Slithering Like A Snake and Beyond: Microscopy of Polymer Dynamics

Original paper: Entangled polymer dynamics beyond reptation


Scientists often draw inspiration from biological organisms to describe phenomena, even when they are studying outside the realm of biology. Physicist Pierre-Gilles de Gennes[1] was no exception. In 1971, after being inspired by the movement of snakes, he proposed reptation theory, or the reptation model, which has since been widely used to describe motions of polymers[2]. As the name “reptation” suggests, de Gennes assumed polymer chains move like snakes. As shown in Figure 1, the model describes a polymer chain’s motion in an environment that is highly populated by other chains (shown in gray) by assuming that the chain is confined in a virtual tube (shown in red) formed by surrounding polymer chains. According to reptation theory, the chain wiggles through this tube, similar to a snake slithering through the woods. As one might imagine, directly imaging the snake-like slithering of polymers is a challenging affair; however, in today’s study, Maram Abadi and coworkers from King Abdullah University of Science and Technology were able to do just that with DNA chains – an example of a polymer – and compared their results to prevailing theory.

A schematic of the reptation model
Figure 1. A schematic of the reptation model. In a crowded and entangled polymer environment, a long and linear polymer chain (black) is located in a virtual tube (red), which traces the chain trajectory. Surrounding polymers are shown in gray. (Adapted from the Wikipedia page for reptation.)

While reptation theory has done fairly well in describing experimental observations of polymers, there are some shortcomings to both the experiments supporting this theory as well as to the theory itself. Namely, previous experiments mostly considered the overall motion of the chain; but local chain motion, such as motion at the ends of a polymer chain, have not been thoroughly studied. In addition, the theory was only designed for polymers with two ends, known as linear polymers. Thus, it does not account for the dynamics of polymers with different geometries, such as those that form rings, known as cyclic polymers. Given these observations, Abadi and coworkers realized that there was more work to be done in the studies of polymer dynamics.

To scrutinize the movements of the polymer chains, the authors used super-resolution fluorescence localization microscopy[3], which lets them monitor the movements beyond the typical microscopy resolution of ~200 nm. This technique allowed Abadi and coworkers to not only observe whole-chain dynamics but also local dynamics. To test the predictions of reptation theory, they chose both linear and cyclic DNAs with fluorescent dyes attached as model polymers for their study.

Fluorescent images of a linear DNA chain collected at different time points
Figure 2. Fluorescent images of a linear DNA chain collected at different time points (indicated in the figure), overlapped for comparison. Insets show the enlarged views of the highlighted areas. (Adapted from the original paper.)

First, linear DNAs were used to confirm what has been known from reptation theory in great detail. Shown above in Figure 2 are images of a linear DNA as a function of time. Their results were consistent with theory. First, polymer chains traveled along virtual tubes that followed the contour of the chain (shown in white boxes in Figure 2A). Second, most of the polymer chain’s displacements were within the confinements of the virtual tubes, which had a diameter around 51–95 nm (shown in red boxes in Figure 2B). Further, they occasionally saw displacements of the DNA that exceeded the size of tube diameter (shown in cyan boxes in Figure 2C), known as constraint release in reptation theory. Finally,  Abadi and coworkers observed that the chain-ends were able to move farther than the centers of the chains, which in turn creates a new tube for further DNA reptation (shown in green boxes in figure 2C). In reptation theory, this is called contour-length fluctuation.

However, there was one particular deviation from the theory found in the authors’ results. While the chain-ends were expected to move more freely than other parts of the chains, the chain-end motions were a lot faster than what is predicted by reptation theory. Therefore, the authors concluded that the motions at the chain-ends were beyond the scope of the reptation theory. These unexpectedly fast movements were not observed in previous experiments, in which only the chain as a whole was considered.

Fluorescent images of cyclic DNAs collected at different time points
Figure 3. Both rows are fluorescent images of cyclic DNAs collected at different time points (indicated in the figure), overlapped for comparison. 3A shows amoeba-like motion, and 3B shows contracting of an open structure. More details can be found in the main text below. (Adapted from the original paper.)

The authors also observed cyclic DNAs using the same methods. As they are not linear, reptation theory fails to accurately explain their movements. The authors observed diverse motion of the cyclic DNAs. You may notice in Figure 3A that the cyclic DNA has a loop-like region, shown in the white boxes. They found that cyclic DNAs repeatedly contract and extend this region, resembling the motions of amoeba. In addition, as shown in the first panel of Figure 3B, some cyclic DNA molecules may start with an open structure. However, as time progresses, these open DNAs may contract into more linear forms and expand back into the open shape again. Thus, Abadi and coworkers were able to show two phenomena that cannot be explained by reptation theory, thus requiring it to be further refined.

The results of this paper support many of the conclusions of reptation theory; however, it does suggest that there is still a need to expand this otherwise well-accepted theory. By considering different geometries and shorter timescales, this theory will be more powerful as a predictor or explainer of novel polymeric material dynamics. Furthering the understanding of polymer dynamics will then help us understand polymer properties for use in a variety of applications that we see in our lives every single day.


 [1] This 1991 Nobel laureate in Physics is also the one who popularized the term “soft matter”.

[2] Polymers are molecules that are consist of repeating chemical structures.

[3] Super-resolution microscopy is a technique that lets us observe things that are smaller than the diffraction limit of ~200 nm, which is the limit that is imposed by the physics of light.

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