Insertion and assembly of membrane proteins via simulation

Interactions of lipids are central to the folding and stability of membrane proteins. Coarse-grained molecular dynamics simulations have been used to reveal the mechanisms of self-assembly of protein/membrane and protein/detergent complexes for representatives of two classes of membrane protein, namely, glycophorin (a simple alpha-helical bundle) and OmpA (a beta-barrel). The accuracy of the coarse-grained simulations is established via comparison with the equivalent atomistic simulations of self-assembly of protein/detergent micelles. The simulation of OmpA/bilayer self-assembly reveals how a folded outer membrane protein can be inserted in a bilayer. The glycophorin/bilayer simulation supports the two-state model of membrane folding, in which transmembrane helix insertion precedes dimer self-assembly within a bilayer. The simulations also suggest that a dynamic equilibrium exists between the glycophorin helix monomer and dimer within a bilayer. The simulated glycophorin helix dimer is remarkably close in structure to that revealed by NMR. Thus, coarse-grained methods may help to define mechanisms of membrane protein (re)folding and will prove suitable for simulation of larger scale dynamic rearrangements of biological membranes.     

Mechanism of helix nucleation and propagation: microscopic view from microsecond time scale MD simulations

Microsecond time scale molecular dynamics simulations of the 13-residue peptide RN24 were carried out to investigate the mechanism of helix nucleation and propagation. An extended and an ideal alpha-helical conformation were used as starting structures. NOE-derived interatomic distances were compared with distances calculated from the simulations, showing good agreement between experimental and simulation results. Based on almost 200 helix nucleation events observed, beta-turn and 3(10)-helix play an important role in helix nucleation; in most cases, helix nucleation is preceded by the formation of a short-lived beta-turn (60% probability) or 3(10)-helix (20% probability), and the conversion from beta-turn to alpha-turn involves bifurcated hydrogen bonds. Helix propagation in RN24 appears to occur preferentially from the N-terminus to the C-terminus, and helix unfolding preferentially in the opposite direction.     

HMGB1–Carbenoxolone Interactions: Dynamics Insights from Combined Nuclear Magnetic Resonance and Molecular Dynamics

The interplay of protein dynamics and molecular recognition is of fundamental importance in biological processes. Atomic‐resolution insights into these phenomena may provide new opportunities for drug discovery. Herein, we have combined NMR relaxation experiments and residual dipolar coupling (RDC) measurements with molecular dynamics (MD) simulations to study the effects of the anti‐inflammatory drug carbenoxolone (CBNX) on the conformational properties and on the internal dynamics of a subdomain (box A) of high‐mobility group B protein (HMGB1). ¹⁵N relaxation data show that CBNX binding enhances the fast pico‐ to nanosecond motions of a loop and partially removes the internal motional anisotropy of the first two helices of box A. Dipolar wave analysis of amide RDC data shows that ligand binding induces helical distortions. In parallel, increased mobility of the loop upon ligand binding is highlighted by the essential dynamics analysis (EDA) of MD simulations. Moreover, simulations detect two possible orientations for CBNX, which induces two possible conformations of helix H3, one being similar to the free form and the second one causing a partial helical distortion. Finally, we introduce a new approach for the analysis of the internal coordination of protein residues that is consistent with experimental data and allows us to pinpoint which substructures of box A are dynamically affected by CBNX. The observations reported here may be useful for understanding the role of protein dynamics in binding at atomic resolution.     

Exploring multiple timescale motions in protein GB3 using accelerated molecular dynamics and NMR spectroscopy

Biological function relies on the complex spectrum of conformational dynamics occurring in biomolecules. We have combined Accelerated Molecular Dynamics (AMD) with experimental results derived from NMR to probe multiple time-scale motions in the third IgG-binding domain of Protein G (GB3). AMD is shown to accurately reproduce the amplitude and distribution of slow motional modes characterized using residual dipolar couplings, reporting on dynamics up to the millisecond timescale. In agreement with experiment, larger amplitude slower motions are localized in the beta-strand/loop motif spanning residues 14-24 and in loop 42-44. Principal component analysis shows these fluctuations participating in the primary mode, substantiating the existence of a correlated motion traversing the beta-sheet that culminates in maximum excursions at the active site of the molecule. Fast dynamics were simulated using extensive standard MD simulations and compared to order parameters extracted from 15N relaxation. Notably 60 2-ns fully solvated MD simulations exploring the different conformational substates sampled from AMD resulted in better reproduction of order parameters compared to the same number of simulations starting from the relaxed crystal structure. This illustrates the inherent dependence of protein dynamics on local conformational topology. The results provide rare insight into the complex hierarchy of dynamics present in GB3 and allow us to develop a model of the conformational landscape native to the protein, appearing as a steep sided potential well whose flat bottom comprises multiple similar but discrete conformational substates.     

Characterization of the dynamics of an essential helix in the U1A protein by time-resolved fluorescence measurements

The RNA recognition motif (RRM), one of the most common RNA-binding domains, recognizes single-stranded RNA. A C-terminal helix that undergoes conformational changes upon binding is often an important contributor to RNA recognition. The N-terminal RRM of the U1A protein contains a C-terminal helix (helix C) that interacts with the RNA-binding surface of a beta-sheet in the free protein (closed conformation), but is directed away from this beta-sheet in the complex with RNA (open conformation). The dynamics of helix C in the free protein have been proposed to contribute to binding affinity and specificity. We report here a direct investigation of the dynamics of helix C in the free U1A protein on the nanosecond time scale using time-resolved fluorescence anisotropy. The results indicate that helix C is dynamic on a 2-3 ns time scale within a 20 degrees range of motion. Steady-state fluorescence experiments and molecular dynamics simulations suggest that the dynamical motion of helix C occurs within the closed conformation. Mutation of a residue on the beta-sheet that contacts helix C in the closed conformation dramatically destabilizes the complex (Phe56Ala) and alters the steady-state fluorescence, but not the time-resolved fluorescence anisotropy, of a Trp in helix C. Mutation of Asp90 in the hinge region between helix C and the remainder of the protein to Ala or Gly subtly alters the dynamics of the U1A protein and destabilizes the complex. Together these results show that helix C maintains a dynamic closed conformation that is stable to these targeted protein modifications and does not equilibrate with the open conformation on the nanosecond time scale.     

Protein motions promote catalysis

A relationship between molecular dynamics motions of noncatalytic residues and enzyme activity has recently been proposed. We present examples where mutations either near or distal from the active site residues modify internal enzyme motion with resulting modification of catalysis. A better understanding of internal protein motions correlated to catalysis will lead to a greater insight into enzyme function.     

Structural characterization of alpha-helices of implicitly solvated poly-alanine

The structural characteristics of alpha-helices in poly-alanine-based peptides have been investigated via molecular dynamics simulation with the goal of understanding the basic features of peptide simulations within the context of a model system, classical molecular dynamics with generalized Born (GB) solvation, and to shed insight into the formation and stabilization of alpha-helices in short peptides. The effects of peptide length, terminal charges, proline substitution, and temperature on the alpha-helical secondary structure have been studied. The simulations have shown that distinct secondary structure begins to develop in peptides with lengths approaching 10 residues while ambiguous structures occur in shorter peptides. The helical content of peptides with lengths > or =10 amino acids is observed to be nearly constant up to (Ala)(40). Interestingly, terminal charges and proline in the second position from the N-terminus alter the secondary structure locally with little effect on the overall alpha-helical content of the peptide. The free energy profile of helix formation was also investigated. A large increase in free energy accompanying the formation of helices with more than two consecutive hydrogen bonds in the (i, i + 4) pattern was observed while the free energy increases linearly with additional hydrogen bonds. Values for the change in enthalpy and entropy of helix nucleation and propagation are reported. Additionally the results obtained from the GB model are compared to explicit solvent simulations of two synthetic alanine-based peptides.     

TRAJELIX: A Computational Tool for the Geometric Characterization of Protein Helices During Molecular Dynamics Simulations

Summary We have developed a computer program with the necessary mathematical formalism for the geometric characterization of distorted conformations of alpha-helices proteins, such as those that can potentially be sampled during typical molecular dynamics simulations. This formalism has been incorporated into TRAJELIX, a new module within the SIMULAID framework (http://inka.mssm.edu/~mezei/simulaid/) that is capable of monitoring distortions of alpha-helices in terms of their displacement, global and local tilting, rotation around their axes, compression/extension, winding/unwinding, and bending. Accurate evaluation of these global and local structural properties of the helix can help study possible intramolecular and intermolecular changes in the helix packing of alpha-helical membrane proteins, as shown here in an application to the interacting helical domains of rhodopsin dimers. Quantification of the dynamic structural behavior of alpha-helical membrane proteins is critical for our understanding of signal transduction, and may enable structure-based design of more specific and efficient drugs.     

General framework for studying the dynamics of folded and nonfolded proteins by NMR relaxation spectroscopy and MD simulation

A general framework is presented for the interpretation of NMR relaxation data of proteins. The method, termed isotropic reorientational eigenmode dynamics (iRED), relies on a principal component analysis of the isotropically averaged covariance matrix of the lattice functions of the spin interactions responsible for spin relaxation. The covariance matrix, which is evaluated using a molecular dynamics (MD) simulation, is diagonalized yielding reorientational eigenmodes and amplitudes that reveal detailed information about correlated protein dynamics. The eigenvalue distribution allows one to quantitatively assess whether overall and internal motions are statistically separable. To each eigenmode belongs a correlation time that can be adjusted to optimally reproduce experimental relaxation parameters. A key feature of the method is that it does not require separability of overall tumbling and internal motions, which makes it applicable to a wide range of systems, such as folded, partially folded, and unfolded biomolecular systems and other macromolecules in solution. The approach was applied to NMR relaxation data of ubiquitin collected at multiple magnetic fields in the native form and in the partially folded A-state using MD trajectories with lengths of 6 and 70 ns. The relaxation data of native ubiquitin are well reproduced after adjustment of the correlation times of the 10 largest eigenmodes. For this state, a high degree of separability between internal and overall motions is present as is reflected in large amplitude and collectivity gaps between internal and overall reorientational modes. In contrast, no such separability exists for the A-state. Residual overall tumbling motion involving the N-terminal beta-sheet and the central helix is observed for two of the largest modes only. By adjusting the correlation times of the 10 largest modes, a high degree of consistency between the experimental relaxation data and the iRED model is reached for this highly flexible biomolecule.     

N2,O2水溶液光谱的分子动力学模拟

用分子动力学模拟方法研究了N2和O2水溶液的光谱性质．给出了能描述分子内部运动的溶质－溶剂相互作用势．对溶质和溶剂原子的速度自相关函数（VACF）作了计算．讨论了所得VACF的性质并计算了其谱密度．溶质分子振动谱出现的红移，与液态N2，O2的Raman实验结果相吻合．模拟得出的转动谱表明了溶剂分子对溶质转动运动的阻滞，模拟结果也表明VACF计算对溶液和液体光谱的研究十分有效．     

Conformational dynamics of the nicotinic acetylcholine receptor channel: a 35-ns molecular dynamics simulation study

The nicotinic acetylcholine receptor (AChR) is the paradigm of ligand-gated ion channels, integral membrane proteins that mediate fast intercellular communication in response to neurotransmitters. A 35-ns molecular dynamics simulation has been performed to explore the conformational dynamics of the entire membrane-spanning region, including the ion channel pore of the AChR. In the simulation, the 20 transmembrane (TM) segments that comprise the whole TM domain of the receptor were inserted into a large dipalmitoylphosphatidylcholine (DPPC) bilayer. The dynamic behavior of individual TM segments and their corresponding AChR subunit helix bundles was examined in order to assess the contribution of each to the conformational transitions of the whole channel. Asymmetrical and asynchronous motions of the M1-M3 TM segments of each subunit were revealed. In addition, the outermost ring of five M4 TM helices was found to convey the effects exerted by the lipid molecules to the central channel domain. Remarkably, a closed-to-open conformational shift was found to occur in one of the channel ring positions in the time scale of the present simulations, the possible physiological significance of which is discussed.     

Conformational flexibility of the group B meningococcal polysaccharide in solution

To elucidate the role of secondary structure in the immune response against alpha(2-->8)-linked polysialic acid, the capsular polysaccharide of Group B meningococci, we have investigated its solution dynamics by using specific models of molecular motion and hydrodynamic modeling to interpret experimental NMR data. (13)C-[(1)H] NMR relaxation times and steady-state NOE enhancements were measured for two aqueous solutions of alpha(2-->8)-linked sialic acid polysaccharides. Each contained a unique distribution of polysaccharide chain lengths, with average lengths estimated at 40 or 400 residues. Models for rigid molecule tumbling, including two based on helical conformations proposed for the polysaccharide,(31) could not explain the NMR measurements. In general for these helices, the correlation times for their overall tumbling that best account for the NMR data correspond to polysaccharide chains between 9 and 18 residues in length, far short of the average lengths estimated for either solution. The effects of internal motions incorporated into these helices was modeled with an effective correlation time representing helix tumbling as well as internal motion. This modeling demonstrated that even with extreme amounts of internal motion, "flexible helices" of 25 residues or more still could not produce the NMR measurements. All data are consistent with internal and segmental motions dominating the nuclear magnetic relaxation of the polysaccharide and not molecular tumbling. Statistical distributions of correlation times have been found specifically for the pyranose rings, linkage groups, and methoxy groups that can account for the measured relaxation times and NOE enhancements. The distributions suggest that considerable flexibility attends the polysaccharide in solution, and the ranges of motional frequencies for the linkage groups and pyranose rings are comparable. We conclude that the Group B meningococcal polysaccharide is a random coil chain in solution, and therefore, does not have antigenic epitopes dependent upon a rigid, ordered conformation.     

Periodic orientational motions of rigid liquid-crystalline polymers in shear flow

The collective periodic motions of liquid-crystalline polymers in a nematic phase in shear flow have, for the first time, been simulated at the particle level by Brownian dynamics simulations. A wide range of parameter space has been scanned by varying the aspect ratio L/D between 10 and 60 at three different scaled volume fractions Lphi/D and an extensive series of shear rates. The influence of the start configuration of the box on the final motion has also been studied. Depending on these parameters, the motion of the director is either characterized as tumbling, kayaking, log-rolling, wagging, or flow-aligning. The periods of kayaking and wagging motions are given by T=4.2(Lphi/D)gamma(-1) for high aspect ratios. Our simulation results are in agreement with theoretical predictions and recent shear experiments on fd viruses in solution. These calculations of elongated rigid rods have become feasible with a newly developed event-driven Brownian dynamics algorithm.     

Quasi-Hamiltonian equations of motion for internal coordinate molecular dynamics of polymers

Conventional molecular dynamics simulations of macromolecules require long computational times because the most interesting motions are very slow compared to the fast oscillations of bond lengths and bond angles that limit the integration time step. Simulation of dynamics in the space of internal coordinates, that is, with bond lengths, bond angles, and torsions as independent variables, gives a theoretical possibility of eliminating all uninteresting fast degrees of freedom from the system. This article presents a new method for internal coordinate molecular dynamics simulations of macromolecules. Equations of motion are derived that are applicable to branched chain molecules with any number of internal degrees of freedom. Equations use the canonical variables and they are much simpler than existing analogs. In the numerical tests the internal coordinate dynamics are compared with the traditional Cartesian coordinate molecular dynamics in simulations of a 56 residue globular protein. For the first time it was possible to compare the two alternative methods on identical molecular models in conventional quality tests. It is shown that the traditional and internal coordinate dynamics require the same time step size for the same accuracy and that in the standard geometry approximation of amino acids, that is, with fixed bond lengths, bond angles, and rigid aromatic groups, the characteristic step size is 4 fs, which is 2 times higher than with fixed bond lengths only. The step size can be increased up to 11 fs when rotation of hydrogen atoms is suppressed. © 1997 by John Wiley & Sons, Inc. J Comput Chem 18 : 1354–1364, 1997     

A normal mode-based geometric simulation approach for exploring biologically relevant conformational transitions in proteins

A three-step approach for multiscale modeling of protein conformational changes is presented that incorporates information about preferred directions of protein motions into a geometric simulation algorithm. The first two steps are based on a rigid cluster normal-mode analysis (RCNMA). Low-frequency normal modes are used in the third step (NMSim) to extend the recently introduced idea of constrained geometric simulations of diffusive motions in proteins by biasing backbone motions of the protein, whereas side-chain motions are biased toward favorable rotamer states. The generated structures are iteratively corrected regarding steric clashes and stereochemical constraint violations. The approach allows performing three simulation types: unbiased exploration of conformational space; pathway generation by a targeted simulation; and radius of gyration-guided simulation. When applied to a data set of proteins with experimentally observed conformational changes, conformational variabilities are reproduced very well for 4 out of 5 proteins that show domain motions, with correlation coefficients r > 0.70 and as high as r = 0.92 in the case of adenylate kinase. In 7 out of 8 cases, NMSim simulations starting from unbound structures are able to sample conformations that are similar (root-mean-square deviation = 1.0-3.1 ?) to ligand bound conformations. An NMSim generated pathway of conformational change of adenylate kinase correctly describes the sequence of domain closing. The NMSim approach is a computationally efficient alternative to molecular dynamics simulations for conformational sampling of proteins. The generated conformations and pathways of conformational transitions can serve as input to docking approaches or as starting points for more sophisticated sampling techniques.     

Collective motion artifacts arising in long‐duration molecular dynamics simulations

We tested a variety of molecular dynamics simulation strategies in long‐duration (up to several nanoseconds) constant‐temperature simulations of liquid water under periodic boundary conditions. Such long durations are necessary to achieve adequate conformational sampling in simulations of membrane assemblies and other large biomolecular systems. Under a variety of circumstances, serious artifacts arise in the form of spurious collective behavior that becomes obvious only after the simulation has gone at least several hundred picoseconds. The potential energy of the system drops and the system changes from a liquid to an icy or glassy state. The underlying cause is accumulated center‐of‐mass motion of the system, coupled with velocity rescaling associated with constant‐temperature control. The velocity rescaling in the constant‐temperature algorithm reduces the thermal velocity as the net center‐of‐mass velocity grows, effectively causing the kinetic energy of the system to drain from thermal motions into coordinated motions. We found that the incidence and magnitude of the underlying artifactual motion leading to the spurious transition is mediated by: choice of method for computing electrostatic interactions; choice of ensemble; size of the simulation cell; SHAKE tolerance; frequency of nonbonded pairlist updating; and closeness of coupling to the temperature bath. The appearance of the spurious transition can be avoided by periodically subtracting net center‐of‐mass motion during the dynamics, or by improving the accuracy of the simulation by means of tightening SHAKE tolerance and updating nonbonded pairlists every timestep. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 121–131, 2000     

Helix forming tendency of valine substituted poly-alanine: a molecular dynamics investigation

In this study, classical molecular dynamics simulations have been carried out on the valine (guest) substituted poly alanine (host) using the host-guest peptide approach to understand the role of valine in the formation and stabilization of helix. Valine has been substituted in the host peptide starting from N terminal to C terminal. Various structural parameters have been obtained from the molecular dynamics simulation to understand the tolerance of helical motif to valine. Depending on the position of valine in the host peptide, it stabilizes (or destabilizes) the formation of the helical structure. The substitution of valine in the poly alanine at some positions has no effect on the helix formation (deformation). It is interesting to observe the coexistence of 3 10 and alpha-helix in the peptides due to the dynamical nature of the hydrogen bonding interaction and sterical interactions.     

Stochastic dynamic simulation of a protein

The internal motions of a small protein, the bovine pancreatic trypsin inhibitor (BPTI) in solution, are investigated in the framework of the Langevin equation. In this approach, the effects of the solvent molecules are incorporated by suitably defining the friction and random forces. The friction coefficients are determined from a molecular dynamics simulation. The details of the rapid fluctuations of protein atoms obtained by stochastic and molecular dynamics simulation techniques are compared by calculating the generalized density of states obtained via an incoherent neutron scattering. Presently, our stochastic dynamics simulation is one order of magnitude faster than the molecular dynamics simulation with the explicit inclusion of the water molecules. Generalizations of the present stochastic dynamics approach for studying the large-scale motion in proteins are briefly outlined and the probability of a further speedup by an additional order of magnitude is discussed.     

1H magic angle rotation NMR in polymer studies

The principles of the method of NMR line narrowing by measurement with spinning of the sample about the magic axis (MAR-NMR) are introduced, with particular emphasis on the effects of internal motion upon the possibilities and limitations of the method. The applications of the method in ¹H-NMR studies of polymer structure and dynamics are then reviewed. Due to both theoretical and experimental limitations, narrowing of dipolar broadened NMR lines by MAR can be observed in ¹H NMR spectra only in those cases where internal motion is anisotropic, or in heterogeneous systems where line width is limited by differences of magnetic susceptibility. In polymers, both solid and liquid, the method makes possible differentiation between isotropic and anisotropic internal motion. In systems with anisotropic internal motion, MAR-NMR makes possible a characterization of motional codes which normally are obscured by residual dipolar interactions, as well as of geometrical restrictions upon these motions.