Effect of ethidium binding and superhelix density on the supercoiling free energy and torsion and bending constants of p30 delta DNA

A quantitative model of a cooperative two-state equilibrium in DNA: experimental tests, insights, and predictions

Quantitative parameters for a two-state cooperative transition in duplex DNAs were finally obtained during the last 5 years. After a brief discussion of observations pertaining to the existence of the two-state equilibrium per se, the lengths, torsion, and bending elastic constants of the two states involved and the cooperativity parameter of the model are simply stated. Experimental tests of model predictions for the responses of DNA to small applied stretching, twisting, and bending stresses, and changes in temperature, ionic conditions, and sequence are described. The mechanism and significance of the large cooperativity, which enables significant DNA responses to such small perturbations, are also noted. The capacity of the model to resolve a number of long-standing and sometimes interconnected puzzles in the extant literature, including the origin of the broad pre-melting transition studied by numerous workers in the 1960s and 1970s, is demonstrated. Under certain conditions, the model predicts significant long-range attractive or repulsive interactions between hypothetical proteins with strong preferences for one or the other state that are bound to well-separated sites on the same DNA. A scenario is proposed for the activation of the ilvPG promoter on a supercoiled DNA by integration host factor.

Torsional mechanics of DNA are regulated by small-molecule intercalation

Whether the bend and twist mechanics of DNA molecules are coupled is unclear. Here, we report the direct measurement of the resistive torque of single DNA molecules to study the effect of ethidium bromide (EtBr) intercalation and pulling force on DNA twist mechanics. DNA molecules were overwound and unwound using recently developed magnetic tweezers where the molecular resistive torque was obtained from Brownian angular fluctuations. The effect of EtBr intercalation on the twist stiffness was found to be significantly different from the effect on the bend persistence length. The twist stiffness of DNA was dramatically reduced at low intercalator concentration (<10 nM); however, it did not decrease further when the intercalator concentration was increased by 3 orders of magnitude. We also determined the dependence of EtBr intercalation on the torque applied to DNA. We propose a model for the elasticity of DNA base pairs with intercalated EtBr molecules to explain the abrupt decrease of twist stiffness at low EtBr concentration. These results indicate that the bend and twist stiffnesses of DNA are independent and can be differently affected by small-molecule binding.

Gel mobilities of linking-number topoisomers and their dependence on DNA helical repeat and elasticity

Agarose-gel electrophoresis has been used for more than thirty years to characterize the linking-number (Lk) distribution of closed-circular DNA molecules. Although the physical basis of this technique remains poorly understood, the gel-electrophoretic behavior of covalently closed DNAs has been used to determine the local unwinding of DNA by proteins and small-molecule ligands, characterize supercoiling-dependent conformational transitions in duplex DNA, and to measure helical-repeat changes due to shifts in temperature and ionic strength. Those results have been analyzed by assuming that the absolute mobility of a particular topoisomer is mainly a function of the integral number of superhelical turns, and thus a slowly varying function of plasmid molecular weight. In examining the mobilities of Lk topoisomers for a series of plasmids that differ incrementally in size over more than one helical turn, we found that the size-dependent agarose-gel mobility of individual topoisomers with identical values of Lk (but different values of the excess linking number, DeltaLk) vary dramatically over a duplex turn. Our results suggest that a simple semi-empirical relationship holds between the electrophoretic mobility of linking-number topoisomers and their average writhe in solution.

A structural transition in duplex DNA induced by ethylene glycol

The twist energy parameter ( E T) that governs the supercoiling free energy, and the linking difference (Delta l) are measured for p30delta DNA in solutions containing 0-40 w/v % ethylene glycol (EG). A plot of E T vs -ln a w, where a w is the water activity, displays the full (reverse) sigmoidal profile of a discrete structural transition. A general theory for the effect of added osmolyte on a cooperative structural transition between two duplex states, 1 right arrow over left arrow 2, is formulated in terms of parameters applicable to individual base-pair subunits. The resulting fraction of base pairs in the 2-state ( f 2 (0)) is incorporated into expressions for the effective torsion and bending elastic constants, the effective twist energy parameter ( E T (eff)), and the change in intrinsic twist (delta l 0). Fitting the expression for E T (eff) to the measured E T values yields reasonably unambiguous estimates of E T 1 and E T 2 , the midpoint value (ln a w) 1/2, and the midpoint slope ( partial differential E T/ partial differential ln a w) 1/2, but does not yield unambiguous estimates of the equilibrium constant ( K 0), the difference in DNA-water preferential interaction coefficient (DeltaGamma), or the inverse cooperativity parameter ( J). Fitting a noncooperative model (assumed J = 1.0) to the data yields K 0 = 0.067 and DeltaGamma = -30.0 per base pair (bp). Essentially equivalent fits are provided by models with a wide range of correlated J, DeltaGamma, and K 0 values. Other results favor DeltaGamma in the range -1.0 to 0, which then requires K 0 > or = 0.914, and a cooperativity parameter, 1/ J > or = 30.0 bp. The measured delta l 0 and circular dichroism (CD) at 272 nm are found to be compatible with curves predicted using the same f 2 (0) values that best-fit the E T data. At least 7-10% of the base pairs are inferred to exist in the 2-state in 0.1 M NaCl in the complete absence of added osmolyte. Compared with the 1-state, the 2-state has a approximately 2.0- to 2.1-fold greater torsion elastic constant, a approximately 0.70-fold smaller bending elastic constant, a approximately 0.91-fold smaller E T value, a approximately 0.2% lower intrinsic twist, a somewhat lower CD near both 272 and 245 nm, and less water and/or more EG in its neighborhood. However, the relative change in preferential interaction coefficient associated with the transition is likely rather slight.

Estimation of the persistence length of DNA from the torsion elastic constant and supercoiling free energy: effect of ethylene glycol

Two different methods are proposed to estimate the persistence length ( P) of DNA from the measured torsion elastic constant (alpha) and the twist energy parameter ( E T ) that governs the supercoiling free energy. The first method involves Monte Carlo simulations and reversible-work calculations of E T for model DNAs that possess the measured alpha and selected trial values of P. Comparison of the computed E T values with the experimental value allows estimation of P (or equivalently the bending elastic constant (kappa beta)) by interpolation. A far simpler, though less accurate, alternative is to solve a previously conjectured analytical relation connecting E T , alpha, kappa beta (or P), and an unknown "constant" ( B). The present simulations are used to ascertain the optimum value of B and to assess the validity and accuracy of that relation. Within the simulation errors, P values obtained from the measured alpha and E T via this analytical expression agree with those determined from the simulations and E T values reckoned from the input alpha and kappa beta by this analytical expression agree with the corresponding simulated values. Although B is found to be insensitive to variation in alpha, it appears to decline slightly with increasing kappa beta. The original analytical expression is modified to take this apparent variation of B with kappa beta into account. By using this modified analytical relation to estimate P (from the measured alpha and E T ) or E T (from the input alpha and kappa beta), much closer agreement is obtained respectively with the values of P or E T obtained from the simulations. As specific examples, these methods are applied to determine P in 0 and 20 w/v % ethylene glycol, which has been shown to induce a structural transition in duplex DNA.

Torsional rigidities of weakly strained DNAs

Measurements on unstrained linear and weakly strained large (> or =340 bp) circular DNAs yield torsional rigidities in the range C = 170-230 fJ fm. However, larger values, in the range C = 270-420 fJ fm, are typically obtained from measurements on sufficiently small (< or =247 bp) circular DNAs, and values in the range C = 300-450 fJ fm are obtained from experiments on linear DNAs under tension. A new method is proposed to estimate torsional rigidities of weakly supercoiled circular DNAs. Monte Carlo simulations of the supercoiling free energies of solution DNAs, and also of the structures of surface-confined supercoiled plasmids, were performed using different trial values of C. The results are compared with experimental measurements of the twist energy parameter, E(T), that governs the supercoiling free energy, and also with atomic force microscopy images of surface-confined plasmids. The results clearly demonstrate that C-values in the range 170-230 fJ fm are compatible with experimental observations, whereas values in the range C > or = 269 fJ fm, are incompatible with those same measurements. These results strongly suggest that the secondary structure of DNA is altered by either sufficient coherent bending strain or sufficient tension so as to enhance its torsional rigidity.

Monte Carlo simulations of locally melted supercoiled DNAs in 20 mM ionic strength

Mesoscopic models of unmelted and locally melted supercoiled DNAs in 20 mM ionic strength are simulated over a range of linking difference from deltal = 0 to -26 turns, or superhelix density from sigma = 0 to -0.062. A domain containing m = 0, 28, or 56 melted basepairs (out of 4349 total) is modeled simply by a region of suitable length with substantially reduced torsion and bending elastic constants. Average structural properties are calculated from the saved configurations, and a reversible work protocol is used to calculate the supercoiling free energy, The cross-writhe between duplex and melted regions (defined herein) is found to be negligibly small. The total writhe, radius of gyration, and ordered elements of the diagonalized inertial tensor are found to be nearly universal functions of the residual linking difference (deltal(r)) associated with the duplex region, independent of m. However, deformability of the tertiary structure, as manifested by the variance of those same properties, is not a universal function of deltal(r)), but depends upon m.delta (SC) varies with deltal(r)) more strongly than deltal(r)) (2)due to the low ionic strength. The twist energy parameter, E (T) obtained from the simulated delta G(SC), deltal(r)), and net twisting strain of the melted region T (D), is found to be independent of m, hence also of the torsion and bending elastic constants of the melted region. However, E(T) increases linearly with -deltalr), which leads to 1). a small overestimation of E (T) for any given deltal(r)) when E(T) is determined from the observed deltal and deltal (r) by the protocol of Bauer and Benham; and 2). a significant enhancement of the apparent slope, -dE(T)/d(T), obtained via the protocol of Bauer and Benham, relative to the actual slope at fixed delta l(r). After taking these two effects into account, the theoretical and experimental values E(T) and -dE(T)/d(T) values agree rather well. For the larger deltal the melted regions are found preferentially in the linker domains between interwound arms, rather than in the apical regions at the ends of interwound arms.

Effects of small neutral osmolytes on the supercoiling free energy and intrinsic twist of p30? DNA

Both theory and experiments are employed to investigate the effects of small neutral osmolytes on the average intrinsic twist (l0), the torsion and bending elastic constants, and the twist energy parameter (ET) that governs the supercoiling free energy. The experimental data for ethylene glycol and acetamide at 37 degrees C suggest, and are interpreted in terms of, a model wherein the DNA exhibits an equilibrium between two distinct conformational states that possess different numbers of bound water molecules and exhibit different intrinsic twists and torsion and bending elastic constants. Expressions are derived to relate the effective ET and l0 to the equilibrium constant, water activity (aw), and number (n) of bound water molecules released per cooperative domain undergoing the two-state transition. The variations of l0 and ET with -ln(aw) are similar for acetamide and ethylene glycol at 37 degrees C. Fitting the theory to those data yields the range n = 103-125 for ethylene glycol and n = 71-113 for acetamide, depending on the assumed value of ET for the dehydrated state. The cooperative domain size of the two-state transition is estimated to exceed about 25-30 base pairs (bp). Between 0 and 19.4 w/v % ethylene glycol, the torsion elastic constant, measured by time-resolved fluorescence polarization anisotropy (FPA), increases by 1.37-fold, whereas the measured ET decreases by 1.15-fold over that same range. The implied decrease in bending rigidity over that range is by a factor of about 0.7. The variations of l0 and ET with increasing -ln(aw) due to added ethylene glycol at 37 degrees C are far smaller than the corresponding variations observed previously at 14 and 15 degrees C. However, at 21 degrees C, upon adding either ethylene glycol or acetamide, l0 and ET initially decline steeply with increasing -ln(aw), with slopes possibly comparable to those seen at 14 and 15 degrees C, but then flatten out and follow curves similar to those at 37 degrees C. Possible origins of such mixed behavior are discussed. The effects of betaine at both 37 and 21 degrees C differ qualitatively and quantitatively in various respects from those of ethylene glycol and acetamide. Upon adding sucrose, l0 initially jumps to higher plateaus at both 37 and 21 degrees C, but its effects on ET cannot be reliably assessed, due to the limited range of -ln(aw).

Effect of polyethylene glycol on the supercoiling free energy of DNA

The supercoiling free energy of pUC19 DNA [2686 base pairs (bp)] was measured in various concentrations of PEG 8000 (polyethylene glycol; molecular weight 8000) by the topoisomer distribution method. The effective twist energy parameter (E(T)) that governs the supercoiling free energy declined linearly by 1.9-fold with increasing w/v % PEG from 0 to 7.5%, which lies below the threshold for intermolecular condensation. In principle, PEG could affect E(T) either via an osmotic exclusion mechanism or by altering the torsion elastic constant, bending rigidity, or self-repulsions of the DNA. Possible alterations of the DNA secondary structure and torsion elastic constant were assessed by CD spectroscopy and time-resolved fluorescence polarization anisotropy of intercalated ethidium. Up to 7.5% PEG, the secondary structure of the DNA remained largely unaltered, as evidenced by (1) the absence of any significant change in the CD spectrum, (2) an extremely small relative decrease (-0.0013) in intrinsic twist, and (3) a negligibly small change in the torsion elastic constant. The observed reduction in E(T) cannot be ascribed primarily to a decrease in torsion elastic constant, and most likely does not stem from a decrease in bending rigidity either. The decrease in medium dielectric constant due to PEG should increase the self-repulsions, and thereby increase E(T), which is opposite to the observed trend. Instead, the observed decline in E(T) is attributed to an osmotic exclusion mechanism. The change in molar volume excluded to the PEG (Delta V(ex)), when the linking difference converts from Delta l = 0 to Delta l = +/-1, was determined from the observed E(T) value and PEG osmotic pressure at each concentration. The experimental Delta V(ex) values agree well with theoretical estimates reckoned for a simple osmotic exclusion model, in which PEG is excluded by hard-core interactions from a concentric cylindrical volume around every duplex segment. The difference in volume excluded to PEG between the Delta l = 0 and the Delta l = +/-1 topoisomers is attributed entirely to the approximately 0.7 additional writhe "crossing" of two duplex strands at roughly 90 degrees, which is known to occur in the latter species. When the separation between the duplex centers at the "crossing" was adjusted so that the theoretical estimate of Delta V(ex) matched the experimental value at each PEG concentration, a value near 5.7 nm was obtained in each case. The invariance and plausible magnitude of this mean separation at the crossing provide strong support for this simple osmotic exclusion model. An alternative model, in which the PEG is excluded from the entire coil envelope of the DNA out to its radius of gyration, perhaps because it decreases the local dielectric constant, was also considered. The estimated difference in excluded volume in that case exceeds the experimental value by a factor of nearly 10(4), and could be ruled out on that basis.

The question of long-range allosteric transitions in DNA

The question of long-range allosteric transitions of DNA secondary structure and their possible involvement in transcriptional activation is discussed in the light of new results. A variety of recent evidence strongly supports a fluctuating long-range description of DNA secondary structure. Balanced equilibria between two or more different secondary structures, and the occurrence of very large domain sizes, have been documented in several instances. Long-range allosteric effects stemming from changes in sequence or secondary structure over a small region of the DNA have been observed to extend over distances up to hundreds of base pairs in some cases. The discovery that coherent bending strain beyond a threshold level in small (N < or = 250 base pairs (bp)] circular DNAs significantly alters the DNA secondary structure has important implications, especially for transcriptional activators that either bend the DNA directly or are involved in the formation of DNA loops of sufficiently small size (N < or = 250 bp). Whether the RNA polymerase is activated primarily via protein: protein contacts, as is widely believed, or instead via a bend-induced allosteric transition of the DNA in such a small loop, is now an open question. Binding of the transcriptional activator Sp1 to linear DNA induces a remarkably long-range change in its secondary structure, and catabolite activator protein binding to a supercoiled DNA behaves similarly, though possibly for different reasons. Compelling evidence for a bend-induced long-range structural transmission effect of the transcriptional activator integration host factor on RNA polymerase activity was recently reported. These results may augur a new paradigm in which allosteric transitions of duplex DNA, as well as of the proteins, are involved in the regulation of transcription.

Restrained torsional dynamics of nuclear DNA in living proliferative mammalian cells

Physical parameters, describing the state of chromatinized DNA in living mammalian cells, were revealed by in situ fluorescence dynamic properties of ethidium in its free and intercalated states. The lifetimes and anisotropy decays of this cationic chromophore were measured within the nuclear domain, by using the ultra-sensitive time-correlated single-photon counting technique, confocal microscopy, and ultra-low probe concentrations. We found that, in living cells: 1) free ethidium molecules equilibrate between extracellular milieu and nucleus, demonstrating that the cation is naturally transported into the nucleus; 2) the intercalation of ethidium into chromatinized DNA is strongly inhibited, with relaxation of the inhibition after mild (digitonin) cell treatment; 3) intercalation sites are likely to be located in chromatin DNA; and 4) the fluorescence anisotropy relaxation of intercalated molecules is very slow. The combination of fluorescence kinetic and fluorescence anisotropy dynamics indicates that the torsional dynamics of nuclear DNA is highly restrained in living cells.

Dynamic twisting correlations in a model DNA with uniform torsion elastic constant

The extent to which the twisting motions of two separate subunits (base pairs) in an elastic filament are correlated is discussed in terms of the two-point correlation function of their azimuthal angular displacements C(Delta,t) identical with <(phi(m)(t) - phi(m)(0))(phi(n)(t) - phi(n)(0))>, where m,n are the sequential subunit indices and Delta = |m - n| is their absolute difference. An approximate expression is derived for C(Delta,t) for an infinitely long model DNA from the analytical theory developed previously to treat the decay of the fluorescence polarization anisotropy of intercalated ethidium. C(Delta,t) is numerically evaluated as a function of Delta for a range of times (20, 40, 60, 80, 100, and 120 ns) for a model DNA with a typical torsion elastic constant. By t = 120 ns, significant dynamic correlations are observed to extend over a domain (Delta) several hundred base pairs. Copyright 1999 John Wiley & Sons, Inc.

Denaturation of supercoiled DNA: a Monte Carlo study

A theoretical investigation of the denaturation characteristics of a supercoiled DNA has been presented employing a Metropolis Monte Carlo algorithm to examine the overall melting profiles of a supercoiled plasmid as the temperature is varied. We show that in contrast to a previously presented algorithm, this much simpler method is sufficient to explain almost all the overall denaturation characteristics and it also correctly calculates the detailed denaturation probabilities of each base pair at various degrees of supercoiling. We also present for the first time a theoretical investigation of the alkaline denaturation of a supercoiled plasmid. Although one can qualitatively reproduce the denaturation profiles using the present Monte Carlo algorithm, the agreement with experiment is not as good as in the case of thermal denaturation. The possible sources of discrepancy between theory and experiment have been discussed.

On the origin of the temperature dependence of the supercoiling free energy

Monte Carlo simulations using temperature-invariant torsional and bending rigidities fail to predict the rather steep decline of the experimental supercoiling free energy with increasing temperature, and consequently fail to predict the correct sign and magnitude of the supercoiling entropy. To illustrate this problem, values of the twist energy parameter (E(T)), which governs the supercoiling free energy, were simulated using temperature-invariant torsion and bending potentials and compared to experimental data on pBR322 over a range of temperatures. The slope, -dE(T)/dT, of the simulated values is also compared to the slope derived from previous calorimetric data. The possibility that the discrepancies arise from some hitherto undetected temperature dependence of the torsional rigidity was investigated. The torsion elastic constant of an 1876-bp restriction fragment of pBR322 was measured by time-resolved fluorescence polarization anisotropy of intercalated ethidium over the range 278-323 K, and found to decline substantially over that interval. Simulations of a 4349-bp model DNA were performed using these measured temperature-dependent torsional rigidities. The slope, -dE(T)/dT, of the simulated data agrees satisfactorily with the slope derived from previous calorimetric measurements, but still lies substantially below that of Duguet's data. Models that involve an equilibrium between different secondary structure states with different intrinsic twists and torsion constants provide the most likely explanation for the variation of the torsion constant with T and other pertinent observations.

Buckling transitions in superhelical DNA: dependence on the elastic constants and DNA size

Buckling transitions in superhelical DNA are sudden changes in shape that accompany a smooth variation in a key parameter, such as superhelical density. Here we explore the dependence of these transitions on the elastic constants for bending and twisting. A and C, important characteristics of DNA's bending and twisting persistence lengths. The large range we explore extends to other elastic materials with self-contact interactions, modeled here by a Debye-Hückel electrostatic potential. Our collective description of DNA shapes and energies over a wide range of p = A/C reveals a dramatic dependence of DNA shape and associated configurational transitions on p: transitions are sharp for large p but masked for small p. In particular, at small p, a nonplanar circular family emerges, in agreement with Jülicher's recent analytical predictions: a continuum of forms (and associated writhing numbers) is also observed. The relevance of these buckling transitions to DNA in solution is examined through studies of size dependence and thermal effects. Buckling transitions smooth considerably as size increases, and this can be explained in part by the lower curvature in larger plasmids. This trend suggests that buckling transitions should not be detectable for isolated (i.e., unbound) DNA plasmids of biological interest, except possibly for very large p. Buckling phenomena would nonetheless be relevant for small DNA loops, particularly for higher values of p, and might have a role in regulatory mechanisms: a small change in superhelical stress could lead to a large configurational change. Writhe distributions as a function of p, generated by Langevin dynamics simulations, reveal the importance of thermal fluctuations. Each distribution range (and multipeaked shape) can be interpreted by our buckling profiles. Significantly, the distributions for moderate to high superhelical densities are most sensitive to p, isolating different distribution patterns. If this effect could be captured experimentally for small plasmids by currently available imaging techniques, such results suggest a slightly different experimental procedure for estimating the torsional stiffness of supercoiled DNA than considered to date.

Effect of anisotropy of the bending rigidity on the supercoiling free energy of small circular DNAs

In principle, the supercoiling free energy of a small circular DNA will be enhanced by increasing the anisotropy of its bending potential at constant persistence length. The magnitude of this effect is investigated by Monte Carlo simulation using an extension of a previously proposed algorithm. The supercoiling free energy at 298 K is simulated for circular DNAs containing N = bp with torsion constant alpha = 5.8 X 10(-12) dyne cm, persistence lengths P = 500 A and 10,000 A, and a range of anisotropies of the bending potential from rho = 1.0 to 16.0. The apparent torsion constants, reckoned from these supercoiling free energies by assuming an isotropic bending potential, are found to increase by less than 3% as the input anisotropy increases from 1.0 to 16.0 When P = 500 A, the apparent torsion constant never rises significantly above the input value over the entire range of input anisotropies. When P = 10,000 A, the apparent torsion constant rises only about 3% above the input value for anisotropies rho = 8.0 and 16.0. Evidently, anisotropy of the bending potential cannot account for the fact that the torsion constants reported for small circular DNAs exceed those reported for long linear DNAs by a factor of 1.6 or more.

Monte Carlo simulations of supercoiling free energies for unknotted and trefoil knotted DNAs

A new Monte Carlo (MC) algorithm is proposed for simulating inextensible circular chains with finite twisting and bending rigidity. This new algorithm samples the relevant Riemann volume elements in a uniform manner, when the constraining potential vanishes. Simulations are performed for filaments comprising 170 subunits, each containing approximately 28 bp, which corresponds to a DNA length of 4770 bp. The bending rigidity is chosen to yield a persistence length, P = 500 A, and the intersubunit potential is taken to be a hard-cylinder potential with diameter d = 50 A. This value of d yields the same second virial coefficient as the electrostatic potential obtained by numerical solution of the Poisson-Boltzmann equation for 150 mM salt. Simulations are performed for unknotted circles and also for trefoil knotted circles using two different values of the torsional rigidity, C = (2.0 and 3.0) x 10(-19) dyne cm2. In the case of unknotted circles, the simulated supercoiling free energy varies practically quadratically with linking difference delta l. The simulated twist energy parameter ET, its slope dET/dT, and the mean reduced writhe <w>/delta l for C = 3 x 10(-19) dyne cm2 all agree well with recent simulations for unknotted circles using the polygon-folding algorithm with identical P, d, and C. The simulated ET vs. delta l data for C = 2.0 x 10(-19) dyne cm2 agree rather well with recent experimental data for p30 delta DNA (4752 bp), for which the torsional rigidity, C = 2.07 x 10(-19) dyne cm2, was independently measured. The experimental data for p30 delta are enormously more likely to have arisen from C = 2.0 x 10(-19) than from C = 3.0 x 10(-19) dyne cm2. Serious problems with the reported experimental assessments of ET for pBR322 and their comparison with simulated data are noted. In the case of a trefoil knotted DNA, the simulated value, (ET)tre, exceeds that of the unknotted DNA, (ET)unk, by approximately equal to 1.40-fold at magnitude of delta l = 1.0, but declines to a plateau about 1.09-fold larger than (ET)unk when magnitude of delta l > or = 15. Although the predicted ratio, (ET)tre/(ET)unk approximately equal to 1.40, agrees fairly well with recent experimental measurements on a 5600-bp DNA, the individual measured ET values, like some of those reported for pBR322, are so large that they cannot be simulated using P = 500 A, d = 50 A, and any previous experimental estimate of C.

A model for the binding of E. coli single-strand binding protein to supercoiled DNA

A model is proposed for the binding of E. coli single strand binding protein (SSB) to supercoiled DNA. The basic tetrameric binding units of SSB are assumed to bind in pairs to the complementary single strands of a locally melted region. The cooperativity of the binding includes contributions from both protein-protein and base-pair stacking interactions. Each bound SSB tetramer is assumed to unwind l = 34 bp, which implies an unwinding angle of 3.27 turns. The resulting loss of superhelical strain is the essential driving force for binding SSB to supercoiled DNAs. All molecular parameters entering into the theory are estimated from available data, except for the composite binding constant (Ka), which is adjusted to best-fit the theory to the fluorescence quenching (FQ) and diffusion coefficient (D0) data of Langowski et al. Very good fits are obtained with optimum values of Ka that are consistent with estimates from other data. This binding model predicts several noteworthy features. (1) SSB binds essentially always in a single contiguous stack on a supercoiled plasmid, and relative fluctuations in stack length are quite small, in agreement with results of electron microscopy studies. (2) The progressive loss of superhelical strain with increasing bound ligand decreases the affinity of the DNA for SSB. This anti-cooperativity offsets the cooperativity of the binding and causes apparent saturation of the binding at rather low binding ratios. Consequently, over the limited span of the measurements, the FQ data can also be satisfactorily fitted by a non-cooperative model comprising a small number of independent sites. (3) When SSB binds to a population of different topoisomers, the distribution of linking differences of the resulting complexes is extremely narrow. Thus, SSB acts to level any differences in superhelical strain in a population of topoisomers. Finally, the effects of restricting binding to a region comprising only part of the plasmid are assessed.

Effect of ethidium binding and superhelix density on the apparent supercoiling free energy and torsion constant of pBR322 DNA

The value of the twist energy parameter (ET) of pBR322 is determined near zero superhelix density from topoisomer distributions created under various conditions. The resulting value, ET = 1155 +/- 65, at 37 degrees C is essentially unaffected by adding 10 mM Mg2+, or by changing the kind of Topo I from chicken-red-cell to calf-thymus. This value significantly exceeds that (ET = 950 +/- 80) measured for p30 delta DNA under identical conditions by the same method in the preceding paper. Decreasing the temperature from 37 to 21 degrees C yields a slightly larger value, ET = 1340 +/- 130, but the statistical significance of the increase is marginal. Attempts to determine reliable ET values for pBR322 at higher superhelix densities by ethidium binding were frustrated by the fact that good fits of the equilibrium dialysis results could not be achieved using a single value of ET. Moreover, the curves of apparent ET versus binding ratio r vary considerably from one preparation to another, and for a given preparation vary with time after cell lysis up to about seven weeks, after which they settle in to nearly reproducible behavior. The apparent ET values obtained from competitive dialysis experiments are typically rather low (ET approximately 700) for small r and nearly native superhelix density, and rise up to 1300 to 1500 with increasing binding ratio (up to r = 0.055) and decreasing negative superhelix density.(ABSTRACT TRUNCATED AT 250 WORDS)