Theory of Ethidium Binding to DNA under Tension and Torque: Possible Role of Cruciforms at Inverted Repeat Sequences.

Celedon et al. reported an unexpectedly low slope of applied torque vs turns (or apparent torsional rigidity) for a long DNA subject to 0.8 pN tension and modest negative torques (up to approximately -5 pN nm) in 3.4 × 10-9 M ethidium (J. Phys. Chem. B 2010, 114, 16929-16935). Extrusion of inverted repeat sequences to create cruciforms with anomalously large association constants for binding 4 ethidiums to the cruciform arms is investigated as a possible explanation for this observation and also for its compatibility with other observations of Celedon et al. The equilibrium between the linear main chain and cruciform states of an inverted repeat sequence under the prevailing tension, torque, and ethidium concentration is treated by first computing the free energy per bp of the linear main chain. This is done for a complex model, wherein every bp in the linear main chain participates in both the recently reviewed cooperative two-state a ⇔ b equilibrium (Quarterly Reviews of Biophysics 2021, 54, e5, 1-25) and in ethidium binding with a modest relative preference for either the a- or b-state. Plausible assumptions are made concerning the relative populations of the cruciform and linear main chain states of an inverted repeat, and also the relative populations of cruciform states with and without 4 bound ethidiums in the presence of tension, torque, and 3.4 × 10-9 M ethidium. Besides a large drop in slope (or apparent torsional rigidity) from 10-9 to 10-8 M ethidium, this theory also predicts maxima between 6.4 × 10-8 and 2.0 × 10-7 M ethidium, a region where no measurements were made. Overall agreement between theoretical and experimental values of the slope (or apparent torsional rigidity), and also the number of negative turns due to bound ethidium at zero torque, is fairly good for all of the ethidium concentrations studied by Celedon et al., provided that there is a modest preference for binding to the b-state. When there is a modest preference for binding to the a-state, the theory significantly underestimates experimental values at the higher ethidium concentrations, likely ruling out that possibility.

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.

Effects of Sequence Changes on the Torsion Elastic Constant and Persistence Length of DNA. Applications of the Two-State Model.

Previous experimental studies of the effects of changes in sequence on the elastic constants and other properties of DNAs are analyzed using the recently parametrized two-state cooperative transition model. With appropriate assumptions regarding the relative preference of particular subsequences for the b and a states, the model gives an approximately quantitative account of the surprisingly large observed effects of replacing 25 bp of natural sequence near the middle of an ∼1100 bp DNA by 16 bp of alternating (CG)8 sequence on the fraction fb of base-pairs in the b-state and on the torsion elastic constant. This demonstrates the effect of the strong cooperativity of the transition to significantly influence the state of the DNA over surprisingly large domains of the flanking DNA. With appropriate assumptions regarding the disposition of nonrelaxing (permanent) and slowly relaxing bends between the a and b states, the two-state model resolves the discrepancy between experimental estimates of the magnitude of the nonrelaxing bends obtained from studies of synthetic straight and natural DNA sequences by cryo-electron microscopy on the one hand and by j-factors inferred from the kinetics of ligase cyclization of small ∼200 bp circular DNAs on the other. Approximately quantitative agreement with the experiments is again obtained.

Temperature-dependence of the bending elastic constant of DNA and extension of the two-state model. Tests and new insights.

Review and analyses of the experimental data indicate that in nearly all cases bending elastic constants of the effective springs between bp of DNA actually undergo a net increase with increasing T from 278 to 315 K. The exceptions to this rule are bending elastic constants obtained from equilibrium topoisomer distributions of a 2686 bp pUC19 DNA by assuming a fixed T-independent value of the torsion elastic constant. When the same data are analyzed using measured T-dependent values of the torsion elastic constant, which decline with increasing T, a modest increase in bending elastic constant with increasing T is obtained. After revising the torsion elastic constants of the previously formulated two-state cooperative transition model to account for additional data, that model is fitted to the bending elastic constants reckoned from the aforementioned topoisomer distributions to determine the best-fit values for each state. The rather good fit implies a strong negative linear correlation between the inverse bending and inverse torsion elastic constants as T is varied. Predictions of the resulting two-state model, wherein each state has fixed bending and torsion elastic constants, agree surprisingly well with single-molecule relative extension and torque data. The same model also yields good agreement with numerous other experimental data. With increasing T the equilibrium is shifted from the (longer, torsionally stiffer, flexurally softer) b-state toward the (shorter, torsionally softer, flexurally stiffer) a-state. This transition is suggested to be the origin of the so-called broad pre-melting transition exhibited by many, but not all, DNAs.

Possible Origin of the Increased Torsion Elastic Constant of Small Circular DNAs: Bending-Induced Axial Tension.

Deforming an intrinsically straight elastic rod into a circle is shown to introduce an axial tension that acts to extend the rod, much like an externally applied force. The response of a circular DNA to such axial tension was reckoned using a previously suggested model of a force-dependent cooperative transition between a shorter torsionally softer a conformation and a longer torsionally stiffer b conformation. Each of three earlier reported optimal sets of parameters, that well-fitted both relative extension vs force and torsion elastic constant vs force data on single DNAs under tension, was applied here to predict torsion elastic constants of the effective springs between base pairs for both linear and circular 181 bp and ∼210.8 bp DNAs under their respective conditions. Predicted values for both linear and circular species agreed well with their corresponding experimental values, which strongly suggests that the observed 1.4- to 1.5-fold enhancement of the torsion elastic constants upon circularization arises from such axial tension. Experimental torsion elastic constants lie in the range (6.4-6.6) × 10-19 J for these linear DNAs and in the range (9.1-9.9) × 10-19 J for the corresponding circles, significantly below the limiting value ∼12 × 10-19 J at tensions exceeding 4 pN.

A possible cooperative structural transition of DNA in the 0.25-2.0 pN range.

The measured effective torsional rigidities of single twisted DNAs under various tensions conflict with theoretical predictions of Moroz and Nelson (MN) at low forces in the 0.25-2.0 pN range. However, MN theory was recently shown to agree well with effective torsional rigidities obtained from simulations, indicating that MN theory is valid down to 0.25 pN for a filament with a constant intrinsic torsional rigidity. Here MN theory is used with an assumed persistence length, 50 nm, to obtain the force-dependent intrinsic torsional rigidity of the filament at each force from its measured effective torsional rigidity. The resulting values rise ∼1.8-fold with increasing force from 0.25 to 2.0 pN. Unexpected behavior of the relative extensions of the untwisted DNAs of Mosconi et al. is noted, and ascribed to a small increase in contour length with force over the 0.18-2.0 pN range. The variations of both the intrinsic torsional rigidity and rise per base pair (bp) with force are suggested to arise from a force-induced shift of a cooperative equilibrium between two conformations with different rises per bp. A two-state nearest-neighbor model is formulated, and ranges of optimal parameters are determined by fitting the model to the experimental differences in rise per bp as a function of force. Optimal adjustment of the torsion elastic constants of the two states enables the same optimal model(s) with fixed parameters to provide reasonably good fits of the experimental torsion elastic constant data. The results reconcile single-molecule measurements on DNAs under tension with numerous results from fluorescence polarization anisotropy, topoisomer distributions, X-ray scattering of DNAs with attached gold colloids, and other kinds of measurements.

Reflections on a measurement of the gravitational constant using a beam balance and 13 tons of mercury.

In 2006, a final result of a measurement of the gravi- tational constant G performed by researchers at the University of Zürich, Switzerland, was published. A value of G=6.674252(122)×10-11 m3 kg-1 s-2 was obtained after an experimental effort that lasted over one decade. Here, we briefly summarize the measurement and discuss the strengths and weaknesses of this approach.

Phenomena associated with gel-water interfaces. Analyses and alternatives to the long-range ordered water hypothesis.

Interfacial regions between certain gels and their surrounding solutions were observed by Pollack and co-workers to exhibit several unexpected phenomena: (1) long-range exclusion of charged microspheres out to typical distances of ~100-200 µm from the gel surface; (2) significant electrostatic potentials extending over comparable distances; (3) a reduced intensity of upward spontaneous thermal IR emission over a region 300-500 µm wide at or near the gel-solution interface; and (4) a significantly lower proton T2 and an apparently reduced H2O self-diffusion coefficient over a zone ~60 µm wide at or near the gel-solution interface in high resolution NMR imaging experiments. To account for such observations, they proposed that a region of long-range ordered water bearing a net negative charge, but lacking mobile charge carriers, extended ~100-200 µm outward from the gel surface. In this paper, various problems associated with the ordered water hypothesis, including contradictions by experiments from many other laboratories, are briefly discussed, and testable alternative explanations for the observed phenomena are proposed. Exclusion zones are suggested to arise from chemotaxis of the microspheres in long-range diffusion gradients of OH(-) (or H(+)) and salt, the theory of which was developed and compared with the observations on non-ionic gels in a companion paper. The same theory together with the expected directions of ion transfers between gel and solution are now used to predict qualitatively the exclusion/attraction behavior of microspheres in the presence of ionic gels and ionomers. The electrostatic potentials are interpreted as long-range liquid-junction potentials arising from the same long-range diffusion gradients of OH(-) (or H(+)) and salt in the unstirred solutions of Pollack and co-workers. Alternative explanations in terms of plausible experimental artifacts are suggested for both the reduced intensity of IR thermal emission and the lower proton T2 and apparent H2O diffusion coefficient in the NMR imaging experiments.

A theory of macromolecular chemotaxis.

A macromolecule in a gradient of a cosolute that is preferentially (relative to the solvent) either attracted to or excluded from the domain of the macromolecule should experience a thermodynamic force and move, respectively, up or down the gradient. A theory of chemotactic forces arising from such preferential interactions, especially short-range ligand binding and excluded volume interactions, is developed via an extension of Kirkwood-Buff theory. The ligand binding result is confirmed for both non-ionic and ionic cosolutes by standard solution thermodynamics. The effect of increasing the electrolyte concentration to diminish the electrostatic free energy of a charged macromolecule is also treated formally via an electrostatic macromolecule-electrolyte preferential interaction coefficient. For short-range interactions, the induced chemotactic velocity is attributed entirely to tangential tractions at the interface between the macromolecule and its surrounding solution. The velocity of a spherical macromolecule driven by such tractions is derived by a hydrodynamic calculation for steady-state creepy flow with a partial slip boundary condition. Qualitative comparisons of theoretical predictions with experimental observations of Zheng and Pollack pertaining to charged microspheres near the surfaces of non-ionic gels suggest that the reported exclusion zones are due to chemotaxis induced by gradients of base (NaOH) (or acid (HCl)) and salt. With a single adjustable parameter, namely, the ratio of slip length to area per surface carboxyl (or amidine) group, this theory yields nearly quantitative agreement with many observations. The estimated slip length for the microspheres is comparable to that obtained for bovine serum albumen by fitting the chemotactic theory to two reported cross-diffusion coefficients. When a solution with a gradient of NaOH is placed in contact with a smooth glass wall, chemotactic surface tractions are predicted to cause convection of the solution toward the acidic end of the gradient, as observed in preliminary experiments.

Supercoiled pseudocircular domains in single-twisted DNAs under tension: Elastic constants and unwinding dynamics in complexes with Topo I.

Extension versus twist data of Koster et al. (Nature 2005, 434, 671-674) are analyzed to obtain C for the main-chain segments and the twist energy parameter (ET ) for the supercoiled pseudocircular (sp) domain(s) from which C is estimated via simulations. The torsional rigidity in the tension-free sp domain(s) (C = 163 fJ fm) is typical of the unstrained DNA and is less than half the value in the main-chain segments under tension (C = 350-410 fJ fm). Tension is suggested to induce a structural transition to a torsionally stiffer state. Data of Koster et al. for the rate of extension owing to unwinding of a covalent complex of DNA with human Topoisomerase Ib (H Topo I) are analyzed to determine the torque and rate of rotation from which an effective friction coefficient is obtained. A Langevin equation for the unwinding motion in a supercoiled DNA:H Topo I complex is solved to obtain the temporal trajectory of the average winding angle and the time-dependent distribution of winding angles. The mean rate constant for the religation reaction is estimated from the measured probability of reaction per turn. We predict that unwinding proceeds rather far during a single-cleavage and religation cycle, and is effectively completely equilibrated during the 3.2 cleavage and religation cycles that occur during each noncovalent binding and dissociation event. H Topo I is predicted to be completely processive as in accord with observations on calf-thymus Topo I (Brewood et al., Biochemistry 2010, 49, 3367-3380).

Calf-thymus topoisomerase I equilibrates metastable secondary structure subsequent to relaxation of superhelical stress.

After relaxation of superhelical stress by various methods not involving topoisomerases, a long-lived metastable secondary structure with an anomalously low torsion elastic constant commonly prevails. The aim here is to ascertain whether such metastable secondary structure also results from the action of calf-thymus topoisomerase I (CT Topo I) on a native supercoiled DNA and, if so, whether the enzyme catalyzes its subsequent equilibration. The action of CT Topo I on supercoiled p30delta DNA was examined over a range of times from 10 min to 6 h. We verify that the enzyme operates in an almost completely processive manner, and at each time point determine the twist energy parameter, E(T), that governs the supercoiling free energy. E(T) is initially low, 533 +/- 60, and remains essentially constant up to at least 360 min, when no further CT Topo I is added. The activity of the rather dilute enzyme dies within approximately 60 min. During the 60 min after a second addition of fresh enzyme at either 60 or 120 min, E(T) rises up to a plateau at approximately 1100, which lies within the consensus equilibrium range, 1000 +/- 100. Over that same time period, the average peak spacing between the gel bands (corresponding to individual topoisomers) decreases somewhat with increasing time of exposure to active CT Topo I. After a third addition of fresh CT Topo I at 240 min, there is no further change in either E(T) or the average gel spacing. These and other observations indicate that active CT Topo I catalyzes the equilibration of a metastable secondary structure with abnormally low torsion and bending elastic constants that prevails after the initial release of superhelical stress. An observed temporal lag of this structural equilibration behind the relaxation of native superhelical DNAs suggests that it may require cleavage and religation events at multiple sites on the DNA. A novel analysis of the unwinding kinetics using literature data accounts for the almost complete processivity of the enzyme. The action of CT Topo I was also examined in the presence of 20 and 40 w/v% ethylene glycol (EG), which shift a secondary structure equilibrium toward an alternative state with altered torsion and bending elastic constants. The present results suggest that the usual metastable state coexists with the EG-induced state, and is equilibrated more rapidly than in the absence of EG.

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.

Effects of ethylene glycol on the torsion elastic constant and hydrodynamic radius of p30delta DNA.

Upon increasing the concentration of ethylene glycol (EG) at 37 degrees C, the twist energy parameter, E(T), which governs the supercoiling free energy, was recently found to undergo a decreasing (or reverse) sigmoidal transition with a midpoint near 20 w/v % EG. In this study, the effects of adding 20 w/v % EG on the torsion elastic constant (alpha) of linear p30delta DNA and on the hydrodynamic radius (R(H)) of a synthetic 24 bp duplex DNA were examined at both 40 and 20 degrees C. The time-resolved fluorescence intensity and fluorescence polarization anisotropy (FPA) of intercalated ethidium were measured in order to assess the effects of 20 w/v % EG on: (1) alpha; (2) R(H); (3) the lifetimes of intercalated and non-intercalated dye; (4) the amplitude of dye wobble in its binding site; and (5) the binding constant for intercalation. The effects of 20 w/v % EG on the circular dichroism (CD) spectrum of the DNA and on the emission spectrum of the free dye were also measured. At 40 degrees C, addition of 20 w/v % EG caused a substantial (1.27- to 1.35-fold) increase in alpha, a significant change in the CD spectrum, and a very small, marginally significant increase in R(H), but little or no change in the amplitude of dye wobble in its binding site or the lifetime of intercalated dye. Together with previously reported measurements of E(T), these results imply that the bending elastic constant of DNA is significantly decreased by 20 w/v % EG at 40 degrees C. At 20 degrees C, addition of 20 w/v % EG caused a marginally significant decrease in alpha and very little change in any other measured properties. Also at 20 degrees C, addition of 30 w/v % betaine caused a marginally significant increase in alpha and significant but modest change in the CD spectrum, but very little change in any other properties.

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.

A contribution to the theory of preferential interaction coefficients.

A simple and complete derivation of the relation between concentration-based preferential interaction coefficients and integrals over the relevant pair correlation functions is presented for the first time. Certain omissions from the original treatment of pair correlation functions in multicomponent thermodynamics are also addressed. Connections between these concentration-based quantities and the more common molality-based preferential interaction coefficients are also derived. The pair correlation functions and preferential interaction coefficients of both solvent (water) and cosolvent (osmolyte) in the neighborhood of a macromolecule contain contributions from short-range repulsions and generic long-range attractions originating from the macromolecule, as well as from osmolyte-solvent exchange reactions beyond the macromolecular surface. These contributions are evaluated via a heuristic analysis that leads to simple insightful expressions for the preferential interaction coefficients in terms of the volumes excluded to the centers of the water and osmolyte molecules and a sum over the contributions of exchanging sites in the surrounding solution. The preferential interaction coefficients are predicted to exhibit the experimentally observed dependence on osmolyte concentration. Molality-based preferential interaction coefficients that were reported for seven different osmolytes interacting with bovine serum albumin are analyzed using the this formulation together with geometrical parameters reckoned from the crystal structure of human serum albumin. In all cases, the excluded volume contribution, which is the volume excluded to osmolyte centers minus that excluded to water centers in units of V1, exceeds in magnitude the contribution of the exchange reactions. Under the assumption that the exchange contribution is dominated by sites in the first surface-contiguous layer, the ratio of the average exchange constant to its neutral random value is determined for each osmolyte. These ratios all lie in the range 1.0 +/- 0.15, which indicates rather slight deviations from random occupation near the macromolecular surface. Finally, a mechanism is proposed whereby the chemical identity of an osmolyte might be concealed from partially ordered multilayers of water in clefts, grooves, and pits, and its consequences are noted.

Can reliable torsion elastic constants be determined from FPA data on 24 and 27 base-pair DNAs?

Torsion elastic constants obtained from fluorescence polarization anisotropy (FPA) measurements on fifty-three 24 and 27 base-pair (bp) DNAs were recently reported [F. Pedone, F. Mazzei, D. Santoni, Sequence-dependent DNA torsional rigidity: a tetranucleotide code, Biophys. Chem. 112 (2004) 77-88; F. Pedone, F. Mazzei, M. Matzeu, F. Barone, Torsional constant of 27-mer DNA oligomers of different sequences, Biophys. Chem. 94 (2001) 175-184]. The problem of extracting reliable torsion elastic constants (alpha) from FPA measurements on such short DNAs is examined in detail. The difficulty is illustrated by two (fictitious) 24 bp DNAs with approximately 5-fold different torsion elastic constants and 10% different initial anisotropies (r(0)), which exhibit practically indistinguishable anisotropy decays for all t>1 ns. FPA data were simulated for 24 bp DNAs with different input values of alpha and r(0) in the presence and absence of Poisson noise, and were fitted using different choices of the adjustable and fixed parameters. Experimental data for a 24 bp DNA were fitted in a similar manner. For either the simulated or experimental FPA data, it was not possible to determine both the initial anisotropy, r(0), and the torsion elastic constant, alpha, in a reliable (i.e. statistically significant) manner in the presence of Poisson noise. When r(0) is assumed to be fixed at any particular value in the fitting protocol, a unique best-fit value of alpha is obtained, but that best-fit alpha is extremely sensitive to small deviations of the assumed fixed value of r(0) away from the input r(0)-value of the simulated data. Pedone et al. fitted their FPA data by assuming that r(0)=0.360, and adjusting alpha, the hydrodynamic radius (R(H)), and effective length (L). In fact, the reported best-fit values of R(H) and L lay significantly outside their expected ranges. When this same fitting protocol is applied to simulated data for 27 bp DNAs, better overall agreement with the reported experimental values (alpha, R(H), and L) is obtained for a model, wherein all DNAs have the same typical input alpha=5.9 x 10(-12) dyn cm, R(H)=10.0 A, and L=27 (3.4)+2.7=94.5 A, but a 1.00- to 1.13-fold range of r(0)-values, than for the model of Pedone et al., wherein all DNAs have the same input r(0)=0.360, R(H)=10.0 A, and L=94.5 A, but a approximately 3-fold range of alpha-values. It is concluded that, in the absence of reliable independent estimates of r(0) for every DNA, the alpha-values reported for 24 and 27 bp DNAs cannot be regarded as experimentally justified. The reliability of the torsion elastic constants reported for the 136 distinct tetranucleotide steps, which are inferred from the values reported for the fifty-three 24 and 27 bp DNAs, is also briefly discussed.