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The International Society of RNA Nanotechnology and Nanomedicine (ISRNN) serves to further the development of a wide variety of functional nucleic acids and other related nanotechnology platforms. To aid in the dissemination of the most recent advancements, a biennial discussion focused on biomotors, viral assembly, and RNA nanobiotechnology has been established where international experts in interdisciplinary fields such as structural biology, biophysical chemistry, nanotechnology, cell and cancer biology, and pharmacology share their latest accomplishments and future perspectives. The results summarized here highlight advancements in our understanding of viral biology and the structure-function relationship of frame-shifting elements in genomic viral RNA, improvements in the predictions of SHAPE analysis of 3D RNA structures, and the understanding of dynamic RNA structures through a variety of experimental and computational means. Additionally, recent advances in the drug delivery, vaccine design, nanopore technologies, biomotor and biomachine development, DNA packaging, RNA nanotechnology, and drug delivery are included in this critical review. We emphasize some of the novel accomplishments, major discussion topics, and present current challenges and perspectives of these emerging fields.

With the rapid rate of COVID-19 infections and deaths, treatments and cures besides hand washing, social distancing, masks, isolation, and quarantines are urgently needed. The treatments and vaccines rely on the basic biophysics of the complex viral apparatus. Although proteins are serving as main drug and vaccine targets, therapeutic approaches targeting the 30,000 nucleotide RNA viral genome form important complementary approaches. Indeed, the high conservation of the viral genome, its close evolutionary relationship to other viruses, and the rise of gene editing and RNA-based vaccines all argue for a focus on the RNA agent itself. One of the key steps in the viral replication cycle inside host cells is the ribosomal frameshifting required for translation of overlapping open reading frames. The RNA frameshifting element (FSE), one of three highly conserved regions of coronaviruses, is believed to include a pseudoknot considered essential for this ribosomal switching. In this work, we apply our graph-theory-based framework for representing RNA secondary structures, "RAG (or RNA-As-Graphs)," to alter key structural features of the FSE of the SARS-CoV-2 virus. Specifically, using RAG machinery of genetic algorithms for inverse folding adapted for RNA structures with pseudoknots, we computationally predict minimal mutations that destroy a structurally important stem and/or the pseudoknot of the FSE, potentially dismantling the virus against translation of the polyproteins. Our microsecond molecular dynamics simulations of mutant structures indicate relatively stable secondary structures. These findings not only advance our computational design of RNAs containing pseudoknots, they pinpoint key residues of the SARS-CoV-2 virus as targets for antiviral drugs and gene editing approaches.

Chromatin structure, dynamics, and function are being intensely investigated by a variety of methods, including microscopy, X-ray diffraction, nuclear magnetic resonance, biochemical crosslinking, chromosome conformation capture, and computation. A range of experimental techniques combined with modeling is clearly valuable to help interpret experimental data and, importantly, generate configurations and mechanisms related to the 3D organization and function of the genome. Contact maps, in particular, as obtained by a variety of chromosome conformation capture methods, are of increasing interest due to their implications on genome structure and regulation on many levels. In this perspective, using seven examples from our group's studies, we illustrate how molecular modeling can help interpret such experimental data. Specifically, we show how computed contact maps related to experimental systems can be used to explain structures of nucleosomes, chromatin higher-order folding, domain segregation mechanisms, gene organization, and the effect on chromatin structure of external and internal fiber parameters, such as nucleosome positioning, presence of nucleosome free regions, histone posttranslational modifications, and linker histone binding. We argue that such computations on multiple spatial and temporal scales will be increasingly important for the integration of genomic, epigenomic, and biophysical data on chromatin structure and related cellular processes.

Monte Carlo simulations of a mesoscale model of oligonucleosomes are analyzed to examine the role of dynamic-linker histone (LH) binding/unbinding in high monovalent salt with divalent ions, and to further interpret noted chromatin fiber softening by dynamic LH in monovalent salt conditions. We find that divalent ions produce a fiber stiffening effect that competes with, but does not overshadow, the dramatic softening triggered by dynamic-LH behavior. Indeed, we find that in typical in vivo conditions, dynamic-LH binding/unbinding reduces fiber stiffening dramatically (by a factor of almost 5, as measured by the elasticity modulus) compared with rigidly fixed LH, and also the force needed to initiate chromatin unfolding, making it consistent with those of molecular motors. Our data also show that, during unfolding, divalent ions together with LHs induce linker-DNA bending and DNA-DNA repulsion screening, which guarantee formation of heteromorphic superbeads-on-a-string structures that combine regions of loose and compact fiber independently of the characteristics of the LH-core bond. These structures might be important for gene regulation as they expose regions of the DNA selectively. Dynamic control of LH binding/unbinding, either globally or locally, in the presence of divalent ions, might constitute a mechanism for regulation of gene expression.

The basic and intrinsically disordered C-terminal domain (CTD) of the linker histone (LH) is essential for chromatin compaction. However, its conformation upon nucleosome binding and its impact on chromatin organization remain unknown. Our mesoscale chromatin model with a flexible LH CTD captures a dynamic, salt-dependent condensation mechanism driven by charge neutralization between the LH and linker DNA. Namely, at low salt concentration, CTD condenses, but LH only interacts with the nucleosome and one linker DNA, resulting in a semi-open nucleosome configuration; at higher salt, LH interacts with the nucleosome and two linker DNAs, promoting stem formation and chromatin compaction. CTD charge reduction unfolds the domain and decondenses chromatin, a mechanism in consonance with reduced counterion screening in vitro and phosphorylated LH in vivo. Divalent ions counteract this decondensation effect by maintaining nucleosome stems and expelling the CTDs to the fiber exterior. Additionally, we explain that the CTD folding depends on the chromatin fiber size, and we show that the asymmetric structure of the LH globular head is responsible for the uneven interaction observed between the LH and the linker DNAs. All these mechanisms may impact epigenetic regulation and higher levels of chromatin folding.

We reassess progress in the field of biomolecular modeling and simulation, following up on our perspective published in 2011. By reviewing metrics for the field's productivity and providing examples of success, we underscore the productive phase of the field, whose short-term expectations were overestimated and long-term effects underestimated. Such successes include prediction of structures and mechanisms; generation of new insights into biomolecular activity; and thriving collaborations between modeling and experimentation, including experiments driven by modeling. We also discuss the impact of field exercises and web games on the field's progress. Overall, we note tremendous success by the biomolecular modeling community in utilization of computer power; improvement in force fields; and development and application of new algorithms, notably machine learning and artificial intelligence. The combined advances are enhancing the accuracy andscope of modeling and simulation, establishing an exemplary discipline where experiment and theory or simulations are full partners.

Background We re-evaluate our RNA-As-Graphs clustering approach, using our expanded graph library and new RNA structures, to identify potential RNA-like topologies for design. Our coarse-grained approach represents RNA secondary structures as tree and dual graphs, with vertices and edges corresponding to RNA helices and loops. The graph theoretical framework facilitates graph enumeration, partitioning, and clustering approaches to study RNA structure and its applications. Methods Clustering graph topologies based on features derived from graph Laplacian matrices and known RNA structures allows us to classify topologies into ‘existing’ or hypothetical, and the latter into, ‘RNA-like’ or ‘non RNA-like’ topologies. Here we update our list of existing tree graph topologies and RAG-3D database of atomic fragments to include newly determined RNA structures. We then use linear and quadratic regression, optionally with dimensionality reduction, to derive graph features and apply several clustering algorithms on our tree-graph library and recently expanded dual-graph library to classify them into the three groups. Results The unsupervised PAM and K-means clustering approaches correctly classify 72–77% of all existing graph topologies and 75–82% of newly added ones as RNA-like. For supervised k-NN clustering, the cross-validation accuracy ranges from 57 to 81%. Conclusions Using linear regression with unsupervised clustering, or quadratic regression with supervised clustering, provides better accuracies than supervised/linear clustering. All accuracies are better than random, especially for newly added existing topologies, thus lending credibility to our approach. General significance Our updated RAG-3D database and motif classification by clustering present new RNA substructures and RNA-like motifs as novel design candidates.

Summary We launch a webserver for RNA structure prediction and design corresponding to tools developed using our RNA-As-Graphs (RAG) approach. RAG uses coarse-grained tree graphs to represent RNA secondary structure, allowing the application of graph theory to analyze and advance RNA structure discovery. Our webserver consists of three modules: (a) RAG Sampler: samples tree graph topologies from an RNA secondary structure to predict corresponding tertiary topologies, (b) RAG Builder: builds three-dimensional atomic models from candidate graphs generated by RAG Sampler, and (c) RAG Designer: designs sequences that fold onto novel RNA motifs (described by tree graph topologies). Results analyses are performed for further assessment/selection. The Results page provides links to download results and indicates possible errors encountered. RAG-Web offers a user-friendly interface to utilize our RAG software suite to predict and design RNA structures and sequences. Availability and implementation The webserver is freely available online at: http://www.biomath.nyu.edu/ragtop/. Supplementary information Supplementary data are available at Bioinformatics online.

Histone tails and their epigenetic modifications play crucial roles in gene expression regulation by altering the architecture of chromatin. However, the structural mechanisms by which histone tails influence the interconversion between active and inactive chromatin remain unknown. Given the technical challenges in obtaining detailed experimental characterizations of the structure of chromatin, multiscale computations offer a promising alternative to model the effect of histone tails on chromatin folding. Here we combine multi-microsecond atomistic molecular dynamics simulations of dinucleosomes and histone tails in explicit solvent and ions, performed with three different state-of-the-art force fields and validated by experimental NMR measurements, with coarse-grained Monte Carlo simulations of 24-nucleosome arrays to describe the conformational landscape of histone tails, their roles in chromatin compaction, and the impact of lysine acetylation, a widespread epigenetic change, on both. We find that while the wild-type tails are highly flexible and disordered, the dramatic increase of secondary-structure order by lysine acetylation unfolds chromatin by decreasing tail availability for crucial fiber-compacting internucleosome interactions. This molecular level description of the effect of histone tails and their charge modifications on chromatin folding explains the sequence sensitivity and underscores the delicate connection between local and global structural and functional effects. Our approach also opens new avenues for multiscale processes of biomolecular complexes.

Oxidative stress promotes genomic instability and human diseases1. A common oxidized nucleoside is 8-oxo-7,8-dihydro-2’-deoxyguanosine found both in DNA (8-oxo-G) and as a free nucleotide (8-oxo-dGTP)2,3. Nucleotide pools are especially vulnerable to oxidative damage4. Therefore cells encode an enzyme (MutT/MTH1) that removes free oxidized nucleotides. This cleansing function is required for cancer cell survival5,6 and to modulate E. coli antibiotic sensitivity in a DNA polymerase (pol)-dependent manner7. How polymerase discriminates between damaged and non-damaged nucleotides is not well understood. This analysis is essential given the role of oxidized nucleotides in mutagenesis, cancer therapeutics, and bacterial antibiotics8. Even with cellular sanitizing activities, nucleotide pools contain enough 8-oxo-dGTP to promote mutagenesis9,10. This arises from the dual coding potential where 8-oxo-dGTP(anti) base pairs with cytosine (Cy) and 8-oxodGTP(syn) utilizes its Hoogsteen edge to base pair with adenine (Ad)11. Here we utilized time-lapse crystallography to follow 8-oxo-dGTP insertion opposite Ad or Cy with human DNA pol β, to reveal that insertion is accommodated in either the syn- or anti-conformation, respectively. For 8-oxo-dGTP(anti) insertion, a novel divalent metal relieves repulsive interactions between the adducted guanine base and the triphosphate of the oxidized nucleotide. With either templating base, hydrogen bonding interactions between the bases are lost as the enzyme reopens after catalysis, leading to a cytotoxic nicked DNA repair intermediate. Combining structural snapshots with kinetic and computational analysis reveals how 8-oxodGTP utilizes charge modulation during insertion that can lead to a blocked DNA repair intermediate.

To interpret recent structures of the R283K mutant of human DNA repair enzyme DNA polymerase β (pol β) differing in the number of Mg(2+) ions, we apply transition path sampling (TPS) to assess the effect of differing ion placement on the transition from the open one-metal to the closed two-metal state. We find that the closing pathway depends on the initial ion position, both in terms of the individual transition states and associated energies. The energy barrier of the conformational pathway varies from 25 to 58 kJ/mol, compared to the conformational energy barrier of 42 kJ/mol for the wild-type pol β reported previously. Moreover, we find a preferred ion route located in the center of the enzyme, parallel to the DNA. Within this route, the conformational pathway is similar to that of the overall open to closed transition of pol β but outside it, especially when the ion starts near active site residues Arg258 and Asp190, the conformational pathway diverges significantly. We hypothesize that our findings should apply generally to pol β, since R283 is relatively far from the active site. Our hypothesis suggests further experimental and computational work. Our studies also underscore the common feature that less active mutants have less stable closed states than their open states, in marked contrast to the wild-type enzyme, where the closed state is significantly more stable than the open form.

The modified base 8-oxo-7,8-dihydro-2′-deoxyguanosine (oxoG) is a common DNA adduct produced by the oxidation of DNA by reactive oxygen species. Kinetic data reveal that DNA polymerase X (pol X) from the African swine fever virus incorporates adenine (dATP) opposite to oxoG with higher efficiency than the non-damaged G:C basepair. To help interpret the kinetic data, we perform molecular dynamics simulations of pol X/DNA complexes, in which the template base opposite to the incoming dNTP (dCTP, dATP, dGTP) is oxoG. Our results suggest that pol X accommodates the oxoGsyn:A mispair by sampling closed active conformations that mirror those observed in traditional Watson-Crick complexes. Moreover, for both the oxoGsyn:A and oxoG:C ternary complexes, conformational sampling of the polymerase follows previously described large subdomain movements, local residue motions, and active site reorganization. Interestingly, the oxoGsyn:A system exhibits superior active site geometry in comparison to the oxoG:C system. Simulations for the other mismatch basepair complexes reveal large protein subdomain movement for all systems, except for oxoG:G, which samples conformations close to the open state. In addition, active site geometry and basepairing of the template base with the incoming nucleotide, reveal distortions and misalignments that range from moderate (i.e., oxoG:Asyn) to extreme (i.e., oxoGanti/syn:G). These results agree with the available kinetic data for pol X and provide structural insights regarding the mechanism by which this polymerase can accommodate incoming nucleotides opposite oxoG. Our simulations also support the notion that α-helix E is involved both in DNA binding and active site stabilization. Our proposed mechanism by which pol X can preferentially accommodate dATP opposite template oxoG further underscores the role that enzyme dynamics and conformational sampling operate in polymerase fidelity and function.

RNA junctions are important structural elements of RNA molecules. They are formed when three or more helices come together in three-dimensional space. Recent studies have focused on the annotation and prediction of coaxial helical stacking (CHS) motifs within junctions. Here we exploit such predictions to develop an efficient alignment tool to handle RNA secondary structures with CHS motifs. Specifically, we build upon our Junction-Explorer software for predicting coaxial stacking and RNAJAG for modelling junction topologies as tree graphs to incorporate constrained tree matching and dynamic programming algorithms into a new method, called CHSalign, for aligning the secondary structures of RNA molecules containing CHS motifs. Thus, CHSalign is intended to be an efficient alignment tool for RNAs containing similar junctions. Experimental results based on thousands of alignments demonstrate that CHSalign can align two RNA secondary structures containing CHS motifs more accurately than other RNA secondary structure alignment tools. CHSalign yields a high score when aligning two RNA secondary structures with similar CHS motifs or helical arrangement patterns, and a low score otherwise. This new method has been implemented in a web server, and the program is also made freely available, at http://bioinformatics.njit.edu/CHSalign/., Comment: 45 pages, 5 figures

Mutations in DNA polymerase β (pol β) have been associated with approximately 30% of human tumors. The E295K mutation of pol β has been linked to gastric carcinoma via interference with base excision repair. To interpret the different behavior of E295K as compared to wild-type pol β in atomic and energetic detail, we resolve a binary crystal complex of E295K at 2.5 Å and apply transition path sampling (TPS) to delineate the closing pathway of the E295K pol β mutant. Conformational changes are important components in the enzymatic pathway that lead to and ready the enzyme for the chemical reaction. Our analyses show that the closing pathway of E295K mutant differs from the wild-type pol β in terms of the individual transition states along the pathway, associated energies, and the active site conformation in the final closed form of the mutant. In particular, the closed state of E295K has a more distorted active site than the active site in the wild-type pol β. In addition, the total energy barrier in the conformational closing pathway is 65 ± 11 kJ/mol, much higher than that estimated for both correct (e.g., G:C) and incorrect (e.g., G:A) wild-type pol β systems (42 ± 8 and 45 ± 7 kJ/mol, respectively). In particular, the rotation of Arg258 is the rate-limiting step in the conformational pathway of E295K due to unfavorable electrostatic and steric interactions. The distorted active site in the closed relative to open state and the high energy barrier in the conformational pathway may explain in part why the E295K mutant is observed to be inactive. Interestingly, however, following the closing of the thumb but prior to the rotation of Arg258, the E295K mutant complex has a similar energy level as compared to the wild-type pol β. This suggests that the E295K mutant may associate with DNA with similar affinity, but it may be hampered in continuing the process of chemistry. Supporting experimental data come from the observation that the catalytic activity of wild-type pol β is hampered when E295K is present: this may arise from the competition between E295K and wild-type enzyme for the DNA. These combined results suggest that the low insertion efficiency of E295K mutant as compared to wild-type pol β may be related to a closed form distorted by unfavorable electrostatic and steric interactions between Arg258 and other key residues. The active site is thus less competent for proceeding to the chemical reaction, which may also involve a higher reaction barrier than the wild-type or may not be possible in this mutant. Our analysis also suggests further experiments for other mutants to test the above hypothesis and dissect the roles of steric and electrostatic factors on enzyme behavior.

Chromatin fibers encountered in various species and tissues are characterized by different nucleosome repeat lengths (NRL) of the linker DNA connecting the nucleosomes. While single cellular organisms and rapidly growing cells with high protein production have short NRL ranging from 160 to 189 base pairs (bp), mature cells usually have longer NRL ranging between 190 and 220 bp. Recently, various experimental studies have examined the effect of NRL on the internal organization of chromatin fiber. Here we investigate by mesoscale modeling of oligonucleosomes the folding patterns for different NRL, with and without linker histone, under typical monovalent salt conditions using both one-start solenoid and two-start zigzag starting configurations. We find that short to medium NRL chromatin fibers (173 to 209 bp) with linker histone condense into irregular zigzag structures, and that solenoid-like features are viable only for longer NRL (226 bp). We suggest that medium NRL are more advantageous for packing and various levels of chromatin compaction throughout the cell cycle than their shortest and longest brethren; the former (short NRL) fold into narrow fibers, while the latter (long NRL) arrays do not easily lead to high packing ratios due to possible linker DNA bending. Moreover, we show that the linker histone has a small effect on the condensation of short-NRL arrays but an important condensation effect on medium-NRL arrays which have linker lengths similar to the linker histone lengths. Finally, we suggest that the medium-NRL species, with densely packed fiber arrangements, may be advantageous for epigenetic control because their histone tail modifications can have a greater effect compared to other fibers due to their more extensive nucleosome interaction network.

DNA polymerases have the venerable task of maintaining genome stability during DNA replication and repair. Errors, nonetheless, occur with error propensities that are polymerase specific. For example, DNA polymerase λ (pol λ) generates single-base deletions through template-strand slippage within short repetitive DNA regions much more readily than does the closely related polymerase β (pol β). Here we present in silico evidence to help interpret pol λ's greater tendency for deletion errors than pol β by its more favorable protein/DNA electrostatic interactions immediately around the extrahelical nucleotide on the template strand. Our molecular dynamics and free energy analyses suggest that pol λ provides greater stabilization to misaligned DNA than aligned DNA. Our study of several pol λ mutants of Lys544 (Ala, Phe, Glu) probes the interactions between the extrahelical nucleotide and the adjacent Lys544 to show that the charge of the 544 residue controls stabilization of the DNA misalignment. In addition, we identify other thumb residues (Arg538, Lys521, Arg517, and Arg514) that play coordinating roles in stabilizing pol λ's interactions with misaligned DNA. Interestingly, their aggregate stabilization effect is more important than that of any one component residue, in contrast to aligned DNA systems, as we determined from mutations of these key residues and energetic analyses. No such comparable network of stabilizing misaligned DNA exists in pol β. Evolutionary needs for DNA repair on substrates with minimal base-pairing, such as those encountered by pol λ in the non-homologous end-joining pathway, may have been solved by a greater tolerance to deletion errors. Other base-flipping proteins share similar binding properties and motions for extrahelical nucleotides.

The simple deletion of nucleotides is common in many organisms. It can be advantageous when it activates genes beneficial to microbial survival in adverse environments, and deleterious when it mutates genes relevant to survival, cancer or degenerative diseases. The classical idea is that simple deletions arise by strand slippage. A prime opportunity for slippage occurs during DNA synthesis, but it remains unclear how slippage is controlled during a polymerization cycle. Here, we report crystal structures and molecular dynamics simulations of mutant derivatives of DNA polymerase lambda bound to a primer-template during strand slippage. Relative to the primer strand, the template strand is in multiple conformations, indicating intermediates on the pathway to deletion mutagenesis. Consistent with these intermediates, the mutant polymerases generate single-base deletions at high rates. The results indicate that dNTP-induced template strand repositioning during conformational rearrangements in the catalytic cycle is crucial to controlling the rate of strand slippage.

Unlike some other DNA polymerases, DNA polymerase lambda (pol lambda) utilizes DNA motion and active-site protein residue rearrangements rather than large-scale protein subdomain changes to transition between its active and inactive states. Pol lambda also has an unusual error tendency to generate single-base deletions (also known as frameshift mutations) resulting from DNA template-strand slippage. An understanding of these features requires an atomic-level link between the various structures and motions involved and observed in biochemical functions. Our simulations of pol lambda ternary complexes of various 517 mutants (Lys, Glu, His, Met, and Gln) reveal discrete orientations of the 517 residue with respect to the DNA and associated interactions (mainly electrostatic) that explain the wide range ( approximately 3-8 A) of mutant-dependent DNA motion observed (Figure 2 of manuscript): (wild-type[R517K approximately R517H approximately R517Q][R517E approximately R517A approximately R517M]). This motion critically impacts stability of the ternary complex and hence drives/hampers the enzyme's catalytic cycle. In addition to pinpointing a trend for interpreting associated frameshift error rates based on template-strand stability, the close connection between DNA movement and active-site protein residue changes suggests that pol lambda's unique architecture facilitates frameshift errors because small variations in the active-site environment (e.g., orientation of 517) can have large effects on the dynamics of the ternary pol lambda complex.

The nature of conformational transitions in DNA polymerase lambda (pol lambda), a low-fidelity DNA repair enzyme in the X-family that fills short nucleotide gaps, is investigated. Specifically, to determine whether pol lambda has an induced-fit mechanism and open-to-closed transition before chemistry, we analyze a series of molecular dynamics simulations from both the binary and ternary states before chemistry, with and without the incoming nucleotide, with and without the catalytic Mg(2+) ion in the active site, and with alterations in active site residues Ile(492) and Arg(517). Though flips occurred for several side-chain residues (Ile(492), Tyr(505), Phe(506)) in the active site toward the binary (inactive) conformation and partial DNA motion toward the binary position occurred without the incoming nucleotide, large-scale subdomain motions were not observed in any trajectory from the ternary complex regardless of the presence of the catalytic ion. Simulations from the binary state with incoming nucleotide exhibit more thumb subdomain motion, particularly in the loop containing beta-strand 8 in the thumb, but closing occurred only in the Ile(492)Ala mutant trajectory started from the binary state with incoming nucleotide and both ions. Further connections between active site residues and the DNA position are also revealed through our Ile(492)Ala and Arg(517)Ala mutant studies. Our combined studies suggest that while pol lambda does not demonstrate large-scale subdomain movements as DNA polymerase beta (pol beta), significant DNA motion exists, and there are sequential subtle side chain and other motions-associated with Arg(514), Arg(517), Ile(492), Phe(506), Tyr(505), the DNA, and again Arg(514) and Arg(517)-all coupled to active site divalent ions and the DNA motion. Collectively, these motions transform pol lambda to the chemistry-competent state. Significantly, analogs of these residues in pol beta (Lys(280), Arg(283), Arg(258), Phe(272), and Tyr(271), respectively) have demonstrated roles in determining enzyme efficiency and fidelity. As proposed for pol beta, motions of these residues may serve as gate-keepers by controlling the evolution of the reaction pathway before the chemical reaction.

The possible conformational changes of DNA polymerase IV (Dpo4) before and after the nucleotidyl-transfer reaction are investigated at the atomic level by dynamics simulations to gain insight into the mechanism of low-fidelity polymerases and identify slow and possibly critical steps. The absence of significant conformational changes in Dpo4 before chemistry when the incoming nucleotide is removed supports the notion that the "induced-fit" mechanism employed to interpret fidelity in some replicative and repair DNA polymerases does not exist in Dpo4. However, significant correlated movements in the little finger and finger domains, as well as DNA sliding and subtle catalytic-residue rearrangements, occur after the chemical reaction when both active-site metal ions are released. Subsequently, Dpo4's little finger grips the DNA through two arginine residues and pushes it forward. These metal ion correlated movements may define subtle, and possibly characteristic, conformational adjustments that operate in some Y-family polymerase members in lieu of the prominent subdomain motions required for catalytic cycling in other DNA polymerases like polymerase beta. Such subtle changes do not easily provide a tight fit for correct incoming substrates as in higher-fidelity polymerases, but introduce in low-fidelity polymerases different fidelity checks as well as the variable conformational-mobility potential required to bypass different lesions.

Our application of transition path sampling to a complex biomolecular system in explicit solvent, the closing transition of DNA polymerase β, unravels atomic and energetic details of the conformational change that precedes the chemical reaction of nucleotide incorporation. The computed reaction profile offers detailed mechanistic insights into, as well as kinetic information on, the complex process essential for DNA synthesis and repair. The five identified transition states extend available experimental and modeling data by revealing highly cooperative dynamics and critical roles of key residues (Arg-258, Phe-272, Asp-192, and Tyr-271) in the enzyme's function. The collective cascade of these sequential conformational changes brings the DNA/DNA polymerase β system to a state nearly competent for the chemical reaction and suggests how subtle residue motions and conformational rate-limiting steps affect reaction efficiency and fidelity; this complex system of checks and balances directs the system to the chemical reaction and likely helps the enzyme discriminate the correct from the incorrect incoming nucleotide. Together with the chemical reaction, these conformational features may be central to the dual nature of polymerases, requiring specificity (for correct nucleotide selection) as well as versatility (to accommodate different templates at every step) to maintain overall fidelity. Besides leading to these biological findings, our developed protocols open the door to other applications of transition path sampling to long-time, large-scale biomolecular reactions.

Motivation Understanding RNA's structural diversity is vital for identifying novel RNA structures and pursuing RNA genomics initiatives. By classifying RNA secondary motifs based on correlations between conserved RNA secondary structures and functional properties, we offer an avenue for predicting novel motifs. Although several RNA databases exist, no comprehensive schemes are available for cataloguing the range and diversity of RNA's structural repertoire. Results Our RNA-As-Graphs (RAG) database describes and ranks all mathematically possible (including existing and candidate) RNA secondary motifs on the basis of graphical enumeration techniques. We represent RNA secondary structures as two-dimensional graphs (networks), specifying the connectivity between RNA secondary structural elements, such as loops, bulges, stems and junctions. We archive RNA tree motifs as ‘tree graphs’ and other RNAs, including pseudoknots, as general ‘dual graphs’. All RNA motifs are catalogued by graph vertex number (a measure of sequence length) and ranked by topological complexity. The RAG inventory immediately suggests candidates for novel RNA motifs, either naturally occurring or synthetic, and thereby might stimulate the prediction and design of novel RNA motifs. Availability The database is accessible on the web at http://monod.biomath.nyu.edu/rna Contact schlick@nyu.edu

Hoogsteen base pairs within duplex DNA typically are only observed in regions containing significant distortion or near sites of drug intercalation. We report here the observation of a Hoogsteen base pair embedded within undistorted, unmodified B-DNA. The Hoogsteen base pair, consisting of a syn adenine base paired with an anti thymine base, is found in the 2.1 A resolution structure of the MATalpha2 homeodomain bound to DNA in a region where a specifically and a non-specifically bound homeodomain contact overlapping sites. NMR studies of the free DNA show no evidence of Hoogsteen base pair formation, suggesting that protein binding favors the transition from a Watson-Crick to a Hoogsteen base pair. Molecular dynamics simulations of the homeodomain-DNA complex support a role for the non-specifically bound protein in favoring Hoogsteen base pair formation. The presence of a Hoogsteen base pair in the crystal structure of a protein-DNA complex raises the possibility that Hoogsteen base pairs could occur within duplex DNA and play a hitherto unrecognized role in transcription, replication and other cellular processes.

Nanosecond dynamics simulations for DNA polymerase b (pol b)/DNA complexes with three mismatched base-pairs, namely GG, CA, or CC (primer/template) at the DNA polymerase active site, are performed to investigate the mechanism of polymerase opening and how the mispairs may affect the DNA extension step; these trajectories are compared to the behavior of a pol b/DNA complex with the correct GC base-pair, and assessed with the aid of targeted molecular dynamics (TMD) simulations of all systems from the closed to the open enzyme state. DNA polymerase conformational changes (subdomain closing and opening) have been suggested to play a critical role in DNA synthesis fidelity, since these changes are associated with the formation of the substrate-binding pocket for the nascent base-pair. Here we observe different large C-terminal subdomain (thumb) opening motions in the simulations of pol b with GC versus GG base-pairs. Whereas the conformation of pol b in the former approaches the observed open state in the crystal structures, the enzyme in the latter does not. Analyses of the motions of active-site protein/ DNA residues help explain these differences. Interestingly, rotation of Arg258 toward Asp192, which coordinates both active-site metal ions in the closed “active” complex, occurs rapidly in the GG simulation. We have previously suggested that this rotation is a key slow step in the closed to open transition. TMD simulations also point to a unique pathway for Arg258 rotation in the GG mispair complex. Simulations of the mismatched systems also reveal distorted geometries in the active site of all the mispair complexes examined. The hierarchy of the distortions (GG . CC . CA) parallels the experimentally deduced inability of pol b to extend these mispairs. Such local distortions would be expected to cause inefficient DNA extension and polymerase dissociation and thereby might lead to proofreading by an extrinsic exonuclease. Thus, our studies on the dynamics of pol b opening in mismatch systems provide structural and dynamic insights to explain experimental results regarding inefficient DNA extension following misincorporation; these details shed light on how proofreading may be invoked by the abnormal active-site geometry. q 2002 Elsevier Science Ltd. All rights reserved

Graph representations have been widely used to analyze and design various economic, social, military, political, and biological networks. In systems biology, networks of cells and organs are useful for understanding disease and medical treatments and, in structural biology, structures of molecules can be described, including RNA structures. In our RNA-As-Graphs (RAG) framework, we represent RNA structures as tree graphs by translating unpaired regions into vertices and helices into edges. Here we explore the modularity of RNA structures by applying graph partitioning known in graph theory to divide an RNA graph into subgraphs. To our knowledge, this is the first application of graph partitioning to biology, and the results suggest a systematic approach for modular design in general. The graph partitioning algorithms utilize mathematical properties of the Laplacian eigenvector (µ2) corresponding to the second eigenvalues (λ2) associated with the topology matrix defining the graph: λ2 describes the overall topology, and the sum of µ2's components is zero. The three types of algorithms, termed median, sign, and gap cuts, divide a graph by determining nodes of cut by median, zero, and largest gap of µ2's components, respectively. We apply these algorithms to 45 graphs corresponding to all solved RNA structures up through 11 vertices (∼ 220 nucleotides). While we observe that the median cut divides a graph into two similar-sized subgraphs, the sign and gap cuts partition a graph into two topologically-distinct subgraphs. We find that the gap cut produces the best biologically-relevant partitioning for RNA because it divides RNAs at less stable connections while maintaining junctions intact. The iterative gap cuts suggest basic modules and assembly protocols to design large RNA structures. Our graph substructuring thus suggests a systematic approach to explore the modularity of biological networks. In our applications to RNA structures, subgraphs also suggest design strategies for novel RNA motifs.

The cooperative folding of proteins implies a description by multibody potentials. Such multibody potentials can be generalized from common two-body statistical potentials through a relation to probability distributions of residue clusters via the Boltzmann condition. In this exploratory study, we compare a four-body statistical potential, defined by the Delaunay tessellation of protein structures, to the Miyazawa–Jernigan (MJ) potential for protein structure prediction, using a lattice chain growth algorithm. We use the four-body potential as a discriminatory function for conformational ensembles generated with the MJ potential and examine performance on a set of 22 proteins of 30–76 residues in length. We find that the four-body potential yields comparable results to the two-body MJ potential, namely, an average coordinate root-mean-square deviation (cRMSD) value of 8 A for the lowest energy configurations of all-α proteins, and somewhat poorer cRMSD values for other protein classes. For both two and four-body potentials, superpositions of some predicted and native structures show a rough overall agreement. Formulating the four-body potential using larger data sets and direct, but costly, generation of conformational ensembles with multibody potentials may offer further improvements. Proteins 2001;43:161–174. © 2001 Wiley-Liss, Inc.

Much progress has been achieved on quantitative assessment of electrostatic interactions on the all-atom level by molecular mechanics and dynamics, as well as on the macroscopic level by models of continuum solvation. Bridging of the two representations-an area of active research-is necessary for studying integrated functions of large systems of biological importance. Following perspectives of both discrete (N-body) interaction and continuum solvation, we present a new algorithm, DiSCO (Discrete Surface Charge Optimization), for economically describing the electrostatic field predicted by Poisson-Boltzmann theory using a discrete set of Debye-Huckel charges distributed on a virtual surface enclosing the macromolecule. The procedure in DiSCO relies on the linear behavior of the Poisson-Boltzmann equation in the far zone; thus contributions from a number of molecules may be superimposed, and the electrostatic potential, or equivalently the electrostatic field, may be quickly and efficiently approximated by the summation of contributions from the set of charges. The desired accuracy of this approximation is achieved by minimizing the difference between the Poisson-Boltzmann electrostatic field and that produced by the linearized Debye-Huckel approximation using our truncated Newton optimization package. DiSCO is applied here to describe the salt-dependent electrostatic environment of the nucleosome core particle in terms of several hundred surface charges. This representation forms the basis for modeling-by dynamic simulations (or Monte Carlo)-the folding of chromatin. DiSCO can be applied more generally to many macromolecular systems whose size and complexity warrant a model resolution between the all-atom and macroscopic levels.

Buckling transitions in superhelical DNA are sudden changes in shape that accompany a smooth variation in a key parameter, such as superhelical density. Here we explore the dependence of these transitions on the elastic constants for bending and twisting. A and C, important characteristics of DNA's bending and twisting persistence lengths. The large range we explore extends to other elastic materials with self-contact interactions, modeled here by a Debye-Huckel electrostatic potential. Our collective description of DNA shapes and energies over a wide range of p = A/C reveals a dramatic dependence of DNA shape and associated configurational transitions on p: transitions are sharp for large p but masked for small p. In particular, at small p, a nonplanar circular family emerges, in agreement with Julicher's recent analytical predictions: a continuum of forms (and associated writhing numbers) is also observed. The relevance of these buckling transitions to DNA in solution is examined through studies of size dependence and thermal effects. Buckling transitions smooth considerably as size increases, and this can be explained in part by the lower curvature in larger plasmids. This trend suggests that buckling transitions should not be detectable for isolated (i.e., unbound) DNA plasmids of biological interest, except possibly for very large p. Buckling phenomena would nonetheless be relevant for small DNA loops, particularly for higher values of p, and might have a role in regulatory mechanisms: a small change in superhelical stress could lead to a large configurational change. Writhe distributions as a function of p, generated by Langevin dynamics simulations, reveal the importance of thermal fluctuations. Each distribution range (and multipeaked shape) can be interpreted by our buckling profiles. Significantly, the distributions for moderate to high superhelical densities are most sensitive to p, isolating different distribution patterns. If this effect could be captured experimentally for small plasmids by currently available imaging techniques, such results suggest a slightly different experimental procedure for estimating the torsional stiffness of supercoiled DNA than considered to date.

Incorporating the cognate instead of non-cognate substrates is crucial for DNA polymerase function. Here we analyze molecular dynamics simulations of DNA polymerase μ (pol μ) bound to different non-cognate incoming nucleotides including A:dCTP, A:dGTP, A(syn):dGTP, A:dATP, A(syn):dATP, T:dCTP, and T:dGTP to study the structure-function relationships involved with aberrant base pairs in the conformational pathway; while a pol μ complex with the A:dTTP base pair is available, no solved non-cognate structures are available. We observe distinct differences of the non-cognate systems compared to the cognate system. Specifically, the motions of active-site residue His329 and Asp330 distort the active site, and Trp436, Gln440, Glu443 and Arg444 tend to tighten the nucleotide-binding pocket when non-cognate nucleotides are bound; the latter effect may further lead to an altered electrostatic potential within the active site. That most of these “gate-keeper” residues are located farther apart from the upstream primer in pol μ, compared to other X family members, also suggests an interesting relation to pol μ's ability to incorporate nucleotides when the upstream primer is not paired. By examining the correlated motions within pol μ complexes, we also observe different patterns of correlations between non-cognate systems and the cognate system, especially decreased interactions between the incoming nucleotides and the nucleotide-binding pocket. Altered correlated motions in non-cognate systems agree with our recently proposed hybrid conformational selection/induced-fit models. Taken together, our studies propose the following order for difficulty of non-cognate system insertions by pol μ: T:dGTP, Author Summary DNA polymerase μ (pol μ) is an enzyme that participates in DNA repair and thus has a central role in maintaining the integrity of genetic information. To efficiently repair the DNA, discriminating the cognate instead of non-cognate nucleotides (“fidelity-checking”) is required. Here we analyze molecular dynamics simulations of pol μ bound to different non-cognate nucleotides to study the structure-function relationships involved in the fidelity-checking mechanism of pol μ on the atomic level. Our results suggest that His329, Asp330, Trp436, Gln440, Glu443, and Arg444 are of great importance for pol μ's fidelity-checking mechanism. We also observe altered patterns of correlated motions within pol μ complex when non-cognate instead of cognate nucleotides are bound, which agrees with our recently proposed hybrid conformational selection/induced-fit models. Taken together, our studies help interpret the available kinetic data of various non-cognate nucleotide insertions by pol μ. We also suggest experimentally testable predictions; for example, a point mutation like E443M may reduce the ability of pol μ to insert the cognate more than of non-cognate nucleotides. Our studies suggest an interesting relation to pol μ's unique ability to incorporate nucleotides when the upstream primer is not paired.

The detailed structure and dynamics of the chromatin fibre and their relation to gene regulation represent important open biological questions. Recent advances in single-molecule force spectroscopy experiments have addressed these questions by directly measuring the forces that stabilize and alter the folded states of chromatin, and by investigating the mechanisms of fibre unfolding. We present examples that demonstrate how complementary modelling approaches have helped not only to interpret the experimental findings, but also to advance our knowledge of force-induced events such as unfolding of chromatin with dynamically bound linker histones and nucleosome unwrapping.

In recent papers, there has been a lively exchange concerning theories for enzyme catalysis, especially the role of protein dynamics/pre-chemistry conformational changes in the catalytic cycle of enzymes. Of particular interest is the notion that substrate-induced conformational changes that assemble the polymerase active site prior to chemistry are required for DNA synthesis and impact fidelity (i.e., substrate specificity). High-resolution crystal structures of DNA polymerase β representing intermediates of substrate complexes prior to the chemical step are available. These structures indicate that conformational adjustments in both the protein and substrates must occur to achieve the requisite geometry of the reactive participants for catalysis. We discuss computational and kinetic methods to examine possible conformational change pathways that lead from the observed crystal structure intermediates to the final structures poised for chemistry. The results, as well as kinetic data from site-directed mutagenesis studies, are consistent with models requiring pre-chemistry conformational adjustments in order to achieve high fidelity DNA synthesis. Thus, substrate-induced conformational changes that assemble the polymerase active site prior to chemistry contribute to DNA synthesis even when they do not represent actual rate-determining steps for chemistry.

DNA polymerases have essential roles in DNA replication and repair. Deciphering the subtle details of the dynamical motion of different polymerases may help in identifying common features of polymerase mechanisms. Here, we analyze by principal component and covariance analyses the essential motions of several X-family DNA polymerases (β, λ, X, and µ) bound to correct and incorrect nucleotides as well as mutant and misaligned DNA complexes bound to the correct nucleotide. Results reveal distinct trends in subdomain/active-site residue motions before correct and incorrect nucleotide insertion that correlate with misinsertion efficiency. For example, correct/incorrect nucleotides enhance/reduce certain correlated motions that impact proper assembly of the active site for catalysis. In like manner, pol λ aligned and misaligned DNA complexes show nearly identical correlated motions, which agrees with pol λ's efficient correct nucleotide insertion within both substrates. Moreover, mutations in pol β's regions of correlated motions have been shown to affect substrate binding, function, and fidelity. Such correlated motion of DNA polymerases can be useful in identifying potential mutations that impair polymerase function and fidelity. It also suggests a ligand-binding mechanism that merges induced-fit with conformational sampling and could assist in the development of therapeutic agents for DNA repair-related diseases.

A combination of detailed energy minimization and molecular dynamics studies of closed circular DNA offers here new information that may be relevant to the dynamics of short DNA chains and/or low superhelical densities. We find a complex dependence of supercoiled DNA energies and geometries on the linking number difference delta Lk as physiological superhelical densities (magnitude of sigma approximately 0.06) are approached. The energy minimization results confirm and extend predictions of classical elasticity theory for the equilibria of elastic rods. The molecular dynamics results suggest how these findings may affect the dynamics of supercoiled DNA. The minimization reveals sudden higher order configurational transitions in addition to the well-known catastrophic buckling from the circle to the figure-8. The competition among the bending, twisting, and self-contact forces leads to different families of supercoiled forms. Some of those families begin with configurations of near-zero twist. This offers the intriguing possibility that nicked DNA may relax to low-twist forms other than the circle, as generally assumed. Furthermore, for certain values of delta Lk, more than one interwound DNA minimum exists. The writhing number as a function of delta Lk is discontinuous in some ranges; it exhibits pronounced jumps as delta Lk is increased from zero, and it appears to level off to a characteristic slope only at higher values of delta Lk. These findings suggest that supercoiled DNA may undergo systematic rapid interconversions between different minima that are both close in energy and geometry. Our molecular dynamics simulations reveal such transitional behavior. We observe the macroscopic bending and twisting fluctuations of interwound forms about the global helix axis as well as the end-over-end tumbling of the DNA as a rigid body. The overall mobility can be related to magnitude of sigma and to the bending, twisting, and van der Waals energy fluctuations. The general character of molecular motions is thus determined by the types of energy minima found at a given delta Lk. Different time scales may be attributed to each type of motion: The overall chain folding occurs on a time scale almost an order of magnitude faster than the end-over-end tumbling. The local bending and twisting of individual chain residues occur at an even faster rate, which in turn correspond to several cycles of local variations for each large-scale bending and straightening motion of the DNA.

Understanding the structural organization of eukaryotic chromatin and its control of gene expression represents one of the most fundamental and open challenges in modern biology. Recent experimental advances have revealed important characteristics of chromatin in response to changes in external conditions and histone composition, such as the conformational complexity of linker DNA and histone tail domains upon compact folding of the fiber. In addition, modeling studies based on high-resolution nucleosome models have helped explain the conformational features of chromatin structural elements and their interactions in terms of chromatin fiber models. This minireview discusses recent progress and evidence supporting structural heterogeneity in chromatin fibers, reconciling apparently contradictory fiber models.

This chapter introduces further topics in nucleic acid structure, building upon the minitutorial of the previous chapter. These topics include DNA sequence effects, DNA hydration, DNA/protein interactions, and the cellular organization of DNA, including supercoiling and chromatin structure. The next chapter expands upon the related topics of alternative hydrogen bonding schemes, non-canonical helical and hybrid structures, DNA mimics, overstretched and understretched DNA, and RNA structure and folding.

The thiamine pyrophosphate (TPP) riboswitch employs modular domains for binding TPP to form a platform for gene expression regulation. Specifically, TPP binding triggers a conformational switch in the RNA from a transcriptionally active “on” state to an inactive “off” state that concomitantly causes the formation of a terminator hairpin and halting of transcription. Here, clustering analysis of energy landscapes at different nucleotide lengths suggests a novel computational tool for analysis of the mechanics of transcription elongation in the presence or absence of the ligand. Namely, we suggest that the riboswitch’s kinetics are tightly governed by a length-dependent switch, whereby the energy landscape has two clusters available during transcription elongation, and where TPP’s binding shifts the preference to one form. Significantly, the biologically active and inactive structures determined experimentally matched well the structures predominant in each computational set. These clustering/structural analyses combined with modular computational design suggest design principles that exploit the above features to analyze as well as create new functions and structures of RNA systems.

To elucidate the role of the histone tails in chromatin compaction and in higher-order folding of chromatin under physiological conditions, we extend a mesoscale model of chromatin [Arya, Zhang, and Schlick, Biophys. J. 91, 133 (2006); Arya and Schlick, Proc. Natl. Acad. Sci. USA 103, 16236 (2006)] to account for divalent cations (Mg2+) and linker histones. Configurations of 24-nucleosome oligonucleosomes in different salt environments and in the presence and absence of linker histones are sampled by a mixture of local and global Monte Carlo methods. Analyses of the resulting ensembles reveals a dynamic synergism between the histone tails, linker histones, and physiological ions in forming compact higher-order structures of chromatin. In the presence of monovalent salt alone, oligonucleosomes remain relatively unfolded and the histone tails do not mediate many internucleosomal interactions. Upon the addition of linker histones and divalent cations, the oligonucleosomes undergo a significant compaction triggered by: a dramatic increase in the internucleosomal interactions mediated by the histone tails; formation of a rigid linker DNA “stem” around the linker histones' C-terminal domains; and reducion in the electrostatic repulsion between linker DNAs via sharp bending in some linker DNAs caused by the divalent cations. Among all histone tails, the H4 tails mediate the most internucleosomal interactions, consistent with experimental observations, followed by the H3, H2A, and H2B tails in decreasing order. Apart from mediating internucleosomal interactions, the H3 tails also contribute to chromatin compaction by attaching to the entering and exiting linker DNA to screen electrotatic repulsion among the linker DNAs. This tendency of the H3 tails to attach to linker DNA, however, decreases significantly upon the addition of linker histones due to competition effects. The H2A and H2B tails do not mediate significant internucleosomal interactions but are important for mediating fiber/fiber intractions, especially in relatively unfolded chromatin in monovalent salt environments.

The nucleotidyl-transfer reaction coupled with the conformational transitions in DNA polymerases is critical for maintaining the fidelity and efficiency of DNA synthesis. We examine here the possible reaction pathways of a Y-family DNA polymerase, Sulfolobus solfataricus DNA polymerase IV (Dpo4), for the correct insertion of dCTP opposite 8-oxoguanine using the quantum mechanics/molecular mechanics (QM/MM) approach, both from a chemistry-competent state and a crystal closed state. The latter examination is important for understanding pre-chemistry barriers to interpret the entire enzyme mechanism, since the crystal closed state is not an ideal state for initiating the chemical reaction. The most favorable reaction path involves initial deprotonation of O3'H via two bridging water molecules to O1A, overcoming an overall potential energy barrier of approximately 20.0 kcal/mol. The proton on O1A-P(alpha) then migrates to the gamma-phosphate oxygen of the incoming nucleotide as O3' attacks P(alpha), and the P(alpha)-O3A bond breaks. The other possible pathway in which the O3'H proton is transferred directly to O1A on P(alpha) has an overall energy barrier of 25.0 kcal/mol. In both reaction paths, the rate-limiting step is the initial deprotonation, and the trigonal-bipyramidal configuration for P(alpha) occurs during the concerted bond formation (O3'-P(alpha)) and breaking (P(alpha)-O3A), indicating the associative nature of the chemical reaction. In contrast, the Dpo4/DNA complex with an imperfect active-site geometry corresponding to the crystal state must overcome a much higher activation energy barrier (29.0 kcal/mol) to achieve a tightly organized site due to hindered O3'H deprotonation stemming from larger distances and distorted conformation of the proton acceptors. This significant difference demonstrates that the pre-chemistry reorganization in Dpo4 costs approximately 4.0 to 9.0 kcal/mol depending on the primer terminus environment. Compared to the higher fidelity DNA polymerase beta from the X-family, Dpo4 has a higher chemical reaction barrier (20.0 vs 15.0 kcal/mol) due to the more solvent-exposed active site.

Summary: Our RNA-As-Graph-Pools (RagPools) web server offers a theoretical companion tool for RNA in vitro selection and related problems. Specifically, it suggests how to construct RNA sequence/structure pools with user-specified properties and assists in analyzing resulting distributions. This utility follows our recently developed approach for engineering sequence pools that links RNA sequence space regions with corresponding structural distributions via a ‘mixing matrix’ approach combined with a graph theory analysis of RNA secondary-structure space; the mixing matrix specifies nucleotide transition rates, and graph theory links sequences to simple graphical objects representing RNA motifs. The companion RagPools web server (‘Designer’ component) provides optimized starting sequences, mixing matrices and associated weights in response to a user-specified target pool structure distribution. In addition, RagPools (‘Analyzer’ component) analyzes the motif distribution of pools generated from user-specified starting sequences and mixing matrices. Thus, RagPools serves as a guide to researchers who aim to synthesize RNA pools with desired properties and/or experiment in silico with various designs by our approach.Availability: The web server is accessible on the web at http://rubin2.biomath.nyu.eduContact: schlick@nyu.edu

DNA polymerases are crucial constituents of the complex cellular machinery for replicating and repairing DNA. Discerning mechanistic pathways of DNA polymerase on the atomic level is important for revealing the origin of fidelity discrimination. Mammalian DNA polymerase beta (pol beta), a small (39 kDa) member of the X-family, represents an excellent model system to investigate polymerase mechanisms. Here, we explore several feasible low-energy pathways of the nucleotide transfer reaction of pol beta for correct (according to Watson-Crick hydrogen bonding) G:C basepairing versus the incorrect G:G case within a consistent theoretical framework. We use mixed quantum mechanics/molecular mechanics (QM/MM) techniques in a constrained energy minimization protocol to effectively model not only the reactive core but also the influence of the rest of the enzymatic environment and explicit solvent on the reaction. The postulated pathways involve initial proton abstraction from the terminal DNA primer O3'H group, nucleophilic attack that extends the DNA primer chain, and elimination of pyrophosphate. In particular, we analyze several possible routes for the initial deprotonation step: (i) direct transfer to a phosphate oxygen O(Palpha) of the incoming nucleotide, (ii) direct transfer to an active site Asp group, and (iii) transfer to explicit water molecules. We find that the most probable initial step corresponds to step (iii), involving initial deprotonation to water, which is followed by proton migration to active site Asp residues, and finally to the leaving pyrophosphate group, with an activation energy of about 15 kcal/mol. We argue that initial deprotonation steps (i) and (ii) are less likely as they are at least 7 and 11 kcal/mol, respectively, higher in energy. Overall, the rate-determining step for both the correct and the incorrect nucleotide cases is the initial deprotonation in concert with nucleophilic attack at the phosphate center; however, the activation energy we obtain for the mismatched G:G case is 5 kcal/mol higher than that of the matched G:C complex, due to active site structural distortions. Taken together, our results support other reported mechanisms and help define a framework for interpreting nucleotide specificity differences across polymerase families, in terms of the concept of active site preorganization or the so-called "pre-chemistry avenue".

With an increasing number of structural, kinetic, and modeling studies of diverse DNA polymerases in various contexts, a complex dynamical view of how atomic motions might define molecular "gates" or checkpoints that contribute to polymerase specificity and efficiency is emerging. Such atomic-level information can offer insights into rate-limiting conformational and chemical steps to help piece together mechanistic views of polymerases in action. With recent advances, modeling and dynamics simulations, subject to the well-appreciated limitations, can access transition states and transient intermediates along a reaction pathway, both conformational and chemical, and such information can help bridge the gap between experimentally determined equilibrium structures and mechanistic enzymology data. Focusing on DNA polymerase beta (pol beta), we present an emerging view of the geometric, energetic, and dynamic selection criteria governing insertion rate and fidelity mechanisms of DNA polymerases, as gleaned from various computational studies and based on the large body of existing kinetic and structural data. The landscape of nucleotide insertion for pol beta includes conformational changes, prechemistry, and chemistry "avenues", each with a unique deterministic or stochastic pathway that includes checkpoints for selective control of nucleotide insertion efficiency. For both correct and incorrect incoming nucleotides, pol beta's conformational rearrangements before chemistry include a cascade of slow and subtle side chain rearrangements, followed by active site adjustments to overcome higher chemical barriers, which include critical ion-polymerase geometries; this latter notion of a prechemistry avenue fits well with recent structural and NMR data. The chemical step involves an associative mechanism with several possibilities for the initial proton transfer and for the interaction among the active site residues and bridging water molecules. The conformational and chemical events and associated barriers define checkpoints that control enzymatic efficiency and fidelity. Understanding the nature of such active site rearrangements can facilitate interpretation of existing data and stimulate new experiments that aim to probe enzyme features that contribute to fidelity discrimination across various polymerases via such geometric, dynamic, and energetic selection criteria.