Torsional and Bending Rigidity of the Double Helix from Data on Small DNA Rings

Abstract

We have calculated the variance of equilibrium distribution of a circular wormlike polymer chain over the writhing number, ?(Wr)²?, as a function of the number of Kuhn statistical segments, n, For large n these data splice well with our earlier results obtained for a circular freely jointed polymer chain. Assuming that ?(ΔLk)²? = ?(ΔTw)²? + ?(Wr)²? we have compared our results with experimental data on the chain length dependence of the ?(ΔLk) ²? value recently obtained by Horowitz and Wang for small DNA rings. This comparison has shown an excellent agreement between theory and experiment and yielded a reliable estimate of the torsional and bending rigidity parameters. Namely, the torsional rigidity constant is C = 3.0·10^?19 erg cm, and the bending rigidity as expressed in terms of the DNA persistence length is a = 500 A. The obtained value of C agrees well with earlier estimates by Shore and Baldwin as well as by Horowitz and Wang whereas the a value is in accord with the data of Hagerman. We have found the data of Shore and Baldwin on the chain length dependence of the ?(ΔLk) ²? value to be entirely inconsistent with our theoretical results.     

Monte Carlo approach to the analysis of the rotational diffusion of wormlike chains

A Monte Carlo analysis is presented which establishes a relationship between the rotational diffusion coefficients and the flexibility (persistence length, P) of short, wormlike chains. The results of this analysis are presented in terms of experimentally observable quantities; namely, the rotational relaxation times for the field-free decay of optical anisotropy. The pertinent theoretical quantity is R, defined as the ratio of the longest rotational relaxation time of a wormlike chain to the transverse rotational relaxation time of a rigid cylinder having the same axial length (L) and segmental volume. R, so defined, is essentially independent of the axial ratio of the cylinder for any value of L/P within the range of validity of the present analysis (axial ratio > 20; 0.1 < L/P < 5). It is pointed out that P can be determined with reasonable accuracy even in the absence of a precise knowledge of the local hydrodynamic radius of the chain.     

Characterization of rodlike RNA fragments.

Native calf thymus DNA was sheared by sonication in a viscous solvent to the molecular-weight range from 3 × 10⁴ to 3 × 10⁵ daltons, and fractionated by gel chromatography. Number and weight average molecular weights (M?_n and M?_w) were determined for individual fractions by electron microscopy; the ratio M?_w/M?_n for the peak fraction is approximately 1.1. Sedimentation coefficients (s⁰_20,w) of these fractionated samples show an approximately linear dependence on the logarithm of the molecular weight M?_w. This behavior is that expected for rodlike molecules, and is in quantitative agreement with the theory of Yamakawa and Fujii [(1973) Macromolecules 6 , 407–415] for the sedimentation coefficient of a wormlike chain with a persistence length of 625 Å, a diameter of 25 Å, and a mass per unit length of 195 daltons/Å. It appears that the wormlike coil model, without excluded volume, can represent the sedimentation behavior of DNA over the entire conformational range from rigid rod to flexible coil, using the above parameters. Equilibrium melting curves were determined for various fractions in aqueous 2.4 M tetraethylammonium bromide. A substantial broadening of the transition and decrease of the melting temperature were observed with decreasing molecular weight. Empirical expressions have been obtained relating both the transition temperature and breadth in this solvent to molecular weight.     

Thermodynamics of DNA Containing Very Stable Chemically Modified Base Pairs

Abstract

DNA chemical modifications caused by the binding of some antitumor drugs give rise to a very strong local stabilization of the double helix. These sites melt at a temperature that is well above the melting temperatures of ordinary AT and GC base pairs. In this work we have examined the melting behavior of DNA containing very stable sites. Analytical expressions were derived and used to evaluate the thermodynamic properties of homopolymers DNA with several different distributions of stable sites. The results were extended to DNA with a heterogeneous sequence of AT and GC base pairs. The results were compared to the melting properties of DNA with ordinary covalent interstrand cross-links. It was found that, as with an ordinary interstrand cross-link, a single strongly stabilized site makes a DNA's melting temperature (T_m ) independent of strand concentration. However in contrast to a DNA with an interstrand cross-link, a strongly stabilized site makes the DNA's T_m independent of DNA length and equal to T _∞, the melting temperature of an infinite length DNA with the same GC-content and without a stabilized site. Moreover, at a temperature where more than 80% of base pairs are melted, the number of ordinary (non-modified) helical base pairs (n) is independent of both the DNA length and the location of the stabilized sites. For this condition, n(T) = (2ω-a) S (1- S ) and S = exp[ΔS(T∞-T)/(RT)] where ω is the number of strongly stabilized sites in the DNA chain, a is the number of DNA ends that contain a stabilized site, and ΔS, T, and R are the base pair entropy change, the temperature, and the universal gas constant per mole. The above expression is valid for a temperature interval that corresponds to n<0.2N for ω=1, and n<0.1N for ω>1, where N is the number of ordinary base pairs in the DNA chain.     

EFFECTIVE POPULATION SIZE AND GENETIC DRIFT IN TRISTYLOUS EICHHORNIA PANICULATA (PONTEDERIACEAE)

Populations of the tristylous, annual Eichhornia paniculata are markedly differentiated with respect to frequency of mating types. This variation is associated with evolutionary changes in mating system, from predominant outcrossing to high self-fertilization. To assess the potential influence of genetic drift acting on this variation, we estimated effective population size in 10 populations from northeastern Brazil using genetic and demographic methods. Effective size (N_e) was inferred from temporal changes in allele frequency at two to eight isozyme loci and also calculated using five demographic variables: 1) the number of flowering individuals (N); 2) temporal fluctuations in N; 3) variance in flower number; 4) frequency of mating types; and 5) selfing rate. Average N_e based on isozyme data was 15.8, range 3.4–70.6, and represented a fraction (mean N_e/N = 0.106) of the census number of individuals (mean N = 762.8; range: 30.5–5,040). Temporal variation in N and variance in flower number each reduced N_e to about a half of N whereas mating type frequencies and selfing rate caused only small reductions in N_e relative to N. All estimates of N_e based on demographic variables were considerably larger than those obtained from genetic data. The two kinds of estimates were in general agreement, however, when all demographic variables were combined into a single measure. Monte Carlo simulations indicated that effective size must be fewer than about 40 for drift to overcome the frequency-dependent selection that maintains the polymorphism for mating type. Applying the average N_e/N value to 167 populations censused in northeastern Brazil indicated that 72% had effective sizes below this number. This suggests that genetic drift is likely to play a dominant role in natural populations of E. paniculata.     

Excluded volume of an intermediate-molecular-weight DNA. A Monte Carlo analysis

A Monte Carlo procedure wasused to determine the effect of excluded volume on the dimensions of an intermediate-molecular-weight DNA for different Na⁺ concentrations. The calculation of α, the parameter for the linear expansion due to excluded volume, was accomplished by generating sets of chains and, for each set, comparing the average radius of gyration for the set of chains that do not overlap to that averaged over the entire set of chains. Each chain was defined by cylinders linked with free rotation and with bend angles generated according to a weighted Gaussian distribution. The chain parameters—contour lenght, cylinder lenght and diameter—were fixed in order to resemble published light-scattering experiments on Col E₁ DNA. Values for α were less than 1.08. for Na⁺ concentrations between 0.007 and 1.0M. A previously reported analytical calculation of the excluded-volume correction of intermediate-sized DNA gave results that are closely similar to those from the Monte Carlo analysis.     

Potential theory for gate adsorption on soft porous crystals

We demonstrate that an adsorption potential at the gate adsorption pressure of soft porous crystals (SPCs) based on the Polanyi's potential theory of adsorption shows a constancy to temperature. This was done using grand canonical Monte Carlo simulations and free energy analysis, which were carried out with a simplified stacked-layer SPC model. This finding implies that the characteristic curve obtained from an experimental gate adsorption isotherm on SPCs can be used to predict the temperature dependence of the gate-opening pressure, even though the potential theory of adsorption does not take into account the deformation of porous solids during the adsorption. We develop a modified potential theory for gate adsorption and show that the derived relation has a form that the Gibbs free energy change due to the host framework deformation per guest molecule, ? ΔG_host/N, and a correction term, C, are added to the expression of the original potential theory of adsorption. The term C is not an empirical correction factor but is the difference of intermolecular interaction potential and entropy between the bulk liquid phase at the saturated state and the adsorbed phase, originating from spatial constraint of adsorbed guest molecules in the host. By evaluating the modified expression for gate adsorption using the simulation results, we demonstrate that the constancy of the adsorption potential to temperature results from a compensation effect between three terms: guest–host interaction potential per guest molecule, ? ΔG_host/N and C, which have a temperature dependence.     

Effects of the nucleoid protein HU on the structure, flexibility, and ring-closure properties of DNA deduced from Monte Carlo simulations

The histone-like HU (heat unstable) protein plays a key role in the organization and regulation of the Escherichia coli genome. The nonspecific nature of HU binding to DNA complicates analysis of the mechanism by which the protein contributes to the looping of DNA. Conventional models of the looping of HU-bound duplexes attribute the changes in biophysical properties of DNA brought about by the random binding of protein to changes in the effective parameters of an ideal helical wormlike chain. Here, we introduce a novel Monte Carlo approach to study the effects of nonspecific HU binding on the configurational properties of DNA directly. We randomly decorated segments of an ideal double-helical DNA with HU molecules that induce the bends and other structural distortions of the double helix find in currently available X-ray structures. We find that the presence of HU at levels approximating those found in the cell reduces the persistence length by roughly threefold compared with that of naked DNA. The binding of protein has particularly striking effects on the cyclization properties of short duplexes, altering the dependence of ring closure on chain length in a way that cannot be mimicked by a simple wormlike model and accumulating at higher-than-expected levels on successfully closed chains. Moreover, the uptake of protein on small minicircles depends on chain length, taking advantage of the HU-induced deformations of DNA structure to facilitate ligation. Circular duplexes with bound HU show much greater propensity than protein-free DNA to exist as negatively supercoiled topoisomers, suggesting a potential role of HU in organizing the bacterial nucleoid. The local bending and undertwisting of DNA by HU, in combination with the number of bound proteins, provide a structural rationale for the condensation of DNA and the observed expression levels of reporter genes in vivo.     

Computer simulation of hydrodynamic properties of semiflexible macromolecules: randomly broken chains, wormlike chains, and analysis of properties of DNA

The translational and rotational diffusion coefficients and the intrinsic viscosity of semiflexible, randomly broken, and wormlike chains have been obtained by Monte Carlo simulation in the context of the rigid-body treatment. Both approximate and rigorous rigid-body hydrodynamics are used, so that the error introduced by the approximate methods can be evaluated. A randomly broken chain and a wormlike chain having the same contour length and persistence length have the same radius of gyration but different values for any of the hydrodynamic properties. The two types of chains are compared in this regard. Considering that the cross section of the chain is represented by a cylinder better than by a string of spheres, we devise a cylindrical correction to be applied to the results simulated for chains of beads. Application is made to the analysis of experimental data for the translational and rotational coefficients of DNA fragments with up to 10(3) base pairs, obtaining the persistence length for each model. The values for the wormlike chain agree well with model-independent values obtained from radii of gyration and with other literature data at varying ionic strength. The randomly broken chain is equally able to reproduce the experimental length dependence of the properties, but the resulting persistence length may be too high.     

Dilute solution of amylose in dimethylsuldoxide

Measurements of light scatting, sedimentation equilibrium, sedimentation velocity, and viscosity were carried out on fractions of native amylose in dimethylsulfoxide at 25°C. The data for statistical radius as a function of weight-average molecular weight M_w suggested a stiff nature of this biopolymer in the solvent studied when interpreted in terms of Kirste's recent calculations with a stiff chain model. The data for sedimentation coefficient were consistent with this suggestion, and when analyzed in terms of the theory Hearst and Stockmayer for wormlike chain, a value of 233 Ų was obtainedd for a/λ, where a is the length of a monomer unit projected on the chain axis and (2λ)^?1is the persistence length of the wormlike chain. The intrinsic viscosity data gave a high a value as 0.91 for the exoponent in the Houwink-Mark-Sakuarada equation, in Substantial agreement with Cowie's prenious work. We attempted to interpret these data by use of the Eizner-Ptitsyn equation for wormlike chains, with omission of the free-drainage term and introduction of the a/λ value obtained from sedimentation data. It was found that, except in the region of M_w above one million, the observed values were fitted well by the E-P theory with a = 1.4 Å and (2λ)^?1 = 87 Å. The disagreement in the high-molecular-weight region was tentatively attributed to excluded volume effect. The a value obtained suggests that the molecular conformation of amylose in dimethylsulfoxide is predominantly helical, in contrast to that of the same polymer in aqueous solutions of simple electrolyte. It was also found that a similar value of a was derived from our data for the second virial coefficient and partial specific volume if the molecule was assumed to be essentially rodlike.     

Viscometry and sedimentation equilibrium of partially hydrolyzed hyaluronate: Comparison with theoretical models of wormlike chains

Fractionated samples of sodium hyaluronate of low molecular weight were used to calibrate the carbazole method for glucuronyl analsis and to determine the density increment (based on dry weight) of 0.444 (±0.003) mL/g in water and 0.386 (±0.003) mL/g for samples dialyzed against 0.2M NaCl. Weight-average molecular weights obtained by high-speed sedimentation equilibrium were used to calibrate the limiting viscosity number [η] in 0.2M NaCl, which gave [η]/M_w = 0.0028 (±0.0002) mL/g, valid to M_w = 0.0028 (±0.0002) mL/g, valid to M_w = 10⁵. Experimental data from this work and the literature, including viscosity and light- and small-angle x-ray scattering measurements, were compared to theoretical chain models of the Kratky-Porod (KP) wormlike and the helical wormlike (HW) chain, as treated by Yamakawa and collaborators. Although either model could be fitted to experimental data about equally well with consistent parameters, provided those for the HW chain were of weakly helical nature, calculation of the unperturbed meansquare end-to-end distance as a function of chain length from a conformational model favored the KP chain alternative. The parameters that provide the best fit to experimental data for the KP wormlike model are a persistence length of 4.5–5 nm and a diameter of 1.1 nm. The latter is resonable for a hydrated hydrodynamic cylinder in view of the approximate unhydrated value of 0.7 nm estimated from the density increment.     

One- and Two-Sample Tests of Kendall's τ

Several methods of testing general one-sample and two-sample hypotheses of Kendall's τ are discussed. The performance of these procedures in typical situations likely to occur in practice was investigated by numerous Monte Carlo experiments. The common one-sample test (H₀: τ = 0) based on the permutational variance performs very similar to bootstrap or jackknife testing for true τ near zero. For true |τ| perhaps greater than 0.4 and moderate sample sizes bootstrap techniques are the methods of choice.     

Simulations of Flexible Manifolds

Monte Carlo simulations of flexible two-dimensional model membranes embedded in three space dimensions are reported. We explain in detail the techniques how to simulate fluid open membranes and fluid closed membranes (vesicles). It is shown that polymerized open membranes are rough and flat. Accordingly, the two larger components of the inertia tensor are proportional to the number of monomers of the surface, λ₃ ≈ λ₂ ～ N, whereas the smallest λ₁ ～ N ^0.65. Polymerized vesicles are isotropic and their mean square radius of gyration is R ² ～ λ _k ～ N. In contrast, fluid membranes and vesicles exhibit crumpled shapes with λ _k ～ N ^0.8 for k = 1,2,3. A monomer on a fluid surface exhibits a time-dependent mean squared displacement of r ² (t) ～ t ^0.8.     

Chemical and histochemical studies of normal and diseased gastrointestinal tract. IV. A comparison of histochemical and chemical methods for the estimation of side chain O-acylated sialic acids

Summary Statistically significant correlations were obtained between a chemical assay for the proportion of colonic epithelial glycoprotein sialic acids with side chainO-acyl substituents and two histochemical methods, the PBT-KOH-PAS sequence (r _s=0.7485 forN=31,P=0.01, one-sided test) and the PAPT-KOH-Bh-PAS procedure (r _s=0.7024 forN=34). A positive correlation (r _s=0.8654 forN=30,P=0.01) was also obtained between the results of the two histochemical procedures. It is concluded that, on average, histochemical observations are a reliable semiquantitative comparative method for the estimation of side chainO-acetylated sialic acids.     

DNA conformation in N,N-dimethyl formamide-H2O solutions

Optical density, viscosity, and light scattering measurements for calf thymus DNA in water–N,N dimethyl formamide (DMF) solutions are presented. DMF content varied between 0 and 60% (v/v) and DNA molecular weight varied between 15 × 10⁶ and 0.5 × 10⁶. Complementary measurements of the solubility of adenine, thymine, guanine, and cytosine in H₂O–DMF mixtures are presented. The denaturation temperature of DNA, manifested by about a 35% increase of optical density, is gradually depressed by increasing DMF content. However, a significant increase of OD occurs even before (and even after) the denaturation point, when DMF content is increased isothermally. The intrinsic viscosity also exhibits a large decrease when DMF content is increased both before and after the denaturation point. Light scattering data for high-molecular-weight DNA in the predenaturation range indicate a decrease of the mean-square radius and a constant molecular weight on increasing DMF content. The results, interpreted in terms of the wormlike chain of Kratky and Porod, indicate a large decrease of the persistence length of DNA. For low-molecular-weight DNA, radius and molecular weight increase with DMF content, indicating intermolecular aggregation. The formation of compact structures of native DNA is discussed in terms of an increased solubility of uncharged bases, and a decreased solubility of phosphate and deoxyribose groups, when a less polar environment is provided by the addition of DMF.     

Characteristic parameters and polydispersity elimination factors for hydrodynamic quantities of semirigid polymers, especially of DNA

Relations are given allowing the calculation of intrinsic viscosity, diffusion constant, and related molecular weights of monodisperse subfractions of polydisperse samples from the measured averages of the hydrodynamic quantities and the individual (reduced) sedimentation constant distribution. The peculiarities resulting from the special behavior of semirigid polymers like DNA are treated. Expressions are derived which describe the dependence of the exponents a_s(a_ηs = a_η/a_s), and a_η of the relations s^o = k_sM^as [η] = k_ηs(s^o)^aηs, and [η] = k_ηM^aη on s^o and [η], respectively, and which are useful for practical and theoretical discussions of the wormlike chain. Furthermore, a generalized exponent rule for a_η and a_s has been suggested, considering the dependence of the Mandelkern-Flory-Scheraga parameter β(?Φ^1/3P^?1) on molecular weight. The results of this paper are applied extensively in the following paper to molecular weight and hydrodynamic properties of homogeneous DNA.     

Sexual recombination under the joint effects of mutation,selection, and random sampling drift

The advantage or disadvantage of sexual reproduction or recombination for the accumulation of mutant genes in a population is studied under the joint effects of recurrent mutations, selection, and random sampling drift. To obtain the rate at which mutant genes are incorporated three different methods are used; numerical integration of Kolmogorov backward equations, simulation of stochastic difference equations, and Monte Carlo experiments. The first two methods are used in a two-locus system to obtain the fixation probability of double mutants and other related quantities under five different selection models. The third one is conducted for a multiple-locus system and the rate of accumulation of mutant genes per locus is studied. Comparison of the results between sexual and asexual populations shows that the effect of recombination depends on initial linkage disequilibrium, mutation rate v, selection intensity s, and population size N_e. The mode of selection is also an important factor and the large effect of recombination is observed when mutant genes are individually deleterious but collectively favorable. Under a given model of selection, the great advantage or disadvantage of recombination is achieved when a large extent of genetic polymorphism is produced not by mutation but by recombination. Extreme values of N_es and N_ev make the effect insignificant. The results of Monte Carlo experiments also reveal the presence of interaction between selection and sampling drift even when the loci segregate independently and selection is multiplicative. Although this interaction is usually small, there are cases in which one locus theory cannot be used freely. In those cases, the effect of recombination is prominent and one locus theory gives an overestimate of the rate.     

Loop energy in DNA

The loop function ?(N), representing the statistical weight of N complementary residues in a closed ring, has been determined by analysis of high-resolution melting curves of a series of recombinant homopoly(A · T)_N inserts in pBR322 DNA, where 150 > N > 50 base pairs (bp). Loops are found more stable and therefore presumably less elastic than expected for an ideal, freely jointed chain. A value of 97 ± 2 bp is obtained for the empirical orientation-stiffness parameter D in the expression for nonideal chains, ?(N) = (N + D)^?1.7. The 10% increase in apparent stiffness over that of an ideal chain closely coincides with the extent of residual stacking in the loop. It is thus concluded that the more favorable loop energy, such as expected of smaller loops, is due to the incipient helical orientation of some residues, predisposing the loop to reclosure. A quantitative loop function is essential for the prediction and assignment of domains in DNA.