Dynamics of the B–A transition of DNA double helices
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《核酸研究医学期刊》
Max Planck Institut für Biophysikalische Chemie, 37077 G?ttingen, Germany
*To whom correspondence should be addressed. Tel: +49 551 201 1438; Fax: +49 551 201 1168; Email: dpoersc@gwdg.de
ABSTRACT
Although the transition from the B-DNA double helix to the A-form is essential for biological function, as shown by the existence of the A-form in many protein–DNA complexes, the dynamics of this transition has not been resolved yet. According to molecular dynamics simulations the transition is expected in the time range of a few nanoseconds. The B–A transition induced by mixing of DNA samples with ethanol in stopped flow experiments is complete within the deadtime, showing that the reaction is faster than 0.2 ms. The reaction was resolved by an electric field jump technique with induction of the transition by a dipole stretching force driving the A- to the B-form. Poly was established as a favourable model system, because of a particularly high cooperativity of the transition and because of a spectral signature allowing separation of potential side reactions. The time constants observed in the case of poly with 1600 bp are in the range around 10 μs. An additional process with time constants of 100 μs is probably due to nucleation. The same time constants (within experimental accuracy ±10%) were observed for a poly sample with 70 bp. Under low salt conditions commonly used for studies of the B–A transition, the time constants are almost independent of the ionic strength. The experimental data show that a significant activation barrier exists in the B–A transition and that the helical states are clearly separated from each other, in contrast to predictions by molecular dynamics simulations.
INTRODUCTION
The transition between the standard B-form of DNA double helices and the A-form was observed during the first X-ray studies (1–4). Fifty years on and the dynamics of this transition has still not been characterized, despite the fact that the B–A transition is known to be essential for processing of genetic information (5–9), e.g. during transcription (9). Molecular dynamics simulations have predicted the transition to proceed within a few nanoseconds (10–14) and the absence of any significant activation barrier has been suggested from a comparison of crystal structures (15–16). This seems to be in contrast with the clear cooperativity of the B–A transition (17). The B–A transition was first detected by Franklin and Gosling (3), who characterized the change of the helix structure as ‘a substantial re-arrangement of the molecule’ (Fig. 1). Does this imply a substantial activation barrier?
Figure 1. Structures of the B- and A-form of the DNA double helix (left and right, respectively). Views of 12 bp segments prepared by VMD (36) from bdl001 (37) and adl046 (38) .
The B–A equilibrium can be analysed conveniently owing to large changes of the circular dichroism and of the UV spectrum (18). The reduction of the relative humidity, inducing the transition from B to A under X-ray conditions, can be generated in solution simply by addition of ethanol. Thus, it may be expected that analysis of the kinetics by one of the standard techniques is a routine task. However, the experimental analysis is not trivial, as shown by several independent attempts without success. Here we present the first experimental data on the dynamics of the B–A reaction.
MATERIALS AND METHODS
DNA from salmon sperm (Sigma) was sonicated to an average chain length of 400 bp under nitrogen. The average chain length of poly (Sigma) was 1600 bp. Part of the poly sample was sonicated under nitrogen and then separated into different fractions by sephacryl S500 column chromatography. Finally the samples were separated further by preparative polyacrylamide gel electrophoresis. Average chain lengths were determined by gel electrophoresis and by analytical ultracentrifugation (sedimentation coefficients). All polynucleotide samples were dialysed extensively, first against high salt buffers (0.2 M NaCl, 1 mM Na-cacodylate, 1 mM EDTA) to remove traces of multivalent ions, and finally against a standard low salt buffer containing 250 μM NaCl, 250 μM Na-cacodylate and 50 μM EDTA.
The state of the samples and of their B–A transition was controlled by CD spectroscopy using a JASCO 720. Absorbance titrations were measured with a Cary 4 spectrophotometer. We used a stopped-flow instrument constructed in this institute (19). Electric field jumps were generated by coaxial cable discharge (20,21). The pulses were applied to a cell machined from macrolon with Pt-electrodes at a distance of 5.5 mm. The quartz windows were inserted in a strain-free mode as previously described (22). The optical path-length was 20 mm. The spectrophotometric detection system was composed of a Hamamatsu L2423 mercury/xenon arc lamp, a Schoeffel GM250 grating monochromator, a Glan air polarizer and a homemade photomultiplier detector. The photo-electric signal was stored on a Tektronix DSA 601A digitizing signal analyser. The experimental data were analysed by a set of programs developed for quantitative characterization of chemical and physical relaxation data (23,24). Convolution of rise or decay curves with the detector response curve (response time constant 0.93 μs used in all measurements) was considered by quantitative deconvolution procedures.
Magic angle measurements
Electric field pulses are known to induce orientation effects in solutions of polynucleotides (25). These orientation effects are usually reflected by large changes of light absorption and are characterized quantitatively in terms of the linear dichroism. In the present investigation we wanted to study field-induced reaction effects (26), which can be separated from orientation effects by using polarized light oriented at the magic angle (55°) with respect to the field vector. The experimental conditions required for reliable magic angle measurements have been discussed in detail elsewhere (22,27).
When reaction effects are small compared to orientation effects, the magic angle conditions should be controlled carefully. Such control involves measurements of the field induced amplitudes A0, A55 and A90 with polarized light oriented at angles = 0°, 55° and 90° with respect to the field vector. The ratio R = (A0 – A55)/( A90 – A55) should be –2. In the present investigation we have rejected data with a deviation larger than 5%.
Data correction
When electric field pulses induce reaction effects, these are reflected in the transients measured at all orientations of the polarized light. Thus, transients measured at = 0° must be corrected by subtraction of the corresponding transients measured at = 55° to get unperturbed dichroism transients. For subtraction the transients were transformed to the same level of light intensity.
Dichroism decay time constants measured at different ethanol content are affected by different viscosities. For quantitative comparison, time constants were corrected to the state of water at 20°C by multiplication with the factor w·Te/(e·293.1), where e and w are the viscosities of the solvent under the conditions of the experiments and of water at 20°C, respectively; Te is the absolute temperature of the solvent used during experiments.
RESULTS
Stopped flow measurements
Because the B–A reaction can be induced by mixing of DNA solutions with ethanol, the technique of choice seems to be stopped flow. However, the analysis turned out to be difficult because of several technical problems. One of them was caused by the difference in the density of the solutions, leading to partial mixing of the solutions by convection. Another problem seems to be due to a difference in the compressibility of the solutions. When these problems were as much under control as possible, optical signals expected for the B–A reaction were not observed. The absence of any amplitude that could be assigned to the B–A reaction shows that the reaction has already gone to completion during the mixing time of 0.2 ms. There are still options which enable analysis of the B–A reaction by flow techniques with increased time resolution. However, these options were not followed at this point, because other techniques with higher time resolution were tested first.
Search for an optimal approach
The reduction of water activity required for induction of the B–A transition has been materialized in solution by addition of ethanol in virtually all previous investigations. Because addition of ethanol at high salt induces aggregation and precipitation, almost all experimental data on the B–A transition published in the literature were obtained at low salt concentrations. Thus, the temperature jump technique based on Joule heating, which requires high salt conditions, cannot be applied at a sufficiently high time resolution. Furthermore, it is known that the temperature dependence of the B–A transition is very limited. According to Ivanov et al. (18) the ‘B–A equilibrium is not influenced by temperature’. Thus, laser temperature jump instruments are not expected to be applicable either. However, the electric field jump technique (20) seems to be promising, because it is optimal for solutions of low salt concentrations and provides a high time resolution. However, first attempts with the electric field jump technique on salmon sperm DNA samples were not successful. Thus, careful optimization of reaction conditions is necessary.
One of the questions is the optimal range of chain lengths. The B–A transition is cooperative with an estimated cooperative length in the range from 10 to 30 bp (17). Optimal amplitudes are expected in the range of chain lengths above the cooperative length. For convenience and to minimize DNA sample costs, readily available polymers are the first choice. The interpretation of data obtained for oligomer samples may be simpler, but the assignment of any relaxation effect to the B–A transition of oligomer samples is expected to be difficult, because other effects like fraying of helix ends contribute with considerable amplitudes.
From the results of other researchers (28,29) it is known that the B–A transition is dependent on the GC content. Thus, the width of the transition for homopolymers is expected to be lower than that for DNA with mixed sequence. This expectation was verified by CD titrations: the B–A transition for poly was narrower than that of natural DNA by a factor of 5. Furthermore, the B–A transition of poly is associated with a favourable UV difference spectrum having isosbestic points (Fig. 2), which can be used for unequivocal assignments of relaxation amplitudes. Polymers with GC base pairs are expected to be less convenient than those with AT base pairs because of the stronger tendency of GC polymers for aggregation.
Figure 2. B–A transition of poly indicated by absorption difference spectra at various ethanol percentages. The absorption spectrum measured at 51.68% ethanol was subtracted from the absorption spectra measured at the given ethanol percentages. in M–1cm–1; % in v/v units; starting concentrations: 40 μM poly, 125 μM NaCl, 125 μM cacodylate pH 7, 25 μM EDTA.
As mentioned above, all transition curves given in the literature have been induced by addition of ethanol (or trifluoro-ethanol). Currently we do not see a reasonable alternative to these experimental conditions, which imply reduction of the ionic strength to very low values, because otherwise aggregation and precipitation cannot be avoided.
Electric field jump experiments
Electric field pulses are known to induce dissociation of ion complexes (26). The amplitudes induced by electric fields increase with the number of charges associated with the reactants. Thus, the first strategy for optimal analysis was coupling of the B–A transition with binding of ligands like spermine. Minyat et al. (30) reported that ‘spermine and spermidine induce the B to A transition of DNA’ in water/ethanol solutions. Thus, it may be expected that electric field pulses applied to a DNA solution in water/ethanol/spermine adjusted close to the midpoint of the B–A transition drive the B–A equilibrium towards the B-form by field-induced dissociation of spermine ions from the DNA. However, the experiments did not reveal the expected amplitude.
For comparison, the reaction was studied in a buffer containing monovalent salt exclusively. In this case reaction amplitudes appeared under magic angle conditions, as shown by the example in Figure 3. The amplitude measured at 280 nm appears only in the limited range of ethanol content from 67 to 75% (Fig. 4) with a clear maximum close to the centre of the B–A transition, which has been determined independently by measurements of CD spectra under the same experimental conditions. The field-induced reaction amplitude is not found outside the B–A transition range. These data clearly demonstrate that these amplitudes reflect the B–A transition. Further evidence comes from the observation that the sign of the field-induced reaction amplitude is reverted at 248 nm, in agreement with the difference spectra found for the B–A transition (Fig. 2). Alternative reaction effects might be either a field-induced helix–coil transition or a field-induced change of the aggregation state. In both cases the observed spectral signature is not consistent with these types of reactions. Furthermore, the distinct dependence of the amplitudes on the ethanol content is clearly not consistent with a helix–coil transition or a change of the aggregation state. Thus, we may conclude that the electric field induces a shift of the B–A equilibrium.
Figure 3. Field-induced change of the transmission I at 280 nm for poly. (a) Corrected dichroism transient (I0 – I55, left scale); (b) magic angle transient (I55, average of five shots, left scale); and (c) enlarged magic angle transient (right scale). The bar indicates the duration of the field pulse. The least squares fits of the magic angle decay (c) by two exponentials (17.5 and 145 μs with relative amplitudes 61 and 39%, respectively) and of the dichroism decay (a) by four exponentials (2.25 μs, 22.2 μs, 165 μs and 1 ms with relative amplitudes 22, 30, 27 and 21%, respectively) cannot be distinguished from the experimental data; the single exponential fit (49 μs) of the magic angle decay is shown as a dotted line. Conditions: 70.2% ethanol v/v, 8°C, 8.5 μM poly, 75 μM NaCl, 75 μM cacodylate pH 7, 15 μM EDTA; field pulse 3.45 x 106 V/m.
Figure 4. Relative magic angle amplitudes A55/A of poly as a function of the ethanol content in % units (v/v). The line represents a Gaussian fit. Conditions: 8°C, 8.5 μM poly, 75 μM NaCl, 75 μM cacodylate pH 7, 15 μM EDTA; field pulse 3.45 x 106 V/m.
Dipolar stretching
The direction of the magic angle effect measured at the wavelength 280 nm clearly shows that the electric field pulses induce a reaction from the A- to the B-form. How does the electric field drive this reaction? The preference for the B-form in the presence of electric fields indicates that B-helices have a higher effective dipole moment. The dipole moments are known to increase strongly with the length of DNA helices (31). The length increment per base pair for B-DNA (3.4 ?) is much higher than that for A-DNA (2.8 ?). These parameters imply that the field-induced reaction is driven by dipolar stretching. Thus, there is an analogy to the currently popular stretching experiments by atomic force devices (32). The main advantage of stretching by electric field pulses is the much higher time resolution.
The first argument for dipolar stretching as the main driving force for the AB reaction under electric field pulses is simply based on the fact that the contour length of DNA helices in the B-form is higher than that in the A-form. Further evidence for this assignment may be obtained from an analysis of the transients observed under electric field pulses. As shown by the example in Figure 5, these transients reveal a special type of coupling. A satisfactory fit requires two exponentials, where the amplitude of the first exponential is opposite to that of the second one. The combination of amplitudes and time constants is consistent with the special case of a relaxation effect with an induction period—corresponding to a zero initial slope. This type of relaxation response is expected for the present reaction, because the A–B reaction can only be driven when the dipole exceeds a threshold level. This threshold level of the dipole moment cannot be induced immediately after pulse application but requires some time for ion polarization and rotation of the polymers into the direction of the field vector. Ion polarization is not associated with any change of UV absorbance and any effect of polymer rotation on the absorbance is suppressed under magic angle conditions. Thus, these processes are not visible directly. However, the influence of these processes is coupled to the A–B reaction, such that the whole process appears as a convolution product. The initial process of dipole development is without change of absorbance, but is reflected in the transient by coupling to the A–B reaction, which is associated with a relatively large change of the absorbance. The expected convolution product is in complete agreement with the observed transient. The first exponential reflects the rise of the dipole moment and the second one describes the A–B reaction at the given electric field strength.
Figure 5. Magic angle rise curve of poly induced by a field pulse of 3.7 x 106 V/m. The fit by two exponentials cannot be distinguished from the experimental data (1.69 and 4.38 μs with relative amplitudes –85 and +185%, respectively); the single exponential fit (6.17 μs) is represented by a dotted line. Conditions: 70.4% ethanol v/v, 8°C, 8.5 μM poly, 75 μM NaCl, 75 μM cacodylate pH 7, 15 μM EDTA.
The dipolar stretching effect is expected to increase with increasing field strength. As shown in Figure 6 the logarithm of the second time constant can be represented at a reasonable accuracy as a linear function of the electric field strength. This dependence is expected for reactions driven by an increase of a permanent dipole moment, when the orientation of molecules is close to saturation (26). As shown in the literature (31), the induced dipole moment of polynucleotides is saturated at the field strengths used in our present experiments and, thus, the field-induced effects of these polynucleotides are as expected for permanent dipoles.
Figure 6. Magic angle rise time of poly as a function of the field strength. Conditions: 70.32% ethanol v/v, 8°C, 75 μM NaCl, 75 μM cacodylate pH 7, 15 μM EDTA.
Time constants of the BA reaction
The relatively high amplitudes observed at the magic angle indicate that the field pulses can drive the reaction close to completion and, thus, the time constants no longer represent relaxation processes. This is also indicated by the fact that the time constants observed in the presence of the electric field (AB reaction) are different from those in the field free state (BA reaction) in most cases (Fig. 7). The transients reflecting the BA reaction show a fast process ( 10 μs) with most of the amplitude and a slow process ( 100 μs) with a small amplitude. Both the fast and slow processes are associated with amplitudes showing a spectral characteristic consistent with the B–A transition but not consistent with a helix–coil transition or a change of the aggregation state. We assign the slow process to nucleation and the fast process to growth of helical regions. This assignment should be checked by future model calculations.
Figure 7. Magic angle time constants of the B–A transition of poly in the field free state (open squares, d1) and of the A–B transition under electric field pulses (filled circles, r2, see text) as a function of the ethanol content in %. Conditions: v/v, 8°C, 8.5 μM poly, 75 μM NaCl, 75 μM cacodylate pH 7, 15 μM EDTA; field pulse 3.45 x 106 V/m.
As shown in Figure 7, the time constant representing the main amplitude of the BA reaction decreases with increasing ethanol content, consistent with an increasing rate of the BA reaction upon ethanol addition. The opposite direction is observed for the process in the presence of the electric field, representing the AB reaction. This dependence on the ethanol content is expected. The time constants for the opposite processes in Figure 7 are equivalent at 71% ethanol, shifted from the midpoint of the B–A equilibrium towards the domain of the A DNA. This is due to the fact that the field pulses accelerate the AB reaction and induce large perturbations of the equilibrium. If the process could be followed without large perturbations, the time constants would be equivalent at any given point of the transition.
Chain length dependence
As a control for our assignment we studied the B–A transition at a different chain length of poly. It is known that the rotational diffusion time constants are very strongly dependent on the chain length, whereas the time constants for the B–A transition are expected to show much less chain length dependence—at least for chain lengths remaining above the cooperative length. We used a poly sample with an average chain length of 70 bp. The dichroism decay (Fig. 8) of this sample was described by two exponentials (1 = 0.83 μs, 2 = 2.19 μs) at a high accuracy, reflecting a distribution of chain lengths between 60 and 80 bp, in agreement with results obtained by gel electrophoresis. The reaction amplitude observed at the magic angle is smaller than that observed for the polymer with 1600 bp, but can still be characterized at a sufficiently high accuracy (Fig. 8). The BA transients observed after pulse termination require two exponentials for a satisfactory fit. Both time constants are close to those observed for the long polymer. The main difference is in the relative amplitude of the slow process, which is clearly smaller than that observed for the long polymer. Thus, the experiments on the 70 bp sample confirm all the expectations in a convincing manner. In particular, these experiments reconfirm that the magic angle separation of reaction effects from orientation processes is reliable.
Figure 8. Field-induced change of the transmission at 280 nm for 70 bp poly at polarizer orientations = 0° and 55° with respect to the field vector. The bar indicates the duration of the field pulse. Corrected dichroism transient (I0 – I55, orange) with a fit of the decay by two exponentials (black, 1 = 0.83 μs, 2 = 2.19 μs, A1 = 61%, A2 = 39%); the magic angle transient (I55, average of five shots) is shown both at the same scale as the dichroism (magenta, left scale) and magnified (blue, right scale) with a fit of the decay by two exponentials (red, 1 = 8.25 μs, 2 = 67.8 μs, A1 = 87%, A2 = 13%) and by one exponential (green). 70.4% ethanol (v/v), 8°C, 8.5 μM poly, 75 μM NaCl, 75 μM cacodylate pH 7, 15 μM EDTA; field pulse 3.45 x 106 V/m.
The time constants of rotational diffusion obtained from the dichroism decay provide a very sensitive measure of the hydrodynamic dimensions. For comparison of time constants measured at different ethanol content, these constants must be corrected to a standard state, because the viscosity of aqueous solutions is a strong function of the ethanol content. Experimental data measured over the B–A transition range were corrected to 100% water content at 20°C (Fig. 9). The corrected time constants clearly show the expected decrease of the hydrodynamic length upon the B–A transition. Using the dichroism decay time constant of the B-form for calibration of the chain length, based on a rise per base pair of 3.4 ?, we get an effective chain length of 76 bp. Using this chain length and the decay time constant measured for the A-form, we get an effective rise per base pair of 3.0 ? for the A-form. These calculations are based on the wormlike chain model with a persistence length of 1000 ? found for DNA at low salt concentrations.
Figure 9. Integral dichroism decay time constants i for 70 bp poly as a function of the ethanol content (v/v) corrected to the state of water at 20°C (75 μM NaCl, 75 μM cacodylate pH 7, 15 μM EDTA; field pulse 3.45 x 106 V/m). i was calculated from the parameters of the two-exponential fit according to i = 1·A1/(A1+A2) + 2·A2/(A1+A2), where 1, 2 are the time constants and A1, A2 the amplitudes of the fit to the dichroism decay (cf. Fig. 8). The line represents a fit by a sigmoidal function.
The corresponding data obtained for poly with 1600 bp cannot be interpreted at the same accuracy, because the decay curve reflects a broad spectrum of time constants. The slowest process remains almost constant over the transition range, suggesting that there is almost no change in the overall dimensions. This may be due to a change in the persistence length upon the B–A transition and/or aggregation of the A-form. (Any change in the persistence length has a minor influence on the results for the 70 bp sample, because its contour length is smaller than the persistence length.)
Ionic strength dependence
Reaction rates of polyelectrolytes are usually strongly dependent on the ionic strength. Thus, the B–A reaction should be analysed at different salt concentrations. However, limitations imposed both by the experimental system and by the method preclude an analysis over a wide range of ionic strengths. At least we succeeded in analysing the reaction at another ionic strength increased by a factor of 4. Under these conditions the midpoint of the B–A transition of poly is shifted to a lower ethanol content (change of the ethanol content by 2% v/v). However, the time constants (Fig. 10) at the midpoint of the transition were found very close to those observed in the standard buffer used above. Thus, the dependence of the time constants on the ionic strength is relatively small, if the same state of transition is considered. Obviously the analysis should be extended to a wider range of ionic strengths in the future.
Figure 10. Magic angle time constants of the B–A transition of poly in the field free state (open squares, d1) and of the A–B-transition under electric field pulses (filled circles, r2, see text) as a function of the ethanol content in %. Conditions: v/v, 8°C, 8.5 μM poly, 300 μM NaCl, 300 μM cacodylate pH 7, 60 μM EDTA; field pulse 3.45 x 106 V/m.
DISCUSSION
Technical problems
Although the B–A transition was observed very early in the history of nucleic acids, the dynamics of this transition has not been determined experimentally in the 50 years since the discovery of the structure of the DNA double helix. This is remarkable since most other properties of the DNA double helix have been investigated exhaustively. Part of the problem is the fact that the B–A reaction cannot be analysed as easily as other comparable reactions. In addition the B–A transition has not been such a focus of interest as other transitions of DNA. However, interest in the B–A transition has been revived recently by detection of A-DNA in many protein–DNA complexes (5–9).
Characterization of B–A dynamics seems to be trivial at first glance, because the transition is associated with a conveniently large change of the absorbance spectrum. Thus, it is not necessary to introduce spectroscopic labels. However, the reaction happens to occur in a segment of the time scale which is not simple to analyse. The time resolution of standard rapid mixing techniques is not sufficient. The temperature jump technique is hardly applicable because of a very small enthalpy change. Thus, the electric field jump technique seems to be the only remaining possibility. This technique is not very popular, because reaction effects must be separated from orientation effects, which requires special experience (22). Under these conditions NMR techniques seem to be a reasonable alternative. However, experience shows that assignment of rates by NMR techniques is not trivial, when the time constants are in the microsecond time-range. In the present case there is another more serious difficulty: the standard conditions used for analysis of the B–A transition in solution favour DNA aggregation. The concentrations required for NMR analysis are much higher than those used in the present investigation for electric field jump experiments. Thus, aggregation would be a serious obstacle for any NMR analysis.
Separation of field-induced effects
Because orientation and reaction effects are closely coupled, when polymers are exposed to electric field pulses, the arguments for the assignment of the B–A reaction effects should be summarized. First of all, both the theoretical basis and the practice of the magic angle technique are well established (22,27). In the present case the successful separation of reaction effects from orientation effects can be demonstrated by several different arguments. The different nature of the effects is already demonstrated by the different spectrum of time constants (Figs 3 and 7). A striking argument for the assignment of the magic angle effect to the B–A reaction is the unique dependence of the amplitude on the ethanol content (Fig. 4). Furthermore, the spectral signature of the magic angle effect is in agreement with the B–A reaction and neither consistent with an orientation effect nor with any effect due to a helix–coil transition or aggregation as potential alternatives. Finally, a clear argument is the difference in the chain length dependence observed for reaction and orientation effects: the dichroism decay time constants are strongly dependent on the chain length, in exact agreement with expectations, whereas the time constants of the magic angle effect are almost independent of the chain length, as expected for reaction effects of chains above the cooperative length. These results clearly demonstrate that the separation of reaction effects from orientation effects was successful.
BA time constants
The time constants for the B–A transition in Figures 3 and 10 were observed for a polymer with an average chain length of 1600 bp in the present experiments. However, these time constants do not reflect a reaction over the full length of this polymer. The average reaction unit is defined by the cooperative length, which has been estimated for the B–A transition to be 10–30 bp (17). Thus, for short oligomers the B–A transition is expected to be broadened, whereas an approximately constant width of the transition is expected for chain lengths above the cooperative length. Experiments with the 70 bp sample confirm this expectation. The time constants for the B–A transition of 70 bp helices are very close to those observed for the polymer, whereas the amplitude of the slow process is much smaller.
The experiments clearly show that the B–A reaction of poly proceeds with time constants of 10 μs. Compared to predictions by molecular dynamics (10–14), this is unexpectedly slow. The activation barriers indicated by the experimental results are also larger than expectations based on X-ray structures, which were interpreted to represent a continuum of structures (15–16) between B- and A-DNA.
Because of the wide difference between predictions and experimental results it may be suspected that there is some process in solution that slows the B–A transition. A candidate for such retardation may be coupling with an aggregation reaction. A strong argument against this interpretation is provided by the dichroism decay time constants reflecting rotational diffusion, which is a very sensitive indicator of aggregation. The values obtained for the 70 bp fraction (Fig. 9) do not show any pertinent extent of aggregation under the conditions of the present experiments. Another potential side reaction is field-induced denaturation of the double helix. The experimental conditions were selected to reduce the extent of this reaction to a minimum. Any residual field-induced denaturation is not expected to affect the B–A reaction, because the cooperative length of the B–A transition is much shorter than that of the helix–coil transition.
The time constants observed for the B–A transition should be compared with those observed previously for various related processes of nucleic acids. Simple stacking reactions in single stranded nucleic acids were observed in the time range from 10 ns to 1 μs, depending on the base and the sugar residue (33). Stacking of bases connected by a simple methylene chain proved to be much faster (34). Thus, the sugar–phosphate chain seems to impose restrictions on the dynamics of base stacking. The relaxation time of double helix unzipping (‘fraying’ of helix ends) is 0.2 μs (33). Stacking rearrangements in simple RNA loops (35) have been observed in the time range from 5 to 40 μs. These time constants demonstrate the level of activation barriers, which are expected to be in the same order of magnitude as those of the B–A transition. From this point of view, the time constants observed in the present investigation are consistent with previous observations.
The rate of the B–A transition has many implications—it represents the internal dynamics of DNA double helices. Most interpretations of the dynamics of DNA chains are based on the assumption of high rates for internal conversions between conformations. These interpretations should be reconsidered.
Obviously the information on the dynamics of the B–A transition should be extended. First of all, the present observations are restricted to the case of AT base pairs. However, there is no reason to expect markedly different time constants for the case of GC pairs. Measurements on GC-containing DNAs are in progress. Another problem is the low ionic strength used in the present investigation. The data described above show that the dependence on ionic strength is relatively small, which seems to be due to a rather small change of electrostatic repulsion during the B–A reaction. However, this conclusion should be confirmed by measurements at higher salt concentrations. There are some indications for B–A transitions at high salt in the literature, but these cases are not nearly as well documented as those in the low salt regime. Because of the limitations in the induction of B–A relaxation effects discussed above, the extension of experimental data on the kinetics of the B–A transition may be difficult.
ACKNOWLEDGEMENT
Part of this project was supported by a grant from the Deutsche Forschungsgemeinschaft.
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*To whom correspondence should be addressed. Tel: +49 551 201 1438; Fax: +49 551 201 1168; Email: dpoersc@gwdg.de
ABSTRACT
Although the transition from the B-DNA double helix to the A-form is essential for biological function, as shown by the existence of the A-form in many protein–DNA complexes, the dynamics of this transition has not been resolved yet. According to molecular dynamics simulations the transition is expected in the time range of a few nanoseconds. The B–A transition induced by mixing of DNA samples with ethanol in stopped flow experiments is complete within the deadtime, showing that the reaction is faster than 0.2 ms. The reaction was resolved by an electric field jump technique with induction of the transition by a dipole stretching force driving the A- to the B-form. Poly was established as a favourable model system, because of a particularly high cooperativity of the transition and because of a spectral signature allowing separation of potential side reactions. The time constants observed in the case of poly with 1600 bp are in the range around 10 μs. An additional process with time constants of 100 μs is probably due to nucleation. The same time constants (within experimental accuracy ±10%) were observed for a poly sample with 70 bp. Under low salt conditions commonly used for studies of the B–A transition, the time constants are almost independent of the ionic strength. The experimental data show that a significant activation barrier exists in the B–A transition and that the helical states are clearly separated from each other, in contrast to predictions by molecular dynamics simulations.
INTRODUCTION
The transition between the standard B-form of DNA double helices and the A-form was observed during the first X-ray studies (1–4). Fifty years on and the dynamics of this transition has still not been characterized, despite the fact that the B–A transition is known to be essential for processing of genetic information (5–9), e.g. during transcription (9). Molecular dynamics simulations have predicted the transition to proceed within a few nanoseconds (10–14) and the absence of any significant activation barrier has been suggested from a comparison of crystal structures (15–16). This seems to be in contrast with the clear cooperativity of the B–A transition (17). The B–A transition was first detected by Franklin and Gosling (3), who characterized the change of the helix structure as ‘a substantial re-arrangement of the molecule’ (Fig. 1). Does this imply a substantial activation barrier?
Figure 1. Structures of the B- and A-form of the DNA double helix (left and right, respectively). Views of 12 bp segments prepared by VMD (36) from bdl001 (37) and adl046 (38) .
The B–A equilibrium can be analysed conveniently owing to large changes of the circular dichroism and of the UV spectrum (18). The reduction of the relative humidity, inducing the transition from B to A under X-ray conditions, can be generated in solution simply by addition of ethanol. Thus, it may be expected that analysis of the kinetics by one of the standard techniques is a routine task. However, the experimental analysis is not trivial, as shown by several independent attempts without success. Here we present the first experimental data on the dynamics of the B–A reaction.
MATERIALS AND METHODS
DNA from salmon sperm (Sigma) was sonicated to an average chain length of 400 bp under nitrogen. The average chain length of poly (Sigma) was 1600 bp. Part of the poly sample was sonicated under nitrogen and then separated into different fractions by sephacryl S500 column chromatography. Finally the samples were separated further by preparative polyacrylamide gel electrophoresis. Average chain lengths were determined by gel electrophoresis and by analytical ultracentrifugation (sedimentation coefficients). All polynucleotide samples were dialysed extensively, first against high salt buffers (0.2 M NaCl, 1 mM Na-cacodylate, 1 mM EDTA) to remove traces of multivalent ions, and finally against a standard low salt buffer containing 250 μM NaCl, 250 μM Na-cacodylate and 50 μM EDTA.
The state of the samples and of their B–A transition was controlled by CD spectroscopy using a JASCO 720. Absorbance titrations were measured with a Cary 4 spectrophotometer. We used a stopped-flow instrument constructed in this institute (19). Electric field jumps were generated by coaxial cable discharge (20,21). The pulses were applied to a cell machined from macrolon with Pt-electrodes at a distance of 5.5 mm. The quartz windows were inserted in a strain-free mode as previously described (22). The optical path-length was 20 mm. The spectrophotometric detection system was composed of a Hamamatsu L2423 mercury/xenon arc lamp, a Schoeffel GM250 grating monochromator, a Glan air polarizer and a homemade photomultiplier detector. The photo-electric signal was stored on a Tektronix DSA 601A digitizing signal analyser. The experimental data were analysed by a set of programs developed for quantitative characterization of chemical and physical relaxation data (23,24). Convolution of rise or decay curves with the detector response curve (response time constant 0.93 μs used in all measurements) was considered by quantitative deconvolution procedures.
Magic angle measurements
Electric field pulses are known to induce orientation effects in solutions of polynucleotides (25). These orientation effects are usually reflected by large changes of light absorption and are characterized quantitatively in terms of the linear dichroism. In the present investigation we wanted to study field-induced reaction effects (26), which can be separated from orientation effects by using polarized light oriented at the magic angle (55°) with respect to the field vector. The experimental conditions required for reliable magic angle measurements have been discussed in detail elsewhere (22,27).
When reaction effects are small compared to orientation effects, the magic angle conditions should be controlled carefully. Such control involves measurements of the field induced amplitudes A0, A55 and A90 with polarized light oriented at angles = 0°, 55° and 90° with respect to the field vector. The ratio R = (A0 – A55)/( A90 – A55) should be –2. In the present investigation we have rejected data with a deviation larger than 5%.
Data correction
When electric field pulses induce reaction effects, these are reflected in the transients measured at all orientations of the polarized light. Thus, transients measured at = 0° must be corrected by subtraction of the corresponding transients measured at = 55° to get unperturbed dichroism transients. For subtraction the transients were transformed to the same level of light intensity.
Dichroism decay time constants measured at different ethanol content are affected by different viscosities. For quantitative comparison, time constants were corrected to the state of water at 20°C by multiplication with the factor w·Te/(e·293.1), where e and w are the viscosities of the solvent under the conditions of the experiments and of water at 20°C, respectively; Te is the absolute temperature of the solvent used during experiments.
RESULTS
Stopped flow measurements
Because the B–A reaction can be induced by mixing of DNA solutions with ethanol, the technique of choice seems to be stopped flow. However, the analysis turned out to be difficult because of several technical problems. One of them was caused by the difference in the density of the solutions, leading to partial mixing of the solutions by convection. Another problem seems to be due to a difference in the compressibility of the solutions. When these problems were as much under control as possible, optical signals expected for the B–A reaction were not observed. The absence of any amplitude that could be assigned to the B–A reaction shows that the reaction has already gone to completion during the mixing time of 0.2 ms. There are still options which enable analysis of the B–A reaction by flow techniques with increased time resolution. However, these options were not followed at this point, because other techniques with higher time resolution were tested first.
Search for an optimal approach
The reduction of water activity required for induction of the B–A transition has been materialized in solution by addition of ethanol in virtually all previous investigations. Because addition of ethanol at high salt induces aggregation and precipitation, almost all experimental data on the B–A transition published in the literature were obtained at low salt concentrations. Thus, the temperature jump technique based on Joule heating, which requires high salt conditions, cannot be applied at a sufficiently high time resolution. Furthermore, it is known that the temperature dependence of the B–A transition is very limited. According to Ivanov et al. (18) the ‘B–A equilibrium is not influenced by temperature’. Thus, laser temperature jump instruments are not expected to be applicable either. However, the electric field jump technique (20) seems to be promising, because it is optimal for solutions of low salt concentrations and provides a high time resolution. However, first attempts with the electric field jump technique on salmon sperm DNA samples were not successful. Thus, careful optimization of reaction conditions is necessary.
One of the questions is the optimal range of chain lengths. The B–A transition is cooperative with an estimated cooperative length in the range from 10 to 30 bp (17). Optimal amplitudes are expected in the range of chain lengths above the cooperative length. For convenience and to minimize DNA sample costs, readily available polymers are the first choice. The interpretation of data obtained for oligomer samples may be simpler, but the assignment of any relaxation effect to the B–A transition of oligomer samples is expected to be difficult, because other effects like fraying of helix ends contribute with considerable amplitudes.
From the results of other researchers (28,29) it is known that the B–A transition is dependent on the GC content. Thus, the width of the transition for homopolymers is expected to be lower than that for DNA with mixed sequence. This expectation was verified by CD titrations: the B–A transition for poly was narrower than that of natural DNA by a factor of 5. Furthermore, the B–A transition of poly is associated with a favourable UV difference spectrum having isosbestic points (Fig. 2), which can be used for unequivocal assignments of relaxation amplitudes. Polymers with GC base pairs are expected to be less convenient than those with AT base pairs because of the stronger tendency of GC polymers for aggregation.
Figure 2. B–A transition of poly indicated by absorption difference spectra at various ethanol percentages. The absorption spectrum measured at 51.68% ethanol was subtracted from the absorption spectra measured at the given ethanol percentages. in M–1cm–1; % in v/v units; starting concentrations: 40 μM poly, 125 μM NaCl, 125 μM cacodylate pH 7, 25 μM EDTA.
As mentioned above, all transition curves given in the literature have been induced by addition of ethanol (or trifluoro-ethanol). Currently we do not see a reasonable alternative to these experimental conditions, which imply reduction of the ionic strength to very low values, because otherwise aggregation and precipitation cannot be avoided.
Electric field jump experiments
Electric field pulses are known to induce dissociation of ion complexes (26). The amplitudes induced by electric fields increase with the number of charges associated with the reactants. Thus, the first strategy for optimal analysis was coupling of the B–A transition with binding of ligands like spermine. Minyat et al. (30) reported that ‘spermine and spermidine induce the B to A transition of DNA’ in water/ethanol solutions. Thus, it may be expected that electric field pulses applied to a DNA solution in water/ethanol/spermine adjusted close to the midpoint of the B–A transition drive the B–A equilibrium towards the B-form by field-induced dissociation of spermine ions from the DNA. However, the experiments did not reveal the expected amplitude.
For comparison, the reaction was studied in a buffer containing monovalent salt exclusively. In this case reaction amplitudes appeared under magic angle conditions, as shown by the example in Figure 3. The amplitude measured at 280 nm appears only in the limited range of ethanol content from 67 to 75% (Fig. 4) with a clear maximum close to the centre of the B–A transition, which has been determined independently by measurements of CD spectra under the same experimental conditions. The field-induced reaction amplitude is not found outside the B–A transition range. These data clearly demonstrate that these amplitudes reflect the B–A transition. Further evidence comes from the observation that the sign of the field-induced reaction amplitude is reverted at 248 nm, in agreement with the difference spectra found for the B–A transition (Fig. 2). Alternative reaction effects might be either a field-induced helix–coil transition or a field-induced change of the aggregation state. In both cases the observed spectral signature is not consistent with these types of reactions. Furthermore, the distinct dependence of the amplitudes on the ethanol content is clearly not consistent with a helix–coil transition or a change of the aggregation state. Thus, we may conclude that the electric field induces a shift of the B–A equilibrium.
Figure 3. Field-induced change of the transmission I at 280 nm for poly. (a) Corrected dichroism transient (I0 – I55, left scale); (b) magic angle transient (I55, average of five shots, left scale); and (c) enlarged magic angle transient (right scale). The bar indicates the duration of the field pulse. The least squares fits of the magic angle decay (c) by two exponentials (17.5 and 145 μs with relative amplitudes 61 and 39%, respectively) and of the dichroism decay (a) by four exponentials (2.25 μs, 22.2 μs, 165 μs and 1 ms with relative amplitudes 22, 30, 27 and 21%, respectively) cannot be distinguished from the experimental data; the single exponential fit (49 μs) of the magic angle decay is shown as a dotted line. Conditions: 70.2% ethanol v/v, 8°C, 8.5 μM poly, 75 μM NaCl, 75 μM cacodylate pH 7, 15 μM EDTA; field pulse 3.45 x 106 V/m.
Figure 4. Relative magic angle amplitudes A55/A of poly as a function of the ethanol content in % units (v/v). The line represents a Gaussian fit. Conditions: 8°C, 8.5 μM poly, 75 μM NaCl, 75 μM cacodylate pH 7, 15 μM EDTA; field pulse 3.45 x 106 V/m.
Dipolar stretching
The direction of the magic angle effect measured at the wavelength 280 nm clearly shows that the electric field pulses induce a reaction from the A- to the B-form. How does the electric field drive this reaction? The preference for the B-form in the presence of electric fields indicates that B-helices have a higher effective dipole moment. The dipole moments are known to increase strongly with the length of DNA helices (31). The length increment per base pair for B-DNA (3.4 ?) is much higher than that for A-DNA (2.8 ?). These parameters imply that the field-induced reaction is driven by dipolar stretching. Thus, there is an analogy to the currently popular stretching experiments by atomic force devices (32). The main advantage of stretching by electric field pulses is the much higher time resolution.
The first argument for dipolar stretching as the main driving force for the AB reaction under electric field pulses is simply based on the fact that the contour length of DNA helices in the B-form is higher than that in the A-form. Further evidence for this assignment may be obtained from an analysis of the transients observed under electric field pulses. As shown by the example in Figure 5, these transients reveal a special type of coupling. A satisfactory fit requires two exponentials, where the amplitude of the first exponential is opposite to that of the second one. The combination of amplitudes and time constants is consistent with the special case of a relaxation effect with an induction period—corresponding to a zero initial slope. This type of relaxation response is expected for the present reaction, because the A–B reaction can only be driven when the dipole exceeds a threshold level. This threshold level of the dipole moment cannot be induced immediately after pulse application but requires some time for ion polarization and rotation of the polymers into the direction of the field vector. Ion polarization is not associated with any change of UV absorbance and any effect of polymer rotation on the absorbance is suppressed under magic angle conditions. Thus, these processes are not visible directly. However, the influence of these processes is coupled to the A–B reaction, such that the whole process appears as a convolution product. The initial process of dipole development is without change of absorbance, but is reflected in the transient by coupling to the A–B reaction, which is associated with a relatively large change of the absorbance. The expected convolution product is in complete agreement with the observed transient. The first exponential reflects the rise of the dipole moment and the second one describes the A–B reaction at the given electric field strength.
Figure 5. Magic angle rise curve of poly induced by a field pulse of 3.7 x 106 V/m. The fit by two exponentials cannot be distinguished from the experimental data (1.69 and 4.38 μs with relative amplitudes –85 and +185%, respectively); the single exponential fit (6.17 μs) is represented by a dotted line. Conditions: 70.4% ethanol v/v, 8°C, 8.5 μM poly, 75 μM NaCl, 75 μM cacodylate pH 7, 15 μM EDTA.
The dipolar stretching effect is expected to increase with increasing field strength. As shown in Figure 6 the logarithm of the second time constant can be represented at a reasonable accuracy as a linear function of the electric field strength. This dependence is expected for reactions driven by an increase of a permanent dipole moment, when the orientation of molecules is close to saturation (26). As shown in the literature (31), the induced dipole moment of polynucleotides is saturated at the field strengths used in our present experiments and, thus, the field-induced effects of these polynucleotides are as expected for permanent dipoles.
Figure 6. Magic angle rise time of poly as a function of the field strength. Conditions: 70.32% ethanol v/v, 8°C, 75 μM NaCl, 75 μM cacodylate pH 7, 15 μM EDTA.
Time constants of the BA reaction
The relatively high amplitudes observed at the magic angle indicate that the field pulses can drive the reaction close to completion and, thus, the time constants no longer represent relaxation processes. This is also indicated by the fact that the time constants observed in the presence of the electric field (AB reaction) are different from those in the field free state (BA reaction) in most cases (Fig. 7). The transients reflecting the BA reaction show a fast process ( 10 μs) with most of the amplitude and a slow process ( 100 μs) with a small amplitude. Both the fast and slow processes are associated with amplitudes showing a spectral characteristic consistent with the B–A transition but not consistent with a helix–coil transition or a change of the aggregation state. We assign the slow process to nucleation and the fast process to growth of helical regions. This assignment should be checked by future model calculations.
Figure 7. Magic angle time constants of the B–A transition of poly in the field free state (open squares, d1) and of the A–B transition under electric field pulses (filled circles, r2, see text) as a function of the ethanol content in %. Conditions: v/v, 8°C, 8.5 μM poly, 75 μM NaCl, 75 μM cacodylate pH 7, 15 μM EDTA; field pulse 3.45 x 106 V/m.
As shown in Figure 7, the time constant representing the main amplitude of the BA reaction decreases with increasing ethanol content, consistent with an increasing rate of the BA reaction upon ethanol addition. The opposite direction is observed for the process in the presence of the electric field, representing the AB reaction. This dependence on the ethanol content is expected. The time constants for the opposite processes in Figure 7 are equivalent at 71% ethanol, shifted from the midpoint of the B–A equilibrium towards the domain of the A DNA. This is due to the fact that the field pulses accelerate the AB reaction and induce large perturbations of the equilibrium. If the process could be followed without large perturbations, the time constants would be equivalent at any given point of the transition.
Chain length dependence
As a control for our assignment we studied the B–A transition at a different chain length of poly. It is known that the rotational diffusion time constants are very strongly dependent on the chain length, whereas the time constants for the B–A transition are expected to show much less chain length dependence—at least for chain lengths remaining above the cooperative length. We used a poly sample with an average chain length of 70 bp. The dichroism decay (Fig. 8) of this sample was described by two exponentials (1 = 0.83 μs, 2 = 2.19 μs) at a high accuracy, reflecting a distribution of chain lengths between 60 and 80 bp, in agreement with results obtained by gel electrophoresis. The reaction amplitude observed at the magic angle is smaller than that observed for the polymer with 1600 bp, but can still be characterized at a sufficiently high accuracy (Fig. 8). The BA transients observed after pulse termination require two exponentials for a satisfactory fit. Both time constants are close to those observed for the long polymer. The main difference is in the relative amplitude of the slow process, which is clearly smaller than that observed for the long polymer. Thus, the experiments on the 70 bp sample confirm all the expectations in a convincing manner. In particular, these experiments reconfirm that the magic angle separation of reaction effects from orientation processes is reliable.
Figure 8. Field-induced change of the transmission at 280 nm for 70 bp poly at polarizer orientations = 0° and 55° with respect to the field vector. The bar indicates the duration of the field pulse. Corrected dichroism transient (I0 – I55, orange) with a fit of the decay by two exponentials (black, 1 = 0.83 μs, 2 = 2.19 μs, A1 = 61%, A2 = 39%); the magic angle transient (I55, average of five shots) is shown both at the same scale as the dichroism (magenta, left scale) and magnified (blue, right scale) with a fit of the decay by two exponentials (red, 1 = 8.25 μs, 2 = 67.8 μs, A1 = 87%, A2 = 13%) and by one exponential (green). 70.4% ethanol (v/v), 8°C, 8.5 μM poly, 75 μM NaCl, 75 μM cacodylate pH 7, 15 μM EDTA; field pulse 3.45 x 106 V/m.
The time constants of rotational diffusion obtained from the dichroism decay provide a very sensitive measure of the hydrodynamic dimensions. For comparison of time constants measured at different ethanol content, these constants must be corrected to a standard state, because the viscosity of aqueous solutions is a strong function of the ethanol content. Experimental data measured over the B–A transition range were corrected to 100% water content at 20°C (Fig. 9). The corrected time constants clearly show the expected decrease of the hydrodynamic length upon the B–A transition. Using the dichroism decay time constant of the B-form for calibration of the chain length, based on a rise per base pair of 3.4 ?, we get an effective chain length of 76 bp. Using this chain length and the decay time constant measured for the A-form, we get an effective rise per base pair of 3.0 ? for the A-form. These calculations are based on the wormlike chain model with a persistence length of 1000 ? found for DNA at low salt concentrations.
Figure 9. Integral dichroism decay time constants i for 70 bp poly as a function of the ethanol content (v/v) corrected to the state of water at 20°C (75 μM NaCl, 75 μM cacodylate pH 7, 15 μM EDTA; field pulse 3.45 x 106 V/m). i was calculated from the parameters of the two-exponential fit according to i = 1·A1/(A1+A2) + 2·A2/(A1+A2), where 1, 2 are the time constants and A1, A2 the amplitudes of the fit to the dichroism decay (cf. Fig. 8). The line represents a fit by a sigmoidal function.
The corresponding data obtained for poly with 1600 bp cannot be interpreted at the same accuracy, because the decay curve reflects a broad spectrum of time constants. The slowest process remains almost constant over the transition range, suggesting that there is almost no change in the overall dimensions. This may be due to a change in the persistence length upon the B–A transition and/or aggregation of the A-form. (Any change in the persistence length has a minor influence on the results for the 70 bp sample, because its contour length is smaller than the persistence length.)
Ionic strength dependence
Reaction rates of polyelectrolytes are usually strongly dependent on the ionic strength. Thus, the B–A reaction should be analysed at different salt concentrations. However, limitations imposed both by the experimental system and by the method preclude an analysis over a wide range of ionic strengths. At least we succeeded in analysing the reaction at another ionic strength increased by a factor of 4. Under these conditions the midpoint of the B–A transition of poly is shifted to a lower ethanol content (change of the ethanol content by 2% v/v). However, the time constants (Fig. 10) at the midpoint of the transition were found very close to those observed in the standard buffer used above. Thus, the dependence of the time constants on the ionic strength is relatively small, if the same state of transition is considered. Obviously the analysis should be extended to a wider range of ionic strengths in the future.
Figure 10. Magic angle time constants of the B–A transition of poly in the field free state (open squares, d1) and of the A–B-transition under electric field pulses (filled circles, r2, see text) as a function of the ethanol content in %. Conditions: v/v, 8°C, 8.5 μM poly, 300 μM NaCl, 300 μM cacodylate pH 7, 60 μM EDTA; field pulse 3.45 x 106 V/m.
DISCUSSION
Technical problems
Although the B–A transition was observed very early in the history of nucleic acids, the dynamics of this transition has not been determined experimentally in the 50 years since the discovery of the structure of the DNA double helix. This is remarkable since most other properties of the DNA double helix have been investigated exhaustively. Part of the problem is the fact that the B–A reaction cannot be analysed as easily as other comparable reactions. In addition the B–A transition has not been such a focus of interest as other transitions of DNA. However, interest in the B–A transition has been revived recently by detection of A-DNA in many protein–DNA complexes (5–9).
Characterization of B–A dynamics seems to be trivial at first glance, because the transition is associated with a conveniently large change of the absorbance spectrum. Thus, it is not necessary to introduce spectroscopic labels. However, the reaction happens to occur in a segment of the time scale which is not simple to analyse. The time resolution of standard rapid mixing techniques is not sufficient. The temperature jump technique is hardly applicable because of a very small enthalpy change. Thus, the electric field jump technique seems to be the only remaining possibility. This technique is not very popular, because reaction effects must be separated from orientation effects, which requires special experience (22). Under these conditions NMR techniques seem to be a reasonable alternative. However, experience shows that assignment of rates by NMR techniques is not trivial, when the time constants are in the microsecond time-range. In the present case there is another more serious difficulty: the standard conditions used for analysis of the B–A transition in solution favour DNA aggregation. The concentrations required for NMR analysis are much higher than those used in the present investigation for electric field jump experiments. Thus, aggregation would be a serious obstacle for any NMR analysis.
Separation of field-induced effects
Because orientation and reaction effects are closely coupled, when polymers are exposed to electric field pulses, the arguments for the assignment of the B–A reaction effects should be summarized. First of all, both the theoretical basis and the practice of the magic angle technique are well established (22,27). In the present case the successful separation of reaction effects from orientation effects can be demonstrated by several different arguments. The different nature of the effects is already demonstrated by the different spectrum of time constants (Figs 3 and 7). A striking argument for the assignment of the magic angle effect to the B–A reaction is the unique dependence of the amplitude on the ethanol content (Fig. 4). Furthermore, the spectral signature of the magic angle effect is in agreement with the B–A reaction and neither consistent with an orientation effect nor with any effect due to a helix–coil transition or aggregation as potential alternatives. Finally, a clear argument is the difference in the chain length dependence observed for reaction and orientation effects: the dichroism decay time constants are strongly dependent on the chain length, in exact agreement with expectations, whereas the time constants of the magic angle effect are almost independent of the chain length, as expected for reaction effects of chains above the cooperative length. These results clearly demonstrate that the separation of reaction effects from orientation effects was successful.
BA time constants
The time constants for the B–A transition in Figures 3 and 10 were observed for a polymer with an average chain length of 1600 bp in the present experiments. However, these time constants do not reflect a reaction over the full length of this polymer. The average reaction unit is defined by the cooperative length, which has been estimated for the B–A transition to be 10–30 bp (17). Thus, for short oligomers the B–A transition is expected to be broadened, whereas an approximately constant width of the transition is expected for chain lengths above the cooperative length. Experiments with the 70 bp sample confirm this expectation. The time constants for the B–A transition of 70 bp helices are very close to those observed for the polymer, whereas the amplitude of the slow process is much smaller.
The experiments clearly show that the B–A reaction of poly proceeds with time constants of 10 μs. Compared to predictions by molecular dynamics (10–14), this is unexpectedly slow. The activation barriers indicated by the experimental results are also larger than expectations based on X-ray structures, which were interpreted to represent a continuum of structures (15–16) between B- and A-DNA.
Because of the wide difference between predictions and experimental results it may be suspected that there is some process in solution that slows the B–A transition. A candidate for such retardation may be coupling with an aggregation reaction. A strong argument against this interpretation is provided by the dichroism decay time constants reflecting rotational diffusion, which is a very sensitive indicator of aggregation. The values obtained for the 70 bp fraction (Fig. 9) do not show any pertinent extent of aggregation under the conditions of the present experiments. Another potential side reaction is field-induced denaturation of the double helix. The experimental conditions were selected to reduce the extent of this reaction to a minimum. Any residual field-induced denaturation is not expected to affect the B–A reaction, because the cooperative length of the B–A transition is much shorter than that of the helix–coil transition.
The time constants observed for the B–A transition should be compared with those observed previously for various related processes of nucleic acids. Simple stacking reactions in single stranded nucleic acids were observed in the time range from 10 ns to 1 μs, depending on the base and the sugar residue (33). Stacking of bases connected by a simple methylene chain proved to be much faster (34). Thus, the sugar–phosphate chain seems to impose restrictions on the dynamics of base stacking. The relaxation time of double helix unzipping (‘fraying’ of helix ends) is 0.2 μs (33). Stacking rearrangements in simple RNA loops (35) have been observed in the time range from 5 to 40 μs. These time constants demonstrate the level of activation barriers, which are expected to be in the same order of magnitude as those of the B–A transition. From this point of view, the time constants observed in the present investigation are consistent with previous observations.
The rate of the B–A transition has many implications—it represents the internal dynamics of DNA double helices. Most interpretations of the dynamics of DNA chains are based on the assumption of high rates for internal conversions between conformations. These interpretations should be reconsidered.
Obviously the information on the dynamics of the B–A transition should be extended. First of all, the present observations are restricted to the case of AT base pairs. However, there is no reason to expect markedly different time constants for the case of GC pairs. Measurements on GC-containing DNAs are in progress. Another problem is the low ionic strength used in the present investigation. The data described above show that the dependence on ionic strength is relatively small, which seems to be due to a rather small change of electrostatic repulsion during the B–A reaction. However, this conclusion should be confirmed by measurements at higher salt concentrations. There are some indications for B–A transitions at high salt in the literature, but these cases are not nearly as well documented as those in the low salt regime. Because of the limitations in the induction of B–A relaxation effects discussed above, the extension of experimental data on the kinetics of the B–A transition may be difficult.
ACKNOWLEDGEMENT
Part of this project was supported by a grant from the Deutsche Forschungsgemeinschaft.
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