Side-chain rotational isomerization in proteins: a mechanism involving gating and transient packing defects

Free-Energy Landscape and Rate Estimation of the Aromatic Ring Flips in Basic Pancreatic Trypsin Inhibitors Using Metadynamics

Aromatic side chains (phenylalanine and tyrosine) of a protein flip by 180° around the Cβ-Cγ axis (χ2 dihedral of the side chain), producing two symmetry-equivalent states. The study of ring flip dynamics with nuclear magnetic resonance (NMR) experiments helps to understand local conformational fluctuations. Ring flips are categorized as slow (milliseconds and onward) or fast (nanoseconds to near milliseconds) based on timescales accessible to NMR experiments. In this study, we investigated the ability of the infrequent metadynamics approach to estimate the flip rate and discriminate between slow and fast ring flips for eight individual aromatic side chains (F4, Y10, Y21, F22, Y23, F33, Y35, and F45) of the basic pancreatic trypsin inhibitor. Well-tempered metadynamics simulations were performed to estimate the ring-flipping free-energy surfaces for all eight aromatic residues. The results indicate that χ2 as a standalone collective variable (CV) is not sufficient to obtain computationally consistent results. Inclusion of a complementary CV, such as χ1(Cα-Cβ), solved the problem for most residues and enabled us to classify fast and slow ring flips. This indicates the importance of librational motions in ring flips. Multiple pathways and mechanisms were observed for residues F4, Y10, and F22. Recrossing events were observed for residues F22 and F33, indicating a possible role of friction effects in ring flipping. The results demonstrate the successful application of infrequent metadynamics to estimate ring flip rates and identify certain limitations of the approach.

Molecular basis of secondary relaxation in stiff-chain glassy polymers

Recent progress in establishing local order in polycarbonate-like glasses using rotational echo double resonance and centerband-only detection of exchange solid-state nuclear magnetic resonance (NMR) has stimulated a renewed attempt to connect molecular motion within glassy polymers and the mechanical properties of the glass. We have in fact established a correlation between molecular motion characterized by NMR and the mechanical secondary relaxation (tan δ) for nine polycarbonate-like glasses. All of the NMR and mechanical data are for T ≪ Tg. The resulting structural insights suggest that the chains of these polymers are simultaneously both Flory random coils and Vol'kenstein bundles. The cooperative motions of groups of bundles can be described qualitatively by a variety of constrained-kinetics models of the glass. All of the models share a common trait for large-amplitude motion: an exponential increase in the time required for an inter-bundle dilation event with a linear increase in bundle group size. This dependence and a locally ordered Vol'kenstein bundle lead to an understanding of the surprising 60° (K) shift of tan δ to higher temperature for ring-fluoro-polycarbonate relative to that of polycarbonate by the apparently minor substitution of a fluorine for a hydrogen on every fourth ring.

Forging tools for refining predicted protein structures

Refining predicted protein structures with all-atom molecular dynamics simulations is one route to producing, entirely by computational means, structural models of proteins that rival in quality those that are determined by X-ray diffraction experiments. Slow rearrangements within the compact folded state, however, make routine refinement of predicted structures by unrestrained simulations infeasible. In this work, we draw inspiration from the fields of metallurgy and blacksmithing, where practitioners have worked out practical means of controlling equilibration by mechanically deforming their samples. We describe a two-step refinement procedure that involves identifying collective variables for mechanical deformations using a coarse-grained model and then sampling along these deformation modes in all-atom simulations. Identifying those low-frequency collective modes that change the contact map the most proves to be an effective strategy for choosing which deformations to use for sampling. The method is tested on 20 refinement targets from the CASP12 competition and is found to induce large structural rearrangements that drive the structures closer to the experimentally determined structures during relatively short all-atom simulations of 50 ns. By examining the accuracy of side-chain rotamer states in subensembles of structures that have varying degrees of similarity to the experimental structure, we identified the reorientation of aromatic side chains as a step that remains slow even when encouraging global mechanical deformations in the all-atom simulations. Reducing the side-chain rotamer isomerization barriers in the all-atom force field is found to further speed up refinement.

Effect of Substitution on the Aniline Moiety of the GPR88 Agonist 2-PCCA: Synthesis, Structure-Activity Relationships, and Molecular Modeling Studies

GPR88, an orphan receptor richly expressed in the striatum, is implicated in a number of basal ganglia-associated disorders. In order to elucidate the functions of GPR88, an in vivo probe appropriate for CNS investigation is required. We previously reported that 2-PCCA was able to modulate GPR88-mediated cAMP production through a Gα_i-coupled pathway. Early structure-activity relationship (SAR) studies suggested that the aniline moiety of 2-PCCA is a suitable site for diverse modifications. Aimed at elucidating structural requirements in this region, we have designed and synthesized a series of analogues bearing a variety of substituents at the phenyl ring of the aniline moiety. Several compounds (e.g., 5j, 5o) showed improved or comparable potency, but have lower lipophilicity than 2-PCCA (clogP 6.19). These compounds provide the basis for further optimization to probe GPR88 in vivo functions. Computational studies confirmed the SAR trends and supported the notion that 4'-substituents on the biphenyl ring exit through a largely hydrophobic binding site to the extracellular loop.

Revisiting the myths of protein interior: studying proteins with mass-fractal hydrophobicity-fractal and polarizability-fractal dimensions

A robust marker to describe mass, hydrophobicity and polarizability distribution holds the key to deciphering structural and folding constraints within proteins. Since each of these distributions is inhomogeneous in nature, the construct should be sensitive in describing the patterns therein. We show, for the first time, that the hydrophobicity and polarizability distributions in protein interior follow fractal scaling. It is found that (barring ‘all-α’) all the major structural classes of proteins have an amount of unused hydrophobicity left in them. This amount of untapped hydrophobicity is observed to be greater in thermophilic proteins, than that in their (structurally aligned) mesophilic counterparts. ‘All-β’(thermophilic, mesophilic alike) proteins are found to have maximum amount of unused hydrophobicity, while ‘all-α’ proteins have been found to have minimum polarizability. A non-trivial dependency is observed between dielectric constant and hydrophobicity distributions within (α+β) and ‘all-α’ proteins, whereas absolutely no dependency is found between them in the ‘all-β’ class. This study proves that proteins are not as optimally packed as they are supposed to be. It is also proved that origin of α-helices are possibly not hydrophobic but electrostatic; whereas β-sheets are predominantly hydrophobic in nature. Significance of this study lies in protein engineering studies; because it quantifies the extent of packing that ensures protein functionality. It shows that myths regarding protein interior organization might obfuscate our knowledge of actual reality. However, if the later is studied with a robust marker of strong mathematical basis, unknown correlations can still be unearthed; which help us to understand the nature of hydrophobicity, causality behind protein folding, and the importance of anisotropic electrostatics in stabilizing a highly complex structure named ‘proteins’.

The dynamics of ligand barrier crossing inside the acetylcholinesterase gorge

The dynamics of ligand movement through the constricted region of the acetylcholinesterase gorge is important in understanding how the ligand gains access to and is released from the active site of the enzyme. Molecular dynamics simulations of the simple ligand, tetramethylammonium, crossing this bottleneck region are conducted using umbrella potential sampling and activated flux techniques. The low potential of mean force obtained is consistent with the fast reaction rate of acetylcholinesterase observed experimentally. From the results of the activated dynamics simulations, local conformational fluctuations of the gorge residues and larger scale collective motions of the protein are found to correlate highly with the ligand crossing.

Acetylcholinesterase: Enhanced Fluctuations and Alternative Routes to the Active Site in the Complex with Fasciculin-2

A 15 ns molecular dynamics simulation is reported for the complex of mouse acetylcholinesterase (mAChE) and the protein neurotoxin fasciculin-2. As compared to a 15 ns simulation of apo-mAChE, the structural fluctuations of the enzyme are substantially increased in magnitude for the enzyme in the complex. Fluctuations of part of the long omega loop (residues 69-96) are particularly enhanced. This loop forms one wall of the active site, and the enhanced fluctuations lead to additional routes of access to the active site.

Characterization of rates of ring-flipping in trimethoprim in its ternary complexes with Lactobacillus casei dihydrofolate reductase and coenzyme analogues

NMR measurements have been used to investigate rates of ring-flipping and the activation parameters for the trimethoxybenzyl ring of the antibacterial drug trimethoprim (TMP) bound to Lactobacillus casei dihydrofolate reductase (DHFR) for a series of ternary complexes formed with analogues of the coenzyme NADPH. Rates were obtained at several temperatures from line shape analyses ((13)C-edited HSQC (1)H spectra) and transfer of magnetization measurements (zz-HSQC) on complexes containing 3'-O-[(13)C]trimethoprim. Examination of the structures of the complexes indicates that ring-flipping can only be achieved following major conformational changes and transient fluctuations of the protein and coenzyme structure around the trimethoxybenzyl ring. There is no simple correlation between rates of ring-flipping and binding constants. The presence of the coenzyme nicotinamide ring (in either its reduced or its oxidized forms) in the binding site close to the trimethoxybenzyl ring moiety is the major factor reducing the ring-flipping on coenzyme binding. Thus, the ternary complex with NADPH shows the largest reduction in the rate of ring-flipping (11 +/- 3 s(-)(1) at 298 K) as compared with the binary complex (793 +/- 80 s(-)(1) at 298 K). Complexes with NADPH analogues that either have no nicotinamide ring or are known to have their nicotinamide rings removed from the binding site show the smallest reductions. For the DHFR.TMP.NADP(+) complex where there are two conformations present, very different rates of ring-flipping were observed for the two forms. The activation parameters (DeltaH() and DeltaS()) for the ring-flipping in all the complexes are discussed in terms of the protein-ligand interactions and the possible constraints on the pathway through the transition state.

Access of ligands to cavities within the core of a protein is rapid

We have investigated the magnitude and timescale of fluctuations within the core of a protein using the exchange kinetics of indole and benzene binding to engineered hydrophobic cavities in T4 lysozyme. The crystal structures of variant-benzene complexes suggest that relatively large scale fluctuations (1-2 angstrom) of backbone atoms are required for entry of these ligands into the core. Nonetheless, these ligands enter the cavities rapidly, with bimolecular rate constants of approximately 10(6)-10(7) M(-1) s(-1) and a low activation barrier, 2-5 kcal mol(-1). These results suggest that protein cores undergo substantial fluctuations on the millisecond to microsecond timescale and that entry of small molecules into protein interiors is not strongly limited by steric occlusion.

Conformational and helicoidal analysis of the molecular dynamics of proteins: "curves," dials and windows for a 50 psec dynamic trajectory of BPTI

A new procedure for the graphic analysis of molecular dynamics (MD) simulations on proteins is introduced, in which comprehensive visualization of results and pattern recognition is greatly facilitated. The method involves determining the conformational and helicoidal parameters for each structure entering the analysis via the method "Curves," developed for proteins by Sklenar, Etchebest, and Lavery (Proteins: Structure, Function Genet. 6:46-60, 1989) followed by a novel computer graphic display of the results. The graphic display is organized systematically using conformation wheels ("dials") for each torsional parameter and "windows" on the range values assumed by the linear and angular helicoidal parameters, and is present in a form isomorphous with the primary structure per se. The complete time evolution of dynamic structure can then be depicted in a set of four composite figures. Dynamic aspects of secondary and tertiary structure are also provided. The procedure is illustrated with an analysis of a 50 psec in vacuo simulation on the 58 residue protein, bovine pancreatic trypsin inhibitor (BPTI), in the vicinity of the local minimum on the energy surface corresponding to a high resolution crystal structure. The time evolution of 272 conformational and 788 helicoidal parameters for BPTI is analyzed. A number of interesting features can be discerned in the analysis, including the dynamic range of conformational and helicoidal motions, the dynamic extent of 2 degrees structure motifs, and the calculated fluctuations in the helix axis. This approach is expected to be useful for a critical analysis of the effects of various assumptions about force field parameters, truncation of potentials, solvation, and electrostatic effects, and can thus contribute to the development of more reliable simulation protocols for proteins. Extensions of the analysis to present differential changes in conformational and helicoidal parameters is expected to be valuable in MD studies of protein complexes with substrates, inhibitors, and effectors and in determining the nature of structural changes in protein-protein interactions.

Protein-ligand dynamics. A 96 picosecond simulation of a myoglobin-xenon complex

A 96 picosecond dynamics trajectory of myoglobin with five xenon-probe ligands in internal cavities is examined to study the effect of protein motions on ligand motion and internal cavity fluctuations. Average structural and energetic properties indicate that the simulation is well behaved. The average protein volume is similar to the volume of the X-ray model and the main-chain atom root-mean-square deviation between the X-ray model and the average dynamical structure is 1.25 A. The protein volume oscillates 3 to 4% around the volume of the X-ray structure. These fluctuations lead to changes in the internal free volume and in the size, shape and location of atom-sized cavity features. Transient cavities produced in the simulation have a crucial role in the movement of two of the ligands. One of the ligands escapes to the protein surface, whilst a second ligand travels through the protein interior. Complex gating processes involving several protein residues are responsible for producing the necessary pores through which the ligand passes between transient cavities or packing defects.

The simulated dynamics of the insulin monomer and their relationship to the molecule's structure

Insulin crystallizes in different forms, some of which show different conformations for the different molecules in the asymmetric unit. This observation leads to the question as to which conformation the molecule will adopt in solution. Molecular dynamics computer simulations of rhombohedral 2 Zn pig insulin have been carried out for both monomers (1 and 2) independently in order to study their behaviour in the absence of quaternary structure and crystal packing forces. These preliminary 120 ps simulations suggest that both monomers converge in solution to very similar conformations which differ from the X-ray structures of both monomer 1 and 2 (Chinese nomenclature), but are closer to the former, as has previously been suggested by an analysis of the crystal packing (Chothia et al. 1983) and by energy minimization (Wodak et al. 1984). The secondary structure of the molecules is basically preserved, as expected. A detailed description of the conformational changes is given.

Dynamic simulations of oxygen binding to myoglobin

We report dynamic simulations of the process by which a dioxygen molecule enters or leaves the heme pocket region of myoglobin along a path between the distal histidine (E7) and valine (E11). Our reaction coordinate measures the distance of the ligand from a "dividing plane" defined by three protein atoms. The equilibrium probability distribution as a function of this coordinate is determined by a series of molecular-dynamic simulations with overlapping "umbrella" constraining potentials; the resulting potential of mean force has a barrier of about 7 kcal/mol for exit from the heme pocket. A comparison of this free energy profile with the corresponding potential energy profile suggests that entropy effects dominate the kinetic barrier. Reactive trajectories are generated from dynamic simulations beginning at the top of the potential of mean force; only a small fraction of these recross the dividing surface, indicating that transition state theory may be a good approximation for this process.

Atomic size packing defects in proteins

The three-dimensional refined high resolution structures of 20 proteins were examined for the presence of packing defects of atomic size or larger. Of the proteins examined, 12 had no such packing defects, 6 proteins had just 1 packing defect, and 2 proteins had 2 or 3 packing defects. These results confirm earlier studies on smaller samples of proteins which demonstrated that proteins are well packed. The atoms that surround the packing defects are almost always hydrophobic (carbon or sulfur). This study also tabulated the number of internal waters in each protein, which varied from 0 to 28.