Diffusion coefficients of segmentally flexible macromolecules with two subunits: A study of broken rods

Abstract

SynopsisA general treatment for the solution dynamics of segmentally flexible macromolecules having two subunits is presented. Bead modeling allows for a complete inclusion of hydrodynamic interactions in this treatment. "he finite size of the beads is also considered, so that it is therefore possible to account properly for torsional motions of the subunits. Expressions for the components of the resistance matrix are derived. From them, the translational and rotational diffusion coefEcients can be calculated. Distinction is made between hinged macromolecules, whose only internal motion is bending, and swivel-jointed macromolecules, for which torsions of the subunits are also allowed. Numerical results are presented for broken rods with the two types of flexibility.The effects of hydrodynamic interaction between arms of broken rods are about 25% for translation and under 10% for rotation. These findings give support to the treatments of Harvey, Wegener, and co-workers in which interactions were neglected. The rotational dynamics of hinged and swivel-jointed rods are compared. Although there are differences in the short-time behavior, the longest relaxation time is the same for the two cases. Finally, the validity of Wegener's rotational diffusion constants is discussed.

Hydrodynamics of segmentally flexible macromolecules

“…Instead of the nine degrees of freedom of the swivel-jointed rod, the hinged rod has only seven, of which six are those proper for a rigid particle, and the remaining one is that corresponding to bending in the particle's plane. Mellado et al (1988) have shown that the Di, coefficient of the hinged rod is the same as that for the swiveljointed rod. However, Dout differs appreciably, and is not nearly constant as in Fig.…”

“…1983;Garcia de la Torre etal. 1985;Mellado et al 1988). The Wegener treatment has been presented for the most general case of a particle with any number of segments, which must be allowed to undergo any type of internal motion• The treatment of Harvey has been presented for the particular case of two segments and one joint which can act either as a universal swivel, or as a hinge allowing only bending (in-plane flexing) but not torsions.…”

“…This is easily done for the simplest case of two subunits: one would calculate the properties as a function of a, and the average is expressed as a particular case of Eq. Mellado et al (1988), with hydrodynamic interaction (HI) (continuous curves) and without HI (dashed curves). The specific unit used for the coefficients is irrelevant; note essentially the magnitude of the HI effect and the e-dependence.…”

“…The HI effects are considered at the beginning of the procedure, in the calculation of the components of the friction tensors, Nt~, N(i) and N(0 Instead of the simple forms described P, tr P, rr • in Eqs. (13)-(16), in the HI case these tensors are calculated using more complex equations that can be found in the literature (Wegener 1982a;Garcia de la Torre et al 1995;Mellado et al 1988). The rest of the procedure is identical to the no-HI case.…”

“…Further- 1985) b Two beads at ends and one bead at the hinge, with a = 0.5 and b = 1. (Harvey et al 1983; Diaz and Garcia de la Torre 1988) c.d Rods with L/a=4 and 20 modeled with 4 and 20 touching beads, respectively, half of them at each arm (Wegener 1982;Mellado et al 1988). …”