Hydration Waters Make Up for the Missing Third Hydrogen Bond in the A·T Base Pair.

Base pairing complementarity is central to DNA function. G·C and A·T pair specificity is thought to originate from the different number of hydrogen bonds the pairs make. Quantifying how many hydrogen bonds exist can be difficult because water molecules in the surrounding can make up for or disrupt direct hydrogen bonds, and the hydration structures around A·T and G·C pairs on duplex DNA are distinct. Large-scale computer simulations have been used here to create a detailed map for the hydration structure on A·T and G·C base pairs in water. The contributions of specific hydration waters to the free energy of each of the hydrogen bonds in the A·T and G·C pairs were computed. Using the equilibrium fractions of hydrated versus unhydrated states from the hydration profiles, the impact of specific bound waters on each hydrogen bond can be uniquely quantified using a thermodynamic construction. The findings suggest that hydration water in the minor groove of an A·T pair can provide up to about 2 kcal/mol of free energy advantage, effectively making up for the missing third hydrogen bond in the A·T pair compared to G·C, rendering the intrinsic thermodynamic stability of the A·T pair almost synonymous with G·C.

Host cell RecA activates a mobile element-encoded mutagenic DNA polymerase.

Homologs of the mutagenic Escherichia coli DNA polymerase V (pol V) are encoded by numerous pathogens and mobile elements. We have used Rum pol (RumA'2B), from the integrative conjugative element (ICE), R391, as a model mobile element-encoded polymerase (MEPol). The highly mutagenic Rum pol is transferred horizontally into a variety of recipient cells, including many pathogens. Moving between species, it is unclear if Rum pol can function on its own or requires activation by host factors. Here, we show that Rum pol biochemical activity requires the formation of a physical mutasomal complex, Rum Mut, containing RumA'2B-RecA-ATP, with RecA being donated by each recipient bacteria. For R391, Rum Mut specific activities in vitro and mutagenesis rates in vivo depend on the phylogenetic distance of host-cell RecA from E. coli RecA. Rum pol is a highly conserved and effective mobile catalyst of rapid evolution, with the potential to generate a broad mutational landscape that could serve to ensure bacterial adaptation in antibiotic-rich environments leading to the establishment of antibiotic resistance.

Nucleic acid folding simulations using a physics-based atomistic free energy model.

Performing full-resolution atomistic simulations of nucleic acid folding has remained a challenge for biomolecular modeling. Understanding how nucleic acids fold and how they transition between different folded structures as they unfold and refold has important implications for biology. This paper reports a theoretical model and computer simulation of the ab initio folding of DNA inverted repeat sequences. The formulation is based on an all-atom conformational model of the sugar-phosphate backbone via chain closure, and it incorporates three major molecular-level driving forces-base stacking, counterion-induced backbone self-interactions, and base pairing-via separate analytical theories designed to capture and reproduce the effects of the solvent without requiring explicit water and ions in the simulation. To accelerate computational throughput, a mixed numerical/analytical algorithm for the calculation of the backbone conformational volume is incorporated into the Monte Carlo simulation, and special stochastic sampling techniques were employed to achieve the computational efficiency needed to fold nucleic acids from scratch. This paper describes implementation details, benchmark results, and the advantages and technical challenges with this approach.

Diagrammatic approaches to RNA structures with trinucleotide repeats.

Trinucleotide repeat expansion disorders are associated with the overexpansion of (CNG) repeats on the genome. Messenger RNA transcripts of sequences with greater than 60-100 (CNG) tandem units have been implicated in trinucleotide repeat expansion disorder pathogenesis. In this work, we develop a diagrammatic theory to study the structural diversity of these (CNG)n RNA sequences. Representing structural elements on the chain's conformation by a set of graphs and employing elementary diagrammatic methods, we have formulated a renormalization procedure to re-sum these graphs and arrive at a closed-form expression for the ensemble partition function. With a simple approximation for the renormalization and applied to extended (CNG)n sequences, this theory can comprehensively capture an infinite set of conformations with any number and any combination of duplexes, hairpins, multiway junctions, and quadruplexes. To quantify the diversity of different (CNG)n ensembles, the analytical equations derived from the diagrammatic theory were solved numerically to derive equilibrium estimates for the secondary structural contents of the chains. The results suggest that the structural ensembles of (CNG)n repeat sequence with n ∼60 are surprisingly diverse, and the distribution is sensitive to the ability of the N nucleotide to make noncanonical pairs and whether the (CNG)n sequence can sustain stable quadruplexes. The results show how perturbations in the form of biases on the stabilities of the various structural motifs, duplexes, junctions, helices, and quadruplexes could affect the secondary structures of the chains and how these structures may switch when they are perturbed.

A Deep Dive into DNA Base Pairing Interactions Under Water.

Base pairing plays a pivotal role in DNA functions and replication fidelity. But while the complementarity between Watson-Crick matched bases is generally believed to arise from the different number of hydrogen bonds in G|C pairs versus A|T, the energetics of these interactions are heavily renormalized by the aqueous solvent. Employing large-scale Monte Carlo simulations, we have extracted the solvent contribution to the free energy for canonical and some noncanonical and stacked base pairs. For all of them, the solvent's contribution to the base pairing free energy is exclusively destabilizing. While the direct hydrogen bonding interactions in the G|C pair is much stronger than A|T, the thermodynamic resistance produced by the solvent also pushes back much stronger against G|C compared to A|T, generating an only ∼1 kcal/mol free energy difference between them. We have profiled the density of water molecules in the solvent adjacent to the bases and observed a "freezing" behavior where waters are recruited into the gap between the bases to compensate for the unsatisfied hydrogen bonds between them. A very small number of water molecules that are associated with the Watson-Crick donor/acceptor atoms turn out to be responsible for the majority of the solvent's thermodynamic resistance to base pairing. The absence or presence of these near-field waters can be used to enhance fidelity during DNA replication.

Experimenting with At-Home General Chemistry Laboratories During the COVID-19 Pandemic.

During the COVID-19 pandemic, an at-home laboratory program was created and implemented for a section of the general chemistry course at the University of Southern California. The experiments were designed to only utilize safe household items and no special equipment. These laboratory activities, spanning over 4 weeks, focused on concepts usually covered in the final one-third of our second-semester chemistry laboratory, including pH, acid-base titrations, buffers, solubility, phase equilibria, and thermodynamics. In this article, we describe the design of the laboratories and our experience with this experiment, while also providing an assessment on how similar activities could be integrated profitably into a regular general chemistry course.

Random Walk Enzymes: Information Theory, Quantum Isomorphism, and Entropy Dispersion.

Activation-induced deoxycytidine deaminase (AID) is a key enzyme in the human immune system. AID binds to and catalyzes random point mutations on the immunoglobulin (Ig) gene, leading to diversification of the Ig gene sequence by random walk motions, scanning for cytidines and turning them to uracils. The mutation patterns deposited by AID on its substrate DNA sequences can be interpreted as random binary words, and the information content of this stochastically generated library of mutated DNA sequences can be measured by its entropy. In this paper, we derive an analytical formula for this entropy and show that the stochastic scanning + catalytic dynamics of AID is controlled by a characteristic length that depends on the diffusion coefficient of AID and the catalytic rate. Experiments showed that the deamination rates have a sequence context dependence, where mutations are generated at higher intensities on DNA sequences with higher densities of mutable sites. We derive an isomorphism between this classical system and a quantum mechanical model and use this isomorphism to explain why AID appears to focus its scanning on regions with higher concentrations of deaminable sites. Using path integral Monte Carlo simulations of the quantum isomorphic system, we demonstrate how AID's scanning indeed depends on the context of the DNA sequence and how this affects the entropy of the library of generated mutant clones. Examining detailed features in the entropy of the experimentally generated clone library, we provide clear evidence that the random walk of AID on its substrate DNA is focused near hot spots. The model calculations applied to the experimental data show that the observed per-site mutation frequencies display similar contextual dependences as observed in the experiments, in which hot motifs are located adjacent to several different types of hot and cold motifs.

Theoretical Model for Solvent-Induced Base Stacking Interactions in Solvent-Free DNA Simulations.

Ultrahigh-throughput conformational sampling of biopolymers like nucleic acids are most effectively carried out without explicit solvents, but the physical origins of almost all inter- and intramolecular interactions controlling nucleic acid structures are rooted in water. Single-stranded (ss) DNAs or RNAs in water are characterized by ensembles of diverse conformations. To properly capture solvent-induced nucleobase stacking interactions in an otherwise solvent-free Monte Carlo algorithm, theoretical models are developed here to describe the solvent entropy and dispersion terms in base stacking free energies. To validate these models, equilibrium ensembles of ss (dA) n and (dT) n sequences ( n = 30, 40, and 50) were simulated, and they quantitatively reproduced experimental small-angle X-ray scattering (SAXS) data. Simulated dA ensembles show substantial stacking. While less prevalent, stacking in dT chains is not negligible. Analysis of SAXS profiles suggests that excess features between wavevector 0.03 and 0.18 Å-1 correlate with stacking, and stacking in dA versus dT chains is chain length-dependent, where (dT)30 and (dA)30 chains have more similar structures, but longer dA chains show more stacking over dT. The average stack length in ss-dA chains is 5-10 nucleotides, yielding an estimate for the overall A|A stacking free energy at ∼1 kcal/mol.

Conformational regulation of Escherichia coli DNA polymerase V by RecA and ATP.

Mutagenic translesion DNA polymerase V (UmuD'2C) is induced as part of the DNA damage-induced SOS response in Escherichia coli, and is subjected to multiple levels of regulation. The UmuC subunit is sequestered on the cell membrane (spatial regulation) and enters the cytosol after forming a UmuD'2C complex, ~ 45 min post-SOS induction (temporal regulation). However, DNA binding and synthesis cannot occur until pol V interacts with a RecA nucleoprotein filament (RecA*) and ATP to form a mutasome complex, pol V Mut = UmuD'2C-RecA-ATP. The location of RecA relative to UmuC determines whether pol V Mut is catalytically on or off (conformational regulation). Here, we present three interrelated experiments to address the biochemical basis of conformational regulation. We first investigate dynamic deactivation during DNA synthesis and static deactivation in the absence of DNA synthesis. Single-molecule (sm) TIRF-FRET microscopy is then used to explore multiple aspects of pol V Mut dynamics. Binding of ATP/ATPγS triggers a conformational switch that reorients RecA relative to UmuC to activate pol V Mut. This process is required for polymerase-DNA binding and synthesis. Both dynamic and static deactivation processes are governed by temperature and time, in which on → off switching is "rapid" at 37°C (~ 1 to 1.5 h), "slow" at 30°C (~ 3 to 4 h) and does not require ATP hydrolysis. Pol V Mut retains RecA in activated and deactivated states, but binding to primer-template (p/t) DNA occurs only when activated. Studies are performed with two forms of the polymerase, pol V Mut-RecA wt, and the constitutively induced and hypermutagenic pol V Mut-RecA E38K/ΔC17. We discuss conformational regulation of pol V Mut, determined from biochemical analysis in vitro, in relation to the properties of pol V Mut in RecA wild-type and SOS constitutive genetic backgrounds in vivo.

Topological Constraints and Their Conformational Entropic Penalties on RNA Folds.

Functional RNAs can fold into intricate structures using a number of different secondary and tertiary structural motifs. Many factors contribute to the overall free energy of the target fold. This study aims at quantifying the entropic costs coming from the loss of conformational freedom when the sugar-phosphate backbone is subjected to constraints imposed by secondary and tertiary contacts. Motivated by insights from topology theory, we design a diagrammatic scheme to represent different types of RNA structures so that constraints associated with a folded structure may be segregated into mutually independent subsets, enabling the total conformational entropy loss to be easily calculated as a sum of independent terms. We used high-throughput Monte Carlo simulations to simulate large ensembles of single-stranded RNA sequences in solution to validate the assumptions behind our diagrammatic scheme, examining the entropic costs for hairpin initiation and formation of many multiway junctions. Our diagrammatic scheme aids in the factorization of secondary/tertiary constraints into distinct topological classes and facilitates the discovery of interrelationships among multiple constraints on RNA folds. This perspective, which to our knowledge is novel, leads to useful insights into the inner workings of some functional RNA sequences, demonstrating how they might operate by transforming their structures among different topological classes.

Unraveling Base Stacking Driving Forces in DNA.

Base stacking is a key determinant of nucleic acid structures, but the precise origin of the thermodynamic driving force behind the stacking of nucleobases remains open. The rather mild stacking free energy measured experimentally, roughly a kcal/mol depending on the identity of the bases, is physiologically significant because while base stacking confers stability to the genome in its double helix form, the duplex also has to be unwound in order to be replicated or transcribed. A stacking free energy that is either too high or too low will over- or understabilize the genome, impacting the storage of genetic information and also its retrieval. While the molecular origin of stacking driving force has been attributed to many different sources including dispersion, electrostatics, and solvent hydrogen bonding, here we show via a systematic decomposition of the stacking free energy using large-scale computer simulations that the dominant driving force stabilizing base stacking is nonhydrophobic solvent entropy. Counteracting this is the conformational entropic penalty on the sugar-phosphate backbone against stacking, while solvent hydrogen-bonding, charge-charge interactions, and dispersive forces produce only secondary perturbations. Solvent entropic forces and DNA backbone conformational strains therefore work against each other, leading to a very mild composite stacking free energy in agreement with experiments.

An implicit divalent counterion force field for RNA molecular dynamics.

How to properly account for polyvalent counterions in a molecular dynamics simulation of polyelectrolytes such as nucleic acids remains an open question. Not only do counterions such as Mg(2+) screen electrostatic interactions, they also produce attractive intrachain interactions that stabilize secondary and tertiary structures. Here, we show how a simple force field derived from a recently reported implicit counterion model can be integrated into a molecular dynamics simulation for RNAs to realistically reproduce key structural details of both single-stranded and base-paired RNA constructs. This divalent counterion model is computationally efficient. It works with existing atomistic force fields, or coarse-grained models may be tuned to work with it. We provide optimized parameters for a coarse-grained RNA model that takes advantage of this new counterion force field. Using the new model, we illustrate how the structural flexibility of RNA two-way junctions is modified under different salt conditions.

Activation-induced deoxycytidine deaminase (AID) co-transcriptional scanning at single-molecule resolution.

Activation-induced deoxycytidine deaminase (AID) generates antibody diversity in B cells by initiating somatic hypermutation (SHM) and class-switch recombination (CSR) during transcription of immunoglobulin variable (IgV) and switch region (IgS) DNA. Using single-molecule FRET, we show that AID binds to transcribed dsDNA and translocates unidirectionally in concert with RNA polymerase (RNAP) on moving transcription bubbles, while increasing the fraction of stalled bubbles. AID scans randomly when constrained in an 8 nt model bubble. When unconstrained on single-stranded (ss) DNA, AID moves in random bidirectional short slides/hops over the entire molecule while remaining bound for ∼ 5 min. Our analysis distinguishes dynamic scanning from static ssDNA creasing. That AID alone can track along with RNAP during transcription and scan within stalled transcription bubbles suggests a mechanism by which AID can initiate SHM and CSR when properly regulated, yet when unregulated can access non-Ig genes and cause cancer.

Atomistic Free Energy Model for Nucleic Acids: Simulations of Single-Stranded DNA and the Entropy Landscape of RNA Stem-Loop Structures.

While single-stranded (ss) segments of DNAs and RNAs are ubiquitous in biology, details about their structures have only recently begun to emerge. To study ssDNA and RNAs, we have developed a new Monte Carlo (MC) simulation using a free energy model for nucleic acids that has the atomisitic accuracy to capture fine molecular details of the sugar-phosphate backbone. Formulated on the basis of a first-principle calculation of the conformational entropy of the nucleic acid chain, this free energy model correctly reproduced both the long and short length-scale structural properties of ssDNA and RNAs in a rigorous comparison against recent data from fluorescence resonance energy transfer, small-angle X-ray scattering, force spectroscopy and fluorescence correlation transport measurements on sequences up to ∼100 nucleotides long. With this new MC algorithm, we conducted a comprehensive investigation of the entropy landscape of small RNA stem-loop structures. From a simulated ensemble of ∼10(6) equilibrium conformations, the entropy for the initiation of different size RNA hairpin loops was computed and compared against thermodynamic measurements. Starting from seeded hairpin loops, constrained MC simulations were then used to estimate the entropic costs associated with propagation of the stem. The numerical results provide new direct molecular insights into thermodynaimc measurement from macroscopic calorimetry and melting experiments.

Random-walk enzymes.

Enzymes that rely on random walk to search for substrate targets in a heterogeneously dispersed medium can leave behind complex spatial profiles of their catalyzed conversions. The catalytic signatures of these random-walk enzymes are the result of two coupled stochastic processes: scanning and catalysis. Here we develop analytical models to understand the conversion profiles produced by these enzymes, comparing an intrusive model, in which scanning and catalysis are tightly coupled, against a loosely coupled passive model. Diagrammatic theory and path-integral solutions of these models revealed clearly distinct predictions. Comparison to experimental data from catalyzed deaminations deposited on single-stranded DNA by the enzyme activation-induced deoxycytidine deaminase (AID) demonstrates that catalysis and diffusion are strongly intertwined, where the chemical conversions give rise to new stochastic trajectories that were absent if the substrate DNA was homogeneous. The C→U deamination profiles in both analytical predictions and experiments exhibit a strong contextual dependence, where the conversion rate of each target site is strongly contingent on the identities of other surrounding targets, with the intrusive model showing an excellent fit to the data. These methods can be applied to deduce sequence-dependent catalytic signatures of other DNA modification enzymes, with potential applications to cancer, gene regulation, and epigenetics.

Residual Conformational Entropies on the Sugar-Phosphate Backbone of Nucleic Acids: An Analysis of the Nucleosome Core DNA and the Ribosome.

A nucleic acid folds according to its free energy, but persistent residual conformational fluctuations remain along its sugar-phosphate backbone even after secondary and tertiary structures have been assembled, and these residual conformational entropies provide a rigorous lower bound for the folding free energy. We extend a recently reported algorithm to calculate the residual backbone entropy along a RNA or DNA given configuration of its bases and apply it to the crystallographic structures of the 23S ribosomal subunit and DNAs in the nucleosome core particle. In the 23S rRNAs, higher entropic strains are concentrated in helices and certain tertiary interaction platforms while residues with high surface accessibility and those not involved in base pairing generally have lower strains. Upon folding, residual backbone entropy in the 23S subunit accounts for an average free energy penalty of +0.47 (kcal/mol)/nt (nt = nucleotide) at 310 K. In nucleosomal DNAs, backbone entropies show periodic oscillations with sequence position correlating with the superhelical twist and shifts in the base-pair-step geometries, and nucleosome positioning on the bound DNA exerts strong influence over where entropic strains are located. In contrast to rRNAs, residual backbone entropies account for a free energy penalty of only +0.09 (kcal/mol)/nt in duplex relative to single-stranded DNAs.

Free energy of RNA-counterion interactions in a tight-binding model computed by a discrete space mapping.

The thermodynamic stability of a folded RNA is intricately tied to the counterions and the free energy of this interaction must be accounted for in any realistic RNA simulations. Extending a tight-binding model published previously, in this paper we investigate the fundamental structure of charges arising from the interaction between small functional RNA molecules and divalent ions such as Mg(2+) that are especially conducive to stabilizing folded conformations. The characteristic nature of these charges is utilized to construct a discretely connected energy landscape that is then traversed via a novel application of a deterministic graph search technique. This search method can be incorporated into larger simulations of small RNA molecules and provides a fast and accurate way to calculate the free energy arising from the interactions between an RNA and divalent counterions. The utility of this algorithm is demonstrated within a fully atomistic Monte Carlo simulation of the P4-P6 domain of the Tetrahymena group I intron, in which it is shown that the counterion-mediated free energy conclusively directs folding into a compact structure.

Conformational entropy of the RNA phosphate backbone and its contribution to the folding free energy.

While major contributors to the free energy of RNA tertiary structures such as basepairing, base-stacking, and charge and counterion interactions have been studied extensively, little is known about the intrinsic free energy of the backbone. To assess the magnitude of the entropic strains along the phosphate backbone and their impact on the folding free energy, we have formulated a mathematical treatment for computing the volume of the main-chain torsion-angle conformation space between every pair of nucleobases along any sequence to compute the corresponding backbone entropy. To validate this method, we have compared the computed conformational entropies against a statistical free energy analysis of structures in the crystallographic database from several-thousand backbone conformations between nearest-neighbor nucleobases as well as against extensive computer simulations. Using this calculation, we analyzed the backbone entropy of several ribozymes and riboswitches and found that their entropic strains are highly localized along their sequences. The total entropic penalty due to steric congestions in the backbone for the native fold can be as high as 2.4 cal/K/mol per nucleotide for these medium and large RNAs, producing a contribution to the overall free energy of up to 0.72 kcal/mol per nucleotide. For these RNAs, we found that low-entropy high-strain residues are predominantly located at loops with tight turns and at tertiary interaction platforms with unusual structural motifs.

A mathematical model for scanning and catalysis on single-stranded DNA, illustrated with activation-induced deoxycytidine deaminase.

We formulated a master equation-based mathematical model to analyze random scanning and catalysis for enzymes that act on single-stranded DNA (ssDNA) substrates. Catalytic efficiencies and intrinsic scanning distances are deduced from the distribution of positions and gap lengths between a series of catalytic events occurring over time, which are detected as point mutations in a lacZα-based reporter sequence containing enzyme target motifs. Mathematical analysis of the model shows how scanning motions become separable from the catalysis when the proper statistical properties of the mutation pattern are used to interpret the readouts. Two-point correlations between all catalytic events determine intrinsic scanning distances, whereas gap statistics between mutations determine their catalytic efficiencies. Applying this model to activation-induced deoxycytidine deaminase (AID), which catalyzes C→U deaminations processively on ssDNA, we have established that deaminations of AGC hot motifs occur at a low rate, ∼0.03 s(-1), and low efficiency, ∼3%. AID performs random bidirectional movements for an average distance of 6.2 motifs, at a rate of about 15 nucleotides per second, and "dwells" at a motif site for 2.7 s while bound >4 min to the same DNA molecule. These results provide new and important insights on how AID may be optimized for generating mutational diversity in Ig genes, and we discuss how the properties of AID acting freely on a "naked" ssDNA relate to the constrained action of AID during transcription-dependent somatic hypermutation and class-switch recombination.