Ligand-induced domain movement in pyruvate kinase: structure of the enzyme from rabbit muscle with Mg2+, K+, and L-phospholactate at 2.7 A resolution.

The structure of rabbit muscle pyruvate kinase crystallized as a complex with Mg2+, K+, and L-phospholactate (L-P-lactate) has been solved and refined to 2.7 A resolution. The crystals, grown from solutions of polyethylene glycol 8000 at pH 7.5, belong to the space group P2(1) and have unit cell parameters a = 144.4 A, b = 112.6 A, c = 171.2 A, and beta = 93.7 degrees. The asymmetric unit contains two tetramers. The crystal structure reveals that the eight subunits within the asymmetric unit adopt several different conformations. These conformations are characterized by differences in the relative positions of protein domains A and B, resulting in different degrees of closure of the active site cleft that occupies the interface between these two domains. The global conformational differences may be described as rotations of the B domain with respect to the (beta/alpha)8-barrel of the A domain. Carbon atoms of the backbone in domain B rotate >20 degrees from the most open to the most closed subunit. The different conformations among subunits within the asymmetric unit are accompanied by 3-3.8 A shifts in the position of Mg2+ and a significant change in the orientation of the phenyl ring of Phe 243. In all of the subunits, Mg2+ coordinates to the protein through the carboxylate side chains of Glu 271 and Asp 295. In the subunit having the most closed conformation, Mg2+ also coordinates to the carboxylate oxygen, the bridging ester oxygen, and a nonbridging phosphoryl oxygen of L-P-lactate. Mg2+ to L-P-lactate coordination is missing in subunits exhibiting a more open conformation. K+ coordinates to four protein ligands and to a phosphoryl oxygen of the L-P-lactate. The position and liganding of K+ are unaffected by the different conformations of the subunits. The side chain of Arg 72, Mg2+, and K+ provides a locus of positive charge for the phosphate moiety of the analog in the closed subunit.

Dielectric behavior of polyelectrolytes. VI. Dynamic response of cylindrical biopolymers to electric fields.

The time dependence of the orientation of a cylindrical biopolymer and the configuration of its counterion complement in the presence of an external electric field is found by solving a model forced diffusion equation. The solution is a high temperature expansion in the external field strength and is used to predict the nature of the dielectric relaxation and the dynamic Kerr effect for such systems. Specific application is made to the dynamic Kerr effect of a DNA oligomer for which experimental data appear in the literature. The analysis yields a value for the surface diffusion coefficient of a sodium ion on DNA at 20 degrees C of 3.8 x 10(-10) m2 s-1.

Dielectric behavior of polyelectrolytes. IV. Electric polarizability of rigid biopolymers in electric fields.

The equilibrium Kerr effect of a system of mobile charges constrained to the surface of biomacromolecules is calculated. Cylindrical and spherical geometries are considered. For the cylinder we determine the anisotropy of electric polarizability as a function of length, temperature, and number of charged species in the low-field regime, and the fraction of the maximum induced dipole in the field direction for higher electric fields. The results are compared to experimental data for DNA oligomers taken from the literature. With spherical geometry we calculate the fractional induced dipole moment as a function of electric field strength and from this deduce the orientation function. The field dependence of the orientation function is compared to experimental data in the literature for bovine disk membrane vesicles.

Dielectric behavior of polyelectrolytes. III. The role of counterion interactions.

The role of the Coulomb forces between the counterions on the surface of polyelectrolytes on the dielectric response is analyzed. An estimate of the maximum dielectric increment (as a function of the number of counterions) is found as a function of the molecular length. The minimum-energy configuration of the counterions on a cylinder is found to be a double helix, suggesting the fundamental importance of electrostatic interactions in determining structure. Solutions of the dynamical equations for a few counterions indicate that a single mode dominates the relaxation which is enhanced by the inter-ion repulsions. A lower bound is found for this mode based on analysis of the system response for short lengths. Sum rules for the rates and amplitudes of the dipolar correlation function are derived and lead to an upper bound for the rate of the dominant mode. These bounds approach one another for the parameters characteristic of restriction fragments of DNA. This permits a prediction of the magnitude and time scale of the dielectric response.

Dielectric behavior of polyelectrolytes II. The cylinder.

The dipolar correlation function for a system of coupterions diffusing on the surface of a polyelectrolyte cylinder is computed. The influence of screened coulombic repulsions on the dielectric increment is determined. Dissociation and reassociation of the counterions to the cylinder is treated microscopically and the coupled bulk diffusion is solved in the presence of the Poisson-Boltzmann potential. It is found that the correlation function contains a small, fast decaying, molecular weight independent part arising from diffusion around the cylinder and a large, slowly decaying, molecular weight dependent part arising from diffusion along the cylinder axis. The dissociation-reassociation kinetics can play a large, possible dominant, role in determining the relaxation rates.