Computational modeling of biological nanopores

Throughout our history, we, humans, have sought to better control and understand our environment. To this end, we have extended our natural senses with a host of sensors—tools that enable us to detect both the very large, such as the merging of two black holes at a distance of 1.3 billion light years from earth, and the very small, such as the identification of individual viral particles from a complex mixture. This dissertation is devoted to studying the physical mechanisms that govern a tiny, yet highly versatile sensor: the biological nanopore. Biological nanopores are protein molecules that form nanometer-sized apertures in lipid membranes. When an individual molecule passes through this aperture (i.e., it "translocates"), the temporary disturbance of the ionic current caused by its passage reveals valuable information on its identity and properties. Despite this seemingly straightforward sensing principle, the complexity of the interactions between the nanopore and the translocating molecule implies that it is often very challenging to unambiguously link the changes in the ionic current with the precise physical phenomena that causes them. It is here that the computational methods employed in this dissertation have the potential to shine, as they are capable of modeling nearly all aspects of the sensing process with near atomistic precision. Beyond familiarizing the reader with the concepts and state-of-the-art of the nanopore field (chapter 1), the primary goals of this dissertation are fourfold: 1. Develop methodologies for accurate modeling of biological nanopores; 2. Investigate the equilibrium electrostatics of biological nanopores; 3. Elucidate the trapping behavior of a protein inside a biological nanopore; 4. Mapping the transport properties of a biological nanopore. In the first results part of this thesis (chapter 3), we used 3D equilibrium simulations, based on numerical solutions of the Poisson-Boltzmann equation, to investigate the electrostatic properties of the pleurotolysin AB (PlyAB), cytolysin A (ClyA), and fragaceatoxin C (FraC) nanopores. In particular, we showed that a few, or even a single, charge reversal mutations can have a high electrostatic impact, resulting in a strongly reduced or even reversed electro-osmotic flow. Additionally, our simulations indicated that lowering the electrolyte pH significantly reduced the influence of negatively charged amino acids, whilst leaving that of the positively charged groups untouched. To elucidate the propensity of the FraC and ClyA pores to translocate DNA, we computed the electrostatic energy costs associated with ssDNA and dsDNA translocation through them. This revealed that the precise placement of positive charges can enable translocation of DNA by either significantly reducing the magnitude of the electrostatic energy barrier, or by allowing the DNA strand to penetrate deep enough within the pore to build up sufficient force to overcome it. Even though the simulations performed in this chapter show that some of the key characteristics of biological nanopores can be derived from their equilibrium electrostatics, it also revealed that a full comprehension requires the addition of nonequilibrium forces. The next chapter (chapter 4) revolves around the immobilization (i.e., 'trapping') of a single protein molecule within a nanopore, which is of importance for applications such as single-molecule enzymology. To this end, we studied the average dwell time of tagged dihydrofolate reductase (DHFRtag), a small protein modified with a positively charged polypeptide at its C-terminus, within ClyA. Concretely, by manipulating its charge distribution, we succeeded in increasing its average dwell time by several orders of magnitude. Further, we derived an analytical transport model for the escape of DHFR tag from the pore, based on the crossing of the steric, electrostatic, electrophoretic, and electro-osmotic energy barriers located at either side of pore. A systematic study of the dwell times as a function of voltage and tag charge, together with extensive equilibrium electrostatic simulations, allowed us to parameterize this double barrier model, revealing properties that are difficult to determine experimentally, such as the translocation probabilities and the force exerted by ClyA's electro-osmotic flow on the protein (≈9pN at –50mV). The relative simplicity of the double barrier model, and the fact that it contains no explicit geometric parameters of DHFRtag, suggested that our approach may be generalizable to other small proteins. In the final chapters, we developed a novel continuum framework for modeling biological nanopores under nonequilibrium conditions (chapter 5) and subsequently applied it to the ClyA nanopore (chapter 6). Even though they are often qualitatively useful, the ability of continuum methods to solve nanoscale transport problems in a quantitative manner is typically poor. To this end, we developed the extended Poisson-Nernst-Planck-Navier-Stokes (ePNP-NS) equations, which self-consistently consider 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. By numerically solving the ePNP- NS equations for a computationally efficient model of ClyA, we were able to simulate the nanofluidic properties of the pore for a wide range of experimentally relevant bias voltages and salt concentrations. We found the simulated ionic conductivities to be in excellent agreement with their experimentally measured counterparts, suggesting that our model is physically accurate. Hence, we used our simulations to provide detailed insights into the true ion selectivity, the ion concentration distributions, the electrostatic potential landscape, the magnitude of the electro-osmotic flow field, and the internal pressure distribution. As such, the ePNP-NS equations provide a means to obtain fundamental new insights into the nanofluidic properties of biological nanopores and paves the way towards their rational engineering. In this dissertation, we showed that simulations, in combination with systematic experiments, can be used as computational 'microscopes' to reveal the physical phenomena that underlie nanopore-based sensing. Whereas simple equilibrium electrostatics are already highly instructive, it is clear that the complex interplay between the nanopore and the translocating analyte molecule mandates a nonequilibrium approach that is both rigorous and self-consistent, such as the ePNP-NS equations. Further improvements could elevate this framework from an after-the-fact analysis method to a powerful design tool for nanopore researchers, providing a means to automatically screen the properties of novel nanopores, or to predict the ionic current signal produced by arbitrary molecules.

Publication year:2021

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