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SHED: Shannon entropy descriptors from topological feature distributions.

A novel set of molecular descriptors called SHED (SHannon Entropy Descriptors) is presented. They are derived from distributions of atom-centered feature pairs extracted directly from the topology of molecules. The value of a SHED is then obtained by applying the information-theoretical concept of Shannon entropy to quantify the variability in a feature-pair distribution. The collection of SHED values reflecting the overall distribution of pharmacophoric features in a molecule constitutes its SHED profile. Similarity between pairs of molecules is then assessed by calculating the Euclidean distance of their SHED profiles. Under the assumption that molecules having similar pharmacological profiles should contain similar features distributed in a similar manner, examples are given to show the ability of SHED for scaffold hopping in virtual chemical screening and pharmacological profiling compared to that of substructural BCI fingerprints and three-dimensional GRIND descriptors.

Combinatorial Chemistry Techniques↗

PubMed2002

A new, entropy based method to support waste and resource management decisions.

A new method is presented to quantify the potential of a system to concentrate or dilute substances. The approach is based on a comprehensive material flow analysis and Shannon's statistical entropy function that is transformed by a three-step procedure. The result is a new function that can be applied to any defined system with known mass-flows and substance concentrations. In combination with materials balances, the method yields quantitatively the Relative Statistical Entropy (RSE) and the Substance Concentrating Efficiency (SCE) of a given system. When applied to compare five solid waste incinerators of increasing technology levels, the method (1) gave evidence of the potential of modern incinerators to control material flows and (2) pointed to future directions for further improvement of incineration technology. Case studies demonstrate that the new tool is well suited to support and complement existing methods for decision making in waste and resource management such as LCA.

Conservation of Natural Resources↗

PubMed2002

Ion-pairing molecular recognition in water: aggregation at low concentrations that is entropy-driven.

Investigations into the thermodynamic parameters that characterize the binding of citrate to tris-guanidinium host 1 in water are reported. The parameters K(a), DeltaH degrees, DeltaS degrees, and DeltaG degrees for the binding event were quantified using isothermal titration calorimetry (ITC) techniques. The 1:1 binding stoichiometry was verified by a Job plot derived from NMR data, and the microcalorimetry data was collected for solutions of 1 and citrate ranging from 1 to 100 mM using phosphate buffer concentrations of 5 and 103 mM. At low buffer concentrations (low ionic strength) complexes with greater than 1:1 stoichiometries were observed by ITC, and K(1) was determined to range from 2.0 x 10(3) to 3.0 x 10(3) M(-1). At higher buffer concentrations (high ionic strength) the higher-order complexes were not detected, and K(1) was determined to be 409 M(-1). The 1:1 association of host 1 and citrate is characterized by a large favorable entropy component and negative enthalpy. However, the complexes with higher-order stoichiometry arise from desolvation processes that result from the association of polyions in aqueous media and is entirely entropy driven. This leads to an unusual observation: the dilution of one component of the host/guest complex leads to the formation of the higher-order complexes. The reason for this observation is discussed.

Calorimetry↗

PubMed2003

Anomeric configuration, glycosidic linkage, and the solution conformational entropy of O-linked disaccharides.

Oligosaccharides perform a large number of biological roles, as dictated by their chemical structure and spatial arrangement. While conformational entropies are usually determined in vacuo by computer modeling, molecular recognition processes normally take place in solution. Here I show results of experiments using size-exclusion chromatography (SEC), an entropically driven solution technique. These clearly differentiate the individual contributions of the alpha and beta anomeric configurations and of the (1 --> 4) and (1 --> 6) glycosidic linkages to the solution conformational entropy of O-linked disaccharides. I also distinguish between the members of the epimeric disaccharide pair isomaltose-melibiose and trace the difference to that between their constituent monosaccharides, alpha-glucose and alpha-galactose.

Carbohydrate Conformation↗

PubMed2003

Configurational entropy and cooperativity between ligand binding and dimerization in glycopeptide antibiotics.

Oligomerization and ligand binding are thermodynamically cooperative processes in many biochemical systems, and the mechanisms giving rise to cooperative behavior are generally attributed to changes in structure. In glycopeptide antibiotics, however, these cooperative processes are not accompanied by significant structural changes. To investigate the mechanism by which cooperativity arises in these compounds, fully solvated molecular dynamics simulations and quasiharmonic normal-mode analysis were performed on chloroeremomycin, vancomycin, and dechlorovancomycin. Configurational entropies were derived from the vibrational modes recovered from ligand-free and ligand-bound forms of the monomeric and dimeric species. Results indicate that both ligand binding and dimerization incur an entropic cost as vibrational activity in the central core of the antibiotic is shifted to higher frequencies with lower amplitudes. Nevertheless, ligand binding and dimerization are cooperative because the entropic cost of both processes occurring together is less than the cost of these processes occurring separately. These reductions in configurational entropy are more than sufficient in magnitude to account for the experimentally observed cooperativity between dimerization and ligand binding. We conclude that biochemical cooperativity can be mediated through changes in vibrational activity, irrespective of the presence or absence of concomitant structural change. This may represent a general mechanism of allostery underlying cooperative phenomena in diverse macromolecular systems.

Anti-Bacterial Agents↗

PubMed2005

Calculation of the entropy and free energy from monte carlo simulations of a peptide stretched by an external force.

Hypothetical scanning Monte Carlo (HSMC) is a method for calculating the absolute entropy, S, and free energy, F, from a trajectory generated by any simulation technique. HSMC was applied initially to fluids (argon and water) and later to peptides and self-avoiding walks on a lattice. In this paper we make a step further and apply it to a model of decaglycine (at T = 300 K) in vacuum with constant bond lengths where external stretching forces are exerted at the end points; the changes in S and F are calculated as the forces are increased. The molecule is placed initially in a helical structure, which is changed to an extended structure after a short simulation time due to the exerted forces. This study has relevance to problems in polymers (e.g., rubber elasticity) and to the analysis of experiments where individual molecules are stretched by atomic force microscopy (AFM), for example. The results for S and F are accurate and are significantly better than those obtained by the quasi-harmonic approximation and the local states method. However, the molecule is quite stiff due to the strong bond angle potentials and the extensions are small even for relatively large forces. Correspondingly, as the force is increased the decrease in the entropy is relatively small while the potential energy is enhanced significantly. Still, differences, TDeltaS, for different forces are obtained with very good accuracy of approximately 0.2 kcal/mol.

Computer Simulation↗

PubMed2006

Thermodynamic properties (enthalpy, bond energy, entropy, and heat capacity) and internal rotor potentials of vinyl alcohol, methyl vinyl ether, and their corresponding radicals.

Vinyl alcohols (enols) have been discovered as important intermediates and products in the oxidation and combustion of hydrocarbons, while methyl vinyl ethers are also thought to occur as important combustion intermediates. Vinyl alcohol has been detected in interstellar media, while poly(vinyl alcohol) and poly(methyl vinyl ether) are common polymers. The thermochemical property data on these vinyl alcohols and methyl vinyl ethers is important for understanding their stability, reaction paths, and kinetics in atmospheric and thermal hydrocarbon-oxygen systems. Enthalpies , entropies , and heat capacities (C(p)()(T)) are determined for CH(2)=CHOH, C(*)H=CHOH, CH(2)=C(*)OH, CH(2)=CHOCH(3), C(*)H=CHOCH(3), CH(2)=C(*)OCH(3), and CH(2)=CHOC(*)H(2). Molecular structures, vibrational frequencies, , and C(p)(T) are calculated at the B3LYP/6-31G(d,p) density functional calculation level. Enthalpies are also determined using the composite CBS-Q, CBS-APNO, and G3 methods using isodesmic work reactions to minimize calculation errors. Potential barriers for internal rotors are calculated at the B3LYP/6-31G(d,p) level and used to determine the hindered internal rotational contributions to entropy and heat capacity. The recommended ideal gas phase values calculated in this study are the following (in kcal mol(-1)): -30.0, -28.9 (syn, anti) for CH(2)=CHOH; -25.6, -23.9 for CH(2)=CHOCH(3); 31.3, 33.5 for C(*)H=CHOH; 27.1 for anti-CH(2)=C(*)OH; 35.6, 39.3 for C(*)H=CHOCH(3); 33.5, 32.2 for CH(2)=C(*)OCH(3); 21.3, 22.0 for CH(2)=CHOC(*)H(2). Bond dissociation energies (BDEs) and group additivity contributions are also determined. The BDEs reveal that the O-H, O-CH(3), C-OH, and C-OCH(3) bonds in vinyl alcohol and methyl vinyl ether are similar in energy to those in the aromatic molecules phenol and methyl phenyl ether, being on average around 3 kcal mol(-1) weaker in the vinyl systems. The keto-enol tautomerization enthalpy for the interconversion of vinyl alcohol to acetaldehyde is determined to be -9.7 kcal mol(-1), while the activation energy for this reaction is calculated as 55.9 kcal mol(-1); this is the simplest keto-enol tautomerization and is thought to be important in the reactions of vinyl alcohol. Formation of the formyl methyl radical (vinoxy radical/vinyloxy radical) from both vinyl alcohol and methyl vinyl ether is also shown to be important, and its reactions are discussed briefly.

Computer Simulation↗

PubMed2003

Parametric scaling from species relative abundances to absolute abundances in the computation of biological diversity: a first proposal using Shannon's entropy.

Traditional diversity measures such as the Shannon entropy are generally computed from the species' relative abundance vector of a given community to the exclusion of species' absolute abundances. In this paper, I first mention some examples where the total information content associated with a given community may be more adequate than Shannon's average information content for a better understanding of ecosystem functioning. Next, I propose a parametric measure of statistical information that contains both Shannon's entropy and total information content as special cases of this more general function.

Biodiversity↗

PubMed2000

Redistribution and loss of side chain entropy upon formation of a calmodulin-peptide complex.

The response of the internal dynamics of calcium-saturated calmodulin to the formation of a complex with a peptide model of the calmodulin-binding domain of the smooth muscle myosin light chain kinase has been studied using NMR relaxation methods. The backbone of calmodulin is found to be unaffected by the binding of the domain, whereas the dynamics of side chains are significantly perturbed. The changes in dynamics are interpreted in terms of a heterogeneous partitioning between structure (enthalpy) and dynamics (entropy). These data provide a microscopic view of the residual entropy of a protein in two functional states and suggest extensive enthalpy/entropy exchange during the formation of a protein-protein interface.

Amino Acid Sequence↗

PubMed2005

Entropy rectifies the Brownian steps of kinesin.

Kinesin is a stepping motor that successively produces forward and backward 8-nm steps along microtubules. Under physiological conditions, the steps powering kinesin's motility are biased in one direction and drive various biological motile processes. The physical mechanism underlying the unidirectional bias of the kinesin steps is not fully understood. Here we explored the mechanical kinetics and thermodynamics of forward and backward kinesin steps by analyzing their temperature and load dependence. Results show that the frequency asymmetry between forward and backward steps is produced by entropy. Furthermore, the magnitude of the entropic asymmetry is 6 k(B)T, more than three times greater than expected from a current model, in which a mechanical conformational change within the kinesin molecular structure directly biases the kinesin steps forward. We propose that the stepping direction of kinesin is preferably caused by an entropy asymmetry resulting from the compatibility between the kinesin and microtubule interaction based on their polar structures.

Animals↗

PubMed1998

The dose-response effects of terbutaline on the variability, approximate entropy and fractal dimension of heart rate and blood pressure.

AIMS: To study the dose-response effects of intravenous terbutaline on the cardiovascular and respiratory autonomic nervous regulation. METHODS: The study followed a randomized, placebo-controlled crossover design in six healthy adult volunteers. The terbutaline dose ranged from 10 to 30 microg min(-1) We continuously measured electrocardiogram, finger systolic arterial pressure (SAP) and flow-volume spirometry in supine and upright positions at baseline and during 3 h drug infusion. The periodic variability components of R-R intervals (time between successive heart beats) and SAP in relation to respiration were assessed using spectral analysis techniques. The regularity of the time series was assessed by approximate entropy (ApEn) and the convolutedness by fractal dimension (FD). RESULTS: Terbutaline dose-dependently decreased total variability of R-R intervals, low frequency (LF) variability of R-R intervals (10 s waves), high frequency (HF) variability of R-R intervals (respiratory variability), total variability of SAP, HF variability of SAP, baroreflex sensitivity, plasma potassium concentration, approximate entropy of R-R interval and of SAP as well as fractal dimension of R-R interval. Terbutaline dose-dependently increased heart rate, LF/HF ratios of R-R intervals and of SAP, LF variability of SAP, minute ventilation and plasma terbutaline concentration. CONCLUSIONS: Terbutaline infusion decreases parasympathetic cardiovascular reactivity, baroreflex sensitivity, dimensionality of heart rate and plasma potassium concentration; it increases sympathetic dominance in cardiovascular autonomic balance, minute ventilation, and the regularity of heart rate and blood pressure time series.

Adrenergic beta-Agonists↗

PubMed2004

Case study of enthalpy-entropy noncompensation.

Enthalpy-entropy noncompensation characterizes the relative changes in the hydration thermodynamic functions upon "transforming" ethane into fluoromethane, chloromethane, bromomethane, and iodomethane. An analysis grounded on a simple statistical mechanical theory of hydration allows a plausible rationalization of such enthalpy-entropy noncompensation. It is shown that increasing the strength of solute-water attractive interactions modifying the chemical nature of a part of the solute molecule, but not its size, is a largely noncompensating process for the hydration of noncharged and nonhydrogen bonding species, and dominates the compensating contribution coming from the reorganization of water H bonds.

Computer Simulation↗

PubMed2005

Calculation of the entropy of random coil polymers with the hypothetical scanning Monte Carlo method.

Hypothetical scanning Monte Carlo (HSMC) is a method for calculating the absolute entropy S and free energy F from a given MC trajectory developed recently and applied to liquid argon, TIP3P water, and peptides. In this paper HSMC is extended to random coil polymers by applying it to self-avoiding walks on a square lattice--a simple but difficult model due to strong excluded volume interactions. With HSMC the probability of a given chain is obtained as a product of transition probabilities calculated for each bond by MC simulations and a counting formula. This probability is exact in the sense that it is based on all the interactions of the system and the only approximation is due to finite sampling. The method provides rigorous upper and lower bounds for F, which can be obtained from a very small sample and even from a single chain conformation. HSMC is independent of existing techniques and thus constitutes an independent research tool. The HSMC results are compared to those obtained by other methods, and its application to complex lattice chain models is discussed; we emphasize its ability to treat any type of boundary conditions for which a reference state (with known free energy) might be difficult to define for a thermodynamic integration process. Finally, we stress that the capability of HSMC to extract the absolute entropy from a given sample is important for studying relaxation processes, such as protein folding.

Biopolymers↗

PubMed2006

Conformational entropy of a pseudoknot polymer.

The thermodynamics and kinetics of ABAB pseudoknot formation owing to reversible intrachain reactions are investigated for a flexible polymer based on the off-lattice Monte Carlo simulations. The polymer is made of N hard spheres tethered by inextensible bonds and consists of two reactive pairs AA and BB with binding energies -epsilon1 and -epsilon2, respectively, and three loop lengths (l1, l2, and l3). Although two intermediate states, loops A and B, may be formed, the folding path goes mainly through the intermediate loop whose free energy reduction associated with coil-to-loop crossover is greater. The conformational entropy loss is found to follow DeltaS=alpha ln N+G, where alpha approximately 2.48 for coil-loop crossover and alpha approximately 2.43 for loop-pseudoknot crossover. The constant G depends on the three loop lengths and the two end-to-reactive site lengths (L1 and L2). For a given total loop length, G is maximum when the three loop lengths are equal (l1=l2=l3). When l1=l3, the entropy loss is minimum if l2=0. However, the condition l1 not equal l3 makes G even smaller. This consequence indicates that asymmetry in loop lengths is thermodynamically favorable and this fact is consistent with observations of pseudoknotted RNA structures.

Algorithms↗

PubMed2006

Crucial importance of translational entropy of water in pressure denaturation of proteins.

We present statistical thermodynamics of pressure denaturation of proteins, in which the three-dimensional integral equation theory is employed. It is applied to a simple model system focusing on the translational entropy of the solvent. The partial molar volume governing the pressure dependence of the structural stability of a protein is expressed for each structure in terms of the excluded volume for the solvent molecules, the solvent-accessible surface area (ASA), and a parameter related to the solvent-density profile formed near the protein surface. It is argued that the entropic effect originating from the translational movement of water molecules plays critical roles in the pressure-induced denaturation. We also show that the exceptionally small size of water molecules among dense liquids in nature is crucial for pressure denaturation. An unfolded structure, which is only moderately less compact than the native structure but has much larger ASA, is shown to turn more stable than the native one at an elevated pressure. The water entropy for the native structure is higher than that for the unfolded structure in the low-pressure region, whereas the opposite is true in the high-pressure region. Such a structure is characterized by the cleft and/or swelling and the water penetration into the interior. In another solvent whose molecular size is 1.5 times larger than that of water, however, the inversion of the stability does not occur any longer. The random coil becomes relatively more destabilized with rising pressure, irrespective of the molecular size of the solvent. These theoretical predictions are in qualitatively good agreement with the experimental observations.

Entropy↗

PubMed2006

Using the principle of entropy maximization to infer genetic interaction networks from gene expression patterns.

We describe a method based on the principle of entropy maximization to identify the gene interaction network with the highest probability of giving rise to experimentally observed transcript profiles. In its simplest form, the method yields the pairwise gene interaction network, but it can also be extended to deduce higher-order interactions. Analysis of microarray data from genes in Saccharomyces cerevisiae chemostat cultures exhibiting energy metabolic oscillations identifies a gene interaction network that reflects the intracellular communication pathways that adjust cellular metabolic activity and cell division to the limiting nutrient conditions that trigger metabolic oscillations. The success of the present approach in extracting meaningful genetic connections suggests that the maximum entropy principle is a useful concept for understanding living systems, as it is for other complex, nonequilibrium systems.

Computational Biology↗

PubMed1997

Mutants of rat intestinal fatty acid-binding protein illustrate the critical role played by enthalpy-entropy compensation in ligand binding.

Site-specific variants of rat intestinal fatty acid-binding protein were constructed to identify the molecular interactions that are important for binding to fatty acids (FAs). Several variants displayed affinities that appeared incompatible with the crystal structure of the protein-FA complex. Thermodynamic measurements provided an explanation for these apparent inconsistencies and revealed that binding affinities often inaccurately reported changes in protein-FA interactions because changes in the binding entropy and enthalpy were usually compensatory. These results demonstrate that understanding the effects of amino acid replacements on ligand binding requires measurements of enthalpy and entropy, in addition to affinity.

Animals↗

PubMed2002

Ligand binding promotes the entropy-driven oligomerization of integrin alpha IIb beta 3.

Integrin alpha(IIb)beta(3) clusters on the platelet surface after binding adhesive proteins in a process that regulates signal transduction. However, the intermolecular forces driving integrin self-association are poorly understood. This work provides new insights into integrin clustering mechanisms by demonstrating how temperature and ligand binding interact to affect the oligomeric state of alpha(IIb)beta(3). The ligand-free receptor, solubilized in thermostable octyl glucoside micelles, exhibited a cooperative transition at approximately 43 degrees C, monitored by changes in intrinsic fluorescence and circular dichroism. Both signals changed in a direction opposite to that for global unfolding, and both were diminished upon binding the fibrinogen gamma-chain ligand-mimetic peptide cHArGD. Free and bound receptors also exhibited differential sensitivity to temperature-enhanced oligomerization, as measured by dynamic light scattering, sedimentation velocity, and sedimentation equilibrium. Van't Hoff analyses of dimerization constants for alpha(IIb)beta(3) complexed with cHArGD, cRGD, or eptifibatide yielded large, favorable entropy changes partly offset by unfavorable enthalpy changes. Transmission electron microscopy showed that ligand binding and 37 degrees C incubation enhanced assembly of integrin dimers and larger oligomers linked by tail-to-tail contacts. Interpretation of these images was aided by threading models for alpha(IIb)beta(3) protomers and dimers based on the ectodomain structure of alpha(v)beta(3). We propose that entropy-favorable nonpolar interactions drive ligand-induced integrin clustering and outside-in signaling.

Adult↗