On the relationship between dissipation and the rate of spontaneous entropy production from linear irreversible thermodynamics

When systems are far from equilibrium, the temperature, the entropy and the thermodynamic entropy production are not defined and the Gibbs entropy does not provide useful information about the physical properties of a system. Furthermore, far from equilibrium, or if the dissipative field changes in time, the spontaneous entropy production of linear irreversible thermodynamics becomes irrelevant. In 2000 we introduced a definition for the dissipation function and showed that for systems of arbitrary size, arbitrarily near or far from equilibrium, the time integral of the ensemble average of this quantity can never decrease. In the low-field limit, its ensemble average becomes equal to the spontaneous entropy production of linear irreversible thermodynamics. We discuss how these quantities are related and why one should use dissipation rather than entropy or entropy production for non-equilibrium systems.     

The generation of complexity in evolution: a thermodynamic and information-theoretical discussion.

It is argued that the evolutionary tendency toward complexity derives from the Second Law of thermodynamics and the set of physicochemical constraints provided by the biosphere. Complexity-generating processes provide the means by which thermodynamic information resulting from solar energy influxes can be dissipated. In particular, reductions in energetic information promote the growth of molecular size, and reductions in configurational information promote aperiodicity in molecular sequences. Natural selection converts the sequence entropy generated in these processes into molecular information.     

The thermodynamics of protein-ligand interaction and solvation: insights for ligand design

Isothermal titration calorimetry is able to provide accurate information on the thermodynamic contributions of enthalpy and entropy changes to free energies of binding. The Structure/Calorimetry of Reported Protein Interactions Online database of published isothermal titration calorimetry studies and structural information on the interactions between proteins and small-molecule ligands is used here to reveal general thermodynamic properties of protein-ligand interactions and to investigate correlations with changes in solvation. The overwhelming majority of interactions are found to be enthalpically favoured. Synthetic inhibitors and biological ligands form two distinct subpopulations in the data, with the former having greater average affinity due to more favourable entropy changes on binding. The greatest correlation is found between the binding free energy and apolar surface burial upon complex formation. However, the free-energy contribution per unit area buried is only 30-50% of that expected from earlier studies of transfer free energies of small molecules. A simple probability-based estimator for the maximal affinity of a binding site in terms of its apolar surface area is proposed. Polar surface area burial also contributes substantially to affinity but is difficult to express in terms of unit area due to the small variation in the amount of polar surface buried and a tendency for cancellation of its enthalpic and entropic contributions. Conventionally, the contribution of apolar desolvation to affinity is attributed to gain of entropy due to solvent release. Although data presented here are supportive of this notion, because the correlation of entropy change with apolar surface burial is relatively weak, it cannot, on present evidence, be confidently considered to be correct. Further, thermodynamic changes arising from small differences between ligands binding to individual proteins are relatively large and, in general, uncorrelated with changes in solvation, suggesting that trends identified across widely differing proteins are of limited use in explaining or predicting the effects of ligand modifications.     

A thermodynamic perspective on food webs: quantifying entropy production within detrital-based ecosystems

Because ecosystems fit so nicely the framework of a "dissipative system", a better integration of thermodynamic and ecological perspectives could benefit the quantitative analysis of ecosystems. One obstacle is that traditional food web models are solely based upon the principles of mass and energy conservation, while the theory of non-equilibrium thermodynamics principally focuses on the concept of entropy. To properly cast classical food web models within a thermodynamic framework, one requires a proper quantification of the entropy production that accompanies resource processing of the food web. Here we present such a procedure, which emphasizes a rigorous definition of thermodynamic concepts (e.g. thermodynamic gradient, disequilibrium distance, entropy production, physical environment) and their correct translation into ecological terms. Our analysis provides a generic way to assess the thermodynamic operation of a food web: all information on resource processing is condensed into a single resource processing constant. By varying this constant, one can investigate the range of possible food web behavior within a given fixed physical environment. To illustrate the concepts and methods, we apply our analysis to a very simple example ecosystem: the detrital-based food web of marine sediments. We examine whether entropy production maximization has any ecological relevance in terms of food web functioning.     

Entropy increase and information loss in Markov models of evolution

Markov models of evolution describe changes in the probability distribution of the trait values a population might exhibit. In consequence, they also describe how entropy and conditional entropy values evolve, and how the mutual information that characterizes the relation between an earlier and a later moment in a lineage’s history depends on how much time separates them. These models therefore provide an interesting perspective on questions that usually are considered in the foundations of physics—when and why does entropy increase and at what rates do changes in entropy take place? They also throw light on an important epistemological question: are there limits on what your observations of the present can tell you about the evolutionary past?     

Transmembrane cooperative linkage in cellular adhesion

Various dynamic cellular activities require precise regulation of extracellular adhesion. Here we propose a simple thermodynamic model that does not depend on affinity regulation of transmembrane adhesion molecules but, rather, is based on the principles of collision-limited reactions. We show that the number of transmembrane adhesion molecules forming extracellular bonds depends on the degree of cytoskeletal damping of their lateral mobility (translational entropy) within the plane of the plasma membrane. This type of transmembrane cooperativity between cytoskeletal linkage and the number of extracellular bonds does not require high affinities to the cytoskeleton (micromolar range) and will be particularly effective at low extracellular affinities of adhesion molecules (millimolar range).     

The pH dependence of the electron self-exchange rate of azurin from Pseudomonas aeruginosa as studied by 1H-NMR

The electron self-exchange rate of azurin from Pseudomonas aeruginosa has been measured by proton NMR as a function of temperature under various conditions of pH, buffer and ionic strength. The rate does not appear very sensitive to variations in the latter parameters. Qualitative thermodynamic compensation is observed for the entropy and enthalpy of activation, with a compensation temperature of 309 +/- 7 K, and an average exchange rate of 1.3 X 10(6) M-1 s-1. The observed high entropy of activation contributes significantly to the high exchange rate. The data are analyzed by considering an encounter complex in which two azurin molecules associate along their hydrophobic patches. Copper-to-copper electron transfer over a distance of 1.5 nm in the complex is facilitated by the favourable disposition of the His-117 ligands.     

Thermodynamic compensation upon binding to exosite 1 and the active site of thrombin

Several lines of experimental evidence including amide exchange and NMR suggest that ligands binding to thrombin cause reduced backbone dynamics. Binding of the covalent inhibitor dPhe-Pro-Arg chloromethyl ketone to the active site serine, as well as noncovalent binding of a fragment of the regulatory protein, thrombomodulin, to exosite 1 on the back side of the thrombin molecule both cause reduced dynamics. However, the reduced dynamics do not appear to be accompanied by significant conformational changes. In addition, binding of ligands to the active site does not change the affinity of thrombomodulin fragments binding to exosite 1; however, the thermodynamic coupling between exosite 1 and the active site has not been fully explored. We present isothermal titration calorimetry experiments that probe changes in enthalpy and entropy upon formation of binary ligand complexes. The approach relies on stringent thrombin preparation methods and on the use of dansyl-l-arginine-(3-methyl-1,5-pantanediyl)amide and a DNA aptamer as ligands with ideal thermodynamic signatures for binding to the active site and to exosite 1. Using this approach, the binding thermodynamic signatures of each ligand alone as well as the binding signatures of each ligand when the other binding site was occupied were measured. Different exosite 1 ligands with widely varied thermodynamic signatures cause a similar reduction in ΔH and a concomitantly lower entropy cost upon DAPA binding at the active site. The results suggest a general phenomenon of enthalpy-entropy compensation consistent with reduction of dynamics/increased folding of thrombin upon ligand binding to either the active site or exosite 1.     

Relationship between digital information and thermodynamic stability in bacterial genomes

Ever since the introduction of the Watson-Crick model, numerous efforts have been made to fully characterize the digital information content of the DNA. However, it became increasingly evident that variations of DNA configuration also provide an “analog” type of information related to the physicochemical properties of the DNA, such as thermodynamic stability and supercoiling. Hence, the parallel investigation of the digital information contained in the base sequence with associated analog parameters is very important for understanding the coding capacity of the DNA. In this paper, we represented analog information by its thermodynamic stability and compare it with digital information using Shannon and Gibbs entropy measures on the complete genome sequences of several bacteria, including Escherichia coli (E. coli), Bacillus subtilis (B. subtilis), Streptomyces coelicolor (S. coelicolor), and Salmonella typhimurium (S. typhimurium). Furthermore, the link to the broader classes of functional gene groups (anabolic and catabolic) is examined. Obtained results demonstrate the couplings between thermodynamic stability and digital sequence organization in the bacterial genomes. In addition, our data suggest a determinative role of the genome-wide distribution of DNA thermodynamic stability in the spatial organization of functional gene groups.     

An analysis of membrane phase transition theories based on kink and jog defects

We derive the geometric properties of isomeric defects referred to as kinks and jogs. With the aid of these geometric properties we are able to list in tabular form according to energy and area all possible kink and jog configurations. This information is the kink and jog single chain density of states in discrete form. We relate the properties of the single chain density of states to the thermodynamic bilayer system. Based on the single chain information, we calculate an upper bound on the entropy change of the membrane phase transition and show that it is less than one half the experimental entropy change of the transition. Finally we show that the discrepancy in the macroscopic value of the entropy results from the fact that the total number of single chain kink and jog defects is orders of magnitude too small.     

Solid model compounds and the thermodynamics of protein unfolding.

Analysis of thermodynamic data on the dissolution of solid cyclic dipeptides into water in terms of group additivity provides a rationale for the enthalpy and entropy convergence temperatures observed for small globular protein denaturation and the dissolution of model compounds into water. Convergence temperatures are temperatures at which the extrapolated enthalpy or entropy changes for a series of related compounds take on a common value. At these temperatures (TH* and TS*) the apolar contributions to the corresponding thermodynamic values (delta H degrees and delta S degrees) are shown to be zero. Other contributions such as hydrogen bonding and configurational effects can then be evaluated and their quantitative effects on the stability of globular proteins assessed. It is shown that the denaturational heat capacity is composed of a large positive contribution from the exposure of apolar groups and a significant negative contribution from the exposure of polar groups in agreement with previous results. The large apolar contribution suggests that a liquid hydrocarbon model of the hydrophobic effect does not accurately represent the apolar contribution to delta H degrees of denaturation. Rather, significant enthalpic stabilizing contributions are found to arise from peptide groups (hydrogen bonding). Combining the average structural features of globular proteins (i.e. number of residues, fraction of buried apolar groups and fraction of hydrogen bonds) with their specific group contributions permits a first-order prediction of the thermodynamic properties of proteins. The predicted values compare well with literature values for cytochrome c, myoglobin, ribonuclease A and lysozyme. The major thermodynamic features are described by the number of peptide and apolar groups in a given protein.     

Searching for quantitative entropy-enthalpy compensation among protein variants

Entropy-enthalpy (SH) compensation occurs when a small change in DeltaG is caused by large, and nearly compensatory, changes in DeltaH and DeltaS. It is considered a ubiquitous property of reactions in water. Because water is intimately involved in protein stability, SH compensation among protein variants, if it exists, could lead to important knowledge about protein-water interactions. In light of recent theoretical work on SH compensation, we gathered thermodynamic data for >200 protein variants to seek evidence for the simplest quantitative model of SH compensation (i.e., The van't Hoff denaturation enthalpy divided by the van't Hoff denaturation entropy is a constant). We conclude that either the data are insufficient to support the idea that quantitative SH compensation is a general feature of variant proteins or that such compensation does not exist. This study reinforces the idea that DeltaH-versus-DeltaS plots should not be used to provide evidence for SH compensation.     

Identification of Clausine E as an inhibitor of fat mass and obesity‐associated protein (FTO) demethylase activity

The alkaloids containing a carbazole nucleus are an established class of natural products with wide range of biological activities. A combination of thermodynamic and enzymatic activity studies provides an insight into the recognition of Clausine E by the fat mass and obesity‐associated protein (FTO). The binding of Clausine E to FTO was driven by positive entropy and negative enthalpy changes. Results also indicated that the hydroxyl group was crucial for the binding of small molecules with FTO. The structural and thermodynamic information provides the basis for the design of more effective inhibitors for FTO demethylase activity.     

Kinetic and thermodynamic characterization of HIV-1 protease inhibitors

Interaction kinetic and thermodynamic analyses provide information beyond that obtained in general inhibition studies, and may contribute to the design of improved inhibitors and increased understanding of molecular interactions. Thus, a biosensor-based method was used to characterize the interactions between HIV-1 protease and seven inhibitors, revealing distinguishing kinetic and thermodynamic characteristics for the inhibitors. Lopinavir had fast association and the highest affinity of the tested compounds, and the interaction kinetics were less temperature-dependent as compared with the other inhibitors. Amprenavir, indinavir and ritonavir showed non-linear temperature dependencies of the kinetics. The free energy, enthalpy and entropy (DeltaG, DeltaH, DeltaS) were determined, and the energetics of complex association (DeltaG(on), DeltaH(on), DeltaS(on)) and dissociation (DeltaG(off), DeltaH(off), DeltaS(off)) were resolved. In general, the energetics for the studied inhibitors was in the same range, with the negative free energy change (DeltaG < 0) due primarily to increased entropy (DeltaS > 0). Thus, the driving force of the interaction was increased degrees of freedom in the system (entropy) rather than the formation of bonds between the enzyme and inhibitor (enthalpy). Although the DeltaG(on) and DeltaG(off) were in the same range for all inhibitors, the enthalpy and entropy terms contributed differently to association and dissociation, distinguishing these phases energetically. Dissociation was accompanied by positive enthalpy (DeltaH(off) > 0) and negative entropy (DeltaS(off) < 0) changes, whereas association for all inhibitors except lopinavir had positive entropy changes (DeltaS(on) > 0), demonstrating unique energetic characteristics for lopinavir. This study indicates that this type of data will be useful for the characterization of target-ligand interactions and the development of new inhibitors of HIV-1 protease.     

The concept of structural entropy in tissue-based diagnosis

The concept of entropy is described and its characteristics discussed as applied in tissue-based diagnosis. The concept of entropy includes at least 2 points of view--thermodynamic and informatics perspectives. Entropy can be defined by various methods: a measure of nonreversible energy or of system heterogeneity or as information content of a message. It is a statistical measure and system feature composed of macrosystems and microsystems. The structural entropy of macrosystems relies on definition of individual events and built-in microsystems. It depends on interaction of events and probability distribution (e.g., Gibbs-Boltzmann). The more generalized q-entropy involves account interaction of neighboring events. The thermodynamic concept of structural entropy can be expanded according to the theorem of Prigogine, introducing entropy flow. In biology, cells usually serve for events in the thermodynamic entropy approach. Entropy has been successfully used to describe tissue sections, nuclei and nuclear substructures such as DNA content, chromosomes and AgNORs. The concept of entropy reveals a close relationship of structural entropy and prognosis-associated diagnosis of malignancies. It is useful in prognosis-associated, tissue-based diagnosis in breast, prostate, bladder and lung cancer and is a promising expansion of image analysis in diagnostic agnosis in breast, prostate, bladder and lung cancer and is a promising expansion of image analysis in diagnostic pathology.     

Kauzmann's paradox and the glass transition

Kauzmann showed that the entropy of a liquid decreases rapidly on cooling towards the kinetic glass transition temperature and extrapolates to unreasonable values at lower temperature. The temperature where the extrapolated liquid entropy meets the crystal entropy is now called the Kauzmann temperature. Thermodynamics, with Planck's statement of the third law, shows that the entropy of a liquid cannot be less than the entropy of a glass with the same enthalpy. This is the thermodynamic condition violated by the Kauzmann extrapolation and it suggests a thermodynamic glass transition. Simulations show that, for the simple models studied and regardless of how the liquid entropy is extrapolated, the Kauzmann temperature cannot be reached because the entropy of glasses with the same enthalpy as the liquid is greater than that of the crystal.     

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.