There is a growing interest in using nanometer sized pores to detect the biological molecules by measuring the ionic current [1-3]. The quasi one-dimensional geometry of the nanopores provides a natural environment for confining the linear molecules such as DNA. The experiments on single-stranded DNA (ssDNA) using the α-hemolysin pore, a self-assembled heptameric transmembrane pore of Staphylococcal α-hemolysin proteins with a diameter ~2.0 nm, and length of 10 nm, raised the possibility for DNA base type detection. It was observed that under an applied voltage, a single-stranded polynucleotide segment could be driven through the α-hemolysin pore, producing an electric current characteristic of the base type of the polynucleotide [1-3]. In the absence of ssDNA, a steady current of ~120 pA was observed at an applied voltage of 100 mV. In contrast, when a polynucleotide consisting of cytosine bases (polyC) was present, the current was reduced by ~95% to about 6 pA under the same voltage; whereas when a polynucleotide consisting of adenine bases (polyA) was in the pore, the current was reduced by 85% to about 15-20 pA. To gain a better understanding to the molecular mechanism of ionic current conduction, we carried out a molecular dynamic study of ssDNA in nanopore. The results suggest a mechanism for the ionic current conduction in which the counterions are transiently bound to the phosphate groups of the polynucleotide due to strong electrostatic attraction, slowing down the migration of the ions, and reducing the ionic current through the nanopore.

Molecular Models and Methods

For simplicity and because of the increasing interest in using inorganic nanopores, we have chosen to model a system of ssDNA molecule in a sodium chloride aqueous solution confined in a non-biological cylindrical pore with a 2.0 nm diameter. The nature of the wall is hydrophilic modeling silica with appropriate parameters.

We used the AMBER force field [4] for the DNA molecules, and the TIP3P model for water [5]. The models for Na⁺ and Cl^- consist of a Lennard-Jones potential and an electric charge [6]. Molecular simulation results presented here were calculated using a cutoff distance of 11.03 Å for the Lennard-Jones and the electrostatic interactions. Simple cutoff is a commonly used approach for the simulation of biomolecular systems and was used in the development of the original model for DNA molecules. The fluid molecules interact with the wall through an integrated form of the Lennard-Jones potential which takes into account both the repulsive and attractive effect of the wall [6,7]. The detail for the models and interaction parameters can be found in a previous publication [8].

Constant NVT molecular dynamics simulations (MD) were carried out. In the simulations, we used a fixed bond length constrained dynamics method for water molecules [9], the velocity Verlet method for the ions, and a multiple time step method for the DNA molecule [10], with a 5:1 ratio between the large time step for intermolecular interactions and small time step for the internal motion. The largest time step in the multiple time step method was the same as in the constraint dynamics and Verlet methods, 2.50 fs. The system temperature was maintained at 298 K by a Berendsen thermostat [11].

Results

Our study shows that because of the highly negative charges on the ssDNA, the Cl^- are strongly repelled by the ssDNA from the nanopore, leading to a near complete depletion of Cl^- in the nanopore region occupied by the ssDNA. Thus, the ionic conduction in nanopore is predominantly due to the migration of the counter ions. The positively charged counterions are strongly adsorbed to the negatively charged DNA phosphate groups, modulated by the bases. The counterions sometimes also adsorb to the atoms with large negative partial charge on the bases. It appears that a common feature for strong adsorption is the high partial charge and the protrusion of the atom from the backbone or the base, thus providing both strong attraction and easy accessibility by the counterions. To quantify the dynamics of the Na⁺-phosphate complex, we determined the residence time of the Na⁺ around a phosphate group. It is reasoned that if the Na⁺ spends considerable amount of time at one phosphate site before dissociating and then captured by another phosphate site near by, its mobility would be substantially reduced, resulting smaller current. We obtained a residence time of several nanoseconds for Na⁺ around a phosphate group, which is ~1-2 orders of magnitude longer than the time for sodium ions to migrate the same intra-base distance (3.4 Å) in bulk solution. The calculated diffusion coefficient for the ions through the nanopore show similar slowing down.

We used the Nernst-Planck equation to determine the ionic current using the calculated diffusion coefficient and the ionic concentration from the simulation. We obtain an ionic current of approximately 5.71 pA through a 2.0 nm pore in the presence of C20 and 12.15 pA in the presence of A20, which are comparable to those measured in experiment.

The simulation results show that the ionic current through nanometer pores in the presence of DNA is significantly reduced by the dramatic slowing down of the counterion migration as a result of long association to the phosphate groups of the ssDNA. This suggests a mechanism in which the counterions migrate through the nanopore by hopping along the backbone of the ssDNA. The adsorption and hence the hopping rate is influenced by the base type which affects the accessibility and binding strength of the ions to the phosphate groups.

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