Molecular recognition and information gain

Molecular recognition is considered as an information transduction process, and information theory is applied to analyze the efficiency of the information transduction during molecular recognition. It is shown that a certain amount of information is gained in the recognition process, and it can be expressed in terms of thermodynamic quantities in the binding process of molecules. The information gain, which can be interpreted as the amount of information extracted from the sequence or structure by a molecule, represents the intrinsic ability of a molecule to recognize specific sequence or structure out of large ambient ensemble based on physical interactions. In contrast with thermodynamic quantities themselves, the information gain is a normalized quantity, and thus serves as a good measure of specificity in the molecular recognition. The information gain, which can be evaluated experimentally, enables us to identify the specific interactions and compare the specificity among different molecules quantitatively. In contrast with macroscopic recognition, specificity of molecular recognition may be severely restricted by the thermodynamic nature of molecular interactions. The thermodynamic meaning of the information gain and its biological implications to molecular recognition are discussed.     

A simple chemical example of hierarchical thermodynamic interactions: the protonation equilibria of inorganic polyprotic acids

A general method for formulating complex thermodynamic systems in terms of hierarchical interactions has been developed, and has been applied in a previous analysis to hemoglobin oxygen binding data. Polyprotic acids can be considered a simple chemical model of thermodynamic interaction between ligand binding events. To further illustrate the hierarchical interaction approach it is applied to the analysis of the thermodynamic interactions between proton binding events in inorganic polyprotic acids. pK values for arsenate, carbonate, chromate, phosphate, phosphite, selenite, sulfide and sulfite were recast into hierarchical interaction terms. The intrinsic K(d,h) for protonation ranged from 8.8 x 10(-13) (M) for phosphate to 1.3 x 10(-6) (M) for chromate. Pairwise interactions (K(d,hh)) between protonation events ranged from 1.3 x 10(4) for phosphite to 9.4 x 10(5) for carbonate. Third order interactions (K(d,hhh)) were 0.91 and 0.51 for arsenate and phosphate, respectively, values relatively close to the no interaction value of 1. A principle feature of systems described by hierarchical interactions is that higher order interactions, representing more complex interactions, are less likely to be significant than lower order interactions, and this is further illustrated by these observations from polyprotic acids. The set of significant hierarchical interaction values can be used to predict values for as yet unobserved events, and projected pK values are made for all the polyprotic acids included in this study. Finally, application of this method to the protonation equilibria of water demonstrates a profound pairwise interaction between protonation events (K(d,hh) = 1.3 x 10(17)), which is attributed to oxygen's small size and lack of polarizability.     

A theoretical model for the prediction of sequence-dependent nucleosome thermodynamic stability

A theoretical model for predicting nucleosome thermodynamic stability in terms of DNA sequence is advanced. The model is based on a statistical mechanical approach, which allows the calculation of the canonical ensemble free energy involved in the competitive nucleosome reconstitution. It is based on the hypothesis that nucleosome stability mainly depends on the bending and twisting elastic energy to transform the DNA intrinsic superstructure into the nucleosomal structure. The ensemble average free energy is calculated starting from the intrinsic curvature, obtained by integrating the dinucleotide step deviations from the canonical B-DNA and expressed in terms of a Fourier series, in the framework of first-order elasticity. The sequence-dependent DNA flexibility is evaluated from the differential double helix thermodynamic stability. A large number of free-energy experimental data, obtained in different laboratories by competitive nucleosome reconstitution assays, are successfully compared to the theoretical results. They support the hypothesis that the stacking energies are the major factor in DNA rigidity and could be a measure of DNA stiffness. A dual role of DNA intrinsic curvature and flexibility emerges in the determination of nucleosome stability. The difference between the experimental and theoretical (elastic) nucleosome-reconstitution free energy for the whole pool of investigated DNAs suggests a significant role for the curvature-dependent DNA hydration and counterion interactions, which appear to destabilize nucleosomes in highly curved DNAs. This model represents an attempt to clarify the main features of the nucleosome thermodynamic stability in terms of physical-chemical parameters and suggests that in molecular systems with a large degree of complexity, the average molecular properties dominate over the local features, as in a statistical ensemble.     

Application of hierarchical thermodynamic interactions to the protonation equilibria of organic polyprotic acids

A general method for formulating complex thermodynamic systems in terms of hierarchical interactions has been developed, and has been applied in a previous analyses to the theoretical analysis of cooperativity in a dimeric protein, to the statistical analysis of hemoglobin oxygen binding data, and to the protonation equilibria of inorganic polyprotic acids. Organic polyprotic acids have served as a demonstration system for the development of concepts and methods for treating complex biochemical equilibria. Glutamic acid is the classic test case for understanding proton-proton interactions in organic polyprotic acids, and this system is analyzed using the concept of hierarchical interactions. Second order interactions were apparent between all three possible proton interactions, as has been established previously. The third order interaction between the three protons was found to be insignificant, indicating that protonation of one site on glutamate has no effect on the interaction between the other two protonation sites. This further reinforces the premise that higher order terms, representing more complex interactions, are less likely to be significant than lower order terms. To allow correlation of the interaction values from glutamate with other organic acids, pairwise interaction values between protonation events were then calculated from known pKd values for a number of diprotic acids and bases. For simple straight chain acids and bases a linear log-log relationship was apparent between the number of intervening atoms between the protons and the pK(d,hh) (pKd of interaction). This relationship extended from three atoms (carbonate) up to 11 atoms (azelaic acid) and applied to both dicarboxylic acids and diamine bases. The pairwise interactions in glutamate also followed this simple relationship.     

Systems biology towards life in silico: mathematics of the control of living cells

Systems Biology is the science that aims to understand how biological function absent from macromolecules in isolation, arises when they are components of their system. Dedicated to the memory of Reinhart Heinrich, this paper discusses the origin and evolution of the new part of systems biology that relates to metabolic and signal-transduction pathways and extends mathematical biology so as to address postgenomic experimental reality. Various approaches to modeling the dynamics generated by metabolic and signal-transduction pathways are compared. The silicon cell approach aims to describe the intracellular network of interest precisely, by numerically integrating the precise rate equations that characterize the ways macromolecules’ interact with each other. The non-equilibrium thermodynamic or ‘lin–log’ approach approximates the enzyme rate equations in terms of linear functions of the logarithms of the concentrations. Biochemical Systems Analysis approximates in terms of power laws. Importantly all these approaches link system behavior to molecular interaction properties. The latter two do this less precisely but enable analytical solutions. By limiting the questions asked, to optimal flux patterns, or to control of fluxes and concentrations around the (patho)physiological state, Flux Balance Analysis and Metabolic/Hierarchical Control Analysis again enable analytical solutions. Both the silicon cell approach and Metabolic/Hierarchical Control Analysis are able to highlight where and how system function derives from molecular interactions. The latter approach has also discovered a set of fundamental principles underlying the control of biological systems. The new law that relates concentration control to control by time is illustrated for an important signal transduction pathway, i.e. nuclear hormone receptor signaling such as relevant to bone formation. It is envisaged that there is much more Mathematical Biology to be discovered in the area between molecules and Life.     

Membrane-bound KRAS approximates an entropic ensemble of configurations

KRAS4B is a membrane-anchored signaling protein and a primary target in cancer research. Predictions from molecular dynamics simulations that have previously shaped our mechanistic understanding of KRAS signaling disagree with recent experimental results from neutron reflectometry, NMR, and thermodynamic binding studies. To gain insight into these discrepancies, we compare this body of biophysical data to back-calculated experimental results from a series of molecular simulations that implement different subsets of molecular interactions. Our results show that KRAS4B approximates an entropic ensemble of configurations at model membranes containing 30% phosphatidylserine lipids, which is not significantly shaped by interactions between the globular G-domain of KRAS4B and the lipid membrane. These findings revise our understanding of KRAS signaling and promote a model in which the protein samples the accessible conformational space in a near-uniform manner while being available to bind to effector proteins.     

Applications of isothermal titration calorimetry in protein science

During the past decade, isothermal titration calorimetry (ITC) has developed from a specialist method for understanding molecular interactions and other biological processes within cells to a more robust, widely used method. Nowadays, ITC is used to investigate all types of protein interactions, including protein-protein interactions, protein-DNA/RNA interactions, protein-small molecule interactions and enzyme kinetics; it provides a direct route to the complete thermodynamic characterization of protein interactions. This review concentrates on the new applications of ITC in protein folding and misfolding, its traditional application in protein interactions, and an overview of what can be achieved in the field of protein science using this method and what developments are likely to occur in the near future. Also, this review discusses some new developments of ITC method in protein science, such as the reverse titration of ITC and the displacement method of ITC.     

Thermodynamics of drug-DNA interactions

Many anticancer, antibiotic, and antiviral drugs exert their primary biological effects by reversibly interacting with nucleic acids. Therefore, these biomolecules represent a major target in drug development strategies designed to produce next generation therapeutics for diseases such as cancer. In order to improve the clinical efficacy of existing drugs and also to design new ones it is necessary to understand the molecular basis of drug-DNA interactions in structural, thermodynamic, and kinetic detail. The past decade has witnessed an increase in the number of rigorous biophysical studies of drug-DNA systems and considerable knowledge has been gained in the energetics of these binding reactions. This is, in part, due to the increased availability of high-sensitivity calorimetric techniques, which have allowed the thermodynamics of drug-DNA interactions to be probed directly and accurately. The focus of this article is to review thermodynamic approaches to examining drug-DNA recognition. Specifically, an overview of a recently developed method of analysis that dissects the binding free energy of these reactions into five component terms is presented. The results of applying this analysis to the DNA binding interactions of both minor groove drugs and intercalators are discussed. The solvent water plays a key role in nucleic acid structure and consequently in the binding of ligands to these biomolecules. Any rational approach to DNA-targeted drug design requires an understanding of how water participates in recognition and binding events. Recent studies examining hydration changes that accompany DNA binding by intercalators will be reviewed. Finally some aspects of cooperativity in drug-DNA interactions are described and the importance of considering cooperative effects when examining these reactions is highlighted.     

Modular response analysis of cellular regulatory networks

The sheer complexity of intracellular regulatory networks, which involve signal transducing, metabolic, and genetic circuits, hampers our ability to carry out a quantitative analysis of their functions. Here, we describe an approach that greatly simplifies this type of analysis by capitalizing on the modular organization of such networks. Steady-state responses of the network as a whole are accounted for in terms of intermodular interactions between the modules alone; processes operating solely within modules need not be considered when analysing signal transfer through the entire network. The intermodular interactions are quantified through (local) response coefficients which populate an interaction map (matrix). This matrix can be derived from a biochemical or molecular biological analysis of (macro) molecular interactions that constitute the regulatory network. The approach is illustrated by two examples: (i) mitogenic signalling through the mitogen-activated protein kinase cascade in the epidermal growth factor receptor network and (ii) regulation of ammonium assimilation in Escherichia coli.     

Effect of hydrodynamic interactions on the diffusion of integral membrane proteins: tracer diffusion in organelle and reconstituted membranes.

A persistent discrepancy exists between theoretical predictions and experimental observations for the diffusion coefficients of integral membrane proteins in lipid bilayers free of immobilized proteins. Current thermodynamic theories overestimate tracer diffusion coefficients at high area fractions. We explore the hypothesis that the combined effect of hydrodynamic and thermodynamic interactions reconciles theory with experiment. We have determined previously the short- and long-time tracer diffusivities, Ds and Dl, respectively, of integral membrane proteins in lipid bilayers as a function of their area fraction, phi. The results are based on two-particle hydrodynamic and thermodynamic interactions and are precise to O(phi). Here we extend the results for Dl to high phi by combining the hydrodynamic results for Ds into theories for Dl based on many-particle thermodynamic interactions. The results compare favorably with the experimental measurements of Dl as a function of protein area fraction for bacteriorhodopsin in reconstituted membranes and for complex III of the mitochondrial inner membrane. The agreement suggests that both hydrodynamic and thermodynamic interactions are important determinants of diffusion coefficients of proteins in lipid bilayers. Additional experiments are required to verify the role of hydrodynamic interactions in protein diffusion in reconstituted systems.     

Swelling of a Lecithin Lamellar Phase Induced by Small Carbohydrate Solutes

In this paper, we consider the effect of adding small carbohydrate solutes (small sugars) to DMPC (1,2-dimyristoyl-sn-glycero-3-phosphocholine) L_α dispersions and the consequences on the force balance at zero osmotic pressure (maximal swelling). We show the importance of long incubations required to obtain samples at thermodynamic equilibrium where molecular diffusion has been completed. The monotonic increase of maximal swelling versus sugar content occurs as a combined effect of the screening of the van der Waals contribution and fluctuations in the lamellar stacks. According to this new approach, it is shown that changes in dielectric properties result in a much less pronounced effect than entropic forces (undulations) generated by the softening of the membranes at high sugar content. However, this sugar-induced swelling cannot be explained quantitatively by adding an entropic contribution to molecular interactions. Quantitative disagreement between the proposed mechanism and our observations is due either to nonadditivity of molecular interactions with entropic forces or to the relation used to account for the entropic contribution.     

Sedimentation equilibrium in macromolecular solutions of arbitrary concentration. I. Self-associating proteins

Relations describing sedimentation equilibrium in solutions of self-associating macromolecules at arbitrary concentration are presented. These relations are obtained by using scaled-particle theory to calculate the thermodynamic activity of each species present at a given radial distance. The results are expected to be valid for solutions of globular proteins under conditions such that interactions between individual solute molecules may be approximated by a hard-particle potential. Sedimentation equilibria in solutions containing either a nonassociating solute or a solute that self-associates according to several different schemes are simulated using the derived relations. The results of these simulations are presented in terms of the dependence of apparent weight-average molecular weight upon solute concentration. Simple empirical relations are presented for estimating the true weight-average molecular weight from the apparent weight-average molecular weight, without reference to any particular self-association scheme. The weight-average molecular weight estimated in this fashion is within a few percent of the true weight-average molecular weight at all experimentally realizable solute concentrations ( < 400 g/L).     

Stereoselective electron transfer between chiral substrates and metal chelates anchored to polypeptides

Electron transfer from ortho-dihydroxy substrates, such as L(+)-ascorbic acid, L-adrenaline, and L-dopa, to iron(III) in [Fe(tetpy)(OH)2]+ ions anchored to sodium poly(L-glutamate) (FeTL) or poly(D-glutamate) (FeTD) was found to proceed stereoselectively when structurally ordered and partially shielded active sites prevent easy approach for redox partner. Oxidant-reductant interactions are then mediated by the polypeptide, whose conformational asymmetry ensures an efficient sterically discriminating environment. Evidence is produced that stereoselectivity chiefly arises from transition state effects, while thermodynamic discrimination is of minor importance. Theoretical models of the diastereomeric electron-transfer complexes were constructed by conformational energy calculations based on Coulombic, nonbonded, and hydrogen-bonded energy terms. The molecular parameters of the models enabled "differential" thermodynamic functions of the diastereomeric pairs and stereoselectivity to be evaluated and satisfactorily compared with those experimentally determined. The models give good insight into the observed topochemical phenomena and support the idea that stereoselectivity is coupled with a remote attack mechanism on the central metal ion where the peripheral tetpy ligand of the active sites acts as an electron-transfer agent.     

N-(thiazol-2-yl)-2-thiophene carboxamide derivatives as Abl inhibitors identified by a pharmacophore-based database screening of commercially available compounds

Suggestions derived from a previous ligand-based ligand design approach and docking calculations aimed at finding compound with affinity toward Abl and molecular scaffolds previously untested as Abl inhibitors, led to the identification of commercially available N-(thiazol-2-yl)-2-thiophene carboxamide derivatives with affinity in a cell-free assay up to low nanomolar concentrations, significantly enhanced with respect to that of their parent compounds previously reported. In particular, among compounds of the Asinex database, molecular docking simulations guided the choice of high-affinity ligands, predicting their binding mode and their interaction pattern with the Abl catalytic binding site. Moreover, affinity of the new compounds was also rationalized in terms of their interactions with the enzyme.     

Effects of thermodynamic nonideality on protein interactions. Equivalence of interpretations based on excluded volume and preferential solvation

Published results on the stabilization of proteins by sucrose (J.C. Lee and S.N. Timasheff, J. Biol. Chem. 256 (1981) 7193) have been reexamined and interpreted in terms of thermodynamic nonideality. The composition dependence of activity coefficients may be accounted for on a statistical-mechanical basis using the concept of excluded volume. An expression is derived in which the effect of sucrose on determination of the partial specific volume of a protein, previously interpreted in terms of preferential protein solvation, is also seen to be attributable to excluded volume. Gel chromatographic studies of the reversible unfolding of alpha-chymotrypsin are presented which demonstrate temperature- and sucrose-mediated changes in the effective volume of the enzyme. These measurements support the quantitative interpretation of the stabilization in terms of thermodynamic nonideality arising from the difference between covolumes for sucrose and the two isomeric states of alpha-chymotrypsin. By establishing the equivalence of the two approaches that have been used to account for the effects of inert solutes on protein transitions, the present investigation eliminates the need for any distinction between such solutes on the basis of molecular size; and also enhances greatly the potential sensitivity of thermodynamic nonideality as a means of probing protein isomerizations, since greater displacement of the equilibrium position may be effected by small rather than by macromolecular solutes present at the same weight concentrations.