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: second-order maximum correlation approximation

The mode coupling diffusion theory is applied to the derivation of local dynamics in proteins in solution. The rotational dynamics of the bonds along the protein sequence are calculated and compared to the experimentally measured nmr (15)N spin-lattice relaxation time T(1), at 36.5, 60.8, and 81.1 MHz of the vnd/NK-2 homeodomain from Drosophila melanogaster. The starting point for the calculations is the experimental three-dimensional solution structure of the homeodomain determined by multidimensional nmr spectroscopy. The higher order mode-coupling computations are compared also with the recently published first-order approximation calculations. The more accurate calculations improve substantially the first-order ORZLD calculations and show that the role of the strength of the hydrodynamic interactions becomes crucial to fix the order of magnitude of the rotational dynanics for these very compact molecules characterized by partial screening of the internal atoms to water. However, the relative mobility of the bonds along the sequence and the differential fluctuations depend only weakly on the hydrodynamic strength but strongly on the geometry of the three-dimensional structure and on the statistics incorporated into the theory. Both rigid and fluctuating dynamic models are examined, with fluctuations evaluated using molecular dynamics simulations. The comparison with nmr data shows that mode coupling diffusion accounts for the T(1) relaxation pattern at low frequency where the rotational tumbling dominates. An important contribution of internal motions in the nanosecond time scale is seen at high frequencies and is discussed in terms of diffusive concepts.     

Diffusive Dynamics in a Detailed Potential: Application to Biological Macromolecules

Abstract

The local dynamics of macromolecules is obtained to second-order in the mode-coupling expansion of the Smoluchowski diffusion theory. The NMR spin-lattice relaxation times of different ¹³C or ¹⁵N nuclei along the chains are calculated and compared to experimental data from the literature. The macromolecules are considered as fluctuating 3D structures undergoing rotational diffusion. The fluctuations can be evaluated with any technique for sampling the configurational space. In the presented test cases Molecular Dynamics simulations have been applied to a DNA fragment and to the NK-2 homeodomain. In the case of the double-stranded DNA fragment d(TpCpGpCpG)₂, second and even first order theories are found to be in close agreement with experimental results. The major advantage of the diffusion technique is that only a good statistics is important as input while the solvent dynamic effects enter through hydrodynamic theory. Application based on Hybrid Monte Carlo schemes coupled with J-walking, are now in progress.     

C-C-A-G-G-C-m5C-T-G-G. Helical fine structure, hydration, and comparison with C-C-A-G-G-C-C-T-G-G.

The self-complementary DNA duplex C-C-A-G-G-C-m5C-T-G-G has been refined against 1.75-A x-ray diffraction data to an R value of 17.4%. In the crystal of space group P6, 10-base pair DNA fragments with characteristic sequence-related fine structure stack end to end to form long antiparallel B-type double helices. As shown by a structure analysis at lower resolution (Heinemann, U., and Alings, C. (1991) EMBO J. 10, 35-43), the overall geometry of C-C-A-G-G-C-m5C-T-G-G is similar to that of the unmethylated analog C-C-A-G-G-C-C-T-G-G despite a different crystal environment. The present high resolution structure analysis permits a detailed comparison of the two duplexes and their hydration spheres. Helical parameters are significantly correlated between both molecules, with the exception of the base pair propeller. Sugar pucker and backbone torsion angles alpha, gamma, delta, and chi show similar mean values, but their individual values deviate significantly between duplexes. In contrast, torsion angles beta, epsilon, and zeta change along the strands of both duplexes in much the same way. The effect of single-site methylation on DNA conformation appears to be small and limited to the base pairs directly involved. Methylation tends to push base pairs toward the minor groove of the helix. A regular minor groove hydration pattern involves dual hydrogen bonding of water molecules to O-4' and base atoms of C-C-A-G-G-C-m5C-T-G-G.     

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     

Relationship of DNA structure to internal dynamics: correlation of helical parameters from NOE-based NMR solution structures of d(GCGTACGC)(2) and d(CGCTAGCG)(2) with (13)C order parameters implies conformational coupling in dinucleotide units

The coupling between the conformational properties of double-stranded DNA and its internal dynamics has been examined. The solution structures of the isomeric DNA oligomers d(GCGTACGC)(2) (UM) and d(CGCTAGCG)(2) (CTSYM) were determined with (1)H NMR spectroscopy by utilizing distance restraints from total relaxation matrix analysis of NOESY cross-peak intensities in restrained molecular dynamics calculations. The root-mean-square deviation of the coordinates for the ensemble of structures was 0.13 A for UM and 0.49 A for CTSYM, with crystallographic equivalent R(c)=0.41 and 0.39 and sixth-root residual R(x)=0.11 and 0.10 for UM and CTSYM, respectively. Both UM and CTSYM are B-form with straight helical axes and show sequence-dependent variations in conformation. The internal dynamics of UM and CTSYM were previously determined by analysis of (13)C relaxation parameters in the context of the Lipari & Szabo model-free formalism. Helical parameters for the two DNA oligomers were examined for linear correlations with the order parameters (S(2)) of groups of (13)C spins in base-pairs and dinucleotide units of UM and CTSYM. Correlations were found for six interstrand base-pair parameters tip, y-displacement, inclination, buckle and stretch with various combinations of S(2) for atoms in Watson-Crick base-pairs and for two inter-base-pair parameters, rise and roll with various combinations of S(2) for atoms in dinucleotides. The correlations for the interstrand base-pair helical parameters indicate that the conformations of the deoxyribose residues of each strand are dynamically coupled. Also, the inter-base-pair separation has a profound effect on the local internal motions available to the DNA, supporting the idea that rise is a principal degree of freedom for DNA conformational variability. The correlations indicate collective atomic motions of spins that may represent specific motional modes in DNA, and that base sequence has a predictable effect on the relative order of groups of spins both in the bases and in the deoxyribose ring of the DNA backbone. These observations suggest that an important functional outcome of DNA base sequence is the modulation of both the conformation and dynamic behavior of the DNA backbone.     

Conformation and dynamics of drug-DNA intercalation.

Molecular dynamics simulations have been undertaken for a B-form dodecanucleotide duplex in solution with and without an intercalated proflavine molecule between the central C.G base pairs. The introduction of this simple intercalator affects both the conformational features and dynamic properties of the oligonucleotide double helix. Changes are seen in the rms atomic fluctuations and anisotropy of phosphate, sugar and base atoms. The backbone conformation is slightly changed on average and more sugars adopt the C3' endo conformation in the simulation of the complex compared with the simulation of the oligonucleotide alone. Both major and minor grooves becomes wider on average with the addition of the intercalating drug. Flanking A.T base pairs on both sides of the intercalation site have undergone an increase in flexibility, with the base pairs, especially at the 5' side, having the N1...N3 hydrogen bonds being broken.     

Crystal structure of MunI restriction endonuclease in complex with cognate DNA at 1.7 A resolution.

The MunI restriction enzyme recognizes the palindromic hexanucleotide sequence C/AATTG (the '/' indicates the cleavage site). The crystal structure of its active site mutant D83A bound to cognate DNA has been determined at 1.7 A resolution. Base-specific contacts between MunI and DNA occur exclusively in the major groove. While DNA-binding sites of most other restriction enzymes are comprised of discontinuous sequence segments, MunI combines all residues involved in the base-specific contacts within one short stretch (residues R115-R121) located at the N-terminal region of the 3(10)4 helix. The outer CG base pair of the recognition sequence is recognized solely by R115 through hydrogen bonds made by backbone and side chain atoms to both bases. The mechanism of recognition of the central AATT nucleotides by MunI is similar to that of EcoRI, which recognizes the G/AATTC sequence. The local conformation of AATT deviates from the typical B-DNA form and is remarkably similar to EcoRI-DNA. It appears to be essential for specific hydrogen bonding and recognition by MunI and EcoRI.     

Backbone dynamics of reduced plastocyanin from the cyanobacterium Anabaena variabilis: regions involved in electron transfer have enhanced mobility

The dynamics of the backbone of the electron-transfer protein plastocyanin from the cyanobacterium Anabaena variabilis were determined from the (15)N and (13)C(alpha) R(1) and R(2) relaxation rates and steady-state [(1)H]-(15)N and [(1)H]-(13)C nuclear Overhauser effects (NOEs) using the model-free approach. The (13)C relaxation studies were performed using (13)C in natural abundance. Overall, it is found that the protein backbone is rigid. However, the regions that are important for the function of the protein show moderate mobility primarily on the microsecond to millisecond time scale. These regions are the "northern" hydrophobic site close to the metal site, the metal site itself, and the "eastern" face of the molecule. In particular, the mobility of the latter region is interesting in light of recent findings indicating that residues also on the eastern face of plastocyanins from prokaryotes are important for the function of the protein. The study also demonstrates that relaxation rates and NOEs of the (13)C(alpha) nuclei of proteins are valuable supplements to the conventional (15)N relaxation measurements in studies of protein backbone dynamics.     

Prediction of methyl-side Chain Dynamics in Proteins

A simple analytical model is presented for the prediction of methyl-side chain dynamics in comparison with S(2) order parameters obtained by NMR relaxation spectroscopy. The model, which is an extension of the local contact model for backbone order parameter prediction, uses a static 3D protein structure as input. It expresses the methyl-group S(2) order parameters as a function of local contacts of the methyl carbon with respect to the neighboring atoms in combination with the number of consecutive mobile dihedral angles between the methyl group and the protein backbone. For six out of seven proteins the prediction results are good when compared with experimentally determined methyl-group S(2) values with an average correlation coefficient r = 0.65+/-0.14. For the unusually rigid cytochrome c(2) no significant correlation between prediction and experiment is found. The presented model provides independent support for the reliability of current side-chain relaxation methods along with their interpretation by the model-free formalism.     

Stabilization of protein by replacement of a fluctuating loop: structural analysis of a chimera of bovine alpha-lactalbumin and equine lysozyme

Equine lysozyme is a calcium-binding lysozyme and an evolutional intermediate between non-calcium binding c-type lysozyme and alpha-lactalbumin. We constructed a chimeric protein by substituting the fluctuating loop of bovine alpha-lactalbumin with the D-helix of equine lysozyme. The substitution affects the protection factors not only in the fluctuating loop but also in the antiparallel beta-sheet, the A- and B-helices, and the loop between the B-helix and the beta-sheet. Amide protons in these regions of the chimera are more protected from exchange than are those of bovine alpha-lactalbumin. We used model-free analysis based on 15N nuclear magnetic resonance relaxation measurements to investigate the dynamics of the main chain of the chimera and showed that the fluctuating loop of the chimera is as rigid as three major helices. When we analyzed the chemical shift deviations and backbone HN-H(alpha) scalar coupling constants, we found that the chimera showed an alpha-helical tendency in residues around the fluctuating loop. Our results suggest that the replacement of a highly fluctuating loop in a protein with a rigid structural element in a homologous one may be useful to stabilize the protein structure.     

Theoretical analysis of DNA intrastrand cross linking by formation of 8,5'-cyclodeoxyadenosine.

Formation of intramolecular cross links by addition of C(5') deoxyribose radicals to the C(8)-N(7) double bond of an attached adenine base was analyzed by ab initio quantum-chemical methods. Conformational preferences that influence the stereospecificity of the reaction were investigated. A good correlation was found between the ratio of experimental yields of R and S stereoisomers of 8,5'-cyclodeoxyadenosine and the relative energy of conformations of the C(5') radical that are precursors to these isomers. Molecular mechanics based on the AMBER force field was used to model the effect of 8,5'-cyclodeoxyadenosine on the conformation of the DNA dodecamer d(CGCGAATTCGCG)2 with the lesion at the A6 position. The R and S stereoisomers of the intrastrand cross link cause comparable levels of DNA distortion with the major conformational changes occurring in backbone torsional angles at the site of the lesion.     

Backbone dynamics of apocytochrome b5 in its native, partially folded state

The backbone dynamics in the native state of apocytochrome b5 were studied using 15N nuclear magnetic spin relaxation measurements. The field (11.7 and 14.1 T) and temperature (10-25 degrees C) dependence of the relaxation parameters (R1, R2, and R1rho) and the 1H-15N NOE established that the protein undergoes multiple time scale internal motions related to the secondary structure. The relaxation data were analyzed with the reduced spectral density mapping approach and within the extended model-free framework. The apoprotein was confirmed to contain a disordered heme-binding loop of approximately 30 residues with dynamics on the sub-nanosecond time scale (0.6 < S2 < 0.7, 100 ps < taue < 500 ps). This loop is attached to a structured hydrophobic core, rigid on the picosecond time scale (S2 > 0.75, taue < 50 ps). The inability to fit the data for several residues with the model-free protocol revealed the presence of correlated motion. An exchange contribution was detected in the transverse relaxation rate (R2) of all residues. The differential temperature response of R2 along the backbone supported slower exchange rates for residues in the loop (tauex > 300 micros) than for the folded polypeptide chain (tauex < 150 micros). The distribution of the reduced spectral densities at the 1H and 15N frequencies followed the dynamic trend and predicted the slowing of the internal motions at 10 degrees C. Comparison of the dynamics with those of the holoprotein [Dangi, B., Sarma, S., Yan, C., Banville, D. L., and Guiles, R. D. (1998) Biochemistry 37, 8289-8302] demonstrated that binding of the heme alters the time scale of motions both in the heme-binding loop and in the structured hydrophobic core.     

The hydrogen-bonding structure in parallel-stranded duplex DNA is reverse Watson-Crick

Raman spectra of the parallel-stranded duplex formed from the deoxyoligonucleotides 5'-d-[(A)10TAATTTTAAATATTT]-3' (D1) and 5'-d[(T)10ATTAAAATTTATAAA]-3' (D2) in H2O and D2O have been acquired. The spectra of the parallel-stranded DNA are then compared to the spectra of the antiparallel double helix formed from the deoxyoligonucleotides D1 and 5'-d(AAATATTTAAAATTA-(T)10]-3' (D3). The Raman spectra of the antiparallel-stranded (aps) duplex are reminiscent of the spectra of poly[d(A)].poly[d(T)] and a B-form structure similar to that adopted by the homopolymer duplex is assigned to the antiparallel double helix. The spectra of the parallel-stranded (ps) and antiparallel-stranded duplexes differ significantly due to changes in helical organization, i.e., base pairing, base stacking, and backbone conformation. Large changes observed in the carbonyl stretching region (1600-1700 cm-1) implicate the involvement of the C(2) carbonyl of thymine in base pairing. The interaction of adenine with the C(2) carbonyl of thymine is consistent wtih formation of reverse Watson-Crick base pairing in parallel-stranded DNA. Phosphate-furanose vibrations similar to those observed for B-form DNA of heterogenous sequence and high A,T content are observed at 843 and 1092 cm-1 in the spectra of the parallel-stranded duplex. The 843-cm-1 band is due to the presence of a sizable population of furanose rings in the C2'-endo conformation. Significant changes observed in the regions from 1150 to 1250 cm-1 and from 1340 to 1400 cm-1 in the spectra of the parallel-stranded duplex are attributed to variations in backbone torsional and glycosidic angles and base stacking.     

Modeling the dynamics of a mutated stem-loop in the SL1 domain of HIV-1Lai genomic RNA by 1H-NOESY spectra

The cross-peaks of ¹H-NOESY spectra at different time delays are compared to a mode-coupling diffusion (MCD) calculation, including the evaluation of the full ¹H relaxation matrix, in the case of a 23 nucleotide fragment of the stem-loop SL1 domain of HIV-1_Lai genomic RNA mutated in a single position. The MCD theory gives significant agreement with ¹H relaxation experiments enabling a thorough understanding of the differential local dynamics along the sequence and particularly of the dynamics of nucleotides in the stem and in the loop. The differential dynamics of this hairpin structure is important in directing the dimerization of the retroviral genome, a fundamental step in the infectious process. The demonstration of a reliable use of time dependent NOE cross-peaks, largely available from NMR solution structure determination, coupled to MCD analysis, to probe the local dynamics of biological macromolecules, is a result of general interest of this paper.     

NMR (13)C-relaxation study of base and sugar dynamics in GCAA RNA hairpin tetraloop

Intramolecular dynamics of a 14-mer RNA hairpin including GCAA tetraloop was investigated by (13)C NMR relaxation. R(1) and R(1rho) relaxation rates were measured for all protonated base carbons as well as for C1' carbons of ribose sugars at several magnetic field strengths. The data has been interpreted in the framework of modelfree analysis [G. Lipari and A. Szabo. J Am Chem Soc 104, 4546-4559 (1982); G. Lipari and A. Szabo. J Am Chem Soc 104, 4559-4570 (1982)] characterizing the internal dynamics of the molecule by order parameters and correlation times for fast motions on picosecond to nanosecond time scale and by contributions of the chemical exchange. The fast dynamics reveals a rather rigid stem and a significantly more flexible loop. The cytosine and the last adenine bases in the loop as well as all the loop sugars exhibit a significant contribution of conformational equilibrium on microsecond to millisecond time scale. The high R(1rho) values detected on both base and sugar moieties of the loop indicate coordinated motions in this region. A semiquantitative analysis of the conformational equilibrium suggests the exchange rates on the order of 10(4) s(-1). The results are in general agreement with dynamics studies of GAAA loops by NMR relaxation and fluorescent spectroscopy and support the data on the GCAA loop dynamics obtained by MD simulations.     

Solution structure of a five-adenine bulge loop within a DNA duplex.

The three-dimensional solution structure of a DNA molecule of the sequence 5'-d(GCATCGAAAAAGCTACG)-3' paired with 5'-d(CGTAGCCGATGC)-3' containing a five-adenine bulge loop (dA(5)-bulge) between two double helical stems was determined by 2D (1)H and (31)P NMR, infrared, and Raman spectroscopy. The DNA in both stems adopt a classical B-form double helical structure with Watson-Crick base pairing and C2'-endo sugar conformation. In addition, the two dG/dC base pairs framing the dA(5)-bulge loop are formed and are stable at least up to 30 degrees C. The five adenine bases of the bulge loop are localized at intrahelical positions within the double helical stems. Stacking on the double helical stem is continued for the first four 5'-adenines in the bulge loop. The total rise (the height) of these four stacked adenines roughly equals the diameter of the double helical stem. The stacking interactions are broken between the last of these four 5'-adenines and the fifth loop adenine at the 3'-end. This 3'-adenine partially stacks on the other stem. The angle between the base planes of the two nonstacking adenines (A10 and A11) in the bulge loop reflects the kinking angle of the global DNA structure. The neighboring cytosines opposite the dA(5)-bulge (being parts of the bulge flanking base pairs) do not stack on one another. This disruption of stacking is characterized by a partial shearing of these bases, such that certain sequential NOEs for this base step are preserved. In the base step opposite the loop, an extraordinary hydrogen bond is observed between the phosphate backbone of the 5'-dC and the amino proton of the 3'-dC in about two-thirds of the conformers. This hydrogen bond probably contributes to stabilizing the global DNA structure. The dA(5)-bulge induces a local kink into the DNA molecule of about 73 degrees (+/-11 degrees ). This kinking angle and the mutual orientation of the two double helical stems agree well with results from fluorescence resonance energy transfer measurements of single- and double-bulge DNA molecules.