Influence of a knot on the strength of a polymer strand

Many experiments have been done to determine the relative strength of different knots, and these show that the break in a knotted rope almost invariably occurs at a point just outside the `entrance' to the knot. The influence of knots on the properties of polymers has become of great interest, in part because of their effect on mechanical properties. Knot theory applied to the topology of macromolecules indicates that the simple trefoil or `overhand' knot is likely to be present with high probability in any long polymer strand. Fragments of DNA have been observed to contain such knots in experiments and computer simulations. Here we use {\it ab initio} computational methods to investigate the effect of a trefoil knot on the breaking strength of a polymer strand. We find that the knot weakens the strand significantly, and that, like a knotted rope, it breaks under tension at the entrance to the knot.Comment: 3 pages, 4 figure

Heteropolymeric Triplex-Based Genomic Assay® to Detect Pathogens or Single-Nucleotide Polymorphisms in Human Genomic Samples

Human genomic samples are complex and are considered difficult to assay directly without denaturation or PCR amplification. We report the use of a base-specific heteropolymeric triplex, formed by native duplex genomic target and an oligonucleotide third strand probe, to assay for low copy pathogen genomes present in a sample also containing human genomic duplex DNA, or to assay human genomic duplex DNA for Single Nucleotide Polymorphisms (SNP), without PCR amplification. Wild-type and mutant probes are used to identify triplexes containing FVL G1691A, MTHFR C677T and CFTR mutations. The specific triplex structure forms rapidly at room temperature in solution and may be detected without a separation step. YOYO-1, a fluorescent bis-intercalator, promotes and signals the formation of the specific triplex. Genomic duplexes may be assayed homogeneously with single base pair resolution. The specific triple-stranded structures of the assay may approximate homologous recombination intermediates, which various models suggest may form in either the major or minor groove of the duplex. The bases of the stable duplex target are rendered specifically reactive to the bases of the probe because of the activity of intercalated YOYO-1, which is known to decondense duplex locally 1.3 fold. This may approximate the local decondensation effected by recombination proteins such as RecA in vivo. Our assay, while involving triplex formation, is sui generis, as it is not homopurine sequence-dependent, as are “canonical triplexes”. Rather, the base pair-specific heteropolymeric triplex of the assay is conformation-dependent. The highly sensitive diagnostic assay we present allows for the direct detection of base sequence in genomic duplex samples, including those containing human genomic duplex DNA, thereby bypassing the inherent problems and cost associated with conventional PCR based diagnostic assays

Theoretical Analysis of the Stress Induced B-Z Transition in Superhelical DNA

We present a method to calculate the propensities of regions within a DNA molecule to transition from B-form to Z-form under negative superhelical stresses. We use statistical mechanics to analyze the competition that occurs among all susceptible Z-forming regions at thermodynamic equilibrium in a superhelically stressed DNA of specified sequence. This method, which we call SIBZ, is similar to the SIDD algorithm that was previously developed to analyze superhelical duplex destabilization. A state of the system is determined by assigning to each base pair either the B- or the Z-conformation, accounting for the dinucleotide repeat unit of Z-DNA. The free energy of a state is comprised of the nucleation energy, the sequence-dependent B-Z transition energy, and the energy associated with the residual superhelicity remaining after the change of twist due to transition. Using this information, SIBZ calculates the equilibrium B-Z transition probability of each base pair in the sequence. This can be done at any physiologically reasonable level of negative superhelicity. We use SIBZ to analyze a variety of representative genomic DNA sequences. We show that the dominant Z-DNA forming regions in a sequence can compete in highly complex ways as the superhelicity level changes. Despite having no tunable parameters, the predictions of SIBZ agree precisely with experimental results, both for the onset of transition in plasmids containing introduced Z-forming sequences and for the locations of Z-forming regions in genomic sequences. We calculate the transition profiles of 5 kb regions taken from each of 12,841 mouse genes and centered on the transcription start site (TSS). We find a substantial increase in the frequency of Z-forming regions immediately upstream from the TSS. The approach developed here has the potential to illuminate the occurrence of Z-form regions in vivo, and the possible roles this transition may play in biological processes

Progressive GAA·TTC Repeat Expansion in Human Cell Lines

Trinucleotide repeat expansion is the genetic basis for a sizeable group of inherited neurological and neuromuscular disorders. Friedreich ataxia (FRDA) is a relentlessly progressive neurodegenerative disorder caused by GAA·TTC repeat expansion in the first intron of the FXN gene. The expanded repeat reduces FXN mRNA expression and the length of the repeat tract is proportional to disease severity. Somatic expansion of the GAA·TTC repeat sequence in disease-relevant tissues is thought to contribute to the progression of disease severity during patient aging. Previous models of GAA·TTC instability have not been able to produce substantial levels of expansion within an experimentally useful time frame, which has limited our understanding of the molecular basis for this expansion. Here, we present a novel model for studying GAA·TTC expansion in human cells. In our model system, uninterrupted GAA·TTC repeat sequences display high levels of genomic instability, with an overall tendency towards progressive expansion. Using this model, we characterize the relationship between repeat length and expansion. We identify the interval between 88 and 176 repeats as being an important length threshold where expansion rates dramatically increase. We show that expansion levels are affected by both the purity and orientation of the repeat tract within the genomic context. We further demonstrate that GAA·TTC expansion in our model is independent of cell division. Using unique reporter constructs, we identify transcription through the repeat tract as a major contributor to GAA·TTC expansion. Our findings provide novel insight into the mechanisms responsible for GAA·TTC expansion in human cells

Theoretical Analysis of Competing Conformational Transitions in Superhelical DNA

We develop a statistical mechanical model to analyze the competitive behavior of transitions to multiple alternate conformations in a negatively supercoiled DNA molecule of kilobase length and specified base sequence. Since DNA superhelicity topologically couples together the transition behaviors of all base pairs, a unified model is required to analyze all the transitions to which the DNA sequence is susceptible. Here we present a first model of this type. Our numerical approach generalizes the strategy of previously developed algorithms, which studied superhelical transitions to a single alternate conformation. We apply our multi-state model to study the competition between strand separation and B-Z transitions in superhelical DNA. We show this competition to be highly sensitive to temperature and to the imposed level of supercoiling. Comparison of our results with experimental data shows that, when the energetics appropriate to the experimental conditions are used, the competition between these two transitions is accurately captured by our algorithm. We analyze the superhelical competition between B-Z transitions and denaturation around the c-myc oncogene, where both transitions are known to occur when this gene is transcribing. We apply our model to explore the correlation between stress-induced transitions and transcriptional activity in various organisms. In higher eukaryotes we find a strong enhancement of Z-forming regions immediately 5′ to their transcription start sites (TSS), and a depletion of strand separating sites in a broad region around the TSS. The opposite patterns occur around transcript end locations. We also show that susceptibility to each type of transition is different in eukaryotes and prokaryotes. By analyzing a set of untranscribed pseudogenes we show that the Z-susceptibility just downstream of the TSS is not preserved, suggesting it may be under selection pressure

Dilute solution properties of semiflexible star and ring polymers

Our recent theoretical and/or Monte Carlo (MC) studies of dilute solution properties of semiflexible stars and rings are briefly summarized. The theoretical results for the intrinsic viscosity [η] of the Kratky–Porod (KP) wormlike three- and four-arm stars are shown, and effects of chain stiffness on [η] of the stars are examined. A comparison of the results for [η] with those for the effective hydrodynamic radius and the second virial coefficient A2 in a good solvent was made for the semiflexible three-arm stars. It was found that [η] is the most suitable object of study to examine the effects of chain stiffness on average chain dimensions of the stars. As for the rings, the MC results for A2 of the ideal KP rings, which is related to the intermolecular topological interactions, are presented and then compared with the data in the literature for ring atactic polystyrene (a-PS) at Θ for large molecular weight M (1 × 10[4]−6 × 10[5]). Even for ring a-PS in such a range of M, the effects of chain stiffness were still remarkable. The effects of the intramolecular topological constraints on the mean-square radius of gyration and the scattering function of the KP rings are also discussed