Fluctuation analysis in small chemically reacting systems

A theory of noise fluctuations is developed which is applicable to systems of any size in which unimolecular or bimolecular reactions are occurring. The main difference between small and large reacting systems is that in the former the probability of finding a particle in a particular state does not obey a Gaussian distribution, but satisfies a distribution which reflects the mechanism of the chemical reaction. This difference is reflected in the main result of the theory: an autocorrelation function that is expressible as a sum of exponentials, the amplitudes of which are explicit functions of the moments of the distribution. Thus, by using small systems, the autocorrelation function,in principle, allows the elucidation of reaction mechanisms. Numerical simulations indicate that for reacting systems having ten or fewer particles, the deviation of the autocorrelation function from a single exponential should be easily detectable, and that estimates of the first four moments of the distribution should be possible. Accurate inference of the distribution, however, will require further mathematical and experimental advances.     

Sizing of vesicles by electric birefringence

A study of the transient, electrically induced birefringence of aqueous suspensions of phospholipid vesicles (liposomes) has indicated a rapid and sensitive method of measuring the size and electrical polarizability anisotropy of these entities.     

Analysis of chemically reacting systems by sedimentation-diffusion equilibrium.

A novel procedure to evaluate equilibrium constants from sedimentation-diffusion equilibrium data of analytical ultracentrifuge runs is proposed. It is shown that, by comparison of a reacting mixture at chemical equilibrium with a non-reacting but equally composed one, the sum of the mean concentrations of the reaction products can immediately be taken from optical absorption or from interferometric measurements. In most but not in all cases the use of stacked double-sector centerpieces is required.     

Transient electric birefringence studies of xanthan solutions

Transient electric birefringence studies have been performed on heat denatured xanthan in 4 m urea. The induced birefringence was positive, the Kerr law was obeyed at low field amplitudes and the birefringence saturated at high fields. The orientation mechanism appears to be mainly induced dipolar in character and the magnitude of the induced dipole moment can be explained on the basis of counterion polarization. The molecules behave as independent rods of mean length 0.65 μm with no evidence for ‘hindered rotation’ in moderately concentrated solutions. The molecular rigidity is attributed to extension of the polyanion due to charge charge repulsions or steric hindrance due to the side chains.     

Determination of proteoglycan dimer geometry by electric birefringence

Proteoglycan solutions contain a certain amount of dimer whose presence may be of significance in arthrotic disorders. By measuring the multicomponent electric birefringence transients of these solutions, and analysing the rotary diffusion coefficients in terms of a recently published theory for bent rod-like molecules, the geometry of the dimer has been determined.     

Analysis of DNA bending by transient electric birefringence

Transient electric birefringence has been used to analyze DNA bending in six restriction fragments containing 171, 174, 207, 263, 289, and 471 bp in three different low ionic strength buffers. The target fragments contain sequences corresponding to the apparent bend centers in pUC19 and Litmus 28, previously identified by the circular permutation assay (Strutz, K.; Stellwagen, N. C. Electrophoresis 1996, 17, 989-995). The target fragments migrate anomalously slowly in polyacrylamide gels and exhibit birefringence relaxation times that are shorter than those of restriction fragments of the same size, taken from nonbent regions of the same plasmids. Apparent bend angles ranging from 30 degrees to 41 degrees were calculated for the target fragments by tau-ratio method. The bend angles of four of the target fragments were independent of temperature from 4 degrees C to 20 degrees C, but decreased when the temperature was increased to 37 degrees C. The bend angles of the other two target fragments were independent of temperature over the entire range examined, 4 degrees -37 degrees C. Hence, the thermal stability of sequence-dependent bends in random-sequence DNA is variable. The bend angles of five of the six target fragments were independent of the presence or absence of Mg2+ ions in the solution, indicating most of the target fragments were stably bent or curved, rather than anisometrically flexible. Restriction fragments containing 219 and 224 bp, with sequences somewhat offset from the sequence of the 207 bp fragment, were also studied. Comparison of the tau-ratios of these overlapping fragments allowed both the bend angle and bend position to be independently determined. These methods should be useful for analyzing sequence-dependent bending in other random-sequence DNAs.     

Transient electric birefringence of agarose gels. I. Unidirectional electric fields

The orientation of agarose gels in pulsed electric fields has been studied by the technique of transient electric birefringence. The unidirectional electric fields ranged from 2 to 20 V/cm in amplitude and 1 to 100 s in duration, values within the range typically used for pulsed field gel electrophoresis (PFGE). Agarose gels varying in concentration from 0.3 to 2.0% agarose were studied. The sign of the birefringence varied randomly from one gel to another, as described previously [J. Stellwagen & N. C. Stellwagen (1989), Nucleic Acids Research, Vol. 17, 1537–1548]. The sign and amplitude of the birefringence also varied randomly at different locations within each gel, indicating that agarose gels contain multiple subdomains that orient independently in the electric field. Three or four relaxation times of alternating sign were observed during the decay of the birefringence. The various relaxation times, which range from 1 to ～ 120 s, can be attributed to hierarchies of aggregates that orient in different directions in the applied electric field. The orienting domains range up to ～ 22 μm in size, depending on the pulsing conditions. The absolute amplitude of the birefringence of the agarose gels increased approximately as the square of the electric field strength. The measured Ker constants are ～ 5 orders of magnitude larger than those observed when short, high-voltage pulses are applied to agarose gels. The increase in the Kerr constants in the low-voltage regime parallels the increase in the relaxation times in low-voltage electric fields. Birefringence saturation saturation curves in both the low- and high-voltage regimes can be fitted by theoretical curves for permanent dipole orientation. The apparent permanent dipole moment increase approximately as the 1.6 power of fiber length, consistent with the presence of overlapping agarose helices in the large fiber bundles orienting in low-voltage electric fields, the optical factor is approximately independent of fiber length. Therefore, the marked increase in the Kerr constants observed in the low-voltage regime is due to the large increase in the electrical orientation factor, which is due in turn to the increased length of the fiber bundles and domains orienting in low-voltage electric fields. Since the size of the fiber bundles and domains approximates the size of the DNA molecules being separated by PFGE, the orientation of the agarose matrix in the applied electric field may facilitate the migration of large DNA molecules during PFGE. © 1994 John Wiley & Sons, Inc.     

Study of hyaluronic acid flexibility by electric birefringence.

Transient-electric-birefringence experiments were conducted on four samples of hyaluronic acid over the molecular-mass (M) range 5 X 10(4)-4 X 10(6) in dilute aqueous solution. The geometrical, optical and electrical characteristics were monitored via the rotary relaxation times, optical-polarizability antisotropies and electrical polarizabilities respectively. Each indicates the molecular conformation to be consistent with some degree of rigidity at low M but that this does not persist at high M. The molecules do not become true random coils, but are best characterized in terms of a persistence length of 20 nm or 20 disaccharide units.     

Rigidity of myosin and myosin rod by electric birefringence

The rotational relaxation times of rabbit myosin and myosin rod have been determined by electric birefringence measurement. The relaxation time of myosin measured in 10 mM pyrophosphate buffers in a pH range of 7.6–9.5 was found to have substantial concentration and pH dependences. The infinite-dilution limit of the relaxation time, τ°, was determined as 38 ± 2 μs, and it was found to be independent of pH. For myosin rod, a possible thermally induced conformational change was investigated in a temperature range of 1–43°C. The rotational relaxation time of myosin rod shows no clear indication of conformational change in this temperature range, and the radius of gyration measurement by light scattering was shown to be consistent with this observation. The steady-state birefringence, however, decreases substantially above around 40°C. This, the myosin rod appears to be only slightly flexible even at physiological temperature, but the possibility of a “melting” or “hinging” of the myosin rod cannot completely be ruled out on the basis of these experiments.     

Transient electric birefringence study of highly dilute agarose solutions

In order to characterize the first step of agarose gelation, highly dilute solutions (2·10^?3 to 0.5 g/L) have been studied by means of the transient electric birefringence technique. The field-free decay curves of the birefringence are well described by a stretched-exponential B(t) ≈ exp(?t/τ)^β; the value of the exponent β is close to 0.5 whatever the agarose concentration. The suspended particles observed by electron microscopy present a rod-like shape with a constant diameter (～50 Å), without any branching; they are polydisperse with a distribution of lengths approximately exponential. The mean length of these fibers, deduced from their mean rotational diffusion coefficient, is proportional to the 0.37 power of the agarose concentration in the solution. Furthermore, these particles possess a strong permanent electrical dipole confirming the side-to-side arrangement of helices into bundles; this dipole is roughly proportional to the particle length, indicating a self-similarity in the unidirectional growth of the agarose fibers, even when approaching the gelling concentration.     

Low field electric birefringence study of monovalent cation-DNA interactions

The effects of monovalent cations on DNA have been studied using static and dynamic electric birefringence. Kerr's law is obeyed in a limited E range (<30 Vcm_?1) and the steady state birefringence values are close for the different cations. The birefringence kinetics have been analysed in terms of three relaxation times. On a semilogarithmice plot of Δn(t), the tail of the curve is linear over a wide range of time for Na⁺, K⁺, NH₄⁺ and Li⁺. Only for Cs⁺ solution is no linear part found and a much longer relaxation time is determined. This only contributes a small part of the total birefringence. With Cs⁺ this contribution is more field-dependent than for the other cations and we observe a larger molecular flexibility. On the other hand, with Li⁺ a greater stiffness of the DNA molecule appears. The electrical polarizabilities anisotropies decrease in the order: Cs⁺ >NH⁺₄ >K⁺ >Na⁺ >Li⁺. There are no significant differences in the optical anisotropy factors.     

Steady-state and transient electric birefringence of solutions of bent-rod macromolecules

We first calculate the steady-state birefringence, expressed in the form of specific Kerr constant, K_sp, of rigid, bent-rod macromolecules. Equations are derived for K_sp as a function of the geometric and electro-optical parameters. We also consider flexibly hinged rods and evaluate K_sp for them by averaging over the angle between the two arms, ?. Next, we turn to the time decay of the electric birefringence. The decay function for rigid bent rods is a sum of three exponential terms, and a procedure for their calculation is indicated. We observe that single-exponential decays can be found for ? > 90° or ? < 60°, in spite of the high electro-optical and hydrodynamic anisotropy of the macromolecule. Special attention is paid to the case of rods with equal arms.     

Investigation of the flexibility of DNA using transient electric birefringence

In the preceding article, a Monte Carlo analysis was presented which provides a quantitative numerical relationship between the rotational diffusion coefficients, as measured by the decay of optical anisotropy following an electric field pulse, and the flexibility (persistence length) of short, wormlike chains. In the present article, the results of the foregoing analysis are applied to the observed rates of decay of birefringence for a series of sequenced DNA fragments ranging in size from 104 to 910 base pairs. Under the conditions used in this study, the DNA fragments exist as native, duplex molecules. Furthermore, conditions are defined in which the observed relaxation times are not dependent on DNA concentration, field strength, or the duration of the pulse. It is pointed out that the ionic atmosphere associated with a wormlike polyion does not exert any significant (direct) influence on the rotational diffusion of the polyion and, therefore, that the rotational relaxation times are a true measure of the configurations of the DNA molecules in solution. Moreover, excluded-volume effects are shown not to be significant for the moderately short molecules employed in this study. The major conclusion of this study is that there is no strong ionic strength dependence of the persistence length for ionic strengths above 1 mM and that the persistence length, under conditions where electrostatic contributions are negligible, is approximately 500 Å. For ionic strengths significantly lower than 1 mM, electrostatic contributions to the stiffness of DNA become significant.     

Investigating the permanent electric dipole moment of beta-lactoglobulin fibrils, using transient electric birefringence

Amyloid fibrils, which are polymeric assemblies of protein molecules, have been intensively studied on a structural level, yet due to complications such as the disorder within the molecules, several aspects of their structure remain mysterious. Similarly, the kinetics of assembly are not well understood. Here we investigate the electric dipole moment of beta-lactoglobulin fibrils, a model amyloid fibril system, by applying the technique of transient electric birefringence. This moment appears to be large, and comparable to the total moment of the constituent protein monomers if they were joined in a chain, head-to-tail, without changing conformation, suggesting an ordered joining of monomers in the fibril. Such an ordered assembly may have implications for the assembly mechanism of beta-lactoglobulin fibrils in particular, and amyloid fibrils in general.