Mode‐coupling Smoluchowski dynamics of a double‐stranded DNA oligomer

The local dynamics of a double‐stranded DNA d(TpCpGpCpG)₂ is obtained to second order in the mode‐coupling expansion of the Smoluchowski diffusion theory. The time correlation functions of bond variables are derived and the ¹³C‐nmr spin–lattice relaxation times T₁ of different ¹³C along the chains are calculated and compared to experimental data from the literature at three frequencies. The DNA is considered as a fluctuating three‐dimensional structure undergoing rotational diffusion. The fluctuations are evaluated using molecular dynamics simulations, with the ensemble averages approximated by time averages along a trajectory of length 1 ns. Any technique for sampling the configurational space can be used as an alternative. For a fluctuating three‐dimensional (3D) structure using the three first‐order vector modes of lower rates, higher order basis sets of second‐rank tensor are built to give the required mode coupling dynamics. Second‐ and even first‐order theories are found to be in close agreement with the experimental results, especially at high frequency, where the differences in T₁ for ¹³C in the base pairs, sugar, and backbone are well described. These atomistic calculations are of general application for studying, on a molecular basis, the local dynamics of fluctuating 3D structures such as double‐helix DNA fragments, proteins, and protein–DNA complexes. © 1999 John Wiley & Sons, Inc. Biopoly 50: 613–629, 1999     

Smoluchowski dynamics of the vnd/NK‐2 homeodomain from Drosophila melanogaster: First‐order mode‐coupling approximation

This work is the first in a series devoted to applying mode coupling diffusion theory to the derivation of local dynamics properties of proteins in solution. The first‐order mode‐coupling approximation, or optimized Rouse–Zimm local dynamics (ORZLD), is applied here to derive the rotational dynamics of the bonds and compare the calculated with the experimental nmr ¹⁵N spin–lattice relaxation time behavior of the vnd/NK‐2 homeodomain from Drosophila melanogaster. The starting point for the calculations is the experimental three‐dimensional structure of the homeodomain determined by multidimensional nmr spectroscopy. The results of the computations are compared with experimentally measured ¹⁵N spin–lattice relaxation times T₁, at 34.5 and 60.8 MHz, to check the first‐order approximation. To estimate the relative importance of internal and overall rotation, both rigid and fluctuating dynamic models are examined, with fluctuations evaluated using molecular dynamics (MD) simulations. The correlation times for the fundamental bond vector time correlation function and for the second‐order bond orientational TCF are obtained as a function of the residue number for vnd/NK‐2. The stability of the corresponding local dynamics pattern for the fluctuating structure as a function of the length of the MD trajectory is presented. Diffusive dynamics, which is essentially free of model parameters even at first order in the mode‐coupling diffusion approach, confirm that local dynamics of proteins can be described in terms of rotational diffusion of a fluctuating quasi‐rigid structure. The comparison with the nmr data shows that the first‐order mode coupling diffusion approximation accounts for the correct order of magnitude of the results and of important qualitative aspects of the data sensitive to conformational changes. Indications are obtained from this study to efficiently extend the theory to higher order in the mode‐coupling expansion. These results demonstrate the promise of the mode‐coupling approach, where the local dynamics of proteins is described in terms of rotational diffusion of a fluctuating quasi‐rigid structure, to analyze nmr spin–lattice relaxation behavior. © 1999 John Wiley & Sons, Inc. Biopoly 49: 235–254, 1999     

Structural similarities and differences between H1- and H2-family DNA minihairpin loops: NMR studies of octameric minihairpins

TheDNA sequences 5′-d(CGC-AC-GCG)-3′ (HPAC), 5′-d(CGC-AA-GCG)-3′ (HPAA), 5′-d(CGC-TC-GCG)-3′ (HPTC), and 5′-d(CGC-CT-GCG)-3′ (HPCT), were studied by means of nmr spectroscopy. At low DNA concentration and no added salt all four molecules adopt a minihairpin structure, containing three Watson–Crick base pairs and a two-residue loop. The structure of the HPAC hairpin is based on quantitative distance restraints, derived by a full relaxation matrix approach (iterative relaxation matrix approach), together with torsion angles obtained from coupling constant analysis. The loop folding is of the H1-family type, characterized by continuous 3′-5′ stacking of the loop bases on the duplex stem. The structure of the HPAA hairpin is similar to that of HPAC, but is more flexible and has a lower thermodynamic stability (T_m 326 K vs 320 K). According to “weakly” distance-constrained simulations in water on the HPAC minihairpin, the typical H1-family loop folding remains intact during the simulation. However, residue-based R factors of simulated nuclear Overhauser effect spectroscopy spectra, free molecular dynamics simulations in vacuo, and unusual chemical shift profiles indicate partial destacking of the loop bases at temperatures below the overall melting midpoint. The dynamic nature of the loop bases gives insight into the geometrical tolerances of stacking between bases in H1-family minihairpin loops. The HPTC and HPCT minihairpins, both containing a pyrimidine base at the first position in the loop, adopt a H2-family type folding, in which the first loop base is loosely bound in the minor groove and the second loop base is stacked upon the helix stem. The thermal stability for these two hairpins corresponds to 327–329 K, but depends on local base sequence. Preference for the type of folding depends on a single substitution from a pyrimidine (H2 family) to a purine (H1 family) at the first position of the miniloop and is explained by differences in base stacking energies, steric size, and the number of possible candidates for hydrogen bonds in the minor groove. In view of newly collected data, previous models of the H1-family and H2-family hairpins had to be revised and are now compatible with the reported HPTC and HPAC structures. The structural difference between the refined structure of HPAC and HPTC show that a conversion between H1-family and H2-family hairpins is geometrically possible by a simple pivot point rotation of 270° along two torsion angles, thereby swiveling the first loop base from a stacked position in a H1-family folding toward a position in the minor groove in a H2-family folding. The second loop residue subsequently shifts to the position of the first base in a concerted fashion. © 1998 John Wiley & Sons, Inc. Biopoly 46: 375–393, 1998     

Structure determination of a pseudotripeptide zinc complex with the COSMOS-NMR force field and DFT methods

A His-X-His pseudotripeptide zinc complex (X is a N-alkyl glycine derivative) similar to the catalytic center of the carbonic anhydrase was computer designed and experimentally synthesized. Using 2D-NMR techniques, all proton, carbon chemical shifts and nuclear overhauser effect signals were assigned. The three-dimensional structure of the complex was determined with the COSMOS (computer simulation of molecular structures) force field by applying ¹³C bond polarization theory chemical shift pseudo forces and restrictions for NOE distances. From molecular dynamics, simulated annealing simulations and geometry optimizations, the three best force field structures were taken for a final investigation by density functional theory calculations.     

Molecular modeling of the interactions of trichosanthin with four substrate analogs

Trichosanthin (TCS) is a ribosome-inactivating protein (RIP) that possesses N-glycosidase activity. It inactivates ribosomes and arrests protein synthesis by removing a specific adenine from 28S rRNA. A molecular dynamics simulated annealing method was applied to study the binding modes of TCS with substrate analogs, three oligonucleotides GAG, GAGA, and CGAGAG, based on the crystal structures of the stable complexes of TCS with NADPH and with the reaction product adenine. A water molecule proposed to be responsible for hydrolyzing the N-glycosidic bond was included in the model. All the oligoribonucleotides can dock into the active cleft of TCS without unfavorable contacts. The interaction energies between TCS and the three oligonucleotides were calculated. The interactions of TCS with NADH were also studied by a molecular dynamics simulated annealing method. The interaction energy between NADH and TCS was compared with that between NADPH and TCS, showing that the lack of 2-phosphate group leads to an energy rise of 20 kcal/mol.     

The proteinopathy of D169G and K263E mutants at the RNA Recognition Motif (RRM) domain of tar DNA-binding protein (tdp43) causing neurological disorders: A computational study

One of the multitasking proteins, transactive response DNA-binding protein 43 (tdp43) plays a key role in RNA regulation and the two pathogenic mutations such as D169G and K263E, located at the RNA Recognition Motif (RRM) of tdp43, are reported to cause neurological disorders such as Amyotrophic Lateral Sclerosis and FrontoTemporal Lobar Degeneration. As the exploration of the proteinopathy demands both structural and functional characterizations of mutants, a comparative analysis on the wild type and mutant tdp43 (D169G and K263E) and their complexes with RNA has been performed using computational approaches. Molecular dynamics simulations revealed comparatively stable mutant structures compared to wild type tdp43. Both mutants show lesser binding affinity toward RNA molecule when compared to the wild type tdp43. Some of the observed features, including the increased solvent-accessible surface area, conformational flexibility as well as unfolding of tdp43, and the altered RNA conformation in tp43-RNA complex, reveal the susceptibility of these mutants to induce conformational changes in tdp43 for a possible aggregation in the cytoplasm. Particularly, the enhanced aggregation propensity of both mutants also evidences the higher probability of cytoplasmic aggregation of tdp43 mutants. Hence, the present analysis highlighting the structural and functional aspects of wild and mutant tdp43 will form the basis to gain insight into the proteinopathy of tdp43 and the related structure-based drug discovery. Thus, tdp43 can be used as target to develop novel therapeutic approaches or drug designing.     

Torsion angle dynamics: Reduced variable conformational sampling enhances crystallographic structure refinement

A reduced variable conformational sampling strategy for macromolecules based on molecular dynamics in torsion angle space is evaluated using crystallographic refinement as a prototypical search problem. Bae and Haug's algorithm for constrained dynamics [Bae, D. S., Haug, E. J. A recursive formulation for constrained mechanical system dynamics. Mech. Struct. Mach. 15:359–382, 1987], originally developed for robotics, was used. Their formulation solves the equations of motion exactly for arbitrary holonomic constraints, and hence differs from commonly used approximation algorithms. It uses gradients calculated in Cartesian coordinates, and thus also differs from internal coordinate formulations. Molecular dynamics can be carried out at significantly higher temperatures due to the elimination of the high frequency bond and angle vibrations. The sampling strategy presented here combines high temperature torsion angle dynamics with repeated trajectories using different initial velocities. The best solutions can be identified by the free R value, or the R value if experimental phase information is appropriately included in the refinement. Applications to crystallographic refinement show a significantly increased radius of convergence over conventional techniques. For a test system with diffraction data to 2 Å resolution, slow-cooling protocols fail to converge if the backbone atom root mean square (rms) coordinate deviation from the crystal structure is greater than 1.25 Å, but torsion angle refinement can correct backbone atom rms coordinate deviations up to approximately 1.7 Å. © 1994 Wiley-Liss, Inc.     

Solution Conformation of [D-Pen2,D-Pen5]enkephalin in Water: A NMR and Molecular Dynamics Study

The solution conformation of [D -Pen²,D -Pen⁵] enkephalin (DPDPE), a highly potent δ-selective opioid agonist, was examined by means of NMR, molecular mechanics and molecular dynamics methods. The structural information in the solvent water was obtained employing one- and two-dimensional methods of ¹H and ¹³C-NMR spectroscopy. Based on the distance geometry technique using the ROE data as input, 400 conformers were obtained and considered in the structure analysis. Alternatively, about 2000 conformers were stochastically generated and related to the NMR data after energy minimization. The structure analysis provides one conformer in agreement with all NMR data, which belongs to the lowest energy conformation group. This structure may serve as a reference conformer for DPDPE analogues synthesized with the aim of activity increase.     

A reduced representation of proteins for use in restraint satisfaction calculations

A reduced representation of paroteins has been developed for use in restraint satisfaction calculations with dynamic simulated annealing. Each amino acid residue is represented by up to four spherical virtual atoms. The virtual bonds and excluded volume of these atoms has ben parameterized by analysis of 83 protein structures determined at high resolution by X-ray crystallography. The use of the new representation in NOE distance restraint satisfaction has been compared with the standard all-atom represntation for the determination of the structures of crambin, eshistatin, and protein G. Using the reduced representation, there is a 30-fold decrease in the computer time needed for generatin a single structure, and up to a 20-fold decrease in the time taken to produce an acceptable structure compared to using the all-atom representation. The root mean square deviation between the mean structure obtain with all-atom and reduced representation si between 1.5 and 1.7 Å for C_α atoms. The new representation is adequate for describing the “low-resolution” features of protein structure such as the general fold and the positions of the secondary structure for more detailed refinement with the full all-atom representation. © 1993 Wiley-Liss, Inc.