Session V40: Nucleic Acids: Structure and Function

Toward multiscale modeling of the chromatin fiber: a coarse grain model for DNA

In eukaryotic cells DNA is compacted a million-fold into a chromatin. Understanding the mechanism of chromatin folding is of great biological importance. All-atom Molecular Dynamics (MD) simulations could provide crucial insights into the electrostatic and structural mechanisms of chromatin folding. However, because of the enormous size of even short chromatin fiber segment and long folding time-scales, atomistic simulations are computationally impractical. Our long-term aim is to build an accurate coarse-grain (CG) model of the chromatin, derived systematically from all-atom simulations of its smaller parts. Here we report the development of the CG model for a linear DNA chain, playing the role of a linker DNA segment in the chromatin. We derived CG inter-DNA electrostatic potential from atomistic simulations with explicit solvent and mobile ions, instead of relying on the standard models of continuum electrostatics, which are inadequate at small intermolecular distances. In addition, we used the ideas of renormalization group theory to construct an optimization scheme for parameterizing the CG force field. This novel approach is designed to accurately reproduce correlations among various CG degrees of freedom. The implementation of these correlations was left as an open question in the prior studies of CG polymer models.   

Sequence and Temperature Dependence of DNA Bending Fluctuations

Recent DNA cyclization experiments measured J factors indicating that DNA may form sharp bends more easily than predicted by the worm-like chain model. One proposed explanation is that local melting of a few base pairs (bp) introduces flexible hinges [Yan, J. et al., \textit{Phys. Rev. E} \textbf{71}, 061905 (2005)]. We incorporate sequence dependence of the local melting into this model and obtain specific predictions for the dependence of J factors on temperature and sequence. We then measure J factors for a 200 bp fragment of lambda DNA and two synthetic 116 bp sequences with different proclivities for melting. The measured temperature and sequence dependence of J factors is found to be in agreement with the sequence dependent model predictions using previously measured free energy costs for melting and reasonable estimates for the flexibility of melted segments of DNA.   

Mechanically unzipping dsDNA with built-in sequence inhomogeneities and bound proteins

We theoretically analyze the force signal from unzipping dsDNA with bound proteins and sequence inhomogeneties. Two different force traces are obtained determined by binding and sequence parameters. Sawtooth force curves, as observed in experiments, are found for short enough designed sequences and binding sites. Longer inhomogeneities lead to force plateaus which correspond to gradual, piece-meal, unzipping of the variant stretch of DNA. We generalize our model to allow comparisons to recent experiments on unzipping decorated DNAs.   

Base-pair elasticity of free and complexed DNA

The elastic properties of the DNA molecule are important for its function. On a base-pair scale, they modulate protein binding strength, while over hundreds of base--pairs, they govern the statistics of DNA loops. We have used the rigid base--pair (RBP) model to link experiments on DNA elasticity across these scales. In a study of the indirect readout mechanism in protein--DNA binding, we compare calculated DNA elastic free energy differences to experimental affinities. While quantitative predictions are beyond the precision of current parameter sets, qualitative predictions are meaningful; we propose a statistical marker for indirect readout sub-sites in a given co-crystal complex structure. Furthermore, we relate the RBP model to the worm--like chain (WLC) by a systematic coarse-graining procedure, reducing a total of 270 parameters to 6, which agree remarkably well with direct experimental results. Introducing sequence randomness adds fluctuations and renormalizes WLC stiffness. On short scales, sequence variability and bending anisotropy have a large effect, exhibiting the limits of applicability of the WLC model.   

Hartree-Fock Cluster Study of Electronic Structures and Nuclear Quadrupole Interactions in Solid Nucleobases.

In recent work [1] we have studied nucleobases attached to a CH$_{3}$ group to simulate the influence of their binding to the sugar rings and the phosphate groups in DNA and RNA and the effect of this binding on the nuclear quadrupole interactions of $^{14}$N, $^{17}$O and $^{2}$H nuclei. Our results from this work have indicated that for $^{17}$O, the binding to the CH$_{3}$ group moves our results from the free nucleobases closer to the experimentally observed data [2] in the solid nucleobases. We are now investigating the solid nucleobases by the first --principles Hartree-Fock cluster procedure that we have employed earlier for the halogen molecular solids [3]. Our results for the binding energy of an imidazole molecule in the molecular solid system and the $^{14}$N, $^{17}$O and $^{2}$H nuclear quadrupole interaction parameters will be presented. \newline [1] T.P. Das et al (at this APS meeting), [2] Gang Wu et al, J. Am.Chem. Soc. 124, 1768(2002). [3] M.M. Aryal et al Hyperfine Interactions (to be published).   

Nuclear Quadrupole Interaction Study as a Probe of Interaction between Nucleobases and Suger Rings and Phosphate Groups in DNA.

We have been investigating the influence of the interaction between the nucleobases and sugar rings and phosphate groups in DNA using Nuclear Quadrupole interactions (NQI) of $^{14}$N and $^{17}$O and $^{2}$H nuclei as probes. We have first simulated the influence of the interaction between a nucleobase and a sugar ring using a CH$_{3}$ group attached to the former. For our electronic structure investigations, we have employed the Hartree-Fock-Roothaan procedure using the Gaussian set of programs. Our preliminary investigations have shown that there are comparable indirect and direct effects on the NQI parameters, the former effect referring to the influence of changes in molecular geometries produced by the CH$_{3}$ group and the direct effect is due to the electronic interaction between the CH$_{3}$ group and the nucleobase. More quantitative results from our current investigations using the actual sugar rings and phosphate groups will be presented as in earlier work by our group[1] for hyperfine interactions of trapped muonium atoms in DNA.[1] R.H. Scheicher et al Physica B \underline {374-375}, 448(2006)   

Extraction of complementary from non-complementary DNA sequences through phase separation and centrifugation

Double stranded deoxyribonucleic acid (DNA) is known to form lyotropic liquid crystal (LC) phases, nematic and then columnar with increasing DNA concentration in water. Single stranded (DNA) does not form liquid crystal phases. We study the phase separation of both long (900bp) and short (6-20bp) DNA. In the mixture solution of a self complementary sequences (scDNA) and non complementary sequences (nscDNA), the scDNA forms DNA double helices and hence forms LC phases while the nscDNA stays in the isotropic phase, the LC appearing in the form of phase separated droplets. We report results of the use of centrifugation to produce complete spatial segregation of complementary and noncomplementary DNA, based on their different LC-formation tendencies.   

Phase Separation and Liquid Crystallization of Complementary Sequences in Mixtures of Random Oligonucleotides

We have investigated the phase behavior of mixtures of DNA oligomers, 8-22 bp in length. When only a fraction of the sample is composed of mutually complementary sequences, and hence the solution is effectively a mixture of single strands (ss) and double stranded helices (ds), the system is found to phase separate via the nucleation of ds-rich liquid crystalline domains from an isotropic background rich in ss. This spontaneous partitioning is the combined result of the free energy gain from the end-to-end stacking and LC ordering of duplexes, and of depletion-type interactions favoring the segregation of the more rigid duplexes from the flexible ss. Phase separation and liquid crystallization are also found in mixtures of oligos with various degrees of randomness in the sequence, enabling to establish the phase behavior in an extended phase space including a radomness axis. The observed phenomena offer a new route to the purification of duplex oligomers and, if in the presence of ligation, could provide a mode of positive feedback for the preferential synthesis of extended complementary oligomers, a mechanism of possible relevance in prebiotic environments.   

Scanning Tunneling Microscopy study of ssDNA-CNT on Au(111) surface

The single-strand deoxyribonucleic acid (ssDNA) - carbon nanotube (CNT) complex on Au(111) surfaces has been studied via scanning tunneling microscopy (STM). The interaction between ssDNA and CNT not only disperses the nanotubes, but also makes the ssDNA more accessible for the STM study. Sputtering on the ssDNA-CNT complex helps to reveal the internal structure. Scanning tunneling spectroscopy (STS) has been carried out to study the electronic structure of the ssDNA-CNT complex.   

Liquid Crystal Alignment on Sheared DNA Films

We have studied the alignment of commercial nematic and smectic A liquid crystals (8CB, 6CB, CCN47, MBBA) on the chiral surface obtained by shearing double stranded DNA on a glass surface. Simple characterization of hybrid cells (DNA-homeotropic) and partially sliding cells (DNA-GLYMO) reveal that the nematic director at the DNA surface is oriented at an angle from 50$^{\circ}$ to 100$^{\circ}$ with respect to the shearing direction, indicating that the liquid crystal molecules align preferentially perpendicularly to the DNA grooves. These observations present clear evidence for a large chiral orientational effect in the anchoring of a typical nematic/SmA LC on dehydrated sheared DNA films.   

Cholesterol improves the transfection efficiency of lipoplexes by increasing the effective membrane charge density

Motivated by its important role in lipid-mediated gene delivery, we have studied the effect of cholesterol on the transfection efficiency (TE) of lamellar, cationic lipid-DNA (CL-DNA) complexes. A successful \textit{in vivo }liposome mixture seems to require cholesterol. Recent work in our group has identified the membrane charge density ($\sigma )$ as a universal parameter for TE of lamellar, DOPC containing CL-DNA complexes (A.J. Lin et al, \textit{Biophys. J.}, 2003, K. Ewert et al, \textit{J. Med. Chem.}, 2002, A. Ahmad et al., \textit{J. Gene Med., }2005), with TE following a universal bell-shaped curve as a function of $\sigma $. Theoretical calculations considering the headgroup area of cholesterol and thus necessarily counting for an increase in $\sigma $, when DOPC is replaced by cholesterol, show that TE strongly deviates from the TE universal curve. However, experimental determination of $\sigma $ via X-ray diffraction shows full agreement with the TE universal curve demonstrating that the real $\sigma $ is higher as predicted, therefore the effective headgroup area of cholesterol is lower as expected by theory, suggesting that cholesterol is inserted deep into lipid bilayer partially hidden by the neighboring lipids. Funding provided by NIH GM-59288 and NSF DMR-0503347.   

Measuring the 3D Size of Large RNA Molecules

Large single-stranded (ss) RNAs are ubiquitous in cells and constitute the genomic content of many viral species. Besides being the primary means of intra-cellular information transfer, some of their functions require them to form stable structural motifs. ssRNA molecules possess intrinsic self-complementarity leading to a partially double-stranded, branched, secondary structure. We measure, in solution, the physical dimensions of several sequences of ssRNA ranging from a few hundred to a few thousand nucleotides in length. Sizes are reported as radii of gyration ($R_g$) and hydrodynamic radii ($R_h$), respectively determined by small-angle x-ray scattering (SAXS) and fluorescence correlation spectroscopy (FCS). For RNAs of fixed nucleotide length ($\sim$2000) and composition, we find that $R_g$s and $R_h$s can vary by over 30$\%$. By changing solvent conditions, we demonstrate that these size discrepancies are a generic property of the secondary structure arising from sequence-dependent base-pairing. Some viral RNAs that self-assemble into spherical protein capsids have highly evolved sequences that code for unusually compact size and shape.   

Predicting the Size of Large RNA Molecules

We present a qualitative theory of how the 3D sizes of large single-stranded (ss) RNA molecules depend on their sequences. The work is motivated by the fact that the genomes of many viruses are large ssRNA molecules and that these RNAs are spontaneously packaged into small rigid protein shells. We argue there has been evolutionary pressure for the genome to have large-scale spatial properties -- including an appropriate radius of gyration, $R_{g }$-- that facilitate and optimize this assembly process. We introduce the average maximum ladder distance (\textit{AMLD}) as a measure of the `extendedness' of the RNA secondary structure. We find that the \textit{AMLDs} of viral ssRNAs are smaller than those of equal-length randomly permuted sequences. By mapping these secondary structures onto simple linear or star polymer models, and using \textit{AMLD} as a measure of effective contour length, we predict that the $R_{g}s$ of viral RNAs are smaller than those of random sequences. More generally, we derive results for how the \textit{AMLDs} of large ssRNAs, and their $R_{g}s$, scale with the number of nucleotides.   

Observations of simple RNA suboptimal structures including pseudoknots suggests that the folding landscape is often funnel shaped

Many RNA structure are known to fold up into complex function structures such as ribosomal RNA, transfer RNA (tRNA), riboswitches, etc. We are currently developing a novel theoretical approach for predicting the base pairing topology of folded RNA structures [1,2], a term known as RNA secondary structure. A good prediction of this base pairing can significantly speed up computation of the full 3D structure of these complex molecules. In recent work, we reported a pseudoknot prediction application using this model [3]. We have now upgraded this application to also predict suboptimal structures. The results of this model suggest that structures like tRNA often have a folding landscape of suboptimal structures that is essentially funnel shaped; similar to what is known to be the case for many simple proteins. This model has also been applied to simple protein structure topology prediction in a similar fashion. [1] Dawson, et al. (2001). \textit{J Theor Biol. }213, 359-386 and 387-412. [2] Dawson, et al. (2006). \textit{Nucleosides, Nucleotides, and Nucleic Acids} 25, 171-189. [3]Dawson, et al. (2007). \textit{PLoS One}, 2, 905.   

Simplified Hamiltonians for coarse-grained properties of large single-stranded RNA molecules

Large single-stranded RNA (ssRNA) molecules with a length of a few thousand to a few tens of thousands of nucleotides are quite common in nature. These RNAs generally have a highly branched secondary structure with many short, double-stranded sections. The secondary structure is important for function. However, the prediction of the thermally accessible secondary structures of large ssRNAs is complicated.There are several computer programs available that predict secondary structures of ssRNA. They produce good results for small molecules but are not very reliable for large ones. We are not interested in ``high-resolution`` structures, however, but in more coarse-grained properties, for example the average three-dimensional size of the molecule. We expect that the available computer programs are useful for determination of these coarse-grained properties but the complicated Hamiltonians they use limit the usefulness of these models for further theoretical investigations. We show that one can simplify these Hamiltonians considerably and still retain important predictive power. The inclusion of stacking energies is crucial but many of the detailed energy rules are not. We define several measures for the size of a secondary structure and we show how these measures are related to each other.