Temporal dynamics of Na/K pump mediated memory traces: insights from conductance-based models of Drosophila neurons.

Sodium potassium ATPases (Na/K pumps) mediate long-lasting, dynamic cellular memories that can last tens of seconds. The mechanisms controlling the dynamics of this type of cellular memory are not well understood and can be counterintuitive. Here, we use computational modeling to examine how Na/K pumps and the ion concentration dynamics they influence shape cellular excitability. In a Drosophila larval motor neuron model, we incorporate a Na/K pump, a dynamic intracellular Na+ concentration, and a dynamic Na+ reversal potential. We probe neuronal excitability with a variety of stimuli, including step currents, ramp currents, and zap currents, then monitor the sub- and suprathreshold voltage responses on a range of time scales. We find that the interactions of a Na+-dependent pump current with a dynamic Na+ concentration and reversal potential endow the neuron with rich response properties that are absent when the role of the pump is reduced to the maintenance of constant ion concentration gradients. In particular, these dynamic pump-Na+ interactions contribute to spike rate adaptation and result in long-lasting excitability changes after spiking and even after sub-threshold voltage fluctuations on multiple time scales. We further show that modulation of pump properties can profoundly alter a neuron's spontaneous activity and response to stimuli by providing a mechanism for bursting oscillations. Our work has implications for experimental studies and computational modeling of the role of Na/K pumps in neuronal activity, information processing in neural circuits, and the neural control of animal behavior.

On the Role of Theory and Modeling in Neuroscience.

In recent years, the field of neuroscience has gone through rapid experimental advances and a significant increase in the use of quantitative and computational methods. This growth has created a need for clearer analyses of the theory and modeling approaches used in the field. This issue is particularly complex in neuroscience because the field studies phenomena that cross a wide range of scales and often require consideration at varying degrees of abstraction, from precise biophysical interactions to the computations they implement. We argue that a pragmatic perspective of science, in which descriptive, mechanistic, and normative models and theories each play a distinct role in defining and bridging levels of abstraction, will facilitate neuroscientific practice. This analysis leads to methodological suggestions, including selecting a level of abstraction that is appropriate for a given problem, identifying transfer functions to connect models and data, and the use of models themselves as a form of experiment.

Could simplified stimuli change how the brain performs visual search tasks? A deep neural network study.

Visual search is a complex behavior influenced by many factors. To control for these factors, many studies use highly simplified stimuli. However, the statistics of these stimuli are very different from the statistics of the natural images that the human visual system is optimized by evolution and experience to perceive. Could this difference change search behavior? If so, simplified stimuli may contribute to effects typically attributed to cognitive processes, such as selective attention. Here we use deep neural networks to test how optimizing models for the statistics of one distribution of images constrains performance on a task using images from a different distribution. We train four deep neural network architectures on one of three source datasets-natural images, faces, and x-ray images-and then adapt them to a visual search task using simplified stimuli. This adaptation produces models that exhibit performance limitations similar to humans, whereas models trained on the search task alone exhibit no such limitations. However, we also find that deep neural networks trained to classify natural images exhibit similar limitations when adapted to a search task that uses a different set of natural images. Therefore, the distribution of data alone cannot explain this effect. We discuss how future work might integrate an optimization-based approach into existing models of visual search behavior.

Dramatically Amplified Thoracic Sympathetic Postganglionic Excitability and Integrative Capacity Revealed with Whole-Cell Patch-Clamp Recordings.

Thoracic paravertebral sympathetic postganglionic neurons (tSPNs) comprise the final integrative output of the distributed sympathetic nervous system controlling vascular and thermoregulatory systems. Considered a non-integrating relay, what little is known of tSPN intrinsic excitability has been determined by sharp microelectrodes with presumed impalement injury. We thus undertook the first electrophysiological characterization of tSPN cellular properties using whole-cell recordings and coupled results with a conductance-based model to explore the principles governing their excitability in adult mice of both sexes. Recorded membrane resistance and time constant values were an order of magnitude greater than values previously obtained, leading to a demonstrable capacity for synaptic integration in driving recruitment. Variation in membrane resistivity was the primary determinant controlling cell excitability with vastly lower currents required for tSPN recruitment. Unlike previous microelectrode recordings in mouse which observed inability to sustain firing, all tSPNs were capable of repetitive firing. Computational modeling demonstrated that observed differences are explained by introduction of a microelectrode impalement injury conductance. Overall, tSPNs largely linearly encoded injected current magnitudes over a broad frequency range with distinct subpopulations differentiable based on repetitive firing signatures. Thus, whole-cell recordings reveal tSPNs have more dramatically amplified excitability than previously thought, with greater intrinsic capacity for synaptic integration and with the ability for maintained firing to support sustained actions on vasomotor tone and thermoregulatory function. Rather than acting as a relay, these studies support a more responsive role and possible intrinsic capacity for tSPNs to drive sympathetic autonomic function.

Feedback control of variability in the cycle period of a central pattern generator.

We address how feedback to a bursting biological pacemaker with intrinsic variability in cycle length can affect that variability. Specifically, we examine a hybrid circuit constructed of an isolated crab anterior burster (AB)/pyloric dilator (PD) pyloric pacemaker receiving virtual feedback via dynamic clamp. This virtual feedback generates artificial synaptic input to PD with timing determined by adjustable phase response dynamics that mimic average burst intervals generated by the lateral pyloric neuron (LP) in the intact pyloric network. Using this system, we measure network period variability dependence on the feedback element's phase response dynamics and find that a constant response interval confers minimum variability. We further find that these optimal dynamics are characteristic of the biological pyloric network. Building upon our previous theoretical work mapping the firing intervals in one cycle onto the firing intervals in the next cycle, we create a theoretical map of the distribution of all firing intervals in one cycle to the distribution of firing intervals in the next cycle. We then obtain an integral equation for a stationary self-consistent distribution of the network periods of the hybrid circuit, which can be solved numerically given the uncoupled pacemaker's distribution of intrinsic periods, the nature of the network's feedback, and the phase resetting characteristics of the pacemaker. The stationary distributions obtained in this manner are strongly predictive of the experimentally observed distributions of hybrid network period. This theoretical framework can provide insight into optimal feedback schemes for minimizing variability to increase reliability or maximizing variability to increase flexibility in central pattern generators driven by pacemakers with feedback.

Degradation of extracellular chondroitin sulfate delays recovery of network activity after perturbation.

Chondroitin sulfate proteoglycans (CSPGs) are widely studied in vertebrate systems and are known to play a key role in development, plasticity, and regulation of cortical circuitry. The mechanistic details of this role are still elusive, but increasingly central to the investigation is the homeostatic balance between network excitation and inhibition. Studying a simpler neuronal circuit may prove advantageous for discovering the mechanistic details of the cellular effects of CSPGs. In this study we used a well-established model of homeostatic change after injury in the crab Cancer borealis to show first evidence that CSPGs are necessary for network activity homeostasis. We degraded CSPGs in the pyloric circuit of the stomatogastric ganglion with the enzyme chondroitinase ABC (chABC) and found that removal of CSPGs does not influence the ongoing rhythm of the pyloric circuit but does limit its capacity for recovery after a networkwide perturbation. Without CSPGs, the postperturbation rhythm is slower than in controls and rhythm recovery is delayed. In addition to providing a new model system for the study of CSPGs, this study suggests a wider role for CSPGs, and perhaps the extracellular matrix in general, beyond simply plastic reorganization (as observed in mammals) and into a foundational regulatory role of neural circuitry.

Distal spike initiation zone location estimation by morphological simulation of ionic current filtering demonstrated in a novel model of an identified Drosophila motoneuron.

Studying ion channel currents generated distally from the recording site is difficult because of artifacts caused by poor space clamp and membrane filtering. A computational model can quantify artifact parameters for correction by simulating the currents only if their exact anatomical location is known. We propose that the same artifacts that confound current recordings can help pinpoint the source of those currents by providing a signature of the neuron's morphology. This method can improve the recording quality of currents initiated at the spike initiation zone (SIZ) that are often distal to the soma in invertebrate neurons. Drosophila being a valuable tool for characterizing ion currents, we estimated the SIZ location and quantified artifacts in an identified motoneuron, aCC/MN1-Ib, by constructing a novel multicompartmental model. Initial simulation of the measured biophysical channel properties in an isopotential Hodgkin-Huxley type neuron model partially replicated firing characteristics. Adding a second distal compartment, which contained spike-generating Na+ and K+ currents, was sufficient to simulate aCC's in vivo activity signature. Matching this signature using a reconstructed morphology predicted that the SIZ is on aCC's primary axon, 70 µm after the most distal dendritic branching point. From SIZ to soma, we observed and quantified selective morphological filtering of fast activating currents. Non-inactivating K+ currents are filtered ∼3 times less and despite their large magnitude at the soma they could be as distal as Na+ currents. The peak of transient component (NaT) of the voltage-activated Na+ current is also filtered more than the magnitude of slower persistent component (NaP), which can contribute to seizures. The corrected NaP/NaT ratio explains the previously observed discrepancy when the same channel is expressed in different cells. In summary, we used an in vivo signature to estimate ion channel location and recording artifacts, which can be applied to other neurons.

Differential effects of conductances on the phase resetting curve of a bursting neuronal oscillator.

The intrinsically oscillating neurons in the crustacean pyloric circuit have membrane conductances that influence their spontaneous activity patterns and responses to synaptic activity. The relationship between the magnitudes of these membrane conductances and the response of the oscillating neurons to synaptic input has not yet been fully or systematically explored. We examined this relationship using the phase resetting curve (PRC), which summarizes the change in the cycle period of a neuronal oscillator as a function of the input's timing within the oscillation. We first utilized a large database of single-compartment model neurons to determine the effect of individual membrane conductances on PRC shape; we found that the effects vary across conductance space, but on average, the hyperpolarization-activated and leak conductances advance the PRC. We next investigated how membrane conductances affect PRCs of the isolated pacemaker kernel in the pyloric circuit of Cancer borealis by: (1) tabulating PRCs while using dynamic clamp to artificially add varying levels of specific conductances, and (2) tabulating PRCs before and after blocking the endogenous hyperpolarization-activated current. We additionally used a previously described four-compartment model to determine how the location of the hyperpolarization-activated conductance influences that current's effect on the PRC. We report that while dynamic-clamp-injected leak current has much smaller effects on the PRC than suggested by the single-compartment model, an increase in the hyperpolarization-activated conductance both advances and reduces the noisiness of the PRC in the pacemaker kernel of the pyloric circuit in both modeling and experimental studies.

Neuronal plasticity: how do neurons know what to do?

A recent study confirms activity-dependent co-regulation of membrane conductances as a mechanism underlying homeostatic regulation of neuronal properties. How multiple cellular and synaptic homeostatic mechanisms interact in a neuronal circuit is best studied with a combination of experimentation and modeling.

Differential roles of nonsynaptic and synaptic plasticity in operant reward learning-induced compulsive behavior.

BACKGROUND: Rewarding stimuli in associative learning can transform the irregularly and infrequently generated motor patterns underlying motivated behaviors into output for accelerated and stereotyped repetitive action. This transition to compulsive behavioral expression is associated with modified synaptic and membrane properties of central neurons, but establishing the causal relationships between cellular plasticity and motor adaptation has remained a challenge. RESULTS: We found previously that changes in the intrinsic excitability and electrical synapses of identified neurons in Aplysia's central pattern-generating network for feeding are correlated with a switch to compulsive-like motor output expression induced by in vivo operant conditioning. Here, we used specific computer-simulated ionic currents in vitro to selectively replicate or suppress the membrane and synaptic plasticity resulting from this learning. In naive in vitro preparations, such experimental manipulation of neuronal membrane properties alone increased the frequency but not the regularity of feeding motor output found in preparations from operantly trained animals. On the other hand, changes in synaptic strength alone switched the regularity but not the frequency of feeding output from naive to trained states. However, simultaneously imposed changes in both membrane and synaptic properties reproduced both major aspects of the motor plasticity. Conversely, in preparations from trained animals, experimental suppression of the membrane and synaptic plasticity abolished the increase in frequency and regularity of the learned motor output expression. CONCLUSIONS: These data establish direct causality for the contributions of distinct synaptic and nonsynaptic adaptive processes to complementary facets of a compulsive behavior resulting from operant reward learning.

Phase maintenance in a rhythmic motor pattern during temperature changes in vivo.

Central-pattern-generating neural circuits function reliably throughout an animal's life, despite constant molecular turnover and environmental perturbations. Fluctuations in temperature pose a problem to the nervous systems of poikilotherms because their body temperature follows the ambient temperature, thus affecting the temperature-dependent dynamics of various subcellular components that constitute neuronal circuits. In the crustacean stomatogastric nervous system, the pyloric circuit produces a triphasic rhythm comprising the output of the pyloric dilator, lateral pyloric, and pyloric constrictor neurons. In vitro, the phase relationships of these neurons are maintained over a fourfold change in pyloric frequency as temperature increases from 7°C to 23°C. To determine whether these temperature effects are also found in intact crabs, in the presence of sensory feedback and neuromodulator-rich environments, we measured the temperature dependence of the pyloric frequency and phases in vivo by implanting extracellular electrodes into Cancer borealis and Cancer pagurus and shifting tank water temperature from 11°C to 26°C. Pyloric frequency in the intact crab increased significantly with temperature (Q10 = 2-2.5), while pyloric phases were generally conserved. For a subset of the C. borealis experiments, animals were subsequently dissected and the stomatogastric ganglion subjected to a similar temperature ramp in vitro. We found that the maximal frequency attained at high temperatures in vivo is lower than it is under in vitro conditions. Our results demonstrate that, over a wide temperature range, the phases of the pyloric rhythm in vivo are generally preserved, but that the frequency range is more restricted than it is in vitro.

The transcription factors islet and Lim3 combinatorially regulate ion channel gene expression.

Expression of appropriate ion channels is essential to allow developing neurons to form functional networks. Our previous studies have identified LIM-homeodomain (HD) transcription factors (TFs), expressed by developing neurons, that are specifically able to regulate ion channel gene expression. In this study, we use the technique of DNA adenine methyltransferase identification (DamID) to identify putative gene targets of four such TFs that are differentially expressed in Drosophila motoneurons. Analysis of targets for Islet (Isl), Lim3, Hb9, and Even-skipped (Eve) identifies both ion channel genes and genes predicted to regulate aspects of dendritic and axonal morphology. Significantly, some ion channel genes are bound by more than one TF, consistent with the possibility of combinatorial regulation. One such gene is Shaker (Sh), which encodes a voltage-dependent fast K(+) channel (Kv1.1). DamID reveals that Sh is bound by both Isl and Lim3. We used body wall muscle as a test tissue because in conditions of low Ca(2+), the fast K(+) current is carried solely by Sh channels (unlike neurons in which a second fast K(+) current, Shal, also contributes). Ectopic expression of isl, but not Lim3, is sufficient to reduce both Sh transcript and Sh current level. By contrast, coexpression of both TFs is additive, resulting in a significantly greater reduction in both Sh transcript and current compared with isl expression alone. These observations provide evidence for combinatorial activity of Isl and Lim3 in regulating ion channel gene expression.

Activation of high and low affinity dopamine receptors generates a closed loop that maintains a conductance ratio and its activity correlate.

Neuromodulators alter network output and have the potential to destabilize a circuit. The mechanisms maintaining stability in the face of neuromodulation are not well described. Using the pyloric network in the crustacean stomatogastric nervous system, we show that dopamine (DA) does not simply alter circuit output, but activates a closed loop in which DA-induced alterations in circuit output consequently drive a change in an ionic conductance to preserve a conductance ratio and its activity correlate. DA acted at low affinity type 1 receptors (D1Rs) to induce an immediate modulatory decrease in the transient potassium current (IA) of a pyloric neuron. This, in turn, advanced the activity phase of that component neuron, which disrupted its network function and thereby destabilized the circuit. DA simultaneously acted at high affinity D1Rs on the same neuron to confer activity-dependence upon the hyperpolarization activated current (Ih) such that the DA-induced changes in activity subsequently reduced Ih. This DA-enabled, activity-dependent, intrinsic plasticity exactly compensated for the modulatory decrease in IA to restore the IA:Ih ratio and neuronal activity phase, thereby closing an open loop created by the modulator. Activation of closed loops to preserve conductance ratios may represent a fundamental operating principle neuromodulatory systems use to ensure stability in their target networks.

Modifying spiking precision in conductance-based neuronal models.

The temporal precision of a neuron's spiking can be characterized by calculating its "jitter," defined as the standard deviation of the timing of individual spikes in response to repeated presentations of a stimulus. Sub-millisecond jitters have been measured for neurons in a variety of experimental systems and appear to be functionally important in some instances. We have investigated how modifying a neuron's maximal conductances affects jitter using the leaky integrate-and-fire (LIF) model and an eight-conductance Hodgkin-Huxley type (HH8) model. We observed that jitter can be largely understood in the LIF model in terms of the neuron's filtering properties. In the HH8 model we found the role of individual conductances in determining jitter to be complicated and dependent on the model's spiking properties. Distinct behaviors were observed for populations with slow (<11.5 Hz) and fast (>11.5 Hz) spike rates and appear to be related to differences in a particular channel's activity at times just before spiking occurs.

Phase response theory extended to nonoscillatory network components.

New tools for analysis of oscillatory networks using phase response theory (PRT) under the assumption of pulsatile coupling have been developed steadily since the 1980s, but none have yet allowed for analysis of mixed systems containing nonoscillatory elements. This caveat has excluded the application of PRT to most real systems, which are often mixed. We show that a recently developed tool, the functional phase resetting curve (fPRC), provides a serendipitous benefit: it allows incorporation of nonoscillatory elements into systems of oscillators where PRT can be applied. We validate this method in a model system of neural oscillators and a biological system, the pyloric network of crustacean decapods.

Input-to-output transformation in a model of the rat hippocampal CA1 network.

Here we use computational modeling to gain new insights into the transformation of inputs in hippocampal field CA1. We considered input-output transformation in CA1 principal cells of the rat hippocampus, with activity synchronized by population gamma oscillations. Prior experiments have shown that such synchronization is especially strong for cells within one millimeter of each other. We therefore simulated a one-millimeter it patch of CA1 with 23,500 principal cells. We used morphologically and biophysically detailed neuronal models, each with more than 1000 compartments and thousands of synaptic inputs. Inputs came from binary patterns of spiking neurons from field CA3 and entorhinal cortex (EC). On average, each presynaptic pattern initiated action potentials in the same number of CA1 principal cells in the patch. We considered pairs of similar and pairs of distinct patterns. In all the cases CA1 strongly separated input patterns. However, CA1 cells were considerably more sensitive to small alterations in EC patterns compared to CA3 patterns. Our results can be used for comparison of input-to-output transformations in normal and pathological hippocampal networks.

Activity-dependent alternative splicing increases persistent sodium current and promotes seizure.

Activity of voltage-gated Na channels (Na(v)) is modified by alternative splicing. However, whether altered splicing of human Na(v)s contributes to epilepsy remains to be conclusively shown. We show here that altered splicing of the Drosophila Na(v) (paralytic, DmNa(v)) contributes to seizure-like behavior in identified seizure mutants. We focus attention on a pair of mutually exclusive alternate exons (termed K and L), which form part of the voltage sensor (S4) in domain III of the expressed channel. The presence of exon L results in a large, non-inactivating, persistent I(Nap). Many forms of human epilepsy are associated with an increase in this current. In wild-type (WT) Drosophila larvae, ∼70-80% of DmNa(v) transcripts contain exon L, and the remainder contain exon K. Splicing of DmNa(v) to include exon L is increased to ∼100% in both the slamdance and easily-shocked seizure mutants. This change to splicing is prevented by reducing synaptic activity levels through exposure to the antiepileptic phenytoin or the inhibitory transmitter GABA. Conversely, enhancing synaptic activity in WT, by feeding of picrotoxin is sufficient to increase I(Nap) and promote seizure through increased inclusion of exon L to 100%. We also show that the underlying activity-dependent mechanism requires the presence of Pasilla, an RNA-binding protein. Finally, we use computational modeling to show that increasing I(Nap) is sufficient to potentiate membrane excitability consistent with a seizure phenotype. Thus, increased synaptic excitation favors inclusion of exon L, which, in turn, further increases neuronal excitability. Thus, at least in Drosophila, this self-reinforcing cycle may promote the incidence of seizure.

Co-variation of ionic conductances supports phase maintenance in stomatogastric neurons.

Neuronal networks produce reliable functional output throughout the lifespan of an animal despite ceaseless molecular turnover and a constantly changing environment. Central pattern generators, such as those of the crustacean stomatogastric ganglion (STG), are able to robustly maintain their functionality over a wide range of burst periods. Previous experimental work involving extracellular recordings of the pyloric pattern of the STG has demonstrated that as the burst period varies, the inter-neuronal delays are altered proportionally, resulting in burst phases that are roughly invariant. The question whether spike delays within bursts are also proportional to pyloric period has not been explored in detail. The mechanism by which the pyloric neurons accomplish phase maintenance is currently not obvious. Previous studies suggest that the co-regulation of certain ion channel properties may play a role in governing neuronal activity. Here, we observed in long-term recordings of the pyloric rhythm that spike delays can vary proportionally with burst period, so that spike phase is maintained. We then used a conductance-based model neuron to determine whether co-varying ionic membrane conductances results in neural output that emulates the experimentally observed phenomenon of spike phase maintenance. Next, we utilized a model neuron database to determine whether conductance correlations exist in model neuron populations with highly maintained spike phases. We found that co-varying certain conductances, including the sodium and transient calcium conductance pair, causes the model neuron to maintain a specific spike phase pattern. Results indicate a possible relationship between conductance co-regulation and phase maintenance in STG neurons.

Responses of a bursting pacemaker to excitation reveal spatial segregation between bursting and spiking mechanisms.

Central pattern generators (CPGs) frequently include bursting neurons that serve as pacemakers for rhythm generation. Phase resetting curves (PRCs) can provide insight into mechanisms underlying phase locking in such circuits. PRCs were constructed for a pacemaker bursting complex in the pyloric circuit in the stomatogastric ganglion of the lobster and crab. This complex is comprised of the Anterior Burster (AB) neuron and two Pyloric Dilator (PD) neurons that are all electrically coupled. Artificial excitatory synaptic conductance pulses of different strengths and durations were injected into one of the AB or PD somata using the Dynamic Clamp. Previously, we characterized the inhibitory PRCs by assuming a single slow process that enabled synaptic inputs to trigger switches between an up state in which spiking occurs and a down state in which it does not. Excitation produced five different PRC shapes, which could not be explained with such a simple model. A separate dendritic compartment was required to separate the mechanism that generates the up and down phases of the bursting envelope (1) from synaptic inputs applied at the soma, (2) from axonal spike generation and (3) from a slow process with a slower time scale than burst generation. This study reveals that due to the nonlinear properties and compartmentalization of ionic channels, the response to excitation is more complex than inhibition.