The Physical Basis of Ion Channel Kinetics: The Importance of Dynamics. In: Layton HE, Weinstein AM, editors. Membrane Transport and Renal Physiology. New York: Springer; 2002. pp. 27-52. [DOI: 10.1007/978-1-4684-9252-1_2]

Memory in Ion Channel Kinetics

Ion channels are transport proteins present in the lipid bilayers of biological membranes. They are involved in many physiological processes, such as the generation of nerve impulses, hormonal secretion, and heartbeat. Conformational changes in the ion channel-forming protein allow the opening or closing of pores to control the ionic flux through the cell membranes. The opening and closing of the ion channel have been classically treated as a random kinetic process, known as a Markov process. Here the time the channel remains in a given state is assumed to be independent of the condition it had in the previous state. More recently, however, several studies have shown that this process is not random but a deterministic one, where both the open and closed dwell-times and the ionic current flowing through the channel are history-dependent. This property is called long memory or long-range correlation. However, there is still much controversy regarding how this memory originates, which region of the channel is responsible for this property, and which models could best reproduce the memory effect. In this article, we provide a review of what is, where it is, its possible origin, and the mathematical methods used to analyze the long-term memory present in the kinetic process of ion channels.

Rational antibody design for undruggable targets using kinetically controlled biomolecular probes

Several important drug targets, e.g., ion channels and G protein-coupled receptors, are extremely difficult to approach with current antibody technologies. To address these targets classes, we explored kinetically controlled proteases as structural dynamics-sensitive druggability probes in native-state and disease-relevant proteins. By using low-Reynolds number flows, such that a single or a few protease incisions are made, we could identify antibody binding sites (epitopes) that were translated into short-sequence antigens for antibody production. We obtained molecular-level information of the epitope-paratope region and could produce high-affinity antibodies with programmed pharmacological function against difficult-to-drug targets. We demonstrate the first stimulus-selective monoclonal antibodies targeting the transient receptor potential vanilloid 1 (TRPV1) channel, a clinically validated pain target widely considered undruggable with antibodies, and apoptosis-inducing antibodies selectively mediating cytotoxicity in KRAS-mutated cells. It is our hope that this platform will widen the scope of antibody therapeutics for the benefit of patients.

Deterministic modeling of single-channel and whole-cell currents

As a complement to the experimental work, mathematical models are extensively used to study the functional properties of ionic channels. Even though it is generally assumed that the gating of ionic channels is a Markovian phenomenon, reports based on non-traditional analyses of experimental recordings suggest that non-Markovian processes might be also present. While the stochastic Markov models are by far the most adopted approach for the modeling of ionic channels, a model based on the idea of a deterministic process underlying the gating of ionic channels was proposed by Liebovitch and Toth (Liebovitch, L.S. and Toth, T.I., 1991. Journal of Theoretical Biology, 148(2), pp.243-267.) Here, by using a voltage-dependent K⁺ channel as a first approximation, we propose a modified version of the deterministic model of Liebovitch and Toth that, in addition to reproducing the single-channel currents simulated by a two-states Markov model, it is capable of reproducing the whole-cell currents produced by a population of K⁺ channels.

Strength-duration relationship for extracellular neural stimulation: numerical and analytical models

The strength-duration relationship for extracellular stimulation is often assumed to be similar to the classical intracellular stimulation model, with a slope asymptotically approaching 1/τ at pulse durations shorter than chronaxy. We modeled extracellular neural stimulation numerically and analytically for several cell shapes and types of active membrane properties. The strength-duration relationship was found to differ significantly from classical intracellular models. At pulse durations between 4 μs and 5 ms stimulation is dominated by sodium channels, with a slope of -0.72 in log-log coordinates for the Hodgkin-Huxley ion channel model. At shorter durations potassium channels dominate and slope decreases to -0.13. Therefore the charge per phase is decreasing with decreasing stimulus duration. With pulses shorter than cell polarization time (∼0.1-1 μs), stimulation is dominated by polarization dynamics with a classical -1 slope and the charge per phase becomes constant. It is demonstrated that extracellular stimulation can have not only lower but also upper thresholds and may be impossible below certain pulse durations. In some regimes the extracellular current can hyperpolarize cells, suppressing rather than stimulating spiking behavior. Thresholds for burst stimuli can be either higher or lower than that of a single pulse, depending on pulse duration. The modeled thresholds were found to be comparable to published experimental data. Electroporation thresholds, which limit the range of safe stimulation, were found to exceed stimulation thresholds by about two orders of magnitude. These results provide a biophysical basis for understanding stimulation dynamics and guidance for optimizing the neural stimulation efficacy and safety.