Atomic force microscopy study of DNA flexibility on short length scales: smooth bending versus kinking

The apparently anomalous flexibility of DNA on short length scales has attracted a lot of attention in recent years. We use atomic force microscopy (AFM) in solution to directly study the DNA bending statistics for small lengths down to one helical turn. The accuracy of experimental estimates could be improved due to a large data volume and a refined algorithm for image processing and measuring bend angles. It is found that, at length scales beyond two helical turns (7 nm), DNA is well described by the harmonic worm-like chain (WLC) model with the bending persistence length of 56 nm. Below this threshold, the AFM data are also described by the WLC model assuming that the accuracy of measured bend angles is limited by the physical width of the double helix. We conclude that the double helical DNA behaves as a uniform elastic rod even at very short length scales. Strong bends due to kinks, melting bubbles and other deviations from the WLC model are statistically negligible.     

Cholinergic ligand-induced affinity changes in Torpedo californica acetylcholine receptor

Measurement of small-angle X-ray scattering from a sample of hyaluronic acid of high molecular weight in 0.05 m HNO₃ gave persistence length plots which agreed in form with theory and led to apparent persistence lengths of from 4 to 6 nm. Similar measurements in 0.2 m NaCl gave plots which deviated somewhat in form from theoretical expectation, but which could be interpreted to give a persistence length of 4 nm in this solvent. Data for intrinsic viscosity [η] as a function of molecular weight were in reasonable agreement with the Yamakawa-Fujii treatment of [η] for the worm-like chain model for a persistence length of about 4 nm in both 0.5 m NaCl and 0.1 m HCl, perhaps slightly higher in the latter. The values of persistence length estimated from [η] depend somewhat on the choice of chain parameters and the method of correction of experimental data to unperturbed solvent conditions. Experimental data for the sedimentation coefficient, while less definitive, were consistent within experimental uncertainty with the same parameters of the worm-like chain model. These calculated results are in substantial agreement with the values derived from small-angle X-ray scattering. A fraction of hyaluronic acid of low molecular weight in 0.05 m HNO₃ gave an estimated molecular weight of 2.7 × 10⁴ and a radius of gyration of 8 nm, in reasonable agreement with expected values based on the worm-like chain model for a persistence length of about 4 nm.     

Effect of chain length and unsaturation on elasticity of lipid bilayers

Micropipette pressurization of giant bilayer vesicles was used to measure both elastic bending k(c) and area stretch K(A) moduli of fluid-phase phosphatidylcholine (PC) membranes. Twelve diacyl PCs were chosen: eight with two 18 carbon chains and degrees of unsaturation from one double bond (C18:1/0, C18:0/1) to six double bonds per lipid (diC18:3), two with short saturated carbon chains (diC13:0, diC14:0), and two with long unsaturated carbon chains (diC20:4, diC22:1). Bending moduli were derived from measurements of apparent expansion in vesicle surface area under very low tensions (0.001-0.5 mN/m), which is dominated by smoothing of thermal bending undulations. Area stretch moduli were obtained from measurements of vesicle surface expansion under high tensions (>0.5 mN/m), which involve an increase in area per molecule and a small-but important-contribution from smoothing of residual thermal undulations. The direct stretch moduli varied little (< +/-10%) with either chain unsaturation or length about a mean of 243 mN/m. On the other hand, the bending moduli of saturated/monounsaturated chain PCs increased progressively with chain length from 0.56 x 10(-19) J for diC13:0 to 1.2 x 10(-19) J for diC22:1. However, quite unexpectedly for longer chains, the bending moduli dropped precipitously to approximately 0.4 x 10(-19) J when two or more cis double bonds were present in a chain (C18:0/2, diC18:2, diC18:3, diC20:4). Given nearly constant area stretch moduli, the variations in bending rigidity with chain length and polyunsaturation implied significant variations in thickness. To test this hypothesis, peak-to-peak headgroup thicknesses h(pp) of bilayers were obtained from x-ray diffraction of multibilayer arrays at controlled relative humidities. For saturated/monounsaturated chain bilayers, the distances h(pp) increased smoothly from diC13:0 to diC22:1 as expected. Moreover, the distances and elastic properties correlated well with a polymer brush model of the bilayer that specifies that the elastic ratio (k(c)/K(A))(1/2) = (h(pp) - h(o))/24, where h(o) approximately 1 nm accounts for separation of the headgroup peaks from the deformable hydrocarbon region. However, the elastic ratios and thicknesses for diC18:2, diC18:3, and diC20:4 fell into a distinct group below the correlation, which showed that poly-cis unsaturated chain bilayers are thinner and more flexible than saturated/monounsaturated chain bilayers.     

Two-state model of acto-myosin attachment-detachment predicts C-process of sinusoidal analysis

The force response of activated striated muscle to length perturbations includes the so-called C-process, which has been considered the frequency domain representation of the fast single-exponential force decay after a length step (phases 1 and 2). The underlying molecular mechanisms of this phenomenon, however, are still the subject of various hypotheses. In this study, we derived analytical expressions and created a corresponding computer model to describe the consequences of independent acto-myosin cross-bridges characterized solely by 1), intermittent periods of attachment (t(att)) and detachment (t(det)), whose values are stochastically governed by independent probability density functions; and 2), a finite Hookian stiffness (k(stiff)) effective only during periods of attachment. The computer-simulated force response of 20,000 (N) cross-bridges making up a half-sarcomere (F(hs)(t)) to sinusoidal length perturbations (L(hs)(t)) was predicted by the analytical expression in the frequency domain, (F(hs)(omega)/L(hs)(omega))=(t(att)/t(cycle))Nk(stiff)(iomega/(t(att)(-1)+iomega)), where t(att) = mean value of t(att), t(cycle) = mean value of t(att) + t(det), k(stiff) = mean stiffness, and omega = 2pi x frequency of perturbation. The simulated force response due to a length step (L(hs)) was furthermore predicted by the analytical expression in the time domain, F(hs)(t)=(t(att)/t(cycle))Nk(stiff)L(hs)e(-t/t(att)). The forms of these analytically derived expressions are consistent with expressions historically used to describe these specific characteristics of a force response and suggest that the cycling of acto-myosin cross-bridges and their associated stiffnesses are responsible for the C-process and for phases 1 and 2. The rate constant 2pic, i.e., the frequency parameter of the historically defined C-process, is shown here to be equal to t(att)(-1). Experimental results from activated cardiac muscle examined at different temperatures and containing predominately alpha- or beta-myosin heavy chain isoforms were found to be consistent with the above interpretation.     

Dynamic light scattering from weakly bending rods: estimation of the dynamic bending rigidity of the M13 virus

A theory is presented for the dynamic structure factor [S(K,t]) of weakly bending rods. This treatment is based on a discrete bead model for the Brownian dynamics in which all bead motions associated with bending are constrained to occur in a plane perpendicular to the end-to-end vector, thus prohibiting extension or contraction along that axis. Preset hydrodynamic interactions are incorporated in a numerically exact manner. The predicted normalized dynamic structure factor S(K,t)/S(K,0) should be valid for short times t such that the rms rotation of the end-to-end vector around any transverse axis is much less than 1.0 radian. With geometrical parameters appropriate for the M13 virus, the intensity autocorrelation function G(2) (K,t) = 1 + magnitude of S(K,t)/S(K,0)2 is calculated over a range of times and scattering vectors K for selected values of the persistence length P. The calculated G(2) (K,t) are fitted to a single exponential with unit baseline over the same range of times as the experimental photon correlation functions, and the apparent diffusion coefficients Dapp (K) are obtained from the best-fit relaxation times. For the sake of completeness, an exact expression is derived for the apparent diffusion coefficient obtained from the initial slope of the dynamic structure factor. However, this does not reduce to the known correct result in the rigid rod limit. To obtain the correct result, the limit of infinite bending rigidity must be taken before the limit of zero time. For this and other reasons, the initial slope value of Dapp (K) is not useful for weakly bending rods. Photon correlation functions are measured for the M13 virus, which is virtually identical to the often-studied fd virus. The experimental photon correlation functions are fitted over 8 relaxation times to a single-exponential plus baseline, and the Dapp (K) are calculated from the best-fit relaxation times. Theoretical curves of Dapp (K) vs K2 for selected values of P are compared with the experimental data, which are satisfactorily reproduced when P = 22000 +/- 2000 A. This dynamic value is close to the static value, P = 20000 +/- 2000 A, reported for the very similar fd virus. The most recent theories of Maeda and Fujime and their dynamic light scattering studies of fd virus are compared with the present results in some detail. Their optimum value of P is in surprisingly good agreement with the present value.     

Structure and Dynamics of Double Helices in Solution: Modes of DNA Bending

Abstract

The long range structure of DNA restriction fragments has been analysed by electro-optical measurements. The overall rotation time constants observed in a low salt buffer with monovalent ions is shown to decrease upon addition of Mg²⁺ or spermine. Since the circular dichroism and also the limiting value of the linear dichroism remain almost constant under these conditions, the effect is attributed to a change of the long range structure. According to a weakly bending rod model, the persistence length decreases from about 600 Å in the absence of Mg²⁺ or spermine to about 350 Å in the presence of these ions. The persistence length measured in the presence of Mg²⁺ is almost independent of temperature in the range of 10 to 40 °C. The nature of DNA bending is analysed by measurements of bending amplitudes and time constants from dichroism decay curves. The observed absence of changes in the bending amplitudes upon addition of Mg²⁺ or spermine, even though addition induces changes of the persistence length by a factor of 2, is hardly consistent with simple thermal bending. The combined results, including the remarkably small temperature dependence of persistence length and bending amplitude, can be explained by the existence of two bending effects: inherent curvature of DNA dominates at low temperature, whereas thermal bending prevails at high temperature. Analysis of bending amplitudes from dichroism decay curves according to an arc model provides an approximate measure for the degree of bending in restriction fragments. The model is consistent with the observed chain length dependence of bending amplitudes and provides an approximate curvature corresponding to a radius of ab out400Å. Thus the curvature observed in restriction fragments is similar to that observed for high molecular DNA condensed into toroids by addition of ions like spermine.

Particularly strong bending of DNA is induced by [CO(NH₃)₆]³⁺, indicated by an apparent persistence length of 200 Å and an increased bending amplitude together with a reduced limit value of the linear dichroism. This effect is attributed to the high charge density of this ion and potential site binding.     

Finite Element Analysis of a New Pedicle Screw-Plate System for Minimally Invasive Transforaminal Lumbar Interbody Fusion

Purpose

Minimally invasive transforaminal lumbar interbody fusion (MI-TLIF) is increasingly popular for the surgical treatment of degenerative lumbar disc diseases. The constructs intended for segmental stability are varied in MI-TLIF. We adopted finite element (FE) analysis to compare the stability after different construct fixations using interbody cage with posterior pedicle screw-rod or pedicle screw-plate instrumentation system.

Methods

A L3–S1 FE model was modified to simulate decompression and fusion at L4–L5 segment. Fixation modes included unilateral plate (UP), unilateral rod (UR), bilateral plate (BP), bilateral rod (BR) and UP+UR fixation. The inferior surface of the S1 vertebra remained immobilized throughout the load simulation, and a bending moment of 7.5 Nm with 400N pre-load was applied on the L3 vertebra to recreate flexion, extension, lateral bending, and axial rotation. Range of motion (ROM) and Von Mises stress were evaluated for intact and instrumentation models in all loading planes.

Results

All reconstructive conditions displayed decreased motion at L4–L5. The pedicle screw-plate system offered equal ROM to pedicle screw-rod system in unilateral or bilateral fixation modes respectively. Pedicle screw stresses for plate system were 2.2 times greater than those for rod system in left lateral bending under unilateral fixation. Stresses for plate were 3.1 times greater than those for rod in right axial rotation under bilateral fixation. Stresses on intervertebral graft for plate system were similar to rod system in unilateral and bilateral fixation modes respectively. Increased ROM and posterior instrumentation stresses were observed in all loading modes with unilateral fixation compared with bilateral fixation in both systems.

Conclusions

Transforaminal lumbar interbody fusion augmentation with pedicle screw-plate system fixation increases fusion construct stability equally to the pedicle screw-rod system. Increased posterior instrumentation stresses are observed in all loading modes with plate fixation, and bilateral fixation could reduce stress concentration.     

The Conformation of Single Stranded Oligonucleotides and of Oligonucleotide-Oligopeptide Complexes from their Rotation Relaxation in the Nanosecond Time Range

Abstract

The conformation of single stranded oligonucleotides is analysed by measurements of their rotation time constants. The oligomers are aligned to some degree by short electric field pulses; after pulse termination the transition to a random orientation is followed by measurements of the linear dichroism. An efficient deconvolution procedure is developed for evaluation of the experimental data obtained in the ns-time range. The increase of rotation time constants observed for chain lengths in the range from 14 to 22 residues are interpreted according to a weakly bending rod model providing a persistence length and a Stokes' diameter. The Stokes' diameters obtained for ribo- and deoxyriboadenylates are about 13Å, in approximate agreement with the expectation for a single stranded helix. The persistence length L = 53Å corresponding to ～16 nucleotide residues found for riboadenylates at 2°C appears to reflect relatively strong stacking interactions at this temperature. However, a comparison with the average length of stacked residues evaluated from available thermodynamic parameters of base stacking indicate that unstacked residues are not completely flexible. Apparently the ribose-phosphate chain provides an essential contribution to the stiffness of oligomers and polymers, even when the bases are unstacked. Addition of 100μM Mg²⁺ leads to an increase of the persistence length to 88Å. Corresponding measurements with deoxyriboadenylates show a slightly lower value of the persistence length than that found for riboadenylates. Addition of LysTrpLys and LysTyrLys to A(pA)₁₉ leads to an increase of the rotation time constant, which corresponds approximately to a length increment by one residue per bound peptide. Since controls performed with LysLeuLys do not show any similar effect, the increase of the time constants induced by LysTrpLys and LysTyrLys is attributed to intercalation of the aromatic amino acids.     

Novel Pedicle Screw and Plate System Provides Superior Stability in Unilateral Fixation for Minimally Invasive Transforaminal Lumbar Interbody Fusion: An In Vitro Biomechanical Study

Purpose

This study aims to compare the biomechanical properties of the novel pedicle screw and plate system with the traditional rod system in asymmetrical posterior stabilization for minimally invasive transforaminal lumbar interbody fusion (MI-TLIF). We compared the immediate stabilizing effects of fusion segment and the strain distribution on the vertebral body.

Methods

Seven fresh calf lumbar spines (L3-L6) were tested. Flexion/extension, lateral bending, and axial rotation were induced by pure moments of ± 5.0 Nm and the range of motion (ROM) was recorded. Strain gauges were instrumented at L4 and L5 vertebral body to record the strain distribution under flexion and lateral bending (LB). After intact kinematic analysis, a right sided TLIF was performed at L4-L5. Then each specimen was tested for the following constructs: unilateral pedicle screw and rod (UR); unilateral pedicle screw and plate (UP); UR and transfacet pedicle screw (TFS); UP and TFS; UP and UR.

Results

All instrumented constructs significantly reduced ROM in all motion compared with the intact specimen, except the UR construct in axial rotation. Unilateral fixation (UR or UP) reduced ROM less compared with the bilateral fixation (UP/UR+TFS, UP+UR). The plate system resulted in more reduction in ROM compared with the rod system, especially in axial rotation. UP construct provided more stability in axial rotation compared with UR construct. The strain distribution on the left and right side of L4 vertebral body was significantly different from UR and UR+TFS construct under flexion motion. The strain distribution on L4 vertebral body was significantly influenced by different fixation constructs.

Conclusions

The novel plate could provide sufficient segmental stability in axial rotation. The UR construct exhibits weak stability and asymmetrical strain distribution in fusion segment, while the UP construct is a good alternative choice for unilateral posterior fixation of MI-TLIF.     

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.     

Two decades of biomonitoring polar bear health in Greenland: a review

Background

Different animal models are used as fracture models in orthopaedic research prior to implant use in humans, although biomechanical forces can differ to a great extend between species due to variable anatomic conditions, particularly with regard to the gait. The rabbit is an often used fracture model, but biomechanical data are very rare. The objective of the present study was to measure axial forces, bending moments, and bending axis directly in the rabbit tibia in vivo. The following hypothesis was tested: Axial forces and bending moments in the mid-diaphysis of rabbit tibia differ from other experimental animals or indirectly calculated data.

Methods

A minifixateur system with 4 force sensors was developed and attached to rabbit tibia (n = 4), which were subsequently ostectomised. Axial forces, bending moments and bending angles were calculated telemetrically during weight bearing in motion between 6 and 42 days post operation.

Results

Highest single values were 201% body weight [% bw] for axial forces and 409% bw cm for bending moments. Whereas there was a continous decrease in axial forces over time after day 10 (P = 0.03 on day 15), a decrease in bending moments was inconsistent (P = 0.03 on day 27). High values for bending moments were frequently, but not consistently, associated with high values for axial forces.

Conclusion

Axial forces in rabbit tibia exceeded axial forces in sheep, and differed from indirectly calculated data. The rabbit is an appropriate fracture model because axial loads and bending moments in rabbit tibia were more closely to human conditions than in sheep tibia as an animal model.     

Winding single-molecule double-stranded DNA on a nanometer-sized reel

A molecular system of a nanometer-sized reel was developed from F₁–ATPase, a rotary motor protein. By combination with magnetic tweezers and optical tweezers, single-molecule double-stranded DNA (dsDNA) was wound around the molecular reel. The bending stiffness of dsDNA was determined from the winding tension (0.9–6.0 pN) and the diameter of the wound loop (21.4–8.5 nm). Our results were in good agreement with the conventional worm-like chain model and a persistence length of 54 ± 9 nm was estimated. This molecular reel system offers a new platform for single-molecule study of micromechanics of sharply bent DNA molecules and is expected to be applicable to the elucidation of the molecular mechanism of DNA-associating proteins on sharply bent DNA strands.     

DNA force-extension curve under uniaxial stretching

Single-molecule experiments indicate that a double-stranded DNA (ds‐DNA) increases in length if put under tension greater than 10 pN; beyond this point, its conformation can no longer be described using an inextensible worm-like chain model. For this purpose, a general sequence-dependent elastic model for tensions greater than 10 pN and for both single-stranded (ss) and ds‐DNA is proposed, and the effective elastic bending and torsional rigidities are determined from experiments to characterise their deformation. The key to this progress is that the bending and torsional deformations of the DNA backbones, the base-stacking interactions and the hydrogen bond force between the complementary base pairs are quantitatively considered in this model. Moreover, this simple elastic model can be used to globally fit to the abrupt B–S experimental transition data over a wide range of DNA molecule extensions. Based on this robust model, further study may be warranted on the mechanical response of ss- and ds‐DNA molecules.     

Flexibility of duplex DNA on the submicrosecond timescale

Using a site-specific, Electron Paramagnetic Resonance (EPR)-active spin probe that is more rigidly locked to the DNA than any previously reported, the internal dynamics of duplex DNAs in solution were studied. EPR spectra of linear duplex DNAs containing 14-100 base pairs were acquired and simulated by the stochastic Liouville equation for anisotropic rotational diffusion using the diffusion tensor for a right circular cylinder. Internal motions have previously been assumed to be on a rapid enough time scale that they caused an averaging of the spin interactions. This assumption, however, was found to be inconsistent with the experimental data. The weakly bending rod model is modified to take into account the finite relaxation times of the internal modes and applied to analyze the EPR spectra. With this modification, the dependence of the oscillation amplitude of the probe on position along the DNA was in good agreement with the predictions of the weakly bending rod theory. From the length and position dependence of the internal flexibility of the DNA, a submicrosecond dynamic bending persistence length of around 1500 to 1700 A was found. Schellman and Harvey (Biophys. Chem. 55:95-114, 1995) have estimated that, out of the total persistence length of duplex DNA, believed to be about 500 A, approximately 1500 A is accounted for by static bends and 750 A by fluctuating bends. A measured dynamic persistence length of around 1500 A leads to the suggestion that there are additional conformations of the DNA that relax on a longer time scale than that accessible by linear CW-EPR. These measurements are the first direct determination of the dynamic flexibility of duplex DNA in 0.1 M salt.     

Statistical mechanics of DNA topoisomers. The helical worm-like chain

Recent experimental data of Shore & Baldwin (1983b) and of Horowitz & Wang (1984) for the apparent twisting coefficient K, which determines the breadth of the Gaussian distribution of DNA topoisomers with different linking numbers N, show that the product of K and nbp (the number of base-pairs) is nearly a constant for nbp approximately greater than 2000, but that it increases sharply with decreasing nbp for nbp approximately less than 2000. The main purpose of the present paper is to explain theoretically such behavior of K as a function of nbp. Thus the statistical mechanics of DNA topoisomers in general is developed on the basis of a twisted worm-like chain, i.e. a special case of the helical worm-like chain. The previous treatments of the N-dependent ring-closure probability, i.e. the distribution of N, which are valid only for small chain length L, are extended to the range of larger L. The variance of N is then shown to be exactly the sum of those of the writhe Wr and the twist Tw. For small values of L, the distribution of Wr is not Gaussian, and its variance or moment (Wr2) increases rather steeply with increasing L. With these and known Monte Carlo results for freely jointed chains, an empirical interpolation formula for (Wr2) is also constructed to be valid for all values of L. It predicts that (Wr2)/L increases monotonically, with increasing L to its coil-limiting value. On the other hand, the distribution of N is actually Gaussian in the practical range of N for all values of L. The conditional distribution of Wr with N fixed is also evaluated. Finally, K is expressed in terms of the torsional constant C, the stiffness parameter lambda-1 (which is equal to the Kuhn segment length and twice the persistence length for this special case), and (Wr2). The derived equation predicts that nbpK decreases monotonically to its coil-limiting value with increasing nbp. This decrease arises from the fluctuation in Wr and its neglect leads to an underestimate of C by 7 to 10%, even for short DNA with nbp approximately equal to 200. From an analysis of the experimental data of the two groups, the estimates of C = 3.1 to 3.2 X 10(-19) erg cm and lambda-1 = 1000 to 1200 A are obtained.     

Orientation relaxation of DNA restriction fragments and the internal mobility of the double helix

The orientation relaxation of 15 DNA restriction fragments (43-4361 base-pairs) is characterized by measurements of linear dichroism using high electric field pulses. The off-field relaxation of fragments of 84 base-pairs or less can be described by single exponentials, which are related to the transverse rotational diffusion of the helix. Fragments of 95 base-pairs or greater exhibit an additional fast component with time constants around 100 ns for fragments of approx. 100 base-pairs, increasing with chain length to about 700 ns for a fragment with 258 base-pairs. The amplitude of this process increases from virtually zero at low fields (approximately equal to 10 kV) to a substantial limit contribution at high fields. According to these results, we suggest that electric fields induce stretching of the DNA fragments from a weakly bent to a more straight form and that the fast component reflects the internal mobility of the DNA chain. The slow off-field components of the orientation are discussed in terms of different models. The data up to helix lengths of about 400 base-pairs can be described by the 'weakly bending rod' model from Hearst using 3.4 A rise per base-pair and 13 A axial radius of the helix. Both the weakly bending rod according to Hearst and the 'wormlike chain' according to Hagerman and Zimm provide a persistence length of 500 A. The on-field relaxation is slower than the corresponding off-field process at low field strengths, but the on-field process is accelerated substantially at high electric fields. These observations are compared with model calculations of Schwarz.     

Electro-optical studies on synthetic polyelectrolytes: IV. Electric polarizability and conformation of poly-N-methyl-2-vinylpyridinium bromide in aqueous solution

Measurements of the relaxation time on aqueous solutions of the title polyelectrolyte as a function of the concentration and of the molecular weight show that its conformation at very high dilution can be better accounted for by a weakly bending rod or worndike chain model, with persistence length ranging from 200 to 400 Å. The analysis of the field strength dependence of the electric birefringence yields electric polarizability values which increase sharply with the dilution and are not significantly dependent upon the molecular weight. This has been tentatively interpreted on the basis of the theories derived by Oosawa and by Mendel and Van der Touw. The partially flexible model proposed by the latter authors allow to identify the electric polarizability calculated from electro-optical data to the specific dielectric increment measured in the high frequency range; both parameters appear to be molecular weight independent. The electric polarizability obtained from the Kerr effect would be originated in the induced dipoles caused by the delocalization of the bound counterions along rigid subunits whose length seems however to differ from the persistence length.     

Structure and dynamics of double helices in solution: modes of DNA bending

The long range structure of DNA restriction fragments has been analysed by electro-optical measurements. The overall rotation time constants observed in a low salt buffer with monovalent ions is shown to decrease upon addition of Mg2+ or spermine. Since the circular dichroism and also the limiting value of the linear dichroism remain almost constant under these conditions, the effect is attributed to a change of the long range structure. According to a weakly bending rod model, the persistence length decreases from about 600 A in the absence of Mg2+ or spermine to about 350 A in the presence of these ions. The persistence length measured in the presence of Mg2+ is almost independent of temperature in the range of 10 to 40 degrees C. The nature of DNA bending is analysed by measurements of bending amplitudes and time constants from dichroism decay curves. The observed absence of changes in the bending amplitudes upon addition of Mg2+ or spermine, even though addition induces changes of the persistence length by a factor of 2, is hardly consistent with simple thermal bending. The combined results, including the remarkably small temperature dependence of persistence length and bending amplitude, can be explained by the existence of two bending effects: inherent curvature of DNA dominates at low temperature, whereas thermal bending prevails at high temperature. Analysis of bending amplitudes from dichroism decay curves according to an arc model provides an approximate measure for the degree of bending in restriction fragments. The model is consistent with the observed chain length dependence of bending amplitudes and provides an approximate curvature corresponding to a radius of about 400 A. Thus the curvature observed in restriction fragments is similar to that observed for high molecular DNA condensed into toroids by addition of ions like spermine. Particularly strong bending of DNA is induced by [Co(NH3)6]3+, indicated by an apparent persistence length of 200 A and an increased bending amplitude together with a reduced limit value of the linear dichroism. This effect is attributed to the high charge density of this ion and potential site binding.     

Structure of heavy and light chain subunits of type A botulinum neurotoxin analyzed by circular dichroism and fluorescence measurements

Summary The secondary and tertiary structural features of botulinum neurotoxin (NT) serotype A, a dichain protein (M_r 145 000), and its two subunits, the heavy (H) and light (L) chains (M_r 97 000 and 53 000, respectively) were examined using circular dichroism and fluorescence spectorscopy. Nearly 70% of the amino acid residues in each of the three polypeptide preparations were found in ordered structure (sum of helix, sheet and turns). Also, the helix, sheet, turns and random coil contents of the dichain NT were nearly equal to the weighted mean of each of these secondary structure parameters of the L and H chains; e.g., sum of helix of L chain (22%) and H chain (18.7%), as weighted mean, 19.8% was similar to that of NT (20%). These agreements suggested that the secondary structures of the subunits of the dichain NT do not significantly change when they are separated as isolated L and H chains. Fluorescence emission maximum of L chain, 4 nm less (blue shift) than that of H chain, suggested relatively more hydrophobic environment of fluorescent tryptophan residue(s) of L chain. Tryptophan fluorescence quantum yields of L chain, H chain and the NT, 0.072, 0.174 and 0.197, respectively, suggested that a) an alteration in the micro-environment of the tryptophan residues was possibly caused by interactions of L and H chain subunits of the NT and b) quantum yields for L and H chains were altered when they are together as subunits of the NT. Possible implications of structural features of the L and H chains, their interactions and the molecular mechanism of action of botulinum NT are assessed.