Accurate modeling of a biological nanopore with an extended continuum framework.

Despite the broad success of biological nanopores as powerful instruments for the analysis of proteins and nucleic acids at the single-molecule level, a fast simulation methodology to accurately model their nanofluidic properties is currently unavailable. This limits the rational engineering of nanopore traits and makes the unambiguous interpretation of experimental results challenging. Here, we present a continuum approach that can faithfully reproduce the experimentally measured ionic conductance of the biological nanopore Cytolysin A (ClyA) over a wide range of ionic strengths and bias potentials. Our model consists of the extended Poisson-Nernst-Planck and Navier-Stokes (ePNP-NS) equations and a computationally efficient 2D-axisymmetric representation for the geometry and charge distribution of the nanopore. Importantly, the ePNP-NS equations achieve this accuracy by self-consistently considering the finite size of the ions and the influence of both the ionic strength and the nanoscopic scale of the pore on the local properties of the electrolyte. These comprise the mobility and diffusivity of the ions, and the density, viscosity and relative permittivity of the solvent. Crucially, by applying our methodology to ClyA, a biological nanopore used for single-molecule enzymology studies, we could directly quantify several nanofluidic characteristics difficult to determine experimentally. These include the ion selectivity, the ion concentration distributions, the electrostatic potential landscape, the magnitude of the electro-osmotic flow field, and the internal pressure distribution. Hence, this work provides a means to obtain fundamental new insights into the nanofluidic properties of biological nanopores and paves the way towards their rational engineering.

Engineering and Modeling the Electrophoretic Trapping of a Single Protein Inside a Nanopore.

The ability to confine and to study single molecules has enabled important advances in natural and applied sciences. Recently, we have shown that unlabeled proteins can be confined inside the biological nanopore Cytolysin A (ClyA) and conformational changes monitored by ionic current recordings. However, trapping small proteins remains a challenge. Here, we describe a system where steric, electrostatic, electrophoretic, and electro-osmotic forces are exploited to immobilize a small protein, dihydrofolate reductase (DHFR), inside ClyA. Assisted by electrostatic simulations, we show that the dwell time of DHFR inside ClyA can be increased by orders of magnitude (from milliseconds to seconds) by manipulation of the DHFR charge distribution. Further, we describe a physical model that includes a double energy barrier and the main electrophoretic components for trapping DHFR inside the nanopore. Simultaneous fits to the voltage dependence of the dwell times allowed direct estimates of the cis and trans translocation probabilities, the mean dwell time, and the force exerted by the electro-osmotic flow on the protein (≅9 pN at -50 mV) to be retrieved. The observed binding of NADPH to the trapped DHFR molecules suggested that the engineered proteins remained folded and functional inside ClyA. Contact-free confinement of single proteins inside nanopores can be employed for the manipulation and localized delivery of individual proteins and will have further applications in single-molecule analyte sensing and enzymology studies.