Validating Solution Ensembles from Molecular Dynamics Simulation by Wide-Angle X-ray Scattering Data

Wide-angle x-ray scattering (WAXS) experiments of biomolecules in solution have become increasingly popular because of technical advances in light sources and detectors. However, the structural interpretation of WAXS profiles is problematic, partly because accurate calculations of WAXS profiles from structural models have remained challenging. In this work, we present the calculation of WAXS profiles from explicit-solvent molecular dynamics (MD) simulations of five different proteins. Using only a single fitting parameter that accounts for experimental uncertainties because of the buffer subtraction and dark currents, we find excellent agreement to experimental profiles both at small and wide angles. Because explicit solvation eliminates free parameters associated with the solvation layer or the excluded solvent, which would require fitting to experimental data, we minimize the risk of overfitting. We further find that the influence from water models and protein force fields on calculated profiles are insignificant up to q ≈ 15 nm^?1. Using a series of simulations that allow increasing flexibility of the proteins, we show that incorporating thermal fluctuations into the calculations significantly improves agreement with experimental data, demonstrating the importance of protein dynamics in the interpretation of WAXS profiles. In addition, free MD simulations up to one microsecond suggest that the calculated profiles are highly sensitive with respect to minor conformational rearrangements of proteins, such as an increased flexibility of a loop or an increase of the radius of gyration by  <  1%. The present study suggests that quantitative comparison between MD simulations and experimental WAXS profiles emerges as an accurate tool to validate solution ensembles of biomolecules.     

A Molecular Dynamics Simulation of an Aqueous Beryllium Chloride Solution

Abstract

A Molecular Dynamics simulation of a 1.1 molal aqueous BeCl₂ solution was performed with the flexible BJH model for water and a newly developed three-body potential for Be²⁺ -H₂O interactions derived from ab-initio calculations. The properties of the potential are discussed and radial distribution functions, angular distributions and dynamic properties of the solution like vibrational modes and hindered rotations are analyzed.     

Structure and Mechanical Characterization of DNA i-Motif Nanowires by Molecular Dynamics Simulation

We studied the structure and mechanical properties of DNA i-motif nanowires by means of molecular dynamics computer simulations. We built up to 230 nm-long nanowires, based on a repeated TC₅ sequence from crystallographic data, fully relaxed and equilibrated in water. The unusual C⋅C⁺ stacked structure, formed by four ssDNA strands arranged in an intercalated tetramer, is here fully characterized both statically and dynamically. By applying stretching, compression, and bending deformations with the steered molecular dynamics and umbrella sampling methods, we extract the apparent Young’s and bending moduli of the nanowire, as well as estimates for the tensile strength and persistence length. According to our results, the i-motif nanowire shares similarities with structural proteins, as far as its tensile stiffness, but is closer to nucleic acids and flexible proteins, as far as its bending rigidity is concerned. Furthermore, thanks to its very thin cross section, the apparent tensile toughness is close to that of a metal. Besides their yet to be clarified biological significance, i-motif nanowires may qualify as interesting candidates for nanotechnology templates, due to such outstanding mechanical properties.     

Structure and Mechanical Characterization of DNA i-Motif Nanowires by Molecular Dynamics Simulation

We studied the structure and mechanical properties of DNA i-motif nanowires by means of molecular dynamics computer simulations. We built up to 230 nm-long nanowires, based on a repeated TC₅ sequence from crystallographic data, fully relaxed and equilibrated in water. The unusual C⋅C⁺ stacked structure, formed by four ssDNA strands arranged in an intercalated tetramer, is here fully characterized both statically and dynamically. By applying stretching, compression, and bending deformations with the steered molecular dynamics and umbrella sampling methods, we extract the apparent Young’s and bending moduli of the nanowire, as well as estimates for the tensile strength and persistence length. According to our results, the i-motif nanowire shares similarities with structural proteins, as far as its tensile stiffness, but is closer to nucleic acids and flexible proteins, as far as its bending rigidity is concerned. Furthermore, thanks to its very thin cross section, the apparent tensile toughness is close to that of a metal. Besides their yet to be clarified biological significance, i-motif nanowires may qualify as interesting candidates for nanotechnology templates, due to such outstanding mechanical properties.     

Solution and Crystal Molecular Dynamics Simulation Study of m4-Cyanovirin-N Mutants Complexed with Di-Mannose

Cyanovirin-N (CVN) is a highly potent anti-HIV carbohydrate-binding agent that establishes its microbicide activity through interaction with mannose-rich glycoprotein gp120 on the virion surface. The m4-CVN and P51G-m4-CVN mutants represent simple models for studying the high-affinity binding site, B^M. A recently determined 1.35 Å high-resolution structure of P51G-m4-CVN provided details on the di-mannose binding mechanism, and suggested that the Arg-76 and Glu-41 residues are critical components of high mannose specificity and affinity. We performed molecular-dynamics simulations in solution and a crystal environment to study the role of Arg-76. Network analysis and clustering were used to characterize the dynamics of Arg-76. The results of our explicit solvent solution and crystal simulations showed a significant correlation with conformations of Arg-76 proposed from x-ray crystallographic studies. However, the crystal simulation showed that the crystal environment strongly biases conformational sampling of the Arg-76 residue. The solution simulations demonstrated no conformational preferences for Arg-76, which would support its critical role as the residue that locks the ligand in the bound state. Instead, a comparative analysis of trajectories from >50 ns of simulation for two mutants revealed the existence of a very stable eight-hydrogen-bond network between the di-mannose ligand and predominantly main-chain atoms. This network may play a key role in the specific recognition and strong binding of mannose oligomers in CVN and its homologs.     

Single-Stranded DNA within Nanopores: Conformational Dynamics and Implications for Sequencing; a Molecular Dynamics Simulation Study

Engineered protein nanopores, such as those based on α-hemolysin from Staphylococcus aureus have shown great promise as components of next-generation DNA sequencing devices. However, before such protein nanopores can be used to their full potential, the conformational dynamics and translocation pathway of the DNA within them must be characterized at the individual molecule level. Here, we employ atomistic molecular dynamics simulations of single-stranded DNA movement through a model α-hemolysin pore under an applied electric field. The simulations enable characterization of the conformations adopted by single-stranded DNA, and allow exploration of how the conformations may impact on translocation within the wild-type model pore and a number of mutants. Our results show that specific interactions between the protein nanopore and the DNA can have a significant impact on the DNA conformation often leading to localized coiling, which in turn, can alter the order in which the DNA bases exit the nanopore. Thus, our simulations show that strategies to control the conformation of DNA within a protein nanopore would be a distinct advantage for the purposes of DNA sequencing.     

Triplex Formation Between DNA and Mixed Purine-Pyrimidine PNA Analog with Lysines in Backbone

Abstract

Melting UV experiments and mixing curves indicated slow triplex formation between lysine comprising PNA and DNA complement in 100mM Na⁺ solution.     

Interpretation of Solution X-Ray Scattering by Explicit-Solvent Molecular Dynamics

Small- and wide-angle x-ray scattering (SWAXS) and molecular dynamics (MD) simulations are complementary approaches that probe conformational transitions of biomolecules in solution, even in a time-resolved manner. However, the structural interpretation of the scattering signals is challenging, while MD simulations frequently suffer from incomplete sampling or from a force-field bias. To combine the advantages of both techniques, we present a method that incorporates solution scattering data as a differentiable energetic restraint into explicit-solvent MD simulations, termed SWAXS-driven MD, with the aim to direct the simulation into conformations satisfying the experimental data. Because the calculations fully rely on explicit solvent, no fitting parameters associated with the solvation layer or excluded solvent are required, and the calculations remain valid at wide angles. The complementarity of SWAXS and MD is illustrated using three biological examples, namely a periplasmic binding protein, aspartate carbamoyltransferase, and a nuclear exportin. The examples suggest that SWAXS-driven MD is capable of refining structures against SWAXS data without foreknowledge of possible reaction paths. In turn, the SWAXS data accelerates conformational transitions in MD simulations and reduces the force-field bias.     

分子动力学模拟与分子生物力学

生物大分子的微观结构动力学决定其生物学功能,其力学-化学耦合规律是分子生物力学的重点关注方向。分子动力学模拟是耦合生物大分子力学-化学性质微观结构动力学基础的有效手段,其结果可用于预测结构-功能关系、指导实验设计和诠释实验结果。本文简要介绍了分子动力学模拟的方法学特点、基本工作原理及其在分子生物力学中的应用,并展望了未来可能的发展方向和应用前景。     

A Molecular Dynamics Simulation Study of Coaxial Stacking in RNA

Abstract

We report on unrestrained molecular dynamics simulations of an RNA tetramer binding to a tetra-nucleotide overhang at the 5′-end of an RNA hairpin (nicked structure) and of the corresponding continuous hairpin with Na⁺ as counterions. The simulations lead to stable structures and in this way a structural model for the coaxially stacked RNA hairpin is generated. The stacking interface in the coaxially stacked nicked hairpin structure is characterized by a reduced twist and shift and a slightly increased propeller twist as compared to the continuous system. This leads to an increased overlap between C22 and G23 in the stacking interface of the nicked structure. In the simulations the continuous RNA hairpin has an almost straight helical axis. On the other hand, the corresponding axis for the nicked structure exhibits a marked kink of 39°. The stacking interface exhibits no increased flexibility as compared to the corresponding base pair step in the continuous structure.     

Molecular Dynamics Simulation of 7, 8-dihydro-8-Oxoguanine DNA

Abstract

To elucidate the effect of guanine lesion produced by the oxidative damage on DNA, 1 nanosecond molecular dynamics simulations of native and oxidized DNA were performed. The target DNA molecules are dodecamer duplex d(CGCGAATTCGCG)2 and its derivative duplex d(C₁G₂C₃(8-oxoG)₄A₅A₆T₇T₈C₉G₁₀C₁₁G₁₂)·d(C₁₃G₁₄C₁₅G₁₆A₁₇A₁₈T₁₉T₂₀C21_G22C₂₃G₂₄), which has one oxidized guanine, 7, 8-dihydro-8-oxoguanine (8-oxoG), at the fourth position. The local structural change due to the lesion of 8-oxoG and the global dynamic structure of the 8-oxoG DNA were studied. It was found that the 8-oxoG DNA remained structurally stable during the simulation due to newly produced hydrogen bonds around the (8-oxoG)₄ residue. However, there were distinguishable differences in structural parameters and dynamic property in the 8-oxoG DNA. The conformation around the (8- oxoG)₄ residue departed from the usual conformation of native DNA and took an unique conformation of ?-ζ in B_II conformation and χ in high anti orientation at the (8-oxoG)₄ residue, and adopted a very low helical twist angle at the C₃:G₂₂—(8-oxoG)₄:C₂₁ step. Further analysis by principal component analysis indicated that the formation of the hydrogen bonds around the (8-oxoG)₄ residue plays a role as a trigger for the conformational transition of the 8-oxoG DNA in the conformational space.     

Structural Study of Cell Attachment Peptide Derived from Laminin by Molecular Dynamics Simulation

Peptides with cell attachment activity are beneficial component of biomaterials for tissue engineering. Conformational structure is one of the important factors for the biological activities. The EF1 peptide (DYATLQLQEGRLHFMFDLG) derived from laminin promotes cell spreading and cell attachment activity mediated by α2β1 integrin. Although the sequence of the EF2 peptide (DFATVQLRNGFPYFSYDLG) is homologous sequence to that of EF1, EF2 does not promote cell attachment activity. To determine whether there are structural differences between EF1 and EF2, we performed replica exchange molecular dynamics (REMD) simulations and conventional molecular dynamics (MD) simulations. We found that EF1 and EF2 had β-sheet structure as a secondary structure around the global minimum. However, EF2 had variety of structures around the global minimum compared with EF1 and has easily escaped from the bottom of free energy. The structural fluctuation of the EF1 is smaller than that of the EF2. The structural variation of EF2 is related to these differences in the structural fluctuation and the number of the hydrogen bonds (H-bonds). From the analysis of H-bonds in the β-sheet, the number of H-bonds in EF1 is larger than that in EF2 in the time scale of the conventional MD simulation, suggesting that the formation of H-bonds is related to the differences in the structural fluctuation between EF1 and EF2. From the analysis of other non-covalent interactions in the amino acid sequences of EF1 and EF2, EF1 has three pairs of residues with hydrophobic interaction, and EF2 has two pairs. These results indicate that several non-covalent interactions are important for structural stabilization. Consequently, the structure of EF1 is stabilized by H-bonds and pairs of hydrophobic amino acids in the terminals. Hence, we propose that non-covalent interactions around N-terminal and C-terminal of the peptides are crucial for maintaining the β-sheet structure of the peptides.     

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.     

Rotation-Vibration Coupling in Liquid Water Investigated by Molecular Dynamics Simulation

Abstract

The standard rotation-vibration decoupling approximation for liquid water is tested using a method based on the split of the molecular dipole fluctuation correlation function into pure rotational, pure vibrational and crossed terms. Our results corroborate the total decoupling between vibrational and rotational motions in liquid water at ambient conditions and provide a tool able to test the reliability of this approximation for molecular liquids at different states.     

Structural Properties of Hybrid Triplex of Polycation Deoxyribonucleic S-methylthiourea (DNmt) Strands with a Complementary DNA Strand,Probed by Nanosecond Molecular Dynamics

Abstract

The replacement of phosphodiester linkages of the polyanion DNA with S-methylthiourea linkers provides the polycation deoxyribonucleic S-methylthiourea (DNmt). Molecular dynamics studies to 1,220 ps of the hybrid triplex formed from octameric DNmt strands d(Tmt)₈ with a complementary DNA oligomer strand d(Ap)₈ have been carried out with explicit water solvent and Na counterions under periodic boundary conditions using the CHARMM force field and the Ewald summation method. The Watson-Crick and Hoogsteen hydrogen-bonding patterns of the A/T tracts remained intact without any structural restraints for triplex structures throughout the simulation. The duplex portion of the triplex structure equilibrated at a B-DNA conformation in terms of the helical rise and other helical parameters. The dynamic structures of the DNmt·DNA·DNmt triplex were determined by examining histograms from the last 800 ps of the dynamics run. These included the hydrogen-bonding pattern (sequence recognition), three-centered bifurcating occurrences, minor groove width variations, and bending of tracts for the hybrid triplex structures. Together with the Watson-Crick hydrogen-bondings, the strong Hoogsteen hydrogen-bondings, the partially maintained three-centered bifurcatings in the Watson-Crick pair, and the medium-strength three-centered bifurcatings in the Hoogsteen pair suggest that the hybrid triplex is energetically favorable as compared to a duplex with similar base stacking, van der Waals interactions, and helical parameters. This is in agreement with our previously reported thermody- namic study, in which only triplex structures were observed in solution. The bending angle measured between the local axis vectors of the first and last helical axis segments is about 20° for the Watson-Crick portion of the averaged structure. Propeller twist (associated with three-centered hydrogen-bonding) up to ?30°, native to DNA AT base pairing, was also observed for the triplex structure. The sugar pseudorotation phase angles and the ring rotation angles for the DNA strand are within the C3′-endo domain and C2′-endo domain for the DNmt strand. Water spines are observed in both minor and major grooves throughout the dynamics run. The molecular dynamics simulations of the structural properties of DNmt·DNA·DNmt hybrid triplex is compared to the DNG·DNA·DNG hybrid triplex (In DNG the -O-(PO₂-)-O- linkers in DNA is replaced by -NH-C(=N₂)-NH-).     

Open-Boundary Molecular Dynamics of a DNA Molecule in a Hybrid Explicit/Implicit Salt Solution

The composition and electrolyte concentration of the aqueous bathing environment have important consequences for many biological processes and can profoundly affect the behavior of biomolecules. Nevertheless, because of computational limitations, many molecular simulations of biophysical systems can be performed only at specific ionic conditions: either at nominally zero salt concentration, i.e., including only counterions enforcing the system’s electroneutrality, or at excessive salt concentrations. Here, we introduce an efficient molecular dynamics simulation approach for an atomistic DNA molecule at realistic physiological ionic conditions. The simulations are performed by employing the open-boundary molecular dynamics method that allows for simulation of open systems that can exchange mass and linear momentum with the environment. In our open-boundary molecular dynamics approach, the computational burden is drastically alleviated by embedding the DNA molecule in a mixed explicit/implicit salt-bathing solution. In the explicit domain, the water molecules and ions are both overtly present in the system, whereas in the implicit water domain, only the ions are explicitly present and the water is described as a continuous dielectric medium. Water molecules are inserted and deleted into/from the system in the intermediate buffer domain that acts as a water reservoir to the explicit domain, with both water molecules and ions free to enter or leave the explicit domain. Our approach is general and allows for efficient molecular simulations of biomolecules solvated in bathing salt solutions at any ionic strength condition.     

Integer Interparticle Distances in Molecular Dynamics Simulation

The paper describes a sequential MD algorithm in which distances between particles are evaluated using fixed point arithmetics. Errors introduced by the method are estimated. Some simulation timings as well as fluctuations of the total energy are compared to the results obtained using floating point arithmetics.     

Molecular Dynamics Simulations of a Calmodulin-peptide Complex in Solution

Abstract

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 Ų, approximately evenly divided between the calmodulin N-terminal, C-terminal and central linker regions. A majority of this buried surface, 803 ·A², 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 pep- tide 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.