Molecular dynamics simulations of calcium-free calmodulin in solution

A 4-ns molecular dynamics simulation of calcium-free calmodulin in solution has been performed, using Ewald summation to treat electrostatic interactions. Our simulation results were mostly consistent with solution experimental studies, including NMR, fluorescence and x-ray scattering. The secondary structures within the N- and C-terminal domains were conserved in the simulation, with trajectory structures similar to the NMR-derived model structure 1CFD. However, the relative orientations of the domains, for which there are no NMR restraints, differed in details between the simulation and the 1CFD model. The most interesting information provided by the simulations is that the dynamics of calcium-free calmodulin in solution is dominated by slow rigid body reorientations of the domains. The interdomain distance fluctuated between 29 and 39 A, and interdomain orientation angle, defined as the pseudo-dihedral formed by the four calcium binding sites, varied between -2 degrees and 108 degrees. Similarly, the domain linker region also exhibited significant fluctuations, with its length varying in the 34-45 A range and its bend angle in the 10-100 degrees range. The simulations are in accord with fluorescence results suggesting that calcium-free calmodulin is more compact and more flexible than the calcium activated form. Surprisingly, quite similar solvent accessibilities of the hydrophobic patches were seen in the calcium-free trajectory described in this work and previously generated calcium-loaded calmodulin simulations. Thus, our simulations suggest a reexamination of the standard model of the structural change of calmodulin upon calcium binding, involving exposure of the hydrophobic patches to solvent.     

Molecular Dynamics Simulations of Calcium-Free Calmodulin in Solution

Abstract

A 4-ns molecular dynamics simulation of calcium-free calmodulin in solution has been performed, using Ewald summation to treat electrostatic interactions. Our simulation results were mostly consistent with solution experimental studies, including NMR, fluorescence and x-ray scattering. The secondary structures within the N- and C-terminal domains were conserved in the simulation, with trajectory structures similar to the NMR-derived model structure 1CFD. However, the relative orientations of the domains, for which there are no NMR restraints, differed in details between the simulation and the 1CFD model. The most interesting information provided by the simulations is that the dynamics of calcium-free calmod- ulin in solution is dominated by slow rigid body reorientations of the domains. The interdomain distance fluctuated between 29 and 39 Å, and interdomain orientation angle, defined as the pseudo-dihedral formed by the four calcium binding sites, varied between ?2° and 108°. Similarly, the domain linker region also exhibited significant fluctuations, with its length varying in the 34–45 Å range and its bend angle in the 10–100° range. The simulations are in accord with fluorescence results suggesting that calcium-free calmodulin is more compact and more flexible than the calcium activated form. Surprisingly, quite similar solvent accessibilities of the hydrophobic patches were seen in the calcium-free trajectory described in this work and previously generated calcium-loaded calmodulin simulations. Thus, our simulations suggest a reexamination of the standard model of the structural change of calmodulin upon calcium binding, involving exposure of the hydrophobic patches to solvent.     

Structure and dynamics of calmodulin in solution.

To characterize the dynamic behavior of calmodulin in solution, we have carried out molecular dynamics (MD) simulations of the Ca2+-loaded structure. The crystal structure of calmodulin was placed in a solvent sphere of radius 44 A, and 6 Cl- and 22 Na+ ions were included to neutralize the system and to model a 150 mM salt concentration. The total number of atoms was 32,867. During the 3-ns simulation, the structure exhibits large conformational changes on the nanosecond time scale. The central alpha-helix, which has been shown to unwind locally upon binding of calmodulin to target proteins, bends and unwinds near residue Arg74. We interpret this result as a preparative step in the more extensive structural transition observed in the "flexible linker" region 74-82 of the central helix upon complex formation. The major structural change is a reorientation of the two Ca2+-binding domains with respect to each other and a rearrangement of alpha-helices in the N-terminus domain that makes the hydrophobic target peptide binding site more accessible. This structural rearrangement brings the domains to a more favorable position for target binding, poised to achieve the orientation observed in the complex of calmodulin with myosin light-chain kinase. Analysis of solvent structure reveals an inhomogeneity in the mobility of water in the vicinity of the protein, which is attributable to the hydrophobic effect exerted by calmodulin's binding sites for target peptides.     

A molecular dynamics simulation of bacteriophage T4 lysozyme.

An analysis of a 400 ps molecular dynamics simulation of the 164 amino acid enzyme T4 lysozyme is presented. The simulation was carried out with all hydrogen atoms modeled explicitly, the inclusion of all 152 crystallographic waters and at a temperature of 300 K. Temporal analysis of the trajectory versus energy, hydrogen bond stability, r.m.s. deviation from the starting crystal structure and radius of gyration, demonstrates that the simulation was both stable and representative of the average experimental structure. Average structural properties were calculated from the enzyme trajectory and compared with the crystal structure. The mean value of the C alpha displacements of the average simulated structure from the X-ray structure was 1.1 +/- 0.1 A; differences of the backbone phi and psi angles between the average simulated structure and the crystal structure were also examined. Thermal-B factors were calculated from the simulation for heavy and backbone atoms and both were in good agreement with experimental values. Relationships between protein secondary structure elements and internal motions were studied by examining the positional fluctuations of individual helix, sheet and turn structures. The structural integrity in the secondary structure units was preserved throughout the simulation; however, the A helix did show some unusually high atomic fluctuations. The largest backbone atom r.m.s. fluctuations were found in non-secondary structure regions; similar results were observed for r.m.s. fluctuations of non-secondary structure phi and psi angles. In general, the calculated values of r.m.s. fluctuations were quite small for the secondary structure elements. In contrast, surface loops and turns exhibited much larger values, being able to sample larger regions of conformational space. The C alpha difference distance matrix and super-positioning analyses comparing the X-ray structure with the average dynamics structure suggest that a 'hinge-bending' motion occurs between the N- and C-terminal domains.     

Structural dynamics of calmodulin and troponin C

We present the results of computational simulation studies of the structures of calmodulin (CAM) and troponin C (TNC). Possible differences between the structures of these molecules in the crystal and in solution were suggested by results from some recent experimental studies, which implied that their conformations in solution may be more compacted than the characteristic dumbbell shape observed in the crystal. The molecular dynamics simulations were carried out with the CHARMM system of programs, and the environment was modeled with a distance-dependent dielectric permittivity and discrete water molecules surrounding the proteins at starting positions identified in the crystals of CAM and TNC. Methods of macromolecular structure analysis, including linear distance plots, distance matrices and a matrix representation of hydrogen bonding, were used to analyze the nature, the extent and the source of structural differences between the computed structures of the molecules and their conformations in the crystal. Following the longest simulation, in which intradomain structure was conserved, the crystallographically observed dumbbell structure of the molecule changed due to a kinking or bending in the region of the central tether helix connecting the two Ca(2+)-binding domains which moved into close proximity. The resulting structure correlates with experimental observations of complexes between CAM and peptides such as melittin and mastoparan. Analysis of the corresponding pair distance distribution functions in comparison to experimental results suggests the dynamic existence of a non-negligible fraction of the compacted structure in aqueous solutions of CAM. In this more nearly globular shape, CAM reveals to the environment two interior pockets that contain a number of hydrophobic residues, in agreement with NMR data suggesting involvement of such residues in the binding of inhibitors and proteins to CAM.     

Model-free methods of analyzing domain motions in proteins from simulation: A comparison of normal mode analysis and molecular dynamics simulation of lysozyme

Model-free methods are introduced to determine quantities pertaining to protein domain motions from normal mode analyses and molecular dynamics simulations. For the normal mode analysis, the methods are based on the assumption that in low frequency modes, domain motions can be well approximated by modes of motion external to the domains. To analyze the molecular dynamics trajectory, a principal component analysis tailored specifically to analyze interdomain motions is applied. A method based on the curl of the atomic displacements is described, which yields a sharp discrimination of domains, and which defines a unique interdomain screw-axis. Hinge axes are defined and classified as twist or closure axes depending on their direction. The methods have been tested on lysozyme. A remarkable correspondence was found between the first normal mode axis and the first principal mode axis, with both axes passing within 3 Å of the alpha-carbon atoms of residues 2, 39, and 56 of human lysozyme, and near the interdomain helix. The axes of the first modes are overwhelmingly closure axes. A lesser degree of correspondence is found for the second modes, but in both cases they are more twist axes than closure axes. Both analyses reveal that the interdomain connections allow only these two degrees of freedom, one more than provided by a pure mechanical hinge. Proteins 27:425–437, 1997. © 1997 Wiley-Liss, Inc.     

Molecular dynamics simulations of DNA and a protein-DNA complex including solvent

The results of a recent nanosecond (ns) molecular dynamics (MD) simulation of the d(CGCGAATTCGCG) double helix in water and a 100 ps MD study of the repressor-operator complex are described. The DNA simulations are analyzed in terms of the structural dynamics, fluctuations in the groove width and bending of the helical axis. The results indicate that the ns dynamical trajectory progresses through a series of three substates of B form DNA, with lifetimes of the order of hundreds of picoseconds (ps). An incipient dynamical equilibrium is evident. A comparison of the calculated axis bending with that observed in corresponding crystal structure data is presented. Simulation of the DNA in complex with the protein and that of the free DNA in solution, starting from the crystal conformation, reveal the dynamical changes that occur on complex formation.     

The conformations of hirudin in solution: a study using nuclear magnetic resonance, distance geometry and restrained molecular dynamics

The solution conformations of the protein hirudin have been investigated by the combined use of distance geometry and restained molecular dynamics calculations. The basis for the structure determination comprised 359 approximate inter-proton distance restrains and 10 phi backbone torsion angle restrains derived from n.m.r. measurements. It is shown that hirudin is composed of three domains: a central core made up of residues 3-30, 37-46 and 56-57; a protruding 'finger' (residues 31-36) consisting of the tip of an antiparallel beta sheet, and an exposed loop (residues 47-55). The structure of each individual domain is relatively well defined with average backbone atomic r.m.s. differences of <2 A between the final seven converged restrained dynamic structures and the mean structure obtained by averaging their coordinates. The orientation of the two minor domains relative to the central core, however, could not be determined as no long-range (i-h >5) interdomain proton-proton contacts could be observed in the two-dimensional nuclear Overhauser enhancement spectra. From the restrained molecular dynamics calculations it appears that the two minor domains exhibit large rigid-body motions relative to the central core.     

Crystal structure of calmodulin

The crystal structure of calmodulin has been determined to 3.6 A resolution. At this resolution the polypeptide chain can be traced. Some of the side chains have tentatively been identified. Refinement of the structure with x-ray diffraction data measured to 1.65 A resolution is continuing. As reported by Babu et al. calmodulin is about 65 A long and 30 A in diameter. Homolog domains 1 and 2 are related by a local twofold axis, as in parvalbumin and in troponin C, and form one end of the molecule. Domains 3 and 4 form the other end. The second alpha-helix of domain 2 and a short interdomain region are continuous with the first helix of domain 3, thereby forming a single helix from residues 67-93. The central region, residues 75-84, of this long helix forms a handle connecting the two pairs of homolog domains. Exclusive of the residues, 75-84, in the handle the closet approach of side chains of pair 1, 2 to pair 3, 4 is 12 A. The spatial relationship of pair 1, 2 to pair 3, 4 is similar in calmodulin to the relationship of the corresponding pairs in troponin C. However, in troponin C there are three additional residues in the handle region of the long alpha-helix and the two pairs are about 5.0 A further apart. On the surface of pair 1, 2 in calmodulin there is one extended region with many hydrophobic side chains from both domain 1 and domain 2. This hydrophobic patch is bounded by two distinct clusters of anionic side chains, one from the beginning of the first helix of domain 1 and on the other side of the hydrophobic surface one from the beginning of the first helix of domain 2. Homologously, the hydrophobic patch on the surface of pair 3, 4 is bounded by two clusters of aspartate and glutamate residues. Either or both of these hydrophobic surfaces may be sites to which calmodulin target proteins bind.     

Molecular dynamics simulations of a calmodulin-peptide complex in solution

We have performed an 4-ns MD simulation of calmodulin complexed with a target peptide in explicit water, under realistic conditions of constant temperature and pressure, in the presence of a physiological concentration of counterions and using Ewald summation to avoid truncation of long-range electrostatic forces. During the simulation the system tended to perform small fluctuations around a structure similar to, but somewhat looser than the starting crystal structure. The calmodulin-peptide complex was quite rigid and did not exhibit any large amplitude domain motions such as previously seen in apo- and calcium-bound calmodulin. We analyzed the calmodulin-peptide interactions by calculating buried surface areas, CHARMM interaction energies and continuum model interaction free energies. In the trajectory, the protein surface area buried by contact with the peptide is 1373 A(2) approximately evenly divided between the calmodulin N-terminal, C-terminal and central linker regions. A majority of this buried surface, 803 A(2), comes from nonpolar residues, in contrast to the protein as a whole, for which the surface is made up of mostly polar and charged groups. Our continuum calculations indicate that the largest favorable contribution to peptide binding comes from burial of molecular surface upon complex formation. Electrostatic contributions are favorable but smaller in the trajectory structures, and actually unfavorable for binding in the crystal structure. Since nonpolar groups make up most of buried surface of the protein, our calculations suggest that the hydrophobic effect is the main driving force for binding the helical peptide to calmodulin, consistent with thermodynamic analysis of experimental data. Besides the burial of nonpolar surface area, secondary contributions to peptide binding come from burial of polar surface and electrostatic interactions. In the nonpolar interactions a crucial role is played by the nine methionines of calmodulin. In the electrostatic interactions the negatively charged protein residues and positively charged peptide residues play a dominant role.     

Elucidating nitric oxide synthase domain interactions by molecular dynamics

Nitric oxide synthase (NOS) is a multidomain enzyme that catalyzes the production of nitric oxide (NO) by oxidizing l ‐Arg to NO and L‐citrulline. NO production requires multiple interdomain electron transfer steps between the flavin mononucleotide (FMN) and heme domain. Specifically, NADPH‐derived electrons are transferred to the heme‐containing oxygenase domain via the flavin adenine dinucleotide (FAD) and FMN containing reductase domains. While crystal structures are available for both the reductase and oxygenase domains of NOS, to date there is no atomic level structural information on domain interactions required for the final FMN‐to‐heme electron transfer step. Here, we evaluate a model of this final electron transfer step for the heme–FMN–calmodulin NOS complex based on the recent biophysical studies using a 105‐ns molecular dynamics trajectory. The resulting equilibrated complex structure is very stable and provides a detailed prediction of interdomain contacts required for stabilizing the NOS output state. The resulting equilibrated complex model agrees well with previous experimental work and provides a detailed working model of the final NOS electron transfer step required for NO biosynthesis.     

Bending of the calmodulin central helix: a theoretical study.

The crystal structure of calcium-calmodulin (CaM) reveals a protein with a typical dumbbell structure. Various spectroscopic studies have suggested that the central linker region of CaM, which is alpha-helical in the crystal structure, is flexible in solution. In particular, NMR studies have indicated the presence of a flexible backbone between residues Lys 77 and Asp 80. This flexibility is related directly to the function of the protein because it enables the N- and C-terminal domains of the protein to move toward each other and bind to the CaM-binding domain of a target protein. We have investigated the flexibility of the CaM central helix by a variety of computational techniques: molecular dynamics (MD) simulations, normal mode analysis (NMA), and essential dynamics (ED) analysis. Our MD results reproduce the experimentally determined location of the bend in a simulation of only the CaM central helix, indicating that the bending point is an intrinsic property of the alpha-helix, for which the remainder of the protein is not important. Interestingly, the modes found by the ED analysis of the MD trajectory are very similar to the lowest frequency modes from the NM analysis and to modes found by an ED analysis of different structures in a set of NMR structures. Electrostatic interactions involving residues Arg 74 and Asp 80 seem to be important for these bending motions and unfolding, which is in line with pH-dependent NMR and CD studies.     

Comparison of the crystal and solution structures of calmodulin and troponin C

X-ray solution scattering data from skeletal muscle troponin C and from calmodulin have been measured. Modeling studies based on the crystal structure coordinates for these proteins show discrepancies between the solution data and the crystal structure that indicate that if the size and shape of the globular domains are the same in solution as in the crystal, the distances between them must be smaller by several angstroms. Bringing the globular domains closer together requires structural changes in the interconnecting helix that joins them.     

Determination of the Individual Roles of the Linker Residues in the Interdomain Motions of Calmodulin Using NMR Chemical Shifts

Many protein molecules are formed by two or more domains whose structures and dynamics are closely related to their biological functions. It is thus important to develop methods to determine the structural properties of these multidomain proteins. Here, we characterize the interdomain motions in the calcium-bound state of calmodulin (Ca^2 +-CaM) using NMR chemical shifts as replica-averaged structural restraints in molecular dynamics simulations. We find that the conformational fluctuations of the interdomain linker, which are largely responsible for the overall interdomain motions of CaM, can be well described by exploiting the information provided by chemical shifts. We thus identify 10 residues in the interdomain linker region that change their conformations upon substrate binding. Five of these residues (Met76, Lys77, Thr79, Asp80 and Ser81) are highly flexible and cover the range of conformations observed in the substrate-bound state, while the remaining five (Arg74, Lys75, Asp78, Glu82 and Glu83) are much more rigid and do not populate conformations typical of the substrate-bound form. The ensemble of conformations representing the Ca^2 +-CaM state obtained in this study is in good agreement with residual dipolar coupling, paramagnetic resonance enhancement, small-angle X-ray scattering and fluorescence resonance energy transfer measurements, which were not used as restraints in the calculations. These results provide initial evidence that chemical shifts can be used to characterize the conformational fluctuations of multidomain proteins.     

Integrating NMR,SAXS, and Atomistic Simulations: Structure and Dynamics of a Two-Domain Protein

Multidomain proteins with two or more independently folded functional domains are prevalent in nature. Whereas most multidomain proteins are linked linearly in sequence, roughly one-tenth possess domain insertions where a guest domain is implanted into a loop of a host domain, such that the two domains are connected by a pair of interdomain linkers. Here, we characterized the influence of the interdomain linkers on the structure and dynamics of a domain-insertion protein in which the guest LysM domain is inserted into a central loop of the host CVNH domain. Expanding upon our previous crystallographic and NMR studies, we applied SAXS in combination with NMR paramagnetic relaxation enhancement to construct a structural model of the overall two-domain system. Although the two domains have no fixed relative orientation, certain orientations were found to be preferred over others. We also assessed the accuracies of molecular mechanics force fields in modeling the structure and dynamics of tethered multidomain proteins by integrating our experimental results with microsecond-scale atomistic molecular dynamics simulations. In particular, our evaluation of two different combinations of the latest force fields and water models revealed that both combinations accurately reproduce certain structural and dynamical properties, but are inaccurate for others. Overall, our study illustrates the value of integrating experimental NMR and SAXS studies with long timescale atomistic simulations for characterizing structural ensembles of flexibly linked multidomain systems.     

Probing the structural changes in the light chain of human coagulation factor VIIa due to tissue factor association.

The crystallographic structure of human coagulation factor VIIa/tissue factor complex bound with calcium ions was used to model the solution structure of the light chain of factor VIIa (residues 1-142) in the absence of tissue factor. The Amber force field in conjunction with the particle mesh Ewald summation method to accommodate long-range electrostatic interactions was used in the trajectory calculations. The estimated TF-free solution structure was then compared with the crystal structure of factor VIIa/tissue factor complex to estimate the restructuring of factor VIIa due to tissue factor binding. The solution structure of the light chain of factor VIIa in the absence of tissue factor is predicted to be an extended domain structure similar to that of the tissue factor-bound crystal. Removal of the EGF1-bound calcium ion is shown by simulation to lead to minor structural changes within the EGF1 domain, but also leads to substantial relative reorientation of the Gla and EGF1 domains.     

Reconciling the solution and X-ray structures of the villin headpiece helical subdomain: molecular dynamics simulations and double mutant cycles reveal a stabilizing cation-pi interaction

The 36-residue helical subdomain of the villin headpiece, HP36, is one of the smallest cooperatively folded proteins, folding on the microsecond time scale. The domain is an extraordinarily popular model system for both experimental and computational studies of protein folding. The structure of HP36 has been determined using X-ray crystallography and NMR spectroscopy, with the resulting structures exhibiting differences in helix packing, van der Waals contacts, and hydrogen bonding. It is important to determine the solution structure of HP36 with as much accuracy as possible since this structure is widely used as a reference for simulations and experiments. We complement the existing data by using all-atom molecular dynamics simulations with explicit solvent to evaluate which of the experimental models is the better representation of HP36 in solution. After simulation for 50 ns initiated with the NMR structure, we observed that the protein spontaneously adopts structures with a backbone conformation, core packing, and C-capping motif on the third helix that are more consistent with the crystal structure. We also examined hydrogen bonding and side chain packing interactions between D44 and R55 and between F47 and R55, respectively, which were observed in the crystal structure but not in the NMR-based solution structure. Simulations showed large fluctuations in the distance between D44 and R55, while the distance between F47 and R55 remained stable, suggesting the formation of a cation-pi interaction between those residues. Experimental double mutant cycles confirmed that the F47-R55 pair has a larger energetic coupling than the D44-R55 interaction. Overall, these combined experimental and computational studies show that the X-ray crystal structure is the better reference structure for HP36 in solution at neutral pH. Our analysis also shows how detailed molecular dynamics simulations combined with experimental validation can help bridge the gap between NMR and crystallographic methods.