An unusual electrooptical effect observed for DNA fragments and its apparent relation to a permanent electric moment associated with bent DNA

On the possibility of the existence of orienting hydrodynamic steering effects in the kinetics of receptor-ligand association

In the vast majority of biologically relevant cases of receptor-ligand complex formation, the binding site of the receptor is a small part of its surface, and moreover, formation of a biologically active complex often requires a specific orientation of the ligand relative to the binding site. Before the formation of the initial form of the complex, only long-range, electrostatic and hydrodynamic interactions can act between the ligand approaching the binding site and the receptor. In this context, the question arises whether as a result of these interactions, there is a pre-orientation of the ligand towards the binding site, which to some extent would accelerate the formation of the complex. The role of electrostatic interactions in the orientation of the ligand relative to the binding site of the receptor is well documented. The analogous role of hydrodynamic interactions, although assessed as very significant by Brune and Kim (PNAS 91, 2930-2934, (1994)), is still debatable. In this article, I present the current state of knowledge on this subject and consider the possibilities of demonstrating the orienting effect of hydrodynamic interactions in the processes of receptor-ligand association, in an experimental way supported by computer simulations.

Prediction of solution properties and dynamics of RNAs by means of Brownian dynamics simulation of coarse-grained models: Ribosomal 5S RNA and phenylalanine transfer RNA

Background

The possibility of validating biological macromolecules with locally disordered domains like RNA against solution properties is helpful to understand their function. In this work, we present a computational scheme for predicting global properties and mimicking the internal dynamics of RNA molecules in solution. A simple coarse-grained model with one bead per nucleotide and two types of intra-molecular interactions (elastic interactions and excluded volume interactions) is used to represent the RNA chain. The elastic interactions are modeled by a set of Hooke springs that form a minimalist elastic network. The Brownian dynamics technique is employed to simulate the time evolution of the RNA conformations.

Results

That scheme is applied to the 5S ribosomal RNA of E. Coli and the yeast phenylalanine transfer RNA. From the Brownian trajectory, several solution properties (radius of gyration, translational diffusion coefficient, and a rotational relaxation time) are calculated. For the case of yeast phenylalanine transfer RNA, the time evolution and the probability distribution of the inter-arm angle is also computed.

Conclusions

The general good agreement between our results and some experimental data indicates that the model is able to capture the tertiary structure of RNA in solution. Our simulation results also compare quite well with other numerical data. An advantage of the scheme described here is the possibility of visualizing the real time macromolecular dynamics.

Electronic supplementary material

The online version of this article (doi:10.1186/s13628-015-0025-7) contains supplementary material, which is available to authorized users.

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.

Electric dichroism transients of aqueous solutions of DNA

In this work we develop a theory of reduced electric linear dichroism transients of DNA fragments in aqueous solution. The DNA fragments are modelled as rigid 'bent-rod molecules' (BRM) with the following physical parameters: electric charge, electric polarizability tensors and hydrodynamical ones, and the average transition probability tensor per molecule. In order to study the growth and decay of electric dichroism transients, the orientational distribution function of the molecules is needed. This function is obtained by solving the time-dependent Fokker-Planck equation in the presence of a low electric field E, using a perturbation method and the Fourier method with time-dependent coefficients. In our calculations the origin of the coordinate system is the mass centre of the BRM. With respect to this centre, the electric dipole moment of the molecule is zero. The developed theory adequately explains the experimental results. We show that the theoretical approach used in this work is equivalent to the one applied in the Brownian dynamics simulation work performed by Porschke and co-workers. We also analyse the effect of a possible electric dipole moment on the transients of the reduced electric linear dichroism in DNA bent fragments.

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.

Macrodipoles. Unusual electric properties of biological macromolecules

The wide range of different effects induced by electric fields in biological macromolecules is clearly due to the unusual quality and quantity of their electric parameters. A general concept for a quantitative description of the polarizability of macromolecules remains to be established. In the case of DNA, experimental data indicate the existence of an effective polarization length N(p); at chain lengths N < N(p) the polarizability increases with N(2), whereas saturation is approached at N > or = N(p). The polarization length decreases with increasing ionic strength in close analogy to the Debye length, but is approximately 10 times larger than the Debye length. The dynamics of DNA polarization at high field strengths has been observed in the ns time range and is consistent with biased field induced ion dissociation. In the range of chain lengths from approximately 400 to approximately 850 base pairs DNA molecules exhibit permanent dipole moments, which are in a preferentially perpendicular direction to the end-to-end-vector, leading to a positive electric dichroism. These results are consistent with a "frozen" ensemble of bent DNA configurations and provide evidence for the existence of slow, non-elastic bending transitions. The electric parameters of proteins are usually dominated by a permanent anisotropy of the charge distribution, corresponding to permanent dipole moments of the order of several hundred Debye up to about 1500 Debye. Relatively small dipole moments of protein monomers add up to millions of Debye, when these proteins are in a vectorial organization in membrane patches, as found for bacteriorhodopsin and Na (+)K (+)-ATPase . In these cases the dipole vector may support vectorial ion transport. It is remarkable that the dipole moments of proteins usually show a relatively small dependence on the salt concentration; a rational for these observations is provided by a dipole potential at the plane of shear for rotational diffusion, which is defined in close analogy to the zeta-potential for translational diffusion. Symmetry breaking leading to huge electric dipole moments may be expected for mixed lipid vesicles: according to model calculations the phase separation of lipid components with and without net charges may lead to very high dipole moments; the expectation has been verified experimentally for vesicles containing DMPA and DMPC. The state of these systems should be extremely sensitive to electric fields. In summary, there is an unusual wide variation of electric parameters associated with biological macromolecules and with biomolecular assemblies, which is the basis for the complexity of different phenomena induced by electric fields in biological systems.

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.

Reversing-pulse electric birefringence of multicomponent systems: the formulation and signal simulation for two axially symmetric components in equilibrium and the appearance of unusual signal patterns

This paper consists of two parts on reversing-pulse electric birefringence (RPEB) signal patterns. The first is the theoretical formulation of two axially symmetric models coexisting in equilibrium in solution. The present RPEB theory is based on the original Tinoco-Yamaoka theory with classical electric dipole moments, which was recently modified and extended by Yamaoka, Sasai, and Kohno to include various electric and optical parameters and most importantly the ion-fluctuation dipole moment <m(3)(2)>(1/2) along the longitudinal direction of axially symmetric molecules. The theory contains the electric polarizability anisotropy Deltaalpha', which can be either positive or negative in relation to the shape of components. The overall signal can be expressed as the sum of the fractions of two components in proportions to the coefficient F(1) or F(2) (=1-F(1)). The second part is the simulation of theoretical RPEB curves for the two-component system with various sets of electric and hydrodynamic parameters for hypothetical but interesting cases. In consideration of the decay behavior, calculated decay curves were compared with experimentally conceivable signals, classifying them into three categories according to cases: F(1)>1, 0<F(1)<1, and F(1)<0. Showing humps and/or dips in profiles the simulated RPEB signal in buildup and reverse transients reveals the mechanism of field orientation and electro-optic properties of molecules in solution. The ratio q=<m(3)(2)>/ktDeltaalpha(') is the crucial factor that controls the pattern of RPEB signals. If q value of one component is positive and the other is negative, the simulated RPEB curves are characterized by three cases: q>0, q<-1, and -1<q<0. If q>0 or q<-1, the resultant patterns are often encountered with experimental signals. If -1<q<0, many anomalous signal patterns appears.

Anomalous electric birefringence behavior of sonicated DNA fragments as observed in reversing-pulse transients and steady-state sign reversal: A multicomponent approach

Anomalous electric birefringence signals of a sonicated and column-fractionated medium-size calf thymus DNA sample (bp=570) in Na(+) solutions were measured at 7 degrees C. The reversing-pulse electric birefringence (RPEB) signal pattern was theoretically calculated in the low electric field region for two axially symmetric models coexisting in equilibrium in solution. The RPEB theory is based on the electric dipole moment due to ion-fluctuation along the longitudinal direction and the electric polarizability anisotropy (Deltaalpha'), together with various electric and optical parameters assigned to the models. An analytical method was developed for the steady-state birefringence of the two-component system in a wide range of electric fields. The NaDNA samples exhibit complex RPEB patterns mixed with negative- and positive-going profiles. An experimental RPEB signal of NaDNA at an absorbance (A(260)) of 8 was fitted to theoretical curve at weak electric fields. The anomalous RPEB signal was attributed to the component 2, which shows a dip in the buildup and another in the reverse processes with a positive sign and a larger relaxation time. For the component 1, a normal DNA profile with negative sign is associated with a narrow dip in the reverse and a faster relaxation time in the decay signal. The field-strength dependence of observed steady-state birefringence delta(infinity) could be fitted for NaDNA at A(260)=8 by the SUSID orientation function with saturated ionic and electronic moments. An apparent positive maximum and the sign reversal in delta(infinity) at weak electric fields is an interplay between the positive component 2 with positive optical factor Deltag and negative Deltaalpha' and the negative component 1 with negative Deltag and positive Deltaalpha'. Possible conformation of two DNA components involved in solution was estimated.

Dynamic electro-optic properties of macromolecules and nanoparticles in solution: A review of computational and simulation methodologies

This paper reviews some theories, and computational and simulation procedures available for the calculation of the time-course of electro-optic properties of particles in solution. For rigid particles, the time evolution of the properties is directly related to their rotational diffusion; therefore, the computational procedures for the calculation of hydrodynamic properties find a direct application in electro-optics. Several of such computational procedures, based on bead models, are reviewed. For flexible particles, the simultaneous effects the external field and the flexibility can be treated with Brownian dynamics simulation. We illustrate the various procedures, with applications to rigid bent rods and flexible, wormlike or hinged rods, trying to show how the absence or presence of flexibility, and its kind, influences the dynamic electro-optic properties, which are therefore valuable sources of information about the conformation of macromolecules and nanoparticles.

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.

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.

Calculation of protein form birefringence using the finite element method

An approach based on the finite element method (FEM) is employed to calculate the optical properties of macromolecules, specifically form birefringence. Macromolecules are treated as arbitrarily shaped particles suspended in a solvent of refraction index n1. The form birefringence of the solution is calculated as the difference in its refractive index when all the particles of refractive index n2 are either parallel to or normal to the direction of the polarization of light. Since the particles of interest are small compared to the wavelength of light, a quasi-static approximation for the refractive index is used, i.e., that it is equal to the square root of the dielectric constant of the suspension. The average dielectric constant of the mixture is calculated using the finite element method. This approach has been tested for ellipsoidal particles and a good agreement with theoretical results has been obtained. Also, numerical results for the motor domains of ncd and kinesin, small arbitrarily shaped proteins with known x-ray structures, show reasonable agreement with the experimental data obtained from transient electric birefringence experiments.

Electrooptical measurements demonstrate a large permanent dipole moment associated with acetylcholinesterase

Acetylcholinesterase (AChE) from krait (Bungarus fasciatus) venom is a soluble, nonamphiphilic monomer of 72 kDa. This snake venom AChE has been analyzed by measurements of the stationary and the transient electric dichroism at different field strengths. The stationary values of the dichroism are consistent with the orientation function for permanent dipoles and are not consistent with the orientation function for induced dipoles. The permanent dipole moment obtained by least-squares fits for a buffer containing 5 mM MES is 1000 D, after correction for the internal directing field, assuming a spherical shape of the protein. The dipole moment decreases with increasing buffer concentration to 880 D at 10 mM MES and 770 D at 20 mM MES. The dichroism decay time constant is 90 ns (+/- 10%) which is clearly larger than the value expected from the size/shape of the protein and indicates contributions from sugar residues attached to the protein. The dichroism rise times observed at low field strengths are larger than the decay times and, thus, support the assignment of a permanent dipole moment, although it has not been possible to approach the limit where the energy of the dipole in the electric field is sufficiently low compared to kT. The experimental value of the permanent dipole moment is similar to that calculated for a model structure of Bungarus fasciatus AChE, which has been constructed from its amino and acid sequence, in analogy to the crystal structure of AChE from Torpedo californica.

On the hydrodynamic analysis of macromolecular conformation

Hydrodynamics provides a powerful complementary role to the traditional "high resolution" techniques for the investigation of macromolecular conformation, especially in dilute solution, conditions which are generally inaccessible to other structural techniques. This paper describes the state of art of hydrodynamic representations for macromolecular conformation, in terms of (1) simple but straightforward ellipsoid of revolution modelling; (2) general triaxial ellipsoid modelling; (3) hydrodynamic bead modelling; (4) the ability, especially for polydisperse macromolecular systems, to distinguish between various conformation types; (5) analysis of macromolecular flexibility.

Linear dichroism spectroscopy of nucleic acids

This review will consider solution studies of structure and interactions of DNA and DNA complexes using linear dichroism spectroscopy, with emphasis on the technique of orientation by flow. The theoretical and experimental background to be given may serve, in addition, as a general introduction into the state of the art of linear dichroism spectroscopy, particularly as it is applied to biophysical problems.

Microscopic behaviour of DNA during electrophoresis: electrophoretic orientation

The study of the behaviour of DNA when subjected to electric fields poses several intriguing problems of fundamental physico-chemical importance. Electric field (Kerr effect) orientation of DNA in free solution as well as migration of DNA in gel electrophoresis are two well-established, but so far rather separate, research fields. Whereas the first one has been generally concerned with basic structural and dynamical properties of DNA (Charney, 1988), the second is closely related to techniques of molecular biology (for a review on DNA electrophoresis, see stellwagen 1987).

Permanent dipole moment of tRNA's and variation of their structure in solution

The structure of six different tRNA molecules has been analyzed in solution by electrooptical measurements and by bead model simulations. The electric dichroism measured as a function of the field strength shows that tRNA's are associated with substantial permanent dipole moments, which are in the range of 1 x 10(-27) cm(identical to 300 D; before correction for the internal directing field). Rotational diffusion time constants of tRNA molecules in their native state at 2 degrees C show a considerable variation. A particularly large value found for tRNA(Tyr) (50 ns) can be explained by its nine additional nucleotide residues. However, remarkable variations remain for tRNA molecules with the standard number of 76 nucleotide residues (tRNA(Phe) [yeast] 41.6 ns, tRNA(Val) [Escherichia coli] 44.9 ns, tRNA(Glu) [E. coli] 46.8 ns; tRNA(Phe) [E. coli] 48.3 ns). These variations indicate modulations of the tertiary structure, which may be due to a change of the L-hinge angle. Bead models are used to simulate both electric and hydrodynamic parameters of tRNA molecules according to the crystal structure of tRNA(Phe) (yeast). The asymmetric distribution of phosphate charges with respect to the center of diffusion leads, under the assumption of a constant charge reduction to 15% by ion condensation, to a theoretical dipole moment of 7.2 x 10(-28) cm, which is in reasonable agreement with the measurements. The dichroism decay curve calculated for tRNA(Phe) (yeast) is also consistent with the measurements and thus the structure in solution and in the crystal must be very similar in this case. However, our measurements also indicate that the structure of some other tRNA's in solution is different, even in cases with the same number of nucleotide residues.

Linear contour length dependence of electrical polarizability of nucleosomal DNA fragments: implications for the flexibility of DNA

The transient electric birefringence of monodisperse oligonucleosomal DNA ranging from 145 to 990 base pairs has been studied. The orientation of fragments can be described in terms of an induced dipole moment with a small contribution of a permanent dipole. The electrical polarizability delta alpha was found to increase linearly with the DNA contour length. This unexpected dependence might result from a bent structure of DNA already considerable for very short segments. The observed delta alpha values agree with a segmental orientation of rigid subunits of length 13-18 nm as estimated in the elastic model of DNA with a kink angle of about 41 degrees.