Effects of the Bead‐Solvent Interaction on the Dynamics of Macromolecules, 1

Abstract

Summary: Hamiltonian dynamics and a chain model are used to study the dynamics of macromolecules immersed in a solution. From the Hamiltonian of the overall system, “macromolecule + solvent,” a master and a Fokker‐Planck equation are then derived for the phase‐space distribution of the macromolecule. In the Fokker‐Planck equation, all the information about the interaction among the beads of the macromolecule as well as the effects of the surrounding solvent is described by friction tensors, which are expressed in terms of the bead‐solvent interaction and the dynamic structure factor of the solvent. To explore the influence of the bead‐solvent potential on the dynamics of macromolecules, the friction tensors are calculated for a dumbbell molecule and for three choices of the interaction (Yukawa, Born‐Mayer, and Lennard‐Jones). Expressions are derived, in particular, for the friction tensor coefficients of the center‐of‐mass and the relative coordinates of the dumbbell. For the long‐term behaviour of the internal momentum autocorrelation function, moreover, an “algebraic decay” is found, in contrast to the (unphysical) exponential decay as known from phenomenological theory.

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

“…[19][20][21][22][23] For the three basic assumptions from above, the diffusion tensor contains all the information about the internal motion of the molecules. Within such a model, the macromolecules is taken as a chain of beads which are coupled to each other by some pairwise potential and surrounded by ͑a large number of͒ solvent particles.…”

“…͑1͒-͑3͒ in mind and by using the techniques of projection operators, now an equation of motion can be derived for the coordinate-space distribution function 22,42 ‫ץ‬ N ͕͑R a ͖;t͒ ‫ץ‬t ͑1͒-͑3͒ in mind and by using the techniques of projection operators, now an equation of motion can be derived for the coordinate-space distribution function 22,42 ‫ץ‬ N ͕͑R a ͖;t͒ ‫ץ‬t…”

“…[1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] For instance, the dynamic light scattering experiments have been carried out in order to describe the translational motion of the macromolecule, which determines the motion of the macromolecule as whole. [19][20][21][22][23] Apart from the translational motion of the molecules, their rotational properties have been studied by various authors, including the work of Wang and Pecora 24 on the restricted rotational diffusion of rigid rodlike molecule. 4 -11 To understand the properties of the macromolecules by means of theoretical methods, they are often treated in terms of a several number of molecular subsystems which are usually referred to as the beads of the macromolecule.…”

Hierarchical Order Parameters for Macromolecular Assembly Simulations. 1. Construction and Dynamical Properties of Order Parameters

“…This idea has resulted in the development of coarse-grained models for macromolecules and their assemblies. An incomplete list would include bead, , shape-based, rigid region decomposition, symmetry constrained, and curvilinear coordinate models, as well as Principal Component Analysis (PCA) and Normal Mode Analysis (NMA) guided approaches. − These models have been successful in investigating structural transitions in a very rich set of biomolecules including alanine polypeptides, ligand binding proteins, transmembrane proteins, , RNA segments, , and virus capsids of different symmetries. , However, they suffer from one or more of the following difficulties: (1) Characteristic variables are not slowly varying in time. (2) Nonlinear motions like macromolecular twist are not readily accounted for.…”

High-order correlation contributions to the friction of macromolecules in solution: A semi-phenomenological Fokker-Planck approach

“…To explore the effects of the solvent onto the dynamics of macromolecules, a Fokker-Planck-type equation (FPE) has been derived recently by us for the time evolution of the phase-space distribution function of a (N -bead) macromolecule [8,10]. In this FPE, all information about the interaction among the beads of the macromolecule as well as the effects from the surrounding solvent is described by means of semi-phenomenological friction tensors which are expressed in terms of the bead-solvent 68001-p1 interaction and the dynamical structure factor of the solvent [8]. Several typical bead-solvent interaction potentials were explored to analyze the dynamical behaviour in different environments [10].…”