanometer length scale complicates experimental studies of membrane partitioning. To gain more insight in the partitioning of a small molecule into the lipid bilayer, we have carried out atomistic computer simulations of hexane in a dioleoyl phosphatidylcholine model membrane. We have been able to obtain spatially resolved free energy, entropy, enthalpy, and heat capacity profiles based on umbrella sampling calculations at three different temperatures. In agreement with experiment, hexane partitions preferentially to the center of the bilayer. This process is driven almost entirely by a favorable entropy change, consistent with the hydrophobic effect. In contrast, partitioning to the densest region of the acyl chains is dominated by a favorable enthalpy change with a small entropy change, which is consistent with the "nonclassical" hydrophobic effect or "bilayer" effect. We explain the features of the entropy and enthalpy profiles in terms of density and free volume in the system.

Computer Simulation↗

PubMed2006

The A-Fx to F(A/B) step in synechocystis 6803 photosystem I is entropy driven.

We have previously reported the enthalpy and volume changes of charge separation in photosystem I from Synechocystis 6803 using pulsed photoacoustics on the microsecond time scale, assigned to the electron-transfer reaction from excited-state P(700) to F(A/B) iron sulfur clusters. In the present work, we focus on the thermodynamics of two steps in photosystem I: (1) P(700) --> A(1)(-)F(X) (<10 ns) and (2) A(1)(-)F(X) --> F(A/B)(-) (20-200 ns). The fit by convolution of photoacoustic waves on the nanosecond and microsecond time scales resolved two kinetic components: (1) a prompt component (<10 ns) with large negative enthalpy (-0.8 +/- 0.1 eV) and large volume change (-23 +/- 2 A(3)), which are assigned to the P(700) --> A(1)(-)F(X) step, and (2) a component with approximately 200 ns lifetime, which has a positive enthalpy (+0.4 +/- 0.2 eV) and a small volume change (-3 +/- 2 A(3)) that are attributed to the A(1)(-)F(X) --> F(A/B)(-) step. For the fast reaction using the redox potentials of A(1)F(X) (-0.67 V) and P(700) (+0.45 V) and the energy of P(700) (1.77 eV), the free energy change for the P(700) --> A(1)(-)F(X) step is -0.63 eV, and thus the entropy change (TDeltaS, T = 25 degrees C) is -0.2 +/- 0.3 eV. For the slow reaction, A(1)(-)F(X) --> F(A/B)(-), taking the free energy of -0.14 eV [Santabara, S.; Heathcote, P; Evans, C. W. Biochim. Biophys. Acta 2005, 1708, 283-310], the entropy change (TDeltaS) is positive, +0.54 +/- 0.3 eV. The positive entropy contribution is larger than the positive enthalpy, which indicates that the A(-)F(X) to F(A/B)(-) step in photosystem I is entropy driven. Other possible contributions to the measured values are discussed.

Acoustics↗