Excluded volume effects on the rate of renaturation of DNA

Lattice model on the rate of DNA hybridization

We develop a lattice model on the rate of hybridization of the complementary single-stranded DNAs (c-ssDNAs). Upon translational diffusion mediated collisions, c-ssDNAs interpenetrate each other to form correct (cc), incorrect (icc), and trap correct contacts (tcc) inside the reaction volume. Correct contacts are those with exact registry matches, which leads to nucleation and zipping. Incorrect contacts are the mismatch contacts which are less stable compared to tcc, which can occur in the repetitive c-ssDNAs. Although tcc possess registry match within the repeating sequences, they are incorrect contacts in the view of the whole c-ssDNAs. The nucleation rate (k_{N}) is directly proportional to the collision rate and the average number of correct contacts (〈n_{cc}〉) formed when both c-ssDNAs interpenetrate each other. Detailed lattice model simulations suggest that 〈n_{cc}〉∝L/V where L is the length of c-ssDNAs and V is the reaction volume. Further numerical analysis revealed the scaling for the average radius of gyration of c-ssDNAs (R_{g}) with their length as R_{g}∝sqrt[L]. Since the reaction space will be approximately a sphere with radius equals to 2R_{g} and V∝L^{3/2}, one obtains k_{N}∝1/sqrt[L]. When c-ssDNAs are nonrepetitive, the overall renaturation rate becomes as k_{R}∝k_{N}L, and one finally obtains k_{R}∝sqrt[L] in line with the experimental observations. When c-ssDNAs are repetitive with a complexity of c, earlier models suggested the scaling k_{R}∝sqrt[L]/c, which breaks down at c=L. This clearly suggests the existence of at least two different pathways of renaturation in the case of repetitive c-ssDNAs, viz., via incorrect contacts and trap correct contacts. The trap correct contacts can lead to the formation of partial duplexes which can keep the complementary strands in the close proximity for a prolonged timescale. This is essential for the extended 1D slithering, inchworm movements, and internal displacement mechanisms which can accelerate the searching for the correct contacts. Clearly, the extent of slithering dynamics will be inversely proportional to the complexity. When the complexity is close to the length of c-ssDNAs, the pathway via incorrect contacts will dominate. When the complexity is much less than the length of c-ssDNA, pathway via trap correct contacts would be the dominating one.

Mechanism of thermal renaturation and hybridization of nucleic acids: Kramers' process and universality in Watson-Crick base pairing

Renaturation and hybridization reactions lead to the pairing of complementary single-stranded nucleic acids. We present here a theoretical investigation of the mechanism of these reactions in vitro under thermal conditions (dilute solutions of single-stranded chains, in the presence of molar concentrations of monovalent salts and at elevated temperatures). The mechanism follows a Kramers' process, whereby the complementary chains overcome a potential barrier through Brownian motion. The barrier originates from a single rate-limiting nucleation event in which the first complementary base pairs are formed. The reaction then proceeds through a fast growth of the double helix. For the DNA of bacteriophages T7, T4, and phiX174, as well as for Escherichia coli DNA, the bimolecular rate k2 of the reaction increases as a power law of the average degree of polymerization <N> of the reacting single-strands: k2 is proportional to <N> alpha. This relationship holds for 100 < or = <N> < or = 50,000 with an experimentally determined exponent alpha = 0.51 +/- 0.01. The length dependence results from a thermodynamic excluded-volume effect. The reacting single-stranded chains are predicted to be in universal good solvent conditions, and the scaling law is determined by the relevant equilibrium monomer contact probability. The value theoretically predicted for the exponent is alpha = 1 - nutheta2, where nu is Flory's swelling exponent (nu approximately equal 0.588), and theta2 is a critical exponent introduced by des Cloizeaux (theta2 approximately equal 0.82), yielding alpha = 0.52 +/- 0.01, in agreement with the experimental results.

A Z-DNA sequence reduces slipped-strand structure formation in the myotonic dystrophy type 2 (CCTG) x (CAGG) repeat

All DNA repeats known to undergo expansion leading to human neurodegenerative disease can form one, or several, alternative conformations, including hairpin, slipped strand, triplex, quadruplex, or unwound DNA structures. These alternative structures may interfere with the normal cellular processes of transcription, DNA repair, replication initiation, or polymerase elongation and thereby contribute to the genetic instability of these repeat tracts. We show that (CCTG) x (CAGG) repeats, in the first intron of the ZNF9 gene associated with myotonic dystrophy type 2, form slipped-strand DNA structures in a length-dependent fashion upon reduplexing. The threshold for structure formation on reduplexing is between 36 and 42 repeats in length. Alternative DNA structures also form in (CCTG)(58) x (CAGG)(58) and larger repeat tracts in plasmids at physiological superhelical densities. This represents an example of a sequence that forms slipped-strand DNA from the energy of DNA supercoiling. Moreover, Z-DNA forms in a (TG) x (CA) tract within the complex repeat sequence 5' of the (CCTG)(n) x (CAGG)(n) repeat in the ZNF9 gene. Upon reduplexing, the presence of the flanking sequence containing the Z-DNA-forming tract reduced the extent of slipped-strand DNA formation by 62% for (CCTG)(57) x (CAGG)(57) compared with 58 pure repeats without the flanking sequence. This finding suggests that the Z-DNA-forming sequence in the DM2 gene locus may have a protective effect of reducing the potential for slipped-strand DNA formation in (CCTG)(n) x (CAGG)(n) repeats.

Hybridization dynamics of surface immobilized DNA

We model the hybridization kinetics of surface attached DNA oligomers with solubilized targets. Using both master equation and rate equation formalisms, we show that, for surface coverages at which the surface immobilized molecules interact, barriers to penetration create a distribution of target molecule concentrations within the adsorbed layer. By approximately enumerating probe and target conformations, we estimate the probability of overlap between complementary probe and target regions as a function of probe density and chain length. In agreement with experiments, we find that as probe molecules interact more strongly, fewer nucleation sites become accessible and binding rates are diminished relative to those in solution. Nucleation sites near the grafted end of the probes are least accessible; thus targets which preferentially bind to this region show more drastic rate reductions than those that bind near the free end of the probe. The implications of these results for DNA-based biosensors are discussed.

Comparative study of sequence-dependent hybridization kinetics in solution and on microspheres

Hybridization kinetics of DNA sequences with known secondary structures and random sequences designed with similar melting temperatures were studied in solution and when one strand was bound to 5 mum silica microspheres. The rates of hybridization followed second-order kinetics and were measured spectrophotometrically in solution and fluorometrically in the solid phase. In solution, the rate constants for the model sequences varied by almost two orders of magnitude, with a decrease in the rate constant with increasing amounts of secondary structure in the target sequence. The random sequences also showed over an order of magnitude difference in the rate constant. In contrast, the hybridization experiments in the solid phase with the same model sequences showed almost no change in the rate constant. Solid phase rate constants were approximately three orders of magnitude lower compared with the solution phase constants for sequences with little or no single-stranded structure. Sequences with a known secondary structure yielded solution phase rate constants as low as 3 x 10(3) M(-1) s(-1) with solid phase rate constants for the same sequences measured at 2.5 x 10(2) M(-1) s(-1). The results from these experiments indicate that (i) solid phase hybridization occurs three orders of magnitude slower than solution phase, (ii) trends observed in structure-dependent kinetics of solution phase hybridization may not be applicable to solid phase hybridization and (iii) model probes with known secondary structure decrease reaction rates; however, even random sequences with no known internal single-stranded structure can yield a broad range of reaction rates.

Theoretical design of antisense RNA structures substantially improves annealing kinetics and efficacy in human cells

The success of antisense therapeutics is not predictable despite their widespread use in biotechnology and molecular medicine. The relationship between RNA structure and biological effectiveness is largely not understood; however, antisense RNA-mediated effects in vivo seem to be related to annealing kinetics in vitro. This study suggests that terminal unpaired nucleotides and overall flexibility of antisense RNA directed against the human immunodeficiency virus type 1 (HIV-1) are related to fast RNA-RNA annealing in vitro as well as to strong inhibition of virus replication in human cells. Annealing rate constants of computer-selected antisense RNA species approach the values for natural antisense RNA in the order of 10(6) M-1s-1. When considering the unfavorable stability in cellular extracts of antisense RNA species that were found to anneal fast in vitro, an antisense effect against HIV-1 in human cells was observed that was 10- to 10,000-fold stronger than that measured for species predicted to anneal slowly. A computer-supported structural design of antisense RNA can serve as a platform to determine RNA-RNA association in vitro and biological effectiveness in living cells.

Rapid renaturation of complementary DNA strands mediated by cationic detergents: a role for high-probability binding domains in enhancing the kinetics of molecular assembly processes

The rate of renaturation for complementary DNA strands can be enhanced greater than 10(4)-fold by the addition of simple cationic detergents, and the reaction is qualitatively and quantitatively very similar to that found with purified heterogeneous nuclear ribonucleoprotein A1 protein. Under optimal conditions, renaturation rates are greater than 2000-fold faster than reactions run in 1 M NaCl at 68 degrees C. The reaction is second-order with respect to DNA concentration, and reaction rates approach or equal the rate with which complementary strands are expected to encounter each other in solution. Renaturation can even be observed well above the expected melting temperature of the duplex DNA, demonstrating that some cationic detergents have DNA double-helix-stabilizing properties. The reaction is also extremely rapid in the presence of up to a 10(6)-fold excess of noncomplementary sequences, establishing that renaturation is specific and relatively independent of heterologous DNA. This finding also implies that up to several thousand potential target sequences can be sampled per strand per second. Such reagents may be useful for procedures that require rapid nucleic acid renaturation, and these results suggest ways to identify and design other compounds that increase the kinetics of association reactions. Moreover, this work provides further support for a model relating the existence of flexible, weakly interacting, repeating domains to their function in rapid molecular assembly processes in vitro and in vivo.

DNA probes: applications of the principles of nucleic acid hybridization

Nucleic acid hybridization with a labeled probe is the only practical way to detect a complementary target sequence in a complex nucleic acid mixture. The first section of this article covers quantitative aspects of nucleic acid hybridization thermodynamics and kinetics. The probes considered are oligonucleotides or polynucleotides, DNA or RNA, single- or double-stranded, and natural or modified, either in the nucleotide bases or in the backbone. The hybridization products are duplexes or triplexes formed with targets in solution or on solid supports. Additional topics include hybridization acceleration and reactions involving branch migration. The second section deals with synthesis or biosynthesis and detection of labeled probes, with a discussion of their sensitivity and specificity limits. Direct labeling is illustrated with radioactive probes. The discussion of indirect labels begins with biotinylated probes as prototypes. Reporter groups considered include radioactive, fluorescent, and chemiluminescent nucleotides, as well as enzymes with colorimetric, fluorescent, and luminescent substrates.

Renaturation of complementary DNA strands mediated by purified mammalian heterogeneous nuclear ribonucleoprotein A1 protein: implications for a mechanism for rapid molecular assembly

Purified heterogeneous nuclear ribonucleoprotein (hnRNP) A1 protein, which is found in vivo associated with heterogeneous nuclear RNA (hnRNA), promotes the rapid renaturation of nucleic acid strands. Maximal renaturation activity requires the glycine-rich carboxyl-terminal one-third of the protein, although the amino-terminal two-thirds also has activity. The A1-mediated reaction is second-order with respect to complementary DNA concentration, and the renaturation rate constant at 37 degrees C with A1 is about 3000-fold greater than in the absence of the protein. At 60 degrees C, the A1-mediated renaturation rate is even faster, and is about 300-fold greater than protein-free reactions carried out at 68 degrees C in 1 M NaCl. Provided that sufficient A1 protein is present to coat all strands in solution, the presence of nonhomologous, single-stranded DNA does not significantly inhibit the reaction. Moreover, renaturation of short strands to their complement contained in very long strands is nearly as efficient as between two short strands. These results indicate that A1 may be useful for procedures that rely on nucleic acid renaturation. We propose that A1 promotes rapid renaturation primarily by reducing the entropic barrier of bimolecular strand association through relatively transient interactions between A1-coated strands. Such interactions, mediated by flexible repeating domains, may act generally to increase the association kinetics of highly specific molecular assemblies in processes such as RNA maturation, transcription, translation, and transport.

Physical parameters affecting the rate and completion of RNA driven hybridization of DNA: new measurements relevant to quantitation based on kinetics

Differences in the RNA-driven hybridization kinetics of genomic DNA and cDNA probes led us to examine physical parameters affecting these reactions. Cloned cDNA complementary to serum albumin (SA) mRNA hybridized in accordance with single component kinetics, whereas cloned SA genomic DNA hybridized more slowly and with multiple component kinetics. This difference is largely attributable to the relatively short and variable lengths of the mRNA complementary regions in the cloned genomic DNA. The rate of mRNA driven hybridization is affected to about half the extent observed for DNA renaturation as Na+ is increased or decreased from 0.18M. In the annealing of nucleic acids of high sequence complexity, after approximately 70% of reaction has been reached, the rate of the reaction is slowed and completion is not reached under "static" conditions. In practical terms, this is not the case for systems of low sequence complexity. This problem can be largely overcome by continuous or frequent mixing of the reactants, so that complex cDNA probes are hybridized essentially to completion, and kinetics can therefore be more readily compared to simple complexity standards.

Circular, but not circularly permuted, deoxyribonucleic acid reacts slower than linear deoxyribonucleic acid with complementary linear deoxyribonucleic acid

The electron microscope was used to count the number of double-stranded linear and circular renaturation products of a 2:1 by weight mixture of restricted double-stranded linear phi X174 RFI and single-stranded circular phi X174 viral deoxyribonucleic acid (DNA). More linear molecules than circular molecules are observed. However, when a 1:1 mixture of aliquots of either phi X174 RFI or SV40 DNA, each previously cleaved with a different single-site restriction enzyme, is denatured and renatured under conditions which assure circularization with out of phase molecules, an equal number of linear and circular molecules is observed. These experiments indicate that the nucleation rate is not affected by circular permutation of linear strands but is decreased approximately 3-fold when one of the reacting strands is circular. An excluded volume theory is developed which is consistent with these as well as previous results concerning the effects of DNA strand lengths on renaturation rates.

Characterization of single-stranded viral DNA sequences present during replication of adenovirus types 2 and 5

Replication intermediates of adenovirus DNA apparently contain extensive stretches of single-stranded DNA. Such single-stranded viral DNA sequences homologous to different regions of the viral genome present in adenovirus-infected cells during viral DNA replication have therefore been characterized by hybridization to the separated strands of restriction endonuclease fragments of 32P-labeled adenovirus types 2 and 5 DNA. Saturation hybridization experiments with infected cell DNA extracted at late times suggest that all regions of the adenovirus genome are represented in the single-stranded fraction, but at unequal frequencies. This nonuniform representation has been characterized in more detail with self-annealed, total cell DNA extracted 18 hr after adenovirus type 2 infection: the concentration of single-stranded sequences homologous to different regions of the viral genome was determined by comparing the rates of hybridization of 32P-labeled, single-stranded DNA probes with such self-annealed 18 hr DNA to the rates of hybridization of the same probes with equal concentrations of their complements. This approach allows the concentration of single-stranded viral DNA sequences in excess of their complements to be determined. Such sequences can be represented by two concentration gradients across the viral genome: those homologous to the r strand increase in concentration from 27.8-40.9 units toward the right end, whereas sequences homologous to the 1 strand increase from an area 27.8-40.9 units toward the left end. The time course of synthesis of single-stranded viral DNA sequences relative to accumulation of total viral DNA during the productive cycle and their behavior following a shift of H5ts125-infected cells in which viral DNA replication has begun from a permissive to a nonpermissive temperature support the contention that these sequences are indeed generated as adenovirus DNA is replicated. These results are therefore discussed in terms of current models of adenovirus DNA replication.

Studies on nucleic acid reassociation kinetics: empirical equations describing DNA reassociation

The rate of appearance of duplex DNA renaturation, measured with single strand specific nuclease, deviates significantly from a second order reaction. Measurements reported in paper I of this series indicate an inhibition in the rate of reassociation of single strand tails on partially reassociated molecules by a factor of at least two. Equations are derived that describe the observed form of reassociation kinetics as measured with hydroxyapatite and with single strand specific nuclease. The free parameter that describes the extent of inhibition of nucleation with single strand tails in these equations has been evaluated by least squares methods and agrees with the experimentally measured value.

Inverted repeat sequences in the Drosophila genome

The properties of inverted repeat (foldback) sequences in Drosophila melanogaster DNA have been studied by HAP chromatography and electron microscope methods. Electron microscope observations show that there is a broad distribution of lengths of the duplex regions of the inverted repeats from very short to greater than 15 kb, with number and weight average values of 1.35 kb and 5.0 kb respectively. About 20% of the inverted repeats are separated by a single-strand spacer with lengths too short to observe, but the other 80% have spacers, P, with lengths ranging from 0.5 kb to greater than 30 kb. The number average and weight average spacer lengths for the total sample are 2.7 kb and 6.1 kb. With respect to the lengths of the spacers, P, between inverted repeats, the Drosophila genome differs from that of most organisms which have been studied where the spacers P are mostly too short to be measured. EM and HAP studies suggest that the average center-to-center spacing between sets of inverted repeats is 40-80 kb. The HAP studies show that there is a broad range of thermal stabilities for the duplexes formed by reassociation of inverted repeat sequences. Kinetic analysis shows that all of the frequency components of the Drosophila genome are present in the inverted repeats, the loops P, and the flanking sequences. There is a somewhat larger proportion of middle repetitive DNA in those inverted repeat duplexes which are resistant to digestion by Mung Bean Endonuclease I. These enzyme resistant duplexes comprise about 3% of the entire genome. It is estimated that there are approximately 2000-4000 inverted repeat pairs in the entire genome.

Chicken leukosis virus genome sequences in DNA from normal chick cells and virus-induced bursal lymphomas

Genome sequences of two recent field isolates of avian leukosis viruses in the DNA of normal and neoplastic chicken cells were studied by DNA-RNA hybridization under conditions of DNA excess. Comparisons were made between 60-70S RNA from these viruses and that of a chicken endogenous type C virus (RAV-0), and of a series of "laboratory" leukosis and sarcoma viruses, by competitive hybridization analysis. A minimum of 18% of the genome sequences of both ALV isolates detected in DNA from lymphomas they induced were not detected in normal chicken DNA. The vast majority of the fraction of RNA sequences from ALV which do form hybrids with normal chick DNA appear to be reacting with the endogenous provirus of RAV-0. The genomic representation of a variety of avian leukosis and sarcoma viruses in normal chicken cells could not be distinguished by these methods (except that 13% of the RAV-0 genome was not shared with any of the other viruses). In contrast, the portion of the ALV genome exogenous to the normal chicken geome showed significant divergence from that of two sarcoma viruses (Pr RSV-C and B-77). The increased hybridization of ALV RNA with lymphoma DNA was used to detect the appearance of ALV specific sequences in the bursa of Fabricius following infection.increased hybridization was correlated with both the time after infection and the extent of replacement of the bursa by lymphoma. About one half of the increase in hybridization preceded histologic evidence of transformation.

Interspersion of repetitive and nonrepetitive DNA sequences in the Drosophila melanogaster genome

Cot analysis shows that the haploid Drosophila genome contains 12 percent rapidly reassociating, highly reiterated DNA, 12 percent middle repetitive DNA with an average reiteration frequency of 70, and 70 percent single-copy DNA. The distribution of the middle repetitive sequences in the genome has been studied by an examination in the electron microscope of the structures obtained when middle repetitive sequences present on large DNA strands reassociate and by the hydroxyapatite binding methods developed by Davidson et al. (1973). At least one third by weight of the middle repetitive sequences are interspersed in single-copy sequences. These interspersed middle repetitive sequences have a fairly uniform distribution of lengths from less than 0.5 to 13 kb, with a number average value of 5.6 kb. The average distance between middle repetitive sequences is greater than 13 kb. The data do not exclude the possibility that essentially all of the middle repetitive sequences have the interspersion pattern described above; however, it is possible that some of the middle repetitive sequences of Drosophila are clustered in stretches of length much greater than 13 kb. The interspersion pattern of the middle repetitive sequences in Drosophila is quite different from that which occurs in the sea urchin, in Xenopus, in rat, and probably many other higher eucaryotes.