Hydrophobic effect in protein folding and other noncovalent processes involving proteins

Optimizing the Poisson Dielectric Boundary with Explicit Solvent Forces and Energies: Lessons Learned with Atom-Centered Dielectric Functions

Accurate implicit solvent models require parameters that have been optimized in a system- or atom-specific manner on the basis of experimental data or more rigorous explicit solvent simulations. Models based on the Poisson or Poisson-Boltzmann equation are particularly sensitive to the nature and location of the boundary which separates the low dielectric solute from the high dielectric solvent. Here, we present a novel method for optimizing the solute radii, which define the dielectric boundary, on the basis of forces and energies from explicit solvent simulations. We use this method to optimize radii for protein systems defined by AMBER ff99 partial charges and a spline-smoothed solute surface. The spline-smoothed surface is an atom-centered dielectric function that enables stable and efficient force calculations. We explore the relative performance of radii optimized with forces alone and those optimized with forces and energies. We show that our radii reproduce the explicit solvent forces and energies more accurately than four other parameter sets commonly used in conjunction with the AMBER force field, each of which has been appropriately scaled for spline-smoothed surfaces. Finally, we demonstrate that spline-smoothed surfaces show surprising accuracy for small, compact systems but may have limitations for highly solvated protein systems. The optimization method presented here is efficient and applicable to any system with explicit solvent parameters. It can be used to determine the optimal continuum parameters when experimental solvation energies are unavailable and the computational costs of explicit solvent charging free energies are prohibitive.

Parameter optimization in differential geometry based solvation models

Differential geometry (DG) based solvation models are a new class of variational implicit solvent approaches that are able to avoid unphysical solvent-solute boundary definitions and associated geometric singularities, and dynamically couple polar and non-polar interactions in a self-consistent framework. Our earlier study indicates that DG based non-polar solvation model outperforms other methods in non-polar solvation energy predictions. However, the DG based full solvation model has not shown its superiority in solvation analysis, due to its difficulty in parametrization, which must ensure the stability of the solution of strongly coupled nonlinear Laplace-Beltrami and Poisson-Boltzmann equations. In this work, we introduce new parameter learning algorithms based on perturbation and convex optimization theories to stabilize the numerical solution and thus achieve an optimal parametrization of the DG based solvation models. An interesting feature of the present DG based solvation model is that it provides accurate solvation free energy predictions for both polar and non-polar molecules in a unified formulation. Extensive numerical experiment demonstrates that the present DG based solvation model delivers some of the most accurate predictions of the solvation free energies for a large number of molecules.

Order and correlation contributions to the entropy of hydrophobic solvation

The entropy of hydrophobic solvation has been explained as the result of ordered solvation structures, of hydrogen bonds, of the small size of the water molecule, of dispersion forces, and of solvent density fluctuations. We report a new approach to the calculation of the entropy of hydrophobic solvation, along with tests of and comparisons to several other methods. The methods are assessed in the light of the available thermodynamic and spectroscopic information on the effects of temperature on hydrophobic solvation. Five model hydrophobes in SPC/E water give benchmark solvation entropies via Widom's test-particle insertion method, and other methods and models are tested against these particle-insertion results. Entropies associated with distributions of tetrahedral order, of electric field, and of solvent dipole orientations are examined. We find these contributions are small compared to the benchmark particle-insertion entropy. Competitive with or better than other theories in accuracy, but with no free parameters, is the new estimate of the entropy contributed by correlations between dipole moments. Dipole correlations account for most of the hydrophobic solvation entropy for all models studied and capture the distinctive temperature dependence seen in thermodynamic and spectroscopic experiments. Entropies based on pair and many-body correlations in number density approach the correct magnitudes but fail to describe temperature and size dependences, respectively. Hydrogen-bond definitions and free energies that best reproduce entropies from simulations are reported, but it is difficult to choose one hydrogen bond model that fits a variety of experiments. The use of information theory, scaled-particle theory, and related methods is discussed briefly. Our results provide a test of the Frank-Evans hypothesis that the negative solvation entropy is due to structured water near the solute, complement the spectroscopic detection of that solvation structure by identifying the structural feature responsible for the entropy change, and point to a possible explanation for the observed dependence on length scale. Our key results are that the hydrophobic effect, i.e. the signature, temperature-dependent, solvation entropy of nonpolar molecules in water, is largely due to a dispersion force arising from correlations between rotating permanent dipole moments, that the strength of this force depends on the Kirkwood g-factor, and that the strength of this force may be obtained exactly without simulation.

Disorder-to-order transition of MAGI-1 PDZ1 C-terminal extension upon peptide binding: thermodynamic and dynamic insights

PDZ domains are highly abundant protein-protein interaction modules commonly found in multidomain scaffold proteins. The PDZ1 domain of MAGI-1, a protein present at cellular tight junctions that contains six PDZ domains, is targeted by the E6 oncoprotein of the high-risk human papilloma virus. Thermodynamic and dynamic studies using complementary isothermal titration calorimetry and nuclear magnetic resonance (NMR) (15)N heteronuclear relaxation measurements were conducted at different temperatures to decipher the molecular mechanism of this interaction. Binding of E6 peptides to the MAGI-1 PDZ1 domain is accompanied by an unusually large and negative change in heat capacity (ΔC(p)) that is attributed to a disorder-to-order transition of the C-terminal extension of the PDZ1 domain upon E6 binding. Analysis of temperature-dependent thermodynamic parameters and (15)N NMR relaxation data of a PDZ1 mutant in which this disorder-to-order transition was abolished allows the unusual thermodynamic signature of E6 binding to be correlated to local folding of the PDZ1 C-terminal extension. Comparison of the exchange contributions observed for wild-type and mutant proteins explains how variation in the solvent-exposed area may compensate for the loss of conformational entropy and further designates a distinct set of a few residues that mediate this local folding phenomena.

Noncovalently assembled nanotubular porous layers for delaying of heating surface failure

Thermal management to prevent extreme heat surge in integrated electronic systems and nuclear reactors is a critical issue. To delay the thermal surge on the heater effectively, we report the benefit of a three dimensional nanotubular porous layer via noncovalent interactions (hydrophobic forces and hydrogen bonds). To observe the contribution of individual noncovalent interactions in a porous network formation, pristine carbon nanotubes (PCNTs) and oxidatively functionalized carbon nanotubes (FCNTs) were compared. Hydrogen-bonded interwoven nanotubular porous layer showed approximately two times critical heat flux (CHF) increase compared to that of a plain surface. It is assumed that the hydrophilic group-tethered nanotubular porous wicks and enhanced fluidity are the main causes for promoting the CHF increase. Reinforced hydrophilicity assists liquid spreading and capillarity-induced liquid pumping, which are estimated by using Electrochemical Impedance Spectroscopy. Also, shear induced thermal conduction, thermal boundary reduction, and rheology of nanoparticles could attribute to CHF enhancement phenomena.

The hydrophobic effect in a simple isotropic water-like model: Monte Carlo study

Using Monte Carlo computer simulations, we show that a simple isotropic water-like model with two characteristic lengths can reproduce the hydrophobic effect and the solvation properties of small and large non-polar solutes. Influence of temperature, pressure, and solute size on the thermodynamic properties of apolar solute solvation in a water model was systematically studied, showing two different solvation regimes. Small particles can fit into the cavities around the solvent particles, inducing additional order in the system and lowering the overall entropy. Large particles force the solvent to disrupt their network, increasing the entropy of the system. At low temperatures, the ordering effect of small solutes is very pronounced. Above the cross-over temperature, which strongly depends on the solute size, the entropy change becomes strictly positive. Pressure dependence was also investigated, showing a "cross-over pressure" where the entropy and enthalpy of solvation are the lowest. These results suggest two fundamentally different solvation mechanisms, as observed experimentally in water and computationally in various water-like models.

Correlating structure and energetics in protein-ligand interactions: paradigms and paradoxes

Predicting protein-binding affinities of small molecules, even closely related ones, is a formidable challenge in biomolecular recognition and medicinal chemistry. A thermodynamic approach to optimizing affinity in protein-ligand interactions requires knowledge and understanding of how altering the structure of a small molecule will be manifested in protein-binding enthalpy and entropy changes; however, there is a relative paucity of such detailed information. In this review, we examine two strategies commonly used to increase ligand potency. The first of these involves introducing a cyclic constraint to preorganize a small molecule in its biologically active conformation, and the second entails adding nonpolar groups to a molecule to increase the amount of hydrophobic surface that is buried upon binding. Both of these approaches are motivated by paradigms suggesting that protein-binding entropy changes should become more favorable, but paradoxes can emerge that defy conventional wisdom.

Ellipticine binds to a human telomere sequence: an additional mode of action as a putative anticancer agent?

Polyguanine sequences fold into G-quadruplex structures in the presence of monovalent cations. It is accepted that the telomeric DNA region consists of G-quadruplex structure. There are reports that potential G-quadruplex forming motifs are also present in the promoter region of some proto-oncogenes such as c-myc, c-kit, KRAS, etc. Small molecules with the potential to stabilize the telomeric DNA quadruplex have emerged as potential anticancer agents. We have studied the interaction of ellipticine, a putative anticancer agent from a plant source, with a human telomeric DNA sequence (H24). Spectroscopic and calorimetric studies indicate that the association of ellipticine with H24 is an entropically driven phenomenon with a 2:3 (H24:ellipticine) stoichiometry. Though ellipticine binding does not induce any major structural perturbation in H24, the association leads to formation of a complex with enhanced thermal stability. An assay with the telomerase repeat amplification protocol shows that ellipticine inhibits telomerase activity in MDAMB-231 breast cancer cell line extracts. This is the first report of the quadruplex binding ability of ellipticine. Using the results, we propose that along with DNA intercalation and/or topoisomerase II inhibition, interaction with the telomeric DNA region and the resultant inhibition of telomerase activity might be an additional mode of action for its anticancer property.

Dynamic Heterogeneous Dielectric Generalized Born (DHDGB): An implicit membrane model with a dynamically varying bilayer thickness

An extension to the heterogeneous dielectric generalized Born (HDGB) implicit membrane formalism is presented to allow dynamic membrane deformations in response to membrane-inserted biomolecules during molecular dynamic simulations. The flexible membrane is implemented through additional degrees of freedom that represent the membrane deformation at the contact points of a membrane-inserted solute with the membrane. The extra degrees of freedom determine the dielectric and non-polar solvation free energy profiles that are used to obtain the solvation free energy in the presence of the membrane and are used to calculate membrane deformation free energies according to an elastic membrane model. With the dynamic HDGB (DHDGB) model the membrane is able to deform in response to the insertion of charged molecules thereby avoiding the overestimation of insertion free energies with static membrane models. The DHDGB model also allows the membrane to respond to the insertion of membrane-spanning solutes with hydrophobic mismatch. The model is tested with the membrane insertion of amino acid side chain analogs, arginine-containing helices, the WALP23 peptide, and the gramicidin A channel.

High-pressure NMR reveals close similarity between cold and alcohol protein denaturation in ubiquitin

Proteins denature not only at high, but also at low temperature as well as high pressure. These denatured states are not easily accessible for experiment, because usually heat denaturation causes aggregation, whereas cold or pressure denaturation occurs at temperatures well below the freezing point of water or pressures above 5 kbar, respectively. Here we have obtained atomic details of the pressure-assisted, cold-denatured state of ubiquitin at 2,500 bar and 258 K by high-resolution NMR techniques. Under these conditions, a folded, native-like and a disordered state exist in slow exchange. Secondary chemical shifts show that the disordered state has structural propensities for a native-like N-terminal β-hairpin and α-helix and a nonnative C-terminal α-helix. These propensities are very similar to the previously described alcohol-denatured (A-)state. Similar to the A-state, (15)N relaxation data indicate that the secondary structure elements move as independent segments. The close similarity of pressure-assisted, cold-denatured, and alcohol-denatured states with native and nonnative secondary elements supports a hierarchical mechanism of folding and supports the notion that similar to alcohol, pressure and cold reduce the hydrophobic effect. Indeed, at nondenaturing concentrations of methanol, a complete transition from the native to the A-state can be achieved at ambient temperature by varying the pressure from 1 to 2,500 bar. The methanol-assisted pressure transition is completely reversible and can also be induced in protein G. This method should allow highly detailed studies of protein-folding transitions in a continuous and reversible manner.

Variational approach for nonpolar solvation analysis

Solvation analysis is one of the most important tasks in chemical and biological modeling. Implicit solvent models are some of the most popular approaches. However, commonly used implicit solvent models rely on unphysical definitions of solvent-solute boundaries. Based on differential geometry, the present work defines the solvent-solute boundary via the variation of the nonpolar solvation free energy. The solvation free energy functional of the system is constructed based on a continuum description of the solvent and the discrete description of the solute, which are dynamically coupled by the solvent-solute boundaries via van der Waals interactions. The first variation of the energy functional gives rise to the governing Laplace-Beltrami equation. The present model predictions of the nonpolar solvation energies are in an excellent agreement with experimental data, which supports the validity of the proposed nonpolar solvation model.

Characterization of the kinetic and thermodynamic landscape of RNA folding using a novel application of isothermal titration calorimetry

A novel isothermal titration calorimetry (ITC) method was applied to investigate RNA helical packing driven by the GAAA tetraloop-receptor interaction in magnesium and potassium solutions. Both the kinetics and thermodynamics were obtained in individual ITC experiments, and analysis of the kinetic data over a range of temperatures provided Arrhenius activation energies (ΔH(‡)) and Eyring transition state entropies (ΔS(‡)). The resulting rich dataset reveals strongly contrasting kinetic and thermodynamic profiles for this RNA folding system when stabilized by potassium versus magnesium. In potassium, association is highly exothermic (ΔH(25°C) = -41.6 ± 1.2 kcal/mol in 150 mM KCl) and the transition state is enthalpically barrierless (ΔH(‡) = -0.6 ± 0.5). These parameters are significantly positively shifted in magnesium (ΔH(25°C) = -20.5 ± 2.1 kcal/mol, ΔH(‡) = 7.3 ± 2.2 kcal/mol in 0.5 mM MgCl(2)). Mixed salt solutions approximating physiological conditions exhibit an intermediate thermodynamic character. The cation-dependent thermodynamic landscape may reflect either a salt-dependent unbound receptor conformation, or alternatively and more generally, it may reflect a small per-cation enthalpic penalty associated with folding-coupled magnesium uptake.

Influence of acylation on the adsorption of GLP-2 to hydrophobic surfaces

Acylation of proteins with a fatty acid chain has proven useful for prolonging the plasma half-lives of proteins. In formulation of acylated protein drugs, knowledge about the effect of acylation with fatty acids on the adsorption behaviour of proteins at interfaces will be valuable. The aim of this work was to study the effect of acylation on the adsorption of GLP-2 from aqueous solution to a hydrophobic surface by comparing the adsorption of the 3766 Da GLP-2 with that of a GLP-2 variant acylated with a 16-carbon fatty acid chain through a β-alanine linker. Adsorption of GLP-2 and acylated GLP-2 were studied with isothermal titration calorimetry, fixed-angle optical reflectometry and total internal reflection fluorescence. Furthermore, the effect of acylation of GLP-2 on the secondary structure was studied with Far-UV CD. Acylation was observed to have several effects on the adsorption of GLP-2. Acylation increased the amount of GLP-2 adsorbing per unit surface area and decreased the initial adsorption rate of GLP-2. Finally, acylation increased the strength of the adsorption, as judged by the lower fraction desorbing upon rinsing with buffer.

Differential geometry based solvation model II: Lagrangian formulation

Solvation is an elementary process in nature and is of paramount importance to more sophisticated chemical, biological and biomolecular processes. The understanding of solvation is an essential prerequisite for the quantitative description and analysis of biomolecular systems. This work presents a Lagrangian formulation of our differential geometry based solvation models. The Lagrangian representation of biomolecular surfaces has a few utilities/advantages. First, it provides an essential basis for biomolecular visualization, surface electrostatic potential map and visual perception of biomolecules. Additionally, it is consistent with the conventional setting of implicit solvent theories and thus, many existing theoretical algorithms and computational software packages can be directly employed. Finally, the Lagrangian representation does not need to resort to artificially enlarged van der Waals radii as often required by the Eulerian representation in solvation analysis. The main goal of the present work is to analyze the connection, similarity and difference between the Eulerian and Lagrangian formalisms of the solvation model. Such analysis is important to the understanding of the differential geometry based solvation model. The present model extends the scaled particle theory of nonpolar solvation model with a solvent-solute interaction potential. The nonpolar solvation model is completed with a Poisson-Boltzmann (PB) theory based polar solvation model. The differential geometry theory of surfaces is employed to provide a natural description of solvent-solute interfaces. The optimization of the total free energy functional, which encompasses the polar and nonpolar contributions, leads to coupled potential driven geometric flow and PB equations. Due to the development of singularities and nonsmooth manifolds in the Lagrangian representation, the resulting potential-driven geometric flow equation is embedded into the Eulerian representation for the purpose of computation, thanks to the equivalence of the Laplace-Beltrami operator in the two representations. The coupled partial differential equations (PDEs) are solved with an iterative procedure to reach a steady state, which delivers desired solvent-solute interface and electrostatic potential for problems of interest. These quantities are utilized to evaluate the solvation free energies and protein-protein binding affinities. A number of computational methods and algorithms are described for the interconversion of Lagrangian and Eulerian representations, and for the solution of the coupled PDE system. The proposed approaches have been extensively validated. We also verify that the mean curvature flow indeed gives rise to the minimal molecular surface and the proposed variational procedure indeed offers minimal total free energy. Solvation analysis and applications are considered for a set of 17 small compounds and a set of 23 proteins. The salt effect on protein-protein binding affinity is investigated with two protein complexes by using the present model. Numerical results are compared to the experimental measurements and to those obtained by using other theoretical methods in the literature.

Differential geometry based solvation model II: Lagrangian formulation

Solvation is an elementary process in nature and is of paramount importance to more sophisticated chemical, biological and biomolecular processes. The understanding of solvation is an essential prerequisite for the quantitative description and analysis of biomolecular systems. This work presents a Lagrangian formulation of our differential geometry based solvation models. The Lagrangian representation of biomolecular surfaces has a few utilities/advantages. First, it provides an essential basis for biomolecular visualization, surface electrostatic potential map and visual perception of biomolecules. Additionally, it is consistent with the conventional setting of implicit solvent theories and thus, many existing theoretical algorithms and computational software packages can be directly employed. Finally, the Lagrangian representation does not need to resort to artificially enlarged van der Waals radii as often required by the Eulerian representation in solvation analysis. The main goal of the present work is to analyze the connection, similarity and difference between the Eulerian and Lagrangian formalisms of the solvation model. Such analysis is important to the understanding of the differential geometry based solvation model. The present model extends the scaled particle theory of nonpolar solvation model with a solvent-solute interaction potential. The nonpolar solvation model is completed with a Poisson-Boltzmann (PB) theory based polar solvation model. The differential geometry theory of surfaces is employed to provide a natural description of solvent-solute interfaces. The optimization of the total free energy functional, which encompasses the polar and nonpolar contributions, leads to coupled potential driven geometric flow and PB equations. Due to the development of singularities and nonsmooth manifolds in the Lagrangian representation, the resulting potential-driven geometric flow equation is embedded into the Eulerian representation for the purpose of computation, thanks to the equivalence of the Laplace-Beltrami operator in the two representations. The coupled partial differential equations (PDEs) are solved with an iterative procedure to reach a steady state, which delivers desired solvent-solute interface and electrostatic potential for problems of interest. These quantities are utilized to evaluate the solvation free energies and protein-protein binding affinities. A number of computational methods and algorithms are described for the interconversion of Lagrangian and Eulerian representations, and for the solution of the coupled PDE system. The proposed approaches have been extensively validated. We also verify that the mean curvature flow indeed gives rise to the minimal molecular surface and the proposed variational procedure indeed offers minimal total free energy. Solvation analysis and applications are considered for a set of 17 small compounds and a set of 23 proteins. The salt effect on protein-protein binding affinity is investigated with two protein complexes by using the present model. Numerical results are compared to the experimental measurements and to those obtained by using other theoretical methods in the literature.

Analysis of peptides and proteins in their binding to GroEL

The GroEL-GroES is an essential molecular chaperon system that assists protein folding in cell. Binding of various substrate proteins to GroEL is one of the key aspects in GroEL-assisted protein folding. Small peptides may mimic segments of the substrate proteins in contact with GroEL and allow detailed structural analysis of the interactions. A model peptide SBP has been shown to bind to a region in GroEL that is important for binding of substrate proteins. Here, we investigated whether the observed GroEL-SBP interaction represented those of GroEL-substrate proteins, and whether SBP was able to mimic various aspects of substrate proteins in GroE-assisted protein folding cycle. We found that SBP competed with substrate proteins, including α-lactalbumin, rhodanese, and malate dehydrogenase, in binding to GroEL. SBP stimulated GroEL ATP hydrolysis rate in a manner similar to that of α-lactalbumin. SBP did not prevent GroES from binding to GroEL, and GroES association reduced the ATPase rates of GroEL/SBP and GroEL/α-lactalbumin to a comparable extent. Binding of both SBP and α-lactalbumin to apo GroEL was dominated by hydrophobic interaction. Interestingly, association of α-lactalbumin to GroEL/GroES was thermodynamically distinct from that to GroEL with reduced affinity and decreased contribution from hydrophobic interaction. However, SBP did not display such differential binding behaviors to apo GroEL and GroEL/GroES, likely due to the lack of a contiguous polypeptide chain that links all of the bound peptide fragments. Nevertheless, studies using peptides provide valuable information on the nature of GroEL-substrate protein interaction, which is central to understand the mechanism of GroEL-assisted protein folding.

Mapping the protein-protein interface between a toxin and its cognate antitoxin from the bacterial pathogen Streptococcus pyogenes

Protein--protein interactions are ubiquitous and essential for most biological processes. Although new proteomic technologies have generated large catalogs of interacting proteins, considerably less is known about these interactions at the molecular level, information that would aid in predicting protein interactions, designing therapeutics to alter these interactions, and understanding the effects of disease-producing mutations. Here we describe mapping the interacting surfaces of the bacterial toxin SPN (Streptococcus pyogenes NAD(+) hydrolase) in complex with its antitoxin IFS (immunity factor for SPN) by using hydrogen-deuterium amide exchange and electrospray ionization mass spectrometry. This approach affords data in a relatively short time for small amounts of protein, typically 5-7 pmol per analysis. The results show a good correspondence with a recently determined crystal structure of the IFS--SPN complex but additionally provide strong evidence for a folding transition of the IFS protein that accompanies its binding to SPN. The outcome shows that mass-based chemical footprinting of protein interaction surfaces can provide information about protein dynamics that is not easily obtained by other methods and can potentially be applied to large, multiprotein complexes that are out of range for most solution-based methods of biophysical analysis.

Dry molten globule intermediates and the mechanism of protein unfolding

New experimental results show that either gain or loss of close packing can be observed as a discrete step in protein folding or unfolding reactions. This finding poses a significant challenge to the conventional two-state model of protein folding. Results of interest involve dry molten globule (DMG) intermediates, an expanded form of the protein that lacks appreciable solvent. When an unfolding protein expands to the DMG state, side chains unlock and gain conformational entropy, while liquid-like van der Waals interactions persist. Four unrelated proteins are now known to form DMGs as the first step of unfolding, suggesting that such an intermediate may well be commonplace in both folding and unfolding. Data from the literature show that peptide amide protons are protected in the DMG, indicating that backbone structure is intact despite loss of side-chain close packing. Other complementary evidence shows that secondary structure formation provides a major source of compaction during folding. In our model, the major free-energy barrier separating unfolded from native states usually occurs during the transition between the unfolded state and the DMG. The absence of close packing at this barrier provides an explanation for why phi-values, derived from a Brønsted-Leffler plot, depend primarily on structure at the mutational site and not on specific side-chain interactions. The conventional two-state folding model breaks down when there are DMG intermediates, a realization that has major implications for future experimental work on the mechanism of protein folding.

Interaction of synthetic HPV-16 capsid peptides with heparin: thermodynamic parameters and binding mechanism

Capsid proteins binding cell surface proteoglycans is a key early event in human papillomavirus (HPV) infection. The positively charged sequences at the C-terminus of the L1 protein and the N- and C-termini of the L2 protein of HPV-16 can efficiently bind to heparin receptors, which were characterized in the present study by quantitative isothermal titration calorimetry experiments primarily, fluorescence spectroscopy, and static right-angle light scattering. The binding constant, K, was at an order of magnitude of 10(7) M(-1) for the two peptides at the N- and C-termini of HPV-16 L2 and segment b at the C-terminus of HPV-16 L1, while that for other L1 analogues were of a smaller order, illustrating that the heparin binding is a typical sequence-specific and -dependent phenomenon. These results suggest that, in addition to L1, the L2 protein may participate in cell surface attachment during HPV infection. Furthermore, the calorimetry results demonstrated that hydrophobic interactions and hydrogen bonding are involved in peptide binding to heparin in addition to the essential electrostatic interactions. Meanwhile, circular dichroism spectroscopy revealed that binding to heparin does not induce obvious secondary structural changes in the peptides.

Interaction between CK2α and CK2β, the subunits of protein kinase CK2: thermodynamic contributions of key residues on the CK2α surface

The protein Ser/Thr kinase CK2 (former name: casein kinase II) exists predominantly as a heterotetrameric holoenzyme composed of two catalytic subunits (CK2α) bound to a dimer of noncatalytic subunits (CK2β). We undertook a study to further understand how these subunits interact to form the tetramer. To this end, we used recombinant, C-terminal truncated forms of human CK2 subunits that are able to form the holoenzyme. We analyzed the interaction thermodynamics between the binding of CK2α and CK2β as well as the impact of changes in temperature, pH, and the ionization enthalpy of the buffer using isothermal titration calorimetry (ITC). With structure-guided alanine scanning mutagenesis we truncated individual side chains in the hydrophobic amino acid cluster located within the CK2α interface to identify experimentally the amino acids that dominate affinity. The ITC results indicate that Leu41 or Phe54 single mutations were most disruptive to binding of CK2β. Additionally, these CK2α mutants retained their kinase activity. Furthermore, the substitution of Leu41 in combination with Phe54 showed that the individual mutations were not additive, suggesting that the cooperative action of both residues played a role. Interestingly, the replacement of Ile69, which has a central position in the interaction surface of CK2α, only had modest effects. The differences between Leu41, Phe54, and Ile69 in interaction relevance correlate with solvent accessibility changes during the transition from unbound to CK2β-bound CK2α. Identifying residues on CK2α that play a key role in CK2α/CK2β interactions is important for the future generation of small molecule drug design.

Differential geometry based solvation model I: Eulerian formulation

This paper presents a differential geometry based model for the analysis and computation of the equilibrium property of solvation. Differential geometry theory of surfaces is utilized to define and construct smooth interfaces with good stability and differentiability for use in characterizing the solvent-solute boundaries and in generating continuous dielectric functions across the computational domain. A total free energy functional is constructed to couple polar and nonpolar contributions to the salvation process. Geometric measure theory is employed to rigorously convert a Lagrangian formulation of the surface energy into an Eulerian formulation so as to bring all energy terms into an equal footing. By minimizing the total free energy functional, we derive coupled generalized Poisson-Boltzmann equation (GPBE) and generalized geometric flow equation (GGFE) for the electrostatic potential and the construction of realistic solvent-solute boundaries, respectively. By solving the coupled GPBE and GGFE, we obtain the electrostatic potential, the solvent-solute boundary profile, and the smooth dielectric function, and thereby improve the accuracy and stability of implicit solvation calculations. We also design efficient second order numerical schemes for the solution of the GPBE and GGFE. Matrix resulted from the discretization of the GPBE is accelerated with appropriate preconditioners. An alternative direct implicit (ADI) scheme is designed to improve the stability of solving the GGFE. Two iterative approaches are designed to solve the coupled system of nonlinear partial differential equations. Extensive numerical experiments are designed to validate the present theoretical model, test computational methods, and optimize numerical algorithms. Example solvation analysis of both small compounds and proteins are carried out to further demonstrate the accuracy, stability, efficiency and robustness of the present new model and numerical approaches. Comparison is given to both experimental and theoretical results in the literature.

A proposal for the revision of molecular boundary typology

Molecular shape is essential in understanding molecular function, and understanding molecular shape requires definition of molecular boundaries. In this paper, we review the conceptual evolution of three molecular boundary types: the van der Waals surface, the Connolly surface, and the Lee-Richards (accessible) surface. Then, we point out the confusion among the names of these surfaces existing in the literature. Since it is desirable to have a well-defined terminology in a discipline, we propose the standard names of the three molecular boundary types and their corresponding volumes in order to maximize consistency among researchers, respect the first individual who defined or computed a surface type, and promote collaboration between biologists and geometers.

Thermodynamic characterization of acacia gum-beta-lactoglobulin complex coacervation

The interactions of beta-lactoglobulin (BLG) with total acacia gum (TAG) in aqueous solutions have been investigated at pH 4.2 and 25 degrees C. Isothermal titration calorimetry (ITC) has been used to determine the type and magnitude of the energies involved in the complexation process of TAG to BLG. Dynamic light scattering (DLS), electrophoretic mobility (mu(E)), turbidity measurements (tau), and optical microscopy were used as complementary methods on the titration mode to better understand the sum of complicated phenomena at the origin of thermodynamic behavior. Two different binding steps were detected. Thermodynamic parameters indicate a first exothermic step with an association constant K(a1) of (48.4 +/- 3.6) x 10(7) M(-1) that appeared to be mostly enthalpy-driven. A positive heat capacity change was obtained corresponding at the signature for electrostatic interactions. The second binding step, 45 times less affinity (K(a2) = (1.1 +/- 0.1) x 10(7) M(-1)), was largely endothermic and more entropy-driven with a negative value of heat capacity change, indicative of a hydrophobic contribution to the binding process. The population distribution of the different species in solution and their sizes were determined through DLS. Dispersion turbidity of particles markedly increased and reached a maximum at a 0.015 TAG/BLG molar ratio. Largely more numerous coacervates appeared at this molar ratio (0.015) and two different kinds of morphologies were noticed for the large coacervates. Above the TAG/BLG molar ratio of 0.015, dispersions turbidity decreased, which might be due to an excess of negative charges onto particles as revealed by electrophoretic mobility measurements. The results presented in this study should provide information about the thermodynamic mechanisms of TAG/BLG binding processes and will facilitate the application of the formed supramolecular assemblies as functional ingredients in food and nonfood systems.

Charge, hydrophobicity, and confined water: putting past simulations into a simple theoretical framework

Water permeates all life, and mediates forces that are essential to the process of macromolecular self-assembly. Predicting these forces in a given biological context is challenging, since water organizes itself differently next to charged and hydrophobic surfaces, both of which are typically at play on the nanoscale in vivo. In this work, we present a simple statistical mechanical model for the forces water mediates between different confining surfaces, and demonstrate that the model qualitatively unifies a wide range of phenomena known in the simulation literature, including several cases of protein folding under confinement.

Thermodynamics of Protein–Ligand Interactions: History, Presence, and Future Aspects

The understanding of molecular recognition processes of small ligands and biological macromolecules requires a complete characterization of the binding energetics and correlation of thermodynamic data with interacting structures involved. A quantitative description of the forces that govern molecular associations requires determination of changes of all thermodynamic parameters, including free energy of binding (deltaG), enthalpy (deltaH), and entropy (deltaS) of binding and the heat capacity change (deltaCp). A close insight into the binding process is of significant and practical interest, since it provides the fundamental know-how for development of structure-based molecular design-strategies. The only direct method to measure the heat change during complex formation at constant temperature is provided by isothermal titration calorimetry (ITC). With this method one binding partner is titrated into a solution containing the interaction partner, thereby generating or absorbing heat. This heat is the direct observable that can be quantified by the calorimeter. The use of ITC has been limited due to the lack of sensitivity, but recent developments in instrument design permit to measure heat effects generated by nanomol (typically 10-100) amounts of reactants. ITC has emerged as the primary tool for characterizing interactions in terms of thermodynamic parameters. Because heat changes occur in almost all chemical and biochemical processes, ITC can be used for numerous applications, e.g., binding studies of antibody-antigen, protein-peptide, protein-protein, enzyme-inhibitor or enzyme-substrate, carbohydrate-protein, DNA-protein (and many more) interactions as well as enzyme kinetics. Under appropriate conditions data analysis from a single experiment yields deltaH, K(B), the stoichiometry (n), deltaG and deltaS of binding. Moreover, ITC experiments performed at different temperatures yield the heat capacity change (deltaCp). The informational content of thermodynamic data is large, and it has been shown that it plays an important role in the elucidation of binding mechanisms and, through the link to structural data, also in rational drug design. In this review we will present a comprehensive overview to ITC by giving some historical background to calorimetry, outline some critical experimental and data analysis aspects, discuss the latest developments, and give three recent examples of studies published with respect to macromolecule-ligand interactions that have utilized ITC technology.

Interactions of surfactants with lipid membranes

Surfactants are surface-active, amphiphilic compounds that are water-soluble in the micro- to millimolar range, and self-assemble to form micelles or other aggregates above a critical concentration. This definition comprises synthetic detergents as well as amphiphilic peptides and lipopeptides, bile salts and many other compounds. This paper reviews the biophysics of the interactions of surfactants with membranes of insoluble, naturally occurring lipids. It discusses structural, thermodynamic and kinetic aspects of membrane-water partitioning, changes in membrane properties induced by surfactants, membrane solubilisation to micelles and other phases formed by lipid-surfactant systems. Each section defines and derives key parameters, mentions experimental methods for their measurement and compiles and discusses published data. Additionally, a brief overview is given of surfactant-like effects in biological systems, technical applications of surfactants that involve membrane interactions, and surfactant-based protocols to study biological membranes.

Novel behavior of heat of micellization of pluronics F68 and F88 in aqueous solutions

It is well understood that the heat of micellization for surfactants is monotonically decreased along with an increase in temperature. However, this behavior for polymeric surfactants has never been carefully examined. In this study, the heat of micellization of poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) (PEO-PPO-PEO) triblock copolymers (Pluronics F68 and F88) in water as a function of temperature is carefully examined by using a high-sensitivity differential scanning calorimeter (HSDSC). The critical micelle temperature (CMT) decreases along with an increase in the concentration of Pluronic F68 (or F88). The heat of micellization decreases along with an increase in the temperature, as expected, when the CMT is higher than 55 and 42 degrees C for Pluronics F68 and F88, respectively. It is interesting to observe that the heat of micellization increases along with the temperature while the temperature is below 55 and 42 degrees C for Pluronics F68 and F88, respectively. The enthalpy-entropy compensation phenomenon for the micellization of Pluronics F68 and F88 in connection with the hydrophobicity is discussed.

Evidence that the bZIP domains of the Jun transcription factor bind to DNA as monomers prior to folding and homodimerization

The Jun oncoprotein belongs to the AP1 family of transcription factors that is collectively engaged in diverse cellular processes by virtue of their ability to bind to the promoters of a wide spectrum of genes in a DNA sequence-dependent manner. Here, using isothermal titration calorimetry, we report detailed thermodynamics of the binding of bZIP domain of Jun to synthetic dsDNA oligos containing the TRE and CRE consensus promoter elements. Our data suggest that binding of Jun to both sites occurs with indistinguishable affinities but with distinct thermodynamic signatures comprised of favorable enthalpic contributions accompanied by entropic penalty at physiological temperatures. Furthermore, anomalously large negative heat capacity changes observed provoke a model in which Jun loads onto DNA as unfolded monomers coupled with subsequent folding and homodimerization upon association. Taken together, our data provide novel insights into the energetics of a key protein-DNA interaction pertinent to cellular signaling and cancer. Our study underscores the notion that the folding and dimerization of transcription factors upon association with DNA may be a more general mechanism employed in protein-DNA interactions and that the conventional school of thought may need to be re-evaluated.

Thermodynamics and folding pathway of tetraloop receptor-mediated RNA helical packing

Little is known about the thermodynamic forces that drive the folding pathways of higher-order RNA structure. In this study, we employ calorimetric [isothermal titration calorimetry (ITC) and differential scanning calorimetry (DSC)] and spectroscopic (NMR and UV) methods to characterize the thermodynamics of the GAAA tetraloop-receptor interaction, utilizing a previously described bivalent construct. ITC studies indicate that the bivalent interaction is enthalpy driven and highly stable, with a binding constant (K(obs)) of 5.5x10(6) M(-1) and enthalpy (DeltaH(obs)(o)) of -33.8 kcal/mol at 45 degrees C in 20 mM KCl and 2 mM MgCl(2). Thus, we derive the DeltaH(obs)(o) for a single tetraloop-receptor interaction to be -16.9 kcal/mol at these conditions. UV absorbance data indicate that an increase in base stacking quality contributes to the enthalpy of complex formation. These highly favorable thermodynamics are consistent with the known critical role for the tetraloop-receptor motif in the folding of large RNAs. Additionally, a significant heat capacity change (DeltaC(p,obs)(o)) of -0.24 kcal mol(-1) K(-1) was determined by ITC. DSC and UV-monitored thermal denaturation experiments indicate that the bivalent tetraloop-receptor construct follows a minimally five-state unfolding pathway and suggest the observed DeltaC(p,obs)(o) for the interaction results from a temperature-dependent unbound receptor RNA structure.

Sequence specific and high affinity recognition of 5'-ACGCGT-3' by rationally designed pyrrole-imidazole H-pin polyamides: thermodynamic and structural studies

Imidazole (Im) and Pyrrole (Py)-containing polyamides that can form stacked dimers can be programmed to target specific sequences in the minor groove of DNA and control gene expression. Even though various designs of polyamides have been thoroughly investigated for DNA sequence recognition, the use of H-pin polyamides (covalently cross-linked polyamides) has not received as much attention. Therefore, experiments were designed to systematically investigate the DNA recognition properties of two symmetrical H-pin polyamides composed of PyImPyIm (5) or f-ImPyIm (3e, f=formamido) tethered with an ethylene glycol linker. These compounds were created to recognize the cognate 5'-ACGCGT-3' through an overlapped and staggered binding motif, respectively. Results from DNaseI footprinting, thermal denaturation, circular dichroism, surface plasmon resonance and isothermal titration microcalorimetry studies demonstrated that both H-pin polyamides bound with higher affinity than their respective monomers. The binding affinity of formamido-containing H-pin 3e was more than a hundred times greater than that for the tetraamide H-pin 5, demonstrating the importance of having a formamido group and the staggered motif in enhancing affinity. However, compared to H-pin 3e, tetraamide H-pin 5 demonstrated superior binding preference for the cognate sequence over its non-cognates, ACCGGT and AAATTT. Data from SPR experiments yielded binding constants of 1.6x10(8)M(-1) and 2.0x10(10)M(-1) for PyImPyIm H-pin 5 and f-ImPyIm H-pin 3e, respectively. Both H-pins bound with significantly higher affinity (ca. 100-fold) than their corresponding unlinked PyImPyIm 4 and f-ImPyIm 2 counterparts. ITC analyses revealed modest enthalpies of reactions at 298 K (DeltaH of -3.3 and -1.0 kcal mol(-1) for 5 and 3e, respectively), indicating these were entropic-driven interactions. The heat capacities (DeltaC(p)) were determined to be -116 and -499 cal mol(-1)K(-1), respectively. These results are in general agreement with DeltaC(p) values determined from changes in the solvent accessible surface areas using complexes of the H-pins bound to (5'-CCACGCGTGG)(2). According to the models, the H-pins fit snugly in the minor groove and the linker comfortably holds both polyamide portions in place, with the oxygen atoms pointing into the solvent. In summary, the H-pin polyamide provides an important molecular design motif for the discovery of future generations of programmable small molecules capable of binding to target DNA sequences with high affinity and selectivity.

Hydration and conformational mechanics of single, end-tethered elastin-like polypeptides

We investigated the effect of temperature, ionic strength, solvent polarity, and type of guest residue on the force-extension behavior of single, end-tethered elastin-like polypeptides (ELPs), using single molecule force spectroscopy (SMFS). ELPs are stimulus-responsive polypeptides that contain repeats of the five amino acids Val-Pro-Gly-Xaa-Gly (VPGXG), where Xaa is a guest residue that can be any amino acid with the exception of proline. We fitted the force-extension data with a freely jointed chain (FJC) model which allowed us to resolve small differences in the effective Kuhn segment length distributions that largely arise from differences in the hydrophobic hydration behavior of ELP. Our results agree qualitatively with predictions from recent molecular dynamics simulations and demonstrate that hydrophobic hydration modulates the molecular elasticity for ELPs. Furthermore, our results show that SMFS, when combined with our approach for data analysis, can be used to study the subtleties of polypeptide-water interactions and thus provides a basis for the study of hydrophobic hydration in intrinsically unstructured biomacromolecules.

Potential for modulation of the hydrophobic effect inside chaperonins

Despite the spontaneity of some in vitro protein-folding reactions, native folding in vivo often requires the participation of barrel-shaped multimeric complexes known as chaperonins. Although it has long been known that chaperonin substrates fold upon sequestration inside the chaperonin barrel, the precise mechanism by which confinement within this space facilitates folding remains unknown. We examine the possibility that the chaperonin mediates a favorable reorganization of the solvent for the folding reaction. We discuss the effect of electrostatic charge on solvent-mediated hydrophobic forces in an aqueous environment. Based on these physical arguments, we construct a simple, phenomenological theory for the thermodynamics of density and hydrogen-bond order fluctuations in liquid water. Within the framework of this model, we investigate the effect of confinement inside a chaperonin-like cavity on the configurational free energy of water by calculating solvent free energies for cavities corresponding to the different conformational states in the ATP-driven catalytic cycle of the prokaryotic chaperonin GroEL. Our findings suggest that one function of chaperonins may involve trapping unfolded proteins and subsequently exposing them to a microenvironment in which the hydrophobic effect, a crucial thermodynamic driving force for folding, is enhanced.