Extended molecular dynamics simulation of the carbon monoxide migration in sperm whale myoglobin

We report the results of an extended molecular dynamics simulation on the migration of photodissociated carbon monoxide in wild-type sperm whale myoglobin. Our results allow following one possible ligand migration dynamics from the distal pocket to the Xe1 cavity via a path involving the other xenon binding cavities and momentarily two additional packing defects along the pathway. Comparison with recent time resolved structural data obtained by Laue crystallography with subnanosecond to millisecond resolution shows a more than satisfactory agreement. In fact, according to time resolved crystallography, CO, after photolysis, can occupy the Xe1 and Xe4 cavities. However, no information on the trajectory of the ligand from the distal pocket to the Xe1 is available. Our results clearly show one possible path within the protein. In addition, although our data refer to a single trajectory, the local dynamics of the ligand in each cavity is sufficiently equilibrated to obtain local structural and thermodynamic information not accessible to crystallography. In particular, we show that the CO motion and the protein fluctuations are strictly correlated: free energy calculations of the migration between adjacent cavities show that the migration is not a simple diffusion but is kinetically or thermodynamically driven by the collective motions of the protein; conversely, the protein fluctuations are influenced by the ligand in such a way that the opening/closure of the passage between adjacent cavities is strictly correlated to the presence of CO in its proximity. The compatibility between time resolved crystallographic experiments and molecular dynamics simulations paves the way to a deeper understanding of the role of internal dynamics and packing defects in the control of ligand binding in heme proteins.     

Quantitative delineation of how breathing motions open ligand migration channels in myoglobin and its mutants

Ligand migration and binding are central to the biological functions of many proteins such as myoglobin (Mb) and it is widely thought that protein breathing motions open up ligand channels dynamically. However, how a protein exerts its control over the opening and closing of these channels through its intrinsic dynamics is not fully understood. Specifically, a quantitative delineation of the breathing motions that are needed to open ligand channels is lacking. In this work, we present and apply a novel normal mode‐based method to quantitatively delineate what and how breathing motions open ligand migration channels in Mb and its mutants. The motivation behind this work springs from the observation that normal mode motions are closely linked to the breathing motions that are thought to open ligand migration channels. In addition, the method provides a direct and detailed depiction of the motions of each and every residue that lines a channel and can identify key residues that play a dominating role in regulating the channel. The all‐atom model and the full force‐field employed in the method provide a realistic energetics on the work cost required to open a channel, and as a result, the method can be used to efficiently study the effects of mutations on ligand migration channels and on ligand entry rates. Our results on Mb and its mutants are in excellent agreement with MD simulation results and experimentally determined ligand entry rates. Proteins 2015; 83:757–770. © 2015 Wiley Periodicals, Inc.     

Nonlinear optical studies of heme protein dynamics: implications for proteins as hybrid states of matter

Protein structure is fundamentally related to function. However, static structures alone are insufficient to understand how a protein works. Dynamics play an equally important role. Given that proteins are highly associated aperiodic systems, it may be expected that protein dynamics would follow glass-like dynamics. However, protein functions occur on time scales orders of magnitude faster than the time scales typically associated with glassy systems. It is becoming clear that the reaction forces driving functions do not sample entirely the large number of configurations available to a protein but are highly directed along an optimized pathway. Could there be any correlation between specific topological features in protein structures and dynamics that leads to strongly correlated atomic displacements in the dynamical response to a perturbation? This review will try to provide an answer by focusing upon recent nonlinear optical studies with the aim of directly observing functionally important protein motions over the entire dynamic range of the protein response function. The specific system chosen is photoinduced dynamics of ligand dissociation at the active site in heme proteins, with myoglobin serving as the simplest model system. The energetics and nuclear motions from the very earliest events involved in bond breaking on the femtosecond time scale all the way out to ligand escape and bimolecular rebinding on the microsecond and millisecond time scale have been mapped out. The picture that is emerging is that the system consists of strongly coupled motions from the very instant the bond breaks at the active site that cascade into low frequency collective modes specific to the protein structure. It is this coupling that imparts the ability of a protein to function on time scales more commensurate with liquids while simultaneously conserving structural integrity akin to solids.     

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.     

Efficient mapping of ligand migration channel networks in dynamic proteins

For many proteins such as myoglobin, the binding site lies in the interior, and there is no obvious route from the exterior to the binding site in the average structure. Although computer simulations for a limited number of proteins have found some transiently open channels, it is not clear if there exist more channels elsewhere or how the channels are regulated. A systematic approach that can map out the whole ligand migration channel network is lacking. Ligand migration in a dynamic protein resembles closely a well-studied problem in robotics, namely, the navigation of a mobile robot in a dynamic environment. In this work, we present a novel robotic motion planning inspired approach that can map the ligand migration channel network in a dynamic protein. The method combines an efficient spatial mapping of protein inner space with a temporal exploration of protein structural heterogeneity, which is represented by a structure ensemble. The spatial mapping of each conformation in the ensemble produces a partial map of protein inner cavities and their inter-connectivity. These maps are then merged to form a super map that contains all the channels that open dynamically. Results on the pathways in myoglobin for gaseous ligands demonstrate the efficiency of our approach in mapping the ligand migration channel networks. The results, obtained in a significantly less amount of time than trajectory-based approaches, are in agreement with previous simulation results. Additionally, the method clearly illustrates how and what conformational changes open or close a channel.     

Classification and annotation of the relationship between protein structural change and ligand binding

The causal relationship between protein structural change and ligand binding was classified and annotated for 839 nonredundant pairs of crystal structures in the Protein Data Bank—one with and the other without a bound low-molecular-weight ligand molecule. Protein structural changes were first classified into either domain or local motions depending on the size of the moving protein segments. Whether the protein motion was coupled with ligand binding was then evaluated based on the location of the ligand binding site and by application of the linear response theory of protein structural change. Protein motions coupled with ligand binding were further classified into either closure or opening motions. This classification revealed the following: (i) domain motions coupled with ligand binding are dominated by closure motions, which can be described by the linear response theory; (ii) local motions frequently accompany order-disorder or α-helix-coil conformational transitions; and (iii) transferase activity (Enzyme Commission   number 2) is the predominant function among coupled domain closure motions. This could be explained by the closure motion acting to insulate the reaction site of these enzymes from environmental water.     

Jumping frequencies in membrane channels. Comparison between stochastic molecular dynamics simulation and rate theory

Permeation of molecules through membrane channels involves local interactions with a limited number of ligand groups. A method for the molecular dynamics simulation of particle movement in small ligand systems is described. It is assumed that the ligand groups carry out thermal vibrations, whereas the rest of the channel molecule and the surroundings act as a heat bath which is coupled via random forces to the motions of the ligands. The simulation technique is applied to a simple system which contains some of the essential features influencing jumping rates in membrane channels, such as flexibility of ligand configuration or inertial effects in the motion of the ligands. Since the simulation is based on strictly microscopic parameters of the particle-ligand system, a rigorous test of the predictions of rate theory is possible. It is found that rate theory describes the general dependence of jumping frequency k' on temperature and on ligand binding strength rather well, although the values of k' obtained by computer simulation are 2-3 times smaller than those predicted by rate theory.     

Structural Assignment of Spectra by Characterization of Conformational Substates in Bound MbCO

Residue motions of the distal heme pocket and bound CO ligand of carbonmonoxy Myoglobin are studied using a combination of molecular dynamics simulations and quantum chemical methods. Using mixed quantum mechanics/molecular mechanics calculations together with sampling from molecular dynamics simulations (QM/MM(MD)), the experimentally observed spectroscopic A₀ and A₁ substates of the bound CO ligand are assigned to the open and closed conformation of His⁶⁴ and the His_ɛ⁶⁴ tautomer, respectively. Several previously proposed origins of the A₃ substate, including rotamers of the doubly protonated His⁶⁴H⁺ side chain, His⁶⁴H⁺ inside the distal pocket, and cooperative motions with Arg⁴⁵, are investigated with QM/MM(MD). However, the signatures of the calculated infrared spectra do not agree with the experimentally observed ones. For additional insight on this, extensive molecular dynamics simulations are used together with improved electrostatics for the bound ligand. A CO fluctuating charge model is developed to describe the ab initio dipole and quadrupole moments of the bound ligand. CO absorption spectra are then obtained directly from the dynamics simulations. Finally, the electrostatics of the heme pocket is examined in detail in an attempt to determine the structural origins of the observed spectroscopic A-states from MD simulations. However, contrary to related simulations for unbound CO in myoglobin, the shifts and splittings for carbonmonoxy Myoglobin are generally small and difficult to relate to structural change. This suggests that coupling of the CO motion to other degrees of freedom, such as the Fe-CO stretching and bending, is important to correctly describe the dynamics of bound CO in myoglobin.     

Myoglobin cavities provide interior ligand pathway

The myoglobin protein binds oxygen and catalyzes NO oxidation. As a key model protein, its dynamics have been well studied by spectroscopy and by crystallography as well as by simulation. Nonetheless, visualization of the mechanism of movement of ligands within myoglobin has been difficult. Coordinates of the A1 and A3 taxonomic spectral states of myoglobin from the 1 A crystal structure (1a6g) are generated as consistent sets of correlated clusters of residues with A or B crystal alternates. Analysis of cavities in these A1 and A3 conformations clarifies the pathway of ligand motion from distal entry through interior movement to the proximal side of the heme. Cavities opened up by buried alternate conformations link the distal to the proximal side of the heme. Structural conservation highlights the relevance of this pathway to human neuroglobin. Cavity migration via myoglobin crystal alternates provides a specific link of protein structure to protein dynamics and protein function and demonstrates the relevance of substates (discrete disorder) to function for all proteins.     

Influence of histidine tag attachment on picosecond protein dynamics

Polyhistidine affinity tags are routinely employed as a convenient means of purifying recombinantly expressed proteins. A tacit assumption is commonly made that His tags have little influence on protein structure and function. Attachment of a His tag to the N-terminus of the robust globular protein myoglobin leads to only minor changes to the electrostatic environment of the heme pocket, as evinced by the nearly unchanged Fourier transform infrared spectrum of CO bound to the heme of His-tagged myoglobin. Experiments employing two-dimensional infrared vibrational echo spectroscopy of the heme-bound CO, however, find that significant changes occur to the short time scale (picoseconds) dynamics of myoglobin as a result of His tag incorporation. The His tag mainly reduces the dynamics on the 1.4 ps time scale and also alters protein motions of myoglobin on the slower, >100 ps time scale, as demonstrated by the His tag's influence on the fluctuations of the CO vibrational frequency, which reports on protein structural dynamics. The results suggest that affinity tags may have effects on protein function and indicate that investigators of affinity-tagged proteins should take this into consideration when investigating the dynamics and other properties of such proteins.     

Structural dynamics of myoglobin

Conformational fluctuations have been invoked to explain the observation that the diffusion of small ligands through a protein is a global phenomenon, as suggested (for example) by the oxygen induced fluorescence quenching of buried tryptophans. In enzymes processing large substrates, a channel to the catalytic site is often seen in the crystal structure; on the other hand in small globular proteins, it is not known if the cavities identified in the interior space are important in controlling their function by defining specific pathways in the diffusion to the active site. This point is addressed in this paper, which reports some relevant results obtained on myoglobin, the hydrogen atom of molecular biology. Protein conformational relaxations have been extensively investigated with myoglobin because the photosensivity of the adduct with CO, O2 and NO allows us to follow events related to the migration of the ligand through the matrix. Results obtained by laser photolysis, molecular dynamics simulations, X-ray diffraction of intermediate states of wt type and mutant myoglobins are briefly summarized. Crystallographic data on the photochemical intermediate of a new triple mutant of sperm whale myoglobin (Mb-YQR) show, for the first time, the photolyzed CO* sitting in one of the Xe-binding cavities, removed from the heme group. These results support the viewpoint that pre-existing 'packing defects' in the protein interior play a major role in controlling the dynamics of ligand binding, including oxygen, and thereby acquire a survival value.     

Counterbalance of ligand‐ and self‐coupled motions characterizes multispecificity of ubiquitin

Date hub proteins are a type of proteins that show multispecificity in a time‐dependent manner. To understand dynamic aspects of such multispecificity we studied Ubiquitin as a typical example of a date hub protein. Here we analyzed 9 biologically relevant Ubiquitin‐protein (ligand) heterodimer structures by using normal mode analysis based on an elastic network model. Our result showed that the self‐coupled motion of Ubiquitin in the complex, rather than its ligand‐coupled motion, is similar to the motion of Ubiquitin in the unbound condition. The ligand‐coupled motions are correlated to the conformational change between the unbound and bound conditions of Ubiquitin. Moreover, ligand‐coupled motions favor the formation of the bound states, due to its in‐phase movements of the contacting atoms at the interface. The self‐coupled motions at the interface indicated loss of conformational entropy due to binding. Therefore, such motions disfavor the formation of the bound state. We observed that the ligand‐coupled motions are embedded in the motions of unbound Ubiquitin. In conclusion, multispecificity of Ubiquitin can be characterized by an intricate balance of the ligand‐ and self‐coupled motions, both of which are embedded in the motions of the unbound form.     

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.     

Nitric Oxide Dynamics in Truncated Hemoglobin: Docking Sites, Migration Pathways, and Vibrational Spectroscopy from Molecular Dynamics Simulations

Atomistic simulations of nitric oxide (NO) dynamics and migration in the trHbN of Mycobacterium tuberculosis are reported. From extensive molecular dynamics simulations (48 ns in total), the structural and energetic properties of the ligand docking sites in the protein have been characterized and a connectivity network between the ligand docking sites has been built. Several novel migration and exit pathways are found and are analyzed in detail. The interplay between a hydrogen-bonding network involving residues Tyr³³ and Gln⁵⁸ and the bound O₂ ligand is discussed and the role of Phe⁶² residue in ligand migration is examined. It is found that Phe⁶² is directly involved in controlling ligand migration. This is reminiscent of His⁶⁴ in myoglobin, which also plays a central role in CO migration pathways. Finally, infrared spectra of the NO molecule in different ligand docking sites of the protein are calculated. The pocket-specific spectra are typically blue-shifted by 5-10 cm⁻¹, which should be detectable in future spectroscopic experiments.     

Simulating nanoscale functional motions of biomolecules

We are describing efficient dynamics simulation methods for the characterization of functional motion of biomolecules on the nanometer scale. Multivariate statistical methods are widely used to extract and enhance functional collective motions from molecular dynamics (MD) simulations. A dimension reduction in MD is often realized through a principal component analysis (PCA) or a singular value decomposition (SVD) of the trajectory. Normal mode analysis (NMA) is a related collective coordinate space approach, which involves the decomposition of the motion into vibration modes based on an elastic model. Using the myosin motor protein as an example we describe a hybrid technique termed amplified collective motions (ACM) that enhances sampling of conformational space through a combination of normal modes with atomic level MD. Unfortunately, the forced orthogonalization of modes in collective coordinate space leads to complex dependencies that are not necessarily consistent with the symmetry of biological macromolecules and assemblies. In many biological molecules, such as HIV-1 protease, reflective or rotational symmetries are present that are broken using standard orthogonal basis functions. We present a method to compute the plane of reflective symmetry or the axis of rotational symmetry from the trajectory frames. Moreover, we develop an SVD that best approximates the given trajectory while respecting the symmetry. Finally, we describe a local feature analysis (LFA) to construct a topographic representation of functional dynamics in terms of local features. The LFA representations are low-dimensional, and provide a reduced basis set for collective motions, but unlike global collective modes they are sparsely distributed and spatially localized. This yields a more reliable assignment of essential dynamics modes across different MD time windows.     

Structural dynamics of myoglobin: spectroscopic and structural characterization of ligand docking sites in myoglobin mutant L29W

We have studied CO binding to the heme and CO migration among protein internal cavities after photodissociation in sperm whale carbonmonoxy myoglobin (MbCO) mutant L29W using Fourier transform infrared (FTIR) spectroscopy combined with temperature derivative spectroscopy (TDS) and kinetic experiments at cryogenic temperatures. Photoproduct intermediates, characterized by CO at particular locations in the protein, were selectively enhanced by applying special laser illumination protocols. These studies were performed on the L29W mutant protein and a series of double mutants constructed so that bulky amino acid side chains block passageways between cavities or fill these sites. Binding of xenon was also employed as an alternative means of occluding cavities. All mutants exhibit two conformations, A(I) and A(II), with distinctly different photoproduct states and ligand binding properties. These differences arise mainly from different positions of the W29 and H64 side chains in the distal heme pocket [Ostermann, A., et al. (2000) Nature 404, 205-208]. The detailed knowledge of the interplay between protein structure, protein dynamics, and ligand migration at cryogenic temperatures allowed us to develop a dynamic model that explains the slow CO and O(2) bimolecular association observed after flash photolysis at ambient temperature.     

Selective excitation of native fluctuations during thermal unfolding simulations: horse heart cytochrome c as a case study

The effect of temperature on the activation of native fluctuation motions during molecular dynamics unfolding simulations of horse heart cytochrome c has been studied. Essential dynamics analysis has been used to analyze the preferred directions of motion along the unfolding trajectories obtained by high temperature simulations. The results of this study have evidenced a clear correlation between the directions of the deformation motions that occur in the first stage of the unfolding process and few specific essential motions characterizing the 300 K dynamics of the protein. In particular, one of those collective motions, involved in the fluctuation of a loop region, is specifically excited in the thermal denaturation process, becoming progressively dominant during the first 500 ps of the unfolding simulations. As further evidence, the essential dynamics sampling performed along this collective motion has shown a tendency of the protein to promptly unfold. According to these results, the mechanism of thermal induced denaturation process involves the selective excitation of one or few specific equilibrium collective motions.     

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.