F. G. Diaz

HYDRO: a computer program for the prediction of hydrodynamic properties of macromolecules

HYDRO is a program for the calculation of sedimentation and diffusion coefficients, rotational relaxation times, and intrinsic viscosities of rigid macromolecules of arbitrary shape that are represented by bead models. Actually, HYDRO contains various FORTRAN callable subroutines that can be linked to the users own programs to account for variability of shape or flexibility. Some hints are given for the use of HYDRO in various situations.

Hydrodynamic interaction effects in the rheological properties of Hookean dumbbells in steady shear flow: a Brownian dynamics simulation study

Abstract In this paper we present a Brownian dynamics simulation study where we employ the algorithm of Ermak and McCammon including solvent flow in the calculation of the rheological properties of Hookean dumbbells in steady shear flow. We have also included the possibility of the excluded volume and we have studied several possibilities with and without hydrodynamic interactions (HI). When hydrodynamic interaction is rigorously treated, the intrinsic viscosity is found to increase. If the Rotne-Prager-Yamakawa HI tensor is used instead of the Oseen tensor, the changes in the material functions are quite small. On the other hand, excluded-volume interactions produce, as expected, an increase in the viscosity. This is so both with and without HI. Our results are compared with those of other works in which the HI tensor is pre-averaged or consistently averaged.

Calculation of the solution properties of flexible macromolecules: methods and applications

While the prediction of hydrodynamic properties of rigid particles is nowadays feasible using simple and efficient computer programs, the calculation of such properties and, in general, the dynamic behavior of flexible macromolecules has not reached a similar situation. Although the theories are available, usually the computational work is done using solutions specific for each problem. We intend to develop computer programs that would greatly facilitate the task of predicting solution behavior of flexible macromolecules. In this paper, we first present an overview of the two approaches that are most practical: the Monte Carlo rigid-body treatment, and the Brownian dynamics simulation technique. The Monte Carlo procedure is based on the calculation of properties for instantaneous conformations of the macromolecule that are regarded as if they were instantaneously rigid. We describe how a Monte Carlo program can be interfaced to the programs in the HYDRO suite for rigid particles, and provide an example of such calculation, for a hypothetical particle: a protein with two domains connected by a flexible linker. We also describe briefly the essentials of Brownian dynamics, and propose a general mechanical model that includes several kinds of intramolecular interactions, such as bending, internal rotation, excluded volume effects, etc. We provide an example of the application of this methodology to the dynamics of a semiflexible, wormlike DNA.

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.

Simulation of non-linear models for polymer chains in flowing solutions

Two non-linear bead and spring models are considered for the Brownian dynamics simulation of the behaviour of polymer chains in a dilute solution under shear or elongational flow. One of them is the HYBRID model whose springs are Hookean at low elongation, and beyond some spring length they follow a Morse potential with a given dissociation energy. This model is suitable for studying polymer fracture in strong flows. In this paper we describe the model and check that it has the proper behaviour in the two regions. The second model is a chain of finitely extensible, non-linear elastic (FENE) springs. Our simulations show several features of the FENE model that agree well with observation. In shear flow, the deformation of the FENE chain at high shear rate deviates from the square law followed at low shear, in agreement with some experiments. The model also predicts the typical shear-thinning, non-Newtonian behaviour of the shear viscosity. In elongational flows, the variation of the chain properties with the elongation rate shows a rather sharp increase at some critical rate that is reminiscent of the so-called coil-stretch transition.

Simulation of the rotational Brownian dynamics of a simple, segmentally flexible model: The elastic trumbbell

The rotational dynamics of a segmentally flexible model, the elastic trumbbell, has been studied using a Brownian dynamics simulation technique. The model is composed of three beads jointed by two bonds. A potential that is quadratic in the bending angle describes the partial flexibility of the model. The correlation analysis of the simulated trajectories gives rotational correlation functions, of which we have preferentially studied those of the second Legendre polynomial of the reorientation angle of the bond and end‐to‐end vectors. The relaxation times derived from these correlation functions are compared with those predicted by other treatments of the rotational dynamics of segmentally flexible macromolecules.

Brownian dynamics simulation of rotational correlation functions of simple rigid models

In this paper we investigate the ability of the Brownian dynamics simulation technique of Ermak and McCammon to evaluate rotational correlation functions of rigid hydrodynamic models. Concretely, we obtain from simulated trajectories the functions 〈Pi[cos θ(t)]〉, i=1,2 where Pi is the ith Legendre polynomial and θ(t) is the angle between two orientations, separated by time t, of a given vector. This function is closely related to the decay of fluorescence anisotropy and other time‐dependent electro‐optical properties. The simulation results are compared with exact results for these functions. We first consider dimers in a variety of conditions regarding the rigid constraint, the hydrodynamic interaction and the relative size of the two spheres. We next study bent trimers, for which the decays are typically multiexponential. In all cases we find that the simulated results of the correlation functions and the exact ones are in rather good agreement up to a time which is determined by the finite length of th...

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.