Theory and Modeling

Theory and Modeling of Polymer Translocation through Proteins and Solid-State Nanopores

Theoretical work using explicit atomistic simulations to investigate how polymer molecules worm through narrow pores is being carried out by Professor Murugappan Muthukumar and his co-workers in collaboration with other members of the Nanopore Group at Harvard.

In the theory (Refs. 1-5), we address the extent of reduction of polymer entropy when the polymer confronts a narrow path. Narrow pores imposes an entropic barrier (Fig.1) for the transport of polymer molecules from a donor compartment to a recipient compartment. This entropic barrier is mitigated (or augmented) by the potential interaction between the polymer and the pore. The sum of the entropic barrier and interaction energy leads to a free energy barrier for translocation of polymer through pores. We have developed a theory (Refs. 2-5) to address the consequences of the free energy barrier on the distribution of translocation time, mean translocation time, and the polymer flux in terms of polymer length, solution conditions, the magnitude of the driving force (electro-chemical potential gradient), and the polymer sequence.

Figure 1

In the simulations, we use the Brownian Dynamics method. The polymer and the protein are represented by the united-atom models (Fig. 2).

Figure 2

Our model of the polymer (DNA) and protein (alpha-Hemolysin) are coarse-grained to allow efficient computation, but are sufficiently detailed to allow us to monitor the effects of 3' versus 5' end of DNA, specific locations of charges on the alpha-Hemolysin channel, relative size of the vestibule and the stem of alpha-Hemolysin, etc. By repeating our simulations thousands of times, we construct the distribution function of translocation times (Fig. 3).

Figure 3

The key advantage of our simulations is the ability to study the trajectory of the polymer in a particular translocation event. We (Ref. 6) are able to identify the molecular origin of broad distribution of translocation time observed in experiments. For example, the vestibule of the alpha-Hemolysin pore acts as an entropic sink and causes a delay in translocation. We are in the process of extending the Brownian Dynamics simulations to semiflexible charged polymers through chemically decorated pores of specific diameter and length (Fig. 4).

Figure 4

We are developing strategies to compute ionic current as a polymer undergoes translocation through a pore. Our strategy is to implement the generalized Poisson-Nernst-Planck formalism (Ref. 7). Another stategy is to combine the Brownian Dynamics simulations and the Poisson-Nernst-Planck scheme. A representative result (Ref. 8) of calculated ionic current as a polymer tranverses a pore is given in Fig. 5.

Figure 5

References
1. Muthukumar M., and A. Baumgartner. 1989. Effects of entropic barriers on polymer dynamics. Macromolecules 22:1937-1941.
2. Muthukumar, M. 1991. Entropic barrier model for polymer diffusion in concentrated polymer solutions and random media. J. Non-Crys. Solids 131-133:654-666.
3. Muthukumar, M. 1999. Polymer translocation through a hole. J. Chem. Phys. 111:10371-10374.
4. Muthukumar, M. 2001. Translocation of a confined polymer through a hole. Phys. Rev. Lett. 86:3188-3191.
5. Muthukumar, M. 2002. Theory of sequence effects on DNA translocation through proteins and nanopores Electrophoresis, 23:1417-142.
6. Kong, C. Y., and M. Muthukumar. 2002. Modeling of Polynucleotide Translocation through protein pores and nanotubes. Electrophoresis, 23, 2697-2703.
7. Muthukumar, M. 1997. Dynamics of polyelectrolyte solutions. J. Chem. Phys. 107:2619-2635.
8. Kong, C. Y., and M. Muthukumar (in preparation).