Single shot detection of alterations across multiple ionic currents from assimilation of cell membrane dynamics.

The dysfunction of ion channels is a causative factor in a variety of neurological diseases, thereby defining the implicated channels as key drug targets. The detection of functional changes in multiple specific ionic currents currently presents a challenge, particularly when the neurological causes are either a priori unknown, or are unexpected. Traditional patch clamp electrophysiology is a powerful tool in this regard but is low throughput. Here, we introduce a single-shot method for detecting alterations amongst a range of ion channel types from subtle changes in membrane voltage in response to a short chaotically driven current clamp protocol. We used data assimilation to estimate the parameters of individual ion channels and from these we reconstructed ionic currents which exhibit significantly lower error than the parameter estimates. Such reconstructed currents thereby become sensitive predictors of functional alterations in biological ion channels. The technique correctly predicted which ionic current was altered, and by approximately how much, following pharmacological blockade of BK, SK, A-type K+ and HCN channels in hippocampal CA1 neurons. We anticipate this assay technique could aid in the detection of functional changes in specific ionic currents during drug screening, as well as in research targeting ion channel dysfunction.

Noise-activated barrier crossing in multiattractor dissipative neural networks.

Noise-activated transitions between coexisting attractors are investigated in a chaotic spiking network. At low noise level, attractor hopping consists of discrete bifurcation events that conserve the memory of initial conditions. When the escape probability becomes comparable to the intrabasin hopping probability, the lifetime of attractors is given by a detailed balance where the less coherent attractors act as a sink for the more coherent ones. In this regime, the escape probability follows an activation law allowing us to assign pseudoactivation energies to limit cycle attractors. These pseudoenergies introduce a useful metric for evaluating the resilience of biological rhythms to perturbations.

Robust neuromorphic coupled oscillators for adaptive pacemakers.

Neural coupled oscillators are a useful building block in numerous models and applications. They were analyzed extensively in theoretical studies and more recently in biologically realistic simulations of spiking neural networks. The advent of mixed-signal analog/digital neuromorphic electronic circuits provides new means for implementing neural coupled oscillators on compact, low-power, spiking neural network hardware platforms. However, their implementation on this noisy, low-precision and inhomogeneous computing substrate raises new challenges with regards to stability and controllability. In this work, we present a robust, spiking neural network model of neural coupled oscillators and validate it with an implementation on a mixed-signal neuromorphic processor. We demonstrate its robustness showing how to reliably control and modulate the oscillator's frequency and phase shift, despite the variability of the silicon synapse and neuron properties. We show how this ultra-low power neural processing system can be used to build an adaptive cardiac pacemaker modulating the heart rate with respect to the respiration phases and compare it with surface ECG and respiratory signal recordings from dogs at rest. The implementation of our model in neuromorphic electronic hardware shows its robustness on a highly variable substrate and extends the toolbox for applications requiring rhythmic outputs such as pacemakers.

Ballistic Hall Photovoltammetry of Magnetic Resonance in Individual Nanomagnets.

We report on ballistic Hall photovoltammetry as a contactless probe of localized spin excitations. Spins resonating in the near field of a two-dimensional electron system are shown to induce a long range electromotive force that we calculate. We use this coupling mechanism to detect the spin wave eigenmodes of a single ferromagnet of sub-100 nm size. The high sensitivity of this detection technique, 380 spins/sqrt[Hz], and its noninvasiveness present advantages for probing magnetization dynamics and spin transport.

Estimation of neuron parameters from imperfect observations.

The estimation of parameters controlling the electrical properties of biological neurons is essential to determine their complement of ion channels and to understand the function of biological circuits. By synchronizing conductance models to time series observations of the membrane voltage, one may construct models capable of predicting neuronal dynamics. However, identifying the actual set of parameters of biological ion channels remains a formidable theoretical challenge. Here, we present a regularization method that improves convergence towards this optimal solution when data are noisy and the model is unknown. Our method relies on the existence of an offset in parameter space arising from the interplay between model nonlinearity and experimental error. By tuning this offset, we induce saddle-node bifurcations from sub-optimal to optimal solutions. This regularization method increases the probability of finding the optimal set of parameters from 67% to 94.3%. We also reduce parameter correlations by implementing adaptive sampling and stimulation protocols compatible with parameter identifiability requirements. Our results show that the optimal model parameters may be inferred from imperfect observations provided the conditions of observability and identifiability are fulfilled.

Enhancing respiratory sinus arrhythmia increases cardiac output in rats with left ventricular dysfunction.

KEY POINTS: Respiratory sinus arrhythmia is physiological pacing of the heart that disappears in cardiovascular disease and is associated with poor cardiac prognosis. In heart failure, cardiac pacing has little, if any, variation in rate at rest. We proposed that reinstatement of respiratory sinus arrhythmia would improve cardiac function in rats with heart failure. Heart failure rats were paced daily for 2 weeks with either respiratory sinus arrhythmia or paced monotonically at a matched heart rate; cardiac function was measured using non-invasive echocardiography. Cardiac output and stroke volume were increased in rats paced with respiratory sinus arrhythmia compared to monotonic pacing, via improvement in systolic function that persisted beyond the pacing treatment period. We propose that respiratory sinus arrhythmia pacing reverse-remodels the heart in heart failure and is worth considering as a new form of cardiac pacemaking. ABSTRACT: Natural pacing of the heart results in heart rate variability, an indicator of good health and cardiac function. A contributor to heart rate variability is respiratory sinus arrhythmia or RSA - an intrinsic respiratory modulated pacing of heart rate. The loss of RSA is associated with poor cardiac prognosis and sudden cardiac death. We tested if reinstatement of respiratory-modulated heart rate (RMH) would improve cardiac performance in heart failure. Heart failure was induced in Wistar rats by ligation of the left anterior descending coronary artery. Rats were unpaced, monotonically paced and RMH paced; the latter had the same average heart rate as the monotonically paced animals. Cardiac function was assessed non-invasively using echocardiography before and after 2 weeks of daily pacing at a time when pacing was turned off. RMH increased cardiac output by 20 ± 8% compared to monotonic pacing (-3 ± 5%; P < 0.05). This improvement in cardiac output was associated with an increase in stroke volume compared to monotonic pacing (P = 0.03) and improvement in circumferential strain (P = 0.02). Improvements in ejection fraction (P = 0.08) and surrogate measures of left ventricle compliance did not reach significance. Increases in contractility (P < 0.05) and coronary blood flow (P < 0.05) were seen in vitro during variable pacing to mimic RMH. Thus, in rats with left ventricular dysfunction, chronic RMH pacing improved cardiac function through improvements in systolic function. As these improvements were made with pacing switched off, we propose the novel idea that RMH pacing causes reverse-remodelling.

Optimal solid state neurons.

Bioelectronic medicine is driving the need for neuromorphic microcircuits that integrate raw nervous stimuli and respond identically to biological neurons. However, designing such circuits remains a challenge. Here we estimate the parameters of highly nonlinear conductance models and derive the ab initio equations of intracellular currents and membrane voltages embodied in analog solid-state electronics. By configuring individual ion channels of solid-state neurons with parameters estimated from large-scale assimilation of electrophysiological recordings, we successfully transfer the complete dynamics of hippocampal and respiratory neurons in silico. The solid-state neurons are found to respond nearly identically to biological neurons under stimulation by a wide range of current injection protocols. The optimization of nonlinear models demonstrates a powerful method for programming analog electronic circuits. This approach offers a route for repairing diseased biocircuits and emulating their function with biomedical implants that can adapt to biofeedback.

Dual Mechanism for the Emergence of Synchronization in Inhibitory Neural Networks.

During cognitive tasks cortical microcircuits synchronize to bind stimuli into unified perception. The emergence of coherent rhythmic activity is thought to be inhibition-driven and stimulation-dependent. However, the exact mechanisms of synchronization remain unknown. Recent optogenetic experiments have identified two neuron sub-types as the likely inhibitory vectors of synchronization. Here, we show that local networks mimicking the soma-targeting properties observed in fast-spiking interneurons and the dendrite-projecting properties observed in somatostatin interneurons synchronize through different mechanisms which may provide adaptive advantages by combining flexibility and robustness. We probed the synchronization phase diagrams of small all-to-all inhibitory networks in-silico as a function of inhibition delay, neurotransmitter kinetics, timings and intensity of stimulation. Inhibition delay is found to induce coherent oscillations over a broader range of experimental conditions than high-frequency entrainment. Inhibition delay boosts network capacity (ln2)-N-fold by stabilizing locally coherent oscillations. This work may inform novel therapeutic strategies for moderating pathological cortical oscillations.

Inhibition delay increases neural network capacity through Stirling transform.

Inhibitory neural networks are found to encode high volumes of information through delayed inhibition. We show that inhibition delay increases storage capacity through a Stirling transform of the minimum capacity which stabilizes locally coherent oscillations. We obtain both the exact and asymptotic formulas for the total number of dynamic attractors. Our results predict a (ln2)^{-N}-fold increase in capacity for an N-neuron network and demonstrate high-density associative memories which host a maximum number of oscillations in analog neural devices.

Ultrafast pressure sensing with transient tunnelling currents.

We report and systematically study large amplitude piezoresistance spikes in thin composite films under stress. These spikes are characterized by a unique double exponential decay which we demonstrate to be the signature of transient tunnelling currents. We establish an expression that predicts the dynamic conductivity of the composite with only three material parameters and use it to infer the magnitude of applied stress from resistance spikes, thus achieving quasi-instantaneous readout unhindered by viscoelastic relaxation. We demonstrate the proof of principle of ultrafast mechanoreceptors based on this effect by making a sensor array which images pressure at close to cinematic speeds with a sensitivity of 50 Pa.

Automatic Construction of Predictive Neuron Models through Large Scale Assimilation of Electrophysiological Data.

We report on the construction of neuron models by assimilating electrophysiological data with large-scale constrained nonlinear optimization. The method implements interior point line parameter search to determine parameters from the responses to intracellular current injections of zebra finch HVC neurons. We incorporated these parameters into a nine ionic channel conductance model to obtain completed models which we then use to predict the state of the neuron under arbitrary current stimulation. Each model was validated by successfully predicting the dynamics of the membrane potential induced by 20-50 different current protocols. The dispersion of parameters extracted from different assimilation windows was studied. Differences in constraints from current protocols, stochastic variability in neuron output, and noise behave as a residual temperature which broadens the global minimum of the objective function to an ellipsoid domain whose principal axes follow an exponentially decaying distribution. The maximum likelihood expectation of extracted parameters was found to provide an excellent approximation of the global minimum and yields highly consistent kinetics for both neurons studied. Large scale assimilation absorbs the intrinsic variability of electrophysiological data over wide assimilation windows. It builds models in an automatic manner treating all data as equal quantities and requiring minimal additional insight.

Utility of a Novel Biofeedback Device for Within-Breath Modulation of Heart Rate in Rats: A Quantitative Comparison of Vagus Nerve vs. Right Atrial Pacing.

In an emerging bioelectronics era, there is a clinical need for physiological devices incorporating biofeedback that permits natural and demand-dependent control in real time. Here, we describe a novel device termed a central pattern generator (CPG) that uses cutting edge analog circuitry producing temporally controlled, electrical stimulus outputs based on the real time integration of physiological feedback. Motivated by the fact that respiratory sinus arrhythmia (RSA), which is the cyclical changes in heart rate every breath, is an essential component of heart rate variability (HRV) (an indicator of cardiac health), we have explored the versatility and efficiency of the CPG for producing respiratory modulation of heart rate in anesthetized, spontaneously breathing rats. Diaphragmatic electromyographic activity was used as the input to the device and its output connected to either the right cervical vagus nerve or the right atrium for pacing heart rate. We found that the CPG could induce respiratory related heart rate modulation that closely mimicked RSA. Whether connected to the vagus nerve or right atrium, the versatility of the device was demonstrated by permitting: (i) heart rate modulation in any phase of the respiratory cycle, (ii) control of the magnitude of heart rate modulation, and (iii) instant adaptation to changes in respiratory frequency. Vagal nerve pacing was only possible following transection of the nerve limiting its effective use chronically. Pacing via the right atrium permitted better flexibility and control of heart rate above its intrinsic level. This investigation now lays the foundation for future studies using this biofeedback technology permitting closer analysis of both the function and dysfunction of RSA.

Experimental observation of multistability and dynamic attractors in silicon central pattern generators.

We report on the multistability of chaotic networks of silicon neurons and demonstrate how spatiotemporal sequences of voltage oscillations are selected with timed current stimuli. A three neuron central pattern generator was built by interconnecting Hodgkin-Huxley neurons with mutually inhibitory links mimicking gap junctions. By systematically varying the timing of current stimuli applied to individual neurons, we generate the phase lag maps of neuronal oscillators and study their dependence on the network connectivity. We identify up to six attractors consisting of triphasic sequences of unevenly spaced pulses propagating clockwise and anticlockwise. While confirming theoretical predictions, our experiments reveal more complex oscillatory patterns shaped by the ratio of the pulse width to the oscillation period. Our work contributes to validating the command neuron hypothesis.

Silicon central pattern generators for cardiac diseases.

Cardiac rhythm management devices provide therapies for both arrhythmias and resynchronisation but not heart failure, which affects millions of patients worldwide. This paper reviews recent advances in biophysics and mathematical engineering that provide a novel technological platform for addressing heart disease and enabling beat-to-beat adaptation of cardiac pacing in response to physiological feedback. The technology consists of silicon hardware central pattern generators (hCPGs) that may be trained to emulate accurately the dynamical response of biological central pattern generators (bCPGs). We discuss the limitations of present CPGs and appraise the advantages of analog over digital circuits for application in bioelectronic medicine. To test the system, we have focused on the cardio-respiratory oscillators in the medulla oblongata that modulate heart rate in phase with respiration to induce respiratory sinus arrhythmia (RSA). We describe here a novel, scalable hCPG comprising physiologically realistic (Hodgkin-Huxley type) neurones and synapses. Our hCPG comprises two neurones that antagonise each other to provide rhythmic motor drive to the vagus nerve to slow the heart. We show how recent advances in modelling allow the motor output to adapt to physiological feedback such as respiration. In rats, we report on the restoration of RSA using an hCPG that receives diaphragmatic electromyography input and use it to stimulate the vagus nerve at specific time points of the respiratory cycle to slow the heart rate. We have validated the adaptation of stimulation to alterations in respiratory rate. We demonstrate that the hCPG is tuneable in terms of the depth and timing of the RSA relative to respiratory phase. These pioneering studies will now permit an analysis of the physiological role of RSA as well as its any potential therapeutic use in cardiac disease.

Estimating parameters and predicting membrane voltages with conductance-based neuron models.

Recent results demonstrate techniques for fully quantitative, statistical inference of the dynamics of individual neurons under the Hodgkin-Huxley framework of voltage-gated conductances. Using a variational approximation, this approach has been successfully applied to simulated data from model neurons. Here, we use this method to analyze a population of real neurons recorded in a slice preparation of the zebra finch forebrain nucleus HVC. Our results demonstrate that using only 1,500 ms of voltage recorded while injecting a complex current waveform, we can estimate the values of 12 state variables and 72 parameters in a dynamical model, such that the model accurately predicts the responses of the neuron to novel injected currents. A less complex model produced consistently worse predictions, indicating that the additional currents contribute significantly to the dynamics of these neurons. Preliminary results indicate some differences in the channel complement of the models for different classes of HVC neurons, which accords with expectations from the biology. Whereas the model for each cell is incomplete (representing only the somatic compartment, and likely to be missing classes of channels that the real neurons possess), our approach opens the possibility to investigate in modeling the plausibility of additional classes of channels the cell might possess, thus improving the models over time. These results provide an important foundational basis for building biologically realistic network models, such as the one in HVC that contributes to the process of song production and developmental vocal learning in songbirds.

Modulation of respiratory sinus arrhythmia in rats with central pattern generator hardware.

We report on the modulation of respiratory sinus arrhythmia in rats with central pattern generator (CPG) hardware made of silicon neurons. The neurons are made to compete through mutually inhibitory synapses to provide timed electrical oscillations that stimulate the peripheral end of vagus nerve at specific points of the respiratory cycle: the inspiratory phase (φ(1)), the early expiratory phase (φ(2)) and the late expiratory phase (φ(3)). In this way the CPG hardware mimics the neuron populations in the brainstem which through connections with cardiac vagal motoneurones control respiratory sinus arrhythmia (RSA). Here, we time the output of the CPG hardware from the phrenic nerve activity recorded from rats while monitoring heart rate changes evoked by vagal nerve stimulation (derived from ECG) controlled by the CPG. This neuroelectric stimulation has the effect of reducing the heart rate and increasing the arterial pressure. The artificially induced RSA strongly depends on the timing of pulses within the breathing cycle. It is strongest when the vagus nerve is stimulated during the inspiratory phase (φ(1)) or the early expiratory phase (φ(2)) in which case the heart rate slows by 50% of the normal rate. Heart rate modulation is less when the same exact stimulus is applied during the late expiratory phase (φ(3)). These trials show that neurostimulation by CPG hardware can augment respiratory sinus arrhythmia. The CPG hardware technology opens a new line of therapeutic possibilities for prosthetic devices that restore RSA in patients where respiratory-cardiac coupling has been lost.

Electron dynamics in inhomogeneous magnetic fields.

This review explores the dynamics of two-dimensional electrons in magnetic potentials that vary on scales smaller than the mean free path. The physics of microscopically inhomogeneous magnetic fields relates to important fundamental problems in the fractional quantum Hall effect, superconductivity, spintronics and graphene physics and spins out promising applications which will be described here. After introducing the initial work done on electron localization in random magnetic fields, the experimental methods for fabricating magnetic potentials are presented. Drift-diffusion phenomena are then described, which include commensurability oscillations, magnetic channelling, resistance resonance effects and magnetic dots. We then review quantum phenomena in magnetic potentials including magnetic quantum wires, magnetic minibands in superlattices, rectification by snake states, quantum tunnelling and Klein tunnelling. The third part is devoted to spintronics in inhomogeneous magnetic fields. This covers spin filtering by magnetic field gradients and circular magnetic fields, electrically induced spin resonance, spin resonance fluorescence and coherent spin manipulation.