The statistical-thermodynamic basis for computation of binding affinities: a critical review

Although the statistical thermodynamics of noncovalent binding has been considered in a number of theoretical papers, few methods of computing binding affinities are derived explicitly from this underlying theory. This has contributed to uncertainty and controversy in certain areas. This article therefore reviews and extends the connections of some important computational methods with the underlying statistical thermodynamics. A derivation of the standard free energy of binding forms the basis of this review. This derivation should be useful in formulating novel computational methods for predicting binding affinities. It also permits several important points to be established. For example, it is found that the double-annihilation method of computing binding energy does not yield the standard free energy of binding, but can be modified to yield this quantity. The derivation also makes it possible to define clearly the changes in translational, rotational, configurational, and solvent entropy upon binding. It is argued that molecular mass has a negligible effect upon the standard free energy of binding for biomolecular systems, and that the cratic entropy defined by Gurney is not a useful concept. In addition, the use of continuum models of the solvent in binding calculations is reviewed, and a formalism is presented for incorporating a limited number of solvent molecules explicitly

Molecular Dynamics simulations of amyloidogenic proteins. Unfolding, misfolding and aggregation.

Proteins are the main bulding blocks of biological systems. Their structure and function have been extensively studied so far both by experiments (Nuclear Magnetic Resonance, X-ray crystallography, Mass Spectrometry, etc.) and modeling strategies (Molecular Dynamics and Monte Carlo simulations, Density Functional Theory. etc.). In vivo in general and in solution in particular, they mostly adopt different and unique secondary and tertiary configurations, owing to their conformational freedom. The route and mechanism by which a specific shape is formed, i.e. the folding, which is not reversible in many cases, is not fully understood for several protein models, nothwithstanding the fulgurant advances achieved in experimental and in silico techniques in the last decades. Under specific conditions (pH, temperature, concentration, etc.), such three-dimensional arrangement as well as the intra/inter-chains interactions can be lost, and species such as disordered or fibrilar aggregates involved in several known human pathologies may develop. In this thesis we probe the atomistic scale conformational dynamics of two amyloidogenic proteins, transthyretin and \u3b22-microglobulin, using molecular dynamics simulations. We aim at understanding the major factors driving the misfolding and/or (un)folding of the latter specified proteins, which play a precursor and prominent role in neurodegrative deseases. To this end the dynamics and dissociation of wild-type and mutant transthyretin is simulated. In particular the behaviour of a triple mutant (designed by Prof. R. Berni and coworkers to be monomeric) is studied. It comes out that the mutation considerably shifts the tetramer-folded monomer equilibrium towards the monomer, making this triple mutant a useful tool for structural and dynamical studies. The interaction of \u3b22-microglobulin with hydrophobic surfaces is studied by molecular dynamics and the thermodynamics of the process is addressed using end-point free energy calculations. The results rationalize experimental observation reported in the literature. Protein conformational dynamics and thermodynamics are currently experimentally probed by the backbone amide hydrogen exchange experiment (HDX). The Bluu-Tramp experiment developed by prof. Esposito and coworkers allows the measurement of free energy, enthalpy and entropy of exchange in a single experiment. A proper comparison between experimental and simulation data require modeling of the process at atomic detail. Hence, we analyze also this aspect and try to relate the amide hydrogen protection observed in NMR experiments to various microscopic properties of the protein structure computed in the simulations. Using free energy calculations we aim at reproducing also the temperature dependence of the process. Given the predominant role of protein association in most biological functions, we introduce a modeling approach to estimate the entropy loss upon complex formation, a contribution which is almost always neglected in many free energy calculation methodologies due to the high dimensionality of the degrees of freedom, and adequate theoretical methods. The approach is applied to the case proteins considered in this thesis and an exact and approximate estimation of the full rotational-translational entropy are obtained in the context of nearest neighbor-based entropy formulation. Overall, this thesis explores various aspects favouring the formation of misfolded and/or (un)folded protein species, ranging from dissociation of an homotetramer of transthyretin engineered in silico, through the interaction of \u3b22-microglobulin with an hydrophobic surface model, to the backbone amide hydrogen exchange pattern of protection of the latter. Lastly and not the least, the thesis presents a computational methodology to address the roto-translational entropy loss upon complex formation of biomolecules

Volume-based solvation models out-perform area-based models in combined studies of wild-type and mutated protein-protein interfaces

<p>Abstract</p> <p>Background</p> <p>Empirical binding models have previously been investigated for the energetics of protein complexation (ΔG models) and for the influence of mutations on complexation (i.e. differences between wild-type and mutant complexes, ΔΔG models). We construct binding models to directly compare these processes, which have generally been studied separately.</p> <p>Results</p> <p>Although reasonable fit models were found for both ΔG and ΔΔG cases, they differ substantially. In a dataset curated for the absence of mainchain rearrangement upon binding, non-polar area burial is a major determinant of ΔG models. However this ΔG model does not fit well to the data for binding differences upon mutation. Burial of non-polar area is weighted down in fitting of ΔΔG models. These calculations were made with no repacking of sidechains upon complexation, and only minimal packing upon mutation. We investigated the consequences of more extensive packing changes with a modified mean-field packing scheme. Rather than emphasising solvent exposure with relatively extended sidechains, rotamers are selected that exhibit maximal packing with protein. This provides solvent accessible areas for proteins that are much closer to those of experimental structures than the more extended sidechain regime. The new packing scheme increases changes in non-polar burial for mutants compared to wild-type proteins, but does not substantially improve agreement between ΔG and ΔΔG binding models.</p> <p>Conclusion</p> <p>We conclude that solvent accessible area, based on modelled mutant structures, is a poor correlate for ΔΔG upon mutation. A simple volume-based, rather than solvent accessibility-based, model is constructed for ΔG and ΔΔG systems. This shows a more consistent behaviour. We discuss the efficacy of volume, as opposed to area, approaches to describe the energetic consequences of mutations at interfaces. This knowledge can be used to develop simple computational screens for binding in comparative modelled interfaces.</p

Protein folding on the ribosome studied using NMR spectroscopy

NMR spectroscopy is a powerful tool for the investigation of protein folding and misfolding, providing a characterization of molecular structure, dynamics and exchange processes, across a very wide range of timescales and with near atomic resolution. In recent years NMR methods have also been developed to study protein folding as it might occur within the cell, in a de novo manner, by observing the folding of nascent polypeptides in the process of emerging from the ribosome during synthesis. Despite the 2.3 MDa molecular weight of the bacterial 70S ribosome, many nascent polypeptides, and some ribosomal proteins, have sufficient local flexibility that sharp resonances may be observed in solution-state NMR spectra. In providing information on dynamic regions of the structure, NMR spectroscopy is therefore highly complementary to alternative methods such as X-ray crystallography and cryo-electron microscopy, which have successfully characterized the rigid core of the ribosome particle. However, the low working concentrations and limited sample stability associated with ribosome-nascent chain complexes means that such studies still present significant technical challenges to the NMR spectroscopist. This review will discuss the progress that has been made in this area, surveying all NMR studies that have been published to date, and with a particular focus on strategies for improving experimental sensitivity

Statics and Dynamics of Strongly Charged Soft Matter

Soft matter materials, such as polymers, membranes, proteins, are often electrically charged. This makes them water soluble, which is of great importance in technological application and a prerequisite for biological function. We discuss a few static and dynamic systems that are dominated by charge effects. One class comprises complexation between oppositely charged objects, for example the adsorption of charged ions or charged polymers (such as DNA) on oppositely charged substrates of different geometry. The second class comprises effective interactions between similarly charged objects. Here the main theme is to understand the experimental finding that similarly and highly charged bodies attract each other in the presence of multi-valent counterions. This is demonstrated using field-theoretic arguments as well as Monte-Carlo simulations for the case of two homogeneously charged bodies. Realistic surfaces, on the other hand, are corrugated and also exhibit modulated charge distributions, which is important for static properties such as the counterion-density distribution, but has even more pronounced consequences for dynamic properties such as the counterion mobility. More pronounced dynamic effects are obtained with highly condensed charged systems in strong electric fields. Likewise, an electrostatically collapsed highly charged polymer is unfolded and oriented in strong electric fields. At the end of this review, we give a very brief account of the behavior of water at planar surfaces and demonstrate using ab-initio methods that specific interactions between oppositely charged groups cause ion-specific effects that have recently moved into the focus of interest.Comment: 61 pages, 31 figures, Physics Reports (2005)-in press (high quality figures available from authors

How Water's Properties Are Encoded in Its Molecular Structure and Energies.

How are water's material properties encoded within the structure of the water molecule? This is pertinent to understanding Earth's living systems, its materials, its geochemistry and geophysics, and a broad spectrum of its industrial chemistry. Water has distinctive liquid and solid properties: It is highly cohesive. It has volumetric anomalies-water's solid (ice) floats on its liquid; pressure can melt the solid rather than freezing the liquid; heating can shrink the liquid. It has more solid phases than other materials. Its supercooled liquid has divergent thermodynamic response functions. Its glassy state is neither fragile nor strong. Its component ions-hydroxide and protons-diffuse much faster than other ions. Aqueous solvation of ions or oils entails large entropies and heat capacities. We review how these properties are encoded within water's molecular structure and energies, as understood from theories, simulations, and experiments. Like simpler liquids, water molecules are nearly spherical and interact with each other through van der Waals forces. Unlike simpler liquids, water's orientation-dependent hydrogen bonding leads to open tetrahedral cage-like structuring that contributes to its remarkable volumetric and thermal properties

Functional Consequences of Protein Dynamics

This thesis explores the possible uses of dynamical fluctuations in protein structure for ligand binding and catalysis. Particular emphasis is placed on the dynamic interpretation of allosteric interactions and a statistical mechanical model of dynamic allostery is presented. This model shows that changes in either low frequency collective motions or random uncorrelated atomic fluctuations of the protein induced by the binding of a ligand can alter the binding properties of other remote ligand binding sites giving rise to allostery. Increases in the frequency of vibrational modes and reductions in uncorrelated motions gives rise to positive cooperativity and is equivalent to a stiffening of the protein structure. Small changes in the dynamics can be treated classically with many changes being required to give observed cooperative free energies. Large shifts in low frequency vibrational modes give much larger contributions to the cooperativity and the use of quantum mechanics is required. The dynamic allostery model predicts that cooperativity arising from dynamic changes is predominantly entropic in origin and complements the more conventional models of allostery which invoke changes in the static conformation of the protein involving domain movement, bond rearrangements and electrostatic effects with consequent effects on the enthalpy. The predictions of this model are tested using laser Raman spectroscopy of solid samples to study low frequency modes in proteins and an allosteric model compound. The small organic molecule which displays positive cooperativity between its two binding sites, shows sizeable shifts to higher frequencies in the low frequency spectrum in agreement with the model. The vibrational shifts seen require only the classical version of the model which when combined with changes in the uncorrelated motions of the atoms in the molecule can account for the observed cooperative free energy. The cooperativity is solely entropic in origin in agreement with published results. High frequency spectra of the molecule in various states of ligation are presented and analysed in terms of localised vibrations of atoms and groups of atoms. The low frequency Raman spectra of lysozyme and its complex with the small inhibitor tri-N-acetyl glucosamine, and of trypsin and its complex with pancreatic trypsin inhibitor all displayed a broad band at 20cm. This band is a superposition of a large number of low frequency modes of the protein and the expected shift in frequency of some modes on inhibitor binding is not visible within such a broad band. The allosteric enzyme glyceraldehyde 3-phosphate dehydrogenase and its complex with the cofactor NAD also shows no changes in its low frequency spectrum. These results and their implications are discussed. High frequency Raman spectra of these enzymes are also presented and analysed

Stochastic dynamics of macromolecular-assembly networks

The formation and regulation of macromolecular complexes provides the backbone of most cellular processes, including gene regulation and signal transduction. The inherent complexity of assembling macromolecular structures makes current computational methods strongly limited for understanding how the physical interactions between cellular components give rise to systemic properties of cells. Here we present a stochastic approach to study the dynamics of networks formed by macromolecular complexes in terms of the molecular interactions of their components. Exploiting key thermodynamic concepts, this approach makes it possible to both estimate reaction rates and incorporate the resulting assembly dynamics into the stochastic kinetics of cellular networks. As prototype systems, we consider the lac operon and phage lambda induction switches, which rely on the formation of DNA loops by proteins and on the integration of these protein-DNA complexes into intracellular networks. This cross-scale approach offers an effective starting point to move forward from network diagrams, such as those of protein-protein and DNA-protein interaction networks, to the actual dynamics of cellular processes.Comment: Open Access article available at http://www.nature.com/msb/journal/v2/n1/full/msb4100061.htm