Folding of Electrostatically Charged Beads-on-a-String: An Experimental Realization of a Theoretical Model

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Entry by Emily Redston, AP 225, Fall 2011

Work in progress


Folding of Electrostatically Charged Beads-on-a-String: An Experimental Realization of a Theoretical Model by Reches, M., Snyder, P.W., and Whitesides, G.M., Proc. Natl. Acad. Sci. USA, 2009, 106, 17644-17649.


"beads-on-a-string" model, electrostatic interactions, polymers, polymer folding, persistence length, triboelectricity, self-assembly


The folding of linear polymers in solution is a subject of enormous importance in areas ranging from materials science to molecular biology. In exploring folding, theorists have developed models at every level of complexity. One of the simplest and most useful of these conceptual models is the “beads-on-a-string” model (a cornerstone of theoretical polymer science). This model represents each monomer of the polymer as a bead, and the backbone of the chain as a flexible string. It has been the basis for many computational models for folding. All theoretical models are, however, necessarily incomplete, and their failure to capture the full complexity of reality stimulates the development of more complex theory. Here the authors defied the conventional strategy of using complex theory to to try to rationalize an even more complex reality; they developed a very simple experimental system to match the simplest theory. They designed a physical model of beads-on-a-string, based on the folding of flexible strings of electrostatically charged beads in two dimensions.

Using a physical system composed of beads of two materials threaded in a defined sequence on a flexible string, they are able to examine the predictions of theoretical beads-on-a-string models. It is a very nice design for several reasons: (1) it is 2-D, (2) the interactions among the beads are electrostatic, (3) the shapes of the beads and properties of the string can be controlled, and (3) the agitation of the beads is well defined. Examination and comparison of two models—one physical and one theoretical— offers a new approach to understanding folding, collapse, and molecular recognition at an abstract level, with particular opportunity to explore the influence of the flexibility of the string and the shape of the beads on the pattern and rate of folding. This system, although much simpler than molecular polymers in 3-D solution, still includes the inevitable nonlinearities of a real physical system. It is, thus, an analog computer designed to extend and to simulate 2-D calculations of beads-on-a-string models of polymer folding and collapse.

The Model

Figure 1. The beads-on-a-string experimental model. (A) An illustration represents an experimental sequence of beads: the blue circles represent Nylon beads, the white, Teflon beads, the gray, PMMA beads, and the black squares represent silver-coated crimp beads. (B) The scheme illustrates the experimental apparatus: a poly(isocyanurate) board supported an aluminum sheet and a circular aluminum frame. On the circular frame was suspended a sheet of paper (pink), which defined the area of the system. (C) A side view of the apparatus shows the paper surface with curved features at the edges (radius ≈3 cm).

The system comprises millimeter-scale Teflon and Nylon-6,6 (spherical or cylindrical) beads (≈ 6 mm in diameter) separated by smaller (≈3 mm) poly(methyl methacrylate) (PMMA) spherical beads, threaded on a flexible string. The smaller, uncharged beads define the distances between the larger beads, and control the flexibility of the string. During agitation of the sequence of beads on a planar, horizontal paper surface, tribocharging generates opposite electrostatic charges on the larger Nylon and Teflon beads, but leaves the smaller PMMA beads essentially uncharged; the resulting electrostatic interactions cause the string to fold.

We generated the beads-on-a-string by threading sequences of spherical (diameter = 6.35 mm) or cylindrical (diameter = 6.35 mm, length = 14.2 mm) Nylon and Teflon beads on a thin flexible string (see Materials and Methods). Beads of this size are easy to handle and machine. To increase the visual contrast between the Teflon and Nylon beads, we stained the Nylon beads with a neutral organic dye; the dye did not significantly change the charge developed on the beads (see SI Text).

Upon agitation on a surface (made of paper) located in the middle of the triboelectric series* (18), Teflon and Nylon beads develop electrostatic charges of similar magnitudes and at similar rates, but with opposite electrical polarities: Teflon charges negatively and Nylon positively (19) (Fig. 1A). The surface on which the beads charged was planar and axially symmetrical, with a slight curvature (radius ≈3 cm) at the perimeter (Fig. 1B and C). This geometry avoided interactions of the beads with the corners of a sharply defined frame

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