Free Energy Of Association Research Articles

Transmembrane Helix Association Affinity Can Be Modulated by Flanking and Noninterfacial Residues

The GxxxG sequence motif mediates the association of transmembrane (TM) helices by providing a site of close contact between them. However, it is not sufficient for strong association. For example, both bacteriophage M13 major coat protein (MCP) and human erythrocyte protein glycophorin A (GpA) contain a GxxxG motif in their TM domains and form a homodimer, but the association affinity of MCP, measured by the ToxCAT in vivo assay, is dramatically weaker than that of GpA. Even when all interfacial residues of MCP were substituted for those of GpA (MCP-GpA), association remained significantly weaker than in GpA. Here we provide an explanation for these experimental observations using molecular dynamics simulations in an implicit membrane (IMM1-GC). The association free energies of GpA29 (GpA with 29 residues all from the wild-type sequence), GpA15p11 (GpA with 15 residues from the wild-type sequence plus 11 flanking residues from the ToxCAT construct), MCP, and MCP-GpA TM helices were calculated and compared. MCP and MCP-GpA have the same flanking residues used in the ToxCAT assay as those in GpA15p11, but the position of the flanking residues relative to the GxxxG motif is different. The calculated association free energies follow experimental observations: the association affinity of MCP-GpA falls between those of GpA15p11 and MCP wild-type. MCP exhibits an equally strong interhelical interaction in the TM domain. A major reason for the weaker association of MCP in the calculations was the noninterfacial residue Lys-40, which in the dimer structure is forced to be buried in the membrane interior. To alleviate the desolvation cost, in MCP and MCP-GpA dimers, Lys-40 gets deprotonated. A second factor that modulates association affinity is the flanking residues. Thanks to them, GpA15p11 exhibits a much stronger association affinity than GpA29. The positioning of the flanking residues is also important, as evidenced by the difference in association affinity between MCP and MCP-GpA on one hand and GpA15p11 on the other. Thus, residues outside the contact interface can exert a significant influence on transmembrane helix association affinity.

Self-Association of Naphthalene at the Air−Ice Interface

We present a molecular dynamics study of the interactions between two molecules of naphthalene present at air-water versus air-ice interfaces. In agreement with the inference from our previous experimental work [Kahan, T. F.; Donaldson, D. J. J. Phys. Chem. A 2007, 111, 1277], the results suggest that self-association of the molecules is more likely to take place on the ice surface than on the water surface. A shorter average distance between the two naphthalene molecules, in conjunction with a stronger interaction energy and free energy of association, point to a stronger tendency to self-associate on ice than on water. The distinct behavior at the two interfaces appears be due to more favorable interactions between naphthalene molecules on liquid water surfaces than on ice surfaces.

Computer Simulation of Protein-Protein Association Processes

Protein-protein interactions are key components of most biological processes. About half of all cellular proteins appear to be parts of larger stable protein complexes whereas transient, pairwise protein-proteins interactions are crucial parts of bioenergetic and signal transduction pathways. Here, we will concentrate on fast assembling protein pairs where complementary electrostatic interactions accelerate the association processes by several orders of magnitude. Brownian and molecular dynamics simulations will be used to identify the energetic principles for these binding phenomena. First, we have studied the association free energy landscape for the barnase:barstar complex by Brownian Dynamics simulations [1]. We will use this system to introduce the concept of diffusional protein protein association on conformational energy landscapes. Interestingly, we found that single protein mutations can drastically alter the shape of the energy landscape and the location of the encounter complex. Secondly, unbiased molecular dynamics simulations were used to study the binding process of a proline-rich peptide to an SH3 domain [2]. In this case, stable complexes were formed within 20 - 130 ns of simulation. Depending on the orientation of the first contacts made, the peptide adopted one of three experimentally known binding modes on the adaptor domain. Association was found to be governed by the synergistic interplay of two types of driving forces for binding. The long-range electrostatic effects play the main role during diffusion and stabilize the transient complexes formed by the electrostatic parts in the interface. At short distances, this then enables partial dewetting at the interfaces to increase the probability for the collapse of the hydrophobic part of the interface and the convergence to the final specific complex. [1] Spaar, A. et al. (2006) Biophys. J. 90, 1913. [2] Ahmad, M. et al. (2008) Angew. Chem. Int. Ed. 47, 7626.

CXC and CC Chemokines Form Mixed Heterodimers: ASSOCIATION FREE ENERGIES FROM MOLECULAR DYNAMICS SIMULATIONS AND EXPERIMENTAL CORRELATIONS

CXC and CC chemokines are involved in numerous biological processes, and their function in situ may be significantly influenced by heterodimer formation, as was recently reported, for example, for CXC chemokines CXCL4/PF4 and CXCL8/IL8 that interact to form heterodimers that modulate chemotactic and cell proliferation activities. Here we used molecular dynamics simulations to determine relative association free energies (overall average and per residue) for homo- and heterodimer pairs of CXC (CXCL4/PF4, CXCL8/IL8, CXCL1/Gro-alpha, and CXCL7/NAP-2) and CC (CCL5/RANTES, CCL2/MCP-1, and CCL8/MCP-2) chemokines. Even though structural homology among monomer folds of all CXC and CC chemokines permits heterodimer assembly, our calculated association free energies depend upon the particular pair of chemokines in terms of the net electrostatic and nonelectrostatic forces involved, as well as (for CC/CXC mixed chemokines) the selection of dimer type (CC or CXC). These relative free energies indicate that association of some pairs of chemokines is more favorable than others. Our approach is validated by correlation of calculated and experimentally determined free energies. Results are discussed in terms of CXC and CC chemokine function and have significant biological implications.

Homodimerization of Neurotensin 1 Receptor Involves Helices 1, 2, and 4: Insights from Quaternary Structure Predictions and Dimerization Free Energy Estimations

A computational approach based upon rigid-body docking, ad hoc filtering, and cluster analysis has been combined with a protocol for dimerization free energy estimations to predict likely interfaces in the neurotensin 1 receptor (NTS1) homodimers. The results of this study suggest that the likely intermonomer interfaces compatible with in vitro binding affinity constants essentially involve helices 1, 2, and 4 and do not include disulfide bridges. The correlative model initially developed on Glycophorin A and herein extended to a G protein-Coupled Receptor (GPCR) appears to be a useful tool for estimating the association free energies of transmembrane proteins independent of the size and shape of the interface. In the desirable future cases, in which in vitro intermonomer binding affinities will be available for other GPCRs, such a correlative model will work as an additional criterion for helping in the selection of the most likely dimers.

Temperature-dependent cooperativity in donor-acceptor substrate binding to the human blood group glycosyltransferases

Affinities of the human blood group glycosyltransferases, alpha-(1-->3)-N-acetylgalactosaminyltransferase (GTA) and alpha-(1-->3)-galactosyltransferase (GTB) for their common acceptor substrate alpha-l-Fucp-(1-->2)-beta-d-Galp-O(CH2)(7)CH3 (1), in the absence and presence of bound uridine 5'-diphosphate (UDP) and Mn2+ were determined using temperature-controlled electrospray ionization mass spectrometry. The presence of bound UDP and Mn(2+) in the donor binding site has a marked influence on the thermodynamic parameters for the association of 1 with GTA and GTB. Both the enthalpy and entropy of association (DeltaH(a), DeltaS(a)) decrease significantly. However, the free energy of association (DeltaG(a)) is unchanged at physiological temperature. The differences in the DeltaH(a) and DeltaS(a) values determined in the presence and absence of bound UDP are attributed to structural changes in the glycosyltransferases induced by the simultaneous binding of 1 and UDP.

Introducing Negative Charges into Bis‐p‐phenylene Crown Ethers: A Study of Bipyridinium‐Based [2]Pseudorotaxanes and [2]Rotaxanes

This paper describes novel host-guest systems comprising viologen cations (guests) and the derivatives of bis-para-phenylene-34-crown-10 (hosts) with anionic groups COO(-) or SO(3)(-). The structure of the resulting charge-compensated host-guest complexes, their association constants and their electrochemical behaviour have been studied. In the solid state, the viologen cations thread the negatively charged crown ethers forming electroneutral zwitterion-like [2]pseudorotaxane salts; in solution this threaded geometry is preserved. The association constants of [2]pseudorotaxane salts incorporating the 1,1'-diethylviologen moiety in solution are significantly higher than those of previously reported analogues. The extrapolated association free energies in non-aqueous media exceed -40 kJ mol(-1) at 25 degrees C. This significant increase of the interaction free energy makes these compounds stable even in aqueous solutions. The association constants of [2]pseudorotaxane salts incorporating sterically more hindered 1,1'-diethyl-3,3'-dimethylviologen moieties are significantly lower. Structurally related [2]rotaxane salts, in which the oppositely charged ionic components are mechanically interlocked, have been prepared in good yields. It has been shown that [2]rotaxane salts incorporating anti-isomers of bisfunctionalised crown ethers are cycloenantiomeric. In both [2]pseudorotaxane and [2]rotaxane salts, the electrostatic interactions between the viologen moieties and the negatively charged crown ethers lead to very significant negative shifts of viologen reduction potentials up to 450 mV. The findings of the present study are valuable for the design of nanoscale molecular electronic devices.

Coarse-grained lattice model for investigating the role of cooperativity in molecular recognition

Equilibrium aspects of the molecular recognition of rigid biomolecules are investigated using coarse-grained lattice models. The analysis is carried out in two stages. First, an ensemble of probe molecules is designed with respect to the target biomolecule. The recognition ability of the probe ensemble is then investigated by calculating the free energy of association. The influence of cooperative and anticooperative effects accompanying the association of the target and probe molecules is studied. Numerical findings are presented and compared to analytical results which can be obtained in the limit of dominating cooperativity and in the mean-field formulation of the models.

Quantitative Model for Binary Measurements of Protein-Protein Interactions

We develop a stochastic model for quantifying the binary measurements of protein-protein interactions. A key concept in the model is the binary response function (BRF) which represents the conditional probability of successfully detecting a protein-protein interaction with a given number of the protein complexes. A popular form of the BRF is introduced and the effect of the sharpness (Hill's coefficient) of this function is studied. Our model is motivated by the recently developed yeast two-hybrid method for measuring protein-protein interaction networks. We suggest that the same phenomenological BRF can also be applied to the mass spectroscopic measurement of protein-protein interactions. Based on the model, we investigate the contributions to the network topology of protein-protein interactions from (i) the distribution of protein binary association free energy, and from (ii) the cellular protein abundance. It is concluded that the association constants among different protein pairs cannot be totally independent. It is also shown that not only the association constants but also the protein abundance could be a factor in producing the power-law degree distribution of protein-protein interaction networks.

In Silico Screening of Mutational Effects on Transmembrane Helix Dimerization: Insights from Rigid-Body Docking and Molecular Dynamics Simulations

In this study, a docking-based protocol has been probed for its ability to predict the effects of 32 single and double mutations on glycophorin A (GpA) homodimerization. Rigid-body docking simulations have been paralleled by molecular dynamics (MD) simulations in implicit membrane. The rigid-body docking-based approach proved effective in reconstituting the native architecture of the GpA dimer for the wild type and the wild-type-like mutants. The good correlative models between the intermolecular interaction descriptors derived both by rigid-body docking simulations and by MD simulations and experimental relative free energies support the assumption that the mutation-induced changes in the association free energy of GpA helices are essentially ascribed to differences in the packing interactions, whereas almost all the variations in the entropic contributions to the association free energy are constant and/or negligible. The MD-based models achieved provide insights into the structural determinants for disruptive and restoring mutational effects. The computational approaches presented in this study are fast and effective, and constitute simple and promising tools for in silico screening of mutational effects on the association properties of integral membrane proteins.

Clustering coefficients of protein-protein interaction networks

The properties of certain networks are determined by hidden variables that are not explicitly measured. The conditional probability (propagator) that a vertex with a given value of the hidden variable is connected to k other vertices determines all measurable properties. We study hidden variable models and find an averaging approximation that enables us to obtain a general analytical result for the propagator. Analytic results showing the validity of the approximation are obtained. We apply hidden variable models to protein-protein interaction networks (PINs) in which the hidden variable is the association free energy, determined by distributions that depend on biochemistry and evolution. We compute degree distributions as well as clustering coefficients of several PINs of different species; good agreement with measured data is obtained. For the human interactome two different parameter sets give the same degree distributions, but the computed clustering coefficients differ by a factor of about 2. This shows that degree distributions are not sufficient to determine the properties of PINs.

Association Free Energy of Dipalmitoylphosphatidylserines in a Mixed Dipalmitoylphosphatidylcholine Membrane

Blood coagulation is strongly dependent on the binding of vitamin K-dependent proteins to cell membranes containing phosphatidylserine (PS) via γ-carboxyglutamic acid (Gla) domains. The process depends on calcium, which can induce nonideal behavior in membranes through domain formation. Such domain separation mediated by Ca 2+ ions or proteins can have an important contribution to the thermodynamics of the interaction between charged peripheral proteins and oppositely charged membranes. To characterize the properties of lipid-lipid interactions, molecular dynamics, and free energy simulations in a mixed bilayer membrane containing dipalmitoylphosphatidylcholine and dipalmitoylphosphatidylserine were carried out. The free energy of association between dipalmitoylphosphatidylserines in the environment of dipalmitoylphosphatidylcholines has been calculated by using a novel approach to the dual topology technique of the PS-PC hybrid. Two different methods, free energy perturbation and thermodynamic integration, were used to calculate the free energy difference. In thermodynamic integration runs three schemes were applied to evaluate the integral at the limits of λ → 0 or λ → 1. Our studies show that the association of two PSs in the environment of PCs is repulsive in the absence of Ca 2+ and becomes favorable in their presence. We also show that the mixed component membrane should exhibit nonideal behavior that will lead to PS clustering.

Simple Physics-Based Analytical Formulas for the Potentials of Mean Force for the Interaction of Amino Acid Side Chains in Water. 1. Approximate Expression for the Free Energy of Hydrophobic Association Based on a Gaussian-Overlap Model

A physics-based model is proposed to derive approximate analytical expressions for the cavity component of the free energy of hydrophobic association of spherical and spheroidal solutes in water. The model is based on the difference between the number and context of the water molecules in the hydration sphere of a hydrophobic dimer and of two isolated hydrophobic solutes. It is assumed that the water molecules touching the convex part of the molecular surface of the dimer and those in the hydration spheres of the monomers contribute equally to the free energy of solvation, and those touching the saddle part of the molecular surface of the dimer result in a more pronounced increase in free energy because of their more restricted mobility (entropy loss) and fewer favorable electrostatic interactions with other water molecules. The density of water in the hydration sphere around a single solute particle is approximated by the derivative of a Gaussian centered on the solute molecule with respect to its standard deviation. On the basis of this approximation, the number of water molecules in different parts of the hydration sphere of the dimer is expressed in terms of the first and the second mixed derivatives of the two Gaussians centered on the first and second solute molecules, respectively, with respect to the standard deviations of these Gaussians, and plausible analytical expressions for the cavity component of the hydrophobic-association energy of spherical and spheroidal solutes are introduced. As opposed to earlier hydration-shell models, our expressions reproduce the desolvation maxima in the potentials of mean force of pairs of nonpolar solutes in water, and their advantage over the models based on molecular-surface area is that they have continuous gradients in the coordinates of solute centers.

Counterions and Water in Polyelectrolyte Multilayers: A Tale of Two Polycations

Attenuated total internal reflectance Fourier transform infrared, ATR-FTIR, spectroscopy was used to compare the water uptake and doping within polyelectrolyte multilayers made from poly(styrene sulfonate), PSS, and a polycation, either poly(allylamine hydrochloride), PAH, or poly(diallyldimethylammonium chloride), PDADMAC. Unlike PDADMA/PSS multilayers, whose water content depended on the solution ionic strength, PAH/PSS multilayers were resistant to doping by NaCl to a concentration of 1.2 M. Using (infrared active) perchlorate salt, the fraction of residual counterions in PDADMA/PSS and PAH/PSS was determined to be 3% and 6%, respectively. The free energy of association between the polymer segments, in the presence of NaClO4, was about 5 kJ mol-1 and -10 kJ mol-1, respectively, for PDADMA/PSS and PAH/PSS, indicating the relatively strong association between the polymer segments in the latter relative to the former. Varying the pH of the solution in contact with the PAH/PSS multilayer revealed a transition to a highly swollen state, interpreted to signal protonation of PAH under much more basic conditions than the pKa of the solution polymer. The increase in the multilayer pKa suggested an interaction energy for PAH/PSS in NaCl of ca. 16 kJ mol-1.

Long-Lived Conformational Isomerism of Protein Dimers: The Role of the Free Energy of Subunit Association

The association of protein subunits to form N-mers (N≥3) does not follow the dependence on the law of mass action predicted by the classical thermodynamic description used for the equilibrium of association of small molecules. For those anomalous cases, a so-called deterministic model has been previously proposed. The latter model was based on the empirical observation that the dynamics of subunit exchange between protein oligomers can be very slow, leading to the existence of long-lived conformational isomers and to a persistently heterogeneous ensemble of oligomers in solution. Contrary to the expectation for a protein dimer, we have recently shown that the subunit association of triosephosphate isomerase (TIM) could also be described as a deterministic process and that long-lived conformational isomers of TIM could be isolated in solution. Here we show that a), observation of hysteresis in pressure dissociation curves is an additional indicator of deterministic behavior; b), the extent of deviation from the classical thermodynamic behavior correlates with the free-energy change of subunit association; and c), experimental manipulation of the free energy of subunit association through the addition of a subdenaturing concentration of a chaotropic agent restores the concentration dependence of subunit association of TIM. A model that explains these features and its biological relevance is discussed.

Ion Pairs of Crystal Violet in Sodium Bis(2-ethylhexyl)sulfosuccinate Reverse Micelles

The interfacial localization and the ion pair formation of the positively charged dye crystal violet (CV) in sodium bis(2-ethylhexyl)sulfosuccinate reverse micelles (AOT RMs) were studied by several structural and spectroscopic techniques and by quantum chemical calculations. The size and shape of the AOT RMs in the presence of CV were investigated by small-angle X-ray scattering, showing that CV does not significantly change the RM structure. CV localization as a function of the water to surfactant molar ratio (w(0)) was characterized by H(1) and (13)C NMR, indicating the close proximity of CV to the sulfosuccinate group of AOT at small and large w(0) values. These results were confirmed by calculation of magnetic shielding constants using the gauge-independent atomic orbital method with the HF/6-31G(d) basis set. Two different types of ion pairs between AOT and CV, i.e., contact ion pair (CIPs) and solvent-separated ion pair (SSIPs), were characterized by UV-vis spectroscopy and quantum chemical calculations using the semiempirical ZINDO-CI method. In nonpolar isotropic solvents CIPs are formed with an association constant (K(ASSOC)) of 2 x 10(4) mol(-1) L in isooctane and 750 mol(-1) L in chloroform. In AOT RMs at low w(0), CV-AOT CIPs are also formed. By increasing w(0), there is a sharp decrease in the CIP association free energy, and SSIPs are formed. (CV(+))(H(2)O)(AOT(-)) SSIPs are stable in the AOT RM up to the largest w(0) tested (w(0) = 33).

Interactions of Tryptophan, Tryptophan Peptides, and Tryptophan Alkyl Esters at Curved Membrane Interfaces

Motivated by ongoing efforts to understand the mechanism of membrane protein crystallogenesis and transport in the lipidic cubic phase, the nature of the interaction between tryptophan and the bilayer/aqueous interface of the cubic phase has been investigated. The association was quantified by partitioning measurements that enabled the free energy of interaction to be determined. Temperature-dependent partitioning was used to parse the association free energy change into its enthalpic and entropic components. As has been observed with tryptophan derivatives interacting with glycerophospholipid bilayers in vesicles, tryptophan partitioning in the cubic phase is enthalpy driven. This is in contrast to partitioning into apolar solvents, which exhibits the classic hydrophobic effect whose hallmark is a favorable entropy change. These results with tryptophan are somewhat surprising given the simplicity, homogeneity, and curvature of the interface that prevails in the case of the cubic phase. Nevertheless, the interaction between tryptophan and the mesophase is very slight as revealed by its low partition coefficient. Additional evidence in support of the interaction was obtained by electronic absorption and fluorescence spectroscopy and fluorescence quenching. Partitioning proved insensitive to the lipid composition of the membrane, examined by doping with glycerophospholipids. However, the interaction could be manipulated in meaningful ways by the inclusion in the aqueous medium of salt, glycerol, or urea. The effects seen with tryptophan were amplified rationally when measurements were repeated using tryptophan alkyl esters and with tryptophan peptides of increasing length. These findings are interpreted in the context of the insertion, folding, and function of proteins in membranes.

Calculating the Free Energy of Association of Transmembrane Helices

A large number of experimental studies have been devoted to quantifying the interaction between transmembrane (TM) helices in detergent micelles and, more recently, in bilayers. Theoretical calculation of association free energy of TM helices would be useful for predicting the propensity of given sequences to oligomerize and for understanding the difference between association in micelles and in bilayers. In this article, the theoretical foundation for calculating the standard association free energy of TM helices is laid out and is applied to glycophorin A in both micelles and bilayers. The standard association free energy is decomposed into the effective energy, translational, rotational, and conformational entropy terms. The effective energy of association is obtained by molecular dynamics simulations in an implicit membrane model. The translational and rotational entropy of association is calculated from the probability distribution of the translational and rotational degrees of freedom obtained from the molecular dynamics simulations. The side-chain conformational entropy of association is estimated from the probability distribution obtained by rigid rotation of all side-chain dihedral angles. The calculated standard association free energy of glycophorin A in N-dodecylphosphocholine micelles is in good agreement with the experimental value. The translational entropy cost is larger, whereas the rotational entropy cost is smaller in bilayers than in micelles. The standard association free energy in 1,2-dimyristoyl-sn-glycero-3-phosphocholine bilayers is calculated to be ∼1.3 kcal/mol more favorable than in N-dodecylphosphocholine micelles, consistent with available experimental data.

Free-energy distribution of binary protein–protein binding suggests cross-species interactome differences

Major advances in large-scale yeast two-hybrid screening have provided a global view of binary protein-protein interactions across species as dissimilar as human, yeast, and bacteria. Remarkably, these analyses have revealed that all species studied have a degree distribution of protein-protein binding that is approximately scale-free (varies as a power law) even though their evolutionary divergence times differ by billions of years. The universal power law shows only the surface of the rich information harbored by these high-throughput data. We develop a detailed mathematical model of the protein-protein interaction network based on association free energy, the biochemical quantity that determines protein-protein interaction strength. This model reproduces the degree distribution of all of the large-scale yeast two-hybrid data sets available and allows us to extract the distribution of free energy, the likelihood that a pair of proteins of a given species will bind. We find that across-species interactomes have significant differences that reflect the strengths of the protein-protein interaction. Our results identify a global evolutionary shift: more evolved organisms have weaker binary protein-protein binding. This result is consistent with the evolution of increased protein unfoldedness and challenges the dogma that only specific protein-protein interactions can be biologically functional.

Mycobacterium tuberculosis H37Rv ESAT‐6–CFP‐10 complex formation confers thermodynamic and biochemical stability

The 6-kDa early secretory antigenic target (ESAT-6) and culture filtrate protein-10 (CFP-10), expressed from the region of deletion-1 (RD1) of Mycobacterium tuberculosis H37Rv, are known to play a key role in virulence. In this study, we explored the thermodynamic and biochemical changes associated with the formation of the 1 : 1 heterodimeric complex between ESAT-6 and CFP-10. Using isothermal titration calorimetry (ITC), we precisely determined the association constant and free energy change for formation of the complex to be 2 x 10(7) M(-1) and -9.95 kcal.mol(-1), respectively. Strikingly, the thermal unfolding of the ESAT-6-CFP-10 heterodimeric complex was completely reversible, with a T(m) of 53.4 degrees C and DeltaH of 69 kcal.mol(-1). Mixing of ESAT-6 and CFP-10 at any temperature below the T(m) of the complex led to induction of helical conformation, suggesting molecular recognition between specific segments of unfolded ESAT-6 and CFP-10. Enhanced biochemical stability of the complex was indicated by protection of ESAT-6 and an N-terminal fragment of CFP-10 from proteolysis with trypsin. However, the flexible C-terminal of CFP-10 in the complex, which has been shown to be responsible for binding to macrophages and monocytes, was cleaved by trypsin. In the presence of phospholipid membranes, ESAT-6, but not CFP-10 and the complex, showed an increase in alpha-helical content and enhanced thermal stability. Overall, complex formation resulted in structural changes, enhanced thermodynamic and biochemical stability, and loss of binding to phospholipid membranes. These features of complex formation probably determine the physiological role of ESAT-6, CFP-10 and/or the complex in vivo. The ITC and thermal unfolding approach described in this study can readily be applied to characterization of the 11 other pairs of ESAT-6 family proteins and for screening ESAT-6 and CFP-10 mutants.