Topological information embodied in local juxtaposition geometry provides a statistical mechanical basis for unknotting by type-2 DNA topoisomerases

Topoisomerases may unknot by recognizing specific DNA juxtapositions. The physical basis of this hypothesis is investigated by considering single-loop conformations in a coarse-grained polymer model. We determine the statistical relationship between the local geometry of a juxtaposition of two chain segments and whether the loop is knotted globally, and ascertain how the knot/unknot topology is altered by a topoisomerase-like segment passage at the juxtaposition. Segment passages at a "free" juxtaposition tend to increase knot probability. In contrast, segment passages at a "hooked" juxtaposition cause more transitions from knot to unknot than vice versa, resulting in a steady-state knot probability far lower than that at topological equilibrium. The reduction in knot population by passing chain segments through a hooked juxtaposition is more prominent for loops of smaller sizes, n, but remains significant even for larger loops: steady-state knot probability is only approximately 2%, and approximately 5% of equilibrium, respectively, for n=100 and 500 in the model. An exhaustive analysis of approximately 6000 different juxtaposition geometries indicates that the ability of a segment passage to unknot correlates strongly with the juxtaposition's "hookedness". Remarkably, and consistent with experiments on type-2 topoisomerases from different organisms, the unknotting potential of a juxtaposition geometry in our polymer model correlates almost perfectly with its corresponding decatenation potential. These quantitative findings suggest that it is possible for topoisomerases to disentangle by acting selectively on juxtapositions with "hooked" geometries.     

Action at Hooked or Twisted-Hooked DNA Juxtapositions Rationalizes Unlinking Preference of Type-2 Topoisomerases

The mathematical basis of the hypothesis that type-2 topoisomerases recognize and act at specific DNA juxtapositions has been investigated by coarse-grained lattice polymer models, showing that selective segment passages at hooked juxtapositions can result in dramatic reductions in catenane and knot populations. The lattice modeling approach is here extended to account for the narrowing of variance of linking number (Lk) of DNA circles by type-2 topoisomerases. In general, the steady-state variance of Lk resulting from selective segment passages at a specific juxtaposition geometry j is inversely proportional to the average linking number, 〈Lk〉_j, of circles with the given juxtaposition. Based on this formulation, we demonstrate that selective segment passages at hooked juxtapositions reduce the variance of Lk. The dependence of this effect on model DNA circle size is remarkably similar to that observed experimentally for type-2 topoisomerases, which appear to be less capable in narrowing Lk variance for small DNA circles than for larger DNA circles. This behavior is rationalized by a substantial cancellation of writhe in small circles with hook-like juxtapositions. During our simulations, we uncovered a twisted variation of the hooked juxtaposition that has an even more dramatic effect on Lk variance narrowing than the hooked juxtaposition. For an extended set of juxtapositions, we detected a significant correlation between the Lk narrowing potential and the logarithmic decatenating and unknotting potentials for a given juxtaposition, a trend reminiscent of scaling relations observed with experimental measurements on type-2 topoisomerases from a variety of organisms. The consistent agreement between theory and experiment argues for type-2 topoisomerase action at hooked or twisted-hooked DNA juxtapositions.     

DNA disentangling by type-2 topoisomerases

A type-2 topoisomerase cleaves a DNA strand, passes another through the break, and then rejoins the severed ends. Because it appears that this action is as likely to increase as to decrease entanglements, the question is: how are entanglements removed? We argue that type-2 topoisomerases have evolved to act at "hooked" juxtapositions of strands (where the strands are curved toward each other). This type of juxtaposition is a natural consequence of entangled long strands. Our model accounts for the observed preference for unlinking and unknotting of short DNA plasmids by type-2 topoisomerases and well explains experimental observations.     

Conformational properties of the iso-1-cytochrome C denatured state: dependence on guanidine hydrochloride concentration

Production of seven single surface histidine variants of yeast iso-1-cytochrome c allowed measurement of the apparent pK(a), pK(a)(obs), for histidine-heme loop formation for loops of nine to 83 amino acid residues under varying denaturing conditions (2 M to 6 M guanidine hydrochloride, gdnHCl). A linear correlation between pK(a)(obs) and the log of the loop size is expected for a random coil, pK(a)(obs) proportional to k log(n), where k is a scaling factor and n is the number of monomers in the loop. For small loops of nine, 16, and 22 monomers, no dependence of pK(a)(obs) on loop size was observed at any denaturant concentration indicating effects from chain stiffness. For larger loops of 37, 56, 72, and 83 monomers, the dependence of pK(a)(obs) on log(n) was linear and the slope of that dependence decreased with increasing concentration of denaturant. The scaling factor obtained at 5 M and 6 M gdnHCl for the larger loop sizes was approximately -2.0, close to the value of -2.2 expected for a random coil with excluded volume. However, scaling factors obtained under less harsh denaturing conditions (2 M to 4.5 M gdnHCl) deviated strongly from that expected for a random coil, being in the range -3 to -4. The gdnHCl dependence of pK(a)(obs) at each loop size was also evaluated to obtain denaturant m-values. Short loops where chain stiffness dominates had similar m-values of approximately 0.25 kcal/mol M. For larger loops m-values decrease with increasing loop size indicating that less hydrophobic area is sequestered when larger loops form. It is known that the earliest events in protein folding involve the formation of simple loops. The data from these studies provide direct insight into the relative probability with which loops of different sizes will form, as well as the factors which affect loop formation.     

The use of restriction fragment length polymorphisms in paternity analysis.

This paper examines the utility of restriction fragment length polymorphisms (RFLPs) for paternity analysis. While, on the average, 99% of falsely accused males can be excluded with the standard battery of blood group antigens, red cell enzymes, serum proteins, and HLA antigens, there are still mother-child pairs for whom the exclusion probability is not high. It has been suggested that additional resolution would be available with RFLPs. We have examined the strategic aspects of using RFLPs for paternity analysis, comparing the efficacy and cost of a multimarker haplotypic set with those of a comparable set of unlinked RFLPs, using published frequencies for the beta-globin complex, the serum albumin region, and the growth hormone region. There are four major findings. (1) Greater resolution is obtained with a carefully chosen set of tightly linked RFLPs producing chromosomal haplotypes than with a comparable set (same allele frequencies) of unlinked markers, but only if it is possible to establish linkage phase unambiguously. (2) Assay of linked sets is cheaper than is the assay of unlinked markers, but the cost advantage is optimized with sets of no more than two or three linked markers. (3) Also, with more than two or three tightly linked markers, the haplotypic frequencies are too poorly estimated to provide a reliable measure of the probability of paternity for unexcluded males, given the sample sizes likely to be available in the near future. (4) Optimal resolution, minimal cost, and acceptable accuracy are obtained with several independent sets of no more than two or three tightly linked RFLP markers each. With current technology, RFLP analysis is more expensive for the same level of genetic resolution than is the standard battery, but gradual replacement of the latter can be anticipated as economies of scale reduce the cost of the DNA technology.     

Viral linkage in HIV-1 seroconverters and their partners in an HIV-1 prevention clinical trial

Background

Characterization of viruses in HIV-1 transmission pairs will help identify biological determinants of infectiousness and evaluate candidate interventions to reduce transmission. Although HIV-1 sequencing is frequently used to substantiate linkage between newly HIV-1 infected individuals and their sexual partners in epidemiologic and forensic studies, viral sequencing is seldom applied in HIV-1 prevention trials. The Partners in Prevention HSV/HIV Transmission Study (ClinicalTrials.gov #{"type":"clinical-trial","attrs":{"text":"NCT00194519","term_id":"NCT00194519"}}NCT00194519) was a prospective randomized placebo-controlled trial that enrolled serodiscordant heterosexual couples to determine the efficacy of genital herpes suppression in reducing HIV-1 transmission; as part of the study analysis, HIV-1 sequences were examined for genetic linkage between seroconverters and their enrolled partners.

Methodology/Principal Findings

We obtained partial consensus HIV-1 env and gag sequences from blood plasma for 151 transmission pairs and performed deep sequencing of env in some cases. We analyzed sequences with phylogenetic techniques and developed a Bayesian algorithm to evaluate the probability of linkage. For linkage, we required monophyletic clustering between enrolled partners'' sequences and a Bayesian posterior probability of ≥50%. Adjudicators classified each seroconversion, finding 108 (71.5%) linked, 40 (26.5%) unlinked, and 3 (2.0%) indeterminate transmissions, with linkage determined by consensus env sequencing in 91 (84%). Male seroconverters had a higher frequency of unlinked transmissions than female seroconverters. The likelihood of transmission from the enrolled partner was related to time on study, with increasing numbers of unlinked transmissions occurring after longer observation periods. Finally, baseline viral load was found to be significantly higher among linked transmitters.

Conclusions/Significance

In this first use of HIV-1 sequencing to establish endpoints in a large clinical trial, more than one-fourth of transmissions were unlinked to the enrolled partner, illustrating the relevance of these methods in the design of future HIV-1 prevention trials in serodiscordant couples. A hierarchy of sequencing techniques, analysis methods, and expert adjudication contributed to the linkage determination process.     

Hairpin formation in DNA computation presents limits for large NP-complete problems

Recently, several DNA computing paradigms for NP-complete problems were presented, especially for the 3-SAT problem. Can the present paradigms solve more than just trivial instances of NP-complete problems? In this paper we show that with high probability potentially deleterious features such as severe hairpin loops would be likely to arise. If DNA strand x of length n and the 'complement' of the reverse of x have l match bases, then x forms a hairpin loop and is called a (n,l)-hairpin format. Let gamma=2l/n. Then gamma can be considered as a measurement of the stability of hairpin loops. Let p(n,l) be the probability that a n-mer DNA strand is a (n,l)-hairpin format, and q(n,l)((m)) be the probability that m ones are chosen at random from 4(n) n-mer oligonucleotides such that at least one of the m ones is a (n,l)-hairpin format. Then, q(n,l)((m))=1-(1-p(n,l))(m)=mp(n,l). If we require q(n,l)((m))相似文献   

Single-molecule spectroscopic determination of lac repressor-DNA loop conformation

The Escherichia coli lactose repressor protein (LacI) provides a classic model for understanding protein-induced DNA looping. LacI has a C-terminal four-helix bundle tetramerization domain that may act as a flexible hinge. In previous work, several DNA constructs, each containing two lac operators bracketing a sequence-induced bend, were designed to stabilize different possible looping geometries. The resulting hyperstable LacI-DNA loops exist as both a compact "closed" form with a V-shaped repressor and also a more "open" form with an extended hinge. The "9C14" construct was of particular interest because footprinting, electrophoretic mobility shift, and ring closure experiments suggested that it forms both geometries. Previous fluorescence resonance energy transfer (FRET) measurements gave an efficiency of energy transfer (ET) of 70%, confirming the existence of a closed form. These measurements could not determine whether open form or intermediate geometries are populated or the timescale of interconversion. We have now applied single-molecule FRET to Cy3, Cy5 double-labeled LacI-DNA loops diffusing freely in solution. By using multiple excitation wavelengths and by carefully examining the behavior of the zero-ET peak during titration with LacI, we show that the LacI-9C14 loop exists exclusively in a single closed form exhibiting essentially 100% ET.     

Identification of selective sweeps using a dynamically adjusted number of linked microsatellites

There is currently large interest in distinguishing the signatures of genetic variation produced by demographic events from those produced by natural selection. We propose a simple multilocus statistical test to identify candidate sites of selective sweeps with high power. The test is based on the variability profile measured in an array of linked microsatellites. We also show that the analysis of flanking markers drastically reduces the number of false positives among the candidates that are identified in a genomewide survey of unlinked loci and find that this property is maintained in many population-bottleneck scenarios. However, for a certain range of intermediately severe population bottlenecks we find genomic signatures that are very similar to those produced by a selective sweep. While in these worst-case scenarios the power of the proposed test remains high, the false-positive rate reaches values close to 50%. Hence, selective sweeps may be hard to identify even if multiple linked loci are analyzed. Nevertheless, the integration of information from multiple linked loci always leads to a considerable reduction of the false-positive rate compared to a genome scan of unlinked loci. We discuss the application of this test to experimental data from Drosophila melanogaster.     

Rotational and hinge dynamics of discoidal high density lipoproteins probed by interchain disulfide bond formation

To develop a detailed double belt model for discoidal HDL, we previously scored inter-helical salt bridges between all possible registries of two stacked antiparallel amphipathic helical rings of apolipoprotein (apo) A-I. The top score was the antiparallel apposition of helix 5 with 5 followed closely by appositions of helix 5 with 4 and helix 5 with 6. The rationale for the current study is that, for each of the optimal scores, a pair of identical residues can be identified in juxtaposition directly on the contact edge between the two antiparallel helical belts of apoA-I. Further, these residues are always in the ‘9th position’ in one of the eighteen 11-mer repeats that make up the lipid-associating domain of apoA-I. To illustrate our terminology, 129j (LL5/5) refers to the juxtaposition of the Cα atoms of G129 (in a ‘9th position’) in the pairwise helix 5 domains. We reasoned that if identical residues in the double belt juxtapositions were mutated to a cysteine and kept under reducing conditions during disc formation, we would have a precise method for determining registration in discoidal HDL by formation of a disulfide-linked apoA-I homodimer. Using this approach, we conclude that 129j (LL5/5) is the major rotamer orientation for double belt HDL and propose that the small ubiquitous gap between the pairwise helix 5 portions of the double belt in larger HDL discoidal particles is significantly dynamic to hinge off the disc edge under certain conditions, e.g., in smaller particles or perhaps following binding of the enzyme LCAT. This article is part of a Special Issue entitled Advances in High Density Lipoprotein Formation and Metabolism: A Tribute to John F. Oram (1945-2010).     

Solvation parameters for predicting the structure of surface loops in proteins: transferability and entropic effects

A new procedure for optimizing parameters of implicit solvation models introduced by us has been applied successfully first to cyclic peptides and more recently to three surface loops of ribonuclease A (Das and Meirovitch, Proteins 2001;43:303-314) using the simplified model E(tot) = E(FF)(epsilon = nr) + Sigma(i) sigma(i)A(i), where sigma(i) are atomic solvation parameters (ASPs) to be optimized, A(i) is the solvent accessible surface area of atom i, E(FF)(epsilon = nr) is the AMBER force-field energy of the loop-loop and loop-template interactions with a distance-dependent dielectric constant, epsilon = nr, where n is a parameter. The loop is free to move while the protein template is held fixed in its X-ray structure; an extensive conformational search for energy minimized loop structures is carried out with our local torsional deformation method. The optimal ASPs and n are those for which the structure with the lowest minimized energy [E(tot)(n,sigma(i))] becomes the experimental X-ray structure, or less strictly, the energy gap between these structures is within 2-3 kcal/mol. To check if a set of ASPs can be defined, which is transferable to a large number of loops, we optimize individual sets of ASPs (based on n = 2) for 12 surface loops from which an "averaged" best-fit set is defined. This set is then applied to the 12 loops and an independent "test" group of 8 loops leading in most cases to very small RMSD values; thus, this set can be useful for structure prediction of loops in homology modeling. For three loops we also calculate the free energy gaps to find that they are only slightly smaller than their energy counterparts, indicating that only larger n will enable reducing too large gaps. Because of its simplicity, this model allowed carrying out an extensive application of our methodology, providing thereby a large number of benchmark results for comparison with future calculations based on n > 2 as well as on more sophisticated solvation models with as yet unknown performance for loops.     

Rotational and hinge dynamics of discoidal high density lipoproteins probed by interchain disulfide bond formation

To develop a detailed double belt model for discoidal HDL, we previously scored inter-helical salt bridges between all possible registries of two stacked antiparallel amphipathic helical rings of apolipoprotein (apo) A-I. The top score was the antiparallel apposition of helix 5 with 5 followed closely by appositions of helix 5 with 4 and helix 5 with 6. The rationale for the current study is that, for each of the optimal scores, a pair of identical residues can be identified in juxtaposition directly on the contact edge between the two antiparallel helical belts of apoA-I. Further, these residues are always in the '9th position' in one of the eighteen 11-mer repeats that make up the lipid-associating domain of apoA-I. To illustrate our terminology, 129j (LL5/5) refers to the juxtaposition of the Cα atoms of G129 (in a '9th position') in the pairwise helix 5 domains. We reasoned that if identical residues in the double belt juxtapositions were mutated to a cysteine and kept under reducing conditions during disc formation, we would have a precise method for determining registration in discoidal HDL by formation of a disulfide-linked apoA-I homodimer. Using this approach, we conclude that 129j (LL5/5) is the major rotamer orientation for double belt HDL and propose that the small ubiquitous gap between the pairwise helix 5 portions of the double belt in larger HDL discoidal particles is significantly dynamic to hinge off the disc edge under certain conditions, e.g., in smaller particles or perhaps following binding of the enzyme LCAT. This article is part of a Special Issue entitled Advances in High Density Lipoprotein Formation and Metabolism: A Tribute to John F. Oram (1945-2010).     

Mendel's First Law: partisan interests and the parliament of genes

Mendel’s First Law requires explanation because of the possibility of ‘meiotic drivers’, genes that distort fair segregation for selfish gain. The suppression of drive, and the restoration of fair segregation, is often attributed to genes at loci unlinked to the drive locus—such genes cannot benefit from drive but do suffer its associated fitness costs. However, selection can also favour suppressors at loci linked to the drive locus, raising the question of whether suppression of drive usually comes from linked or unlinked loci. Here, I study linked and unlinked suppression in a two-locus model with initial stable polymorphism at the drive locus. I find that the invasion rate of suppressors is a decreasing function of the recombination fraction between the drive and suppressor loci. Surprisingly, the relative likelihood of unlinked vs. linked suppression increases with the strength of drive and is insensitive to the fitness costs of the driver allele. I find that the chromosomal position of the driver influences how rapidly it is suppressed, with a driver in the middle of a chromosome suppressed more rapidly than a driver near the tip. When drive is strong, only a small number of chromosomes are required for suppression usually to derive from unlinked loci. In contrast, when drive is weak, and especially when suppressor alleles are associated with fitness costs, suppression will usually come from linked loci unless the genome comprises many chromosomes.Subject terms: Evolutionary genetics, Population genetics     

The Goldilocks effect: human infants allocate attention to visual sequences that are neither too simple nor too complex

Human infants, like immature members of any species, must be highly selective in sampling information from their environment to learn efficiently. Failure to be selective would waste precious computational resources on material that is already known (too simple) or unknowable (too complex). In two experiments with 7- and 8-month-olds, we measure infants' visual attention to sequences of events varying in complexity, as determined by an ideal learner model. Infants' probability of looking away was greatest on stimulus items whose complexity (negative log probability) according to the model was either very low or very high. These results suggest a principle of infant attention that may have broad applicability: infants implicitly seek to maintain intermediate rates of information absorption and avoid wasting cognitive resources on overly simple or overly complex events.     

A four-element based transposon system for allele specific tagging in plants—Theoretical considerations

The two-element transposon constructs, utilizing either Ac/Ds or Spm/dSpm, allow random tagging of genes in heterologous model species, but are inadequate for directed tagging of specific alleles of agronomic importance. We propose the use of Ac/Ds in conjunction with Spm/dSpm to develop a four-element system for directed tagging of crop-specific alleles. The four-element based construct would include both Ds and dSpm along with relevant marker genes and would function in two steps. In the first step dSpm(Ds) stocks (a minimum of two) would be crossed to a line containing transposases of Spm and unlinked integrations would be selected from segregating population by the use of a negative selection marker to develop stocks representing integration of dSpm(Ds) at a large number of locations in the genome. Selections would be made for a line in which dSpm(Ds) shows partial or complete linkage to the allele of interest. In the second step selected line would be crossed to a line containing Ac transposase to induce transpositions of Ds element to linked sites thereby exploiting the natural tendency of Ds element to jump to linked sites. Unlinked jumps of dSpm(Ds) and linked jumps of Ds could be monitored by appropriate marker genes. The proposed model would allow tagging of allele of interest in chromosome addition lines and also help in the efficient use of genic male sterility systems for hybrid seed production by tightly marking the fertility restorer gene with a negative selection marker.     

<Emphasis Type="Italic">TDT-HET</Emphasis>: A new transmission disequilibrium test that incorporates locus heterogeneity into the analysis of family-based association data

Background  

Locus heterogeneity is one of the most documented phenomena in genetics. To date, relatively little work had been done on the development of methods to address locus heterogeneity in genetic association analysis. Motivated by Zhou and Pan's work, we present a mixture model of linked and unlinked trios and develop a statistical method to estimate the probability that a heterozygous parent transmits the disease allele at a di-allelic locus, and the probability that any trio is in the linked group. The purpose here is the development of a test that extends the classic transmission disequilibrium test (TDT) to one that accounts for locus heterogeneity.     

How topoisomerase IV can efficiently unknot and decatenate negatively supercoiled DNA molecules without causing their torsional relaxation

Freshly replicated DNA molecules initially form multiply interlinked right-handed catenanes. In bacteria, these catenated molecules become supercoiled by DNA gyrase before they undergo a complete decatenation by topoisomerase IV (Topo IV). Topo IV is also involved in the unknotting of supercoiled DNA molecules. Using Metropolis Monte Carlo simulations, we investigate the shapes of supercoiled DNA molecules that are either knotted or catenated. We are especially interested in understanding how Topo IV can unknot right-handed knots and decatenate right-handed catenanes without acting on right-handed plectonemes in negatively supercoiled DNA molecules. To this end, we investigate how the topological consequences of intersegmental passages depend on the geometry of the DNA-DNA juxtapositions at which these passages occur. We observe that there are interesting differences between the geometries of DNA-DNA juxtapositions in the interwound portions and in the knotted or catenated portions of the studied molecules. In particular, in negatively supercoiled, multiply interlinked, right-handed catenanes, we detect specific regions where DNA segments belonging to two freshly replicated sister DNA molecules form left-handed crossings. We propose that, due to its geometrical preference to act on left-handed crossings, Topo IV can specifically unknot supercoiled DNA, as well as decatenate postreplicative catenanes, without causing their torsional relaxation.     

Linkage and the Limits to Natural Selection

The probability of fixation of a favorable mutation is reduced if selection at other loci causes inherited variation in fitness. A general method for calculating the fixation probability of an allele that can find itself in a variety of genetic backgrounds is applied to find the effect of substitutions, fluctuating polymorphisms, and deleterious mutations in a large population. With loose linkage, r, the effects depend on the additive genetic variance in relative fitness, var (W), and act by reducing effective population size by (N/N(e)) = 1 + var (W)/2r(2). However, tightly linked loci can have a substantial effect not predictable from N(e). Linked deleterious mutations reduce the fixation probability of weakly favored alleles by exp(-2U/R), where U is the total mutation rate and R is the map length in Morgans. Substitutions can cause a greater reduction: an allele with advantage s < s(crit) = (π(2)/6) log(e) (S/s)[var(W)/R] is very unlikely to be fixed. (S is the advantage of the substitution impeding fixation.) Fluctuating polymorphisms at many (n) linked loci can also have a substantial effect, reducing fixation probability by exp [ &2Kn var(W)/R] [K = -1/E((u - u)(2)/uv) depending on the frequencies (u,v) at the selected polymorphisms]. Hitchhiking due to all three kinds of selection may substantially impede adaptation that depends on weakly favored alleles.