Maximum-entropy decomposition of fluorescence correlation spectroscopy data: application to liposome–human serum albumin association

Fluorescence correlation spectroscopy was used to measure the diffusion behavior of a mixture of DMPC or DMPC/DMPG liposomes with human serum albumin (HSA) and mesoporphyrin (MP), which was used as the fluorescent label for liposomes and HSA as well. For decomposing the fluorescence intensity autocorrelation function (ACF) into components corresponding to a liposome population, HSA and MP, we used a maximum entropy procedure that computes a distribution of diffusion times consistent with the ACF data. We found that a simple parametric non-linear fit with a discrete set of decay components did not converge to a stable parameter set. The distribution calculated with the maximum entropy method was stable and the average size of the particles calculated from the effective diffusion time was in good agreement with the data determined using the discrete-component fit.     

Improved pKa calculations through flexibility based sampling of a water-dominated interaction scheme

Ionizable groups play critical roles in biological processes. Computation of pK(a)s is complicated by model approximations and multiple conformations. Calculated and experimental pK(a)s are compared for relatively inflexible active-site side chains, to develop an empirical model for hydration entropy changes upon charge burial. The modification is found to be generally small, but large for cysteine, consistent with small molecule ionization data and with partial charge distributions in ionized and neutral forms. The hydration model predicts significant entropic contributions for ionizable residue burial, demonstrated for components in the pyruvate dehydrogenase complex. Conformational relaxation in a pH-titration is estimated with a mean-field assessment of maximal side chain solvent accessibility. All ionizable residues interact within a low protein dielectric finite difference (FD) scheme, and more flexible groups also access water-mediated Debye-Hückel (DH) interactions. The DH method tends to match overall pH-dependent stability, while FD can be more accurate for active-site groups. Tolerance for side chain rotamer packing is varied, defining access to DH interactions, and the best fit with experimental pK(a)s obtained. The new (FD/DH) method provides a fast computational framework for making the distinction between buried and solvent-accessible groups that has been qualitatively apparent from previous work, and pK(a) calculations are significantly improved for a mixed set of ionizable residues. Its effectiveness is also demonstrated with computation of the pH-dependence of electrostatic energy, recovering favorable contributions to folded state stability and, in relation to structural genomics, with substantial improvement (reduction of false positives) in active-site identification by electrostatic strain.     

Two different proteins that compete for binding to thrombin have opposite kinetic and thermodynamic profiles

Thrombin binds thrombomodulin (TM) at anion binding exosite 1, an allosteric site far from the thrombin active site. A monoclonal antibody (mAb) has been isolated that competes with TM for binding to thrombin. Complete binding kinetic and thermodynamic profiles for these two protein-protein interactions have been generated. Binding kinetics were measured by Biacore. Although both interactions have similar K(D)s, TM binding is rapid and reversible while binding of the mAb is slow and nearly irreversible. The enthalpic contribution to the DeltaG(bind) was measured by isothermal titration calorimetry and van't Hoff analysis. The contribution to the DeltaG(bind) from electrostatic steering was assessed from the dependence of the k(a) on ionic strength. Release of solvent H(2)O molecules from the interface was assessed by monitoring the decrease in amide solvent accessibility at the interface upon protein-protein binding. The mAb binding is enthalpy driven and has a slow k(d). TM binding appears to be entropy driven and has a fast k(a). The favorable entropy of the thrombin-TM interaction seems to be derived from electrostatic steering and a contribution from solvent release. The two interactions have remarkably different thermodynamic driving forces for competing reactions. The possibility that optimization of binding kinetics for a particular function may be reflected in different thermodynamic driving forces is discussed.     

The effect of the polyproline II (PPII) conformation on the denatured state entropy

Polyproline II (PPII) is reported to be a dominant conformation in the unfolded state of peptides, even when no prolines are present in the sequence. Here we use isothermal titration calorimetry (ITC) to investigate the PPII bias in the unfolded state by studying the binding of the SH3 domain of SEM-5 to variants of its putative PPII peptide ligand, Sos. The experimental system is unique in that it provides direct access to the conformational entropy change of the substituted amino acids. Results indicate that the denatured ensemble can be characterized by at least two thermodynamically distinct states, the PPII conformation and an unfolded state conforming to the previously held idea of the denatured state as a random collection of conformations determined largely by hard-sphere collision. The probability of the PPII conformation in the denatured states for Ala and Gly were found to be significant, approximately 30% and approximately 10%, respectively, resulting in a dramatic reduction in the conformational entropy of folding.     

On the properties and sequence context of structurally ambivalent fragments in proteins

The goal of this work is to characterize structurally ambivalent fragments in proteins. We have searched the Protein Data Bank and identified all structurally ambivalent peptides (SAPs) of length five or greater that exist in two different backbone conformations. The SAPs were classified in five distinct categories based on their structure. We propose a novel index that provides a quantitative measure of conformational variability of a sequence fragment. It measures the context-dependent width of the distribution of (phi,xi) dihedral angles associated with each amino acid type. This index was used to analyze the local structural propensity of both SAPs and the sequence fragments contiguous to them. We also analyzed type-specific amino acid composition, solvent accessibility, and overall structural properties of SAPs and their sequence context. We show that each type of SAP has an unusual, type-specific amino acid composition and, as a result, simultaneous intrinsic preferences for two distinct types of backbone conformation. All types of SAPs have lower sequence complexity than average. Fragments that adopt helical conformation in one protein and sheet conformation in another have the lowest sequence complexity and are sampled from a relatively limited repertoire of possible residue combinations. A statistically significant difference between two distinct conformations of the same SAP is observed not only in the overall structural properties of proteins harboring the SAP but also in the properties of its flanking regions and in the pattern of solvent accessibility. These results have implications for protein design and structure prediction.     

Investigations into sequence and conformational dependence of backbone entropy,inter-basin dynamics and the Flory isolated-pair hypothesis for peptides

The populations and transitions between Ramachandran basins are studied for combinations of the standard 20 amino acids in monomers, dimers and trimers using an implicit solvent Langevin dynamics algorithm and employing seven commonly used force-fields. Both the basin populations and inter-conversion rates are influenced by the nearest neighbor's conformation and identity, contrary to the Flory isolated-pair hypothesis. This conclusion is robust to the choice of force-field, even though the use of different force-fields produces large variations in the populations and inter-conversion rates between the dominant helical, extended beta, and polyproline II basins. The computed variation of conformational and dynamical properties with different force-fields exceeds the difference between explicit and implicit solvent calculations using the same force-field. For all force-fields, the inter-basin transitions exhibit a directional dependence, with most transitions going through extended beta conformation, even when it is the least populated basin. The implications of these results are discussed in the context of estimates for the backbone entropy of single residues, and for the ability of all-atom simulations to reproduce experimental protein folding data.     

Effect of backbone cyclization on protein folding stability: chain entropies of both the unfolded and the folded states are restricted

Circular versions of a large number of proteins have been designed by connecting the N and C termini via peptide linkers. A motivation for these designs is the assumed enhancement in folding stability, because backbone cyclization reduces the chain entropy of the unfolded state. Here, it is recognized that backbone cyclization also reduces the chain entropy of a flexible peptide linker in the folded state. Specifically, the end-to-end distance of the linker is restricted to fluctuations around the average displacement between the N and C termini of the folded protein. The balance of the chain-entropy reductions in the folded and unfolded states is used to predict the change in the unfolding free energy, deltadeltaG(cycl), by backbone cyclization. Predicted values of deltadeltaG(cycl) are in quantitative agreement with results of a careful study on cyclizing the 34 residue PIN1 WW domain by linkers with two to seen residues. The experimental results of an optimal linker length l=4 and a maximum stabilization of 1.7 kcal/mol are reproduced. Calculations of deltadeltaG(cycl) for a broad selection of circular proteins suggest that the stabilizing effect of backbone cyclization is modest, reflecting entropy reductions in both the unfolded and the folded states.     

Block structure and stability of the genetic code

It is known that different codons may be unified into larger groups related to the hierarchical structure, approximate hidden symmetries, and evolutionary origin of the universal genetic code. Using a simplified evolutionary motivated two-letter version of genetic code, the general principles of the most stable coding are discussed. By the complete enumeration in such a reduced code it is strictly proved that the maximum stability with respect to point mutations and shifts in the reading frame needs the fixation of the middle letters within codons in groups with different physico-chemical properties, thus, explaining a key feature of the universal genetic code. The translational stability of the genetic code is studied by the mapping of code onto de Bruijn graph providing both the compact visual representation of mutual relationships between different codons as well as between codons and protein coding DNA sequence and a powerful tool for the investigation of stability of protein coding. Then, the results are extended to four-letter codes. As is shown, the universal genetic code obeys mainly the principles of optimal coding. These results demonstrate the hierarchical character of optimization of universal genetic code with strictly optimal coding being evolved at the earliest stages of molecular evolution. Finally, the universal genetic code is compared with the other natural variants of genetic codes.     

Information gain for genetic parameter estimation with incorporation of marker data

Genetic marker data has been increasingly incorporated into segregation analysis, as combined segregation and linkage analysis has been performed more frequently. In this article, we study the extent of information gains with incorporation of marker data in segregation analysis, a topic that has not been investigated rigorously. Specifically, the current study is to investigate the influence of marker data on genetic model parameter estimation. A variance matrix criterion (as the inverse of the Fisher information matrix) and a relative entropy criterion (a measure of flatness of expected log-likelihood surface) are used to quantify the information gains. Our results indicate that substantial information gain can be achieved with the incorporation of marker data. The amount of variance reduction increases as the heterozygosity of the linked marker increases and as the trait gets closer to the linked marker(s). Incorporation of marker data in larger pedigrees also yields greater information gains based on both criteria. The effect of pedigree structure is also studied.