Fluctuation-Driven Transport in Biological Nanopores. A 3D Poisson–Nernst–Planck Study

Living systems display a variety of situations in which non-equilibrium fluctuations couple to certain protein functions yielding astonishing results. Here we study the bacterial channel OmpF under conditions similar to those met in vivo, where acidic resistance mechanisms are known to yield oscillations in the electric potential across the cell membrane. We use a three-dimensional structure-based theoretical approach to assess the possibility of obtaining fluctuation-driven transport. Our calculations show that remarkably high voltages would be necessary to observe the actual transport of ions against their concentration gradient. The reasons behind this are the mild selectivity of this bacterial pore and the relatively low efficiencies of the oscillating signals characteristic of membrane cells (random telegraph noise and thermal noise)

Scaling Behavior of Ionic Transport in Membrane Nanochannels

Ionic conductance in membrane channels exhibits a power-law dependence on electrolyte concentration (G ∼ c α ). The many scaling exponents, α, reported in the literature usually require detailed interpretations concerning each particular system under study. Here, we critically evaluate the predictive power of scaling exponents by analyzing conductance measurements in four biological channels with contrasting architectures. We show that scaling behavior depends on several interconnected effects whose contributions change with concentration so that the use of oversimplified models missing critical factors could be misleading. In fact, the presence of interfacial effects could give rise to an apparent universal scaling that hides the channel distinctive features. We complement our study with 3D structure-based Poisson−Nernst−Planck (PNP) calculations, giving results in line with experiments and validating scaling arguments. Our findings not only provide a unified framework for the study of ion transport in confined geometries but also highlight that scaling arguments are powerful and simple tools with which to offer a comprehensive perspective of complex systems, especially those in which the actual structure is unknown

Electrokinetic Lattice Boltzmann solver coupled to Molecular Dynamics: application to polymer translocation

We develop a theoretical and computational approach to deal with systems that involve a disparate range of spatio-temporal scales, such as those comprised of colloidal particles or polymers moving in a fluidic molecular environment. Our approach is based on a multiscale modeling that combines the slow dynamics of the large particles with the fast dynamics of the solvent into a unique framework. The former is numerically solved via Molecular Dynamics and the latter via a multi-component Lattice Boltzmann. The two techniques are coupled together to allow for a seamless exchange of information between the descriptions. Being based on a kinetic multi-component description of the fluid species, the scheme is flexible in modeling charge flow within complex geometries and ranging from large to vanishing salt concentration. The details of the scheme are presented and the method is applied to the problem of translocation of a charged polymer through a nanopores. In the end, we discuss the advantages and complexities of the approach

Homogenization of the Poisson-Nernst-Planck Equations for Ion Transport in Charged Porous Media

Effective Poisson-Nernst-Planck (PNP) equations are derived for macroscopic ion transport in charged porous media under periodic fluid flow by an asymptotic multi-scale expansion with drift. The microscopic setting is a two-component periodic composite consisting of a dilute electrolyte continuum (described by standard PNP equations) and a continuous dielectric matrix, which is impermeable to the ions and carries a given surface charge. Four new features arise in the upscaled equations: (i) the effective ionic diffusivities and mobilities become tensors, related to the microstructure; (ii) the effective permittivity is also a tensor, depending on the electrolyte/matrix permittivity ratio and the ratio of the Debye screening length to the macroscopic length of the porous medium; (iii) the microscopic fluidic convection is replaced by a diffusion-dispersion correction in the effective diffusion tensor; and (iv) the surface charge per volume appears as a continuous "background charge density", as in classical membrane models. The coefficient tensors in the upscaled PNP equations can be calculated from periodic reference cell problems. For an insulating solid matrix, all gradients are corrected by the same tensor, and the Einstein relation holds at the macroscopic scale, which is not generally the case for a polarizable matrix, unless the permittivity and electric field are suitably defined. In the limit of thin double layers, Poisson's equation is replaced by macroscopic electroneutrality (balancing ionic and surface charges). The general form of the macroscopic PNP equations may also hold for concentrated solution theories, based on the local-density and mean-field approximations. These results have broad applicability to ion transport in porous electrodes, separators, membranes, ion-exchange resins, soils, porous rocks, and biological tissues

Competition and Response: from Active Matter to Electrolytes under Confinement

[eng] Most systems in Nature manifest complex transport phenomena arising from the interplay of multiple time and length scales, be them intrinsic in the system’s dynamics or externally enforced. It is the case, for instance, of a colony of migrating cells whose competing mechanisms of self-propulsion and interaction allow for the reorganization into different tissues. Or, by ‘zooming in’ and looking at the same system on a different scale, it is the case of the ionic channels located in the membranes of the aforesaid cells. These channels typically exhibit extraordinary ion selectivity and water permeability due to the interplay between geometric confinement, surface properties and external drivings. Whether to investigate the collective structures of the former system, or the nanofluidic properties of the latter one rests on the interests of the reader. In any case, she will find some food for thought in this thesis. Here we aim at the study of the transport properties of two very different classes of systems: active matter and electrolytes under confinement. In the examples above drawn from biology, cell tissues belongs to the class of active matter and protein channels are the archetype nanometric ionic systems. We tackle the problem from a purely statistical physics viewpoint by constructing minimal models to study the system’s response to outside influences and, by doing so, learn something about its internal properties. In the case of active matter, the challenge resides in the intrinsically out-of-equilibrium nature of its constituents, having the ability to self-propel by consuming fuel stored in the environment. In Part I of the manuscript, we study how the interplay between self-propulsion and steric interactions affects the linear response of active systems. First, we construct a very general theoretical framework which allows to derive general constraints that arbitrarily out-of-equilibrium systems must fulfilled. Then, we apply it to two different minimal models of active systems to derive generalized fluctuation-dissipation relations and Green-Kubo expressions. In Part II of the manuscript we investigate the surface-dominated transport of electrolytes in (i) a nanofluidic diode and (ii) a scanning ionic conductance microscopy configuration. In both cases, we develop a theory of ionic conductivity that rationalizes previous experimental results. By doing so, we shed light on the importance of the surface versus bulk competition in controlling ionic transport and we propose a new approach to exploit it for the imaging of surface charge with nanometric resolution.[spa] La mayoría de los sistemas en la Naturaleza manifiestan fenómenos de transporte complejos que surgen de la interacción de múltiples escalas de tiempo y longitud, ya sean intrínsecas en la dinámica del sistema o forzadas externamente. Es el caso, por ejemplo, de una colonia de células migratorias cuyos mecanismos competitivos de autopropulsión e interacción permiten la reorganización en diferentes tejidos; o, al "acercar" y mirar el mismo sistema en una escala diferente, es el caso de los canales iónicos ubicados en las membranas de las células mencionadas. Estos canales exhiben típicamente una selectividad de iones extraordinaria y permeabilidad al agua debido a la interacción entre el confinamiento geométrico, las propiedades de la superficie y los conductos externos. Ya sea para investigar las estructuras colectivas del primer sistema, o las propiedades nanofluídicas del último, se basa en los intereses del lector. En cualquier caso, encontrará algo de reflexión en esta tesis

Physics of Ionic Conduction in Narrow Biological and Artificial Channels

The book reprints a set of important scientific papers applying physics and mathematics to address the problem of selective ionic conduction in narrow water-filled channels and pores. It is a long-standing problem, and an extremely important one. Life in all its forms depends on ion channels and, furthermore, the technological applications of artificial ion channels are already widespread and growing rapidly. They include desalination, DNA sequencing, energy harvesting, molecular sensors, fuel cells, batteries, personalised medicine, and drug design. Further applications are to be anticipated.The book will be helpful to researchers and technologists already working in the area, or planning to enter it. It gives detailed descriptions of a diversity of modern approaches, and shows how they can be particularly effective and mutually reinforcing when used together. It not only provides a snapshot of current cutting-edge scientific activity in the area, but also offers indications of how the subject is likely to evolve in the future

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., "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 cause 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, 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; and (4) Mapping the transport properties of a biological nanopore. In the first results chapter of this thesis (Chapter 3), we used 3D equilibrium simulations [...]Comment: PhD thesis, 306 pages. Source code available at https://github.com/willemsk/phdthesis-tex