Interactions between identical DNA double helices

Meiosis: Dances Between Homologs

The raison d'être of meiosis is shuffling of genetic information via Mendelian segregation and, within individual chromosomes, by DNA crossing-over. These outcomes are enabled by a complex cellular program in which interactions between homologous chromosomes play a central role. We first provide a background regarding the basic principles of this program. We then summarize the current understanding of the DNA events of recombination and of three processes that involve whole chromosomes: homolog pairing, crossover interference, and chiasma maturation. All of these processes are implemented by direct physical interaction of recombination complexes with underlying chromosome structures. Finally, we present convergent lines of evidence that the meiotic program may have evolved by coupling of this interaction to late-stage mitotic chromosome morphogenesis.

Impact of Ion-Mixing Entropy on Orientational Preferences of DNA Helices: FRET Measurements and Computer Simulations

Biological processes require DNA and RNA helices to pack together in specific interhelical orientations. While electrostatic repulsion between backbone charges is expected to be maximized when helices are in parallel alignment, such orientations are commonplace in nature. To better understand how the repulsion is overcome, we used experimental and computational approaches to investigate how the orientational preferences of DNA helices depend on the concentration and valence of mobile cations. We used Förster resonance energy transfer (FRET) to probe the relative orientations of two 24-bp helices held together via a freely rotating PEG linker. At low cation concentrations, the helices preferred more "cross"-like orientations over those closer to parallel, and this preference was reduced with increasing salt concentrations. The results were in good quantitative agreement with Poisson-Boltzmann (PB) calculations for monovalent salt (Na+). However, PB underestimated the ability of mixtures of monovalent and divalent ions (Mg2+) to reduce the conformational preference. As a complementary approach, we performed all-atom molecular dynamics (MD) simulations and found better agreement with the experimental results. While MD and PB predict similar electrostatic forces, MD predicts a greater accumulation of Mg2+ in the ion atmosphere surrounding the DNA. Mg2+ occupancy is predicted to be greater in conformations close to the parallel orientation than in conformations close to the crossed orientation, enabling a greater release of Na+ ions and providing an entropic gain (one bound ion for two released). MD predicts an entropy gain larger than that of PB because of the increased Mg2+ occupancy. The entropy changes have a negligible effect at low Mg2+ concentrations because the free energies are dominated by electrostatic repulsion. However, as the Mg2+ concentration increases, charge screening is more effective and the mixing entropy produces readily detectable changes in packing preferences. Our results underline the importance of mixing entropy of counterions in nucleic acid interactions and provide a new understanding on the impact of a mixed ion atmosphere on the packing of DNA helices.

Sequence-Dependent Orientational Coupling and Electrostatic Attraction in Cation-Mediated DNA-DNA Interactions

Condensation of DNA is vital for its biological functions and controlled nucleic acid assemblies. However, the mechanisms of DNA condensation are not fully understood due to the inability of experiments to access cation distributions and the complex interplay of energetic and entropic forces during assembly. By constructing free energy surfaces using exhaustive sampling and detailed analysis of cation distributions, we elucidate the mechanism of DNA condensation in different salt conditions and with different DNA sequences. We found that DNA condensation is facilitated by the correlated dynamics of the localized cations at the grooves of DNA helices. These dynamics are strongly dependent on the salt conditions and DNA sequences. In the presence of magnesium ions, major groove binding facilitates attraction. In contrast, in the presence of polyvalent cations, minor groove binding serves to create charge patterns, leading to condensation. Our findings present a novel advancement in the field and have broad implications for understanding and controlling nucleic acid complexes in vivo and in vitro.

Effective Interactions between Double-Stranded DNA Molecules in Aqueous Electrolyte Solutions: Effects of Molecular Architecture and Counterion Valency

A computational investigation of the effects of molecular topology, namely, linear and circular, as well as counterion valency, on the ensuing pairwise effective interactions between DNA molecules in an unlinked state is presented. Umbrella sampling simulations have been performed through the introduction of bias potential along a reaction coordinate defined as the distance between the centers-of-mass of pairs of DNA molecules, and effective pair interaction potentials have been computed by employing the weighted histogram analysis method. An interesting comparison can be drawn between the different DNA topologies studied here, especially with regard to the contrasting effects of divalent counterions on the effective pair potentials: while DNA-DNA repulsion in short center-of-mass distances decreases significantly in the presence of divalent counterion-ions (as compared to monovalent ions) for linear DNA, the opposite effect occurs for the DNA minicircles. This can be attributed to the fact that linear DNA fragments can easily adopt relative orientations that minimize electrostatic and steric repulsions by rotating relative to one another and by exhibiting more pronounced bending due to the presence of free ends.

Homologous pairing in short double-stranded DNA-grafted colloidal microspheres

Homologous pairing (HP), i.e., the pairing of similar or identical double-stranded DNA, is an insufficiently understood fundamental biological process. HP is now understood to also occur without protein mediation, but crucial mechanistic details remain poorly established. Unfortunately, systematic studies of sequence dependence are not practical due to the enormous number of nucleotide permutations and multiple possible conformations involved in existing biophysical strategies even when using as few as 150 basepairs. Here, we show that HP can occur in DNA as short as 18 basepairs in a colloidal microparticle-based system. Exemplary systematic studies include resolving opposing reports of the impact of % AT composition, validating the impact of nucleotide order and triplet framework and revealing isotropic bendability to be crucial for HP. These studies are enabled by statistical analysis of crystal size and fraction within coexisting fluid-crystal phases of double-stranded DNA-grafted colloidal microspheres, where crystallization is predicated by HP.

The Effects of Flexibility on dsDNA–dsDNA Interactions

A detailed understanding of the physical mechanism of ion-mediated dsDNA interactions is important in biological functions such as DNA packaging and homologous pairing. We report the potential of mean force (PMF) or the effective solvent mediated interactions between two parallel identical dsDNAs as a function of interhelical separation in 0.15 M NaCl solution. Here, we study the influence of flexibility of dsDNAs on the effective interactions by comparing PMFs between rigid models and flexible ones. The role of flexibility of dsDNA pairs in their association is elucidated by studying the energetic properties of Na⁺ ions as well as the fluctuations of ions around dsDNAs. The introduction of flexibility of dsDNAs softens the vdW contact wall and induces more counterion fluctuations around dsDNAs. In addition, flexibility facilitates the Na⁺ ions dynamics affecting their distribution. The results quantify the extent of attraction influenced by dsDNA flexibility and further emphasize the importance of non-continuum solvation approaches.

Direct Measurement of Interhelical DNA Repulsion and Attraction by Quantitative Cross-Linking

To better understand the forces that mediate nucleic acid compaction in biology, we developed the disulfide cross-linking approach xHEED (X-linking of Helices to measure Electrostatic Effects at Distance) to measure the distance-dependent encounter frequency of two DNA helices in solution. Using xHEED, we determined the distance that the electrostatic potential extends from DNA helices, the dependence of this distance on ionic conditions, and the magnitude of repulsion when two helices approach one another. Across all conditions tested, the potential falls to that of the bulk solution within 15 Å of the major groove surface. For separations of ∼30 Å, we measured a repulsion of 1.8 kcal/mol in low monovalent ion concentration (30 mM Na+), with higher Na+ concentrations ameliorating this repulsion, and 2 M Na+ or 100 mM Mg2+ eliminating it. Strikingly, we found full screening at very low Co3+ concentrations and net attraction at higher concentrations, without the higher-order DNA condensation that typically complicates studies of helical attraction. Our measurements define the relevant distances for electrostatic interactions of nucleic-acid helices in biology and introduce a new method to propel further understanding of how these forces impact biological processes.

Dynamics of Cations around DNA and Protein as Revealed by 23Na Diffusion NMR Spectroscopy

Counterions are vital for the structure and function of biomolecules. However, the behavior of counterions remains elusive due to the difficulty in characterizing mobile ions. Here, we demonstrate that the dynamics of cations around biological macromolecules can be revealed by ²³Na diffusion nuclear magnetic resonance (NMR) spectroscopy. NMR probe hardware capable of generating strong magnetic field gradients enables ²³Na NMR-based diffusion measurements for Na⁺ ions in solutions of biological macromolecules and their complexes. The dynamic properties of Na⁺ ions interacting with the macromolecules can be investigated using apparent ²³Na diffusion coefficients measured under various conditions. Our diffusion data clearly show that Na⁺ ions retain high mobility within the ion atmosphere around DNA. The ²³Na diffusion NMR method also permits direct observation of the release of Na⁺ ions from nucleic acids upon protein-nucleic acid association. The entropy change due to the ion release can be estimated from the diffusion data.

Coarse-Grained Simulations of DNA Reveal Angular Dependence of Sticky-End Binding

Annealing between sticky ends of DNA is an intermediate step in ligation. It can also be utilized to program specific binding sites for DNA tile and origami assembly. This reaction is generally understood as a bimolecular reaction dictated by the local concentration of the sticky ends. Its dependence on the relative orientation between the sticky ends, however, is less understood. Here we report on the interactions between DNA sticky ends using the coarse-grained oxDNA model; specifically, we consider how the orientational alignment of the double-stranded DNA (dsDNA) segments affects the time required for the sticky ends to bind, τ_b. We specify the orientation of the dsDNA segments with three parameters: θ, which measures the angle between the helical axes, and ϕ₁ and ϕ₂, which measure rotations of each strand around the helical axis. We find that the binding time depends strongly on both θ and ϕ₂: ∼20-fold change with θ and 10-fold change with ϕ₂. The binding time is the fastest when the helical axes of duplexes are pointing toward each other and the sticky ends protrude from the farthest two points. Our result is relevant for predicting hybridization efficiency of sticky ends that are rotationally restricted.

Interactions Between Nucleosomes: From Atomistic Simulation to Polymer Model

The organization of genomes in space and time dimension plays an important role in gene expression and regulation. Chromatin folding occurs in a dynamic, structured way that is subject to biophysical rules and biological processes. Nucleosomes are the basic unit of chromatin in living cells, and here we report on the effective interactions between two nucleosomes in physiological conditions using explicit-solvent all-atom simulations. Free energy landscapes derived from umbrella sampling simulations agree well with recent experimental and simulation results. Our simulations reveal the atomistic details of the interactions between nucleosomes in solution and can be used for constructing the coarse-grained model for chromatin in a bottom-up manner.

Effects of Model Shape, Volume, and Softness of the Capsid for DNA Packaging of phi29

Double-stranded DNA is under extreme confinement when packed in phage phi29 with osmotic pressures approaching 60 atm and densities near liquid crystalline. The shape of the capsid determined from experiment is elongated. We consider the effects of the capsid shape and volume on the DNA distribution. We propose simple models for the capsid of phage phi29 to capture volume, shape, and wall flexibility, leading to an accurate DNA density profile. The effect of the packaging motor twisting the DNA on the resulting density distribution has been explored. We find packing motor induced twisting leads to a greater numbers of defects formed. The emergence of defects such as bubbles or large roll angles along the DNA shows a sequence dependence, and the resulting flexibility leads to an inhomogeneous distribution of defects occurring more often at TpA steps and AT-rich regions. In conjunction with capsid elongation, this has effects on the global DNA packing structures.

Dynamics of Ionic Interactions at Protein-Nucleic Acid Interfaces

Molecular association of proteins with nucleic acids is required for many biological processes essential to life. Electrostatic interactions via ion pairs (salt bridges) of nucleic acid phosphates and protein side chains are crucial for proteins to bind to DNA or RNA. Counterions around the macromolecules are also key constituents for the thermodynamics of protein–nucleic acid association. Until recently, there had been only a limited amount of experiment-based information about how ions and ionic moieties behave in biological macromolecular processes. In the past decade, there has been significant progress in quantitative experimental research on ionic interactions with nucleic acids and their complexes with proteins. The highly negatively charged surfaces of DNA and RNA electrostatically attract and condense cations, creating a zone called the ion atmosphere. Recent experimental studies were able to examine and validate theoretical models on ions and their mobility and interactions with macromolecules. The ionic interactions are highly dynamic. The counterions rapidly diffuse within the ion atmosphere. Some of the ions are released from the ion atmosphere when proteins bind to nucleic acids, balancing the charge via intermolecular ion pairs of positively charged side chains and negatively charged backbone phosphates. Previously, the release of counterions had been implicated indirectly by the salt-concentration dependence of the association constant.

Recently, direct detection of counterion release by NMR spectroscopy has become possible and enabled more accurate and quantitative analysis of the counterion release and its entropic impact on the thermodynamics of protein–nucleic acid association. Recent studies also revealed the dynamic nature of ion pairs of protein side chains and nucleic acid phosphates. These ion pairs undergo transitions between two major states. In one of the major states, the cation and the anion are in direct contact and form hydrogen bonds. In the other major state, the cation and the anion are separated by water. Transitions between these states rapidly occur on a picosecond to nanosecond time scale. When proteins interact with nucleic acids, interfacial arginine (Arg) and lysine (Lys) side chains exhibit considerably different behaviors. Arg side chains show a higher propensity to form rigid contacts with nucleotide bases, whereas Lys side chains tend to be more mobile at the molecular interfaces. The dynamic ionic interactions may facilitate adaptive molecular recognition and play both thermodynamic and kinetic roles in protein–nucleic acid interactions.

The lac repressor hinge helix in context: The effect of the DNA binding domain and symmetry

The Lac system of genes has been an important model system in understanding gene regulation. When the dimer lac repressor protein binds to the correct DNA sequence, the hinge region of the protein goes through a disorder to order transition. The hinge region is disordered when binding to nonoperator sequences. This region of the protein must pay a conformational entropic penalty to order when it is bound to operator DNA. Structural studies show that this region is flexible. Previous simulations showed that this region is disordered when free in solution without the DNA binding domain present. Our simulations corroborate that this region is extremely flexible in solution, but we find that the presence of the DNA binding domain proximal to the hinge helix and salt make the ordered conformation more favorable even without DNA present.