Understanding the mechanisms of action of membrane proteins requires the elucidation of their structures to high resolution. The critical step in accomplishing this by x-ray crystallography is the routine availability of well-ordered three-dimensional crystals. We have devised a novel, rational approach to meet this goal using quasisolid lipidic cubic phases. This membrane system, consisting of lipid, water, and protein in appropriate proportions, forms a structured, transparent, and complex three-dimensional lipidic array, which is pervaded by an intercommunicating aqueous channel system. Such matrices provide nucleation sites ("seeding") and support growth by lateral diffusion of protein molecules in the membrane ("feeding"). Bacteriorhodopsin crystals were obtained from bicontinuous cubic phases, but not from micellar systems, implying a critical role of the continuity of the diffusion space (the bilayer) on crystal growth. Hexagonal bacteriorhodopsin crystals diffracted to 3.7 A resolution, with a space group P6(3), and unit cell dimensions of a = b = 62 A, c = 108 A; alpha = beta = 90 degrees and gamma = 120 degrees.

https://www.pnas.org/content/pnas/93/25/14532.full.pdf

Lipidic cubic phases: a novel concept for the crystallization of membrane proteins.

OMP Peptide Signals Initiate the Envelope-Stress Response by Activating DegS Protease via Relief of Inhibition Mediated by Its PDZ Domain

Membrane protein crystallization.

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

/pdf/modeling-and-simulation-of-ion-channels-4ltx589032.pdf

Modeling and simulation of ion channels.

A lipid’s eye view of membrane protein crystallization in mesophases

The structure of OmpF porin in a tetragonal crystal form

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The structure of OmpF porin in a tetragonal crystal form