On the truncation of long-range electrostatic interactions in DNA

Long-range interactions are known to play an important role in highly polar biomolecules like DNA. In molecular dynamics simulations of nucleic acids and proteins, an accurate treatment of the long-range interactions are crucial for achieving stable nanosecond trajectories. In this report, we evaluate the structural and dynamic effects on a highly charged oligonucleotide in aqueous solution from different long-range truncation methods. Two group-based truncation methods, one with a switching function and one with a force-switching function were found to fail to give accurate stable trajectories close to the crystal structure. For these group-based truncation methods, large root mean square (rms) deviations from the initial structure were obtained and severe distortions of the oligonucleotide were observed. Another group-based truncation scheme, which used an abrupt truncation at 8. 0 A or at 12.0 A was also investigated. For the short cutoff distance, the conformations deviated far away from the initial structure and were significantly distorted. However, for the longer cutoff, where all necessary electrostatic interactions were included, the trajectory was quite stable. For the particle mesh Ewald (PME) truncation method, a stable DNA simulation with a heavy atom rms deviation of 1.5 A was obtained. The atom-based truncation methods also resulted in stable trajectories, according to the rms deviation from the initial B-DNA structure, of between 1.5 and 1.7 A for the heavy atoms. In these stable simulations, the heavy atom rms deviations were approximately 0.6-1.0 A lower for the bases than for the backbone. An increase of the cutoff radius from 8 to 12 A decreased the rms deviation by approximately 0.2 A for the atom-based truncation method with a force-shifting function, but increased the computational time by a factor of 2. Increasing the cutoff from 12 to 18 A for the atom-based truncation method with a force-shifting function requires 2-3 times more computational time, but did not significantly change the rms deviation. Similar rms deviations from the initial structure were found for the atom-based method with a force-shifting function and for the PME method. The computational cost was longer for the PME method with a cutoff of 12. 0 A for the direct space nonbonded calculations than for the atom-based truncation method with a force-shifting function and a cutoff of 12.0 A. If a nonperiodic boundary, e.g., a spherical boundary, was used, a considerable speedup could be achieved. From the rms fluctuations, the terminal nucleotides and especially the cytidines were found to be more flexible than the nonterminal nucleotides. The B-DNA form of the oligonucleotide was maintained throughout the simulations and is judged to depend on the parameters of the energy function and not on the truncation method used to handle the long-range electrostatic interactions. To perform accurate and stable simulations of highly charged biological macromolecules, we recommend that the atom-based force-shift method or the PME method should be used for the long-range electrostatics interactions.     

The sampling properties of some distance geometry algorithms applied to unconstrained polypeptide chains: a study of 1830 independently computed conformations

In this paper we study the statistical geometry of ensembles of poly (L-alanine) conformations computed by several different distance geometry algorithms. Since basic theory only permits us to predict the statistical properties of such ensembles a priori when the distance constraints have a very simple form, the only constraints used for these calculations are those necessary to obtain reasonable bond lengths and angles, together with a lack of short- and long-range atomic overlaps. The geometric properties studied include the squared end-to-end distance and radius of gyration of the computed conformations, in addition to the usual rms coordinate and phi/psi angle deviations among these conformations. The distance geometry algorithms evaluated include several variations of the well-known embed algorithm, together with optimizations of the torsion angles using the ellipsoid and variable target function algorithms. The conclusions may be summarized as follows: First, the distribution with which the trial distances are chosen in most implementations of the embed algorithm is not appropriate when no long-range upper bounds on the distances are present, because it leads to unjustifiably expanded conformations. Second, chosing the trial distances independently of one another leads to a lack of variation in the degree of expansion, which in turn produces a relatively low rms square coordinate difference among the members of the ensemble. Third, when short-range steric constraints are present, torsion angle optimizations that start from conformations obtained by choosing their phi/psi angles randomly with a uniform distribution between -180 degrees and +180 degrees do not converge to conformations whose angles are uniformly distributed over the sterically allowed regions of the phi/psi plane. Finally, in an appendix we show how the sampling obtained with the embed algorithm can be substantially improved upon by the proper application of existing methodology.     

An evaluation of implicit and explicit solvent model systems for the molecular dynamics simulation of bacteriophage T4 lysozyme

In this report we examine several solvent models for use in molecular dynamics simulations of protein molecules with the Discover program from Biosym Technologies. Our goal was to find a solvent system which strikes a reasonable balance among theoretical rigor, computational efficiency, and experimental reality. We chose phage T4 lysozyme as our model protein and analyzed 14 simulations using different solvent models. We tested both implicit and explicit solvent models using either a linear distance-dependent dielectric or a constant dielectric. Use of a linear distance-dependent dielectric with implicit solvent significantly diminished atomic fluctuations in the protein and kept the protein close to the starting crystal structure. In systems using a constant dielectric and explicit solvent, atomic fluctuations were much greater and the protein was able to sample a larger portion of conformational space. A series of nonbonded cutoff distances (9.0, 11.5, 15.0, 20.0 Å) using both abrupt and smooth truncation of the nonbonded cutoff distances were tested. The method of dual cutoffs was also tested. We found that a minimum nonbonded cutoff distance of 15.0 Å was needed in order to properly couple solvent and solute. Distances shorter than 15.0 Å resulted in a significant temperature gradient between the solvent and solute. In all trajectories using the proprietary Discover switching function, we found significant denaturation in the protein backbone; we were able to run successful trajectories only in those simulations that used no switching function. We were able to significantly reduce the computational burden by using dual cutoffs and still calculate a quality trajectory. In this method, we found that an outer cutoff distance of 15.0 Å and an inner cutoff distance of 11.5 worked well. While a 10 Å shell of explicit water yielded the best results, a 6 A shell of water yielded satisfactory results with nearly a 40% reduction in computational cost. © 1994 John Wiley & Sons, Inc.     

酵母基因上游区与内含子可能的短程和长程转录协同增效作用

根据实验观察到的DNA成环和弯折机制,以140bp为分界点,探讨高频转录基因上游区与内含子之间可能存在的短程和长程转录协同增效作用（synergy）。用与随机序列做对比的方法,抽提出最近距离在140bp以下的寡核苷酸对,以及最近距离在140bp以上的寡核苷酸对。仔细分析两种距离下的可能的协同寡核苷酸对的位置特征和碱基组分,发现短程协同作用的寡核苷酸对的平均最近距离都在110bp以下,位于上游区的CCAA是一个很明显的特征;而长程协同作用的寡核苷酸对的平均最近距离集中在250-400bp,并且在多数寡核苷酸对中,位于上游区的寡核苷酸是GC丰富的正调控元件。     

Analysis of the relative contributions of the nuclear Overhauser interproton distance restraints and the empirical energy function in the calculation of oligonucleotide structures using restrained molecular dynamics

The relative contributions of the interproton distance restraints derived from nuclear Overhauser enhancement measurements and of the empirical energy function in the determination of oligonucleotide structures by restrained molecular dynamics are investigated. The calculations are based on 102 intraresidue and 126 interresidue interproton distance restraints derived from short mixing time two-dimensional nuclear Overhauser enhancement data on the dodecamer 5'd(CGCGPATTCGCG)2 [Clore, G.M., Oschkinat, H., McLaughlin, L.W., Benseler, F., Scalfi Happ, C., Happ, E., & Gronenborn, A.M. (1988) Biochemistry 27, 4185-4197]. Eight interproton distance restraint lists were made up with errors ranging from -0.1/+0.2 to -1.2/+1.3 A for r less than 2.5 A and from -0.2/+0.3 to -1.3/+1.4 A for r greater than or equal to 2.5 A. These restraints were incorporated into the total energy function of the system in the form of square-well potentials with force constants set sufficiently high to ensure that the deviations between calculated distances and experimental restraints were very small (average interproton distance rms deviation of less than 0.06 A). For each data set, six calculations were carried out, three starting from classical A-DNA and three from classical B-DNA. The results show that structural changes occurring during the course of restrained molecular dynamics and the degree of structural convergence are determined by the interproton distance restraints. All the structures display similar small deviations from idealized geometry and have the same values for the nonbonding energy terms comprising van der Waals, electrostatic, and hydrogen-bonding components. Thus, the function of the empirical energy function is to maintain near perfect stereochemistry and nonbonded interactions.(ABSTRACT TRUNCATED AT 250 WORDS)     

Weighted neighbor joining: a likelihood-based approach to distance-based phylogeny reconstruction

We introduce a distance-based phylogeny reconstruction method called "weighted neighbor joining," or "Weighbor" for short. As in neighbor joining, two taxa are joined in each iteration; however, the Weighbor criterion for choosing a pair of taxa to join takes into account that errors in distance estimates are exponentially larger for longer distances. The criterion embodies a likelihood function on the distances, which are modeled as correlated Gaussian random variables with different means and variances, computed under a probabilistic model for sequence evolution. The Weighbor criterion consists of two terms, an additivity term and a positivity term, that quantify the implications of joining the pair. The first term evaluates deviations from additivity of the implied external branches, while the second term evaluates confidence that the implied internal branch has a positive branch length. Compared with maximum-likelihood phylogeny reconstruction, Weighbor is much faster, while building trees that are qualitatively and quantitatively similar. Weighbor appears to be relatively immune to the "long branches attract" and "long branch distracts" drawbacks observed with neighbor joining, BIONJ, and parsimony.     

Explicit-solvent molecular dynamics simulations of a DNA tetradecanucleotide duplex: lattice-sum versus reaction-field electrostatics

Five long-timescale (10 ns) explicit-solvent molecular dynamics simulations of a DNA tetradecanucleotide dimer are performed using the GROMOS 45A4 force field and the simple-point-charge water model, in order to investigate the effect of the treatment of long-range electrostatic interactions as well as of the box shape and size on the structure and dynamics of the molecule (starting from an idealised B-DNA conformation). Long-range electrostatic interactions are handled using either a lattice-sum (LS) method (particle–particle–particle–mesh; one simulation performed within a cubic box) or a cutoff-based reaction-field (RF) method (four simulations, with long-range cutoff distances of 1.4 or 2.0 nm and performed within cubic or truncated octahedral periodic boxes). The overall double-helical structure, including Watson–Crick (WC) base-pairing, is well conserved in the simulation employing the LS scheme. In contrast, the WC base-pairing is nearly completely disrupted in the four simulations employing the RF scheme. These four simulations result in highly distorted compact (cutoff distance of 1.4 nm) or extended (cutoff distance of 2 nm) structures, irrespective of the shape and size of the computational box. These differences observed between the two schemes seem correlated with large differences in the radial distribution function between charged entities (backbone phosphate groups and sodium counterions) within the system.     

MC-Net: a method for the construction of phylogenetic networks based on the Monte-Carlo method

Background  

A phylogenetic network is a generalization of phylogenetic trees that allows the representation of conflicting signals or alternative evolutionary histories in a single diagram. There are several methods for constructing these networks. Some of these methods are based on distances among taxa. In practice, the methods which are based on distance perform faster in comparison with other methods. The Neighbor-Net (N-Net) is a distance-based method. The N-Net produces a circular ordering from a distance matrix, then constructs a collection of weighted splits using circular ordering. The SplitsTree which is a program using these weighted splits makes a phylogenetic network. In general, finding an optimal circular ordering is an NP-hard problem. The N-Net is a heuristic algorithm to find the optimal circular ordering which is based on neighbor-joining algorithm.     

Local electrostatic optimization in proteins.

A simple electrostatic model has been used to investigate the extent to which the structure of protein molecules is organized to optimize the internal electrostatic interactions. We find that the model provides a favorable total intra-protein electrostatic energy for almost all polar and charged groups of atoms, suggesting a high degree of structural optimization. By contrast, a significant fraction of individual group-group interactions are found to be unfavorable. An analysis as a function of the range of interactions included shows the electrostatic organization is generally relatively short range (up to 6 or 7 A between group centers). Although the model is very simple, it is useful for assessing the overall quality of protein experimental structures, for pin-pointing some types of errors and as a guide to improving protein design.     

Application of distance geometry to protein tertiary structure calculations

A general approach to the problem of molecular conformation is advanced. We describe a formalism that permits experimental and theoretical information to be incorporated into a set of upper and lower bounds on intramolecular distances. Structures (conformations) meeting these bounds can be readily generated and compared with each other. To illustrate the use of the method, we have employed a simple “firehose” model for protein folding to predict the long-range hydrophobic interactions in a small protein: pancreatic trypsin inhibitor. Models of this type lead to the proper hairpin turns and a reasonable set of long-range contacts for this protein. Application of the distance geometry method then yields backbone conformations with errors of 4–8 Å compared to the native structure. We discuss both the merits and shortcomings of the firehose model and the relation between distance geometry and energy minimization techniques.     

Correlation analysis of dissimilarity matrices

Distance-based methods have been a valuable tool for ecologists for decades. Indirectly, distance-based ordination and cluster analysis, in particular, have been widely practiced as they allow the visualization of a multivariate data set in a few dimensions. The explicitly distance-based Mantel test and multiple regression on distance matrices (MRM) add hypothesis testing to the toolbox. One concern for ecologists wishing to use these methods lies in deciding whether to combine data vectors into a compound multivariate dissimilarity to analyze them individually. For Euclidean distances on scaled data, the correlation of a pair of multivariate distance matrices can be calculated from the correlations between the two sets of individual distance matrices if one set is orthogonal, demonstrating a clear link between individual and compound distances. The choice between Mantel and MRM should be driven by ecological hypotheses rather than mathematical concerns. The relationship between individual and compound distance matrices also provides a means for calculating the maximum possible value of the Mantel statistic, which can be considerably less than 1 for a given analysis. These relationships are demonstrated with simulated data. Although these mathematical relationships are only strictly true for Euclidean distances when one set of variables is orthogonal, simulations show that they are approximately true for weakly correlated variables and Bray–Curtis dissimilarities.     

Phylogenetic Inference with Weighted Codon Evolutionary Distances

We develop a new approach to estimate a matrix of pairwise evolutionary distances from a codon-based alignment based on a codon evolutionary model. The method first computes a standard distance matrix for each of the three codon positions. Then these three distance matrices are weighted according to an estimate of the global evolutionary rate of each codon position and averaged into a unique distance matrix. Using a large set of both real and simulated codon-based alignments of nucleotide sequences, we show that this approach leads to distance matrices that have a significantly better treelikeness compared to those obtained by standard nucleotide evolutionary distances. We also propose an alternative weighting to eliminate the part of the noise often associated with some codon positions, particularly the third position, which is known to induce a fast evolutionary rate. Simulation results show that fast distance-based tree reconstruction algorithms on distance matrices based on this codon position weighting can lead to phylogenetic trees that are at least as accurate as, if not better, than those inferred by maximum likelihood. Finally, a well-known multigene dataset composed of eight yeast species and 106 codon-based alignments is reanalyzed and shows that our codon evolutionary distances allow building a phylogenetic tree which is similar to those obtained by non-distance-based methods (e.g., maximum parsimony and maximum likelihood) and also significantly improved compared to standard nucleotide evolutionary distance estimates.     

Molecular Dynamics Simulations of Proteins in Water Without the Truncation of Long-range Coulomb Interactions

A new program package (COSMOS90) for molecular dynamics simulations was developed to simulate large molecular systems consisting of more than tens of thousands of atoms without the truncation of long-range coulomb interactions. This program package was based on a new approximation scheme (PPPC) for calculating efficiently the coulomb interactions without sacrificing accuracy. In this approximation scheme, the group of charges at a long distance from each atom was represented by a total charge and total dipole moment of the group. In order to assess the accuracy of PPPC and the ability of COSMOS90, molecular dynamics simulations were carried out for a large system consisting of 16108 atoms (human lysozyme in water) for 50 ps using this program package. The coulomb energy per solute atom was calculated with only five percent of the error found in the 10 Å cut-off approximation (about 0.9 kcal/mol versus 18 kcal/mol, respectively). The molecular dynamics simulations using COSMOS90 require no more CPU time than the simulations based on the 10 Å cut-off approximation of the conventional programs for macromolecular simulations.     

Improvement of distance-based phylogenetic methods by a local maximum likelihood approach using triplets

We introduce a new approach to estimate the evolutionary distance between two sequences. This approach uses a tree with three leaves: two of them correspond to the studied sequences, whereas the third is chosen to handle long-distance estimation. The branch lengths of this tree are obtained by likelihood maximization and are then used to deduce the desired distance. This approach, called TripleML, improves the precision of evolutionary distance estimates, and thus the topological accuracy of distance-based methods. TripleML can be used with neighbor-joining-like (NJ-like) methods not only to compute the initial distance matrix but also to estimate new distances encountered during the agglomeration process. Computer simulations indicate that using TripleML significantly improves the topological accuracy of NJ, BioNJ, and Weighbor, while conserving a reasonable computation time. With randomly generated 24-taxon trees and realistic parameter values, combining NJ with TripleML reduces the number of wrongly inferred branches by about 11% (against 2.6% and 5.5% for BioNJ and Weighbor, respectively). Moreover, this combination requires only about 1.5 min to infer a phylogeny of 96 sequences composed of 1,200 nucleotides, as compared with 6.5 h for FastDNAml on the same machine (PC 466 MHz).     

Genetic identification of Southern Ocean octopod samples using mtCOI

East Antarctic octopods were identified by sequencing mtCOI and using four analytical approaches: Neighbor-joining by Kimura-2-Parameter-based distances, character-based, BLAST, and Bayesian Inference of Phylogeny. Although the distance-based analytical approaches identified a high proportion of the sequences (99.5% to genus and 88.1% to species level), these results are undermined by the absence of a clear gap between intra- and interspecific variation. The character-based approach gave highly conflicting results compared to the distance-based methods and failed to identify apomorphic characters for many of the species. While a DNA independent approach is necessary for validation of the method comparisons, crude morphological observations give early support to the distance-based results and indicate extensive range expansions of several species compared to previous studies. Furthermore, the use of distance-based phylogenetic methods nevertheless group specimens into plausible species clades that are highly useful in non-taxonomical or non-systematic studies.     

Testing predictions of foraging theory for a sit-and-wait forager, Anolis gingivinus

Research in foraging theory has been dominated by studies ofactive foragers choosing among patches and among prey withina patch. Studies of central-place foraging have mainly focusedon loading decisions of an animal provisioning a central place.The problem faced by a sit-and-wait forager that encountersprey at a distance has received little attention. In this studywe tested foraging theory predictions for such foragers, Anolisgingivinus females in the West Indies island of Anguilla. Wepresented lizards with antlion larvae at various distances.Experiment 1 showed that an individual's probability of pursuingprey decreases with the prey's distance and is best describedby a sigmoidal function (which may be as steep as a step function).This function's inflection point defines a cutoff distance.Experiment 3 tested how cutoff distance changes as a functionof prey size. Cutoff distances were greater for larger prey,as predicted for an energy-maximizing forager. Experiments 2and 4 tested how cutoff distance changes as a function of preyabundance. As predicted, cutoff distance were greater at a sitewhere prey abundance was lower. Furthermore, cutoff distancesdecreased immediately following prey augmentation and returnedto previous values within one day of ending augmentation. Thus,moles' foraging behavior is a dynamic process, consistent withthe qualitative predictions of foraging theory. We attributethe success of this study in supporting fundamental foragingtheory predictions to the lizards exhibiting natural behaviorunder field conditions and to particular advantages of studyingsit-and-wait foragers.     

Cutoff size does strongly influence molecular dynamics results on solvated polypeptides.

The behavior of a 17-residue model peptide is analyzed by means of molecular dynamics simulations including explicitly more than a thousand water molecules. On the basis of the charge-group concept, Coulomb interactions are truncated for three values of the cutoff radius: 0.6, 1.0, and 1.4 nm. It is found that the stability of an alpha-helix, which acts as a common starting configuration, is a function of the cutoff size. While the overall stability of the helix is conserved in a simulation using a cutoff of 1.0 nm, it is lost within a very short period of 100 ps when the cutoff is increased to 1.4 nm. This demonstrates that the commonly used cutoff size of 1.0 nm is inappropriate because it does not ensure the convergence of Coulomb interactions. In order to permit an independent judgment, we have performed a 225-ps simulation using the Ewald summation technique, which is more elaborate but circumvents the problem to find an appropriate cutoff value. In contrast to the 1.4-nm cutoff trajectory, the Ewald technique simulation conserves the helical character of the peptide conformation. This demonstrates that even 1.4 nm is too short a cutoff. Due to the fundamental uncertainty introduced by the use of a simple cutoff, this truncation scheme seems questionable for molecular dynamics simulations of solvated biomolecules.     

Factors affecting the errors in the estimation of evolutionary distances between sequences

Phylogenetic methods that use matrices of pairwise distances between sequences (e.g., neighbor joining) will only give accurate results when the initial estimates of the pairwise distances are accurate. For many different models of sequence evolution, analytical formulae are known that give estimates of the distance between two sequences as a function of the observed numbers of substitutions of various classes. These are often of a form that we call "log transform formulae". Errors in these distance estimates become larger as the time t since divergence of the two sequences increases. For long times, the log transform formulae can sometimes give divergent distance estimates when applied to finite sequences. We show that these errors become significant when t approximately 1/2 |lambda(max)|(-1) logN, where lambda(max) is the eigenvalue of the substitution rate matrix with the largest absolute value and N is the sequence length. Various likelihood-based methods have been proposed to estimate the values of parameters in rate matrices. If rate matrix parameters are known with reasonable accuracy, it is possible to use the maximum likelihood method to estimate evolutionary distances while keeping the rate parameters fixed. We show that errors in distances estimated in this way only become significant when t approximately 1/2 |lambda(1)|(-1) logN, where lambda(1) is the eigenvalue of the substitution rate matrix with the smallest nonzero absolute value. The accuracy of likelihood-based distance estimates is therefore much higher than those based on log transform formulae, particularly in cases where there is a large range of timescales involved in the rate matrix (e.g., when the ratio of transition to transversion rates is large). We discuss several practical ways of estimating the rate matrix parameters before distance calculation and hence of increasing the accuracy of distance estimates.     

Theoretical distribution of truncation lengths in incremental truncation libraries

Incremental truncation is a method for constructing libraries of every one base pair truncation of a segment of DNA. Incremental truncation libraries can be created using a time-dependent nuclease method or through the incorporation of alpha-phosphothioate dNTPs by PCR or by primer extension (THIO(pcr) truncation and THIO(extension) truncation, respectively). Libraries created by the fusion of two truncation libraries, known as ITCHY libraries, can be created using the above methods or by the incremental truncation-like method SHIPREC. Knowing and being able to tailor the distribution of truncations in incremental truncation, ITCHY and SHIPREC libraries would be beneficial for their use in protein engineering and other applications. However, the experimental determination of the distributions would require extensive, cost-prohibitive, DNA sequencing to obtain statistically relevant data. Instead, a theoretical prediction of the distributions was developed. Time-dependent incremental truncation libraries had the most uniform distribution of truncation lengths, but were biased against longer truncations. Essentially uniform distribution over the desired truncation range (from zero to N(max) base pairs) required that truncations be prepared up to at least 1.2-1.5 N(max). THIO(pcr) and THIO(extension) truncation libraries had a very nonuniform distribution of truncation lengths with a bias against longer truncations. Such nonuniformity could be significantly diminished by decreasing the incorporation rate of alphaS-dNTPs but at the expense of having a large fraction of the DNA truncated beyond the desired range or completely degraded. ITCHY libraries created using time-dependent truncation had the most uniform distribution of possible fusions and had the highest fraction of the library being parental-length fusions. However, the distribution of parental-length fusions was biased against fusions near the beginning/ends of genes unless the truncation libraries are prepared with a uniform distribution up to N(max). In contrast, SHIPREC libraries and THIO(pcr) ITCHY libraries, by the very nature of the nonuniform distributions of the truncated DNA, are ensured of having a uniform distribution of fusion points in parental-length fusions. This comes at the expense of having a smaller fraction of the library being parental-length fusions; however, this limitation can be overcome by performing size selection on the library.