Functional Significance of Hierarchical Tiers in Carbonmonoxy Myoglobin: Conformational Substates and Transitions Studied by Conformational Flooding Simulations

Binding Kinetics in Drug Discovery

Over the last years, researchers have increasingly become interested in measuring and understanding drugs' binding kinetics, namely the time in which drug and its target associate and dissociate. Historically, drug discovery programs focused on the optimization of target affinity as a proxy of in-vivo efficacy. However, often the efficacy of a ligand is not appropriately described by the in-vitro measured drug-receptor affinity, but rather depends on the lifetime of the in-vivo drug-receptor interaction. In this review we review recent works that highlight the importance of binding kinetics, molecular determinants for rational optimization and the recent emergence of computational methods as powerful tools in measuring and understanding binding kinetics.

Principles and Overview of Sampling Methods for Modeling Macromolecular Structure and Dynamics

Investigation of macromolecular structure and dynamics is fundamental to understanding how macromolecules carry out their functions in the cell. Significant advances have been made toward this end in silico, with a growing number of computational methods proposed yearly to study and simulate various aspects of macromolecular structure and dynamics. This review aims to provide an overview of recent advances, focusing primarily on methods proposed for exploring the structure space of macromolecules in isolation and in assemblies for the purpose of characterizing equilibrium structure and dynamics. In addition to surveying recent applications that showcase current capabilities of computational methods, this review highlights state-of-the-art algorithmic techniques proposed to overcome challenges posed in silico by the disparate spatial and time scales accessed by dynamic macromolecules. This review is not meant to be exhaustive, as such an endeavor is impossible, but rather aims to balance breadth and depth of strategies for modeling macromolecular structure and dynamics for a broad audience of novices and experts.

Photolytic Cross-Linking to Probe Protein-Protein and Protein-Matrix Interactions in Lyophilized Powders

Protein structure and local environment in lyophilized formulations were probed using high-resolution solid-state photolytic cross-linking with mass spectrometric analysis (ssPC-MS). In order to characterize structure and microenvironment, protein-protein, protein-excipient, and protein-water interactions in lyophilized powders were identified. Myoglobin (Mb) was derivatized in solution with the heterobifunctional probe succinimidyl 4,4'-azipentanoate (SDA) and the structural integrity of the labeled protein (Mb-SDA) confirmed using CD spectroscopy and liquid chromatography/mass spectrometry (LC-MS). Mb-SDA was then formulated with and without excipients (raffinose, guanidine hydrochloride (Gdn HCl)) and lyophilized. The freeze-dried powder was irradiated with ultraviolet light at 365 nm for 30 min to produce cross-linked adducts that were analyzed at the intact protein level and after trypsin digestion. SDA-labeling produced Mb carrying up to five labels, as detected by LC-MS. Following lyophilization and irradiation, cross-linked peptide-peptide, peptide-water, and peptide-raffinose adducts were detected. The exposure of Mb side chains to the matrix was quantified based on the number of different peptide-peptide, peptide-water, and peptide-excipient adducts detected. In the absence of excipients, peptide-peptide adducts involving the CD, DE, and EF loops and helix H were common. In the raffinose formulation, peptide-peptide adducts were more distributed throughout the molecule. The Gdn HCl formulation showed more protein-protein and protein-water adducts than the other formulations, consistent with protein unfolding and increased matrix interactions. The results demonstrate that ssPC-MS can be used to distinguish excipient effects and characterize the local protein environment in lyophilized formulations with high resolution.

Elucidating the ensemble of functionally-relevant transitions in protein systems with a robotics-inspired method

Background

Many proteins tune their biological function by transitioning between different functional states, effectively acting as dynamic molecular machines. Detailed structural characterization of transition trajectories is central to understanding the relationship between protein dynamics and function. Computational approaches that build on the Molecular Dynamics framework are in principle able to model transition trajectories at great detail but also at considerable computational cost. Methods that delay consideration of dynamics and focus instead on elucidating energetically-credible conformational paths connecting two functionally-relevant structures provide a complementary approach. Effective sampling-based path planning methods originating in robotics have been recently proposed to produce conformational paths. These methods largely model short peptides or address large proteins by simplifying conformational space.

Methods

We propose a robotics-inspired method that connects two given structures of a protein by sampling conformational paths. The method focuses on small- to medium-size proteins, efficiently modeling structural deformations through the use of the molecular fragment replacement technique. In particular, the method grows a tree in conformational space rooted at the start structure, steering the tree to a goal region defined around the goal structure. We investigate various bias schemes over a progress coordinate for balance between coverage of conformational space and progress towards the goal. A geometric projection layer promotes path diversity. A reactive temperature scheme allows sampling of rare paths that cross energy barriers.

Results and conclusions

Experiments are conducted on small- to medium-size proteins of length up to 214 amino acids and with multiple known functionally-relevant states, some of which are more than 13Å apart of each-other. Analysis reveals that the method effectively obtains conformational paths connecting structural states that are significantly different. A detailed analysis on the depth and breadth of the tree suggests that a soft global bias over the progress coordinate enhances sampling and results in higher path diversity. The explicit geometric projection layer that biases the exploration away from over-sampled regions further increases coverage, often improving proximity to the goal by forcing the exploration to find new paths. The reactive temperature scheme is shown effective in increasing path diversity, particularly in difficult structural transitions with known high-energy barriers.

The energy profiles of atomic conformational transition intermediates of adenylate kinase

The elastic network interpolation (ENI) (Kim et al., Biophys J 2002;83:1620-1630) is a computationally efficient and physically realistic method to generate conformational transition intermediates between two forms of a given protein. However it can be asked whether these calculated conformations provide good representatives for these intermediates. In this study, we use ENI to generate conformational transition intermediates between the open form and the closed form of adenylate kinase (AK). Based on C(alpha)-only intermediates, we construct atomic intermediates by grafting all the atoms of known AK structures onto the C(alpha) atoms and then perform CHARMM energy minimization to remove steric conflicts and optimize these intermediate structures. We compare the energy profiles for all intermediates from both the CHARMM force-field and from knowledge-based energy functions. We find that the CHARMM energies can successfully capture the two energy minima representing the open AK and closed AK forms, while the energies computed from the knowledge-based energy functions can detect the local energy minimum representing the closed AK form and show some general features of the transition pathway with a somewhat similar energy profile as the CHARMM energies. The combinatorial extension structural alignment (Shindyalov et al., 1998;11:739-747) and the k-means clustering algorithm are then used to show that known PDB structures closely resemble computed intermediates along the transition pathway.

Dissociation aided and side chain sampling enhanced Hamiltonian replica exchange

A new application of Hamiltonian replica exchange method is suggested: The potential energy function is adjusted in such a way that repulsive forces between atoms of solute are reinforced. This dissociation action helps the system to escape from the local minima on the free energy landscape. Compared with other Hamiltonian replica exchange methods in which the potential energy between solute atoms and between solute and solvent atoms was reduced, and compared with the temperature replica exchange method, the new scheme displays superior ability to overcome large free energy barrier in a model system. For protein simulation, the side chain conformation sampling turns out to be an issue and an enhancement method is introduced. Combining the dissociation aided method with the specific side chain sampling technique is proven to be a help to explore the complex energy landscape of protein, which is demonstrated by three independent ab initio folding simulations on the trpzip2 peptide.

Structural biology by NMR: structure, dynamics, and interactions

The function of bio-macromolecules is determined by both their 3D structure and conformational dynamics. These molecules are inherently flexible systems displaying a broad range of dynamics on time-scales from picoseconds to seconds. Nuclear Magnetic Resonance (NMR) spectroscopy has emerged as the method of choice for studying both protein structure and dynamics in solution. Typically, NMR experiments are sensitive both to structural features and to dynamics, and hence the measured data contain information on both. Despite major progress in both experimental approaches and computational methods, obtaining a consistent view of structure and dynamics from experimental NMR data remains a challenge. Molecular dynamics simulations have emerged as an indispensable tool in the analysis of NMR data.

Roadmap methods for protein folding

Protein folding refers to the process whereby a protein assumes its intricate three-dimensional shape. This chapter reviews a class of methods for studying the folding process called roadmap methods. The goal of these methods is not to predict the folded structure of a protein, but rather to analyze the folding kinetics. It is assumed that the folded state is known. Roadmap methods maintain a graph representation of sampled conformations. By analyzing this graph one can predict structure formation order, the probability of folding, and get a coarse view of the energy landscape.

A molecular dynamics study of slow base flipping in DNA using conformational flooding

Individual DNA bases are known to be able to flip out of the helical stack, providing enzymes with access to the genetic information otherwise hidden inside the helix. Consequently, base flipping is a necessary first step to many more complex biological processes such as DNA transcription or replication. Much remains unknown about this elementary step, despite a wealth of experimental and theoretical studies. From the theoretical point of view, the involved timescale of milliseconds or longer requires the use of enhanced sampling techniques. In contrast to previous theoretical studies employing umbrella sampling along a predefined flipping coordinate, this study attempts to induce flipping without prior knowledge of the pathway, using information from a molecular dynamics simulation of a B-DNA fragment and the conformational flooding method. The relevance to base flipping of the principal components of the simulation is assayed, and a combination of modes optimally related to the flipping of the base through either helical groove is derived for each of the two bases of the central guanine-cytosine basepair. By applying an artificial flooding potential along these collective coordinates, the flipping mechanism is accelerated to within the scope of molecular dynamics simulations. The associated free energy surface is found to feature local minima corresponding to partially flipped states, particularly relevant to flipping in isolated DNA; further transitions from these minima to the fully flipped conformation are accelerated by additional flooding potentials. The associated free energy profiles feature similar barrier heights for both bases and pathways; the flipped state beyond is a broad and rugged attraction basin, only a few kcal/mol higher in energy than the closed conformation. This result diverges from previous works but echoes some aspects of recent experimental findings, justifying the need for novel approaches to this difficult problem: this contribution represents a first step in this direction. Important structural factors involved in flipping, both local (sugar-phosphate backbone dihedral angles) and global (helical axis bend), are also identified.

Protein-Folding Dynamics: Overview of Molecular Simulation Techniques

Molecular dynamics (MD) is an invaluable tool with which to study protein folding in silico. Although just a few years ago the dynamic behavior of a protein molecule could be simulated only in the neighborhood of the experimental conformation (or protein unfolding could be simulated at high temperature), the advent of distributed computing, new techniques such as replica-exchange MD, new approaches (based on, e.g., the stochastic difference equation), and physics-based reduced models of proteins now make it possible to study protein-folding pathways from completely unfolded structures. In this review, we present algorithms for MD and their extensions and applications to protein-folding studies, using all-atom models with explicit and implicit solvent as well as reduced models of polypeptide chains.

Minimum free energy pathways and free energy profiles for conformational transitions based on atomistic molecular dynamics simulations

An efficient method for the calculation of minimum free energy pathways and free energy profiles for conformational transitions is presented. Short restricted perturbation-targeted molecular dynamics trajectories are used to generate an approximate free energy surface. Approximate reaction pathways for the conformational change are constructed from one-dimensional line segments on this surface using a Monte Carlo optimization. Accurate free energy profiles are then determined along the pathways by means of one-dimensional adaptive umbrella sampling simulations. The method is illustrated by its application to the alanine "dipeptide." Due to the low computational cost and memory demands, the method is expected to be useful for the treatment of large biomolecular systems.

Determination of conformational free energies of peptides by multidimensional adaptive umbrella sampling

We improve the multidimensional adaptive umbrella sampling method for the computation of conformational free energies of biomolecules. The conformational transition between the alpha-helical and beta-hairpin conformational states of an alanine decapeptide is used as an example. Convergence properties of the weighted-histogram-analysis-based adaptive umbrella sampling can be improved by using multiple replicas in each adaptive iteration and by using adaptive updating of the bounds of the umbrella potential. Using positional root-mean-square deviations from structures of the alpha-helical and beta-hairpin reference states as reaction coordinates, we obtained well-converged free energy surfaces of both the in-vacuum and in-solution decapeptide systems. From the free energy surfaces well-converged relative free energies between the two conformational states can be derived. Advantages and disadvantages of different methods for obtaining conformational free energies as well as implications of our results in studying conformational transitions of proteins and in improving force field are discussed.

Analyzing large-scale structural change in proteins: comparison of principal component projection and Sammon mapping

Effective analysis of large-scale conformational transitions in macromolecules requires transforming them into a lower dimensional representation that captures the dominant motions. Herein, we apply and compare two different dimensionality reduction techniques, namely, principal component analysis (PCA), a linear method, and Sammon mapping, which is nonlinear. The two methods are used to analyze four different protein transition pathways of varying complexity, obtained by using either the conjugate peak refinement method or constrained molecular dynamics. For the return-stroke in myosin, both Sammon mapping and PCA show that the conformational change is dominated by a simple rotation of a rigid body. Also, in the case of the T-->R transition in hemoglobin, both methods are able to identify the two main quaternary transition events. In contrast, in the cases of the unfolding transition of staphylococcal nuclease or the signaling switch of Ras p21, which are both more complex conformational transitions, only Sammon mapping is able to identify the distinct phases of motion.

Combining docking and molecular dynamic simulations in drug design

A rational approach is needed to maximize the chances of finding new drugs, and to exploit the opportunities of potential new drug targets emerging from genomic and proteomic initiatives, and from the large libraries of small compounds now readily available through combinatorial chemistry. Despite a shaky early history, computer-aided drug design techniques can now be effective in reducing costs and speeding up drug discovery. This happy outcome results from development of more accurate and reliable algorithms, use of more thoughtfully planned strategies to apply them, and greatly increased computer power to allow studies with the necessary reliability to be performed. Our review focuses on applications and protocols, with the main emphasis on critical analysis of recent studies where docking calculations and molecular dynamics (MD) simulations were combined to dock small molecules into protein receptors. We highlight successes to demonstrate what is possible now, but also point out drawbacks and future directions. The review is structured to lead the reader from the simpler to more compute-intensive methods. Thus, while inexpensive and fast docking algorithms can be used to scan large compound libraries and reduce their size, more accurate but expensive MD simulations can be applied when a few selected ligand candidates remain. MD simulations can be used: during the preparation of the protein receptor before docking, to optimize its structure and account for protein flexibility; for the refinement of docked complexes, to include solvent effects and account for induced fit; to calculate binding free energies, to provide an accurate ranking of the potential ligands; and in the latest developments, during the docking process itself to find the binding site and correctly dock the ligand a priori.

Molecular dynamics simulation of sperm whale myoglobin: effects of mutations and trapped CO on the structure and dynamics of cavities

The results of extended (80-ns) molecular dynamics simulations of wild-type and YQR triple mutant of sperm whale deoxy myoglobin in water are reported and compared with the results of the simulation of the intermediate(s) obtained by photodissociation of CO in the wild-type protein. The opening/closure of pathways between preexistent cavities is different in the three systems. For the photodissociated state, we previously reported a clear-cut correlation between the opening probability and the presence of the photolyzed CO in the proximity of the passage; here we show that in wild-type deoxy myoglobin, opening is almost random. In wild-type deoxy myoglobin, the passage between the distal pocket and the solvent is strictly correlated to the presence/absence of a water molecule that simultaneously interacts with the distal histidine side chain and the heme iron; conversely, in the photodissociated myoglobin, the connection with the bulk solvent is always open when CO is in the vicinity of the A pyrrole ring. In YQR deoxy myoglobin, the mutated Gln(E7)64 is stably H-bonded with the mutated Tyr(B10)29. The essential dynamics analysis unveils a different behavior for the three systems. The motion amplitude is progressively restricted in going from wild-type to YQR deoxy myoglobin and to wild-type myoglobin photoproduct. In all cases, the principal motions involve mainly the same regions, but their directions are different. Analysis of the dynamics of the preexisting cavities indicates large fluctuations and frequent connections with the solvent, in agreement with the earlier hypothesis that some of the ligand may escape from the protein through these pathways.

Enhanced sampling by multiple molecular dynamics trajectories: carbonmonoxy myoglobin 10 μs A0 → A1–3 transition from ten 400 picosecond simulations

The utility of multiple trajectories to extend the time scale of molecular dynamics simulations is reported for the spectroscopic A-states of carbonmonoxy myoglobin (MbCO). Experimentally, the A0-->A(1-3) transition has been observed to be 10 micros at 300 K, which is beyond the time scale of standard molecular dynamics simulations. To simulate this transition, 10 short (400 ps) and two longer time (1.2 ns) molecular dynamics trajectories, starting from five different crystallographic and solution phase structures with random initial velocities centered in a 37 A radius sphere of water, have been used to sample the native-fold of MbCO. Analysis of the ensemble of structures gathered over the cumulative 5.6 ns reveals two biomolecular motions involving the side chains of His64 and Arg45 to explain the spectroscopic states of MbCO. The 10 micros A0-->A(1-3) transition involves the motion of His64, where distance between His64 and CO is found to vary up to 8.8 +/- 1.0 A during the transition of His64 from the ligand (A(1-3)) to bulk solvent (A0). The His64 motion occurs within a single trajectory only once, however the multiple trajectories populate the spectroscopic A-states fully. Consequently, multiple independent molecular dynamics simulations have been found to extend biomolecular motion from 5 ns of total simulation to experimental phenomena on the microsecond time scale.

Conformational sampling for the impatient

Several new methods for sampling conformations of biomolecules have appeared recently. A brief review thereof is presented, with particular emphasis on applications that have been published, and suitability for different kinds of systems. Four methods (namely: RESPA, replica-exchange molecular dynamics, CONCOORD and Gaussian network method) are readily applicable for biomolecular systems.

Myoglobin-CO substate structures and dynamics: multidimensional vibrational echoes and molecular dynamics simulations

Spectrally resolved infrared stimulated vibrational echo data were obtained for sperm whale carbonmonoxymyoglobin (MbCO) at 300 K. The measured dephasing dynamics of the CO ligand are in agreement with dephasing dynamics calculated with molecular dynamics (MD) simulations for MbCO with the residue histidine-64 (His64) having its imidazole epsilon nitrogen protonated (N(epsilon)-H). The two conformational substate structures B(epsilon) and R(epsilon) observed in the MD simulations are assigned to the spectroscopic A(1) and A(3) conformational substates of MbCO, respectively, based on the agreement between the experimentally measured and calculated dephasing dynamics for these substates. In the A(1) substate, the N(epsilon)-H proton and N(delta) of His64 are approximately equidistant from the CO ligand, while in the A(3) substate, the N(epsilon)-H of His64 is oriented toward the CO, and the N(delta) is on the surface of the protein. The MD simulations show that dynamics of His64 represent the major source of vibrational dephasing of the CO ligand in the A(3) state on both femtosecond and picosecond time scales. Dephasing in the A(1) state is controlled by His64 on femtosecond time scales, and by the rest of the protein and the water solvent on longer time scales.

An electrostatic model for the frequency shifts in the carbonmonoxy stretching band of myoglobin: correlation of hydrogen bonding and the stark tuning rate

The effect of internal and applied external electric fields on the vibrational stretching frequency for bound CO (nu(CO)) in myoglobin mutants was studied using density functional theory. Geometry optimization and frequency calculations were carried out for an imidazole-iron-porphine-carbonmonoxy adduct with various small molecule hydrogen-bonding groups. Over 70 vibrational frequency calculations of different model geometries and hydrogen-bonding groups were compared to derive overall trends in the C-O stretching frequency (nu(CO)) in terms of the C-O bond length and Mulliken charge. Simple linear functions were derived to predict the Stark tuning rate using an approach analogous to the vibronic theory of activation.(1) Potential energy calculations show that the strongest interaction occurs for C-H or N-H hydrogen bonding nearly perpendicular to the Fe-C-O bond axis. The calculated frequencies are compared to the structural data available from 18 myoglobin crystal structures, supporting the hypothesis that the vast majority of hydrogen-bonding interactions with CO occur from the side, rather than the end, of the bound CO ligand. The nu(CO) frequency shifts agree well with experimental frequency shifts for multiple bands, known as A states, and site-directed mutations in the distal pocket of myoglobin. The model calculations quantitatively explain electrostatic effects in terms of specific hydrogen-bonding interactions with bound CO in heme proteins.

Molecular dynamics simulations

Molecular dynamics simulations have become a standard tool for the investigation of biomolecules. Simulations are performed of ever bigger systems using more realistic boundary conditions and better sampling due to longer sampling times. Recently, realistic simulations of systems as complex as transmembrane channels have become feasible. Simulations aid our understanding of biochemical processes and give a dynamic dimension to structural data; for example, the transformation of harmless prion protein into the disease-causing agent has been modeled.

Molecular dynamics force probe simulations of antibody/antigen unbinding: entropic control and nonadditivity of unbinding forces

Unbinding of a spin-labeled dinitrophenyl (DNP) hapten from the monoclonal antibody AN02 F(ab) fragment has been studied by force probe molecular dynamics (FPMD) simulations. In our nanosecond simulations, unbinding was enforced by pulling the hapten molecule out of the binding pocket. Detailed inspection of the FPMD trajectories revealed a large heterogeneity of enforced unbinding pathways and a correspondingly large flexibility of the binding pocket region, which exhibited induced fit motions. Principal component analyses were used to estimate the resulting entropic contribution of approximately 6 kcal/mol to the AN02/DNP-hapten bond. This large contribution may explain the surprisingly large effect on binding kinetics found for mutation sites that are not directly involved in binding. We propose that such "entropic control" optimizes the binding kinetics of antibodies. Additional FPMD simulations of two point mutants in the light chain, Y33F and I96K, provided further support for a large flexibility of the binding pocket. Unbinding forces were found to be unchanged for these two mutants. Structural analysis of the FPMD simulations suggests that, in contrast to free energies of unbinding, the effect of mutations on unbinding forces is generally nonadditive.