Intrinsic vescosity of a once-broken rod

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.

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.

Hydrodynamics of segmentally flexible macromolecules

Segmentally flexible macromolecules are composed of a few rigid subunits linked by joints which are more or less flexible. The dynamics in solution of this type of macromolecule present special aspects that are reviewed here. Three alternative approaches are described. One is the rigid-body treatment, which is shown to be valid for overall dynamic properties such as translational diffusion and intrinsic viscosity. Another approach is the Harvey-Wegener treatment, which is particularly suited for rotational diffusion. The simplest version of this treatment, which ignores hydrodynamic interaction (HI) effects, is found to be quite accurate when compared to a more rigorous version including HI. A third approach is the Brownian dynamics simulation that, albeit at some computational cost, might describe rigorously cases of arbitrary complexity. This technique has been used to test the approximations in the rigid-body and Harvey-Wegener treatments, thus allowing a better understanding of their validity. Brownian trajectories of simplified models such as the trumbbell and the broken rod have been simulated. The comparison of the decay rates of some correlation functions with the predictions of the two treatments leads to a general conclusion: the Harvey-Wegener treatment determines the initial rate, while the long-time behavior is dominated by the rigid-body relaxation time. As an example of application to a specific biological macromolecule, we present a simulation of an immunoglobulin molecule, showing how Brownian Dynamics can be used to predict rotational and internal dynamics. Another typical example is myosin. Literature data of hydrodynamic properties of whole myosin and the myosin rod are compared with predictions from the Harvey-Wegener and rigid-body treatments. The present situation of the problem on myosin flexibility is analyzed, and some indications are given for future experimental and simulation work.

Transport properties of rigid bent-rod macromolecules and of semiflexible broken rods in the rigid-body treatment. Analysis of the flexibility of myosin rod

The translational diffusion coefficients, rotational relaxation times and intrinsic viscosities of rigid bent rods, composed by two rodlike arms joined rigidly at an angle alpha, have been evaluated for varying conformation using the latest advances in hydrodynamic theory. We have considered semiflexible rods in which the joint is an elastic hinge or swivel, with a potential V(alpha) = 1/2Q alpha 2 with constant Q. Accepting the rigid-body treatment, we calculate properties of broken rods by averaging alpha-dependent values for rigid rods. The results are finally used to interpret literature values of the properties of myosin rod. Q is regarded as an adjustable parameter, and the value fitted is such that the average bending angle of myosin rod is approximately 60 degrees.

Differences in the electric birefringence of spectrin dimers and tetramers as shown by the fast reversing electric pulse method

The electric birefringence of purified spectrin has been examined in medium of low ionic strength at 20 degrees C and for electric fields smaller than 4 X 10(4) V m(-1), using the reversing electric pulse method. This technique allows study of the permanent and induced dipole electric moment of macromolecules more easily than in measurements using only rectangular pulses. We show that spectrin heterodimers and heterotetramers have different electro-optical properties. The relaxation time of the tetramer (7 microseconds) is significantly longer than that of the dimer (4.5 microseconds). Tetramers and dimers have also different polarizability parameters.

Human spectrin. V. A comparative electro-optic study of heterotetramers and heterodimers

The electrically induced birefringence of human spectrin heterotetramer and heterodimer solutions at 5 degrees C has been studied. 1. The steady-state birefringence, delta, was found to be approximately proportional to the electric field strength, E, when E greater than or equal to 0.2 kV/mm. For spectrin solutions the specific linear coefficient, delta/(E x c), therefore is a more relevant parameter for describing birefringence saturation behavior when E greater than or equal to 0.2 kV/mm than the commonly used Kerr constant. At 5 degrees C were measured delta/(E x c) = (27 +/- 5) x 10(-8)m4 x V(-1) x kg(-1) for heterodimers and heterotetramers. 2. At 5 degrees C both heterotetramers and heterodimers exhibited more than one birefringence relaxation time and the shortest of these was for both molecules found to be 4.2 +/- 1.0 microseconds. This indicates that the spectrin molecules are highly flexible. The birefringence build-up time for heterotetramers and heterodimers was found to be 20 +/- 7 microseconds and 15 +/- 5 microseconds, respectively.

Hydrodynamic properties of complex, rigid, biological macromolecules: theory and applications

Among the Various methods for characterizing macromolecules in solution, hydrodynamic techniques play a major role. Since the advent of the ultracentrifuge and the development of viscometric apparatus, sedimentation coefficients and intrinsic viscosities have been extensively used to learn about the size and shape of synthetic and biological polymers. More recently, refined techniques such as quasielastic light scattering, transient electric birefringence and fluorescence anisotropy decay have made it possible to obtain in a simple and rapid way quantitative information of high precision on the translational and rotational brownian dynamics of dissolved macromolecules.