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In two previous studies [J. Chern. Phys. 91, 1287 95, 1234] we had examined the dynamics of coupled, internal translational, and rotational motions in a rigid or pseudorigid N-sphere macromolecular model using the rotational-translational Brownian dynamics algorithm of Dickinson et af. [J. Chern. Soc. Faraday Trans. 2 81, 5.,91 (1985)]. In the present study, those works are generalized to include all possible internal tfexible motions in an N-sphere macromolecular model. In general, for the N-sphere system there are 6(N-1) degrees of configurational freedom, although not all modes may be active in any particular application. Using the language of small oscillation theory, the deviations in the generalized coordinates associated with the "joints" connecting the spheres to one another are described in terms of quadratic potentials. From these potentials, the components of the generalized forces (torques and forces) are obtained for subsequent use in the Brownian dynamics algorithm. The degree of flexibility for any particular mode in the Nsphere system can be controlled by a single constant in the associated quadratic potential function. By taking the appropriate limits of these constants, the complete range of flexibility, viz., from "torque (or force)-free" to "rigid" can be approximately realized at any point in the N-sphere system. The model given is, therefore, capable of simulating all types of macromolecular motions. As a specific example, we studied the linear elastic rotator, where all modes (translational and rotational) are constrained except for rotations about the line of center of the spheres. Brownian dynamics results expressed in terms of rotational correlation functions were in good agreement with analytical solutions obtainable for this highly symmetric system. The algorithm given here is believed to be particularly useful in the study of the dynamics of biological macromolecules where "flexibility" is often critical to the functionality of the macromolecule [

The problems of the gas dynamic interactions of two ber) flows. For intermediate and large Knudsen numspherical particles and a single spherical particle with a ber (free-molecule) flows, these functions are only plane wall are reviewed here. The resistance and mobilknown in their asymptotic limit of infinitely large interity functions that describe the relationship between the particle or particle-wall separation distances (isolated forces and torques acting on the spheres with their particles). Potentially useful analytical and computatranslational and angular velocities are summarized for tional methods to treat these regimes are also reviewed. continuum and near-continuum (small Knudsen num-

The problem of the hydrodynamic interaction of two unequal-sized spheres in a slightly rarefied gas is treated following the singular perturbation scheme of Sone & Onishi (1978), valid at small, but finite, particle Knudsen numbers. In this method the solution to the linearized BGKW transport equation governing the gas molecular motion consists of two parts: one describing a Knudsen layer where the actual microscopic boundary conditions are applied and the other describing a Hilbert region where the Stokes equations of continuum hydrodynamics hold. The Knudsen-layer solution establishes the ‘slip’ boundary conditions for the Stokes equations. Here we clearly distinguish between particle ‘slip’ due to the type of boundary conditions and particle ‘slip’ due to lengthscale effects as measured by the Knudsen number. The present analysis has been carried out to first order in particle Knudsen number for the case of diffuse reflective molecular boundary conditions. General relationships between the first- and zero-order velocity fields, both of which are written in the form of Lamb's (1932) solution to the Stokes equation, are established. It is illustrated how these general relationships can be used to determine the force and torque acting on a single sphere translating and rotating in a slightly rarefied gas. Finally, we have treated the two-sphere problem in a slightly rarefied gas using the twin multipole expansion method of Jeffrey & Onishi (1984). Here again, general relationships are established between the solutions of the first-order fluid velocity field and the zero-order velocity field, the latter being shown to recover Jeffrey & Onishi's results for stick boundary conditions. These general relationships are subsequently used to determine the complete resistance and mobility matrices of the two-sphere system. The symmetric properties of the resistance and mobility matrices are demonstrated for slip boundary conditions, in agreement with the general proof of Landau & Lifshitz (1980) and Bedeaux, Albano & Mazur (1977).

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A former investigation [R. Ying and M. H. Peters, J. Chem. Phys. 91, 1287 (1989)] on the rotational dynamics of rigid and partially flexible macromolecules in solution by means of Brownian dynamics simulation methods is extended to a trimer or three-body macromolecular model. We present expressions for the torque constraints in rigid and semirigid trimer systems that allows for a comprehensive simulation of the translational, rotational, and coupled translational–rotational motions of the three interacting spherical Brownian particles comprising the trimer (trumbell). The torque constraint expressions are verified by comparisons of the Brownian dynamics simulation results to exact analytical results for a rigid trimer system (Appendix). Computer simulations and analytical solutions for the rigid trimer system indicate that the inclusions of rotational motions of the model’s elements can have an appreciable effect on macromolecular dynamics. Macromolecular flexibility can also be easily introduced into the model through varying the parameters of the torque and force constraint expressions. Extensions to an N-body macromolecular model are also outlined based on the trimer system studied here.

This work investigates the rotational dynamics of rigid and partially flexible macromolecules in solution by means of Brownian dynamics simulation techniques. In a previous study by Diaz et al. [J. Chem. Phys. 87, 6021 (1987)] on the rotational correlation functions of rigid models, the effect on rotational dynamics from pure rotations of the model’s elements has been neglected due to the difficulty of introducing rotational constraints in the simulations. We present expressions for rotational constraints in a rigid dimer system, which makes it possible to completely describe the translational, rotational, and coupled translational–rotational motions for interacting spherical Brownian particles by employing the generalized algorithm of Dickinson et al. [J. Chem. Soc. Faraday Trans. 2 81, 591 (1985)]. Theoretical studies indicate, and our simulation calculations confirm, that the pure rotational effects are appreciable. The torque constraint expressions are verified by comparison of the simulation results to the exact analytical results for the rigid dimer system. The torque constraint expressions also allow us to examine the effects of flexibility on the rotational correlation functions for a dimer system.