SynopsisThe fluorescence anisotropy of a general rigid body is formally the sum of five exponentials. We show that, to a high degree of approximation, there are relationships between the five time constants. As we define the time constants here, T I 2 75, ~2 z 73, and ~1 -l + 3~4 -l = 4 T 2 -l .In practical cases, a t most only three exponentials will be observed, and, of these, only two are independent.Using a numerical integration procedure, Perrin's equations for the rotational and translational diffusion of a general ellipsoid are solved. Rotational friction coefficients, frictional ratio, rotational relaxation times, and the five exponential terms in the fluorescence anisotropy are tabulated as functions of the axial ratios of the ellipsoid.In principle, the three axes of a general ellipsoid may be determined by a simultaneous measurement of the anisotropy and the linear diffusion constant. We examine, and illustrate, the effect of experimental error on such a determination. * Since we base our work on Perrin's equations, to avoid confusion we note here that Perrin's definition of Di differed by a factor of y4 from that used by W e b e P and all later workers. The difference is discussed on p. 179 of Memming's paper (see Ref. 14). Perrin's Eqs. (90) and (91) are independent of this definition and therefore agree with modern usage.

SynopsisThe intensity of Raman scattering from the various Raman active vibrations of poly-(riboadenylic acid), poly(rihocytidy1ic acid), poly(ribouridy1ic acid), and poly(riboinosinic arid) in moderately dilute solutions were examined as the temperature was changed to alter their conformation. It was found that certain highly intense, highly polarized Raman bands from the totally symmetric, i.e., in-plane, ring vibrations of the nucleic acid bases become less intense as the chains become more ordered in solution. Since these vibrations occur a t frequencies which are markedly different for each type of base, Raman spectroscopy appears to provide a new method for the characterizing of the average conformation of each of the bases in solution. A theory for the resonant Raman effect is given in which it is shown that a decrease in resonant Raman intensity is to be expected if one obtains a decrease in the intensity of the corresponding ultraviolet absorption band with which the incident light is resonant. If i t is assumed that certain Raman bands derive their intensity predominantly from the first few ultraviolet absorption intensities, then a qualitative explanation of our observed conformational dependence of the ordinary Raman intensities can be obtained.

Low-frequency Raman bands (lower than 50 cm-') exist in certain proteins. They are dependent upon the conformation of the protein molecule, but are relatively independent of the form of the sample, i.e., whether it is a film or a crystal.Low-frequency Raman spectra were obtained from samples of a-chymotrypsin that had been prepared in several ways. A peak at about 29 cm-' was found for all samples except the one that had been denatured with sodium dodecyl sulfate. Such low frequency motions must arise from vibrations that involve all, or very large portions, of the protein molecule.In the past few years the technique of laser Raman spectroscopy has been used with considerable success to obtain the Raman active vibrations of several proteins (1-4). However, if one examines the published spectra, it is apparent that it has been impossible in the past to obtain the Raman bands in proteins that lie below 150 cm-'. The reason for this is that the scattering due to the Rayleigh component is too large for a double-grating monochromator to discriminate against. Recently, in this laboratory, we have shown how to obtain Raman spectra only a few wave numbers from the exciting line on synthetic polymers, such as polyethylene and poly-i-alanine, by the iodine filter technique (5-7) and a Spex double-grating monochromator. More recently, we have also found it possible to obtain these low frequency bands using a Cary triple-grating monochromator. For the work reported here, we have used both of these instruments and have obtained equivalent results on each. This has been of the greatest help in elimination of the possibility of experimental artifacts. From our work with these instruments it is possible to show, for the first time, that definite low-frequency motions exist in many common proteins and that these vibrations appear to be sensitive to the conformation of the protein. As we will discuss below, such low-frequency motions must arise from vibrations that involve either all or very large portions of the protein molecule. Thus, it appears from our measurements that large portions of the protein molecule are constantly undergoing a coherent periodic vibration. The existence of such vibrations is of considerable interest even though the exact assignment of the motion is not possible at present.Figs. la and b show the low-frequency Raman spectra of samples of a-chymotrypsin that were prepared in several ways. In every case, except the sample that had been denatured with SDS, a pronounced peak at about 29 cm-' is found. It is apparent that there is some splitting of the peak in the single crystal and also some slight change in the shape of the peak with deuteration and acylation. However, upon denaturation with SDS the peak at 29 cm-' vanishes. Rather intense Raman scattering throughout the region of 20-150 cm-' is observed on the denatured material, but it is broad and structureless-a fact that probably reflects the decrease in the order of the protein conformation.The fact that this low-frequency band is dependent ...

Ultrafast, laser-induced pH jump with time-resolved photoacoustic detection has been used to investigate the early protonation steps leading to the formation of the compact acid intermediate (I) of apomyoglobin (ApoMb). When ApoMb is in its native state (N) at pH 7.0, rapid acidification induced by a laser pulse leads to two parallel protonation processes. One reaction can be attributed to the binding of protons to the imidazole rings of His24 and His119. Reaction with imidazole leads to an unusually large contraction of -82 +/- 3 ml/mol, an enthalpy change of 8 +/- 1 kcal/mol, and an apparent bimolecular rate constant of (0.77 +/- 0.03) x 10(10) M(-1) s(-1). Our experiments evidence a rate-limiting step for this process at high ApoMb concentrations, characterized by a value of (0. 60 +/- 0.07) x 10(6) s(-1). The second protonation reaction at pH 7. 0 can be attributed to neutralization of carboxylate groups and is accompanied by an apparent expansion of 3.4 +/- 0.2 ml/mol, occurring with an apparent bimolecular rate constant of (1.25 +/- 0.02) x 10(11) M(-1) s(-1), and a reaction enthalpy of about 2 kcal/mol. The activation energy for the processes associated with the protonation of His24 and His119 is 16.2 +/- 0.9 kcal/mol, whereas that for the neutralization of carboxylates is 9.2 +/- 0.9 kcal/mol. At pH 4.5 ApoMb is in a partially unfolded state (I) and rapid acidification experiments evidence only the process assigned to carboxylate protonation. The unusually large contraction and the high energetic barrier observed at pH 7.0 for the protonation of the His residues suggests that the formation of the compact acid intermediate involves a rate-limiting step after protonation.

Chromatin core particles containing 146 base pairs of DNA have been found to undergo a single defined transition below 10 mM ionic strength as studied by both sedimentation velocity and tyrosine fluorescence anisotropy. A method is described for the preparation of such core particles from chicken erythrocytes with greater than 50% yield.

We report dynamic fluorescence anisotropy measurements on the purified dityrosine derivative of calmodulin which was generated during UV irradiation of Ca2+-containing solutions of bovine brain calmodulin [Malencik, D. A., & Anderson, S. R. (1987) Biochemistry 26, 695]. Measurements were made by using a high repetition rate picosecond laser source combined with a microchannel plate photomultiplier. This permits the collection of very low noise anisotropy curves with essentially no convolution artifact. Measured anisotropies at high calcium concentrations are monoexponential, and at 20 degrees C, we recover a correlation time of 9.9 ns. When the temperature is varied from 4.8 to 31.8 degrees C, the recovered correlation time is proportional to the viscosity and inversely proportional to the absolute temperature, behavior expected for the rotational diffusion of a macromolecule whose conformation is independent of the temperature. The correlation time is compared to the theory describing the rotational diffusion of a dumbell. At high calcium concentrations, the cross-linked calmodulin is elongated and has a length equal or nearly equal to that predicted by X-ray crystallographic results. In the absence of calcium, the molecule becomes highly compact and exhibits significant segmental motion. Intermediate calcium ion concentrations result in an intermediate degree of elongation and segmental motion. A small increase in the measured rotational correlation time of calmodulin upon the binding of melittin and mastoparan indicates that these peptides cause no major changes in the elongation of the molecule. When the cross-linked calmodulin is bound to troponin I, the complex rotates as a unit with a single rotational correlation time of 22 ns.

We have developed an instrumental setup that uses transient absorption to monitor protein folding/unfolding processes following a laser-induced, ultrafast release of protons from o-nitrobenzaldehyde. The resulting increase in [H(+)], which can be more than 100 microM, is complete within a few nanoseconds. The increase in [H(+)] lowers the pH of the solution from neutrality to approximately 4 at the highest laser pulse energy used. Protein structural rearrangements can be followed by transient absorption, with kinetic monitoring over a broad time range (approximately 10 ns to 500 ms). Using this pH-jump/transient absorption technique, we have examined the dissociation kinetics of non-native axial heme ligands (either histidine His26 or His33) in GuHCl-unfolded Fe(III) cytochrome c (cyt c). Deligation of the non-native ligands following the acidic pH-jump occurs as a biexponential process with different pre-exponential factors. The pre-exponential factors markedly depend on the extent of the pH-jump, as expected from differences in the pK(a) values of His26 and His33. The two lifetimes were found to depend on temperature but were not functions of either the magnitude of the pH-jump or the pre-pulse pH of the solution. The activation energies of the deligation processes support the suggestion that GuHCl-unfolded cyt c structures with non-native histidine axial ligands represent kinetic traps in unfolding.

Photoactivatable caged protons have been used to trigger proton transfer reactions in aqueous solutions of acetate, glutamate, and poly-L-glutamic acid, and the volumetric and enthalpic changes have been detected and characterized by means of time-resolved photoacoustics. Neutralization of carboxylates in aqueous solutions invariably results in an expansion of the solution due to the disappearance of two charges and is accompanied by little enthalpic change. The reactions occur with thermally activated, apparent bimolecular rates on the order of 10(10) M(-1)s(-1). In the case of aqueous solutions of poly-L-glutamic acid at pH around the pK(a) of the coil-to-helix transition, diffusional binding of a proton by carboxylates is followed by a sequential reaction with rate 1.06 (+/- 0.05) x 10(7)s(-1). This step is not thermally activated in the temperature range we have investigated and is likely related to local formation of hydrogen bonds near the protonation site. This structural event may constitute a rate-limiting step in helix propagation.