Non-Markovian noise mediated through anomalous diffusion within ion channels

Computational membrane biophysics: From ion channel interactions with drugs to cellular function

The rapid development of experimental and computational techniques has changed fundamentally our understanding of cellular-membrane transport. The advent of powerful computers and refined force-fields for proteins, ions, and lipids has expanded the applicability of Molecular Dynamics (MD) simulations. A myriad of cellular responses is modulated through the binding of endogenous and exogenous ligands (e.g. neurotransmitters and drugs, respectively) to ion channels. Deciphering the thermodynamics and kinetics of the ligand binding processes to these membrane proteins is at the heart of modern drug development. The ever-increasing computational power has already provided insightful data on the thermodynamics and kinetics of drug-target interactions, free energies of solvation, and partitioning into lipid bilayers for drugs. This review aims to provide a brief summary about modeling approaches to map out crucial binding pathways with intermediate conformations and free-energy surfaces for drug-ion channel binding mechanisms that are responsible for multiple effects on cellular functions. We will discuss post-processing analysis of simulation-generated data, which are then transformed to kinetic models to better understand the molecular underpinning of the experimental observables under the influence of drugs or mutations in ion channels. This review highlights crucial mathematical frameworks and perspectives on bridging different well-established computational techniques to connect the dynamics and timescales from all-atom MD and free energy simulations of ion channels to the physiology of action potentials in cellular models. This article is part of a Special Issue entitled: Biophysics in Canada, edited by Lewis Kay, John Baenziger, Albert Berghuis and Peter Tieleman.

Solvent-shared pairs of densely charged ions induce intense but short-range supra-additive slowdown of water rotation

Magnesium and sulfate ions in solvent-shared (SIP) ion pair configuration supra-additively slowdown the rotation of water molecules between them; water molecules around solvent-separated (2SIP) ion pairs show only additive slowdown.

Fractal physiology and the fractional calculus: a perspective

This paper presents a restricted overview of Fractal Physiology focusing on the complexity of the human body and the characterization of that complexity through fractal measures and their dynamics, with fractal dynamics being described by the fractional calculus. Not only are anatomical structures (Grizzi and Chiriva-Internati, 2005), such as the convoluted surface of the brain, the lining of the bowel, neural networks and placenta, fractal, but the output of dynamical physiologic networks are fractal as well (Bassingthwaighte et al., 1994). The time series for the inter-beat intervals of the heart, inter-breath intervals and inter-stride intervals have all been shown to be fractal and/or multifractal statistical phenomena. Consequently, the fractal dimension turns out to be a significantly better indicator of organismic functions in health and disease than the traditional average measures, such as heart rate, breathing rate, and stride rate. The observation that human physiology is primarily fractal was first made in the 1980s, based on the analysis of a limited number of datasets. We review some of these phenomena herein by applying an allometric aggregation approach to the processing of physiologic time series. This straight forward method establishes the scaling behavior of complex physiologic networks and some dynamic models capable of generating such scaling are reviewed. These models include simple and fractional random walks, which describe how the scaling of correlation functions and probability densities are related to time series data. Subsequently, it is suggested that a proper methodology for describing the dynamics of fractal time series may well be the fractional calculus, either through the fractional Langevin equation or the fractional diffusion equation. A fractional operator (derivative or integral) acting on a fractal function, yields another fractal function, allowing us to construct a fractional Langevin equation to describe the evolution of a fractal statistical process. Control of physiologic complexity is one of the goals of medicine, in particular, understanding and controlling physiological networks in order to ensure their proper operation. We emphasize the difference between homeostatic and allometric control mechanisms. Homeostatic control has a negative feedback character, which is both local and rapid. Allometric control, on the other hand, is a relatively new concept that takes into account long-time memory, correlations that are inverse power law in time, as well as long-range interactions in complex phenomena as manifest by inverse power-law distributions in the network variable. We hypothesize that allometric control maintains the fractal character of erratic physiologic time series to enhance the robustness of physiological networks. Moreover, allometric control can often be described using the fractional calculus to capture the dynamics of complex physiologic networks.