Flexibility-induced effects in the Brownian motion of colloidal trimers

Abstract

Shape changes resulting from segmental flexibility are ubiquitous in molecular and biological systems, and are expected to affect both the diffusive motion and (biological) function of dispersed objects. The recent development of colloidal structures with freely jointed bonds have now made a direct experimental investigation of diffusive shape-changing objects possible. Here, we show the effect of segmental flexibility on the simplest possible model system, a freely jointed cluster of three spherical particles, and validate long-standing theoretical predictions. We find that, in addition to the rotational diffusion time, an analogous conformational diffusion time governs the relaxation of the diffusive motion, unique to flexible assemblies, and that their translational diffusivity differs by a small but measurable amount. We also uncovered a Brownian quasiscallop mode, where diffusive motion is coupled to Brownian shape changes. Our findings could have implications for molecular and biological systems where diffusion plays an important role, such as functional site availability in lock-and-key protein interactions.

Conformations and diffusion of flexibly linked colloidal chains

“…a palindromic sequence) and a cholesterol anchor that inserts itself into the lipid bilayer due to hydrophobic interactions (see Supplementary Material of Verweij and Moerman et al [31], strands PA-A and PA-B). To image the 1.93 µm CSLBs we used a flow cell coated with poly(2-hydroxyethyl acrylate) (pHEA) polymers [31]. Self-assembly experiments were performed in a buffer of pH 7.4, containing 50 mm NaCl and 10 mm HEPES.…”

“…Because the chains are sedimented to the bottom substrate, we consider only the quasi-2D, in-plane diffusivity. For the flexible trimers, we followed the methods outlined in Verweij and Moerman et al [31]. For the flexible tetramer chains, we calculated a 5×5 diffusion tensor, where the five degrees of freedom correspond to translational diffusivity in x and y, rotational diffusivity and the flexibilities of the tetramer, which are described by the diffusivities of the opening angles θ 1 , θ 2 .…”

“…The diffusion tensor elements of the tetramer chains were determined analogously to the trimers [31]. Briefly, for each pair of frames, we determined the initial shape of the chain, which is determined by θ 1 , θ 2 .…”

“…(i.e. ρ = (1/3, 1/3, 1/3)),x is parallel to the end-to-end vector, which is the same definition as in our previous work [31].ŷ is then chosen such thatx andŷ form a right-handed coordinate system, where the direction ofŷ is chosen to point away from the central part of the cluster towards the tracking point, i.e. along r t.p.…”

“…Recently, we have studied both numerically and experimentally the effect of segmental flexibility [31] in a simple model system consisting of a freely-jointed chain of three spherical colloidal particles, also called trimers or trumbbells [32,33]. This was made possible for the first time thanks to the development of colloidal structures with freely-jointed bonds [34].…”