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We consider the selective permeation of ions through narrow water-filled channels in the presence of strong interaction between the ions. These interactions lead to highly correlated ionic motion, which can conveniently be described via the concept of a quasiparticle. Here, we connect the quasiparticle’s effective potential and the multi-ion potential of the mean force, found through molecular dynamics simulations, and we validate the method on an analytical toy model of the KcsA channel. Possible future applications of the method to the connection between molecular dynamical calculations and the experimentally measured current-voltage and current-concentration characteristics of the channel are discussed.

The highly selective permeation of ions through biological ion channels is an unsolved problem of noise and fluctuations. In this paper, we motivate and introduce a non-equilibrium and self-consistent multi-species kinetic model, with the express aims of comparing with experimental recordings of current versus voltage and concentration and extracting important permeation parameters. For self-consistency, the behavior of the model at the two-state, i.e., selective limit in linear response, must agree with recent results derived from an equilibrium statistical theory. The kinetic model provides a good fit to data, including the key result of an anomalous mole fraction effect.

The problem of predicting selective transport of ions through nano-pores from their structure in the biological and nano-technological systems is addressed. We use a molecular dynamics simulation to provide insight into the key physical parameters of nano-pores and develop a self-consistent analytic theory describing ionic conduction and selectivity through these devices. We analyse the ion's dehydration and excess chemical potential, derive an expression for the conductivity of the nano-pore, and emphasize the role of fluctuations in its performance. The theory is verified by comparison of the predicted current-voltage characteristics with the molecular dynamics results and experimental data obtained for a graphene nano-pore and the KcsA biological channel.

Just lifting a finger involves the coordinated opening and closing of billions of ion channels. These natural nanotubes play an essential role in the physiology of all living creatures, from bacteria to humans [1, 2]. By providing for the exchange of ions across cellular membranes, they control a vast range of biological processes, and their dysfunction leads to numerous diseases.

A discrete electrostatic/diffusion model has been developed to describe the selective permeation of ion channels, based on ionic Coulomb blockade (ICB) and quantised dehydration (QD). It has been applied to describe selectivity phenomena measured in the bacterial NaChBac sodium channel and some of its mutants. Site-directed mutagenesis and the whole-cell patch-clamp technique were used to investigate how the value $Q_f$ of the fixed charge at the selectivity filter (SF) affected both valence and alike-charge selectivity. The new ICB/QD model predicts that increasing ${Q_f}$ should lead to a shift of selectivity sequences towards larger ion sizes and charges, a result that agrees with the present experiments and with earlier work. Comparison of the model with experimental data provides evidence for an {\it effective charge} $Q_f^*$ at the SF that is smaller in magnitude than the nominal $Q_f$ corresponding to the charge on the isolated protein residues. Furthermore, $Q_f^*$ was different for aspartate and glutamate charged rings and also depended on their position within the SF. It is suggested that protonation of the residues within the restricted space is an important factor in significantly reducing the effective charge of the EEEE ring. Values of $Q_f^*$ derived from experiments on the anomalous mole fraction effect (AMFE) agree well with expectations based on the ICB/QD model and have led to the first clear demonstration of the expected ICB oscillations in Ca$^{2+}$ conduction as a function of the fixed charge. Pilot studies of the dependence of Ca$^{2+}$ conduction on pH are consistent with the predictions of the model.

There is an increasing need for everyday communications to be both secure and resistant to external perturbations. We have therefore created an experimental implementation of the coupling-function-based secure communication protocol, in order to assess its robustness to channel noise. The transmitter and receiver are implemented on single-board computers, thereby facilitating communication of the analog electronic signals. The information signals are encrypted at the transmitter as the timevariability of nonlinear coupling functions between dynamical systems. This results in a complicated nonlinear mixing and scrambling of the information. To replicate the channel noise, analog white noise is added to the encrypted signals. After digitization at the receiver, the decryption is performed with dynamical Bayesian inference to take account of time-varying dynamics in the presence of noise. The dynamical Bayesian approach effectively separates the deterministic information signals from the perturbations of dynamical channel noise. The experimental realization has demonstrated the feasibility, and established the performance, of the protocol for secure, reliable, communication even with high levels of channel noise.

We now know a great deal about the nature of life on Earth. We understand how it functions and, in many cases, how it can be modified; but how it arose here in the first place remains an enduring mystery. It is well established that life in some form, probably akin to bacteria, was already flourishing about 3.8 billion years ago, i.e. almost as soon as the young Earth had cooled enough for it not to be cooked. Once life had appeared, it is not difficult to envisage how the combination of random mutation and Darwinian evolution (survival of the fittest) has brought us and the Earth to where we are today. There remain some notable residual problems, e.g. the seemingly improbable appearance of the complicated eukaryotic cell which forms the building blocks for the higher forms of life like plants and people but, in a rough-and-ready kind of way, the story seems clear and convincing. Unfortunately, however, no evidence remains about how the process got started.

Background. The selectivity of biological cation channels is defined by a short, narrow selectivity filter, having a negative net fixed charge Qf. Voltage gated bacterial channels (NaChBac and some others) are frequently used in biophysics as simplified models of mammalian calcium and sodium channels. We report an experimental, analytic and numerical study of the effects of Qf and bulk ionic concentrations of Ca2+ and Na+ on conduction and selectivity of NaChBac channels, wild type and Qf-varied mutants. Methods. Site-directed mutagenesis and voltage clamp recordings were used to investigate the Na+/Ca2+ selectivity, divalent blockade and anomalous mole fraction effect (AMFE) for different NaChBac wild type/mutants channels and the properties dependence on Qf. Experimental results were compared with Brownian dynamics simulations and with analytic predictions of the ionic Coulomb blockade (ICB) model, which was extended to encompass bulk concentration effects. Results. It was shown that changing of Qf from –4e (for LESWAS wild type) to –8e (for LEDWAS mutant) leads to strong divalent blockade of the Na+ current by micromolar amounts of Ca2+ ions, similar to the effects seen in mammalian calcium channels. The BD simulations revealed a concentration-related logarithmic shift of the conduction bands. These results were shown to be consistent with ICB model predictions. Conclusions. The extended ICB model explains the experimental (divalent blockade and AMFE) and simulated (multi-ion bands and their concentration-related shifts) selectivity phenomena of NaChBac channel and its charge-varied mutants. These results extend the understanding of ion channel selectivity and may also be applicable to biomimetic nanopores with charged walls.

The role of nonlinear dissipation in vibrational resonance (VR) is investigated in an inhomogeneous system characterized by a symmetric and spatially-periodic potential, and subjected to non-uniform, state-dependent, damping and a bi-harmonic driving force. The contributions of the parameters of the high frequency signal to the system’s effective dissipation are examined theoretically in comparison to linearly-damped systems, for which the parameter of interest is the effective stiffness in the equation of slow vibration. We show that the VR effect can be enhanced by varying the nonlinear dissipation parameters; and that it can be induced by a parameter that is shared by the damping inhomogeneity and the system potential. Furthermore, we have apparently identified the origin of the nonlinear-dissipation-enhanced response: we provide evidence of its connection to an Hopf bifurcation, accompanied by monotonic attractor enlargement in the VR regime.

The dynamical systems found in Nature are rarely isolated. Instead they interact and influence each other. The coupling functions that connect them contain detailed information about the functional mechanisms underlying the interactions and prescribe the physical rule specifying how an interaction occurs. Here, we aim to present a coherent and comprehensive review encompassing the rapid progress made recently in the analysis, understanding and applications of coupling functions. The basic concepts and characteristics of coupling functions are presented through demonstrative examples of different domains, revealing the mechanisms and emphasizing their multivariate nature. The theory of coupling functions is discussed through gradually increasing complexity from strong and weak interactions to globally-coupled systems and networks. A variety of methods that have been developed for the detection and reconstruction of coupling functions from measured data is described. These methods are based on different statistical techniques for dynamical inference. Stemming from physics, such methods are being applied in diverse areas of science and technology, including chemistry, biology, physiology, neuroscience, social sciences, mechanics and secure communications. This breadth of application illustrates the universality of coupling functions for studying the interaction mechanisms of coupled dynamical systems.

We report the first calorimetric detection of individual He2* excimers within a bath of superfluid 4He. The detector used in this work is a single superconducting titanium transition edge sensor (TES) with an energy resolution of 1 eV, immersed directly in the helium bath. He2* excimers are produced in the surrounding bath using an external gamma-ray source. These excimers exist either as short-lived singlet or long-lived triplet states. We demonstrate detection (and discrimination) of both states: in the singlet case the calorimeter records the absorption of a prompt 15 eV photon, and in the triplet case the calorimeter records a direct interaction of the molecule with the TES surface, which deposits a distinct fraction of the 15 eV, released upon decay, into the surface. We also briefly discuss the detector fabrication and characterization.

The dynamical systems found in Nature are rarely isolated. Instead they interact and influence each other. The coupling functions that connect them contain detailed information about the functional mechanisms underlying the interactions and prescribe the physical rule specifying how an interaction occurs. Here, we aim to present a coherent and comprehensive review encompassing the rapid progress made recently in the analysis, understanding and applications of coupling functions. The basic concepts and characteristics of coupling functions are presented through demonstrative examples of different domains, revealing the mechanisms and emphasizing their multivariate nature. The theory of coupling functions is discussed through gradually increasing complexity from strong and weak interactions to globally-coupled systems and networks. A variety of methods that have been developed for the detection and reconstruction of coupling functions from measured data is described. These methods are based on different statistical techniques for dynamical inference. Stemming from physics, such methods are being applied in diverse areas of science and technology, including chemistry, biology, physiology, neuroscience, social sciences, mechanics and secure communications. This breadth of application illustrates the universality of coupling functions for studying the interaction mechanisms of coupled dynamical systems.

We report an experimental study of the influences of the fixed charge and bulk ionic concentrations on the conduction of biological ion channels, and we consider the results within the framework of the ionic Coulomb blockade model of permeation and selectivity. Voltage clamp recordings were used to investigate the Na$^+$/Ca$^{2+}$ anomalous mole fraction effect (AMFE) exhibited by the bacterial sodium channel NaChBac and its mutants. Site-directed mutagenesis was used to study the effect of either increasing or decreasing the fixed charge in their selectivity filters for comparison with the predictions of the Coulomb blockade model. The model was found to describe well some aspects of the experimental (divalent blockade and AMFE) and simulated (discrete multi-ion conduction and occupancy band) phenomena, including a concentration-dependent shift of the Coulomb staircase. These results substantially extend the understanding of ion channel selectivity and may also be applicable to biomimetic nanopores with charged walls.

It has long been appreciated that Physics is essential to the understanding of many aspects of biology. As Jacques Prost points out in his Preface to Physics and Biology, the explosion of research activity at the interface between the two subjects over the last twenty years has led to investment on an unprecedented scale.

Classical ionic conduction through an inorganic monolayer nanopore is analogous to the quantum-mechanical phenomenon of electronic Coulomb blockade in quantum dots.

The flow of ions through a biological ion channel can be considered as transitions between occupied energy levels in the channel and either of the connecting bulk reservoirs [2]. Discreteness of ions and an electrostatic exclusion principle ensure that the number of channel energy levels equals the number of occupying ions. Using these fundamental physical principles we have recently introduced [1] an ionic Coulomb blockade (ICB) theory developed by analogy with the similar phenomenon of electron tunnelling in quantum dots [2,3]. In this picture channel selectivity is governed by energy level changes [1]. We present details of the ICB theory for ion transitions through the channel. It incorporates physiological solutions and channel properties: physical dimension, voltage drop and fixed charge, and hence allows for comparison with physiological data. The set of kinetic equations obtained using ICB is analysed. The channel probability of occupancy as a function of transition rates (and hence fixed charge and number of ions) is obtained in the steady-state approximation. It is shown that this probability displays the staircase structure familiar from analysis of occupancy in quantum dots. It is also shown that current through the channel displays sharp peaks as a function of fixed charge, hence relating channel selectivity to the structure and position of energy levels. The contribution of hydration energy is also discussed. We anticipate that inclusion of this energy into ICB theory will provide an important insight into the selectivity and conductivity of ion channels.

Neutron reflectometry offers a unique opportunity for the direct observation of nano-stratification in 3He-4He mixtures in the ultra-low temperature limit. Unfortunately the results of recent experiments could not be well-modelled on account of a seemingly anomalous variation of reflectivity with momentum transfer. We now hypothesize that this effect is attributable to an optical distortion caused by the liquid’s meniscus near the container wall. The validity of this idea is tested and confirmed through a subsidiary experiment on a D2O sample, showing that the meniscus can significantly distort results if the beam size in the horizontal plane is comparable with, or bigger than, the diameter of the container. The meniscus problem can be eliminated if the beam size is substantially smaller than the diameter of the container, such that reflection takes place only from the flat region of the liquid surface thus excluding the meniscus tails. Practical measures for minimising the meniscus distortion effect are discussed.

The precise mechanisms underlying general anæsthesia pose important and still open questions. To address them, we have studied anæsthesia induced by the widely-used (intravenous) propofol and (inhalational) sevoflurane anæsthetics, computing cross-frequency coupling functions between neuronal, cardiac, and respiratory oscillations in order to determine their mutual interactions. The phase domain coupling function reveals the form of the function defining the mechanism of an interaction, as well as its coupling strength. Using a method based on dynamical Bayesian inference, we have thus identified and analyzed the coupling functions for six relationships. By quantitative assessment of the forms and strengths of the couplings, we have revealed how these relationships are altered by anæsthesia, also showing that some of them are differently affected by propofol and sevoflurane. These findings, together with the novel coupling function analysis, offer a new direction in the assessment of general anæsthesia and neurophysiological interactions in general.

The highly selective permeation of ions through biological ion channels can be described and explained in terms of fluctuational dynamics under the influence of powerful electrostatic forces. Hence valence selectivity, e.g. between Ca2+ and Na+ in calcium and sodium channels, can be described in terms of ionic Coulomb blockade, which gives rise to distinct conduction bands and stop-bands as the fixed negative charge Qf at the selectivity filter of the channel is varied. This picture accounts successfully for a wide range of conduction phenomena in a diversity of ion channels. A disturbing anomaly, however, is that what appears to be the same electrostatic charge and structure (the so-called EEEE motif) seems to select Na+ conduction in bacterial channels but Ca2+ conduction in mammalian channels. As a possible resolution of this paradox it is hypothesised that an additional charged protein residue on the permeation path of the mammalian channel increases |Qf | by e, thereby altering the selectivity from Na+ to Ca2+. Experiments are proposed that will enable the hypothesis to be tested.

It has long been appreciated that Physics is essential to the understanding of many aspects of biology. As Jacques Prost points out in his Preface to Physics and Biology, the explosion of research activity at the interface between the two subjects over the last twenty years has led to investment on an unprecedented scale.

The balance and functionality of the cardiovascular system are maintained by a network of couplings between the different oscillations involved. We study the effect of ageing on these interactions through the application of wavelet analysis, and by the use of dynamical Bayesian inference to compute coupling functions. The method, applied to phases extracted from microvascular flow recorded by laser Doppler flowmetry (LDF), reveals the coupling functions between oscillations propagated to the smallest vessels. Consistent with earlier work based on analysis of cardiac and respiratory phases obtained from direct measurements, our analysis demonstrates an impairment of the propagated cardio-respiratory coupling with ageing. The coupling weakens despite the increased cardiac component in the LDF with ageing. Our results bring new insight to the effect of ageing on cardiovascular regulation that might help improve the diagnostic potential of LDF monitors.

The conduction and selectivity of calcium/sodium ion channels are described in terms of ionic Coulomb blockade, a phenomenon based on charge discreteness, an electrostatic exclusion principle, and stochastic ion motion through the channel. This novel approach provides a unified explanation of numerous observed and modelled conductance and selectivity phenomena, including the anomalous mole fraction effect and discrete conduction bands. Ionic Coulomb blockade and resonant conduction are similar to electronic Coulomb blockade and resonant tunnelling in quantum dots. The model is equally applicable to other nanopores.

Depth of anaesthesia monitors usually analyse cerebral function with or without other physiological signals; noninvasive monitoring of the measured cardiorespiratory signals alone would offer a simple, practical alternative. We aimed to investigate whether such signals, analysed with novel, non-linear dynamic methods, would distinguish between the awake and anaesthetised states. We recorded ECG, respiration, skin temperature, pulse and skin conductivity before and during general anaesthesia in 27 subjects in good cardiovascular health, randomly allocated to receive propofol or sevoflurane. Mean values, variability and dynamic interactions were determined. Respiratory rate (p = 0.0002), skin conductivity (p = 0.03) and skin temperature (p = 0.00006) changed with sevoflurane, and skin temperature (p = 0.0005) with propofol. Pulse transit time increased by 17% with sevoflurane (p = 0.02) and 11% with propofol (p = 0.007). Sevoflurane reduced the wavelet energy of heart (p = 0.0004) and respiratory (p = 0.02) rate variability at all frequencies, whereas propofol decreased only the heart rate variability below 0.021 Hz (p < 0.05). The phase coherence was reduced by both agents at frequencies below 0.145 Hz (p < 0.05), whereas the cardiorespiratory synchronisation time was increased (p < 0.05). A classification analysis based on an optimal set of discriminatory parameters distinguished with 95% success between the awake and anaesthetised states. We suggest that these results can contribute to the design of new monitors of anaesthetic depth based on cardiovascular signals alone.