Brownian dynamics simulation of rotational correlation functions of simple rigid models

Rotational Brownian dynamics of semiflexible broken rods

Using the Brownian dynamics simulation technique, we study the rotational dynamics of a semiflexible broken rod. We employ a suitable bead model with stiff springs between beads and strong forces opposing to bending, except at the joint where flexibility is variable. We consider mostly broken rods with equal arms. From the simulated Brownian trajectories we obtain the correlation function for the second order Legendre polynomial of the reorientational angle of the end-to-end vector and of the arm vector. These correlation functions are closely related to fluorescence anisotropy decay and electric birefringence decay, respectively. In the first case, the relaxation time for a completely flexible rod agrees with the Harvey-Wegener theory, and in the second, the longest relaxation time agrees well with that obtained from the rigid-body treatment over the whole range of flexibility. Furthermore, we discuss the relative importance of flexibility in both types of decay. Finally, we present results for a case with unequal arms, confirming the validity of the Harvey-Wegener theory and the rigid-body treatment.

Effects of the bead-bead potential on the restricted rotational diffusion of nonrigid macromolecules

The influence of the bead-bead interaction on the rotational dynamics of macromolecules which are immersed into a solution has been investigated by starting from the microscopic theory of the macromolecular motion, i.e., from a Fokker-Planck equation for the phase-space distribution function. From this equation, we then derived an explicit expression for the configuration-space distribution function of a nonrigid molecule which is immobilized on a surface. This function contains all the information about the interaction among the beads as well as the effects from the surrounding solvent particles and from the surface. For the restricted rotational motion, the dynamics of the macromolecules can now be characterized in terms of a rotational diffusion coefficient as well as a radial distribution functions. Detailed computations for the rotational diffusion coefficient and the distribution functions have been carried out for HOOKEAN, finitely extensible nonlinear elastic, and a DNA type bead-bead interaction.

Bead-model calculation of scattering diagrams: Brownian dynamics study of flexibility in immunoglobulin IgG1

We consider the calculation of the angular dependence of the scattering intensities for models composed of spherical elements of arbitrary size, in which some of the spheres may have a size close to that of the whole particle. This minimizes the number of spheres and makes it possible to use the same bead models for the prediction of scattering diagrams and hydrodynamics properties. A simple expression is employed for the scattering intensity. Particularly, we discuss the validity of some versions of the Debye scattering equation for bead models. The method could be used for any macromolecule either rigid or with conformational variability. The application of the method to a simple model for IgG1 shows that influence of flexibility in the scattering curve is stronger by the end of the first decade of decay and also shows that the range of linearity in the Guinier region is not a good method to characterize flexibility between arms, because it is very likely that experimental errors will hide the small differences between the extreme cases appreciated in our calculations.

Hydrodynamic study of flexibility in immunoglobulin IgG1 using Brownian dynamics and the Monte Carlo simulations of a simple model

A simple bead model is proposed for the antibody molecule immunoglobulin IgG1. The partial flexibility of the hinge is represented by a quadratic potential associated to the angles between arms. Conformational and hydrodynamic properties are calculated using Monte Carlo (rigid-body) and Brownian dynamics simulations. Comparison of experimental and calculated values for some overall properties allows the assignment of dimensions and other model parameters. The Brownian dynamics technique is used next to simulate a rotational correlation function that is comparable with the decay of fluorescence emission anisotropy. This is done with varying flexibility at the hinge. The longest relaxation time shows a threefold decrease when going from the rigid Y-shaped conformation to the completely flexible case. The calculations are in good agreement with the decay times observed for IgG1. A flexibility analysis of the latter indicates that a variability of +/- 55 degrees (standard deviation) in the angle between the Fab arms.