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Tamar Schlick

Publications and source records attributed to Tamar Schlick.

At least 19 recordsLinked to original sources
PubMed2025

The influence of 10n and 10n+5 linker lengths on chromatin fiber topologies explored by mesoscale modeling.

The structural organization of chromatin is intricately influenced by the length of linker DNA connecting nucleosomes. Some studies have suggested preferred linker lengths of 10n and 10n+5 base pairs (bp) (n = integer). Because these lengths dictate the rotational orientation of successive nucleosomes in the fiber axis, they can markedly affect chromatin fiber compaction and topology. Using a refined mesoscale chromatin model with 5-bp resolution, we investigate the influence of linker DNA periodicity, linker histone density, salt concentration, and starting fiber topology on chromatin architecture for regular fibers versus "life-like" fibers, the latter with irregular spacing between nucleosomes. Our results reveal that regular fibers with 10n linkers exhibit compact zigzag configurations, whereas 10n+5 linkers generate more open and flexible structures. However, these effects are pronounced only for short linker lengths, as longer linkers are more heterogeneous. Moreover, increased linker histone density further enhances compaction for long linker lengths, and lower salt concentration modifies chromatin topologies, diminishing periodicity-driven effects. In addition, any periodicity effect in tightly packed solenoid configurations is much less pronounced. All these trends for regular fibers are reduced in life-like fibers with irregularly spaced nucleosomes, despite having the same average spacing. Moreover, the trend details depend highly on specific features of the fiber architecture as designed in experiments and simulations. Overall, our study highlights how reported differences depend on modeling details and emphasizes the role of linker DNA length in regulating chromatin fiber architecture and its potential implications for genome accessibility and expression.

Chromatin↗
PubMed2025

Molecular dynamics simulations reveal subtle consequences of H3K9 and H3K27 tri-methylation on chromatin constituents.

Epigenetic modifications of histone tails are key mechanisms of genome regulation. In particular, tri-methylation of lysines (K) 9 and K27 of the histone H3 tail is important for genome silencing. In this work, we explore, using all-atom molecular dynamics simulations, the effect of these two epigenetic marks on the structure and interactions of the H3 tail in several contexts: isolated tails, nucleosomes, chromatosomes, and stacked nucleosomes. Overall, we find that although the isolated tails do not show significant conformational changes upon methylation, a more flexible and extended H3 tail compared to the native tail results in the nucleosome systems, with K9 methylation effects more pronounced. This change could facilitate the interaction of the tail with protein readers like heterochromatin protein 1 or Polycomb group. We also observe that both methylations increase the interactions of the H3 tail with the linker DNA in the context of the chromatosome, producing a chromatosome with tighter linker DNA, which could favor chromatin compaction. For stacked nucleosomes mimicking i±2 zigzag interactions, methylation of either K9 or K27 reduces the interactions of one of the H3 tails with its parental nucleosome and increases its interactions with the nonparental nucleosome, which could also help compact the chromatin fiber. In the three nucleosome-containing systems, we observe an asymmetry between the two tails, especially in the chromatosome, where one tail extends to interact with the linker DNA. This asymmetry modulates the effect that methylation has on each tail. Thus, overall, methylations of K9 and K27 have a subtle but notable impact on the H3 tail structure and its interactions within the chromatin fiber. These results help explain how this epigenetic modification compacts chromatin fibers and promotes longer-range interactions; these changes also guide how to approximate these effects in coarse-grained chromatin models.

Histones↗
PubMed2005

Modular RNA architecture revealed by computational analysis of existing pseudoknots and ribosomal RNAs.

Modular architecture is a hallmark of RNA structures, implying structural, and possibly functional, similarity among existing RNAs. To systematically delineate the existence of smaller topologies within larger structures, we develop and apply an efficient RNA secondary structure comparison algorithm using a newly developed two-dimensional RNA graphical representation. Our survey of similarity among 14 pseudoknots and subtopologies within ribosomal RNAs (rRNAs) uncovers eight pairs of structurally related pseudoknots with non-random sequence matches and reveals modular units in rRNAs. Significantly, three structurally related pseudoknot pairs have functional similarities not previously known: one pair involves the 3' end of brome mosaic virus genomic RNA (PKB134) and the alternative hammerhead ribozyme pseudoknot (PKB173), both of which are replicase templates for viral RNA replication; the second pair involves structural elements for translation initiation and ribosome recruitment found in the viral internal ribosome entry site (PKB223) and the V4 domain of 18S rRNA (PKB205); the third pair involves 18S rRNA (PKB205) and viral tRNA-like pseudoknot (PKB134), which probably recruits ribosomes via structural mimicry and base complementarity. Additionally, we quantify the modularity of 16S and 23S rRNAs by showing that RNA motifs can be constructed from at least 210 building blocks. Interestingly, we find that the 5S rRNA and two tree modules within 16S and 23S rRNAs have similar topologies and tertiary shapes. These modules can be applied to design novel RNA motifs via build-up-like procedures for constructing sequences and folds.

Algorithms↗
PubMed2004

Candidates for novel RNA topologies.

Because the functional repertiore of RNA molecules, like proteins, is closely linked to the diversity of their shapes, uncovering RNA's structural repertoire is vital for identifying novel RNAs, especially in genomic sequences. To help expand the limited number of known RNA families, we use graphical representation and clustering analysis of RNA secondary structures to predict novel RNA topologies and their abundance as a function of size. Representing the essential topological properties of RNA secondary structures as graphs enables enumeration, generation, and prediction of novel RNA motifs. We apply a probabilistic graph-growing method to construct the RNA structure space encompassing the topologies of existing and hypothetical RNAs and cluster all RNA topologies into two groups using topological descriptors and a standard clustering algorithm. Significantly, we find that nearly all existing RNAs fall into one group, which we refer to as "RNA-like"; we consider the other group "non-RNA-like". Our method predicts many candidates for novel RNA secondary topologies, some of which are remarkably similar to existing structures; interestingly, the centroid of the RNA-like group is the tmRNA fold, a pseudoknot having both tRNA-like and mRNA-like functions. Additionally, our approach allows estimation of the relative abundance of pseudoknot and other (e.g. tree) motifs using the "edge-cut" property of RNA graphs. This analysis suggests that pseudoknots dominate the RNA structure universe, representing more than 90% when the sequence length exceeds 120 nt; the predicted trend for <100 nt agrees with data for existing RNAs. Together with our predictions for novel "RNA-like" topologies, our analysis can help direct the design of functional RNAs and identification of novel RNA folds in genomes through an efficient topology-directed search, which grows much more slowly in complexity with RNA size compared to the traditional sequence-based search.

Algorithms↗
PubMed2004

Biomolecular free energy profiles by a shooting/umbrella sampling protocol, "BOLAS".

We develop an efficient technique for computing free energies corresponding to conformational transitions in complex systems by combining a Monte Carlo ensemble of trajectories generated by the shooting algorithm with umbrella sampling. Motivated by the transition path sampling method, our scheme "BOLAS" (named after a cowboy's lasso) preserves microscopic reversibility and leads to the correct equilibrium distribution. This makes possible computation of free energy profiles along complex reaction coordinates for biomolecular systems with a lower systematic error compared to traditional, force-biased umbrella sampling protocols. We demonstrate the validity of BOLAS for a bistable potential, and illustrate the method's scope with an application to the sugar repuckering transition in a solvated deoxyadenosine molecule.

Algorithms↗
PubMed2004

Deformations of promoter DNA bound to carcinogens help interpret effects on TATA-element structure and activity.

The TATA-box binding protein (TBP) is required by eukaryotic RNA polymerases for correct transcription initiation. TBP binds to the minor groove of an 8 base pair (bp) DNA-promoter element known as the TATA box and severely bends the TATA box. The promoter-DNA substrate can be damaged by components present in the cell or the environment to produce covalent carcinogen-DNA adducts. These may lead to transcription blockage or unfaithful transcription. Benzo[a]pyrene (BP) is a widespread environmental chemical carcinogen which can be metabolically converted to DNA-reactive enantiomeric (+) and (-)-anti-benzo[a]pyrene diol epoxides (BPDEs). Recent experimental studies of a pair of stereoisomeric adenine adducts, derived from (+) and (-)-anti-BPDEs, have revealed how these lesions influence the complexation of TBP with the TATA box. Depending on the adduct's location in the TATA box and its stereochemistry, the stability of monomeric TATA-TBP complexes was found to increase or decrease relative to the unmodified DNA. We report here analyses of molecular-dynamics simulations to interpret these findings. Structural analyses of 12 DNA-protein systems representing different combinations of adduct stereoisomer type and placement within the promoter reveal that the location of the adduct within the TATA octamer determines whether the stability of TATA-TBP complexes is increased or decreased. The effect on binding stability can be interpreted in terms of conformational freedom and major-groove space available to BP due to the hydrogen bonds and inserted phenylalanines of the TATA-TBP complex; that is, depending on the position of the adenine to which BP is covalently bound, BP can be accommodated in an intercalated or major-groove orientation with ease or with difficulty (due to interference with TATA-TBP interactions). The unravelled structures and interactions thus reveal the effect of different adduct locations on TATA-TBP complex formation and suggest how transcription initiation may be affected by the presence of a bulky BP.

Base Sequence↗
PubMed2004

Critical role of magnesium ions in DNA polymerase beta's closing and active site assembly.

To dissect the effects of the nucleotide-binding and catalytic metal ions on DNA polymerase mechanisms for DNA repair and synthesis, aside from the chemical reaction, we investigate their roles in the conformational transitions between closed and open states and assembly/disassembly of the active site of polymerase beta/DNA complexes before and after the chemical reaction of nucleotide incorporation. Using dynamics simulations, we find that closing before chemical reaction requires both divalent metal ions in the active site while opening after the chemical reaction is triggered by release of the catalytic metal ion. The critical closing is stabilized by the interaction of the incoming nucleotide with conserved catalytic residues (Asp190, Asp192, Asp256) and the two functional magnesium ions; without the catalytic ion, other protein residues (Arg180, Arg183, Gly189) coordinate the incomer's triphosphate group through the nucleotide-binding ion. Because we also note microionic heterogeneity near the active site, Mg(2+) and Na(+) ions can diffuse into the active site relatively rapidly, we suggest that the binding of the catalytic ion itself is not a rate-limiting conformational or overall step. However, geometric adjustments associated with functional ions and proper positioning in the active site, including subtle but systematic motions of protein side chains (e.g., Arg258), define slow or rate-limiting conformational steps that may guide fidelity mechanisms. These sequential rearrangements are likely sensitively affected when an incorrect nucleotide approaches the active site. Our suggestion that subtle and slow adjustments of the nucleotide-binding and catalytic magnesium ions help guide polymerase selection for the correct nucleotide extends descriptions of polymerase pathways and underscores the importance of the delicate conformational events both before and after the chemical reaction to polymerase efficiency and fidelity mechanisms.

Binding Sites↗
PubMed2004

RAG: RNA-As-Graphs web resource.

BACKGROUND: The proliferation of structural and functional studies of RNA has revealed an increasing range of RNA's structural repertoire. Toward the objective of systematic cataloguing of RNA's structural repertoire, we have recently described the basis of a graphical approach for organizing RNA secondary structures, including existing and hypothetical motifs. DESCRIPTION: We now present an RNA motif database based on graph theory, termed RAG for RNA-As-Graphs, to catalogue and rank all theoretically possible, including existing, candidate and hypothetical, RNA secondary motifs. The candidate motifs are predicted using a clustering algorithm that classifies RNA graphs into RNA-like and non-RNA groups. All RNA motifs are filed according to their graph vertex number (RNA length) and ranked by topological complexity. CONCLUSIONS: RAG's quantitative cataloguing allows facile retrieval of all classes of RNA secondary motifs, assists identification of structural and functional properties of user-supplied RNA sequences, and helps stimulate the search for novel RNAs based on predicted candidate motifs.

Computational Biology↗
PubMed2004

Orchestration of cooperative events in DNA synthesis and repair mechanism unraveled by transition path sampling of DNA polymerase beta's closing.

Our application of transition path sampling to a complex biomolecular system in explicit solvent, the closing transition of DNA polymerase beta, 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 beta 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.

DNA Polymerase beta↗
PubMed2004

Structural motifs in ribosomal RNAs: implications for RNA design and genomics.

The various motifs of RNA molecules are closely related to their structural and functional properties. To better understand the nature and distributions of such structural motifs (i.e., paired and unpaired bases in stems, junctions, hairpin loops, bulges, and internal loops) and uncover characteristic features, we analyze the large 16S and 23S ribosomal RNAs of Escherichia coli. We find that the paired and unpaired bases in structural motifs have characteristic distribution shapes and ranges; for example, the frequency distribution of paired bases in stems declines linearly with the number of bases, whereas that for unpaired bases in junctions has a pronounced peak. Significantly, our survey reveals that the ratio of total (over the entire molecule) unpaired to paired bases (0.75) and the fraction of bases in stems (0.6), junctions (0.16), hairpin loops (0.12), and bulges/internal loops (0.12) are shared by 16S and 23S ribosomal RNAs, suggesting that natural RNAs may maintain certain proportions of bases in various motifs to ensure structural integrity. These findings may help in the design of novel RNAs and in the search (via constraints) for RNA-coding motifs in genomes, problems of intense current focus.

Base Sequence↗
PubMed2004

RAG: RNA-As-Graphs database--concepts, analysis, and features.

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

Algorithms↗
PubMed2004

Highly organized but pliant active site of DNA polymerase beta: compensatory mechanisms in mutant enzymes revealed by dynamics simulations and energy analyses.

To link conformational transitions noted for DNA polymerases with kinetic results describing catalytic efficiency and fidelity, we investigate the role of key DNA polymerase beta residues on subdomain motion through simulations of five single-residue mutants: Arg-283-Ala, Tyr-271-Ala, Asp-276-Val, Arg-258-Lys, and Arg-258-Ala. Since a movement toward a closed state was only observed for R258A, we suggest that Arg(258) is crucial in modulating motion preceding chemistry. Analyses of protein/DNA interactions in the mutant active site indicate distinctive hydrogen bonding and van der Waals patterns arising from compensatory structural adjustments. By comparing closed mutant complexes with the wild-type enzyme, we interpret experimentally derived nucleotide binding affinities in molecular terms: R283A (decreased), Y271A (increased), D276V (increased), and R258A (decreased). Thus, compensatory interactions (e.g., in Y271A with adjacent residues Phe(272), Asn(279), and Arg(283)) increase the overall binding affinity for the incoming nucleotide although direct interactions may decrease. Together with energetic analyses, we predict that R258G might increase the rate of nucleotide insertion and maintain enzyme fidelity as R258A; D276L might increase the nucleotide binding affinity more than D276V; and R283A/K280A might decrease the nucleotide binding affinity and increase misinsertion more than R283A. The combined observations regarding key roles of specific residues (e.g., Arg(258)) and compensatory interactions echo the dual nature of polymerase active site, namely versatility (to accommodate various basepairs) and specificity (for preserving fidelity) and underscore an organized but pliant active site essential to enzyme function.

Binding Sites↗
PubMed2004

In silico evidence for DNA polymerase-beta's substrate-induced conformational change.

Structural information for mammalian DNA pol-beta combined with molecular and essential dynamics studies have provided atomistically detailed views of functionally important conformational rearrangements that occur during DNA repair and replication. This conformational closing before the chemical reaction is explored in this work as a function of the bound substrate. Anchors for our study are available in crystallographic structures of the DNA pol-beta in "open" (polymerase bound to gapped DNA) and "closed" (polymerase bound to gapped DNA and substrate, dCTP) forms; these different states have long been used to deduce that a large-scale conformational change may help the polymerase choose the correct nucleotide, and hence monitor DNA synthesis fidelity, through an "induced-fit" mechanism. However, the existence of open states with bound substrate and closed states without substrates suggest that substrate-induced conformational closing may be more subtle. Our dynamics simulations of two pol-beta/DNA systems (with/without substrates at the active site) reveal the large-scale closing motions of the thumb and 8-kDa subdomains in the presence of the correct substrate--leading to nearly perfect rearrangement of residues in the active site for the subsequent chemical step of nucleotidyl transfer--in contrast to an opening trend when the substrate is absent, leading to complete disassembly of the active site residues. These studies thus provide in silico evidence for the substrate-induced conformational rearrangements, as widely assumed based on a variety of crystallographic open and closed complexes. Further details gleaned from essential dynamics analyses clarify functionally relevant global motions of the polymerase-beta/DNA complex as required to prepare the system for the chemical reaction of nucleotide extension.

Binding Sites↗
PubMed2003

Exploring the repertoire of RNA secondary motifs using graph theory; implications for RNA design.

Understanding the structural repertoire of RNA is crucial for RNA genomics research. Yet current methods for finding novel RNAs are limited to small or known RNA families. To expand known RNA structural motifs, we develop a two-dimensional graphical representation approach for describing and estimating the size of RNA's secondary structural repertoire, including naturally occurring and other possible RNA motifs. We employ tree graphs to describe RNA tree motifs and more general (dual) graphs to describe both RNA tree and pseudoknot motifs. Our estimates of RNA's structural space are vastly smaller than the nucleotide sequence space, suggesting a new avenue for finding novel RNAs. Specifically our survey shows that known RNA trees and pseudoknots represent only a small subset of all possible motifs, implying that some of the 'missing' motifs may represent novel RNAs. To help pinpoint RNA-like motifs, we show that the motifs of existing functional RNAs are clustered in a narrow range of topological characteristics. We also illustrate the applications of our approach to the design of novel RNAs and automated comparison of RNA structures; we report several occurrences of RNA motifs within larger RNAs. Thus, our graph theory approach to RNA structures has implications for RNA genomics, structure analysis and design.

Algorithms↗
PubMed2003

Inherent speedup limitations in multiple time step/particle mesh Ewald algorithms.

Multiple time step (MTS) algorithms present an effective integration approach to reduce the computational cost of dynamics simulations. By using force splitting to allow larger time steps for the more slowly varying force components, computational savings can be realized. The Particle-Mesh-Ewald (PME) method has been independently devised to provide an effective and efficient treatment of the long-range electrostatics interactions. Here we examine the performance of a combined MTS/PME algorithm previously developed for AMBER on a large polymerase beta/DNA complex containing 40,673 atoms. Our goal is to carefully combine the robust features of the Langevin/MTS (LN) methodology implemented in CHARMM-which uses position rather than velocity Verlet with stochasticity to make possible outer time steps of 150 fs-with the PME formulation. The developed MTS/PME integrator removes fast terms from the reciprocal-space Ewald component by using switch functions. We analyze the advantages and limitations of the resulting scheme by comparing performance to the single time step leapfrog Verlet integrator currently used in AMBER by evaluating different time-step protocols using three assessors for accuracy, speedup, and stability, all applied to long (i.e., nanosecond) simulations to ensure proper energy conservation. We also examine the performance of the algorithm on a parallel, distributed shared-memory computer (SGI Origin 2000 with 8 300-MHz R12000 processors). Good energy conservation and stability behavior can be demonstrated, for Newtonian protocols with outer time steps of up to 8 fs and Langevin protocols with outer time steps of up to 16 fs. Still, we emphasize the inherent limitations imposed by the incorporation of MTS methods into the PME formulation that may not be widely appreciated. Namely, the limiting factor on the largest outer time-step size, and hence speedup, is an intramolecular cancellation error inherent to PME. This error stems from the excluded-nonbonded correction term contained in the reciprocal-space component. This cancellation error varies in time and introduces artificial frequencies to the governing dynamics motion. Unfortunately, we find that this numerical PME error cannot be easily eliminated by refining the PME parameters (grid resolution and/or order of interpolating polynomial). We suggest that methods other than PME for fast electrostatics may allow users to reap the full advantages from MTS algorithms.

Algorithms↗
PubMed2003

Sequence-dependent solution structure and motions of 13 TATA/TBP (TATA-box binding protein) complexes.

The TATA element is a well-known example of a DNA promoter sequence recognized by the TATA box binding protein (TBP) through its intrinsic motion and deformability. Although TBP recognizes the TATA element octamer unusually (through the minor groove, which lacks the distinctive features of the major groove), single base-pair replacements alter transcriptional activity. Recent crystallographic experiments have suggested that TATA/TBP complexes differing by a single base pair retain substantial structural similarity despite their functional differences in activating transcription. To investigate the subtle role of sequence-dependent motion within the TATA element and certain aspects of its effect on assembly of the transcriptional complex, we examine 5-ns dynamics trajectories of 13 variant TATA/TBP complexes differing from each other by a single base pair. They include the wild-type (WT) adenovirus 2 major late promoter (AdMLP) TATA element, TATAAAAG (the octamer specifies positions -31 to -24 with respect to the transcription initiation site), and the variants A31 (i.e., AATAAAAG), T30, A29, C29, G28, T28, T27, G26, T26, C25, T25, and T24. Our simulated TATA/TBP complexes develop sequence-dependent structure and motion trends that may lead to favorable orientations for high-activity variants (with respect to binding TFIIA, TFIIB, and other transcription factors), while conversely, accelerate dissociation of low-activity TATA/TBP complexes. The motions that promote favorable geometries for preinitiation complexes include small rotations between TBP's N- and C-terminal domains, sense strand DNA backbone "slithering," and rotations in TBP's H2 and H2' helices. Low-activity variants tend to translate the H1 and H1' helices and withdraw the intercalating phenylalanines. These cumulative DNA and protein motions lead to a spatial spread of complex orientations up to 4 A; this is associated with an overall bend of the variant TATA/TBP complexes that spans 93 degrees to 110 degrees (107 degrees for the crystal reference). Taken together, our analyses imply larger differences when these local structural and bending changes are extended to longer DNA (upstream and downstream) and suggest that specific local TATA/TBP motions (e.g., shifts in TBP helices and TATA bases and backbone) play a role in modulating the formation and maintenance of the transcription initiation complex.

Base Sequence↗
PubMed2003

Constructing irregular surfaces to enclose macromolecular complexes for mesoscale modeling using the discrete surface charge optimization (DISCO) algorithm.

Salt-mediated electrostatics interactions play an essential role in biomolecular structures and dynamics. Because macromolecular systems modeled at atomic resolution contain thousands of solute atoms, the electrostatic computations constitute an expensive part of the force and energy calculations. Implicit solvent models are one way to simplify the model and associated calculations, but they are generally used in combination with standard atomic models for the solute. To approximate electrostatics interactions in models on the polymer level (e.g., supercoiled DNA) that are simulated over long times (e.g., milliseconds) using Brownian dynamics, Beard and Schlick have developed the DiSCO (Discrete Surface Charge Optimization) algorithm. DiSCO represents a macromolecular complex by a few hundred discrete charges on a surface enclosing the system modeled by the Debye-Hückel (screened Coulombic) approximation to the Poisson-Boltzmann equation, and treats the salt solution as continuum solvation. DiSCO can represent the nucleosome core particle (>12,000 atoms), for example, by 353 discrete surface charges distributed on the surfaces of a large disk for the nucleosome core particle and a slender cylinder for the histone tail; the charges are optimized with respect to the Poisson-Boltzmann solution for the electric field, yielding a approximately 5.5% residual. Because regular surfaces enclosing macromolecules are not sufficiently general and may be suboptimal for certain systems, we develop a general method to construct irregular models tailored to the geometry of macromolecules. We also compare charge optimization based on both the electric field and electrostatic potential refinement. Results indicate that irregular surfaces can lead to a more accurate approximation (lower residuals), and the refinement in terms of the electric field is more robust. We also show that surface smoothing for irregular models is important, that the charge optimization (by the TNPACK minimizer) is efficient and does not depend on the initial assigned values, and that the residual is acceptable when the distance to the model surface is close to, or larger than, the Debye length. We illustrate applications of DiSCO's model-building procedure to chromatin folding and supercoiled DNA bound to Hin and Fis proteins. DiSCO is generally applicable to other interesting macromolecular systems for which mesoscale models are appropriate, to yield a resolution between the all-atom representative and the polymer level.

Algorithms↗