Kinetics of the B-A transition of DNA: analysis of potential contributions to a reaction barrier.

Because of open problems in the relation between results obtained by relaxation experiments and molecular dynamics simulations on the B-A transition of DNA, relaxation measurements of the B-A dynamics have been extended to a wider range of conditions. Field-induced reaction effects are measured selectively by the magic angle technique using a novel cell construction preventing perturbations from cell window anisotropy. The kinetics was recorded for the case of poly[d(AT)] up to the salt concentration limit of 4.4 mM, where aggregation does not yet interfere. Now experimental data on the B-A dynamics are available for poly[d(AT)] at salt concentrations of 0.18, 0.73, 2.44 and 4.4 mM. In all cases, a spectrum of time constants is found, ranging from ~ 10 µs up to components approaching ~ 1 ms. The relatively small dependence of these data on the salt concentration indicates that electrostatic effects on the kinetics are not as strong as may be expected. The ethanol content at the transition center is a linear function of the logarithm of the salt concentration, and the slope is close to that expected from polyelectrolyte theory. The B-A transition dynamics was also measured in D2O at a salt concentration of 2.4 mM: the center of the transition is found at 20.0 mol/l H2O and at 20.1 mol/l D2O with an estimated accuracy of ± 0.1 mol/l; the spectrum of time constants at the respective transition centers is very similar. The experimental results are discussed regarding the data obtained by molecular dynamics simulations.

Boundary conditions for free A-DNA in solution and the relation of local to global DNA structures at reduced water activity.

Because of repeated claims that A-DNA cannot exist without aggregation or condensation, the state of DNA restriction fragments with 84-859 bp has been analyzed in aqueous solutions upon reduction of the water activity. Rotational diffusion times τ (d) measured by electric dichroism at different water activities with a wide variation of viscosities are normalized to values τ (c) at the viscosity of water, which indicate DNA structures at a high sensitivity. For short helices (chain lengths [Formula: see text] ≤ persistence length p), cooperative formation of A-DNA is reflected by the expected reduction of the hydrodynamic length; the transition to the A-form is without aggregation or condensation upon addition of ethanol at monovalent salt ≤1 mM. The aggregation boundary, indicated by a strong increase of τ (c), is shifted to higher monovalent salt (≥4 mM) when ethanol is replaced by trifluoroethanol. The BA transition is not indicated anymore by a cooperative change of τ (c) for [Formula: see text] ¼ p; τ (c) values for these long chains decrease upon reduction of the water activity continuously over the full range, including the BA transition interval. This suggests a non-cooperative BC transition, which induces DNA curvature. The resulting wide distribution of global structures hides changes of local length during the BA transition. Free A-DNA without aggregation/condensation is found at low-salt concentrations where aggregation is inhibited and/or very slow. In an intermediate range of solvent conditions, where the A-form starts to aggregate, a time window remains that can be used for analysis of free A-DNA in a quasi-equilibrium state.

Recognition of operator DNA by Tet repressor.

The recognition of operator DNA by Tet repressor was analyzed by fluorescence stopped flow measurements. The main part of the fluorescence change observed for the reaction of the repressor with operator DNA reflects a second-order binding reaction including the expected concentration dependence. Global fitting of transients measured at different concentrations reveal at least one intramolecular step in addition to the bimolecular step. The rate constant for the bimolecular step is strongly salt dependent approaching the limit of diffusion control 2×10(8) M(-1) s(-1) at 50 mM NaCl and decreasing to 5×10(4) M(-1) s(-1) at 600 mM NaCl. These data are consistent with initial formation of a pre-equilibrium complex; electrostatic steering resulting from the high dipole moment of the repressor may contribute to the strong salt dependence. The rate constants of the intramolecular step are in the range of ~0.1 s(-1). Fluorescence quenching is salt dependent; the overall binding constant to operator O1 at 150 mM NaCl is 5×10(8) M(-1); binding constants at different salt concentrations indicate ~5 ion contacts for the specific complex of the Tet repressor dimer. The binding constant to operator O2 is higher than to O1 by a factor of ~2 at 400 mM NaCl.

Electro-optical analysis of macromolecular structure and dynamics.

Electro-optical effects are induced by external electric field pulses applied to solutions or suspensions and are recorded by various optical techniques. These effects are very useful for the characterization of macromolecular structures and their dynamics in solution. One of the field-induced effects is alignment of molecular dipoles, which can be detected at a very high sensitivity by measurements of the dichroism or the birefringence. Stationary values of these optical parameters recorded at different electric field strengths can be used to characterize dipole moments and to determine the orientation of chromophores with respect to the dipole vector. The transients reflect rotational diffusion, providing a particularly accurate measure of size and shape. The internal flexibility is also reflected in these transients. Another type of field-induced effect is chemical relaxation, which can be detected selectively and is very useful for the characterization of reactions, like ligand binding and conformation changes. The techniques based on electric field effects are unique in the sense that problems can be solved, which are difficult or even impossible to be sorted out by other techniques.

Allosteric control of cAMP receptor binding dynamics.

The intrinsic fluorescence of the cyclic AMP receptor is a sensitive indicator of the reaction with DNA, but signals are perturbed by a photoreaction. A ratio procedure is shown to be useful for correction. The reaction of the protein with DNA indicated by corrected transients extends over a broad time range not only at low salt concentrations but also at physiological salt concentrations. The initial binding step can be recorded preferentially at low salt pH 7 and is shown to be very similar for specific and nonspecific DNA. The rate constant for initial binding at 13.5 mM salt pH 7 is 2 × 10(8) M(-1) s(-1). Slow reaction steps up to times of several hundred seconds are observed both at low and high salt; the magnitude and sign of fluorescence amplitudes are strongly dependent on salt and pH. At 100 mM salt pH 8, the slow reaction step observed for the binding of the cyclic AMP receptor protein to promoter DNA is strongly shifted to longer times upon reduction of the cAMP concentration. The observed cAMP dependence is described quantitatively by a model implying that binding of the receptor to promoter DNA requires two cAMP molecules per protein dimer and is not consistent with a model assuming that a single cAMP is sufficient for activation. The rate constant for binding of the protein·dimer·(cAMP)(2) complex to the promoter is 1.3 × 10(8) M(-1) s(-1), close to the limit of diffusion control. Equilibration of specific complexes takes ~100 s at physiological concentrations of the reaction components.

Structures during binding of cAMP receptor to promoter DNA: promoter search slowed by non-specific sites.

The kinetics of cAMP receptor (CAP) binding to promoter DNA has been studied by stopped-flow electric-dichroism at a reduced salt concentration, where the coupling of non-specific and specific binding can be observed directly. Amplitudes, rise and decay times of dichroism transients provide detailed information about the reaction and the structure of intermediates over more than six orders of magnitude on the time scale. CAP binding during the first milliseconds after mixing is indicated by an increase of both rise- and decay-time constants. A particularly large increase of rise times reflects initial formation of non-symmetric complexes by protein binding to non-specific sites at DNA ends. The increase of the hydrodynamic dimensions continues up to ~1 s, before a decrease of time constants reflects transition to compact states with bent DNA up to the time range of ~10(3) s. The slow approach to CAP-induced DNA bending is due to non-specific complexes, which are formed initially and are converted slowly to the specific complex. At the salt concentration of 13.5 mM, conversion to specific complexes with bent DNA is completed after ~40 s at pH 8 compared to >10(3) s at pH 7, resulting from a higher affinity of CAP to non-specific sites at pH 7 than 8 by a factor of ~100. Thus, under the given conditions non-specific sites delay rather than facilitate formation of the specific complex with bent DNA. Experimental data obtained for a non-specific DNA clearly indicate the impact of pseudo-sites. The different electro-optical parameters have been combined in global fits.

Electric birefringence at small angles from crossed position: enhanced sensitivity and special effects.

Measurements of electric birefringence with increased sensitivity are possible using lasers with high intensity and stability, provided that perturbations resulting from stray light and strain in cell windows can be reduced. A new type of cell window is designed for minimal strain and is used in a standard birefringence setup with optimized components. The new instrument is characterized by a stray-light constant of 2 × 10(-7) and a negligible residual birefringence. Thus, measurements can be extended to small angles from the crossed position providing birefringence signals of high amplitudes at favorable signal-to-noise ratios. Special effects at small angles from the crossed position like a divergent increase of relative amplitudes to extreme values, a nonlinear response, a new type of electro-optical anomaly, and a simple bypass around this anomaly are observed and shown to be consistent with the theory. The technique proves to be particularly useful for measurements at physiological salt concentrations, where signals for most systems are too small under conventional conditions.

Allosteric control of promoter DNA bending by cyclic AMP receptor and cyclic AMP.

The structure of the cyclic AMP receptor-promoter complex in solution was studied in the range of 0.2-50 microM cAMP by measurements of the electric birefringence at 0.1 M salt using a lac promoter DNA with 121 bp and with the CAP binding site at its center. An excess of protein required for complete conversion of the promoter DNA into the specific complex seems to be partly due to nonspecific binding. The specific complex is associated with a decay time constant of 1.36 micros at 3 degrees C, a positive birefringence, and a permanent dipole moment demonstrated by pulse reversal. These attributes were observed at cAMP concentrations between 3 and 50 muM and are characteristic of the specific complex. Model calculations demonstrate that the DNA bending angle under these conditions is 92 degrees . The observed positive birefringence does not result from the combination of the calculated quasi-permanent dipole and the orientation of the helix axes alone but is due to coupling of translational and rotational diffusion. When the cAMP concentration is decreased below 3 microM, the positive birefringence turns to a negative one with a transition center at 1.5 microM. The transition is too narrow for a model with induction of the specific cyclic AMP receptor-promoter complex after binding of a single cAMP to the cyclic AMP receptor dimer but is consistent with induction of this complex after binding of two cAMP molecules. The cyclic AMP receptor-promoter complex is driven into its specific bent form in vitro in the range of cAMP concentrations corresponding to that required for gene regulation in vivo.

Effects of hydrodynamic coupling on electro-optical transients.

The effects resulting from coupling between translational and rotational diffusion on electro-optical transients were analyzed by Brownian dynamics simulations. Diffusion tensors, including translational-rotational coupling tensors, were derived from bead model simulations. Optical and electrical parameters were assigned according to models and experimental data. Hydrodynamic coupling has a strong impact on the shape of electro-optical transients for objects with a nonsymmetric structure. As expected, hydrodynamic coupling in general does not affect the time constants derived from decay curves. However, special attention is required at singular points, where amplitudes are inverted. Under these conditions, transients are observed with artificially reduced time constants, suggesting compact structures. False conclusions may be avoided, when experimental data are analyzed over a sufficiently wide range of conditions. Because transients induced upon reversal of the field vector are strongly affected by hydrodynamic coupling, dipole types cannot be assigned from these transients simply according to standard rules, when the shape of the objects is nonsymmetric. The time constants obtained from exponential fitting of rise-curves show unexpected dependencies on the field strength, which are mainly due to superposition of individual components with amplitudes of opposite sign that are not resolved upon fitting. Dipole parameters obtained from stationary degrees of orientation via orientation functions may also be strongly affected by hydrodynamic coupling. The high sensitivity of electro-optical transients on details of molecular shape and optical and electrical parameters provides a powerful approach to molecular analysis, but quantitative assignments require special care. When symmetry is lost, which must be expected because of bending in many cases, hydrodynamic coupling effects cannot be neglected.

Unique physical signature of DNA curvature and its implications for structure and dynamics.

A particularly sensitive birefringence technique is used to analyze a curved DNA fragment with 118 bp and a standard DNA with 119 bp. At salt concentrations from 0.5 to 10 mM, both fragments show the usual negative stationary birefringence and monotonic transients - differences are relatively small. At 100 mM salt the curved DNA shows a positive stationary birefringence and non-monotonic transients with processes having amplitudes of opposite sign, whereas signals of the standard DNA remain as usual. Transients induced by reversal of the field vector indicate the existence of a permanent dipole for the curved DNA. 2-MHz-ac pulses induce a negative stationary birefringence in both DNAs. These results are consistent with calculations on models for curved DNA predicting a quasi-permanent dipole and a positive dichroism/birefringence. The quasi-permanent dipole results from the loss of symmetry in the charge distribution of the curved polyelectrolyte. The appearance of the unique signature of curvature at high salt is mainly due to a strong decrease of the polarizability by about 2 orders of magnitude. The special mode of orientation resulting from the quasi-permanent dipole is expected to contribute to the gel migration anomaly. The time constants of birefringence decay for the curved fragment are shorter than those of the 119 bp fragment by a factor of approximately 1.10 at 0.6 mM salt, whereas this factor is approximately 1.20 at 100 mM Na+. If both fragments were normal DNA with 3.4 A rise per base pair, the factor would be approximately 1.02. At high salt and high electric field strengths the factor increases up to 1.37. The implications for the bending dynamics and the potential to distinguish static from dynamic persistence by field reversal experiments are discussed. The dependence of the curvature on the salt concentration indicated by the time constants is consistent with a clear decrease of the electrophoretic anomaly at decreasing salt concentration.

The nature of "unusual" electro-optical transients observed for DNA.

Unusual electro-optical transients have been observed for many different polymers and colloidal systems. These effects provoked serious confusion, because a simple-minded interpretation can be completely misleading. The case of double helical DNA is of particular interest, because DNA has been studied in more detail than other systems and because of its biological function. DNA is subject to bending, which implies a loss of symmetry. Due to its high charge density, non-symmetric conformations must have a non-symmetric distribution of charges leading to a torque of considerable magnitude in the presence of external electric fields. The dipole moment describing this torque must be calculated in a coordinate system with its origin at the center of diffusion. The resulting dipole values are in the range of thousands of Debye units. Because the new dipole type is analogous to but not identical with permanent dipoles, the notation "quasi-permanent" dipole is suggested. Application of this concept, using commonly accepted parameters for DNA and established procedures for calculation of electro-optical transients, leads to "unusual" transients. Thus, these transients must be expected from well-known parameters of DNA double helices. The influence of the quasi-permanent dipole moment may be amplified considerably by hydrodynamic coupling. This effect has been demonstrated for the case of smoothly bent rods. Both model calculations and experiments illustrate the danger of getting data that may be completely misleading. For example, depending on pulse amplitudes and/or pulse lengths, electro-optical decays may be accelerated artificially due to superposition of decay components with opposite amplitudes. Experiments show that unusual transients and apparent acceleration effects disappear, when high frequency sine pulses are used for the electro-optical analysis of DNA. Electro-optical effects depend upon the internal dynamics of the object under investigation. In general, the dynamics of DNA bending was assumed to be fast compared to rotational diffusion. Because stacking rearrangements in single stranded nucleic acids are relatively slow and recently the dynamics of the B-A transition was observed in the time range >1 micros, it is likely that there are also relatively slow rearrangements between bending conformers. Bending transitions are expected to be relatively fast, when there are no activation barriers in the bending pathway, and may be slow, when activation barriers must be passed between bending conformers.

The dynamics of the B-A transition of natural DNA double helices.

The dynamics of the B-A transition of DNA double helices with different GC contents and various chain lengths has been characterized by an electric field pulse technique. The field-induced B-A reaction is separated from orientation effects using the magic angle technique. Amplitudes reflecting the B-A reaction are observed selectively in the limited range of ethanol contents, where CD spectra demonstrate the B-A transition. The maximum amplitude appears at 1-2% higher ethanol content than the center of the B-A transition observed by CD because electric field pulses induce a relatively large perturbation from the A- toward the B-form. The relaxation curves measured after pulse termination reflect a spectrum of up to three relaxation processes. For DNA's with approximately 50% GC, the main part of the amplitude ( approximately 75%) is associated with time constants of approximately 2 micros, and another major component appears with time constants of 50-100 micros. These relaxation effects have been observed for DNA samples with 859, 2629, 7160, and 48501 bp. The time constant associated with the main amplitude increases with decreasing GC content from approximately 2 micros at 50% GC to approximately 3 mus at 41% GC and approximately 10 micros at 0% GC at the center of the B-A transition. Model calculations on the kinetics of cooperative linear Ising lattices predict the appearance of a distinct maximum of the mean relaxation time at the center of the transition. The absence of such maximum in our experimental data indicates a low cooperativity of the B-A transition with a nucleation parameter of approximately 0.1. The rate of the B-A transition is lower by approximately 3 orders of magnitude than that predicted by molecular dynamics simulations.

Strong effect of hydrodynamic coupling on the electric dichroism of bent rods.

The effect of hydrodynamic coupling on the spatial orientation of rigid bent rods in electric fields has been analyzed by Brownian dynamics simulations. Bead models for smoothly bent rods were constructed with dimensions of DNA double helices, and established simulation procedures were used to calculate their diffusion tensor, including the translational-rotational coupling tensor. The electric and optical parameters were assigned on the basis of known properties of double helices. Brownian dynamics simulations of the orientation of these models in electric fields showed that both transients and amplitudes of the calculated dichroism are very strongly dependent on translational-rotational coupling over a wide range of electric field strengths. For example, the stationary dichroism of a smoothly bent 179 bp DNA fragment calculated at low field strengths is positive in the presence and negative in the absence of hydrodynamic coupling. The transients are converted from a biphasic to a monophasic shape, when hydrodynamic coupling is turned off. The large changes resulting from hydrodynamic coupling were controlled by calculations based on analytical expressions derived for electrooptical response curves in the limit of low electric field strengths; the results obtained by this independent approach are in very satisfactory agreement with our Brownian dynamics simulations. The effect is strongly dependent on the electric dipole and on its direction. In the absence of any dipole the coupling effect was not observed. The coupling effect increases with the size of the bent rods. Because most macromolecular structures are known to have induced and/or permanent dipole moments, large effects of hydrodynamic coupling on both the amplitudes and the transients of the electric dichroism/birefringence must be expected in general for structures with nonsymmetric shape.

Dynamics of the B-A transition of DNA double helices.

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 approximately 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[d(A-T)] 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[d(A-T)] with approximately 1600 bp are in the range around 10 micros. An additional process with time constants of approximately 100 micros is probably due to nucleation. The same time constants (within experimental accuracy +/-10%) were observed for a poly[d(A-T)] sample with approximately 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.

Strong bending of purple membranes in the M-state.

Structure changes of purple membranes during the photocycle were analysed in solution by measurements of the electric dichroism. The D96N-mutant was used to characterize the M-state at neutral pH. The transition from the resting state to 61% photo-stationary M-state is associated with a strong reduction of the dichroism decay time constant by a factor of approximately 2. Because the change of the time constant is independent of the bacteriorhodopsin concentration, the effect is not attributed to light-induced dissociation but to light-induced bending of purple membranes. After termination of light-activation the dichroism decay of the resting state is restored with a time constant close to that of the M-state decay, which is more than two orders of magnitude slower than proton transfer to the bulk. Thus, bending is not due to asymmetric protonation but to the structure of the M-state. A very similar reduction of decay time constants at a corresponding degree of light-activation was found for wild-type bacteriorhodopsin at pH-values 7.8-9.3, where the lifetime of the M-state is extended. Light-induced bending is also reflected in changes of the stationary dichroism, whereas the overall permanent dipole moment remains almost constant, suggesting compensation of changes in molecular and global contributions. Bead model simulations indicate that disks of approximately 1 microm diameter are bent at a degree of photo-activation of 61% to a radius of approximately 0.25 microm, assuming a cylindrical bending modus. The large light-induced bending effect is consistent with light-induced opening of the protein on the cytoplasmic side of the membrane detected by electron crystallography, which is amplified due to coupling of monomers in the membrane. Bending may function as a mechanical signal.