Conformational dependence of electrostatic potential derived charges of a lipid headgroup: Glycerylphosphorylcholine

Atomic monopoles are routinely determined through a least squares fit to molecular electrostatic potentials. We report studies of the variation in atomic monopoles with variation in conformation for the zwitterionic polar head group of lecithins, a common class of lipid. The monopole of one atom, a relatively buried carbon, varied by 1.3 electron units between different conformers. “Exterior” atoms, as seen previously, showed smaller changes in charge and smaller estimated standard deviations. The total charge of local groups of atoms varied less than the charge of individual atoms, indicating that shifts in charge occurred mostly between neighboring atoms. This effect might be reflected in the high correlations seen between charges of many neighboring atoms. These correlations, while present for many logical groupings of atoms (such as within methylene and methyl groups), are curiously absent between some bonded atoms. Monopoles were fit to multiple conformations simultaneously to provide a charge set that could optimally reproduce the electrostatic potential of all the conformers as a means of generating monopoles for molecular dynamics simulations or other studies where conformation varies. In some cases, the charges on chemically equivalent atoms (e.g., the hydrogen atoms in a methyl group) were different by more than their estimated error of fit. These studies lead to the suggestion that a minimum error in reported charges is on the order of 10%. All conformations show that the positive charge of the trimethylalkyl ammonium group is carried by the methyl hydrogens; the total charge on the nine hydrogens is over 2 electron units, counterbalanced by negative monopoles on the carbons. The presence of this diffuse cloud of substantial charge would appear to be a disindicator of the use of a “united” atoms approach for these methyl groups. The effects of the charge variation on intermolecular interactions is also examined.     

Single-molecule Michaelis-Menten equations

This paper summarizes our present theoretical understanding of single-molecule kinetics associated with the Michaelis-Menten mechanism of enzymatic reactions. Single-molecule enzymatic turnover experiments typically measure the probability density f(t) of the stochastic waiting time t for individual turnovers. While f(t) can be reconciled with ensemble kinetics, it contains more information than the ensemble data; in particular, it provides crucial information on dynamic disorder, the apparent fluctuation of the catalytic rates due to the interconversion among the enzyme's conformers with different catalytic rate constants. In the presence of dynamic disorder, f(t) exhibits a highly stretched multiexponential decay at high substrate concentrations and a monoexponential decay at low substrate concentrations. We derive a single-molecule Michaelis-Menten equation for the reciprocal of the first moment of f(t), 1/, which shows a hyperbolic dependence on the substrate concentration [S], similar to the ensemble enzymatic velocity. We prove that this single-molecule Michaelis-Menten equation holds under many conditions, in particular when the intercoversion rates among different enzyme conformers are slower than the catalytic rate. However, unlike the conventional interpretation, the apparent catalytic rate constant and the apparent Michaelis constant in this single-molecule Michaelis-Menten equation are complicated functions of the catalytic rate constants of individual conformers. We also suggest that the randomness parameter r, defined as <(t - )2> / t2, can serve as an indicator for dynamic disorder in the catalytic step of the enzymatic reaction, as it becomes larger than unity at high substrate concentrations in the presence of dynamic disorder.     

Novel inhibitor discovery through virtual screening against multiple protein conformations generated via ligand-directed modeling: a maternal embryonic leucine zipper kinase example

Kinase targets have been demonstrated to undergo major conformational reorganization upon ligand binding. Such protein conformational plasticity remains a significant challenge in structure-based virtual screening methodology and may be approximated by screening against an ensemble of diverse protein conformations. Maternal embryonic leucine zipper kinase (MELK), a member of serine-threonine kinase family, has been recently found to be involved in the tumerogenic state of glioblastoma, breast, ovarian, and colon cancers. We therefore modeled several conformers of MELK utilizing the available chemogenomic and crystallographic data of homologous kinases. We carried out docking pose prediction and virtual screening enrichment studies with these conformers. The performances of the ensembles were evaluated by their ability to reproduce known inhibitor bioactive conformations and to efficiently recover known active compounds early in the virtual screen when seeded with decoy sets. A few of the individual MELK conformers performed satisfactorily in reproducing the native protein-ligand pharmacophoric interactions up to 50% of the cases. By selecting an ensemble of a few representative conformational states, most of the known inhibitor binding poses could be rationalized. For example, a four conformer ensemble is able to recover 95% of the studied actives, especially with imperfect scoring function(s). The virtual screening enrichment varied considerably among different MELK conformers. Enrichment appears to improve by selection of a proper protein conformation. For example, several holo and unliganded active conformations are better to accommodate diverse chemotypes than ATP-bound conformer. These results prove that using an ensemble of diverse conformations could give a better performance. Applying this approach, we were able to screen a commercially available library of half a million compounds against three conformers to discover three novel inhibitors of MELK, one from each template. Among the three compounds validated via experimental enzyme inhibition assays, one is relatively potent (15; K(d) = 0.37 μM), one moderately active (12; K(d) = 3.2 μM), and one weak but very selective (9; K(d) = 18 μM). These novel hits may be utilized to assist in the development of small molecule therapeutic agents useful in diseases caused by deregulated MELK, and perhaps more importantly, the approach demonstrates the advantages of choosing an appropriate ensemble of a few conformers in pursuing compound potency, selectivity, and novel chemotypes over using single target conformation for structure-based drug design in general.     

Insights into the interplay between electronic structure and protein dynamics: The case of ubiquitin

A quantum mechanical analysis of an experimental ensemble comprising 128 conformers of the protein ubiquitin has been carried out with the aid of LMO–SCF–COSMO calculations. The permanent dipole moment of the protein fluctuates in the range from 131 to 283 D while the energy-weighted average dipole has a magnitude of 197 D. The HOMO–LUMO energy gap of the conformational ensemble ranges from 7.389 to 8.397 eV and appears to being affected mainly by fluctuations in the HOMO energy. An inspection of the frontier orbitals of the 128 conformers indicates that their localization is not affected by the protein dynamics.     

Searching and optimizing structure ensembles for complex flexible sugars

NMR restrictions are suitable to specify the geometry of a molecule when a single well-defined global free energy minimum exists that is significantly lower than other local minima. Carbohydrates are quite flexible, and therefore, NMR observables do not always correlate with a single conformer but instead with an ensemble of low free energy conformers that can be accessed by thermal fluctuations. In this communication, we describe a novel procedure to identify and weight the contribution to the ensemble of local minima conformers based on comparison to residual dipolar couplings (RDCs) or other NMR observables, such as scalar couplings. A genetic algorithm is implemented to globally minimize the R factor comparing calculated RDCs to experiment. This is done by optimizing the weights of different conformers derived from the exhaustive local minima conformational search program, fast sugar structure prediction software (FSPS). We apply this framework to six human milk sugars, LND-1, LNF-1, LNF-2, LNF-3, LNnT, and LNT, and are able to determine corresponding population weights for the ensemble of conformers. Interestingly, our results indicate that in all cases the RDCs can be well represented by only a few most important conformers. This confirms that several, but not all of the glycosidic linkages in histo-blood group "epitopes" are quite rigid.     

Structural characterization of flexible proteins using small-angle X-ray scattering

Structural analysis of flexible macromolecular systems such as intrinsically disordered or multidomain proteins with flexible linkers is a difficult task as high-resolution techniques are barely applicable. A new approach, ensemble optimization method (EOM), is proposed to quantitatively characterize flexible proteins in solution using small-angle X-ray scattering (SAXS). The flexibility is taken into account by allowing for the coexistence of different conformations of the protein contributing to the experimental scattering pattern. These conformers are selected using a genetic algorithm from a pool containing a large number of randomly generated models covering the protein configurational space. Quantitative criteria are developed to analyze the EOM selected models and to determine the optimum number of conformers in the ensemble. Simultaneous fitting of multiple scattering patterns from deletion mutants, if available, provides yet more detailed local information about the structure. The efficiency of EOM is demonstrated in model and practical examples on completely or partially unfolded proteins and on multidomain proteins interconnected by linkers. In the latter case, EOM is able to distinguish between rigid and flexible proteins and to directly assess the interdomain contacts.     

Monitoring copopulated conformational states during protein folding events using electrospray ionization-ion mobility spectrometry-mass spectrometry

The precise mechanism of protein folding remains elusive and there is a deficiency of biophysical techniques that are capable of monitoring the individual behavior of copopulated protein conformers during the folding process. Herein, an ion mobility spectrometry (IMS) device integrated with electrospray ionization mass spectrometry (ESI-MS) has been used to successfully separate and analyze protein conformers differing in cross section and/or charge state. In an initial test, an ensemble of folded and partially folded conformers of the protein cytochrome c was separated. A detailed study undertaken on the amyloidogenic protein beta(2)-microglobulin (beta(2)m), which forms fibrils by protein unfolding followed by self-aggregation and is responsible for the disease dialysis-related amyloidosis, has generated important insights into its folding landscape. Initially, a systematic titration of beta(2)m over the pH range 2 to 7 using ESI-IMS-MS allowed individual conformers to be monitored and quantified throughout the acid denaturation process. Furthermore, a comparison of wild-type beta(2)m with single and double amino acid variants with a range of folding stabilities and propensities for amyloid fibril formation has provided illuminating evidence of the role of different conformers in protein stability and amyloidogenic aggregation. The ESI-IMS-MS data presented here not only demonstrate an important and informative further dimension to ESI-MS, but also illustrate the potential of the ESI-IMS-MS technique for unravelling protein folding enigmas in general and studying protein misfolding diseases in particular.     

Importance of solvent accessibility and contact surfaces in modeling side-chain conformations in proteins

Contact surface area and chemical properties of atoms are used to concurrently predict conformations of multiple amino acid side chains on a fixed protein backbone. The combination of surface complementarity and solvent-accessible surface accounts for van der Waals forces and solvation free energy. The scoring function is particularly suitable for modeling partially buried side chains. Both iterative and stochastic searching approaches are used. Our programs (Sccomp-I and Sccomp-S), with relatively fast execution times, correctly predict chi1 angles for 92-93% of buried residues and 82-84% for all residues, with an RMSD of approximately 1.7 A for side chain heavy atoms. We find that the differential between the atomic solvation parameters and the contact surface parameters (including those between noncomplementary atoms) is positive; i.e., most protein atoms prefer surface contact with other protein atoms rather than with the solvent. This might correspond to the driving force for maximizing packing of the protein. The influence of the crystal packing, completeness of rotamer library and precise positioning of Cbeta atoms on the accuracy of side-chain prediction are examined. The Sccomp-S and Sccomp-I programs can be accessed through the Web (http://sgedg.weizmann.ac.il/sccomp.html) and are available for several platforms.     

Relationship among ligand conformations in solution, in the solid state, and at the Hsp90 binding site: geldanamycin and radicicol

The unknown effects of a receptor's environment on a ligand's conformation presents a difficult challenge in predicting feasible bioactive conformations, particularly if the receptor is ill-defined. The primary hypothesis of this work is that a structure's conformational ensemble in solution presents viable candidates for protein binding. The experimental solution profile can be achieved with the NAMFIS (NMR analysis of molecular flexibility in solution) method, which deconvolutes the average NMR spectrum of small flexible molecules into individual contributing conformations with varying populations. Geldanamycin and radicicol are structurally different macrocycles determined by X-ray crystallography to bind to a common site on the cellular chaperone heat shock protein 90 (Hsp90). Without benefit of a receptor structure, NAMFIS has identified the bioactive conformers of geldanamycin and radicicol in CDCl3 solution with populations of 4% and 21%, respectively. Conversely, docking the set of NAMFIS conformers into the unliganded proteins with GLIDE followed by MM-GBSA scoring reproduces the experimental crystallographic binding poses.     

Structure and dynamics of the Abeta(21-30) peptide from the interplay of NMR experiments and molecular simulations

We combine molecular dynamics simulations and new high-field NMR experiments to describe the solution structure of the Abeta(21-30) peptide fragment that may be relevant for understanding structural mechanisms related to Alzheimer's disease. By using two different empirical force-field combinations, we provide predictions of the three-bond scalar coupling constants ((3)J(H(N)H(alpha))), chemical-shift values, (13)C relaxation parameters, and rotating-frame nuclear Overhauser effect spectroscopy (ROESY) crosspeaks that can then be compared directly to the same observables measured in the corresponding NMR experiment of Abeta(21-30). We find robust prediction of the (13)C relaxation parameters and medium-range ROESY crosspeaks by using new generation TIP4P-Ew water and Amber ff99SB protein force fields, in which the NMR validates that the simulation yields both a structurally and dynamically correct ensemble over the entire Abeta(21-30) peptide. Analysis of the simulated ensemble shows that all medium-range ROE restraints are not satisfied simultaneously and demonstrates the structural diversity of the Abeta(21-30) conformations more completely than when determined from the experimental medium-range ROE restraints alone. We find that the structural ensemble of the Abeta(21-30) peptide involves a majority population (approximately 60%) of unstructured conformers, lacking any secondary structure or persistent hydrogen-bonding networks. However, the remaining minority population contains a substantial percentage of conformers with a beta-turn centered at Val24 and Gly25, as well as evidence of the Asp23 to Lys28 salt bridge important to the fibril structure. This study sets the stage for robust theoretical work on Abeta(1-40) and Abeta(1-42), for which collection of detailed NMR data on the monomer will be more challenging because of aggregation and fibril formation on experimental timescales at physiological conditions. In addition, we believe that the interplay of modern molecular simulation and high-quality NMR experiments has reached a fruitful stage for characterizing structural ensembles of disordered peptides and proteins in general.     

Sulfonated molecules that bind a partially structured species of beta2-microglobulin also influence refolding and fibrillogenesis

Human beta2-microglobulin (beta2-m) is a small amyloidogenic protein responsible for dialysis-related amyloidosis, which represents a severe complication of long-term hemodialysis. A therapeutic approach for this amyloidosis could be based on the stabilization of beta2-m through the binding to a small molecule, to possibly inhibit protein misfolding and amyloid fibril formation. The search of a strong ligand of this protein is extremely challenging: by using CE in affinity and refolding experiments we study the effect that previously selected sulfonated molecules have on the equilibrium between the native form and an ensemble of conformers populating the slow phase of beta2-m folding. These data are correlated with the effect that the same molecules exert on in vitro fibrillogenesis experiments.     

Chloride ion conduction without water coordination in the pore of ClC protein

In the present work, we have found by an atomistic molecular dynamics simulation that hydrogen atoms originating from the residues of a prokaryotic ClC protein (EcClC) stabilize the chloride ion without water molecules in the pore of ClC protein. When the chloride ion conduction is simulated by pulling a chloride ion along the pore axis, the free energy barrier for chloride ion conduction is calculated to be low (4 kcal/mol), although the chloride ion is stripped of its hydration shell as it passes through the dehydrated pore region. The calculation of the number of hydrogen atoms surrounding the chloride ion reveals that water molecules hydrating the chloride ion are replaced by polar and non‐polar hydrogen atoms protruding from the protein residues. From the analysis of the pair interaction energy between the chloride ion and these hydrogen atoms, it is realized that the hydrogen atoms from the protein residues stabilize the chloride ion at the dehydrated region instead of water molecules, by which the energetic penalty for detaching water molecules from the permeating ion is compensated. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

[4+3] Cycloaddition of Donor–Acceptor Cyclopropanes with Amphiphilic Benzodithioloimine as Surrogate for ortho‐Bisthioquinone

Donor–acceptor cyclopropanes were reacted with amphiphilic benzodithioloimine to give seven‐membered heterocycles with two sulfur atoms. Formally, this transformation can be regarded as a [4+3] cycloaddition reaction of the three‐membered ring and ortho‐bisthioquinone. The benzodithioloimine serves as a surrogate for this highly reactive diene. The structure of the products was confirmed by X‐ray crystallography. Broad signals in ¹³C NMR studies suggest that several conformers, slowly interconverting on the NMR timescale, are present at room temperature.     

Generation of multiple pharmacophore hypotheses using multiobjective optimisation techniques

Summary Pharmacophore methods provide a way of establishing a structure--activity relationship for a series of known active ligands. Often, there are several plausible hypotheses that could explain the same set of ligands and, in such cases, it is important that the chemist is presented with alternatives that can be tested with different synthetic compounds. Existing pharmacophore methods involve either generating an ensemble of conformers and considering each conformer of each ligand in turn or exploring conformational space on-the-fly. The ensemble methods tend to produce a large number of hypotheses and require considerable effort to analyse the results, whereas methods that vary conformation on-the-fly typically generate a single solution that represents one possible hypothesis, even though several might exist. We describe a new method for generating multiple pharmacophore hypotheses with full conformational flexibility being explored on-the-fly. The method is based on multiobjective evolutionary algorithm techniques and is designed to search for an ensemble of diverse yet plausible overlays which can then be presented to the chemist for further investigation.     

Where does the electron go? Electron distribution and reactivity of peptide cation radicals formed by electron transfer in the gas phase

We report the first detailed analysis at correlated levels of ab initio theory of experimentally studied peptide cations undergoing charge reduction by collisional electron transfer and competitive dissociations by loss of H atoms, ammonia, and N-C alpha bond cleavage in the gas phase. Doubly protonated Gly-Lys, (GK + 2H) (2+), and Lys-Lys, (KK + 2H) (2+), are each calculated to exist as two major conformers in the gas phase. Electron transfer to conformers with an extended lysine chain triggers highly exothermic dissociation by loss of ammonia from the Gly residue, which occurs from the ground ( X ) electronic state of the cation radical. Loss of Lys ammonium H atoms is predicted to occur from the first excited ( A ) state of the charge-reduced ions. The X and A states are nearly degenerate and show extensive delocalization of unpaired electron density over spatially remote groups. This delocalization indicates that the captured electron cannot be assigned to reduce a particular charged group in the peptide cation and that superposition of remote local Rydberg-like orbitals plays a critical role in affecting the cation-radical reactivity. Electron attachment to ion conformers with carboxyl-solvated Lys ammonium groups results in spontaneous isomerization by proton-coupled electron transfer to the carboxyl group forming dihydroxymethyl radical intermediates. This directs the peptide dissociation toward NC alpha bond cleavage that can proceed by multiple mechanisms involving reversible proton migrations in the reactants or ion-molecule complexes. The experimentally observed formations of Lys z (+*) fragments from (GK + 2H) (2+) and Lys c (+) fragments from (KK + 2H) (2+) correlate with the product thermochemistry but are independent of charge distribution in the transition states for NC alpha bond cleavage. This emphasizes the role of ion-molecule complexes in affecting the charge distribution between backbone fragments produced upon electron transfer or capture.     

Theoretical study of the V(4F)?+?NO(2��r)?��?VO(4��?)?+?N(4S��) reaction compared with the Sc(2D) and Ti(3F) cases

To understand the title reaction, the MRCI, CCSD, CCSD(T), and DFT calculations have been done. A large domain of the ground-state potential energy surface has been explored including the activation energy barrier to form the triatomic complex, two stable intermediate complexes, V[NO] and NVO, the transition state connecting these two conformers, and the detachment of the nitrogen atom. We compared this reaction with the similar ones involving the Sc and Ti atoms. The activation barrier to form the VNO complex made from the ionic-covalent coupling decreases to approach the experimental data when the electron correlation effect is better included as in the Sc and Ti systems. The transition state connecting the two conformers was calculated to be higher than in the Sc and Ti cases probably due to larger number of nonbonding valence electrons and is probably too high with respect to the reactant energy level to allow the interconversion between the two conformers in the VNO. The direct concerted substitution (abstraction) reaction is improbable because this process will have to overcome a too high potential barrier. We have also found the transition state connecting two conformers of ScNO.     

Conformational Ensemble of Disordered Proteins Probed by Solvent Paramagnetic Relaxation Enhancement (sPRE)

Characterization of the conformational ensemble of disordered proteins is highly important for understanding protein folding and aggregation mechanisms, but remains a computational and experimental challenge owing to the dynamic nature of these proteins. New observables that can provide unique insights into transient residual structures in disordered proteins are needed. Here using denatured ubiquitin as a model system, NMR solvent paramagnetic relaxation enhancement (sPRE) measurements provide an accurate and highly sensitive probe for detecting low populations of residual structure in a disordered protein. Furthermore, a new ensemble calculation approach based on sPRE restraints in conjunction with residual dipolar couplings (RDCs) and small‐angle X‐ray scattering (SAXS) is used to define the conformational ensemble of disordered proteins at atomic resolution. The approach presented should be applicable to a wide range of dynamic macromolecules.     

N6H6结构和性质的理论研究

采用密度泛函理论的b3lyp方法在6-311＋＋G**基组上对15种分子式为N₆H₆的氮氢化合物进行了理论计算, 并且应用了自然键轨道理论(Nature Bond Orbital, NBO)和分子中的原子理论(Atoms In Molecules, AIM)分析了这些化合物的成键特征和相对稳定性. NBO分析表明N原子孤对电子到相邻的氮氮键的超共轭作用是影响氮氮键长变化的主要因素, AIM计算的氮氮键的键临界点电荷密度与键长呈反比关系. 而且, NBO的立体和超共轭分析表明立体交换排斥能和超共轭作用对这些分子的相对稳定性起了重要作用. G3MP2计算结果表明氮氢化合物的生成热均为正, 并且环状分子的能量和生成热都高于链状分子.     

Mapping long-range interactions in alpha-synuclein using spin-label NMR and ensemble molecular dynamics simulations

The intrinsically disordered protein alpha-synuclein plays a key role in the pathogenesis of Parkinson's disease (PD). We show here that the native state of alpha-synuclein consists of a broad distribution of conformers with an ensemble-averaged hydrodynamic radius significantly smaller than that expected for a random coil structure. This partial condensation is driven by interactions between the highly charged C-terminus and a large hydrophobic central region of the protein sequence. We suggest that this structure could inhibit the formation of alpha-synuclein aggregates, which are thought to be the cytotoxic species responsible for neurodegeneration in PD.