Practical applications of solid-state nanopores for DNA detection and sequencing require the electrophoretic motion of DNA through the nanopores to be precisely controlled. Controlling the motion of single-stranded DNA presents a particular challenge, in part because of the multitude of conformations that a DNA strand can adopt in a nanopore. Through continuum, coarse-grained and atomistic modeling, we demonstrate that local heating of the nanopore volume can be used to alter the electrophoretic mobility and conformation of single-stranded DNA. In the nanopore systems considered, the temperature near the nanopore is modulated via a nanometer-size heater element that can be radiatively switched on and off. The local enhancement of temperature produces considerable stretching of the DNA fragment confined within the nanopore. Such stretching is reversible, so that the conformation of DNA can be toggled between compact (local heating is off) and extended (local heating is on) states. The effective thermophoretic force acting on single-stranded DNA in the vicinity of the nanopore is found to be sufficiently large (4-8 pN) to affect such changes in the DNA conformation. The local heating of the nanopore volume is observed to promote single-file translocation of DNA strands at transmembrane biases as low as 10 mV, which opens new avenues for using solid-state nanopores for detection and sequencing of DNA.

Transport of ions through pores in membranes is a process of fundamental importance to cell biology. In living organisms, such transport is facilitated by ion channels that utilize the ionic flux to perform diverse biological functions, such as cell-cell communication and signaling, osmotic stress response, muscle contraction, etc. The action of ion channels is responsible for most of what we (humans) perceive as reality in the form of sound, smell, sight, taste and touch, and forms the physiological basis for thought. Biomimetic ion channels are ubiquitous in engineering, with application ranging from water desalination to fuel cells. Since the discovery of excitable ionic membranes, modeling and simulation have been an integral part of the development of the field. From the early studies of Hodgkin and Huxley to the most recent fully atomistic simulations of ion conductance, the key challenge in this area remains the prediction of electrical response of a membrane incorporating ion channels to external stimuli such as transmembrane voltage, chemical ligands, tension, etc. The ever increasing complexity of the computational models of ion channels reflects the dramatic advances of our experimental knowledge about these systems, most importantly, fully atomistic structures of several ion channels1–3 and direct experimental observations of a single channel’s action,4–7 with more discoveries yet to come. Here, we review efforts to model and simulate ion channels that occurred within the past ten years. First, we briefly describe early phenomenological models of excitable membranes and briefly review recent developments in this area. Next, we describe several membrane channel systems that have been studied extensively by various computational approaches. Our selection of systems is based solely on their popularity among modelers and is neither intended to provide a representative overview of the evolutionary development of ion channels nor presented in any particular historical order. Next, we describe the most common computational methods used to study ion channels. Table 1 links the systems and methods by providing explicit references to the studies of specific systems performed using specific methods. The second half of the review is organized according to the most typical questions of interest: ion binding and permeation pathways, ion conductance, selectivity and gating. The last section summarizes recent development in the field of stochastic sensors—biomimetic ion channels with promising applications in biomedical diagnostics. At the end of this review, we briefly describe our perspective on the development of the field within the next ten years. Table 1 Modeling and simulation studies in the general area of ion channels organized according to the system type and computational models employed. 2 Early phenomenological models Early work on phenomenological modeling of ion channels actually occurred well before the existence of ion channels had been established, or even surmised.395 Rather, researchers were attempting to understand the mechanism of signal propagation in nerve cells. Nerve cells at rest maintain an action potential, defined as the electrical potential of the nerve interior relative to the exterior. Rest action potentials are negative and generally in the range of −40 to −95 mV.395 Interestingly, the axons of nerve cells support the transmission of a pulse of slightly positive action potential, which carries the signals used for communication in a neural network. The technique used by Hodgkin and Huxley, called a voltage clamp, is illustrated schematically in Figure 1a. In a voltage clamp experiment, the transmembrane voltage is held constant, and the resulting current is measured. Such experiments determine the membrane permeability as a function of voltage and time. Figure 1 Evolution of the equivalent circuit diagrams of nerve axon models. (a) Schematic representation of an axon. Conductance experiments are performed by maintaining a given transmembrane voltage and measuring the resulting ionic current. (b) Cable model of ... Early models described the axon as a “cable”, with a conductive core surrounded by a less conductive, capacitive sheath, later identified as a membrane. This model corresponds to the circuit diagram shown in Figure 1b. Further experiments showed that during excitation the membrane permeability increases dramatically. Additionally, it was found that assigning a variable electromotive force, or emf, to the membrane provided a better fit to the experimental data, yielding the circuit diagram shown in Figure 1c. Finally, the brilliant experiments and insight of Hodgkin and Huxley396 established that the currents associated with action potential changes were in fact carried by multiple ion species, primarily K+ and Na+. This conceptual leap removed the need for a variable emf in the equivalent circuit diagram, instead assigning separate emfs and resistances for transport of K+ and Na+ species. They also found a small, so-called “leakage” current associated with a constant resistance. The final circuit model is shown in Figure 1d. The realization that changes in the action potential were manifested through multiple ion species was a major advance. Experiments isolating the K+ and Na+ permeability of the membrane revealed a fascinating twist: under an externally applied potential, K+ resistance drops and stays low, while Na+ resistance drops initially but then returns to its previous level. Figure 2 shows the conductance of squid axon to sodium and potassium. Figure 2 Conductance of squid axon membrane to sodium (a) and potassium (b) at various applied voltages. Voltage was held at the rest value of −65 mV, then increased to the displayed value at t = 0. While potassium conductance rises and saturates under ... The Hodgkin-Huxley, or HH, model describes the behavior of the two independent ionic resistances introduced in Figure 1d. For convenience, we restate these quantities as their inverses, the ionic conductances gK and gNa. In the model, gK and gNa vary between zero and maximum values ḡK and ḡNa, respectively. In other words, gK=xKg¯KgNa=xNag¯Na The goal of the HH model is to describe the behavior of the coefficients xK and xNa. In the model, xK and xNa are only dependent on time and voltage. We first describe how the potassium coefficient xK is represented in the HH model. To best fit the experimental data, the HH model supposes that four independent particles control the potassium conductance. Although Hodgkin and Huxley did not know of the existence of ion channels, here we will assume that the particles control a potassium channel. Figure 3a schematically shows a potassium channel and the controlling particles. Each particle may be in one of two states: active or inactive. In order for the channel to conduct, all four particles must be active. Following Hodgkin and Huxley, let us say that the probability of a particle being active is n. The probability of the channel being conductive is then n4. The average current is then Figure 3 (a, b) Schematics of potassium (a) and sodium (b) channels considered in the Hodgkin- Huxley model. In the HH model, the conductance of a potassium channel is controlled by four activating particles (black circles), while the conductance of a sodium channel ... IK=n4g¯K(V-eK) (1) where V is the applied voltage and eK is the emf of the potassium channel. The emf originates in the ion concentration gradient across the membrane, which is driven by ion pumps such as Na+-K+ ATPase.398

The charge of a DNA molecule is a crucial parameter in many DNA detection and manipulation schemes such as gel electrophoresis and lab-on-a-chip applications. Here, we study the partial reduction of the DNA charge due to counterion binding by means of nanopore translocation experiments and all-atom molecular dynamics (MD) simulations. Surprisingly, we find that the translocation time of a DNA molecule through a solid-state nanopore strongly increases as the counterions decrease in size from K+ to Na+ to Li+, both for double-stranded DNA (dsDNA) and single-stranded DNA (ssDNA). MD simulations elucidate the microscopic origin of this effect: Li+ and Na+ bind DNA stronger than K+. These fundamental insights into the counterion binding to DNA also provide a practical method for achieving at least 10-fold enhanced resolution in nanopore applications.

Using all-atom molecular dynamics and atomic-resolution Brownian dynamics, we simulate the translocation of single-stranded DNA through graphene nanopores and characterize the ionic current blockades produced by DNA nucleotides. We find that transport of single DNA strands through graphene nanopores may occur in single nucleotide steps. For certain pore geometries, hydrophobic interactions with the graphene membrane lead to a dramatic reduction in the conformational fluctuations of the nucleotides in the nanopores. Furthermore, we show that ionic current blockades produced by different DNA nucleotides are, in general, indicative of the nucleotide type, but very sensitive to the orientation of the nucleotides in the nanopore. Taken together, our simulations suggest that strand sequencing of DNA by measuring the ionic current blockades in graphene nanopores may be possible, given that the conformation of DNA nucleotides in the nanopore can be controlled through precise engineering of the nanopore surface.

Molecular dynamics (MD) simulations have become a standard method for the rational design and interpretation of experimental studies of DNA translocation through nanopores. The MD method, however, offers a multitude of algorithms, parameters, and other protocol choices that can affect the accuracy of the resulting data as well as computational efficiency. In this chapter, we examine the most popular choices offered by the MD method, seeking an optimal set of parameters that enable the most computationally efficient and accurate simulations of DNA and ion transport through biological nanopores. In particular, we examine the influence of short-range cutoff, integration timestep and force field parameters on the temperature and concentration dependence of bulk ion conductivity, ion pairing, ion solvation energy, DNA structure, DNA-ion interactions, and the ionic current through a nanopore.

Using nanopores to sequence DNA rapidly and at a low cost has the potential to radically transform the field of genomic research. However, despite all the exciting developments in the field, sequencing DNA using a nanopore has yet to be demonstrated. Among the many problems that hinder development of the nanopore sequencing methods is the inability of current experimental techniques to visualize DNA conformations in a nanopore and directly relate the microscopic state of the system to the measured signal. We have recently shown that such tasks could be accomplished through computation. This chapter provides step-by-step instructions of how to build atomic scale models of biological and solid-state nanopore systems, use the molecular dynamics method to simulate the electric field-driven transport of ions and DNA through the nanopores, and analyze the results of such computational experiments.

Microtubules (MTs) are the largest type of cellular filament, essential in processes ranging from mitosis and meiosis to flagellar motility. Many of the processes depend critically on the mechanical properties of the MT, but the elastic moduli, notably the Young's modulus, are not directly revealed in experiment, which instead measures either flexural rigidity or response to radial deformation. Molecular dynamics (MD) is a method that allows the mechanical properties of single biomolecules to be investigated through computation. Typically, MD requires an atomic resolution structure of the molecule, which is unavailable for many systems, including MTs. By combining structural information from cryo-electron microscopy and electron crystallography, we have constructed an all-atom model of a complete MT and used MD to determine its mechanical properties. The simulations revealed nonlinear axial stress-strain behavior featuring a pronounced softening under extension, a possible plastic deformation transition under radial compression, and a distinct asymmetry in response to the two senses of twist. This work demonstrates the possibility of combining different levels of structural information to produce all-atom models suitable for quantitative MD simulations, which extends the range of systems amenable to the MD method and should enable exciting advances in our microscopic knowledge of biology.

Microtubules (MTs) are the largest type of cytoskeletal filament, and are essential in processes ranging from mitosis and meiosis to flaggelar motility. Many of these functions depend critically on the elastic properties of the MT, but the axial Young's and shear moduli have not been directly measured in experiments, which have instead measured flexural rigidity or radial elastic properties. Molecular Dynamics (MD) can reveal mechanical characteristics of biopolymers inaccessible to experiment, as well as the microscopic mechanisms underlying them, on the single-molecule level. However, while the atomic structures of alpha- and beta-tubulin have been solved, the only published structures of a complete MT are cryo-electron microscopy (cryo-EM) maps far from atomic resolution. To build our all-atom model, we used a 3-D energy potential based on a cryo-EM map as a target for the crystallographic tubulin dimer structure. By applying forces derived from this potential in an MD simulation, tubulin was made to adopt an MT conformation, yielding an all-atom model of a complete MT. Utilizing periodic boundary conditions and custom anisotropic pressure control, we could simulate the stretching and compression of an effectively infinite MT, while a force script was used to apply shear stress, thereby allowing individual determination of the elastic moduli. This work demonstrates the utility of Molecular Dynamics for determining the elastic properties of biological filaments despite the lack of a crystallized filament, opening the door to the study of other biopolymers.

The transport of biomolecules across cell boundaries is central to cellular function. While structures of many membrane channels are known, the permeation mechanism is known only for a select few. Molecular dynamics (MD) is a computational method that can provide an accurate description of permeation events at the atomic level, which is required for understanding the transport mechanism. However, due to the relatively short time scales accessible to this method, it is of limited utility. Here, we present a method for all-atom simulation of electric field-driven transport of large solutes through membrane channels, which in tens of nanoseconds can provide a realistic account of a permeation event that would require a millisecond simulation using conventional MD. In this method, the average distribution of the electrostatic potential in a membrane channel under a transmembrane bias of interest is determined first from an all-atom MD simulation. This electrostatic potential, defined on a grid, is subsequently applied to a charged solute to steer its permeation through the membrane channel. We apply this method to investigate permeation of DNA strands, DNA hairpins, and alpha-helical peptides through alpha-hemolysin. To test the accuracy of the method, we computed the relative permeation rates of DNA strands having different sequences and global orientations. The results of the G-SMD simulations were found to be in good agreement in experiment.