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Structural fluctuations and conformational entropy in proteins: entropy balance in an intramolecular reaction in methemoglobin.

The reversible intramolecular binding of the distal histidine side chain to the heme iron in methemoglobin is of special interest due to the very large negative reaction entropy which overcompensates the large reaction enthalpy. It may be considered as a prominent example of the ability of proteins (including enzymes) to provide global entropy in a local process. In this work new experiments and model calculations are reported which aim at finding the structural elements contributing to the reaction entropy. Geometrical studies prove the implication of the 20 residue E-helix being shifted by more than 2 A. Vibrational entropies are calculated by a procedure derived from the method of Karplus and Kushik. It turns out that neither the histidine alone nor the complete E-helix contribute more than 15 per cent of the required entropy.

Amino Acid Sequence

Thermodynamical studies of oxygen equilibrium of hemoglobin. Nonuniform heats and entropy changes for the individual oxygenation steps and enthalpy-entropy compensation.

Precise oxygen equilibrium curves of human adult hemoglobin were determined by the automatic recording method at several temperatures in the presence and absence of 2,3-diphosphoglycerate (DPG) or inositol hexaphosphate (IHP) with 0.05 M 2,2-bis(hydroxymethyl)-2,2',2''-nitrolotriethanol (bis-tris) buffers (pH 7.4) containing 0.1 M Cl-. The equilibrium data were analyzed according to the Adair scheme, and the heats, deltaHi (i = 1,2,3,4) and the entropy changes, deltaSi (i = 1,2,3,4), for the individual oxygenation steps were obtained. The shape of the equilibrium curve varies on temperature changes whether DPG or IHP is present or absent. In consequence, the deltaHi value depends on i and on the presence of DPG and IHP. Behavior of deltaSi is similar to that of deltaHi. The similar behavior of deltaHi and deltaSi resulted in a compensation phenomenon. The contribution of T cdeltaSi to the free energy change is compensated by the contribution of deltaHi at the first three oxygenation steps but not at the fourth step, and for i = 1,2, and 3 changes of T cdeltaSi value upon the addition of DPG and IHP are compensated by accompanied changes of deltaHi value, where T c (= 260 K) is the compensation temperature. A major part of both the enthalpy-entropy compensation and nonuniformity of deltaHi and deltaSi appears to be attributable to contributions of the oxygen-linked binding of Cl-, DPG and IHP, by hemoglobin. The present results do not necessarily support the earlier idea of Wyman that the cooperative oxygenbinding is essentially an entropy effect.

Adult

Tissue-Level Transcriptomic Entropy Reveals Organ-Specific Aging Patterns and Predicts Cancer Progression.

Although aging and cancer share complex molecular mechanisms, distinguishing causative factors from byproducts remains challenging. Here, we investigated the role of tissue transcriptomic entropy-a measure of transcriptional disorder-in aging and cancer processes by analyzing RNA-sequencing data from over 25,000 samples from human and mouse tissues. We found that entropy changes during aging are highly tissue-specific, with some tissues showing increased entropy while others exhibit decreased or stable entropy levels. Moreover, transcriptomic entropy strongly correlates with age-related processes, showing positive associations with proliferation, cellular senescence, somatic mutation burden, and cellular reprogramming, whereas it negatively correlates with stemness. In cancer, we observed that primary tumors generally display higher entropy than normal tissue, with its levels further increasing in metastatic stages. Cancer treatment modulated entropy patterns in multiple contexts, with changes suggesting a role for transcriptional complexity in tumor plasticity and therapy resistance. Elevated entropy levels predicted poor survival outcomes in multiple cancer types, suggesting its potential as a prognostic marker. Furthermore, differential expression analysis revealed that entropy-associated genes are enriched in developmental processes and depleted in metabolic pathways, indicating a possible link to cellular dedifferentiation. Finally, we found increased entropy in various age-related disorders beyond cancer, suggesting that transcriptomic entropy may be a common feature in age-related diseases. Our findings establish transcriptomic entropy as a fundamental parameter in aging and cancer progression, offering new insights into disease mechanisms.

Humans

Entropies of coding and noncoding sequences of DNA and proteins.

The entropies of protein coding genes from Escherichia coli were calculated according to Boltzmann's formula. Entropies of the coding regions were compared to the entropies of noncoding or miscoding ones. With nucleotides as code units, the entropies of the coding regions, when compared to the entropies of complete sequences (leader and coding region as well as trailer), were seen to be lower but with a marginal statistical significance. With triplets of nucleotides as code units, the entropies of correct reading frames were significantly lower than the entropies of frameshifts +1 and -1. With amino acids as code units, the results were opposite: Biologically functional proteins had significantly higher entropies than proteins translated from the frameshifted sequences. We attempt to explain this paradox with the hypothesis that the genetic code may have the ability of lowering information content (increasing entropy) of proteins while translating them from DNA. This ability might be beneficial to bacteria because it would make the functional proteins more probable (having a higher entropy) than nonfunctional proteins translated from frameshifted sequences.

Amino Acids

Effects of exercise and chills on entropy production in human body.

Entropy flows and changes of entropy content for naked subjects in the respiration calorimeter in exercise and chills are calculated from the energetic data given by Hardy et al. (1938, J. Nutr. 16, 477) and Du Bois (1939, Bull. N.Y. Acad. Med. 15, 143). By use of these values, entropy productions in the human body in exercise and chills are estimated. The entropy production in mild exercise is 1.5-2.4 times as great as that in basal conditions. The entropy production in violent exercise is six to eight times as great as that before exercise. The entropy production in chills in cold environments is about twice as large as that in basal conditions. The entropy production in a malarial chill is about four times of that in normal subjects. These increases in entropy production will be due to the increase in heat production within the body. It seems that there is a parallel between energy and entropy viewpoints for human physiology.

Cold Temperature

Entropy principle for human development, growth and aging.

Entropy productions within nude subjects in respiration calorimeters are calculated from the corresponding energetic data obtained by Du Bois et al. (1952, J. Nutr. 48, 257-293.). The entropy production for men is constant at environmental temperatures from 24-34 degrees C. The metabolic entropy production comprises 98.6% of the total entropy production. The entropy production for women shows a minimum at 30 degrees C (the middle of the neutral zone), a small rise in the cold zone and a trend toward a rise in the warm zone; the average entropy production for women is 8.7% smaller than that for men. The entropy production rises from 0-2 years of age, and decreases rapidly from 2-25 years of age and then gradually to 85 years of age. The entropy production does not seem to achieve a minimum or a level in the lives of men and women. Based on these results, a three-stage hypothesis of entropy production in human life is proposed.

Aged

Public nuisance and entropy increase.

Public nuisance if the inevitable physical conclusion of the second law of thermodynamics, the increase of entropy, under which humans make efforts to build up order, that is, to make states of lower entropy, scattering much entropy into the environment. In other words, humans live on negentropy, negative entropy. Saving of negentropy is the first means of conserving the environment. Soon after C. E. Shanon had introduced the idea of entropy in information theory, N. Wiener showed the relation between entropy of thermodynamics and entropy of information. Wiener showed that the paradox of Maxwell is not a contradiction if we consider the entropy of demon's information. This idea is very suggestive. Moral principles, tax systems, and price mechanisms are effective for the conservation of the environment. Good information systems can conserve good environments. This is the second means. The third way is the use of biological systems. For example, in sewage treatment plants the active sludge purifies polluted water. The reason why microorganisms can select some substances in polluted water is that they have received the information by heredity, the information carried by the double helical structure of DNA.

Environment

Research on multi-trait genome association study method based on Shannon information entropy.

BACKGROUND: Genetic analysis of complex traits is crucial for elucidating disease mechanisms and biological inheritance processes. However, traditional Genome-wide Association Study (GWAS) for single trait often fail to capture the synergistic effects of genetic loci on multiple traits. METHODS: This study proposes a method for analyzing the association between multiple traits and gene regions based on Shannon information entropy. Innovatively, Shannon information entropy is introduced to integrate gene region information as genetic entropy, thereby constructing an Inverse Shannon Entropy-Multi-Trait Association Analysis of Gene Region genetic model (InvSE-MTAGR). Furthermore, a partial regression test is applied to the model to establish the Inverse Partial Shannon Entropy-Multi-Trait Association Analysis of Gene Region method (InvPSE-MTAGR). When performing multi-trait analysis with InvSE-MTAGR, the method achieved statistical significance by accumulating minor effects, thereby enhancing the ability to identify pleiotropic gene regions. RESULTS: The simulation results showed that the proposed multi-trait gene region association analysis method performed well in terms of both Type I error rate control and statistical power. Leveraging tomato and sorghum datasets for validation, the proposed multi-trait gene region association analysis method based on Shannon information entropy accurately pinpointed most of the gene regions harboring candidate genes. CONCLUSION: The study reveals the advantage of multi-trait method in integrating weak-effect pleiotropic signals and capturing the correlation among traits, which provides an efficient theoretical tool for dynamic analysis of complex multi-trait genetic networks and multi-target collaborative breeding of crops.

Genome-Wide Association Study

Thermodynamic changes in the binding of Ca2+ to a mutant human lysozyme (D86/92). Enthalpy-entropy compensation observed upon Ca2+ binding to proteins.

The thermodynamic change in the binding of Ca2+ to a mutant human lysozyme having an engineered Ca2+ binding site (Kuroki, R., Taniyama, Y., Seko, C., Nakamura, H., Kikuchi, M., and Ikehara, M. (1989) Proc. Natl. Acad. Sci. U. S. A. 86, 6903-6907) was analyzed by calorimetry and interpreted in terms of structural information obtained from x-ray crystallography. It was found that the enthalpic contribution for the Ca2+ binding reaction was small, driven primarily by entropy release (10 kcal/mol). This release of entropy was also observed in some organic chelators. Moreover, through the information of the tertiary structures of the apo- and holomutant lysozyme, it was confirmed that the entropy release (10 kcal/mol) upon the binding of Ca2+ arises primarily from the release of bound water molecules hydrating the free Ca2+. Previous studies of Ca2+ binding to proteins have involved significant changes in protein conformation. They can now be reevaluated to determine the contribution of conformational changes to Ca2+ binding. After removing the thermodynamic contribution of Ca2+ binding itself, it is found that upon the binding of Ca2+ the enthalpy change is negative but is almost compensated by the negative entropy change. The negative change in both enthalpy and entropy is characteristic of values seen in the thermodynamic change upon the folding of proteins.

Amino Acid Sequence

Thermodynamics of drug-DNA interactions: entropy-driven intercalation and enthalpy-driven outside binding in the ellipticine series.

Viscosimetric and kinetic results allow one to characterize three modes of DNA binding in the ellipticine series: (1) Ellipticine and its 9 methoxy derivative, which present maximal DNA lengthening properties and bind DNA through a single step mechanism, can be considered as pure intercalators. (2) Ellipticinium derivatives and short-chain substituted oxazolopyridocarbazoles, which present intermediate DNA lengthening properties, bind DNA through a two-step mechanism, one being intercalation. (3) Long-chain substituted oxazolopyridocarbazole derivatives, which display the smallest DNA lengthening properties, bind DNA through a single-step mechanism, probably resulting from an outside binding mode. The viscosimetric and kinetic results are compared with the thermodynamic results obtained from the temperature dependence of the binding constants. It appears that drugs binding on the outside of the DNA double helix tend to have large enthalpy and small entropy contributions, whereas pure intercalating drugs have contributions from both enthalpy and entropy, with entropy dominating by about 2:1. Drugs showing two binding modes exhibit a continuum between the aforementioned extremes, with no breaks in behavior. From this comparison, a correlation between thermodynamic data and DNA binding modes is proposed. Possible molecular implications of both enthalpy and entropy to DNA binding free energy are discussed.

Buffers

Rate of polymer formation and entropy production during competitive replication.

The rate of increase in the mean polymer formation rate constant during competitive replication by Qbeta RNA variants (Kramer et al., 1974) has been shown to agree statistically with the variance in their formation rate constants. This result demonstrates that Fisher's fundamental theorem of natural selection (Fisher, 1930) can define time variations in the mean rate of synthesis for a heterogeneous population of replicating polymers. It was also revealed that RNA replication, far from equilibrium, accompanied a progressive decrease in the order of the entropy production derivative, with respect to time, that reached a maximum (with the next higher order being zero). Maximization of entropy at equilibrium, in compliance with the second law of thermodynamics, therefore appears as a natural extension of the earlier non-equilibrium pattern of entropy production within the system. The order of the zero-valued entropy production derivative was shown to be determined by the chemical affinity, and its rate of decrease was specified by the mean polymer formation rate constant.

Biological Evolution

Observations on maximum entropy processing of MR images.

A maximum entropy (MAXENT) criteria for MR image processing optimizations has previously shown poor performance, but this note observes that there are two entirely different kinds of "data transmission" applications which appear to have been intermixed. In the two cases, "image entropy" actually refers to different kinds of data variables. The previous literature formulations are for transfer of data in which pixel-locations are the transmitted variable, and these pixels may be neither uniform nor constant. The second application concerns the MRI data set for display. Its data variables are image pixel-values of magnetization intensity, and the data transfer mode has the sense of visual display. When MAXENT criteria are modified to address an array of pixel-value intensities, and use a pixel-value information entropy rather than pixel-locations entropy, then successful data processing results. Restoring display visualization from highly nonuniform surface coils for lumbar spine scans are demonstrated, as an example of MAXENT usefulness.

Image Processing, Computer-Assisted

Entropy and cortical activity: information theory and PET findings.

Functional segregation requires convergence and divergence of neuroanatomical connections. Furthermore, the nature of functional segregation suggests that (1) signals in convergent afferents are correlated and (2) signals in divergent efferents are uncorrelated. The aim of this article is to show that this arrangement can be predicted mathematically, using information theory and an idealized model of cortical processing. In theory, the existence of bifurcating axons limits the number of independent output channels from any small cortical region, relative to the number of inputs. An information theoretic analysis of this special (high input:output ratio) constraint indicates that the maximal transfer of information between inputs, to a cortical region, and its outputs will occur when (1) extrinsic connectivity to the area is organized such that the entropy of neural activity in afferents is optimally low and (2) connectivity intrinsic to the region is arranged to maximize the entropy measured at the initial segments of projection neurons. Under the constraints of the model, a low entropy is synonymous with high correlations between axonal firing rates (and vice versa). Consequently this antisymmetric arrangement of functional activity in convergent and divergent connections underlying functional segregation is exactly that predicted by the principle of maximum preservation of information, considered in the context of axonal bifurcation. The hypothesis that firing in convergent afferents is correlated (has low entropy) and spatially coherent was tested using positron emission tomographic measurements of cortical synaptic function in man. This hypothesis was confirmed.

Afferent Pathways

Heat capacity and entropy changes of the major isotype of the toad (Bufo) parvalbumin induced by calcium binding.

The possible structural changes in the major isotype of parvalbumin from the toad (Bufo bufo japonicus) skeletal muscle caused by Ca2+ and Mg2+ binding have been analyzed by microcalorimetric titrations. Parvalbumin was titrated with Ca2+ in both the absence and presence of Mg2+ and with Mg2+ in the absence of Ca2+, at pH 7.0, and at 5 degrees, 15 degrees, and 25 degrees C. The two sites in a molecule were equivalent on Mg2(+)-Ca2+ exchange, but distinguishable on Ca2+ and Mg2+ binding. The reactions of parvalbumin with Ca2+ are exothermic at every temperature in both the absence and presence of Mg2+, but those with Mg2+ are always endothermic except for the binding to site 1 at 25 degrees C. The magnitudes of the hydrophobic and internal vibrational contributions to the heat capacity and entropy changes of parvalbumin on Ca2+ and Mg2+ binding and Mg2(+)-Ca2+ exchange have been estimated by the empirical method of Sturtevant [Sturtevant, J. M. (1977) Proc. Natl Acad. Sci. USA 74, 2236-2240]. Although no major conformational changes were noted between Ca2(+)- and Mg2(+)-bound forms of toad parvalbumin, the conformational difference was larger in Ca2+ (or Mg2+) binding to site 1 than site 2. This may indicate that the metal-free form is much less stable than any form with Ca2+ (or Mg2+) bound at one site at least. On Mg2(+)-Ca2+ exchange, the vibrational as well as hydrophobic entropy is only slightly increased in a parallel manner. In contrast, on Ca2+ (or Mg2+) binding, the hydrophobic entropy increases but the vibrational entropy decreases; the former indicates the sequestering of nonpolar groups from the surface to the interior of a molecule, and the latter suggests that the overall structures are tightened on Ca2+ (or Mg2+) binding but loosened on Mg2(+)-Ca2+ exchange. Despite the clear distinctions in the thermodynamic features, the conformational changes of toad parvalbumin are essentially the same as those of the two isotypes of bullfrog parvalbumins on Ca2+ binding and Mg2(+)-Ca2+ exchange.

Animals

The estimation of the Kolmogorov entropy from a time series and its limitations when performed on EEG.

A method to estimate a lower bound of the Kolmogorov entropy-the so called K2-entropy-from a time series is presented which avoids use of the generalized correlation integral. The influence of the norm is studied. The method is demonstrated on some standard examples. The entropy of the attractor apparent in the EEG of the foetal sheep is estimated and the results are compared with results obtained from synthesized data featuring some basic properties of EEG. This gives an insight into the limitations of the procedure.

Animals

Thermodynamics of the interaction of aristololactam-beta-D-glucoside with DNA. Ionic strength dependence of enthalpy and entropy.

The interaction of aristololactam-beta-D-glucoside with calf thymus DNA has been studied by measuring the changes in the absorbance of the alkaloid over a wide range of temperatures and sodium chloride concentrations. The binding parameters obtained are best fit by the neighbour exclusion model. The salt and temperature dependence of the binding constants are used to estimate the thermodynamic parameters involved in the interaction of the alkaloid with DNA. It is observed that aristololactam-beta-D-glucoside binding to DNA is an exothermic process over the entire range of salt and temperature, and the estimated values of enthalpy and entropy change are strongly dependent on the ionic strength of the solution. The enthalpy and entropy changes compensate one another to produce a relatively small Gibbs' free energy change. The possibility that aristololactam-beta-D-glucoside exists as a monovalent cation at neutral pH and the possible molecular contribution to the enthalpy and entropy changes of the aristololactam-beta-D-glucoside-DNA complex are discussed.

Alkaloids

Quantification of EEG irregularity by use of the entropy of the power spectrum.

A new method for quantifying irregularity of EEGs is proposed in this study. The entropy, an information measure, determines the uniformity of proportion distribution. The peakedness or flatness of the distribution of the EEG power spectrum, representing EEG rhythmicity, can be measured by the entropy, because the power spectrum consists of proportions of power at each frequency. The irregularity of the EEG was measured by the entropy of the power spectrum, called an irregularity index (II). The II was obtained from the power spectrum at F3, F4, C3, C4, P3, P4, O1 and O2 during rest and mental arithmetic in 10 normal subjects. Relative band powers of delta, theta, alpha and beta bands and alpha peak frequency were also obtained. EEGs during rest were significantly more irregular anteriorly than in the occipital areas. Alpha activity was also more irregular in the anterior region. A greater degree of EEG desynchronization during mental arithmetic was found over the left hemisphere and the right occipital area. The II was more sensitive to such desynchronization than alpha band power and alpha peak frequency. The differences in spectral structures between rest and mental arithmetic conditions, mainly over the left hemisphere, were also confirmed by the Kullback-Leibler information.

Adolescent

Morphology of branching trees related to entropy.

Analyses of river systems by geomorphologists have suggested that for minimal entropy production in the movement of water down the river the fall in altitude should be equal in each order of branching of the tributaries. In this paper the same concepts have been applied to the bronchial tree and pulmonary arterial tree, assuming that the energy associated with pressure difference is analogous to that associated with altitude difference in rivers. The morphology of the bronchial tree is such that, given laminar flow or air, the calculated pressure difference across each order is equal. This may indicate that the bronchial tree is designed for minimal entropy production. In the arterial tree, however, this result is not obtained, probably because we do not know how to calculate the pressure drop in blood flowing through a branching system. It is therefore not currently possible, on the basis of this approach, to say whether the pulmonary arterial tree is designed for minimal entropy production or not.

Airway Resistance