Polymer Translocation through a Nanopore

Hendrick de Haan

The passage of a polymer across a membrane through a constricting passage way is central to many biological processes: transport of proteins across cells, DNA packing into cells, etc. Further, with recent advances in nanofabrication, it is now possible to manufacture solid state nanopores that are able to confine individual DNA strands. With these applications in mind, we are using a variety of simulation techniques to both carefuly quantify the dynamics of translocation and to examine the process in novel setups. The project is roughly broken up into two parts: i) a careful examination of the dynamics of unbiased translocation ii) translocation in asymmetric systems.

Dynamics of Unbiased Translocation

Although most examples of translocation involve a driving force of some kind, the unbiased process presents an interesting system itself and a thorough description of the dynamics of this process are useful to understand the driven case. In the absence of a driving mechansim, the dynamics of translocation essentially amount to diffusion over the entropic barrier intrinsic to crossing the membrane. To study this system, we employ two different approaches. First, we have developed a simple model of translocation as a single random walker traversing the entropic barrier. With this model, the dynamics can be studied by both direct Monte Carlo simulations as well as the exact numerical approach to gain insight into the dyanmics of the "ideal" translocation process. From this work, we have uncovered interesting features of the entropic barrier and the impact of differing boundary conditions LINK PAPER.

Extending to a more realistic model, we also perform extensive Langevin Dynamics simulations of trasnlocation with the Espresso simulations package. With this approach, we have demonstrated that the scaling laws are sensitive to the details of the simulation setup LINK PAPER - a result which may help resolve disagreement between reported values. Additionally, we have developed novel measuresments to characterize memory effects in the system to probe the viscosity dependent scaling laws. Finally, presenting a new way to quantify the translocaiton process, we have shown that while the scaling of the total translocation time with polymer length varies with simulation details, a characterization of the steps of the process agrees with theoretical predictions. From this work, we have developed a model of translocation as the diffusion of a local minimum.

Translocation Driven by System Asymmetry

We are also examining the case of driven translocation. Here, instead of applying an external field, a driving mechanism is incoporated by introducing an asymmetry to the system. Two methods for doing this are being studied: placing obstacles on both sides of the membrane and varying the viscosity across the membrane. For the obstacle system, interesting results arise from including either a gradient of obstacle density across the membrane or a difference in the obstacle ordering across the system. While it is obvious that the polymer will tend to the side of the membrane with lower obstacle density, the mechanism leading to the disordered side being greatly preferred over the ordered side is more subtle. Here, the entropic trapping resulting from areas of low obstacle density plays a critical role.

Similar results have been obtained for a system in which the viscosity on one side of the pore is lower than the other. Again, a preferential direction is established as the polymer tends to the low viscosity side. Interestingly, this problem can quite effectively be reduced to a single random walker at a viscosity interface and correspondingly, we have developed a methodology for studying this system by Monte Carlo simulations.

Both the obstacle work and viscosity work have implications for natural instances of translocation. Considering a polymer crossing the cell membrane, there are inclusions on both the intracellular and extracellular side. Large inclusions will have an impact similar to immobile obstacles while small inclusions that don't necessarily block space but impede diffusion amount to modifications of the effective viscosity of the fluid.

Related Manuscripts:

2010       Variation in the alpha Scaling Exponent with Nanopore Width
2010       The Importance of Introducing a Waiting Time for Lattice Monte Carlo Simulations of a Polymer Translocation Process

Confinement Electrophoresis

DNA blocking in a gel

Biofilms

Flow Field Fractionation

Polymer Translocation

DNA moving through obstacles

End-Labeled Free-Solution Electrophoresis

DNA moving through obstacles

Ratchet funnels for swimming bacteria

Free Solution Electrophoresis of Polyelectrolytes

Electro Osmotic Flow

Diffusion in Arrays of Cavities

Lattice Monte-Carlo Methods