A theory of thermal fluctuations in DNA miniplasmids.

A recent analysis of the normal modes of vibration of a ring formed by bringing together and sealing, with or without the addition of twist, the ends of rods that are straight when stress free is taken as the basis for a theory of the statistical thermodynamics of a canonical ensemble of DNA minicircles with specified linking number difference deltaLk and number N of base pairs. It is assumed that N corresponds to a circumference in the range of one or two persistence lengths. For such an ensemble, the theory yields an expression for the average writhe (Wr), which can be employed to calculate the free energy, entropy, and enthalpy of supercoiling, deltaGsc, deltaSsc, and deltaHsc. The results obtained for the dependence of deltaGsc on deltaLk and N are in accord with experimental observations of equilibrium distributions of topoisomers of plasmids with N approximately 200 bp.     

Torsional rigidity of DNA and length dependence of the free energy of DNA supercoiling

By analyzing the Boltzmann populations of DNA topoisomers that differ only in their linking numbers, the dependence of the free energy delta G tau of DNA supercoiling on the linking number alpha has been determined for DNA rings as small as 200 base-pairs (bp) in length. All experimental data can be fitted by the relation delta G tau = K (alpha-alpha)2, where alpha is a constant for a given DNA at a given set of conditions and K is a DNA length-dependent proportionality constant. For DNA rings with length N larger than 2000 bp, K is inversely proportional to N and the product NK is nearly a constant around 1150 RT X bp. For rings smaller than 2000 bp NK increases steadily with decreasing N; for a 200 bp ring NK is 3900 RT X bp. The increase in NK when N decreases can be interpreted as a result of the decrease in the contribution of the fluctuation in the writhing number to the equilibrium distribution in alpha. Assuming that the writhing contribution approaches zero for DNA rings 200 bp in size, the torsional rigidity of the DNA double helix is calculated to be 2.9 X 10(-19) erg cm. In addition, the large value of K for the small circles allows precise calculation of the helical repeat of DNA. For the 210 bp rings, the repeat is measured to be 10.54 bp.     

The distribution of end-to-end distances of the weakly bending rod model

The weakly bending rod model is an approximation to a worm-like chain in the limit where the ratio L(0)/P of the contour length L(0) to the persistence length P is not too large. The range of validity of the weakly bending rod model is investigated by deriving analytical expressions for its distribution of end-to-end distances P(L) and its moments and numerically comparing the results with corresponding values for the worm-like chain model. No general, closed form analytical expression for either P(L) or the average length of a worm-like chain exists, so those quantities are obtained by Monte Carlo simulations. Exact analytical expressions for and for the worm-like chain are employed in the comparison of the computed moments. Moments calculated for the approximate distributions of Daniels and Yamakawa and Stockmayer are also compared with the others. In addition, P(L) and its moments for the alternative model of Winkler et al. are compared with the others. The weakly bending rod model gives a reasonably good account of both P(L) and , m = 1,2,4, over the range L(0)/P /= 1.0. In contrast, the alternative model of Winkler et al. yields rather poor results in the rodlike domain.     

Variance of writhe for wormlike DNA rings with excluded volume

We have calculated the variance of the equilibrium distribution of a circular wormlike polymer chain over the writhing number, less than (Wr)2 greater than, with allowance for the excluded volume effects. Within this model the less than (Wr)2 greater than value is a function of the number of Kuhn statistical segments, n, and the chain diameter, d measured in Kuhn statistical lengths, b. Simulated DNA chains varied from 200 to 10,000 base pairs and the d value varied from 0.02 to 0.2. Theory predicts a considerable ionic strength dependence of the DNA superhelix energy as a consequence of the change in the DNA diameter. A comparison with the available experimental data has yielded an estimate of the DNA torsional rigidity, the Kuhn statistical length, and the effective diameter of the double helix under conditions of the complete screening of the DNA electrostatic potential.     

Calculation of the degree of superhelical DNA in model chromatin fibers

Effect of the length of DNA internucleosome regions (L) on writhing number (Wr) was analysed. It has been shown that Wr(L) is a periodic function. In any period Wr decreases, if L increases. The process of chromatin activation is proposed. The value sigma is shown to be equal to -0.086 for certainly inactive and -0.107 for potentially active and active chromatin models.     

Pulling-speed-dependent force-extension profiles for semiflexible chains

We present theory and simulations to describe nonequilibrium stretching of semiflexible chains that serve as models of DNA molecules. Using a self-consistent dynamical variational approach, we calculate the force-extension curves for worm-like chains as a function of the pulling speed, v(0). Due to nonequilibrium effects the stretching force, which increases with v(0), shows nonmonotonic variations as the persistence length increases. To complement the theoretical calculations we also present Langevin simulation results for extensible worm-like chain models for the dynamics of stretching. The theoretical force-extension predictions compare well with the simulation results. The simulations show that, at high enough pulling speeds, the propagation of tension along the chain conformations transverse to the applied force occurs by the Brochard-Wyart's stem-flower mechanism. The predicted nonequilibrium effects can only be observed in double-stranded DNA at large ( approximately 100 microm/s) pulling speeds.     

Step-wise DNA relaxation and decatenation by NaeI-43K.

Nae I protein was originally isolated for its restriction endonuclease properties. Nae I was later discovered to either relax or cleave supercoiled DNA, depending upon whether Nae I position 43 contains a lysine (43K) or leucine (43L) respectively. Nae I-43K DNA relaxation activity appears to be the product of coupling separate endonuclease and ligase domains within the same polypeptide. Whereas Nae I relaxes supercoiled DNA like a topoisomerase, even forming a transient covalent intermediate with the substrate DNA, Nae I shows no obvious sequence similarity to the topoisomerases. To further characterize the topoisomerase activity of Nae I, we report here that Nae I-43K changes the linking number of a single negatively supercoiled topoisomer of pBR322 by units of one and therefore is a type I topoisomerase. Positively supercoiled pBR322 was resistant to Nae I-43K. At low salt concentration Nae I-43K was processive; non-saturating amounts of enzyme relaxed a fraction of the DNA. At high salt concentration the same non-saturating amounts of Nae I-43K partially relaxed all the DNA in a step-wise fashion to give a Gaussian distribution of topoisomers, demonstrating a switch from a processive to a distributive mode of action. Nae I-43K decatenated kinetoplast DNA containing nicked circles, implying that Nae I-43K can cleave opposite a nick. The products of the reaction are decatenated nicked circles under both processive and distributive conditions. The behavior of Nae I-43K is consistent with that of a prokaryotic type I topoisomerase.     

Probing single-stranded DNA conformational flexibility using fluorescence spectroscopy

Single-stranded DNA (ssDNA) is an essential intermediate in various DNA metabolic processes and interacts with a large number of proteins. Due to its flexibility, the conformations of ssDNA in solution can only be described using statistical approaches, such as flexibly jointed or worm-like chain models. However, there is limited data available to assess such models quantitatively, especially for describing the flexibility of short ssDNA and RNA. To address this issue, we performed FRET studies of a series of oligodeoxythymidylates, (dT)N, over a wide range of salt concentrations and chain lengths (10 < or = N < or = 70 nucleotides), which provide systematic constraints for testing theoretical models. Unlike in mechanical studies where available ssDNA conformations are averaged out during the time it takes to perform measurements, fluorescence lifetimes may act here as an internal clock that influences fluorescence signals depending on how fast the ssDNA conformations fluctuate. A reasonably good agreement could be obtained between our data and the worm-like chain model provided that limited relaxations of the ssDNA conformations occur within the fluorescence lifetime of the donor. The persistence length thus estimated ranges from 1.5 nm in 2 M NaCl to 3 nm in 25 mM NaCl.     

The elastic rod model for DNA and its application to the tertiary structure of DNA minicircles in mononucleosomes.

Explicit solutions to the equations of equilibrium in the theory of the elastic rod model for DNA are employed to develop a procedure for finding the configuration that minimizes the elastic energy of a minicircle in a mononucleosome with specified values of the minicircle size N in base pairs, the extent w of wrapping of DNA about the histone core particle, the helical repeat h(0)b of the bound DNA, and the linking number Lk of the minicircle. The procedure permits a determination of the set Y(N, w, h(0)b) of integral values of Lk for which the minimum energy configuration does not involve self-contact, and graphs of writhe versus w are presented for such values of Lk. For the range of N of interest here, 330 < N < 370, the set Y(N, w, h(0)b) is of primary importance: when Lk is not in Y(N, w, h(0)b), the configurations compatible with Lk have elastic energies high enough to preclude the occurrence of an observable concentration of topoisomer Lk in an equilibrium distribution of topoisomers. Equilibrium distributions of Lk, calculated by setting differences in the free energy of the extranucleosomal loop equal to differences in equilibrium elastic energy, are found to be very close to Gaussian when computed under the assumption that w is fixed, but far from Gaussian when it is assumed that w fluctuates between two values. The theoretical results given suggest a method by which one may calculate DNA-histone binding energies from measured equilibrium distributions of Lk.     

Molecular mechanics of cardiac titin's PEVK and N2B spring elements.

Titin is a giant elastic protein that is responsible for the majority of passive force generated by the myocardium. Titin's force is derived from its extensible I-band region, which, in the cardiac isoform, comprises three main extensible elements: tandem Ig segments, the PEVK domain, and the N2B unique sequence (N2B-Us). Using atomic force microscopy, we characterized the single molecule force-extension curves of the PEVK and N2B-Us spring elements, which together are responsible for physiological levels of passive force in moderately to highly stretched myocardium. Stretch-release force-extension curves of both the PEVK domain and N2B-Us displayed little hysteresis: the stretch and release data nearly overlapped. The force-extension curves closely followed worm-like chain behavior. Histograms of persistence length (measure of chain bending rigidity) indicated that the single molecule persistence lengths are approximately 1.4 and approximately 0.65 nm for the PEVK domain and N2B-Us, respectively. Using these mechanical characteristics and those determined earlier for the tandem Ig segment (assuming folded Ig domains), we modeled the cardiac titin extensible region in the sarcomere and calculated the extension of the various spring elements and the forces generated by titin, both as a function of sarcomere length. In the physiological sarcomere length range, predicted values and those obtained experimentally were indistinguishable.     

Variance of Writhe for Wormlike DNA Rings with Excluded Volume

Abstract

We have calculated the variance of the equilibrium distribution of a circular wormlike polymer chain over the writhing number, <((Wr)² )>, with allowance for the excluded volume effects. Within this model the <((Wr)² )> value is a function of the number of Kuhn statistical segments, n, and the chain diameter, d measured in Kuhn statistical lengths, b. Simulated DNA chains varied from 200 to 10,000 base pairs and the d value varied from 0.02 to 0.2. Theory predicts a considerable ionic strength dependence of the DNA superhelix energy as a consequence of the change in the DNA diameter. A comparison with the available experimental data has yielded an estimate of the DNA torsional rigidity, the Kuhn statistical length, and the effective diameter of the double helix under conditions of the complete screening of the DNA electrostatic potential.     

Evaluation of elastic properties of atomistic DNA models

A number of intriguing aspects in dynamics of double-helical DNA is related to the coupling between its macroscopic and microscopic states. A link between the elastic properties of long DNA chains and their atom-level dynamics can be established by comparing the worm-like chain model of polymer DNA with the conformational ensembles produced by molecular dynamics simulations. This problem is complicated by the complexity of the DNA structure, the small size of DNA fragments, and relatively short trajectory durations accessible in computer simulations of microscopic DNA dynamics. A careful study of all these aspects has been performed by using longer DNA fragments and increased durations of MD trajectories as compared to earlier such investigations. Special attention is paid to the necessary conditions and criteria of time convergence, and the possibility to increase the sampling by using constrained DNA models and simplified simulation conditions. It is found that dynamics of 25-mer duplexes with regular sequences agrees well with the worm-like chain theory and that accurate evaluation of DNA elastic parameters requires at least two turns of the double helix and approximately 20-ns duration of trajectories. Bond length and bond-angle constraints affect the estimates within numerical errors. In contrast, simplified treatment of solvation can strongly change the observed elastic parameters of DNA. The elastic parameters evaluated for AT- and GC-alternating duplexes reasonably agree with experimental data and suggest that, in different basepair sequences, the torsional and stretching elasticities vary stronger than the bending stiffness.     

Scanning tunneling microscopy of mercapto-hexyl-oligonucleotides attached to gold.

6-mercapto hexyl-oligonucleotides bind to a gold surface strongly enough to permit imaging by a scanning tunneling microscope (STM). STM images showed worm-like chains that were approximately 12-(A-wide for single-stranded DNA and 20-(A-wide for double-stranded DNA. The chain lengths corresponded to 3.4 +/- 0.4 A per basepair for double-stranded DNA and 2.2 +/- 0.4 A per base for single-stranded DNA. This unexpectedly short length for single-stranded DNA was confirmed using oligomers with both single- and double-stranded regions. When the attachment of the samples was weakened (by imaging in water or scraping with the STM tip) the images changed to pairs of "blobs," apparently reflecting the attachment points of the molecules to the gold surface. Given this interpretation, images of DNA containing a five-base bulge imply that the bulge bends the oligomer by 90 degrees +/- 20 degrees.     

Separation of plasmid DNA topoisomers by multimodal chromatography

The ability to analyze the distribution of topoisomers in a plasmid DNA sample is important when evaluating the quality of preparations intended for gene therapy and DNA vaccination or when performing biochemical studies on the action of topoisomerases and gyrases. Here, we describe the separation of supercoiled (sc) and open circular (oc) topoisomers by multimodal chromatography. A medium modified with the ligand N-benzyl-N-methyl ethanolamine and an elution scheme with increasing NaCl concentration are used to accomplish the baseline separation of sc and oc plasmid. The utility of the method is demonstrated by quantitating topoisomers in a purified plasmid sample.     

Mechanics of F-actin characterized with microfabricated cantilevers

In this report we characterized the longitudinal elasticity of single actin filaments manipulated by novel silicon-nitride microfabricated levers. Single actin filaments were stretched from zero tension to maximal physiological tension, P(0). The obtained length-tension relation was nonlinear in the low-tension range (0-50 pN) with a resultant strain of approximately 0.4-0.6% and then became linear at moderate to high tensions (approximately 50-230 pN). In this region, the stretching stiffness of a single rhodamine-phalloidin-labeled, 1-microm-long F-actin is 34.5 +/- 3.5 pN/nm. Such a length-tension relation could be characterized by an entropic-enthalpic worm-like chain model, which ascribes most of the energy consumed in the nonlinear portion to overcoming thermal undulations arising from the filament's interaction with surrounding solution and the linear portion to the intrinsic stretching elasticity. By fitting the experimental data with such a worm-like chain model, an estimation of persistence length of approximately 8.75 microm was derived. These results suggest that F-actin is more compliant than previously thought and that thin filament compliance may account for a substantial fraction of the sarcomere's elasticity.     

C. botulinum neurotoxin types A and E: isolated light chain breaks down into two fragments. Comparison of their amino acid sequences with tetanus neurotoxin

The flaccid paralysis in the neuromuscular disease botulism appears to depend on the coordinated roles of the approximately 50 kDa light and approximately 100 kDa heavy chain subunits of the approximately 150 kDa neurotoxic protein produced by Clostridium botulinum (J. Biol. Chem. (1987) 262, 2660 and Eur. J. Biochem. (1988) 177, 683). We observed that the light chain after separation from its conjugate heavy chain, in the presence of dithiothreitol and 2 M urea, begins to split into approximately 28 and approximately 18 kDa fragments. The other subunit-the approximately 100 kDa heavy chain following its isolation-and the parent approximately 150 kDa dichain neurotoxin do not break down under comparable conditions. This cleavage was examined in the neurotoxin serotypes A and E. The cleavage does not appear to be due to a protease. Partial amino acid sequences established that: i) the approximately 28-kDa and approximately 18-kDa fragments comprise the N- and C-terminal regions of the light chain, respectively; ii) the light chain of the neurotoxin serotypes A and E break down at precise peptide bonds; iii) the peptide bonds cleaved in serotypes A and E are five residues apart; and iv) the portions of the approximately 18 kDa fragments of serotype A and E neurotoxin sequenced so far are highly homologous to the corresponding region of tetanus neurotoxin produced by Clostridium tetani. The partial N-terminal sequence of the approximately 28 kDa fragment matches with the N-terminal sequence of the intact L chain. The 47 residues of the approximately 18-kDa fragment of type A sequenced from its N-terminal are: -Y.E.M.S.G.L.E.V.S.F.E.E.L.R.T.F.G.G.H.D.A.K.F.I.D.S.L.Q.E.N.E.F.R.L.Y.Y .Y. N.K.F.K. D.I.A.S.T.L.-. These align with those of tetanus neurotoxin beginning at its residue #259 (Tyr); the 18 underlined residues of the above 47 residues (i.e. 38%) are identical in positions between the two proteins. The 41 residues sequenced from the approximately 18 kDa fragment of type E botulinum neurotoxin are: -K.G.I.N.I.E.E.F.L. T.F.G.N.N.D.L.N.I.I.T.V.A.Q.Y.N.D.I.Y.T.N.L.L.N.D.Y.R. K.I.A.X.K. L.-.(ABSTRACT TRUNCATED AT 250 WORDS)