Dynamic clamp analyses of cardiac, endocrine, and neural function

Perturbation-specific responses by two neural circuits generating similar activity patterns

A fundamental question in neuroscience is whether neuronal circuits with variable circuit parameters that produce similar outputs respond comparably to equivalent perturbations.^1-4 Work on the pyloric rhythm of the crustacean stomatogastric ganglion (STG) showed that highly variable sets of intrinsic and synaptic conductances can generate similar circuit activity patterns.^5-9 Importantly, in response to physiologically relevant perturbations, these disparate circuit solutions can respond robustly and reliably,^10-12 but when exposed to extreme perturbations the underlying circuit parameter differences produce diverse patterns of disrupted activity.^7,12,13 In this example, the pyloric circuit is unchanged; only the conductance values vary. In contrast, the gastric mill rhythm in the STG can be generated by distinct circuits when activated by different modulatory neurons and/or neuropeptides.^14-21 Generally, these distinct circuits produce different gastric mill rhythms. However, the rhythms driven by stimulating modulatory commissural neuron 1 (MCN1) and bath-applying CabPK (Cancer borealis pyrokinin) peptide generate comparable output patterns, despite having distinct circuits that use separate cellular and synaptic mechanisms.^22-25 Here, we use these two gastric mill circuits to determine whether such circuits respond comparably when challenged with persisting (hormonal: CCAP) or acute (sensory: GPR neuron) metabotropic influences. Surprisingly, the hormone-mediated action separates these two rhythms despite activating the same ionic current in the same circuit neuron during both rhythms, whereas the sensory neuron evokes comparable responses despite acting via different synapses during each rhythm. These results highlight the need for caution when inferring the circuit response to a perturbation when that circuit is not well defined physiologically.

Patch Clamp Technology in the Twenty-First Century

In the almost four decades since its inception, the patch clamp technique has transitioned from a specialist skill to a method commonly used among many others in a lab. Development of patch clamp instrumentation has not been steady: A boost of product releases in rapid succession by multiple manufacturers in the 1990s had slowed to a trickle by the mid-2000s. In 2016, Sutter Instrument's entry into the market of turnkey patch clamp amplifier systems, defined as an amplifier with matching data acquisition hardware and software, caused a fresh breeze in a field in danger of going stale. Sutter has meanwhile completed the product line, culminating in the flagship dPatch^® Ultra-fast, Low-noise Digital Amplifier. The dPatch System constitutes a contemporary, digital design that features many firsts, including digital signal compensation, an extremely high bandwidth and fully integrated dynamic clamp capability, paired with the increasingly popular SutterPatch^® Software.This chapter compares feature sets of the new Sutter instrumentation with the established platforms by the other two providers of turnkey systems, Axon Instruments by Molecular Devices and HEKA Elektronik by Harvard Bioscience. A variety of products from other manufacturers, who rely on combination with components from other sources rather than offering turnkey systems, are listed, but for their conceptual diversity not compared at a great level of detail. The chapter further covers architectural considerations for patch clamp systems, headstage design, data acquisition strategies and efficient structuring of the recorded data, controlling and monitoring periphery, advanced technologies, such as software lock-in amplifier capability and dynamic clamp features, and application modules for efficient analysis of action potentials and postsynaptic events.

Shaw and Shal voltage-gated potassium channels mediate circadian changes in Drosophila clock neuron excitability

As in mammals, Drosophila circadian clock neurons display rhythms of activity with higher action potential firing rates and more positive resting membrane potentials during the day. This rhythmic excitability has been widely observed but, critically, its regulation remains unresolved. We have characterized and modelled the changes underlying these electrical activity rhythms in the lateral ventral clock neurons (LNvs). We show that currents mediated by the voltage-gated potassium channels Shaw (Kv3) and Shal (Kv4) oscillate in a circadian manner. Disruption of these channels, by expression of dominant negative (DN) subunits, leads to changes in circadian locomotor activity and shortens lifespan. LNv whole-cell recordings then show that changes in Shaw and Shal currents drive changes in action potential firing rate and that these rhythms are abolished when the circadian molecular clock is stopped. A whole-cell biophysical model using Hodgkin-Huxley equations can recapitulate these changes in electrical activity. Based on this model and by using dynamic clamp to manipulate clock neurons directly, we can rescue the pharmacological block of Shaw and Shal, restore the firing rhythm, and thus demonstrate the critical importance of Shaw and Shal. Together, these findings point to a key role for Shaw and Shal in controlling circadian firing of clock neurons and show that changes in clock neuron currents can account for this. Moreover, with dynamic clamp we can switch the LNvs between morning-like and evening-like states of electrical activity. We conclude that changes in Shaw and Shal underlie the daily oscillation in LNv firing rate.

Mathematical Modelling of Endocrine Systems

Hormone rhythms are ubiquitous and essential to sustain normal physiological functions. Combined mathematical modelling and experimental approaches have shown that these rhythms result from regulatory processes occurring at multiple levels of organisation and require continuous dynamic equilibration, particularly in response to stimuli. We review how such an interdisciplinary approach has been successfully applied to unravel complex regulatory mechanisms in the metabolic, stress, and reproductive axes. We discuss how this strategy is likely to be instrumental for making progress in emerging areas such as chronobiology and network physiology. Ultimately, we envisage that the insight provided by mathematical models could lead to novel experimental tools able to continuously adapt parameters to gradual physiological changes and the design of clinical interventions to restore normal endocrine function.

Membrane potential resonance frequency directly influences network frequency through electrical coupling

Oscillatory networks often include neurons with membrane potential resonance, exhibiting a peak in the voltage amplitude as a function of current input at a nonzero (resonance) frequency (f_res). Although f_res has been correlated to the network frequency (f_net) in a variety of systems, a causal relationship between the two has not been established. We examine the hypothesis that combinations of biophysical parameters that shift f_res, without changing other attributes of the impedance profile, also shift f_net in the same direction. We test this hypothesis, computationally and experimentally, in an electrically coupled network consisting of intrinsic oscillator (O) and resonator (R) neurons. We use a two-cell model of such a network to show that increasing f_res of R directly increases f_net and that this effect becomes more prominent if the amplitude of resonance is increased. Notably, the effect of f_res on f_net is independent of the parameters that define the oscillator or the combination of parameters in R that produce the shift in f_res, as long as this combination produces the same impedance vs. frequency relationship. We use the dynamic clamp technique to experimentally verify the model predictions by connecting a model resonator to the pacemaker pyloric dilator neurons of the crab Cancer borealis pyloric network using electrical synapses and show that the pyloric network frequency can be shifted by changing f_res in the resonator. Our results provide compelling evidence that f_res and resonance amplitude strongly influence f_net, and therefore, modulators may target these attributes to modify rhythmic activity.

Novel description of ionic currents recorded with the action potential clamp technique: application to excitatory currents in suprachiasmatic nucleus neurons

The traditional method of recording ionic currents in neurons has been with voltage-clamp steps. Other waveforms such as action potentials (APs) can be used. The AP clamp method reveals contributions of ionic currents that underlie excitability during an AP (Bean BP. Nat Rev Neurosci 8: 451-465, 2007). A novel usage of the method is described in this report. An experimental recording of an AP from the literature is digitized and applied computationally to models of ionic currents. These results are compared with experimental AP-clamp recordings for model verification or, if need be, alterations to the model. The method is applied to the tetrodotoxin-sensitive sodium ion current, INa, and the calcium ion current, ICa, from suprachiasmatic nucleus (SCN) neurons (Jackson AC, Yao GL, Bean BP. J Neurosci 24: 7985-7998, 2004). The latter group reported voltage-step and AP-clamp results for both components. A model of INa is constructed from their voltage-step results. The AP clamp computational methodology applied to that model compares favorably with experiment, other than a modest discrepancy close to the peak of the AP that has not yet been resolved. A model of ICa was constructed from both voltage-step and AP-clamp results of this component. The model employs the Goldman-Hodgkin-Katz equation for the current-voltage relation rather than the traditional linear dependence of this aspect of the model on the Ca(2+) driving force. The long-term goal of this work is a mathematical model of the SCN AP. The method is general. It can be applied to any excitable cell.

Computation of reduced energy input current stimuli for neuron phase models

A regularly spiking neuron can be studied using a phase model. The effect of an input stimulus current on the phase time derivative is captured by a phase response curve. This paper adapts a technique that was previously applied to conductance-based models to discover optimal input stimulus currents for phase models. First, the neuron phase response θ(t) due to an input stimulus current i(t) is computed using a phase model. The resulting θ(t) is taken to be a reference phase r(t). Second, an optimal input stimulus current i(*)(t) is computed to minimize a weighted sum of the square-integral `energy' of i(*)(t) and the tracking error between the reference phase r(t) and the phase response due to i(*)(t). The balance between the conflicting requirements of energy and tracking error minimization is controlled by a single parameter. The generated optimal current i(*)t) is then compared to the input current i(t) which was used to generate the reference phase r(t). This technique was applied to two neuron phase models; in each case, the current i(*)(t) generates a phase response similar to the reference phase r(t), and the optimal current i(*)(t) has a lower `energy' than the square-integral of i(t). For constant i(t), the optimal current i(*)(t) need not be constant in time. In fact, i(*)(t) is large (possibly even larger than i(t)) for regions where the phase response curve indicates a stronger sensitivity to the input stimulus current, and smaller in regions of reduced sensitivity.

Is there a relationship between brain-derived neurotrophic factor for driving neuronal auditory circuits with onset of auditory function and the changes following cochlear injury or during aging?

Brain-derived neurotrophic factor, BDNF, is one of the most important neurotrophic factors acting in the peripheral and central nervous system. In the auditory system its function was initially defined by using constitutive knockout mouse mutants and shown to be essential for survival of neurons and afferent innervation of hair cells in the peripheral auditory system. Further examination of BDNF null mutants also revealed a more complex requirement during re-innervation processes involving the efferent system of the cochlea. Using adult mouse mutants defective in BDNF signaling, it could be shown that a tonotopical gradient of BDNF expression within cochlear neurons is required for maintenance of a specific spatial innervation pattern of outer hair cells and inner hair cells. Additionally, BDNF is required for maintenance of voltage-gated potassium channels (KV) in cochlear neurons, which may form part of a maturation step within the ascending auditory pathway with onset of hearing and might be essential for cortical acuity of sound-processing and experience-dependent plasticity. A presumptive harmful role of BDNF during acoustic trauma and consequences of a loss of cochlear BDNF during aging are discussed in the context of a partial reversion of this maturation step. We compare the potentially beneficial and harmful roles of BDNF for the mature auditory system with those BDNF functions known in other sensory circuits, such as the vestibular, visual, olfactory, or somatosensory system.

A novel analysis of excitatory currents during an action potential from suprachiasmatic nucleus neurons

A new application of the action potential (AP) voltage-clamp technique is described based on computational analysis. An experimentally recorded AP is digitized. The resulting Vi vs. ti data set is applied to mathematical models of the ionic conductances underlying excitability for the cell from which the AP was recorded to test model validity. The method is illustrated for APs from suprachiasmatic nucleus (SCN) neurons and the underlying tetrodotoxin-sensitive Na(+) current, INa, and the Ca(2+) current, ICa. Voltage-step recordings have been made for both components from SCN neurons (Jackson et al. 2004). The combination of voltage-step and AP clamp results provides richer constraints for mathematical models of voltage-gated ionic conductances than either set of results alone, in particular the voltage-step results. For SCN neurons the long-term goal of this work is a realistic mathematical model of the SCN AP in which the equations for I(Na) and I(Ca) obtained from this analysis will be a part. Moreover, the method described in this report is general. It can be applied to any excitable cell.

Assisted closed-loop optimization of SSVEP-BCI efficiency

We designed a novel assisted closed-loop optimization protocol to improve the efficiency of brain-computer interfaces (BCI) based on steady state visually evoked potentials (SSVEP). In traditional paradigms, the control over the BCI-performance completely depends on the subjects' ability to learn from the given feedback cues. By contrast, in the proposed protocol both the subject and the machine share information and control over the BCI goal. Generally, the innovative assistance consists in the delivery of online information together with the online adaptation of BCI stimuli properties. In our case, this adaptive optimization process is realized by (1) a closed-loop search for the best set of SSVEP flicker frequencies and (2) feedback of actual SSVEP magnitudes to both the subject and the machine. These closed-loop interactions between subject and machine are evaluated in real-time by continuous measurement of their efficiencies, which are used as online criteria to adapt the BCI control parameters. The proposed protocol aims to compensate for variability in possibly unknown subjects' state and trait dimensions. In a study with N = 18 subjects, we found significant evidence that our protocol outperformed classic SSVEP-BCI control paradigms. Evidence is presented that it takes indeed into account interindividual variabilities: e.g., under the new protocol, baseline resting state EEG measures predict subjects' BCI performances. This paper illustrates the promising potential of assisted closed-loop protocols in BCI systems. Probably their applicability might be expanded to innovative uses, e.g., as possible new diagnostic/therapeutic tools for clinical contexts and as new paradigms for basic research.

MATLAB implementation of a dynamic clamp with bandwidth of >125 kHz capable of generating I Na at 37 °C

We describe the construction of a dynamic clamp with a bandwidth of >125 kHz that utilizes a high-performance, yet low-cost, standard home/office PC interfaced with a high-speed (16 bit) data acquisition module. High bandwidth is achieved by exploiting recently available software advances (code-generation technology and optimized real-time kernel). Dynamic-clamp programs are constructed using Simulink, a visual programming language. Blocks for computation of membrane currents are written in the high-level MATLAB language; no programming in C is required. The instrument can be used in single- or dual-cell configurations, with the capability to modify programs while experiments are in progress. We describe an algorithm for computing the fast transient Na(+) current (I Na) in real time and test its accuracy and stability using rate constants appropriate for 37 °C. We then construct a program capable of supplying three currents to a cell preparation: I Na, the hyperpolarizing-activated inward pacemaker current (I f) and an inward-rectifier K(+) current (I K1). The program corrects for the IR drop due to electrode current flow and also records all voltages and currents. We tested this program on dual patch-clamped HEK293 cells where the dynamic clamp controls a current-clamp amplifier and a voltage-clamp amplifier controls membrane potential, and current-clamped HEK293 cells where the dynamic clamp produces spontaneous pacing behavior exhibiting Na(+) spikes in otherwise passive cells.

Generalization of the dynamic clamp concept in neurophysiology and behavior

The idea of closed-loop interaction in in vitro and in vivo electrophysiology has been successfully implemented in the dynamic clamp concept strongly impacting the research of membrane and synaptic properties of neurons. In this paper we show that this concept can be easily generalized to build other kinds of closed-loop protocols beyond (or in addition to) electrical stimulation and recording in neurophysiology and behavioral studies for neuroethology. In particular, we illustrate three different examples of goal-driven real-time closed-loop interactions with drug microinjectors, mechanical devices and video event driven stimulation. Modern activity-dependent stimulation protocols can be used to reveal dynamics (otherwise hidden under traditional stimulation techniques), achieve control of natural and pathological states, induce learning, bridge between disparate levels of analysis and for a further automation of experiments. We argue that closed-loop interaction calls for novel real time analysis, prediction and control tools and a new perspective for designing stimulus-response experiments, which can have a large impact in neuroscience research.

Fast-activating voltage- and calcium-dependent potassium (BK) conductance promotes bursting in pituitary cells: a dynamic clamp study

The electrical activity pattern of endocrine pituitary cells regulates their basal secretion level. Rat somatotrophs and lactotrophs exhibit spontaneous bursting and have high basal levels of hormone secretion, while gonadotrophs exhibit spontaneous spiking and have low basal hormone secretion. It has been proposed that the difference in electrical activity between bursting somatotrophs and spiking gonadotrophs is due to the presence of large conductance potassium (BK) channels on somatotrophs but not on gonadotrophs. This is one example where the role of an ion channel type may be clearly established. We demonstrate here that BK channels indeed promote bursting activity in pituitary cells. Blocking BK channels in bursting lacto-somatotroph GH4C1 cells changes their firing activity to spiking, while further adding an artificial BK conductance via dynamic clamp restores bursting. Importantly, this burst-promoting effect requires a relatively fast BK activation/deactivation, as predicted by computational models. We also show that adding a fast-activating BK conductance to spiking gonadotrophs converts the activity of these cells to bursting. Together, our results suggest that differences in BK channel expression may underlie the differences in electrical activity and basal hormone secretion levels among pituitary cell types and that the rapid rate of BK channel activation is key to its role in burst promotion.

Antidromic potential spread modulates the receptor responses in the stretch receptor neurons of the crayfish

The effects of antidromic potential spread were investigated in the stretch receptor neurons of the crayfish. Current and potential responses to conductance changes were recorded in the dynamic clamp condition and compared to those obtained by using some conventional clamp methods and a compartmental neuron model. An analogue circuit was used for dynamic calculation of the injected receptor current as a function of the membrane potential and the given conductance change. Alternatively, receptor current responses to a mechanical stimulus were recorded and compared when the cell was voltage clamped to a previously recorded impulse wave form and the resting potential, respectively. Under dynamic clamp, the receptor current had an oscillating waveform which contrasts with the conventional recordings. Frequency, amplitude and sign of the oscillations were dependent on the applied conductance level, reversal potential and electrotonic attenuation. Mean current amplitude and frequency of the evoked impulse responses were smaller under dynamic clamp, especially for large conductance increases. However, firing frequency was larger if plotted against the mean current response. Recorded responses were similar to those calculated in the model. It was not possible to evoke any adaptation in the slowly adapting neuron by using the dynamic clamp. Evoked potential change served as a self limiting response, preventing the depolarization block. However, impulse duration was significantly shorter in the rapidly adapting neuron when the dynamic clamp was used. It was concluded that, in the stretch receptor neurons during a conductance increase, antidromic potential spread modulates the receptor responses and contributes to adaptation.

Dynamic clamp with StdpC software

Dynamic clamp is a powerful method that allows the introduction of artificial electrical components into target cells to simulate ionic conductances and synaptic inputs. This method is based on a fast cycle of measuring the membrane potential of a cell, calculating the current of a desired simulated component using an appropriate model and injecting this current into the cell. Here we present a dynamic clamp protocol using free, fully integrated, open-source software (StdpC, for spike timing-dependent plasticity clamp). Use of this protocol does not require specialist hardware, costly commercial software, experience in real-time operating systems or a strong programming background. The software enables the configuration and operation of a wide range of complex and fully automated dynamic clamp experiments through an intuitive and powerful interface with a minimal initial lead time of a few hours. After initial configuration, experimental results can be generated within minutes of establishing cell recording.

Timescales of multineuronal activity patterns reflect temporal structure of visual stimuli

The investigation of distributed coding across multiple neurons in the cortex remains to this date a challenge. Our current understanding of collective encoding of information and the relevant timescales is still limited. Most results are restricted to disparate timescales, focused on either very fast, e.g., spike-synchrony, or slow timescales, e.g., firing rate. Here, we investigated systematically multineuronal activity patterns evolving on different timescales, spanning the whole range from spike-synchrony to mean firing rate. Using multi-electrode recordings from cat visual cortex, we show that cortical responses can be described as trajectories in a high-dimensional pattern space. Patterns evolve on a continuum of coexisting timescales that strongly relate to the temporal properties of stimuli. Timescales consistent with the time constants of neuronal membranes and fast synaptic transmission (5–20 ms) play a particularly salient role in encoding a large amount of stimulus-related information. Thus, to faithfully encode the properties of visual stimuli the brain engages multiple neurons into activity patterns evolving on multiple timescales.

Geometry and dynamics of activity-dependent homeostatic regulation in neurons

To maintain activity in a functional range, neurons constantly adjust membrane excitability to changing intra- and extracellular conditions. Such activity-dependent homeostatic regulation (ADHR) is critical for normal processing of the nervous system and avoiding pathological conditions. Here, we posed a homeostatic regulation problem for the classical Morris-Lecar (ML) model. The problem was motivated by the phenomenon of the functional recovery of stomatogastric neurons in crustaceans in the absence of neuromodulation. In our study, the regulation of the ionic conductances in the ML model depended on the calcium current or the intracellular calcium concentration. We found an asymptotic solution to the problem under the assumption of slow regulation. The solution provides a full account of the regulation in the case of correlated or anticorrelated changes of the maximal conductances of the calcium and potassium currents. In particular, the solution shows how the target and parameters of the regulation determine which perturbations of the conductances can be compensated by the ADHR. In some cases, the sets of compensated initial perturbations are not convex. On the basis of our analysis we formulated specific questions for subsequent experimental and theoretical studies of ADHR.

Electrical Coupling and Passive Membrane Properties of AII Amacrine Cells

AII amacrine cells in the mammalian retina are connected via electrical synapses to on-cone bipolar cells and to other AII amacrine cells. To understand synaptic integration in these interneurons, we need information about the junctional conductance ( gj), the membrane resistance ( rm), the membrane capacitance ( Cm), and the cytoplasmic resistivity ( Ri). Due to the extensive electrical coupling, it is difficult to obtain estimates of rm, as well as the relative contribution of the junctional and nonjunctional conductances to the total input resistance of an AII amacrine cell. Here we used dual voltage-clamp recording of pairs of electrically coupled AII amacrine cells in an in vitro slice preparation from rat retina and applied meclofenamic acid (MFA) to block the electrical coupling and isolate single AII amacrines electrically. In the control condition, the input resistance ( Rin) was ∼620 MΩ and the apparent rm was ∼760 MΩ. After block of electrical coupling, determined by estimating gj in the dual recordings, Rin and rm were ∼4,400 MΩ, suggesting that the nongap junctional conductance of an AII amacrine cell is ∼16% of the total input conductance. Control experiments with nucleated patches from AII amacrine cells suggested that MFA had no effect on the nongap junctional membrane of these cells. From morphological reconstructions of AII amacrine cells filled with biocytin, we obtained a surface area of ∼900 μm2 which, with a standard value for Cm of 0.01 pF/μm2, corresponds to an average capacitance of ∼9 pF and a specific membrane resistance of ∼41 kΩ cm2. Together with information concerning synaptic connectivity, these data will be important for developing realistic compartmental models of the network of AII amacrine cells.

Parallel regulation of a modulator-activated current via distinct dynamics underlies comodulation of motor circuit output

The cellular mechanisms underlying comodulation of neuronal networks are not elucidated in most systems. We are addressing this issue by determining the mechanism by which a peptide hormone, crustacean cardioactive peptide (CCAP), modulates the biphasic (protraction/retraction) gastric mill (chewing) rhythm driven by the projection neuron MCN1 in the crab stomatogastric ganglion. MCN1 activates this rhythm by slow peptidergic (CabTRP Ia) and fast GABAergic excitation of the reciprocally inhibitory central pattern generator neurons LG (protraction) and Int1 (retraction), respectively. MCN1 synaptic transmission is limited to the retraction phase, because LG inhibits MCN1 during protraction. Bath-applied CCAP also excites both LG and Int1, but selectively prolongs protraction. Here, we use computational modeling and dynamic-clamp manipulations to establish that CCAP prolongs the gastric mill protractor (LG) phase and maintains the retractor (Int1) phase duration by activating the same modulator-activated inward current (I(MI)) in LG as MCN1-released CabTRP Ia. However, the CCAP-activated current (I(MI-CCAP)) and MCN1-activated current (I(MI-MCN1)) exhibit distinct time courses in LG during protraction. This distinction results from I(MI-CCAP) being regulated only by postsynaptic voltage, whereas I(MI-MCN1) is also regulated by LG presynaptic inhibition of MCN1. Hence, without CCAP, retraction and protraction duration are determined by the time course of I(MI-MCN1) buildup and feedback inhibition-mediated decay, respectively, in LG. With I(MI-CCAP) continually present, the impact of the feedback inhibition is reduced, prolonging protraction and maintaining retraction duration. Thus, comodulation of rhythmic motor activity can result from convergent activation, via distinct dynamics, of a single voltage-dependent current.

Membrane resonance in bursting pacemaker neurons of an oscillatory network is correlated with network frequency

Network oscillations typically span a limited range of frequency. In pacemaker-driven networks, including many central pattern generators (CPGs), this frequency range is determined by the properties of bursting pacemaker neurons and their synaptic connections; thus, factors that affect the burst frequency of pacemaker neurons should play a role in determining the network frequency. We examine the role of membrane resonance of pacemaker neurons on the network frequency in the crab pyloric CPG. The pyloric oscillations (frequency of approximately 1 Hz) are generated by a group of pacemaker neurons: the anterior burster (AB) and the pyloric dilator (PD). We examine the impedance profiles of the AB and PD neurons in response to sinusoidal current injections with varying frequency and find that both neuron types exhibit membrane resonance, i.e., demonstrate maximal impedance at a given preferred frequency. The membrane resonance frequencies of the AB and PD neurons fall within the range of the pyloric network oscillation frequency. Experiments with pharmacological blockers and computational modeling show that both calcium currents I(Ca) and the hyperpolarization-activated inward current I(h) are important in producing the membrane resonance in these neurons. We then demonstrate that both the membrane resonance frequency of the PD neuron and its suprathreshold bursting frequency can be shifted in the same direction by either direct current injection or by using the dynamic-clamp technique to inject artificial conductances for I(h) or I(Ca). Together, these results suggest that membrane resonance of pacemaker neurons can be strongly correlated with the CPG oscillation frequency.

Virtual Partner Interaction (VPI): exploring novel behaviors via coordination dynamics

Inspired by the dynamic clamp of cellular neuroscience, this paper introduces VPI -- Virtual Partner Interaction -- a coupled dynamical system for studying real time interaction between a human and a machine. In this proof of concept study, human subjects coordinate hand movements with a virtual partner, an avatar of a hand whose movements are driven by a computerized version of the Haken-Kelso-Bunz (HKB) equations that have been shown to govern basic forms of human coordination. As a surrogate system for human social coordination, VPI allows one to examine regions of the parameter space not typically explored during live interactions. A number of novel behaviors never previously observed are uncovered and accounted for. Having its basis in an empirically derived theory of human coordination, VPI offers a principled approach to human-machine interaction and opens up new ways to understand how humans interact with human-like machines including identification of underlying neural mechanisms.

Tracking and control of neuronal Hodgkin-Huxley dynamics

Nonlinear ensemble state estimation offers a paradigm-shifting improvement in our ability to observe, predict, and control the state of spiking neuronal systems. We use an ensemble Kalman filter to predict hidden states and future trajectories in the Hodgkin-Huxley equations, reconstruct ion dynamics, control neuronal activity including a strategy for dynamic conductance clamping, and show the feasibility of controlling pathological cellular activity such as seizures.

Causes of transient instabilities in the dynamic clamp

The dynamic clamp is a widely used method for integrating mathematical models with electrophysiological experiments. This method involves measuring the membrane voltage of a cell, using it to solve computational models of ion channel dynamics in real-time, and injecting the calculated current(s) back into the cell. Limitations of this technique include those associated with single electrode current clamping and the sampling effects caused by the dynamic clamp. In this study, we show that the combination of these limitations causes transient instabilities under certain conditions. Through physical experiments and simulations, we show that dynamic clamp instability is directly related to the sampling delay and the maximum simulated conductance being injected. It is exaggerated by insufficient electrode series resistance and capacitance compensation. Increasing the sampling rate of the dynamic clamp system increases dynamic clamp stability; however, this improvement, is constrained by how well the electrode series resistance and capacitance are compensated. At present, dynamic clamp sampling rates are justified solely on the temporal dynamics of the models being simulated; here we show that faster rates increase the stable range of operation for the dynamic clamp system. In addition, we show that commonly accepted levels of resistance compensation nevertheless significantly compromise the stability of a dynamic clamp system.

Dynamic action potential clamp as a powerful tool in the development of a gene-based bio-pacemaker

The development of a genetically engineered 'biological pacemaker', or 'bio-pacemaker', is a rapidly emerging field of research. One of the approaches in this field is to turn intrinsically quiescent myocardial cells, i.e., atrial or ventricular cells, into pacemaker cells by making them express the cardiac hyperpolarization-activated 'pacemaker current' If (known in neurophysiology as Ih), which is encoded by the hyperpolarization-activated cyclic nucleotide-modulated (HCN) gene family. We carried out 'dynamic action potential clamp' (dAPC) experiments in which we record current from a HEK-293 cell transfected with HCN4, which is the dominant HCN isoform in the sinoatrial (SA) node. This HCN4-transfected HEK-293 cell is voltage-clamped by the action potential generated in a real-time simulation of a human atrial cell (Courtemanche-Ramirez-Nattel model). In a continuous feedback loop, this current is injected into the atrial cell, so that this cell effectively expresses an HCN4-based pacemaker current. With sufficiently high 'expression levels' of HCN4 current the atrial cell is turned into a pacemaker cell with an SA nodal like action potential. Lower expression levels are sufficient if the inward rectifier potassium current (IK1), which is largely responsible for the stable resting potential of atrial cells, is 'down-regulated' by 50%, thus mimicking the gene therapy strategy to create a bio-pacemaker by down-regulation of IK1 and (over-)expression of If. Our dAPC experiments provide direct insights into the effects of introducing HCN4 current into an atrial cell, illustrating that dynamic action potential clamp can be a powerful tool in the process of developing a gene-based bio-pacemaker.

Electrical Synapses Between AII Amacrine Cells: Dynamic Range and Functional Consequences of Variation in Junctional Conductance

AII amacrine cells form a network of electrically coupled interneurons in the mammalian retina and tracer coupling studies suggest that the junctional conductance ( Gj) can be modulated. However, the dynamic range of Gjand the functional consequences of varying Gjover the dynamic range are unknown. Here we use whole cell recordings from pairs of coupled AII amacrine cells in rat retinal slices to provide direct evidence for physiological modulation of Gj, appearing as a time-dependent increase from about 500 pS to a maximum of about 3,000 pS after 30–90 min of recording. The increase occurred in recordings with low- but not high-resistance pipettes, suggesting that it was related to intracellular washout and perturbation of a modulatory system. Computer simulations of a network of electrically coupled cells verified that our recordings were able to detect and quantify changes in Gjover a large range. Dynamic-clamp electrophysiology, with insertion of electrical synapses between AII amacrine cells, allowed us to finely and reversibly control Gjwithin the same range observed for physiologically coupled cells and to examine the quantitative relationship between Gjand steady-state coupling coefficient, synchronization of subthreshold membrane potential fluctuations, synchronization and transmission of action potentials, and low-pass filter characteristics. The range of Gjvalues over which signal transmission was modulated depended strongly on the specific functional parameter examined, with the largest range observed for action potential transmission and synchronization, suggesting that the full range of Gjvalues observed during spontaneous run-up of coupling could represent a physiologically relevant dynamic range.

Characterization of a potassium-based leak conductance in the medial nucleus of the trapezoid body

Principal neurons of the medial nucleus of the trapezoid body (MNTB) integrate the large, excitatory inputs from anteroventral cochlear nucleus (AVCN) bushy cells with conventional inhibitory inputs to produce an inhibitory output to the lateral and medial superior olive. This circuit is critical in the sound localization pathway of the auditory brainstem. Many ionic currents act in concert to produce the rapid phase-locked firing properties characteristic of MNTB principal neurons. We report here that MNTB neurons of the mouse possess a 2-4nS instantaneous potassium-based leak current, probably mediated by TWIK two-pore potassium leak channels. The function of the leak current was examined by modulating its magnitude with a dynamic clamp. The leak current modulates the resting voltage by 5mV/nS, reduces the input resistance of the cell by 5MOmega/nS and reduces the membrane time constant by 0.075 micros/nS. The leak current also modulates spike timing. Given leak channels are highly regulated, they are well placed to influence the firing properties, and action potential timing in principal neurons of the MNTB.

A scriptable DSP-based system for dynamic conductance injection

A variety of software and hardware systems have been developed to inject controlled electrical conductances into excitable cells, to investigate the physiological mechanisms of action potential generation. These systems face several challenges: the need to model complex conductances, including voltage-gated ion channels, synaptic conductances controlled by electrical models of entire cells or even networks of cells, to do so rapidly and stably, with precisely controlled update intervals of 20micros or less, and to present an easy and flexible interface to the user, allowing new experiments to be designed and executed easily. In this paper I describe a new software system (SM-2) which is designed to meet these requirements, and which runs on the current generation of digital-signal-processing (DSP) analog input-output I/O boards, hosted in Windows PCs. Its key innovation is its configurability by simple user-written text scripts, or "scriptability", which gives it a high flexibility of purpose, and allows non-programmers the capacity to rapidly design and use new Hodgkin-Huxley-type active conductances, conductances with arbitrary current-voltage relationships, Markov process conductance mechanisms with user-specified rate matrices, and hybrid networks of virtual cells. At the same time, the hardware platform allows this to be achieved with a fast and accurately timed input-computation-output cycle.

From response to stimulus: adaptive sampling in sensory physiology

Sensory systems extract behaviorally relevant information from a continuous stream of complex high-dimensional input signals. Understanding the detailed dynamics and precise neural code, even of a single neuron, is therefore a non-trivial task. Automated closed-loop approaches that integrate data analysis in the experimental design ease the investigation of sensory systems in three directions: First, adaptive sampling speeds up the data acquisition and thus increases the yield of an experiment. Second, model-driven stimulus exploration improves the quality of experimental data needed to discriminate between alternative hypotheses. Third, information-theoretic data analyses open up novel ways to search for those stimuli that are most efficient in driving a given neuron in terms of its firing rate or coding quality. Examples from different sensory systems show that, in all three directions, substantial progress can be achieved once rapid online data analysis, adaptive sampling, and computational modeling are tightly integrated into experiments.

A novel approach to physiology education for biomedical engineering students

It is challenging for biomedical engineering programs to incorporate an indepth study of the systemic interdependence of cells, tissues, and organs into the rigorous mathematical curriculum that is the cornerstone of engineering education. To be sure, many biomedical engineering programs require their students to enroll in anatomy and physiology courses. Often, however, these courses tend to provide bulk information with only a modicum of live tissue experimentation. In the Electrical, Computer, and Biomedical Engineering Department of the University of Rhode Island, this issue is addressed to some extent by implementing an experiential physiology laboratory that addresses research in electrophysiology and biomechanics. The two-semester project-based course exposes the students to laboratory skills in dissection, instrumentation, and physiological measurements. In a novel approach to laboratory intensive learning, the course meets on six Sundays throughout the semester for an 8-h laboratory period. At the end of the course, students are required to prepare a two-page conference paper and submit the results to the Northeast Bioengineering Conference (NEBC) for consideration. Students then travel to the conference location to present their work. Since the inception of the course in the fall of 2003, we have collectively submitted 22 papers to the NEBC. This article will discuss the nature of the experimentation, the types of experiments performed, the goals of the course, and the metrics used to determine the success of the students and the research.

Hybrid systems analysis of the control of burst duration by low-voltage-activated calcium current in leech heart interneurons

The leech heartbeat CPG is paced by the alternating bursting of pairs of mutually inhibitory heart interneurons that form elemental half-center oscillators. We explore the control of burst duration in heart interneurons using a hybrid system, where a living, pharmacologically isolated, heart interneuron is connected with artificial synapses to a model heart interneuron running in real-time, by focusing on a low-voltage-activated (LVA) calcium current I(CaS). The transition from silence to bursting in this half-center oscillator occurs when the spike frequency of the bursting interneuron declines to a critical level, f(Final), at which the inhibited interneuron escapes owing to a build-up of the hyperpolarization-activated cation current, I(h). We varied I(CaS) inactivation time constant either in the living heart interneuron or in the model heart interneuron. In both cases, varying I(CaS) inactivation time constant did not affect f(Final) of either interneuron, but in the varied interneuron, the time constant of decline of spike frequency during bursts to f(Final) and thus the burst duration varied directly and nearly linearly with I(CaS) inactivation time constant. Bursts of the opposite, nonvaried interneuron did not change. We show also that control of burst duration by I(CaS) inactivation does not require synaptic interaction by reconstituting autonomous bursting in synaptically isolated living interneurons with injected I(CaS). Therefore inactivation of LVA calcium current is critically important for setting burst duration and thus period in a heart interneuron half-center oscillator and is potentially a general intrinsic mechanism for regulating burst duration in neurons.

Dynamic clamp: a powerful tool in cardiac electrophysiology

Dynamic clamp is a collection of closely related techniques that have been employed in cardiac electrophysiology to provide direct answers to numerous research questions regarding basic cellular mechanisms of action potential formation, action potential transfer and action potential synchronization in health and disease. Building on traditional current clamp, dynamic clamp was initially used to create virtual gap junctions between isolated myocytes. More recent applications include the embedding of a real pacemaking myocyte in a simulated network of atrial or ventricular cells and the insertion of virtual ion channels, either simulated in real time or simultaneously recorded from an expression system, into the membrane of an isolated myocyte. These applications have proven that dynamic clamp, which is characterized by the real-time evaluation and injection of simulated membrane current, is a powerful tool in cardiac electrophysiology. Here, each of the three different experimental configurations used in cardiac electrophysiology is reviewed. Also, directions are given for the implementation of dynamic clamp in the cardiac electrophysiology laboratory. With the growing interest in the application of dynamic clamp in cardiac electrophysiology, it is anticipated that dynamic clamp will also prove to be a powerful tool in basic research on biological pacemakers and in identification of specific ion channels as targets for drug development.