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

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Wiki Entry by Robin Kirkpatrick, AP 225, Fall 2011

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

Introduction

One of the simplest models in protein folding is the beads on string model where each monomer is modeled as a hard sphere, and are linked via a flexible string. To test this theory, the authors developed a simple model consisting of two bead types (Nylon and Teflon) connected via a flexible Nylon string with small PMMAA beads in between which act as spacers. To give the beads electrostatic charge , the sequence is agitated on a piece of paper. The nylon beads acquire a positive charge, while the teflon beads acquire a negative charge. The PMMAA beads remain relatively neutral. The model is allowed to self assemble, thus simulating simple a 2D polymer system.

Results

The experimental set-up is shown below in Figure 1. Briefly, strings composed of either spherical or cylindrical beads are laced onto a Nylon string with silver coated crimp beads on each side of the large spheres. Small PMMAA beads are used as spaced in between the large Teflon/Nylon beads. An extended string is placed on a piece of paper supported by aluminum on an agitator. The silver is in the middle of the triboelectric series , and is thus assumed to not contribute to the charge on the other beads. The small PMMAA beads were used to make a well defined length between the large beads, in addition to preventing the string from crossing over itself.

RGW1.jpg

The rigidity of the string was controlled by the number of PMMAA spacer beads. Figure 2 below shows the results after the system was allowed to come to equilibrium after agitation for different number of spacer beads. Presence of one spacer bead resulted in no contact formation for the string with spherical beads, but yielded a larger number of contacts for a cylindrical beads. However, the cylindrical bead string yielded no contacts without spacer beads.

RGW2.jpg


RNA Hairpin

To simulate an RNA polymer, the authors threaded long and short cylindrical beads as the longer beads should hold more charge, and thus be analagous to 3 hydrogen bond base pairs (GC pairing), vs having the weaker 2 hydrogen bond pairing (AU). The authors observed that the sequence analogous to GGCAUAAUAGCC. As expected, their model reached a global minimum (as evidence by being stable after an hour under agitation) and reached the hairpin structure reproducibly. The authors repeated the experiment for the inverted sequence AAUGCGGCGAUU which theoretically should not form a hairpin. This was observed experimentally as shown in Figure 3C in the right hand column. Rather, the system samples many local minima as evidence by sampling numerous configurations over multiple experiments.

RGW3.jpg


Polymer Chain Models

The surface to volume ratio determines the physical behavior of a polymer chain. Thus short 2D chains are analogous to longer 3D chains. To simlate a long system, 40 monomeric units with 3 spacers was constructed, which is analagous to a 200 unit system. The authors verified that the conformations were a result of electrostatic forces, charge was neutralized using an electrostatic gun. Figure 5 shows the number of correct bonds formed as a function of time (Teflon-Nylon) while Figure 4 shows the observations of the experiment. There were several different energy minima in this system as evidence by the several different conformations.

RGW4.jpg

RGW5.jpg


Discussion

The authors present a simple method of a simple model and show that the results are consistent. It would be of interest to contruct use this sytem for more complex models, designing the system to model solvent effects, etc. Though simple in construction, this technique of using an 'analog computer' to solve a non-linear problem exactly is a powerful method that would be interesting to extent to other systems.

Keywords

Polymer Physics, Electrostatics, triboelectric series, RNA