DNA persistence length revisited

DNA restriction fragments ranging from 79 to 789 base pairs in length have been characterized by transient electric birefringence (TEB) measurements at various temperatures between 4 and 43 degrees C. The DNA fragments do not contain runs of four or more adenine residues in a row and migrate with normal electrophoretic mobilities in polyacrylamide gels, indicating that they are not intrinsically curved or bent. The low ionic strength buffers used for the measurements contained 1 mM Tris Cl, pH 8.0, EDTA, and variable concentrations of Na(+) or Mg(2+) ions. The rotational relaxation times were obtained by fitting the TEB field-free decay signals with a nonlinear least-squared fitting program; the decay of the birefringence was monoexponential for fragments < or = 241 base pair (bp) in length and multiexponential for larger fragments. The terminal relaxation times, characteristic of the end-over-end rotation of the DNA molecules, were then used to determine the persistence length (p) and hydrodynamic radius (r) of DNA as a function of temperature and ionic strength, using several different hydrodynamic models. The specific values obtained for p and r are model dependent. The wormlike chain model of P. J. Hagerman and B. H. Zimm (Biopolymers 1981, Vol. 20, pp. 1481-1502) combined with the revised Broersma equation (J. Newman et al., Journal of Mol Biol 1997, Vol. 116, pp. 593-606) appears to be the most suitable for describing the flexibility of DNA in low ionic strength solutions. The values of p and r obtained from the global least squares fitting of this equation are independent of DNA length, and the deviations of the individual values from the average are reasonably small. The consensus r value calculated for DNA in various low ionic strength solutions containing 1 mM Tris buffer is 14.7 +/- 0.4 A at 20 degrees C. The consensus p values decrease from 814 approximately 564 A in solutions containing 1 mM Tris buffer plus 0.2-1 mM NaCl and decrease still further to 440 A in solutions containing 0.2 mM Mg(2+) ions. The persistence length exhibits a shallow maximum at 20 degrees C and decreases slowly upon either increasing or decreasing the temperature, regardless of the model used to fit the data. By contrast, the consensus values of the hydrodynamic radius are independent of temperature. The calculated persistence lengths and hydrodynamic radii are compared with other data in the literature.     

Temperature dependence of DNA persistence length

We have determined the temperature dependence of DNA persistence length, a, using two different methods. The first approach was based on measuring the j-factors of short DNA fragments at various temperatures. Fitting the measured j-factors by the theoretical equation allowed us to obtain the values of a for temperatures between 5°C and 42°C. The second approach was based on measuring the equilibrium distribution of the linking number between the strands of circular DNA at different temperatures. The major contribution into the distribution variance comes from the fluctuations of DNA writhe in the nicked circular molecules which are specified by the value of a. The computation-based analysis of the measured variances was used to obtain the values of a for temperatures up to 60°C. We found a good agreement between the results obtained by these two methods. Our data show that DNA persistence length strongly depends on temperature and accounting for this dependence is important in quantitative comparison between experimental results obtained at different temperatures.     

Viscosity behaviour and persistence length of sodium xanthan in aqueous sodium chloride

Zero-shear-rate intrinsic viscosities [eta] of sodium xanthan in aqueous NACl at 25 degrees C were determined for five samples ranging in weight- average molecular weight from 2 x 10(5) to 4 x 10(6) at salt concentrations Cs between 0.005 and 1 M, at which the polysaccharide maintains its double-helical structure. The measured [eta] for every sample was almost independent of Cs, in contrast to usual observations on flexible polyelectrolytes. The persistence length q of sodium xanthan was determined as a function of Cs by use of the theory of Yamakawa et al. for [eta] of an unperturbed worm-like cylinder, and from its Cs dependence the intrinsic persistence length q(o) ( = q at infinite ionic strength) was estimated to be 106 nm. This q(o) value was roughly twice as large as that of double-stranded DNA, indicating a high intrinsic rigidity of the xanthan double helix. The electrostatic contribution ( = q - q(o)) to q was only about 10% even at the lowest Cs of 0.005 M. Thus, it was concluded that above Cs = 0.005 M, the double- helical structure of sodium xanthan is hardly stiffened by electrostatic interactions between charged groups.     

Contribution of the intrinsic curvature to measured DNA persistence length

The persistence length of DNA, a, depends both on the intrinsic curvature of the double helix and on the thermal fluctuations of the angles between adjacent base-pairs. We have evaluated two contributions to the value of a by comparing measured values of a for DNA containing a generic sequence and for an "intrinsically straight" DNA. In each 10 bp segment of the intrinsically straight DNA an initial sequence of five bases is repeated in the sequence of the second five bases, so any bends in the first half of the segment are compensated by bends in the opposite direction in the second half. The value of a for the latter DNA depends, to a good approximation, on thermal fluctuations only; there is no intrinsic curvature. The values of a were obtained from measurements of the cyclization efficiency for short DNA fragments, about 200 bp in length. This method determines the persistence length of DNA with exceptional accuracy, due to the very strong dependence of the cyclization efficiency of short fragments on the value of a. We find that the values of a for the two types of DNA fragment are very close and conclude that the contribution of the intrinsic curvature to a is at least 20 times smaller than the contribution of thermal fluctuations. The relationship between this result and the angles between adjacent base-pairs, which specify the intrinsic curvature, is analyzed.     

Single-molecule measurements of the persistence length of double-stranded RNA

Over the past few years, it has become increasingly apparent that double-stranded RNA (dsRNA) plays a far greater role in the life cycle of a cell than previously expected. Numerous proteins, including helicases, polymerases, and nucleases interact specifically with the double helix of dsRNA. To understand the detailed nature of these dsRNA-protein interactions, the (bio)chemical, electrostatic, and mechanical properties of dsRNA need to be fully characterized. We present measurements of the persistence length of dsRNA using two different single-molecule techniques: magnetic tweezers and atomic force microscopy. We deduce a mean persistence length for long dsRNA molecules of 63.8 +/- 0.7 nm from force-extension measurements with the magnetic tweezers. We present atomic force microscopy images of dsRNA and demonstrate a new method for analyzing these, which yields an independent, yet consistent value of 62 +/- 2 nm for the persistence length. The introduction of these single-molecule techniques for dsRNA analysis opens the way for real-time, quantitative analysis of dsRNA-protein interactions.     

Flow birefringence of T7 phage DNA: Dependence on salt concentration

We have determined extinction angles and flow birefringence of T7 bacteriophage DNA over a wide range of shear, polymer concentration, and solvent ionic strength. From these data, information on the simple salt dependence of coil permeability to solvent and on short-range intrachain interactions (persistence length) was obtained. At all ionic strengths, our results are consistent with a partially draining coil in the Gaussian subchain dynamical theory of Rouse-Zimm-Tschoegl-Bloomfield. Salt dependence of persistence length is comparable to, although somewhat less than, that obtained previously using similar methods with a fivefold higher-molecular-weight DNA (T2 bacteriophage DNA). Possible reasons for observed discrepancies are analyzed, and the results of this work are compared in detail to other current studies of solvent ionic strength dependence in persistence length and hydrodynamic properties of DNA.     

Force-induced melting of the DNA double helix. 2. Effect of solution conditions

In this paper, we consider the implications of the general theory developed in the accompanying paper, to interpret experiments on DNA overstretching that involve variables such as solution temperature, pH, and ionic strength. We find the DNA helix-coil phase boundary in the force-temperature space. At temperatures significantly below the regular (zero force) DNA melting temperature, the overstretching force, f(ov)(T), is predicted to decrease nearly linearly with temperature. We calculate the slope of this dependence as a function of entropy and heat-capacity changes upon DNA melting. Fitting of the experimental f(ov)(T) dependence allows determination of both of these quantities in very good agreement with their calorimetric values. At temperatures slightly above the regular DNA melting temperature, we predict stabilization of dsDNA by moderate forces, and destabilization by higher forces. Thus the DNA stretching curves, f(b), should exhibit two rather than one overstretching transitions: from single stranded (ss) to double stranded (ds) and then back at the higher force. We also predict that any change in DNA solution conditions that affects its melting temperature should have a similar effect on DNA overstretching force. This result is used to calculate the dependence of DNA overstretching force on solution pH, f(ov)(pH), from the known dependence of DNA melting temperature on pH. The calculated f(ov)(pH) is in excellent agreement with its experimental determination (M. C. Williams, J. R. Wenner, I. Rouzina, and V. A. Bloomfield, Biophys. J., accepted for publication). Finally, we quantitatively explain the measured dependence of DNA overstretching force on solution ionic strength for crosslinked and noncrosslinked DNA. The much stronger salt dependence of f(ov) in noncrosslinked DNA results from its lower linear charge density in the melted state, compared to crosslinked or double-stranded overstretched S-DNA.     

Hierarchical extensibility in the PEVK domain of skeletal-muscle titin

Titin is the main determinant of passive muscle force. Physiological extension of titin derives largely from its PEVK (Pro-Glu-Val-Lys) domain, which has a different length in different muscle types. Here we characterized the elasticity of the full-length, human soleus PEVK domain by mechanically manipulating its contiguous, recombinant subdomain segments: an N-terminal (PEVKI), a middle (PEVKII), and a C-terminal (PEVKIII) one third. Measurement of the apparent persistence lengths revealed a hierarchical arrangement according to local flexibility: the N-terminal PEVKI is the most rigid and the C-terminal PEVKIII is the most flexible segment within the domain. Immunoelectron microscopy supported the hierarchical extensibility within the PEVK domain. The effective persistence lengths decreased as a function of ionic strength, as predicted by the Odijk-Skolnick-Fixman model of polyelectrolyte chains. The ionic strength dependence of persistence length was similar in all segments, indicating that the residual differences in the elasticity of the segments derive from nonelectrostatic mechanisms.     

A Mesoscale Model of DNA and Its Renaturation

A mesoscale model of DNA is presented (3SPN.1), extending the scheme previously developed by our group. Each nucleotide is mapped onto three interaction sites. Solvent is accounted for implicitly through a medium-effective dielectric constant and electrostatic interactions are treated at the level of Debye-Hückel theory. The force field includes a weak, solvent-induced attraction, which helps mediate the renaturation of DNA. Model parameterization is accomplished through replica exchange molecular dynamics simulations of short oligonucleotide sequences over a range of composition and chain length. The model describes the melting temperature of DNA as a function of composition as well as ionic strength, and is consistent with heat capacity profiles from experiments. The dependence of persistence length on ionic strength is also captured by the force field. The proposed model is used to examine the renaturation of DNA. It is found that a typical renaturation event occurs through a nucleation step, whereby an interplay between repulsive electrostatic interactions and colloidal-like attractions allows the system to undergo a series of rearrangements before complete molecular reassociation occurs.     

Magnetic birefringence study of the electrostatic and intrinsic persistence length of DNA

Magnetic birefringence experiments were performed on solutions of DNA of intermediate molecular weight at several concentrations (c_p) over a wide range of ionic strengths (of NaCl and MgCl₂). The specific Cotton-Mouton constant (CM/c_p) is found to be independent of c_p when contributions from c_p to the ionic strength (μ_eff) are taken into account according to the concept of counterion condensation. For μ_eff ? 10^?2M, CM/c_p is also independent of the ionic strength; the plateau value results in an acceptable value of the intrinsic persistence length, when a revised theoretical expression for the magnetic birefringence of wormlike chains is used, combined with new experimental data for the monomeric optical and magnetic anisotropy. For μ_eff < 10^?2M, CM/c_p strongly, or wealky, increases with decreasing μ_eff, depending on the valency of the counterion used (Na⁺ or Mg²⁺, respectively). This increase agrees quantitatively with the variation of the electrostatic persistence length as predicted by Odijk [(1977) J. Polym. Sci. Polym. Phys. Ed. 15 , 477–483], Odijk and Houwaart [(1978) J. Polym. Sci. Polym. Phys. Ed. 16 , 627–639], and by Skolnick and Fixman [(1977) Macromolecules 10 , 944–948]. A comparison with other experimental data seems to reveal the importance of excluded-volume effects, which are particularly pronounced in the low-salt regime.     

Electrophoretic charge density and persistence length of DNA as measured by fluorescence microscopy

Individual ethidium-stained DNA molecules, embedded in an agarose gel made with electrophoresis buffer (0.05 molar salt), are observed using a fluorescence microscope. In the first experiment, open circular 66 kilobase pair (kbp) plasmids, immobilized by agarose fibers threaded through their centers, display entropic "rubber" elasticity. The charged molecules extend in an electric field of several volts per centimeter and contract to a compact random coil when the field is removed. The extension of the plasmids as a function of field strength is consistent with the freely jointed chain model when the effective electrophoretic charge density is set at 15 e-per persistence length. In a second experiment, stained linear 48.5 kbp DNA molecules are observed as random coils immobilized in agarose. A measure of their size, here named the "maximal-X-extent," is taken for 100 molecules and found to average 1.47 mu. A Monte Carlo computer simulation of random coils (freely jointed chain model) gives the same maximal-X-extent value when the persistence length is set at 0.08 mu.     

Measuring the persistence length of MCF7 cell microtubules in vitro

The dynamic and mechanical properties of mammalian neural microtubules have been widely studied; however, similar knowledge about these properties is limited for non-neural microtubules, which, unlike neural microtubules, consist of different β-tubulin isotypes. In this study, we report, for the first time, an estimated value for the persistence length of a single non-neural microtubule polymerized from purified tubulin from human breast cancer cell lines (MCF7 tubulin). The method of measurement is based on an analysis of the local curvature of a microtubule as a result of thermal fluctuations. In parallel, we measured the persistence length of a single bovine brain microtubule under similar conditions. The results of our measurements indicate a higher value for the persistence length of MCF7 microtubules in vitro as compared to the persistence length of a neural microtubule. The difference can be associated with different β-tubulin isotypes in the structure of MCF7 microtubules.     

An absolute method for the determination of the persistence length of native DNA from electron micrographs.

Information on spatial correlation in the tangent direction along electron microscope images of filamentous molecule is shown to be obtainable by the analysis of statistical fluctuations in curvature, yielding an absolute measure of the persistence parameter a_micro. The relationship of a_micro, a local, microscopic parameter, to the persistence length introduced by Kratky and Porod is discussed. The hypotheses underlying the assumed theoretical model concern (1) the shape of the angle distribution, assumed to be Gaussian; (2) the passage from a three- to a two-dimensional situation, which is supposed to occur by deformation of the flexible chain in a manner that preserves the memory of the spatial correlation in orientation (except for the blocking of one degree of freedom); and (3) the adsorption conditions, which should meet the equilibrium requirement as closely as possible. The analytical method has been checked on computer simulated “Gaussian” molecules: the study of the simulated sample was essential in solving the problems connected with minimum statistics requirements and the effect of the reading error. Experimental images obtained for T2 DNA fragments at different ionic strengths by Kleinschmidt's adsorption technique have been analyzed by means of an automatic flying spot digitizer, the “Precision Encoder and Pattern Recognition.” The results show that adsorbed molecules do in fact “remember” the rigidity they possessed in solution and that the Gaussian hypothesis is well verified. Consequently, the slopes of log cosθ (l) or θ² (l) may be used indifferently in the estimate of a_micro. The dependence of this parameter on ionic strength in the range explored shows the expected behavior.     

Heterogeneity and persistence length in human ocular mucins

Atomic force microscopy (AFM) has been used to investigate the heterogeneity and flexibility of human ocular mucins and their subunits. We have paid particular attention, in terms of theory and experiment, to the problem of inducing the polymers to assume equilibrium conformations at a surface. Mucins deposited from a buffer containing Ni(2+) ions adopt extended conformations on mica akin to those observed for DNA under similar conditions. The heterogeneity of the intracellular native mucins is evident from a histogram of contour lengths, reflecting, in part, the diversity of mucin gene products expressed. Reduction of the native mucin with dithiothreitol, thereby breaking the S==S bonds between cysteine residues, causes a marked reduction in polymer length. These results reflect the modes of transport and assembly of newly synthesized mucins in vivo. By modifying the worm-like chain model for applicability to two dimensions, we have confirmed that under the conditions employed mucin adsorbs to mica in an equilibrated conformation. The determined persistence length of the native mucin, 36 nm, is consistent with that of an extended, flexible polymer; such characteristics will influence the properties of the gels formed in vivo.     

A refined calculation of the solution dimensions of the complex between gene 32 protein and single stranded DNA based on estimates of the bending persistence length

The rotation diffusion coefficient of a complex of GP32, the single stranded DNA binding protein of the bacteriophage T4, with a single stranded DNA fragment with about 270 bases was determined to obtain further information on the flexibility of this particle. The rotation diffusion of these molecules is used as a sensitive measure of the flexibility of different DNA protein complexes. Using the theory of Hagerman and Zimm (Biopolymers 20, 1481 (1981)) and assuming a bending persistence length of about 35 nanometer it can be shown that the axial increment for GP32 complexes with single stranded DNA is close to 0.5 nm per base. The value for the bending persistence length is in agreement with values found for much larger DNA protein complexes using light scattering experiments. This value for the persistence length also implies that the complex is thin. The radius is estimated to be around 1.7 nm, which shows a moderate degree of hydration. With this set of parameters we can describe all the hydrodynamic experiments on GP32 complexes from 76 to more than 7000 bases obtained using electric birefringence, quasi-elastic light scattering and sedimentation experiments performed in our group over the last few years.     

Investigation of the flexibility of DNA using transient electric birefringence

In the preceding article, a Monte Carlo analysis was presented which provides a quantitative numerical relationship between the rotational diffusion coefficients, as measured by the decay of optical anisotropy following an electric field pulse, and the flexibility (persistence length) of short, wormlike chains. In the present article, the results of the foregoing analysis are applied to the observed rates of decay of birefringence for a series of sequenced DNA fragments ranging in size from 104 to 910 base pairs. Under the conditions used in this study, the DNA fragments exist as native, duplex molecules. Furthermore, conditions are defined in which the observed relaxation times are not dependent on DNA concentration, field strength, or the duration of the pulse. It is pointed out that the ionic atmosphere associated with a wormlike polyion does not exert any significant (direct) influence on the rotational diffusion of the polyion and, therefore, that the rotational relaxation times are a true measure of the configurations of the DNA molecules in solution. Moreover, excluded-volume effects are shown not to be significant for the moderately short molecules employed in this study. The major conclusion of this study is that there is no strong ionic strength dependence of the persistence length for ionic strengths above 1 mM and that the persistence length, under conditions where electrostatic contributions are negligible, is approximately 500 Å. For ionic strengths significantly lower than 1 mM, electrostatic contributions to the stiffness of DNA become significant.     

Persistence length of DNA

In the wormlike chain (Kratky-Porod) model of DNA the stiffness of the chain is determined by the persistence length, a. The persistence length may be evaluated from light-scattering measurements of the molecular weight and the mean-square radius if the samples are not polydisperse or if the polydispersity can be quantitatively determined. The persistence length can also be evaluated with the aid of hydro dynamic theory from measurements of intrinsic viscosity and sedimentation coefficient. Data taken from the literature and from other studies by the authors are examined by these methods. The light-scattering method yields a value of a of 900 ± 200 Å the hydrodynamic data yield 600 ± 100 Å. These values are considerably larger than those obtained by most previous authors.     

Polyelectrolyte contribution to the persistence length of DNA

The difference between the theories of Manning, on the one hand, and of Odijk and Skolnick and Fixman, on the other, for the polyelectrolyte contribution to the persistence length of DNA is shown to arise entirely from a subtle geometrical error in the theory of Manning. The corrected theory of Manning predicts a negligible polyelectrolyte contribution in 1.0M NaCl and only 33 Å in 0.01M NaCl, thus giving a change in total persistence length by a factor of only 1.07 over that range, in agreement with Odijk. Pertinent data in the literature indicate that the persistence length must change by a factor of ≤ 1.6 between 1.0 and 0.01M NaCl, and very likely by less than a factor of 1.4. Evidently, the intrinsic rigidity of the uncharged double-strand filament dominates the bending rigidity at NaCl concentrations above 0.01M.