There and (slowly) back again: entropy-driven hysteresis in a model of DNA overstretching

When pulled along its axis, double-stranded DNA elongates abruptly at a force of ∼65 pN. Two physical pictures have been developed to describe this overstretched state. The first proposes that strong forces induce a phase transition to a molten state consisting of unhybridized single strands. The second picture introduces an elongated hybridized phase called S-DNA. Little thermodynamic evidence exists to discriminate directly between these competing pictures. Here we show that within a microscopic model of DNA we can distinguish between the dynamics associated with each. In experiment, considerable hysteresis in a cycle of stretching and shortening develops as temperature is increased. Since there are few possible causes of hysteresis in a system whose extent is appreciable in only one dimension, such behavior offers a discriminating test of the two pictures of overstretching. Most experiments are performed upon nicked DNA, permitting the detachment (unpeeling) of strands. We show that the long-wavelength progression of the unpeeled front generates hysteresis, the character of which agrees with experiment only if we assume the existence of S-DNA. We also show that internal melting can generate hysteresis, the degree of which depends upon the nonextensive loop entropy of single-stranded DNA.     

Fine structure in the B-A transition of native DNA

The B-A transition caused by high ethanol concentrations has been studied by the multi-dimensional spectrophotometer equipped with the computer-controlled microbullet. When ethanol concentration is increased, the CD signal at 270 nm of linearized ColEl DNA exhibits a biphasic transition; the first broad one and the second sharp one. The B-A transition of the ColEl DNA is much broader than that of alternative copolymers with shorter lengths. In addition, each PvuII restriction fragment of ColEl DNA has a different transition curve. Therefore the stability of the B-A transition varies along a long DNA molecule. The second transition is speculated to be caused by aggregation. When ethanol concentration is decreased, on the other hand, only a single transition shifted to lower ethanol concentration is observed. Thus the B-A transition curve has a hysteresis. A slow dissociation rate of the aggregation seems to cause the hysteresis.     

Interaction of cationic surfactants with DNA: a single-molecule study

The interaction of cationic surfactants with single dsDNA molecules has been studied using force-measuring optical tweezers. For hydrophobic chains of length 12 and greater, pulling experiments show characteristic features (e.g. hysteresis between the pulling and relaxation curves, force-plateau along the force curves), typical of a condensed phase (compaction of a long DNA into a micron-sized particle). Depending on the length of the hydrophobic chain of the surfactant, we observe different mechanical behaviours of the complex (DNA-surfactants), which provide evidence for different binding modes. Taken together, our measurements suggest that short-chain surfactants, which do not induce any condensation, could lie down on the DNA surface and directly interact with the DNA grooves through hydrophobic–hydrophobic interactions. In contrast, long-chain surfactants could have their aliphatic tails pointing away from the DNA surface, which could promote inter-molecular interactions between hydrophobic chains and subsequently favour DNA condensation.     

Surviving the sun: repair and bypass of DNA UV lesions

Structural studies of UV-induced lesions and their complexes with repair proteins reveal an intrinsic flexibility of DNA at lesion sites. Reduced DNA rigidity stems primarily from the loss of base stacking, which may manifest as bending, unwinding, base unstacking, or flipping out. The intrinsic flexibility at UV lesions allows efficient initial lesion recognition within a pool of millions to billions of normal DNA base pairs. To bypass the damaged site by translesion synthesis, the specialized DNA polymerase η acts like a molecular "splint" and reinforces B-form DNA by numerous protein-phosphate interactions. Photolyases and glycosylases that specifically repair UV lesions interact directly with UV lesions in bent DNA via surface complementation. UvrA and UvrB, which recognize a variety of lesions in the bacterial nucleotide excision repair pathway, appear to exploit hysteresis exhibited by DNA lesions and conduct an ATP-dependent stress test to distort and separate DNA strands. Similar stress tests are likely conducted in eukaryotic nucleotide excision repair.     

A quantitative model of the effect of unreplicated DNA on cell cycle progression in frog egg extracts

A critical goal in cell biology is to develop a systems-level perspective of eukaryotic cell cycle controls. Among these controls, a complex signaling network (called ‘checkpoints’) arrests progression through the cell cycle when there is a threat to genomic integrity such as unreplicated or damaged DNA. Understanding the regulatory principles of cell cycle checkpoints is important because loss of checkpoint regulation may be a requisite step on the roadway to cancer. Mathematical modeling has proved to be a useful guide to cell cycle regulation by revealing the importance of bistability, hysteresis and time lags in governing cell cycle transitions and checkpoint mechanisms. In this report, we propose a mathematical model of the frog egg cell cycle including effects of unreplicated DNA on progression into mitosis. By a stepwise approach utilizing parameter estimation tools, we build a model that is grounded in fundamental behaviors of the cell cycle engine (hysteresis and time lags), includes new elements in the signaling network (Myt1 and Chk1 kinases), and fits a large and diverse body of data from the experimental literature. The model provides a validated framework upon which to build additional aspects of the cell cycle checkpoint signaling network, including those control signals in the mammalian cell cycle that are commonly mutated in cancer.     

Subpiconewton dynamic force spectroscopy using magnetic tweezers

We introduce a simple method for dynamic force spectroscopy with magnetic tweezers. This method allows application of subpiconewton force and twist control by calibration of the applied force from the height of the magnets. Initial dynamic force spectroscopy experiments on DNA molecules revealed a large hysteresis that is caused by viscous drag on the magnetic bead and will conceal weak interactions. When smaller beads are used, this hysteresis is sufficiently reduced to reveal intramolecular interactions at subpiconewton forces. Compared with typical quasistatic force spectroscopy, a significant reduction of measurement time is achieved, allowing the real-time study of transient structures and reaction intermediates. As a proof of principle, nucleosome-nucleosome interactions on a subsaturated chromatin fiber were analyzed.     

Mechanical stability of low-humidity single DNA molecules

DNA electrostatic character is mostly determined by both water and counterions activities in the phosphate backbone, which together with base sequence, further confer its higher order structure. The authors overstretch individual double-stranded DNA molecules in water-ethanol solutions to investigate the modulation of its mechanical stability by hydration and polycations. The authors found that DNA denatures as ethanol concentration is increased and spermine concentration decreased. This is manifested by an increase in melting hysteresis between the stretch and release curves, with sharp transition at 10% ethanol and reentrant behavior at 60%, by a loss of cooperativity in the overstretching transition and by a dramatic decrease of both the persistence length and the flexural rigidity. Changes in base-stacking stability which are characteristic of the B-A transition between 70 and 80% ethanol concentration do not manifest in the mechanical properties of the double-helical molecule at low or high force or in the behavior of the overstretching and melting transitions within this ethanol concentration range. This is consistent with a mechanism in which A-type base-stacking is unstable in the presence of tension. Binding of motor proteins to DNA locally reduces the number of water molecules and therefore, our results may shed light on analogous reduced-water activity of DNA conditions caused by other molecules, which interact with DNA in vivo.     

Modeling of Hysteresis in Gene Regulatory Networks

Hysteresis, observed in many gene regulatory networks, has a pivotal impact on biological systems, which enhances the robustness of cell functions. In this paper, a general model is proposed to describe the hysteretic gene regulatory network by combining the hysteresis component and the transient dynamics. The Bouc-Wen hysteresis model is modified to describe the hysteresis component in the mammalian gene regulatory networks. Rigorous mathematical analysis on the dynamical properties of the model is presented to ensure the bounded-input-bounded-output (BIBO) stability and demonstrates that the original Bouc-Wen model can only generate a clockwise hysteresis loop while the modified model can describe both clockwise and counter clockwise hysteresis loops. Simulation studies have shown that the hysteresis loops from our model are consistent with the experimental observations in three mammalian gene regulatory networks and two E.coli gene regulatory networks, which demonstrate the ability and accuracy of the mathematical model to emulate natural gene expression behavior with hysteresis. A comparison study has also been conducted to show that this model fits the experiment data significantly better than previous ones in the literature. The successful modeling of the hysteresis in all the five hysteretic gene regulatory networks suggests that the new model has the potential to be a unified framework for modeling hysteresis in gene regulatory networks and provide better understanding of the general mechanism that drives the hysteretic function.     

Mechanical stability of single DNA molecules

Using a modified atomic force microscope (AFM), individual double-stranded (ds) DNA molecules attached to an AFM tip and a gold surface were overstretched, and the mechanical stability of the DNA double helix was investigated. In lambda-phage DNA the previously reported B-S transition at 65 piconewtons (pN) is followed by a second conformational transition, during which the DNA double helix melts into two single strands. Unlike the B-S transition, the melting transition exhibits a pronounced force-loading-rate dependence and a marked hysteresis, characteristic of a nonequilibrium conformational transition. The kinetics of force-induced melting of the double helix, its reannealing kinetics, as well as the influence of ionic strength, temperature, and DNA sequence on the mechanical stability of the double helix were investigated. As expected, the DNA double helix is considerably destabilized under low salt buffer conditions (相似文献   

Behavior of supercoiled DNA.

We study DNA supercoiling in a quantitative fashion by micromanipulating single linear DNA molecules with a magnetic field gradient. By anchoring one end of the DNA to multiple sites on a magnetic bead and the other end to multiple sites on a glass surface, we were able to exert torsional control on the DNA. A rotating magnetic field was used to induce rotation of the magnetic bead, and reversibly over- and underwind the molecule. The magnetic field was also used to increase or decrease the stretching force exerted by the magnetic bead on the DNA. The molecule's degree of supercoiling could therefore be quantitatively controlled and monitored, and tethered-particle motion analysis allowed us to measure the stretching force acting on the DNA. Experimental results indicate that this is a very powerful technique for measuring forces at the picoscale. We studied the effect of stretching forces ranging from 0.01 pN to 100 pN on supercoiled DNA (-0.1 < sigma < 0.2) in a variety of ionic conditions. Other effects, such as stretching-relaxing hysteresis and the braiding of two DNA molecules, are discussed.     

Nanomechanics of Diaminopurine-Substituted DNA

2,6-diaminopurine (DAP) is a nucleobase analog of adenine. When incorporated into double-stranded DNA (dsDNA), it forms three hydrogen bonds with thymine. Rare in nature, DAP substitution alters the physical characteristics of a DNA molecule without sacrificing sequence specificity. Here, we show that in addition to stabilizing double-strand hybridization, DAP substitution also changes the mechanical and conformational properties of dsDNA. Thermal melting experiments reveal that DAP substitution raises melting temperatures without diminishing sequence-dependent effects. Using a combination of atomic force microscopy (AFM), magnetic tweezer (MT) nanomechanical assays, and circular dichroism spectroscopy, we demonstrate that DAP substitution increases the flexural rigidity of dsDNA yet also facilitates conformational shifts, which manifest as changes in molecule length. DAP substitution increases both the static and dynamic persistence length of DNA (measured by AFM and MT, respectively). In the static case (AFM), in which tension is not applied to the molecule, the contour length of DAP-DNA appears shorter than wild-type (WT)-DNA; under tension (MT), they have similar dynamic contour lengths. At tensions above 60 pN, WT-DNA undergoes characteristic overstretching because of strand separation (tension-induced melting) and spontaneous adoption of a conformation termed S-DNA. Cyclic overstretching and relaxation of WT-DNA at near-zero loading rates typically yields hysteresis, indicative of tension-induced melting; conversely, cyclic stretching of DAP-DNA showed little or no hysteresis, consistent with the adoption of the S-form, similar to what has been reported for GC-rich sequences. However, DAP-DNA overstretching is distinct from GC-rich overstretching in that it happens at a significantly lower tension. In physiological salt conditions, evenly mixed AT/GC DNA typically overstretches around 60 pN. GC-rich sequences overstretch at similar if not slightly higher tensions. Here, we show that DAP-DNA overstretches at 52 pN. In summary, DAP substitution decreases the overall stability of the B-form double helix, biasing toward non-B-form DNA helix conformations at zero tension and facilitating the B-to-S transition at high tension.     

Evaluation of pyrimidine PNA binding to ssDNA targets from nonequilibrium melting experiments.

Slow kinetics of homopyrimidine PNA binding to single stranded DNA and RNA targets is manifested in significant hysteresis in thermal UV absorption experiments. We have compared temperatures of dissociation (Tdis) and reassociation (Tass) for triplexes formed by DNA and single or bis PNAs with K50 derived from gel mobility experiments. Results indicated there was no correlation between Tdis and K50 while reasonable correlation between Tass and K50 was found. This correlation enabled use of easy thermal UV absorption experiments for evaluation of PNA binding to DNA/RNA targets.     

The dnaB gene product of Escherichia coli. II. Single stranded DNA-dependent ribonucleoside triphosphatase activity.

The single-stranded DNA-dependent ribonucleoside triphosphatase activity of the Escherichia coli dnaB gene product was characterized. Purine ribonucleoside triphosphates were the preferred substrates, but all ribonucleoside triphosphates were cleaved at the gamma position to yield ribonucleoside diphosphates and Pi. The enzyme required Mg2+, which could be replaced by Mn2+ but with lower activity. The pH optimum was 7.5 in either Tris-HCl or phosphate buffer. The Km for MgATP was 0.59 mM and the Vmax was 8.7 nmol/min/microgram of protein at 30 degrees. The DNA requirement was best satisfied with either fd or phiX174 single-stranded DNA (Km 0.033 mM nucleotides); maximal rate of nucleoside diphosphate formation occurred with 1 dnaB molecule/fd or phiX174 single-stranded DNA molecule. The dnaB gene product was found to have hysteretic properties and the hysteresis appeared to be due to a dissociation and reassociation of the enzyme.     

Short electric-field pulses convert DNA from "condensed" to "free" conformation

Electric-field pulses of e.g. 20 kV/cm and 100 μs induce a strong decrease in the scattered light intensity of DNA condensed by spermine. Analysis of this effect demonstrates that the decrease of the scattered light intensity results from decondensation of DNA. The decondensation reaction requires an electric-field strength exceeding a threshold value. Complete decondensation can be achieved at field strength that are only slightly higher than the threshold value. The decondensation process is strongly accelerated at high electric-field strengths. At 30 kV/cm, the decondensation time constant is ～8 μs, corresponding to an acceleation factor of 10⁵ relative to the field-free decondensation reaction. The dependence of the time constants on the electric-field strength suggests that the field-induced decondensation is due to a dissociation field effect. The condensation process observed after electric-field pulses at low concentrations of DNA and spermine shows a characteristic induction period, which strongly depends on the spermine concentration. This induction period reflects the time required for the binding of spermine to DNA, until the degree of binding is sufficiently high for the condensation reaction. The fast dissociation of condensed DNA by electric-field pulses together with a relatively long lifetime of the free DNA results in a reaction cycle resembling a hysteresis loop.     

Hysteresis in poly‐2′‐deoxycytidine i‐motif folding is impacted by the method of analysis as well as loop and stem lengths

In DNA, i‐motif (iM) folds occur under slightly acidic conditions when sequences rich in 2′‐deoxycytidine (dC) nucleotides adopt consecutive dC self base pairs. The pH stability of an iM is defined by the midpoint in the pH transition (pH_T) between the folded and unfolded states. Two different experiments to determine pH_T values via circular dichroism (CD) spectroscopy were performed on poly‐dC iMs of length 15, 19, or 23 nucleotides. These experiments demonstrate two points: (1) pH_T values were dependent on the titration experiment performed, and (2) pH‐induced denaturing or annealing processes produced isothermal hysteresis in the pH_T values. These results in tandem with model iMs with judicious mutations of dC to thymidine to favor particular folds found the hysteresis was maximal for the shorter poly‐dC iMs and those with an even number of base pairs, while the hysteresis was minimal for longer poly‐dC iMs and those with an odd number of base pairs. Experiments to follow the iM folding via thermal changes identified thermal hysteresis between the denaturing and annealing cycles. Similar trends were found to those observed in the CD experiments. The results demonstrate that the method of iM analysis can impact the pH_T parameter measured, and hysteresis was observed in the pH_T and T_m values.     

Cooperative function of ammonium polyacrylate with antifreeze protein type I

Activity of antifreeze proteins (AFPs) and antifreeze glycoproteins (AFGPs) is often determined by thermal hysteresis, which is the difference between the melting temperature and the nonequilibrium freezing temperature of ice in AF(G)P solutions. In this study, we confirmed that thermal hysteresis of AFP type I is significantly enhanced by a cooperative function of ammonium polyacrylate (NH4PA). Thermal hysteresis of mixtures of AFP type I and NH4PA was much larger than the sum of each thermal hysteresis of AFP type I and NH4PA alone. In mixed solutions of AFP type I and NH4PA in the thermal hysteresis region, hexagonal pyramidal-shaped pits densely formed on ice surfaces close to the basal planes. The experimental results suggest that the cooperative function of NH4PA with AFP type I was caused either by the increase in adsorption sites of AFP type I on ice or by the adsorption of AFP type I aggregates on ice.     

Physico-chemical description of a condensed form of DNA

When exposed to a low pH, in various ionic strength conditions and in sufficiently dilute solutions, DNA undergoes a transition, revealed by an increase in optical density. A careful analysis shows that, associated with this transition, there is an effective decrease in absorbance, overcompensated by an increase in scattering. The conditions for the new transition can be summarized conveniently by a graph in a pH–Na⁺ molarity diagram. If the pH of a DNA solution is progressively lowered at constant Na⁺ concentration, one finds first the melting transition (I), and at lower pH values, the new transition (II). If the same experiment is performed on pre-denatured DNA, only transition II will be found. If native DNA is brought directly to the low pH conditions, without allowing it to denature irreversibly at intermediate pH values, transition II is reversible (with a small hysteresis effect). DNA, initially native, neutralized after prolonged exposures to the low pH, recovers the buoyant density value of native DNA, along with the absorption and scattering properties of the native state. The experiments are consistent with the interpretation that a new state exists in which DNA, still double stranded, assumes a very compact shape (of the order of 1500 Å in diameter for T2 DNA), with a hyperchromicity value of 10–14% above the native value. Nearly monodisperse suspensions of DNA molecule in this apparent state may be obtained only at very low concentrations (～0.25 μg/ml). At 1 μg DNA/ml aggregation is noticeable. The possible connection with the condition of intraphage DNA is discussed.     

The adsorption of DNA in the mercury electrolyte interface. 3. Reaction of DNA in the mercury-electrolyte interface

The adsorption of deoxyribonucleic acid in the mercury-electrolyte interface was investigated. The effect of this adsorption on the differential capacity of the electrical double layer at the interface between a stationary mercury drop electrode (HMDE) and a buffered aqueous sodium chloride solution was measured. The dependences of this differential capacity on potential, time, and pH was studied in the presence of native and also of denatured DNA. These results were compared with the adsorption of model compounds and with the general theory of the adsorption of polymers. The structure of the adsorbed DNA molecules corresponds to an alternating arrangement of two-dimensional, totally adsorbed sequences and three-dimensional loops extending into the solution. The adsorbed sequences and loops consist of several segments with a specific free-energy change of adsorption. Essentially this energy determines the distribution of the segments between adsorbed sequences and loops. The absolute value of this energy change per segment is fairly large in the case of negatively charged poly-electrolyte DNA at the weakly positively charged interface near the electrocapillary maximum (ECM). The fraction of totally adsorbed segments is relatively large in this potential region. The more negative the potential the lower is the absolute value of free energy change of adsorption per segment. Under the conditions unfavorable for the adsorption, only a few segments can be adsorbed. Most of the segments of the adsorbed DNA molecules extend into the solution and therefore fairly high interface concentrations can be reached. Thus, the arrangement of DNA molecules in the electrode surface is changed when the potential is altered from values near the ECM to more negative ones. This change should produce the wave on the differential capacity curves at a little more negative potential than that of ECM. At a more negative potential, intermolecular interactions between the loops extending into the solution may occur. The adsorption tendency of the resulting associates is higher than that of the isolated molecules. Therefore the isolated molecules desorb at sufficient negatively charged interface producing a round wave while the associates stay adsorbed. At this potential it is impossible for native DNA to generate associates because they are formed from the isolated molecules. This explains the hysteresis loop of the curves of differential capacity vs. potential by using the HMDE. The desorption of the associates is indicated by a sharp wave at much more negative potential. For denatured DNA the associates arise from the very few isolated adsorbed molecules at this potential; therefore, no hysteresis loop occurs. The association constant of denatured DNA must be much higher than that of the native DNA. The reasons for this are discussed.