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.

Synaptic Strengths Dominate Phasing of Motor Circuit: Intrinsic Conductances of Neuron Types Need Not Vary across Animals.

Identified neurons and the networks they compose produce stereotypical, albeit individually unique, activity across members of a species. We propose, for a motor circuit driven by a central pattern generator (CPG), that the uniqueness derives mainly from differences in synaptic strength rather than from differences in intrinsic membrane conductances. We studied a dataset of recordings from six leech (Hirudo sp.) heartbeat control networks, containing complete spiking activity patterns from inhibitory premotor interneurons, motor output spike patterns, and synaptic strength patterns to investigate the source of uniqueness. We used a conductance-based multicompartmental motor neuron model to construct a bilateral motor circuit model, and controlled it by playing recorded input spike trains from premotor interneurons to generate output inhibitory synaptic patterns similar to experimental measurements. By generating different synaptic conductance parameter sets of this circuit model, we found that relative premotor synaptic strengths impinging onto motor neurons must be different across individuals to produce animal-specific output burst phasing. Obtaining unique outputs from each individual's circuit model did not require different intrinsic ionic conductance parameters. Furthermore, changing intrinsic conductances failed to compensate for modified synaptic strength patterns. Thus, the pattern of synaptic strengths of motor neuron inputs is critical for the phasing of this motor circuit and can explain individual differences. When intrinsic conductances were allowed to vary, they exhibited the same conductance correlations across individuals, suggesting a motor neuron "type" required for proper network function. Our results are general and may translate to other systems and neuronal networks that control output phasing.

Local synaptic inputs support opposing, network-specific odor representations in a widely projecting modulatory neuron.

Serotonin plays different roles across networks within the same sensory modality. Previously, we used whole-cell electrophysiology in Drosophila to show that serotonergic neurons innervating the first olfactory relay are inhibited by odorants (Zhang and Gaudry, 2016). Here we show that network-spanning serotonergic neurons segregate information about stimulus features, odor intensity and identity, by using opposing coding schemes in different olfactory neuropil. A pair of serotonergic neurons (the CSDns) innervate the antennal lobe and lateral horn, which are first and second order neuropils. CSDn processes in the antennal lobe are inhibited by odors in an identity independent manner. In the lateral horn, CSDn processes are excited in an odor identity dependent manner. Using functional imaging, modeling, and EM reconstruction, we demonstrate that antennal lobe derived inhibition arises from local GABAergic inputs and acts as a means of gain control on branch-specific inputs that the CSDns receive within the lateral horn.

Output variability across animals and levels in a motor system.

Rhythmic behaviors vary across individuals. We investigated the sources of this output variability across a motor system, from the central pattern generator (CPG) to the motor plant. In the bilaterally symmetric leech heartbeat system, the CPG orchestrates two coordinations in the bilateral hearts with different intersegmental phase relations (Δϕ) and periodic side-to-side switches. Population variability is large. We show that the system is precise within a coordination, that differences in repetitions of a coordination contribute little to population output variability, but that differences between bilaterally homologous cells may contribute to some of this variability. Nevertheless, much output variability is likely associated with genetic and life history differences among individuals. Variability of Δϕ were coordination-specific: similar at all levels in one, but significantly lower for the motor pattern than the CPG pattern in the other. Mechanisms that transform CPG output to motor neurons may limit output variability in the motor pattern.

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.

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.

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.

Dendritic sodium channels regulate network integration in globus pallidus neurons: a modeling study.

The globus pallidus (GP) predominantly contains GABAergic projection neurons that occupy a central position in the indirect pathway of the basal ganglia. They have long dendrites that can extend through one-half the diameter of the GP in rats, potentially enabling convergence and interaction between segregated basal ganglia circuits. Because of the length and fine diameter of GP dendrites, however, it is unclear how much influence distal synapses have on spiking activity. Dendritic expression of fast voltage-dependent Na(+) channels (NaF channels) can enhance the importance of distal excitatory synapses by allowing for dendritic spike initiation and by subthreshold boosting of EPSPs. Antibody labeling has demonstrated the presence of NaF channel proteins in GP dendrites, but the quantitative expression density of the channels remains unknown. We built a series of nine GP neuron models that differed only in their dendritic NaF channel expression level to assess the functional impact of this parameter. The models were all similar in their basic electrophysiological features; however, higher expression levels of dendritic NaF channels increased the relative effectiveness of distal inputs for both excitatory and inhibitory synapses, broadening the effective extent of the dendritic tree. Higher dendritic NaF channel expression also made the neurons more resistant to tonic inhibition and highly sensitive to clustered synchronous excitation. The dendritic NaF channel expression pattern may therefore be a critical determinant of convergence for both the striatopallidal and subthalamopallidal projections, while also dictating which spatiotemporal input patterns are most effective at driving GP neuron output.

Model calcium sensors for network homeostasis: sensor and readout parameter analysis from a database of model neuronal networks.

In activity-dependent homeostatic regulation (ADHR) of neuronal and network properties, the intracellular Ca(2+) concentration is a good candidate for sensing activity levels because it is correlated with the electrical activity of the cell. Previous ADHR models, developed with abstract activity sensors for model pyloric neurons and networks of the crustacean stomatogastric ganglion, showed that functional activity can be maintained by a regulation mechanism that senses activity levels solely from Ca(2+). At the same time, several intracellular pathways have been discovered for Ca(2+)-dependent regulation of ion channels. To generate testable predictions for dynamics of these signaling pathways, we undertook a parameter study of model Ca(2+) sensors across thousands of model pyloric networks. We found that an optimal regulation signal can be generated for 86% of model networks with a sensing mechanism that activates with a time constant of 1 ms and that inactivates within 1 s. The sensor performed robustly around this optimal point and did not need to be specific to the role of the cell. When multiple sensors with different time constants were used, coverage extended to 88% of the networks. Without changing the sensors, it extended to 95% of the networks by letting the sensors affect the readout nonlinearly. Specific to this pyloric network model, the sensor of the follower pyloric constrictor cell was more informative than the pacemaker anterior burster cell for producing a regulatory signal. Conversely, a global signal indicating network activity that was generated by summing the sensors in individual cells was less informative for regulation.

Database analysis of simulated and recorded electrophysiological datasets with PANDORA's toolbox.

Neuronal recordings and computer simulations produce ever growing amounts of data, impeding conventional analysis methods from keeping pace. Such large datasets can be automatically analyzed by taking advantage of the well-established relational database paradigm. Raw electrophysiology data can be entered into a database by extracting its interesting characteristics (e.g., firing rate). Compared to storing the raw data directly, this database representation is several orders of magnitude higher efficient in storage space and processing time. Using two large electrophysiology recording and simulation datasets, we demonstrate that the database can be queried, transformed and analyzed. This process is relatively simple and easy to learn because it takes place entirely in Matlab, using our database analysis toolbox, PANDORA. It is capable of acquiring data from common recording and simulation platforms and exchanging data with external database engines and other analysis toolboxes, which make analysis simpler and highly interoperable. PANDORA is available to be freely used and modified because it is open-source (http://software.incf.org/software/pandora/home).

Channel density distributions explain spiking variability in the globus pallidus: a combined physiology and computer simulation database approach.

Globus pallidus (GP) neurons recorded in brain slices show significant variability in intrinsic electrophysiological properties. To investigate how this variability arises, we manipulated the biophysical properties of GP neurons using computer simulations. Specifically, we created a GP neuron model database with 100,602 models that had varying densities of nine membrane conductances centered on a hand-tuned model that replicated typical physiological data. To test the hypothesis that the experimentally observed variability can be attributed to variations in conductance densities, we compared our model database results to a physiology database of 146 slice recordings. The electrophysiological properties of generated models and recordings were assessed with identical current injection protocols and analyzed with a uniform set of measures, allowing a systematic analysis of the effects of varying voltage-gated and calcium-gated conductance densities on the measured properties and a detailed comparison between models and recordings. Our results indicated that most of the experimental variability could be matched by varying conductance densities, which we confirmed with additional partial block experiments. Further analysis resulted in two key observations: (1) each voltage-gated conductance had effects on multiple measures such as action potential waveform and spontaneous or stimulated spike rates; and (2) the effect of each conductance was highly dependent on the background context of other conductances present. In some cases, such interactions could reverse the effect of the density of one conductance on important excitability measures. This context dependence of conductance density effects is important to understand drug and neuromodulator effects that work by affecting ion channels.

A stochastic population approach to the problem of stable recruitment hierarchies in spiking neural networks.

Synchrony-driven recruitment learning addresses the question of how arbitrary concepts, represented by synchronously active ensembles, may be acquired within a randomly connected static graph of neuron-like elements. Recruitment learning in hierarchies is an inherently unstable process. This paper presents conditions on parameters for a feedforward network to ensure stable recruitment hierarchies. The parameter analysis is conducted by using a stochastic population approach to model a spiking neural network. The resulting network converges to activate a desired number of units at each stage of the hierarchy. The original recruitment method is modified first by increasing feedforward connection density for ensuring sufficient activation, then by incorporating temporally distributed feedforward delays for separating inputs temporally, and finally by limiting excess activation via lateral inhibition. The task of activating a desired number of units from a population is performed similarly to a temporal k-winners-take-all network.

Temporal binding as an inducer for connectionist recruitment learning over delayed lines.

The temporal correlation hypothesis proposes using distributed synchrony for the binding of different stimulus features. However, synchronized spikes must travel over cortical circuits that have varying length pathways, leading to mismatched arrival times. This raises the question of how initial stimulus-dependent synchrony might be preserved at a destination binding site. Earlier, we proposed constraints on tolerance and segregation parameters for a phase-coding approach, within cortical circuits, to address this question [Proceedings of the International Joint Conference on Neural Networks, Washington, DC, 2001]. The purpose of the present paper is twofold. First, we conduct simulation experiments to test the proposed constraints. Second, we explore the practicality of temporal binding to drive a process of long-term memory formation based on a recruitment learning method [Biol. Cybernet. 46 (1982) 27]. A network based on Valiant's neuroidal architecture [Circuits of the mind, 1994] is used to demonstrate the coalition between temporal binding and recruitment. Complementing similar approaches, we implement a continuous-time learning procedure allowing computation with spiking neurons. The viability of the proposed binding scheme is investigated by conducting simulation studies which examine binding errors. In the simulation, binding errors cause the perception of illusory conjunctions among features belonging to separate objects. Our results indicate that when tolerance and segregation parameters obey our proposed constraints, the assemblies of correct bindings are dominant over assemblies of spurious bindings in reasonable operating conditions.