Intrachain reactions of supercoiled DNA simulated by Brownian dynamics

We considered an irreversible biochemical intrachain reaction of supercoiled DNA as a random event that occurs, with certain probability, at the instant of collision between two reactive groups bound to distant DNA sites. Using the Brownian dynamics technique, we modeled this process for a supercoiled DNA molecule of 2.5 kb length in dilute aqueous solution at an NaCl concentration of 0.1 M. We calculated the mean reaction time tau(Sigma) as a function of the intrinsic second-order rate constant k(I), the reaction radius R, and the contour separation S of the reactive groups. At the diffusion-controlled limit (k(I) --> infinity), the kinetics of reaction are determined by the mean time tau(F) of the first collision. The dependence of tau(F) on R is close to inversely proportional, implying that the main contribution to the productive collisions is made by bending of the superhelix axis. At sufficiently small k(I), the mean reaction time can be satisfactory approximated by tau(Sigma) = tau(F)(app) + 1/(k(I)c(L)), where c(L) is the local concentration of one reactive group around the other, and tau is an adjustable parameter, which we called the apparent time of the first collision. The value of tau depends on R very weakly and is approximately equal to the mean time of the first collision caused by mutual reptation of two DNA strands forming the superhelix. The quasi-one-dimensional reptation process provides the majority of productive collisions at small k(I) values.     

Brownian dynamics simulations of supercoiled DNA with bent sequences.

The recently presented Brownian dynamics model for superhelical DNA is extended to include local curvature of the DNA helix axis. Here we analyze the effect of a permanent bend on the structure and dynamics of an 1870-bp superhelix with delta Lk = -10. Furthermore, we define quantitative expressions for computing structural parameters such as loop positions, superhelix diameter, and plectonemic content for trajectories of superhelical DNA, and assess the convergence toward global equilibrium. The structural fluctuations in an interwound superhelix, as reflected in the change in end loop positions, seem to occur by destruction/creation of loops rather than by a sliding motion of the DNA around its contour. Their time scale is on the order of 30-100 microseconds. A permanent bend changes the structure and the internal motions of the DNA drastically. The position of the end loop is fixed at the permanent bend, and the local motions of the chain are enhanced near the loops. A displacement of the bend from the end loop to a position inside the plectonemic part of the superhelix results in the formation of a new loop and the disappearance of the old one; we estimate the time involved in this process to be about 0.5 ms.     

Rotational dynamics of curved DNA fragments studied by fluorescence polarization anisotropy

The rotational dynamics of short DNA fragments with or without intrinsic curvature were studied using time-resolved phase fluorimetry of intercalated ethidium with detection of the anisotropy. Parameters determined were the spinning diffusion coefficient of the DNA fragments about the long axis and the zero-time ethidium fluorescence anisotropy. We find a significant decrease in the spinning diffusion coefficient for all curved fragments compared to the straight controls. This decrease is likewise evident in rotational diffusion coefficients computed from DNA structures obtained by a curvature prediction program for these sequences. Using a hinged-cylinder model, we can identify the change in rotational diffusion coefficient with a permanent bend of 13-16 degrees per helix turn for the sequences studied. Moreover, for some of the curved fragments an increased flexibility has to be assumed in addition to the permanent bend in order to explain the data.     

General methods for analysis of sequential "n-step" kinetic mechanisms: application to single turnover kinetics of helicase-catalyzed DNA unwinding

Helicase-catalyzed DNA unwinding is often studied using "all or none" assays that detect only the final product of fully unwound DNA. Even using these assays, quantitative analysis of DNA unwinding time courses for DNA duplexes of different lengths, L, using "n-step" sequential mechanisms, can reveal information about the number of intermediates in the unwinding reaction and the "kinetic step size", m, defined as the average number of basepairs unwound between two successive rate limiting steps in the unwinding cycle. Simultaneous nonlinear least-squares analysis using "n-step" sequential mechanisms has previously been limited by an inability to float the number of "unwinding steps", n, and m, in the fitting algorithm. Here we discuss the behavior of single turnover DNA unwinding time courses and describe novel methods for nonlinear least-squares analysis that overcome these problems. Analytic expressions for the time courses, f(ss)(t), when obtainable, can be written using gamma and incomplete gamma functions. When analytic expressions are not obtainable, the numerical solution of the inverse Laplace transform can be used to obtain f(ss)(t). Both methods allow n and m to be continuous fitting parameters. These approaches are generally applicable to enzymes that translocate along a lattice or require repetition of a series of steps before product formation.     

Dual binding modes for an HMG domain from human HMGB2 on DNA

High mobility group B (HMGB) proteins contain two HMG box domains known to bind without sequence specificity into the DNA minor groove, slightly intercalating between basepairs and producing a strong bend in the DNA backbone. We use optical tweezers to measure the forces required to stretch single DNA molecules. Parameters describing DNA flexibility, including contour length and persistence length, are revealed. In the presence of nanomolar concentrations of isolated HMG box A from HMGB2, DNA shows a decrease in its persistence length, where the protein induces an average DNA bend angle of 114 +/- 21 degrees for 50 mM Na+, and 87 +/- 9 degrees for 100 mM Na+. The DNA contour length increases from 0.341 +/- 0.003 to 0.397 +/- 0.012 nm per basepair, independent of salt concentration. In 50 mM Na+, the protein does not unbind even at high DNA extension, whereas in 100 mM Na+, the protein appears to unbind only below concentrations of 2 nM. These observations support a flexible hinge model for noncooperative HMG binding at low protein concentrations. However, at higher protein concentrations, a cooperative filament mode is observed instead of the hinge binding. This mode may be uniquely characterized by this high-force optical tweezers experiment.     

Structure of the Tet repressor and Tet repressor-operator complexes in solution from electrooptical measurements and hydrodynamic simulations

The Tet repressor protein and tet operator DNA fragments and their complexes have been analyzed by electrooptical procedures. The protein shows a positive linear dichroism at 280 nm, a negative linear dichroism at 248 nm, and a strong permanent dipole moment of 3.5 X 10(-27) C m, which is independent of the salt concentration within experimental accuracy. Its rotation time constant of 40 ns indicates an elongated structure, which is consistent with a prolate ellipsoid of 100 A for the long axis and 40 A for the short axis. The time constant can also be fitted by a cylinder of length 78 A and diameter 37 A, which is consistent with nuclease protection data reported on repressor-operator complexes, if the cylinder axis is aligned parallel to the DNA axis. Addition of tetracycline induces changes of the limit dichroism but very little change of the rotation time constant. The rotation time constants observed for the operator DNA fragments show some deviations from the values expected from their contour length; however, these deviations remain relatively small. Formation of repressor-operator complexes leads to some increase of the DNA rotation time constants. Simulations by bead models demonstrate that these time constants can be explained without any major change of the hydrodynamic dimension of the components. The data for the complexes are fitted by bead models with smooth bending of the DNA corresponding to a radius of curvature of 500 A, but at the given accuracy, we cannot rule out that the DNA in the complex remains straight or is bent to a smaller radius of approximately 400 A. Thus, binding of the Tet repressor, which is a helix-turn-helix protein as judged from its sequence, to its operator seems to induce minor bending but does not induce strong bending of the DNA double helix.     

Structure of DNA within three isometric bacteriophages.

This paper describes a model for the structure of DNA contained in three morphologically similar bacteriophages--T7, P22 and phiCd-1--based on the transient electric dichroism of intact phage. The reduced dichroism of each of the phages at perfect orientation is within the range +0.12 to +0.19. Assuming that the phage orientation axis is that which passes from the apex through the tail, the measured dichroism suggests that DNA is wrapped in closely packed, co-axial solenoids with the axis of the solenoids tipped 43.5 degrees +/- 2.5 degrees from the orientation axis of the phage. All three phages show a large permanent dipole moment, with respective values of 5600, 200,000 and 500,000 Debye for T7, phiCd-1 and P22. The radius of the equivalent sphere for the three phages calculated from the rotational relaxation time for the rise of dichroism is in agreement with birefringence and electron microscope observations. The circular dichroism spectra of all three bacteriophages indicate that the local DNA helicity is similar in each case.     

The visualization of amplicons after polymerase chain reaction

Linear DNA molecules amplified by the polymerase chain reaction were visualized by atomic force microscopy. The measured contour length of the PCR product of 1414 bp sequence was 435 +/- 15 nm. Considering that the calculated value of the distance between the nucleotides along the duplex axis is 0.31 nm, it was assumed that linear DNA molecules on the surface of mica, which serve as a support in the atomic force microscopy method, are in the A form. The influence of surface properties of the mica and the sample drying procedure on the conformation of adsorbed DNA molecules is discussed. Possible reasons for the Gaussian distribution of the contour length of the synthesized amplicon are considered.     

Particle size distribution in DMPC vesicles solutions undergoing different sonication times

Size distribution of dimyristoylphosphatidylcholine liposome suspensions was investigated by dynamic-light scattering (DLS) as a function of the sonication time (t(s)). Cumulant expansion (second- and third-order) and regularized Laplace inversion (CONTIN) of dynamic single-angle laser light-scattering data were performed. With both methods, the intensity-weighted mean hydrodynamic radius r(I) depended on the investigated lengthscale. The number-weighted mean hydrodynamic radius (r(N)), obtained from CONTIN by modeling dimyristoylphosphatidylcholine vesicles as thin-walled hollow spheres, resulted as independent on the lengthscale. However, the r(N) value obtained from cumulant expansions remained lengthscale-dependent. Therefore, the number-weighted radius distribution function is highly asymmetric. The number-weighted mean radius, the standard deviation, and the number-weighted radius at the peak (r(N)(peak)) all decreased to a plateau when increasing sonication time. At t(s) longer than 1 h, the r(N)(peak) compares well with the radius of unilamellar vesicles in equilibrium with monomers predicted on a thermodynamic basis. The reliability of our analysis is proved by the comparison of experimental Rayleigh ratios with simulated ones, using the normalized number-weighted radius distribution function p(N)(r) determined by DLS data. A perfect agreement was obtained at longer sonication times, and the average aggregation number was determined. At lower t(s) values, simulations did not match experimental data, and this discrepancy was ascribed to the presence of large and floppy unilamellar vesicles with ellipsoidal shapes. Our investigation shows that, from single-angle DLS data, the radius distribution function of the vesicles can only be obtained if p(N)(r) is known.     

Dynamic bending rigidity of a 200-bp DNA in 4 mM ionic strength: a transient polarization grating study

DNA may exhibit three different kinds of bends: 1) permanent bends; 2) slowly relaxing bends due to fluctuations in a prevailing equilibrium between differently curved secondary conformations; and 3) rapidly relaxing dynamic bends within a single potential-of-mean-force basin. The dynamic bending rigidity (kappa(d)), or equivalently the dynamic persistence length, P(d) = kappa(d)/k(B)T, governs the rapidly relaxing bends, which are responsible for the flexural dynamics of DNA on a short time scale, t < or = 10(-5) s. However, all three kinds of bends contribute to the total equilibrium persistence length, P(tot), according to 1/P(tot) congruent with 1/P(pb) + 1/P(sr) + 1/P(d), where P(pb) is the contribution of the permanent bends and P(sr) is the contribution of the slowly relaxing bends. Both P(d) and P(tot) are determined for the same 200-bp DNA in 4 mM ionic strength by measuring its optical anisotropy, r(t), from 0 to 10 micros. Time-resolved fluorescence polarization anisotropy (FPA) measurements yield r(t) for DNA/ethidium complexes (1 dye/200 bp) from 0 to 120 ns. A new transient polarization grating (TPG) experiment provides r(t) for DNA/methylene blue complexes (1 dye/100 bp) over a much longer time span, from 20 ns to 10 micros. Accurate data in the very tail of the decay enable a model-independent determination of the relaxation time (tau(R)) of the end-over-end tumbling motion, from which P(tot) = 500 A is estimated. The FPA data are used to obtain the best-fit pairs of P(d) and torsion elastic constant (alpha) values that fit those data equally well, and which are used to eliminate alpha as an independent variable. When the relevant theory is fitted to the entire TPG signal (S(t)), the end-over-end rotational diffusion coefficient is fixed at its measured value and alpha is eliminated in favor of P(d). Neither a true minimum in chi-squared nor a satisfactory fit could be obtained for P(d) anywhere in the range 500-5000 A, unless an adjustable amplitude of azimuthal wobble of the methylene blue was admitted. In that case, a well-defined global minimum and a reasonably good fit emerged at P(d) = 2000 A and (1/2) = 25 degrees. The discrimination against P(d) values <1600 A is very great. By combining the values, P(tot) = 500 A and P(d) = 2000 A with a literature estimate, P(pb) = 1370 A, a value P(sr) = 1300 A is estimated for the contribution of slowly relaxing bends. This value is analyzed in terms of a simple model in which the DNA is divided up into domains containing m bp, each of which experiences an all-or-none equilibrium between a straight and a uniformly curved conformation. With an appropriate estimate of the average bend angle per basepair of the curved conformation, a lower bound estimate, m = 55 bp, is obtained for the domain size of the coherently bent state. Previous measurements suggest that this coherent bend is not directional, or phase-locked, to the azimuthal orientation of the filament.     

Single-particle tracking of oriC-GFP fluorescent spots during chromosome segregation in Escherichia coli

DNA regions close to the origin of replication were visualized by the green fluorescent protein (GFP)-Lac repressor/lac operator system. The number of oriC-GFP fluorescent spots per cell and per nucleoid in batch-cultured cells corresponded to the theoretical DNA replication pattern. A similar pattern was observed in cells growing on microscope slides used for time-lapse experiments. The trajectories of 124 oriC-GFP spots were monitored by time-lapse microscopy of 31 cells at time intervals of 1, 2, and 3 min. Spot positions were determined along the short and long axis of cells. The lengthwise movement of spots was corrected for cell elongation. The step sizes of the spots showed a Gaussian distribution with a standard deviation of approximately 110 nm. Plots of the mean square displacement versus time indicated a free diffusion regime for spot movement along the long axis of the cell, with a diffusion coefficient of 4.3+/-2.6x10(-5) microm2/s. Spot movement along the short axis showed confinement in a region of the diameter of the nucleoid ( approximately 800 nm) with an effective diffusion coefficient of 2.9+/-1.7x10(-5) microm2/s. Confidence levels for the mean square displacement analysis were obtained from numerical simulations. We conclude from the analysis that within the experimental accuracy--the limits of which are indicated and discussed--there is no evidence that spot segregation requires any other mechanism than that of cell (length) growth.     

Modulation of intramolecular interactions in superhelical DNA by curved sequences: a Monte Carlo simulation study.

A Monte Carlo model for the generation of superhelical DNA structures at thermodynamic equilibrium (Klenin et al., 1991; Vologodskii et al., 1992) was modified to account for the presence of local curvature. Equilibrium ensembles of a 2700-bp DNA chain at linking number difference delta Lk = -15 were generated, with one or two permanent bends up to 120 degrees inserted at different positions. The computed structures were then analyzed with respect to the number and positions of the end loops of the interwound superhelix, and the intramolecular interaction probability of different segments of the DNA. We find that the superhelix structure is strongly organized by permanent bends. A DNA segment with a 30 degrees bend already has a significantly higher probability of being at the apex of a superhelix than the control, and for a 120 degrees bend the majority of DNAs have one end loop at the position of the bend. The entropy change due to the localization of a 120 permanent bend in the end loop is estimated to be -17 kJ mol-1 K-1. When two bends are inserted, the conformation of the superhelix is found to be strongly dependent on their relative positions: the straight interwound form dominates when the two bends are separated by 50% of the total DNA length, whereas the majority of the superhelices are in a branched conformation when the bends are separated by 33%. DNA segments in the vicinity of the permanent bend are strongly oriented with respect to each other.     

Probing DNA conformational changes with high temporal resolution by tethered particle motion

The tethered particle motion (TPM) technique informs about conformational changes of DNA molecules, e.g. upon looping or interaction with proteins, by tracking the Brownian motion of a particle probe tethered to a surface by a single DNA molecule and detecting changes of its amplitude of movement. We discuss in this context the time resolution of TPM, which strongly depends on the particle-DNA complex relaxation time, i.e. the characteristic time it takes to explore its configuration space by diffusion. By comparing theory, simulations and experiments, we propose a calibration of TPM at the dynamical level: we analyze how the relaxation time grows with both DNA contour length (from 401 to 2080 base pairs) and particle radius (from 20 to 150 nm). Notably we demonstrate that, for a particle of radius 20 nm or less, the hydrodynamic friction induced by the particle and the surface does not significantly slow down the DNA. This enables us to determine the optimal time resolution of TPM in distinct experimental contexts which can be as short as 20 ms.     

ESR signal of the iron-sulfur center F(X) and its function in the homodimeric reaction center of Heliobacterium modesticaldum

Electron transfer in the membranes and the type I reaction center (RC) core protein complex isolated from Heliobacterium modesticaldum was studied by optical and ESR spectroscopy. The RC is a homodimer of PshA proteins. In the isolated membranes, illumination at 14 K led to accumulation of a stable ESR signal of the reduced iron-sulfur center F(B)(-) in the presence of dithiothreitol, and an additional 20 min illumination at 230 K induced the spin-interacting F(A)(-)/F(B)(-) signal at 14 K. During illumination at 5 K in the presence of dithionite, we detected a new transient signal with the following values: g(z)= 2.040, g(y)= 1.911, and g(x)= 1.896. The signal decayed rapidly with a 10 ms time constant after the flash excitation at 5 K and was attributed to the F(X)(-)-type center, although the signal shape was more symmetrical than that of F(X)(-) in photosystem I. In the purified RC core protein, laser excitation induced the absorption change of a special pair, P800. The flash-induced P800(+) signal recovered with a fast 2-5 ms time constant below 150 K, suggesting charge recombination with F(X)(-). Partial destruction of the RC core protein complex by a brief exposure to air increased the level of the P800(+)A(0)(-) state that gave a lifetime (t(1/2)) of 100 ns at 77 K. The reactions of F(X) and quinone were discussed on the basis of the three-dimensional structural model of RC that predicts the conserved F(X)-binding site and the quinone-binding site, which is more hydrophilic than that in the photosystem I RC.     

B-S transition in short oligonucleotides

Stretching experiments with long double-stranded DNA molecules in physiological ambient revealed a force-induced transition at a force of 65 pN. During this transition between B-DNA and highly overstretched S-DNA the DNA lengthens by a factor of 1.7 of its B-form contour length. Here, we report the occurrence of this so-called B-S transition in short duplexes consisting of 30 basepairs. We employed atomic-force-microscope-based single molecule force spectroscopy to explore the unbinding mechanism of two short duplexes containing 30 or 20 basepairs by pulling at the opposite 5' termini. For a 30-basepair-long DNA duplex the B-S transition is expected to cause a length increase of 6.3 nm and should therefore be detectable. Indeed 30% of the measured force-extension curves exhibit a region of constant force (plateau) at 65 pN, which corresponds to the B-S transition. The observed plateaus show a length between 3 and 7 nm. This plateau length distribution indicates that the dissociation of a 30-basepair duplex mainly occurs during the B-S transition. In contrast, the measured force-extension curves for a 20-basepair DNA duplex exhibited rupture forces below 65 pN and did not show any evidence of a B-S transition.     

Relationship between curved DNA conformations and slow gel migration

We propose some specific DNA conformations that explain, in terms of molecular conformations, the anomalous gel electrophoretic behavior of the sequences (VA4T4X), and (V2A3T3X2)i where V and X are either G or C. Previously (J. Biomole. Struct. Dyn. 4, 41, 1986) we considered hydrophobic interactions among aliphatic hydrocarbon groups in A/T sequences. In the sequences (T)n.(A)n, the T's are slightly bent to yield structures with tightly stacked methyl groups along one side of the major groove. By folding together the two pairs of stacked methyls on the opposite sides of the major groove. TTAA might yield a relatively sharp bend. On this basis, we show below that the sequences (VT4A4X)i might form a very tightly coiled super-helix whereas the sequences (VA4T4X)i form a broad super-helix of radius approximately 120 A for i = 25. The sequence (V2A3T3X2)i forms a slightly smaller radius super-helix. The time of passage through the gel has been taken to be inversely proportional to the smallest dimension of the molecule. Specifically we are taking the ratio of the apparent molecular weight to the actual molecular weight to be related to the moment of inertia I1 about the smallest principal axis of the molecular conformation. We find a good fit to the experimental gel mobility data of Hagerman (2) if we assume this ratio to be proportional to (I1)1/5.     

Refinement of the solution structure of a branched DNA three-way junction.

We have refined the structure of the DNA Three-Way Junction complex, TWJ-TC, described in the companion paper by quantitative analysis of two 2D NOESY spectra (mixing times 60 and 200 ms) obtained in D2O solution. NOESY crosspeak intensities extracted from these spectra were used in two kinds of refinement procedure: 1) distance-restrained energy minimization (EM) and molecular dynamics (MD) and 2) full relaxation matrix back calculation refinement. The global geometry of the refined model is very similar to that of a published, preliminary model (Leontis, 1993). Two of the helical arms of the junction are stacked. These are Helix 1, defined by basepairs S1-G1/S3-C12 through S1-C5/S3-G8 and Helix 2, which comprises basepairs S1-C6/S2-G5 through S1-G10/S2-G1. The third helical arm (Helix 3), comprised of basepairs S2-C6/S3-G5 through S2-C10/S3-G1 extends almost perpendicularly from the axis defined by Helices 1 and 2. The bases S1-C5 and S1-C6 of Strand 1 are continuously stacked across the junction region. The conformation of this strand is close to that of B-form DNA along its entire length, including the S1-C5 to S1-C6 dinucleotide step at the junction. The two unpaired bases S3-T6 and S3-C7 lie outside of the junction along the minor groove of Helix 1 and largely exposed to solvent. Analysis of the refined structure reveals that the glycosidic bond of S3-T6 exists in the syn conformation, allowing the methyl group of this residue to contact the hydrophobic surface of the minor groove of Helix 1, at S3-G11.(ABSTRACT TRUNCATED AT 250 WORDS)     

Photoaccumulation of two ascorbyl free radicals per photosystem I at 200 K

Illumination of photosystem I (PSI) from the cyanobacterium Synechocystis sp. PCC 6803 at 200 K in the presence of ascorbate leads to the formation of two ascorbyl radicals per PSI, which are formed by P700(+) reduction by ascorbate. During photoaccumulation, one half of the ascorbyl radicals is formed with a halftime of 1 min and the other half with a halftime of 7 min. Pulsed electron paramagnetic resonance (EPR) experiments with protonated/deuterated PSI show that a PSI proton/deuteron is strongly coupled to the ascorbyl radical. Our data indicate that reactive ascorbate molecules bind to PSI at two specific locations, which might be symmetrically located with respect to the pseudo-C(2) axis of symmetry of the heterodimeric core of PSI. Reduction of P700(+) by ascorbate leads to multiple turnover of PSI photochemistry, resulting in partial photoaccumulation of the doubly reduced species (F(A)(-), F(B)(-)). A modified form of F(B)(-)-in accordance with Chamorovsky and Cammack [Biochim. Biophys. Acta 679 (1982) 146-155], but not of F(A)(-), is observed by EPR after illumination at 200 K, which indicates that reduction of F(B) at 200 K is followed by some relaxation process, in line with this cluster being the most exposed to the solvent.     

The role of DNA twist in the packaging of viral genomes

We performed molecular dynamics simulations of the genome packaging of bacteriophage P4 using two coarse-grained models of DNA. The first model, 1DNA6 (one pseudo-atom per six DNA basepairs), represents DNA as a string of beads, for which DNA torsions are undefined. The second model, 3DNA6 (three pseudo-atoms per six DNA basepairs), represents DNA as a series of base planes with torsions defined by the angles between successive planes. Bacteriophage P4 was packaged with 1DNA6, 3DNA6 in a torsionally relaxed state, and 3DNA6 in a torsionally strained state. We observed good agreement between the packed conformation of 1DNA6 and the packed conformations of 3DNA6. The free energies of packaging were in agreement, as well. Our results suggest that DNA torsions can be omitted from coarse-grained bacteriophage packaging simulations without significantly altering the DNA conformations or free energies of packaging that the simulations predict.