Sergio A. Hassan

A critical analysis of continuum electrostatics: The screened Coulomb potential–implicit solvent model and the study of the alanine dipeptide and discrimination of misfolded structures of proteins

An analysis of the screened Coulomb potential–implicit solvent model (SCP–ISM) is presented showing that general equations for both the electrostatic and solvation free energy can be derived in a continuum approach, using statistical averaging of the polarization field created by the solvent around the molecule. The derivation clearly shows how the concept of boundary, usually found in macroscopic approaches, is eliminated when the continuum model is obtained from a microscopic treatment using appropriate averaging techniques. The model is used to study the alanine dipeptide in aqueous solution, as well as the discrimination of native protein structures from misfolded conformations. For the alanine dipeptide the free energy surface in the ϕ–ψ space is calculated and compared with recently reported results of a detailed molecular dynamics simulation using an explicit representation of the solvent, and with other available data. The study showed that the results obtained using the SCP–ISM are comparable to those of the explicit water calculation and compares favorably to the FDPB approach. Both transition states and energy minima show a high correlation (r > 0.98) with the results obtained in the explicit water analysis. The study of the misfolded structures of proteins comprised the analysis of three standard decoy sets, namely, the EMBL, Park and Levitt, and Bakers CASP3 sets. In all cases the SCP–ISM discriminated well the native structures of the proteins, and the best‐predicted structures were always near‐native (cRMSD ∼2 Å). Proteins 2002;47:45–61.

Molecular dynamics simulations of peptides and proteins with a continuum electrostatic model based on screened Coulomb potentials

A continuum electrostatics approach for molecular dynamics (MD) simulations of macromolecules is presented and analyzed for its performance on a peptide and a globular protein. The approach incorporates the screened Coulomb potential (SCP) continuum model of electrostatics, which was reported earlier. The model was validated in a broad set of tests some of which were based on Monte Carlo simulations that included single amino acids, peptides, and proteins. The implementation for large‐scale MD simulations presented in this article is based on a pairwise potential that makes the electrostatic model suitable for fast analytical calculation of forces. To assess the suitability of the approach, a preliminary validation is conducted, which consists of (i) a 3‐ns MD simulation of the immunoglobulin‐binding domain of streptococcal protein G, a 56‐residue globular protein and (ii) a 3‐ns simulation of Dynorphin, a biological peptide of 17 amino acids. In both cases, the results are compared with those obtained from MD simulations using explicit water (EW) molecules in an all‐atom representation. The initial structure of Dynorphin was assumed to be an α‐helix between residues 1 and 9 as suggested from NMR measurements in micelles. The results obtained in the MD simulations show that the helical structure collapses early in the simulation, a behavior observed in the EW simulation and consistent with spectroscopic data that suggest that the peptide may adopt mainly an extended conformation in water. The dynamics of protein G calculated with the SCP implicit solvent model (SCP‐ISM) reveals a stable structure that conserves all the elements of secondary structure throughout the entire simulation time. The average structures calculated from the trajectories with the implicit and explicit solvent models had a cRMSD of 1.1 Å, whereas each average structure had a cRMSD of about 0.8Å with respect to the X‐ray structure. The main conformational differences of the average structures with respect to the crystal structure occur in the loop involving residues 8–14. Despite the overall similarity of the simulated dynamics with EW and SCP models, fluctuations of side‐chains are larger when the implicit solvent is used, especially in solvent exposed side‐chains. The MD simulation of Dynorphin was extended to 40 ns to study its behavior in an aqueous environment. This long simulation showed that the peptide has a tendency to form an α‐helical structure in water, but the stabilization free energy is too weak, resulting in frequent interconversions between random and helical conformations during the simulation time. The results reported here suggest that the SCP implicit solvent model is adequate to describe electrostatic effects in MD simulation of both peptides and proteins using the same set of parameters. It is suggested that the present approach could form the basis for the development of a reliable and general continuum approach for use in molecular biology, and directions are outlined for attaining this long‐term goal. Proteins 2003;51:109–125.

Computer simulation of ion cluster speciation in concentrated aqueous solutions at ambient conditions.

Dynamic simulations are used to investigate ion cluster formation in unsaturated aqueous NaCl at 25 degrees C. Statistical, structural, and dynamic properties are reported. An effort is made to identify general behaviors that are expected to hold beyond the limitations of the force field. Above approximately 1 M, clusters with more than ten ions begin to form after approximately 10-20 ns of simulation time, but no evidence of irreversible ion aggregation is observed. Cluster survival times are estimated, showing that the kinetics become increasingly complex as salt is added, leading to multiple decay rates. Cluster dipole moment distributions show characteristic peaks that reflect the preferred conformations of clusters in solution. These are modulated by electrostatic and liquid-structure forces and are described in detail for clusters of up to five ions. For a given size and charge, the cluster morphology is independent of salt concentration. Below approximately 2 M, clusters affect the structure of water in their first hydration shells, so dipole moments parallel to the cluster macrodipoles are induced. These effects show a weak dependence with concentration below approximately 2 M, but vanish in the 2-3 M range. A possible connection with the structural transition recently suggested by NMR data in concentrated electrolytes is discussed. The effects of electrostatics on cluster speciation and morphology are discussed based on results from a set of simulations carried out with the ionic charges removed.

Long Dynamics Simulations of Proteins Using Atomistic Force Fields and a Continuum Representation of Solvent Effects: Calculation of Structural and Dynamic Properties

Long dynamics simulations were carried out on the B1 immunoglobulin‐binding domain of streptococcal protein G (ProtG) and bovine pancreatic trypsin inhibitor (BPTI) using atomistic descriptions of the proteins and a continuum representation of solvent effects. To mimic frictional and random collision effects, Langevin dynamics (LD) were used. The main goal of the calculations was to explore the stability of tens‐of‐nanosecond trajectories as generated by this molecular mechanics approximation and to analyze in detail structural and dynamical properties. Conformational fluctuations, order parameters, cross correlation matrices, residue solvent accessibilities, pKa values of titratable groups, and hydrogen‐bonding (HB) patterns were calculated from all of the trajectories and compared with available experimental data. The simulations comprised over 40 ns per trajectory for ProtG and over 30 ns per trajectory for BPTI. For comparison, explicit water molecular dynamics simulations (EW/MD) of 3 ns and 4 ns, respectively, were also carried out. Two continuum simulations were performed on each protein using the CHARMM program, one with the all‐atom PAR22 representation of the protein force field (here referred to as PAR22/LD simulations) and the other with the modifications introduced by the recently developed CMAP potential (CMAP/LD simulations). The explicit solvent simulations were performed with PAR22 only. Solvent effects are described by a continuum model based on screened Coulomb potentials (SCP) reported earlier, i.e., the SCP‐based implicit solvent model (SCP–ISM). For ProtG, both the PAR22/LD and the CMAP/LD 40‐ns trajectories were stable, yielding Cα root mean square deviations (RMSD) of about 1.0 and 0.8 Å respectively along the entire simulation time, compared to 0.8 Å for the EW/MD simulation. For BPTI, only the CMAP/LD trajectory was stable for the entire 30‐ns simulation, with a Cα RMSD of ≈1.4 Å, while the PAR22/LD trajectory became unstable early in the simulation, reaching a Cα RMSD of about 2.7 Å and remaining at this value until the end of the simulation; the Cα RMSD of the EW/MD simulation was about 1.5 Å. The source of the instabilities of the BPTI trajectories in the PAR22/LD simulations was explored by an analysis of the backbone torsion angles. To further validate the findings from this analysis of BPTI, a 35‐ns SCP–ISM simulation of Ubiquitin (Ubq) was carried out. For this protein, the CMAP/LD simulation was stable for the entire simulation time (Cα RMSD of ≈1.0 Å), while the PAR22/LD trajectory showed a trend similar to that in BPTI, reaching a Cα RMSD of ≈1.5 Å at 7 ns. All the calculated properties were found to be in agreement with the corresponding experimental values, although local deviations were also observed. HB patterns were also well reproduced by all the continuum solvent simulations with the exception of solvent‐exposed side chain–side chain (sc–sc) HB in ProtG, where several of the HB interactions observed in the crystal structure and in the EW/MD simulation were lost. The overall analysis reported in this work suggests that the combination of an atomistic representation of a protein with a CMAP/CHARMM force field and a continuum representation of solvent effects such as the SCP–ISM provides a good description of structural and dynamic properties obtained from long computer simulations. Although the SCP–ISM simulations (CMAP/LD) reported here were shown to be stable and the properties well reproduced, further refinement is needed to attain a level of accuracy suitable for more challenging biological applications, particularly the study of protein–protein interactions. Proteins 2005.

Ab Initio Computational Modeling of Loops in G-Protein- Coupled Receptors: Lessons from the Crystal Structure of Rhodopsin

With the help of the crystal structure of rhodopsin an ab initio method has been developed to calculate the three‐dimensional structure of the loops that connect the transmembrane helices (TMHs). The goal of this procedure is to calculate the loop structures in other G‐protein coupled receptors (GPCRs) for which only model coordinates of the TMHs are available. To mimic this situation a construct of rhodopsin was used that only includes the experimental coordinates of the TMHs while the rest of the structure, including the terminal domains, has been removed. To calculate the structure of the loops a method was designed based on Monte Carlo (MC) simulations which use a temperature annealing protocol, and a scaled collective variables (SCV) technique with proper structural constraints. Because only part of the protein is used in the calculations the usual approach of modeling loops, which consists of finding a single, lowest energy conformation of the system, is abandoned because such a single structure may not be a representative member of the native ensemble. Instead, the method was designed to generate structural ensembles from which the single lowest free energy ensemble is identified as representative of the native folding of the loop. To find the native ensemble a successive series of SCV‐MC simulations are carried out to allow the loops to undergo structural changes in a controlled manner. To increase the chances of finding the native funnel for the loop, some of the SCV‐MC simulations are carried out at elevated temperatures. The native ensemble can be identified by an MC search starting from any conformation already in the native funnel. The hypothesis is that native structures are trapped in the conformational space because of the high‐energy barriers that surround the native funnel. The existence of such ensembles is demonstrated by generating multiple copies of the loops from their crystal structures in rhodopsin and carrying out an extended SCV‐MC search. For the extracellular loops e1 and e3, and the intracellular loop i1 that were used in this work, the procedure resulted in dense clusters of structures with Cα‐RMSD ∼0.5 Å. To test the predictive power of the method the crystal structure of each loop was replaced by its extended conformations. For e1 and i1 the procedure identifies native clusters with Cα‐RMSD ∼0.5 Å and good structural overlap of the side chains; for e3, two clusters were found with Cα‐RMSD ∼1.1 Å each, but with poor overlap of the side chains. Further searching led to a single cluster with lower Cα‐RMSD but higher energy than the two previous clusters. This discrepancy was found to be due to the missing elements in the constructs available from experiment for use in the calculations. Because this problem will likely appear whenever parts of the structural information are missing, possible solutions are discussed. Proteins 2006.

Effects of Electric Fields on Proton Transport Through Water Chains

Molecular dynamics simulations on quantum energy surfaces are carried out to study the effects of perturbing electric fields on proton transport (PT) in protonated water chains. As an idealized model of a hydrophobic cavity in the interior of a protein the water molecules are confined into a carbon nanotube (CNT). The water chain connects a hydrated hydronium ion (H3O+) at one end of the CNT and an imidazole molecule at the other end. Without perturbing electric fields PT from the hydronium proton donor to the imidazole acceptor occurs on a picosecond time scale. External perturbations to PT are created by electric fields of varying intensities, normal to the CNT axis, generated by a neutral pair of charges on the nanotube wall. For fields above approximately 0.5 VA, the hydronium ion is effectively trapped at the CNT center, and PT blocked. Fields of comparable strength are generated inside proteins by nearby polar/charged amino acids. At lower fields the system displays a rich dynamic behavior, where the excess charge shuttles back and forth along the water chain before reaching the acceptor group on the picosecond time scale. The effects of the perturbing field on the proton movement are analyzed in terms of structural and dynamic properties of the water chain. The implications of these observations on PT in biomolecular systems and its control by external perturbing fields are discussed.

Water-exclusion and liquid-structure forces in implicit solvation.

A continuum model of solvation is proposed to describe (i) long-range electrostatic effects of water exclusion resulting from incomplete and anisotropic hydration in crowded environments and (ii) short-range effects of liquid-structure forces on the hydrogen-bond interactions at solute/water interfaces. The model is an extension of the phenomenological screened coulomb potential-based implicit model of solvation. The developments reported here allow a more realistic representation of highly crowded and spatially heterogeneous environments, such as those in the interior of a living cell. Only the solvent is treated as a continuum medium. It is shown that the electrostatic effects of long-range water-exclusion can strongly affect protein-protein binding energies and are then related to the thermodynamics of complex formation. Hydrogen-bond interactions modulated by the liquid structure at interfaces are calibrated based on systematic calculations of potentials of mean force in explicit water. The electrostatic component of the model is parametrized for monovalent, divalent and trivalent ions. The conceptual and practical aspects of the model are discussed based on simulations of protein complexation and peptide folding. The current implementation is ~1.5 times slower than the gas-phase force field and exhibits good parallel performance.

Evidence that proline focuses movement of the floppy loop of arylalkylamine N-acetyltransferase (EC 2.3.1.87).

Arylalkylamine N-acetyltransferase (AANAT) catalyzes the N-acetylation of serotonin, the penultimate step in the synthesis of melatonin. Pineal AANAT activity increases at night in all vertebrates, resulting in increased melatonin production. This increases circulating levels of melatonin, thereby providing a hormonal signal of darkness. Kinetic and structural analysis of AANAT has determined that one element is floppy. This element, termed Loop 1, is one of three loops that comprise the arylalkylamine binding pocket. During the course of chordate evolution, Loop 1 acquired the tripeptide CPL, and the enzyme became highly active. Here we focused on the functional importance of the CPL tripeptide and found that activity was markedly reduced when it was absent. Moreover, increasing the local flexibility of this tripeptide region by P64G and P64A mutations had the counterintuitive effect of reducing activity and reducing the overall movement of Loop 1, as estimated from Langevin dynamics simulations. Binding studies indicate that these mutations increased the off-rate constant of a model substrate without altering the dissociation constant. The structural kink and local rigidity imposed by Pro-64 may enhance activity by favoring configurations of Loop 1 that facilitate catalysis and do not become immobilized by intramolecular interactions.

Structure Calculation of Protein Segments Connecting Domains with Defined Secondary Structure: A Simulated Annealing Monte Carlo Combined with Biased Scaled Collective Variables Technique

A method for modeling segments of proteins that connect regions with defined secondary structure is illustrated with a study of long segments (8–13 amino acids) that include parts of defined secondary structure motifs. Loop structure calculation can be considered a particular case of this more challenging problem. The new algorithm first finds conformations representative of the segment structure tethered to the protein at one terminus only, and subsequently drives the free end of the segment towards its attachment point using a reversed harmonic constrained simulated annealing scheme. An adjustable force constant drives the free terminal towards the attachment point, using the Monte Carlo (MC) technique of scaled collective variables (SCV). Each segment is initially placed in an extended conformation with the N-terminus covalently bound to the protein, and MC simulated annealing is carried out to find the preferred conformations of the segment. The resulting families of conformations prepare the segment for attachment of the C-terminus. In the second stage a hierarchical protocol drives the segment’s C-terminus towards its final position in the protein. The free C-terminus is attached to a dummy residue, identical to the target residue where the segment will be connected. Successive MC simulations are carried out using the SCV method with increasingly larger values of the harmonic force constant that slowly stabilize the free energy surface to ensure the correct orientation of the segment region with the rest of the system. The performance of the method was evaluated for eight segments in the a-subunit of the G protein transducin for which a high-resolution X-ray crystal structure (2.0 A) is available. The calculation was performed using the all-atom representation and the CHARMM force field with the electrostatic effects of the solvent described implicitly by the new SCP general continuum model. The segments that are most exposed to solvent are found to be represented best with this method.

Specific and Non-Specific Protein Association in Solution: Computation of Solvent Effects and Prediction of First-Encounter Modes for Efficient Configurational Bias Monte Carlo Simulations

Weak and ultraweak protein-protein association play a role in molecular recognition and can drive spontaneous self-assembly and aggregation. Such interactions are difficult to detect experimentally, and are a challenge to the force field and sampling technique. A method is proposed to identify low-population protein-protein binding modes in aqueous solution. The method is designed to identify preferential first-encounter complexes from which the final complex(es) at equilibrium evolve. A continuum model is used to represent the effects of the solvent, which accounts for short- and long-range effects of water exclusion and for liquid-structure forces at protein/liquid interfaces. These effects control the behavior of proteins in close proximity and are optimized on the basis of binding enthalpy data and simulations. An algorithm is described to construct a biasing function for self-adaptive configurational-bias Monte Carlo of a set of interacting proteins. The function allows mixing large and local changes in the spatial distribution of proteins, thereby enhancing sampling of relevant microstates. The method is applied to three binary systems. Generalization to multiprotein complexes is discussed.