Thomas Simonson

Crystallography & NMR system: A new software suite for macromolecular structure determination.

A new software suite, called Crystallography & NMR System (CNS), has been developed for macromolecular structure determination by X-ray crystallography or solution nuclear magnetic resonance (NMR) spectroscopy. In contrast to existing structure-determination programs, the architecture of CNS is highly flexible, allowing for extension to other structure-determination methods, such as electron microscopy and solid-state NMR spectroscopy. CNS has a hierarchical structure: a high-level hypertext markup language (HTML) user interface, task-oriented user input files, module files, a symbolic structure-determination language (CNS language), and low-level source code. Each layer is accessible to the user. The novice user may just use the HTML interface, while the more advanced user may use any of the other layers. The source code will be distributed, thus source-code modification is possible. The CNS language is sufficiently powerful and flexible that many new algorithms can be easily implemented in the CNS language without changes to the source code. The CNS language allows the user to perform operations on data structures, such as structure factors, electron-density maps, and atomic properties. The power of the CNS language has been demonstrated by the implementation of a comprehensive set of crystallographic procedures for phasing, density modification and refinement. User-friendly task-oriented input files are available for nearly all aspects of macromolecular structure determination by X-ray crystallography and solution NMR.

IMPLICIT SOLVENT MODELS

Implicit solvent models for biomolecular simulations are reviewed and their underlying statistical mechanical basis is discussed. The fundamental quantity that implicit models seek to approximate is the solute potential of mean force, which determines the statistical weight of solute conformations, and which is obtained by averaging over the solvent degrees of freedom. It is possible to express the total free energy as the reversible work performed in two successive steps. First, the solute is inserted in the solvent with zero atomic partial charges; second, the atomic partial charges of the solute are switched from zero to their full values. Consequently, the total solvation free energy corresponds to a sum of non-polar and electrostatic contributions. These two contributions are often approximated by simple geometrical models (such as solvent exposed area models) and by macroscopic continuum electrostatics, respectively. One powerful route is to approximate the average solvent density distribution around the solute, i.e. the solute-solvent density correlation functions, as in statistical mechanical integral equations. Recent progress with semi-analytical approximations makes continuum electrostatics treatments very efficient. Still more efficient are fully empirical, knowledge-based models, whose relation to explicit solvent treatments is not fully resolved, however. Continuum models that treat both solute and solvent as dielectric continua are also discussed, and the relation between the solute fluctuations and its macroscopic dielectric constant(s) clarified.

Macromolecular electrostatics: continuum models and their growing pains

Theoretical understanding of macromolecular electrostatics has advanced substantially over the past year. Continuum models have given promising results for calculating protein-ligand binding free energy differences, as well as pK(a)s and redox properties, particularly with explicit treatment of multiple conformers. Generalized Born and other techniques have led to the first molecular dynamics simulations of proteins and RNA with continuum solvent. Continuum and microscopic descriptions of dielectric relaxation have been critically compared.

Electrostatics and dynamics of proteins

Proteins are the working chemists of living cells. They are complex macromolecules, which display a rich and sometimes counterintuitive behaviour on many length- and timescales. They contain charged and polar groups, and electrostatic interactions control important aspects of their structure and function. Experiments and computer simulations have been used intensively to probe their electrostatic and dielectric properties. A simple framework to rationalize the results is continuum electrostatics, even though proteins are smaller than the usual, macroscopic length scales of continuum theory. We discuss selected topics, including protein structure, dynamics, and solvation; the dielectric response of proteins at large (macromolecular) and small (atomic) length scales, and the physical and numerical basis of current continuum models of proteins and protein solvation.

Protein molecular dynamics with the generalized born/ACE solvent model

Implicit solvent models are increasingly important for the study of proteins in aqueous solution. Here, the generalized Born (GB) solvent polarization model as implemented in the analytical ACE potential [Schaefer and Karplus (1996) J Phys Chem 100:1578] is used to perform molecular dynamics simulations of two small, homologous proteins: the immunoglobulin‐binding domain of streptococcal protein G and the Ras binding domain of Raf. Several model parameterizations are compared through more than 60 ns of simulation. Results are compared with two simpler solvent models—an accessible surface area model and a distant‐dependent dielectric model, with finite‐difference Poisson calculations, with existing explicit solvent simulations, and with experimental data. The simpler models yield stable but distorted structures. The best GB/ACE implementation uses a set of atomic Voronoi volumes reported recently, obtained by averaging over a large database of crystallographic protein structures. A 20% reduction is applied to the volumes, compensating in an average sense for an excessive de‐screening of individual charges inherent in the ACE self‐energy and for an undersolvation of dipolar groups inherent in the GB screening function. This GB/ACE parameterization yields stable trajectories on the 0.5–1‐ns time scale that deviate moderately (∼1.5–2.5 Å) from the X‐ray structure, reproduce approximately the surface distribution of charged, polar, and hydrophobic groups, and reproduce accurately backbone flexibility as measured by amide NMR‐order parameters. Over longer time scales (1.5–3 ns), some of the protein G runs escape from the native energy basin and deviate strongly (3 Å) from the native structure. The conformations sampled during the transition out of the native energy basin are overstabilized by the GB/ACE solvation model, as compared with a numerical treatment of the full dielectric continuum model. Proteins 2001;45:144–158.

Microscopic theory of the dielectric properties of proteins.

This paper investigates the microscopic mechanisms of charge screening in proteins. The screening of an arbitrary perturbing charge density by a protein and its surrounding solution is characterized by a generalized susceptibility, which is approximately given by the mean dipole-dipole correlation matrix of the system. This susceptibility is a microscopic quantity; the sum of its matrix elements gives the macroscopic susceptibility of continuum electrostatics. When screening of a single perturbing point charge is considered, this susceptibility reduces to a scalar quantity, dependent on position within the protein. The contribution of the positional degrees of freedom of the protein atoms can be estimated from molecular dynamics simulations. This contribution gives rise to large spatial variations of the susceptibility, whose significance for protein function is discussed. The model is applied to the small alpha helix deca-alanine, and to the electron-transfer protein cytochrome c. The results agree qualitatively with previous normal mode calculations. The importance, and the large spatial variations, of charge screening by deca-alanine suggest that dielectric screening may play a role in the binding of charged ligands by helices. In cytochrome c, the dielectric susceptibility in response to a point charge is at a minimum in the central heme region, resulting in a lowering of the reorganization free energy for charge transfer to and from the heme.

Gaussian fluctuations and linear response in an electron transfer protein

In response to charge separation or transfer, polar liquids respond in a simple linear fashion. A similar linear response for proteins might be expected from the central limit theorem and is postulated in widely used theories of protein electrostatics, including the Marcus electron transfer theory and dielectric continuum theories. Although these theories are supported by a variety of experimental data, the exact validity of a linear protein dielectric response has been difficult to determine. Molecular dynamics simulations are presented that establish a linear dielectric response of both protein and surrounding solvent over the course of a biologically relevant electron transfer reaction: oxido-reduction of yeast cytochrome c in solution. Using an umbrella-sampling free energy approach with long simulations, an accurate treatment of long-range electrostatics and both classical and quantum models of the heme, good agreement is obtained with experiment for the redox potential relative to a heme–octapeptide complex. We obtain a reorganization free energy that is only half that for heme–octapeptide and is reproduced with a dielectric continuum model where the heme vicinity has a dielectric constant of only 1.1. This value implies that the contribution of protein reorganization to the electron transfer free energy barrier is reduced almost to the theoretical limit (a dielectric of one), and that the fluctuations of the electrostatic potential on the heme have a simple harmonic form, in accord with Marcus theory, even though the fluctuations of many individual protein groups (especially at the protein surface) are anharmonic.

Molecular Dynamics Simulations Show That Conformational Selection Governs the Binding Preferences of Imatinib for Several Tyrosine Kinases

Tyrosine kinases transmit cellular signals through a complex mechanism, involving their phosphorylation and switching between inactive and active conformations. The cancer drug imatinib binds tightly to several homologous kinases, including Abl, but weakly to others, including Src. Imatinib specifically targets the inactive, so-called “DFG-out” conformation of Abl, which differs from the preferred, “DFG-in” conformation of Src in the orientation of a conserved Asp-Phe-Gly (DFG) activation loop. However, recent x-ray structures showed that Src can also adopt the DFG-out conformation and uses it to bind imatinib. The Src/Abl-binding free energy difference can thus be decomposed into two contributions. Contribution i measures the different protein-imatinib interactions when either kinase is in its DFG-out conformation. Contribution ii depends on the ability of imatinib to select or induce this conformation, i.e. on the relative stabilities of the DFG-out and DFG-in conformations of each kinase. Neither contribution has been measured experimentally. We use molecular dynamics simulations to show that contribution i is very small, 0.2 ± 0.6 kcal/mol; imatinib interactions are very similar in the two kinases, including long range electrostatic interactions with the imatinib positive charge. Contribution ii, deduced using the experimental binding free energy difference, is much larger, 4.4 ± 0.9 kcal/mol. Thus, conformational selection, easy in Abl, difficult in Src, underpins imatinib specificity. Contribution ii has a simple interpretation; it closely approximates the stability difference between the DFG-out and DFG-in conformations of apo-Src. Additional calculations show that conformational selection also governs the relative binding of imatinib to the kinases c-Kit and Lck. These results should help clarify the current framework for engineering kinase signaling.

An Overview of Electrostatic Free Energy Computations for Solutions and Proteins.

Free energy simulations for electrostatic and charging processes in complex molecular systems encounter specific difficulties owing to the long-range, 1/r Coulomb interaction. To calculate the solvation free energy of a simple ion, it is essential to take into account the polarization of nearby solvent but also the electrostatic potential drop across the liquid-gas boundary, however distant. The latter does not exist in a simulation model based on periodic boundary conditions because there is no physical boundary to the system. An important consequence is that the reference value of the electrostatic potential is not an ion in a vacuum. Also, in an infinite system, the electrostatic potential felt by a perturbing charge is conditionally convergent and dependent on the choice of computational conventions. Furthermore, with Ewald lattice summation and tinfoil conducting boundary conditions, the charges experience a spurious shift in the potential that depends on the details of the simulation system such as the volume fraction occupied by the solvent. All these issues can be handled with established computational protocols, as reviewed here and illustrated for several small ions and three solvated proteins.

Alchemical free energy simulations for biological complexes: powerful but temperamental …

Free energy simulations compare multiple ligand:receptor complexes by “alchemically” transforming one into another, yielding binding free energy differences. Since their introduction in the 1980s, many technical and theoretical obstacles were surmounted, and the method (“MDFE,” since molecular dynamics are often used) has matured into a powerful tool. We describe its current status, its effectiveness, and the challenges it faces. MDFE has provided chemical accuracy for many systems but remains expensive, with significant human overhead costs. The bottlenecks have shifted, partly due to increased computer power. To study diverse sets of ligands, force field availability and accuracy can be a major difficulty. Another difficulty is the frequent need to consider multiple states, related to sidechain protonation or buried waters, for example. Sophisticated, automated methods to sample these states are maturing, such as constant pH simulations. Meanwhile, combinations of MDFE and simpler approaches, like continuum dielectric models, can be very effective. As illustrations, we show how, with careful force field parameterization, MDFE accurately predicts binding specificities between complex tetracycline ligands and their targets. We describe substrate binding to the aspartyl‐tRNA synthetase enzyme, where many distinct electrostatic states play a role, and a histidine and a Mg2+ ion act as coupled switches that help enforce a strict preference for the aspartate substrate, relative to several analogs. Overall, MDFE has achieved a predictive status, where novel ligands can be studied and molecular recognition elucidated in depth. It should play an increasing role in the analysis of complex cellular processes and biomolecular engineering. Copyright