The role of hydrophobic microenvironments in modulating pKa shifts in proteins.

The screened Coulomb potential (SCP) method, combined with a quantitative description of the microenvironments around titratable groups, based on the Hydrophobic Fragmental Constants developed by Rekker, has been applied to calculate the pK(a) values of groups embedded in extremely hydrophobic microenvironments in proteins. This type of microenvironment is not common; but constitutes a small class, where the protein's architecture has evolved to lend special properties to the embedded residue. They are of significant interest because they are frequently important in catalysis and in proton and electron transfer reactions. In the SCP treatment these special cases are treated locally and therefore do not affect the accuracy of the pK(a) values calculated for other residues in less hydrophobic environments. Here the calibration of the algorithm is extended with the help of earlier results from lysozyme and of three mutants of staphylococcal nuclease (SNase) that were specially designed to measure the energetics of ionization of titratable groups buried in extremely hydrophobic microenvironments. The calibrated algorithm was subsequently applied to a fourth mutant of SNase and then to a very large dimeric amine oxidase of 1284 residues, where 334 are titratable. The observed pK(a) shifts of the buried residues are large (up to 4.7 pK units), and all cases are well reproduced by the calculations with a root mean square error of 0.22. These results support the hypothesis that protein electrostatics can only be described correctly and self-consistently if the inherent heterogeneity of these systems is properly accounted for.

Key issues in the computational simulation of GPCR function: representation of loop domains.

Some key concerns raised by molecular modeling and computational simulation of functional mechanisms for membrane proteins are discussed and illustrated for members of the family of G protein coupled receptors (GPCRs). Of particular importance are issues related to the modeling and computational treatment of loop regions. These are demonstrated here with results from different levels of computational simulations applied to the structures of rhodopsin and a model of the 5-HT2A serotonin receptor, 5-HT2AR. First, comparative Molecular Dynamics (MD) simulations are reported for rhodopsin in vacuum and embedded in an explicit representation of the membrane and water environment. It is shown that in spite of a partial accounting of solvent screening effects by neutralization of charged side chains, vacuum MD simulations can lead to severe distortions of the loop structures. The primary source of the distortion appears to be formation of artifactual H-bonds, as has been repeatedly observed in vacuum simulations. To address such shortcomings, a recently proposed approach that has been developed for calculating the structure of segments that connect elements of secondary structure with known coordinates, is applied to 5-HT2AR to obtain an initial representation of the loops connecting the transmembrane (TM) helices. The approach consists of a simulated annealing combined with biased scaled collective variables Monte Carlo technique, and is applied to loops connecting the TM segments on both the extra-cellular and the cytoplasmic sides of the receptor. Although this initial calculation treats the loops as independent structural entities, the final structure exhibits a number of interloop interactions that may have functional significance. Finally, it is shown here that in the case where a given loop from two different GPCRs (here rhodopsin and 5-HT2AR) has approximately the same length and some degree of sequence identity, the fold adopted by the loops can be similar. Thus, in such special cases homology modeling might be used to obtain initial structures of these loops. Notably, however, all other loops in these two receptors appear to be very different in sequence and structure, so that their conformations can be found reliably only by ab initio, energy based methods and not by homology modeling.

Mutations in PTPN11, encoding the protein tyrosine phosphatase SHP-2, cause Noonan syndrome.

Noonan syndrome (MIM 163950) is an autosomal dominant disorder characterized by dysmorphic facial features, proportionate short stature and heart disease (most commonly pulmonic stenosis and hypertrophic cardiomyopathy). Webbed neck, chest deformity, cryptorchidism, mental retardation and bleeding diatheses also are frequently associated with this disease. This syndrome is relatively common, with an estimated incidence of 1 in 1,000-2,500 live births. It has been mapped to a 5-cM region (NS1) [corrected] on chromosome 12q24.1, and genetic heterogeneity has also been documented. Here we show that missense mutations in PTPN11 (MIM 176876)-a gene encoding the nonreceptor protein tyrosine phosphatase SHP-2, which contains two Src homology 2 (SH2) domains-cause Noonan syndrome and account for more than 50% of the cases that we examined. All PTPN11 missense mutations cluster in interacting portions of the amino N-SH2 domain and the phosphotyrosine phosphatase domains, which are involved in switching the protein between its inactive and active conformations. An energetics-based structural analysis of two N-SH2 mutants indicates that in these mutants there may be a significant shift of the equilibrium favoring the active conformation. This implies that they are gain-of-function changes and that the pathogenesis of Noonan syndrome arises from excessive SHP-2 activity.

A self-consistent, microenvironment modulated screened coulomb potential approximation to calculate pH-dependent electrostatic effects in proteins.

An improved approach is presented for calculating pH-dependent electrostatic effects in proteins using sigmoidally screened Coulomb potentials (SCP). It is hypothesized that a key determinant of seemingly aberrant behavior in pKa shifts is due to the properties of the unique microenvironment around each residue. To help demonstrate this proposal, an approach is developed to characterize the microenvironments using the local hydrophobicity/hydrophilicity around each residue of the protein. The quantitative characterization of the microenvironments shows that the protein is a complex mosaic of differing dielectric regions that provides a physical basis for modifying the dielectric screening functions: in more hydrophobic microenvironments the screening decreases whereas the converse applies to more hydrophilic regions. The approach was applied to seven proteins providing more than 100 measured pKa values and yielded a root mean square deviation of 0.5 between calculated and experimental values. The incorporation of the local hydrophobicity characteristics into the algorithm allowed the resolution of some of the more intractable problems in the calculation of pKa. Thus, the divergent shifts of the pKa of Glu-35 and Asp-66 in hen egg white lysozyme, which are both about 90% buried, was correctly predicted. Mechanistically, the divergence occurs because Glu-35 is in a hydrophobic microenvironment, while Asp-66 is in a hydrophilic microenvironment. Furthermore, because the calculation of the microenvironmental effects takes very little CPU time, the computational speed of the SCP formulation is conserved. Finally, results from different crystal structures of a given protein were compared, and it is shown that the reliability of the calculated pKa values is sufficient to allow identification of conformations that may be more relevant for the solution structure.

Functional role of arginine-11 in the N-terminal helix of skeletal troponin C: combined mutagenesis and molecular dynamics investigation.

The two main structural differences between calmodulin (CaM) and skeletal troponin C (sTnC) are the absence in CaM of (i) the short N-terminal helix in TnC and (ii) the triplet KGK (residues 91-93; numbering according to chicken sTnC). It was recently shown that deletion of both structural groups from sTnC imparted to the resulting construct the CaM-like ability to activate phosphodiesterase (PDE) and to regulate force development in smooth muscle. To continue probing of the structural basis of the differential behavior of sTnC and CaM, residue Arg-11 in rabbit sTnC was mutated to Ala because the interactions of Arg-11 with distal residues in the N-terminal domain seem to link the N-terminal helix to the rest of the structure. The mutant exhibits CaM-like function in its ability to activate PDE (about 50% of CaM at 5 microM concentration). If, in addition, the KGK triplet is also deleted, PDE activation increases to about 80%. Both constructs retain their TnC function to nearly 100%. To explore the mechanistic basis of this remarkable observation, computational simulations of the molecular dynamics (MD) were carried out for both wild-type 4Ca2+.sTnC and the 4Ca2+.R11A mutant, and the results were compared to those from earlier simulations of 4Ca2+.CaM. Two types of structural changes observed from such simulations of the molecular dynamics of CaM had been considered to have a functional role: (i) a compaction to a more globular form and (ii) a reorientation of the Ca-binding domains around the central tether helix.(ABSTRACT TRUNCATED AT 250 WORDS)

Electrostatic effects in proteins: comparison of dielectric and charge models.

Two approaches for calculating electrostatic effects in proteins are compared and ana analysis is presented of the dependence of calculated properties on the model used to define the charge distribution. Changes in electrostatic free energy have been calculated using a screened Coulomb potential (SCP) with a distance-dependent effective dielectric permittivity to model bulk solvent effects and a finite difference approach to solve the Poisson-Boltzmann (FDPB) equation. The properties calculated include shifts in dissociation constants of ionizable groups, the effect of annihilating surface charges on the binding of metals, and shifts in redox potentials due to changes in the charge of ionizable groups. In the proteins considered the charged sites are separated by 3.5-12 A. It is shown that for the systems studied in this distance range the SCP yields calculated values which are at least as accurate as those obtained from solution of the FDPB equation. In addition, in the distance range 3-5 A the SCP gives substantially better results than the FDPB equation. Possible sources of this difference between the two methods are discussed. Shifts in binding constants and redox potentials were calculated with several standard charge sets, and the resulting values show a variation of 20-40% between the 'best' and 'worst' cases. From this study it is concluded that in most applications, changes in electrostatic free energies can be calculated economically and reliably using an SCP approach with a single functional form of the screening function.

Electrostatic screening in molecular dynamics simulations.

The screened Coulombic potential has been shown to describe satisfactorily equilibrium properties like pK shifts, the effects of charged groups on redox potentials and binding constants of metal ions. To test how well the screening of the electrostatic potential describes the dynamical trajectory of a macromolecular system, a series of comparative simulations have been carried out on a protein system which explicitly included water molecules and a system in vacuo. For the system without solvent the results of using (i) the standard potential form were compared with results of (ii) the potential where the Coulomb term was modified by the inclusion of a distance dependent dielectric, epsilon (r), to model the screening effect of bulk water, and (iii) standard potential modified by reducing the charge on ionized residue side chains. All molecular dynamics simulations have been carried out on bovine pancreatic trypsin inhibitor. Comparisons between the resulting trajectories, averaged structures, hydrogen bonding patterns and properties such as solvent accessible surface area and radius of gyration are described. The results show that the dynamical behaviour of the protein calculated with a screened electrostatic term compares more favourably with the time-dependent structural changes of the full system with explicitly included water than the standard vacuum simulation.

Structural dynamics of calmodulin and troponin C.

We present the results of computational simulation studies of the structures of calmodulin (CAM) and troponin C (TNC). Possible differences between the structures of these molecules in the crystal and in solution were suggested by results from some recent experimental studies, which implied that their conformations in solution may be more compacted than the characteristic dumbbell shape observed in the crystal. The molecular dynamics simulations were carried out with the CHARMM system of programs, and the environment was modeled with a distance-dependent dielectric permittivity and discrete water molecules surrounding the proteins at starting positions identified in the crystals of CAM and TNC. Methods of macromolecular structure analysis, including linear distance plots, distance matrices and a matrix representation of hydrogen bonding, were used to analyze the nature, the extent and the source of structural differences between the computed structures of the molecules and their conformations in the crystal. Following the longest simulation, in which intradomain structure was conserved, the crystallographically observed dumbbell structure of the molecule changed due to a kinking or bending in the region of the central tether helix connecting the two Ca(2+)-binding domains which moved into close proximity. The resulting structure correlates with experimental observations of complexes between CAM and peptides such as melittin and mastoparan. Analysis of the corresponding pair distance distribution functions in comparison to experimental results suggests the dynamic existence of a non-negligible fraction of the compacted structure in aqueous solutions of CAM. In this more nearly globular shape, CAM reveals to the environment two interior pockets that contain a number of hydrophobic residues, in agreement with NMR data suggesting involvement of such residues in the binding of inhibitors and proteins to CAM.

Graphical representation of hydrogen bonding patterns in proteins.

A graphical representation of the intramolecular hydrogen bonding in a protein is described, which provides a direct and easily interpretable display of its secondary and tertiary structural elements. The representation is constructed by scanning the coordinate list for all potential proton donor (PD)--proton acceptor (PA) pairs, and any pair which satisfies certain preset distance and angle criteria is classified as being H-bonded. The resulting list of H-bonds is mapped onto an N x N matrix, where N is the number of residues in the protein, by assigning an element ij of the matrix to all the PA-PD pairs between atoms of residues i and j. Subsequently graphical objects are generated for all elements which are labeled as representing one or more H-bonds, and which can then be plotted or displayed in a way analogous to the graphical representation of the distance matrix (DM). In contrast to the DM, the hydrogen bonding matrix (HBM) is sparse, which allows the patterns representing secondary and tertiary structural motifs to be quickly and clearly recognized. In addition, changes in structure are easily identifiable from changes in the H-bonding patterns. The analysis and interpretation of the HBM is discussed using aspartate amino-transferase and calmodulin as examples.

Comparison of dielectric response models for simulating electrostatic effects in proteins.

Two recent approaches for calculating pK shifts in proteins are compared. The first of these uses Coulomb's law with a distance-dependent dielectric permittivity, epsilon (r), to model the screening effects of the environment, and the second uses a finite difference approach to solve Poisson's equation. It is shown that an explicit form of epsilon (r) which has been fitted to experimentally determined values of the dielectric permittivity in a range from 1 to 21 A can be approximated by a linear form in the functionally significant range of charge separations of approximately 3-10 A, but for distances greater than 10 A the effective permittivity is strongly nonlinear. A statistical analysis of the errors in calculated pK shifts due to electrostatic interactions between charges with separations greater than 10 A shows that there are only marginal differences in reliability between using Coulomb's law with an appropriate form of epsilon (r) or the finite difference approach for solving Poisson's equation. Thus it is concluded that pK shifts can be calculated just as well, and with considerably less effort, using Coulomb's law.

Electronic determinants of the anti-inflammatory action of benzoic and salicylic acids.

Ab initio, quantum chemical methods have been used to study the possible modes of binding of benzoic and salicylic acids to cyclooxygenase which lead to their anti-inflammatory action. The biological data for this work were obtained from full dose response curves of the inhibitory potency of active compounds on prostaglandin production in mouse macrophages. With the help of simple regression analysis the most important reactivity indices are identified and the ionization state of the active species is discussed. From the physical significance implied by these regressions and an analysis of the electronic charge distributions of the frontier orbitals, a two-way charge transfer model is proposed. The electrostatic potentials of active and inactive congeners have been analyzed, and it is shown that an electrostatic orientation effect seems to make an important contribution to the binding of the active molecules to their receptor site. An electrostatic potential model of the binding site is proposed, and it is shown that this model is able to rationalize the source of activity or inactivity of the investigated substances.

Quantum chemical analysis of structure-activity relationships in nonsteroidal anti-inflammatory drugs.

Ab initio, quantum chemical methods are being used to analyze and interpret structure-activity relationships in nonsteroidal anti-inflammatory drugs. The biological data for this study derive from full dose-response curves of the inhibitory potency of phenols, salicylates, and benzoates on prostaglandin production in mouse macrophages. To date, about 80 compounds have been assayed and from this group a sample of 30 has been selected for calculation. The results show a correlation between the potency of the active compounds and the orbital energy of the highest occupied molecular orbital (HOMO) with a correlation coefficient of r approximately 0.8. These results indicate that potency increases with decreasing binding strength of the pi-HOMO electrons, suggesting that charge transfer may be important for interaction with specific or nonspecific binding sites.