Activity-independent coregulation of IA and Ih in rhythmically active neurons

Ih block reveals separation of timescales in pyloric rhythm response to temperature changes in Cancer borealis

Motor systems operate over a range of frequencies and relative timing (phase). We studied the role of the hyperpolarization-activated inward current (Ih) in regulating these features in the pyloric rhythm of the stomatogastric ganglion (STG) of the crab, Cancer borealis, as temperature was altered from 11°C to 21°C. Under control conditions, rhythm frequency increased monotonically with temperature, while the phases of the pyloric dilator (PD), lateral pyloric (LP), and pyloric (PY) neurons remained constant. Blocking Ih with cesium (Cs+) phase advanced PD offset, LP onset, and LP offset at 11°C, and the latter two further advanced as temperature increased. In Cs+ the frequency increase with temperature diminished and the Q10 of the frequency dropped from ~1.75 to ~1.35. Unexpectedly in Cs+, the frequency dynamics became non-monotonic during temperature transitions; frequency initially dropped as temperature increased, then rose once temperature stabilized, creating a characteristic 'jag'. Interestingly, these jags persisted during temperature transitions in Cs+ when the pacemaker was isolated by picrotoxin, although the temperature-induced change in frequency recovered to control levels. Overall, these data suggest that Ih plays an important role in maintaining smooth transitory responses and persistent frequency increases by different mechanisms in the pyloric circuitry during temperature fluctuations.

Ih Block Reveals Separation of Timescales in Pyloric Rhythm Response to Temperature Changes in Cancer borealis

Motor systems operate over a range of frequencies and relative timing (phase). We studied the contribution of the hyperpolarization-activated inward current (Ih) to frequency and phase in the pyloric rhythm of the stomatogastric ganglion (STG) of the crab, Cancer borealis as temperature was altered from 11°C to 21°C. Under control conditions, the frequency of the rhythm increased monotonically with temperature, while the phases of the pyloric dilator (PD), lateral pyloric (LP), and pyloric (PY) neurons remained constant. When we blocked Ih with cesium (Cs+) PD offset, LP onset, and LP offset were all phase advanced in Cs+ at 11°C, and the latter two further advanced as temperature increased. In Cs+ the steady state increase in pyloric frequency with temperature diminished and the Q10 of the pyloric frequency dropped from ~1.75 to ~1.35. Unexpectedly in Cs+, the frequency displayed non-monotonic dynamics during temperature transitions; the frequency initially dropped as temperature increased, then rose once temperature stabilized, creating a characteristic "jag". Interestingly, these jags were still present during temperature transitions in Cs+ when the pacemaker was isolated by picrotoxin, although the temperature-induced change in frequency recovered to control levels. Overall, these data suggest that Ih plays an important role in the ability of this circuit to produce smooth transitory responses and persistent frequency increases by different mechanisms during temperature fluctuations.

M-type potassium currents differentially affect activation of motoneuron subtypes and tune recruitment gain

The size principle is a key mechanism governing the orderly recruitment of motor units and is believed to be dependent on passive properties of the constituent motoneurons. However, motoneurons are endowed with voltage-sensitive ion channels that create non-linearities in their input-output functions. Here we describe a role for the M-type potassium current, conducted by KCNQ channels, in the control of motoneuron recruitment in mice. Motoneurons were studied with whole-cell patch clamp electrophysiology in transverse spinal slices and identified based on delayed (fast) and immediate (slow) onsets of repetitive firing. M-currents were larger in delayed compared to immediate firing motoneurons, which was not reflected by variations in the presence of Kv7.2 or Kv7.3 subunits. Instead, a more depolarized spike threshold in delayed-firing motoneurons afforded a greater proportion of the total M-current to become activated within the subthreshold voltage range, which translated to a greater influence on their recruitment with little influence on their firing rates. Pharmacological activation of M-currents also influenced motoneuron recruitment at the population level, producing a rightward shift in the recruitment curve of monosynaptic reflexes within isolated mouse spinal cords. These results demonstrate a prominent role for M-type potassium currents in regulating the function of motor units, which occurs primarily through the differential control of motoneuron subtype recruitment. More generally, these findings highlight the importance of active properties mediated by voltage-sensitive ion channels in the differential control of motoneuron recruitment, which is a key mechanism for the gradation of muscle force. KEY POINTS: M-currents exert an inhibitory influence on spinal motor output. This inhibitory influence is exerted by controlling the recruitment, but not the firing rate, of high-threshold fast-like motoneurons, with limited influence on low-threshold slow-like motoneurons. Preferential control of fast motoneurons may be linked to a larger M-current that is activated within the subthreshold voltage range compared to slow motoneurons. Larger M-currents in fast compared to slow motoneurons are not accounted for by differences in Kv7.2 or Kv7.3 channel composition. The orderly recruitment of motoneuron subtypes is shaped by differences in the contribution of voltage-gated ion channels, including KCNQ channels. KCNQ channels may provide a target to dynamically modulate the recruitment gain across the motor pool and readily adjust movement vigour.

Biological complexity facilitates tuning of the neuronal parameter space

The electrical and computational properties of neurons in our brains are determined by a rich repertoire of membrane-spanning ion channels and elaborate dendritic trees. However, the precise reason for this inherent complexity remains unknown, given that simpler models with fewer ion channels are also able to functionally reproduce the behaviour of some neurons. Here, we stochastically varied the ion channel densities of a biophysically detailed dentate gyrus granule cell model to produce a large population of putative granule cells, comparing those with all 15 original ion channels to their reduced but functional counterparts containing only 5 ion channels. Strikingly, valid parameter combinations in the full models were dramatically more frequent at -6% vs. -1% in the simpler model. The full models were also more stable in the face of perturbations to channel expression levels. Scaling up the numbers of ion channels artificially in the reduced models recovered these advantages confirming the key contribution of the actual number of ion channel types. We conclude that the diversity of ion channels gives a neuron greater flexibility and robustness to achieve a target excitability.

Energy-efficient network activity from disparate circuit parameters

Neural circuits can produce similar activity patterns from vastly different combinations of channel and synaptic conductances. These conductances are tuned for specific activity patterns but might also reflect additional constraints, such as metabolic cost or robustness to perturbations. How do such constraints influence the range of permissible conductances? Here we investigate how metabolic cost affects the parameters of neural circuits with similar activity in a model of the pyloric network of the crab Cancer borealis . We present a machine learning method that can identify a range of network models that generate activity patterns matching experimental data and find that neural circuits can consume largely different amounts of energy despite similar circuit activity. Furthermore, a reduced but still significant range of circuit parameters gives rise to energy-efficient circuits. We then examine the space of parameters of energy-efficient circuits and identify potential tuning strategies for low metabolic cost. Finally, we investigate the interaction between metabolic cost and temperature robustness. We show that metabolic cost can vary across temperatures but that robustness to temperature changes does not necessarily incur an increased metabolic cost. Our analyses show that despite metabolic efficiency and temperature robustness constraining circuit parameters, neural systems can generate functional, efficient, and robust network activity with widely disparate sets of conductances.

Neuromodulation reduces interindividual variability of neuronal output

In similar states, neural circuits produce similar outputs across individuals despite substantial interindividual variability in neuronal ionic conductances and synapses. Circuit states are largely shaped by neuromodulators that tune ionic conductances. It is therefore possible that, in addition to producing flexible circuit output, neuromodulators also contribute to output similarity despite varying ion channel expression. We studied whether neuromodulation at saturating concentrations can increase the output similarity of a single identified neuron across individual animals. Using the LP neuron of the crab stomatogastric ganglion (STG), we compared the variability of f-I curves and rebound properties in the presence of neuropeptides. The two neuropeptides we used converge to activate the same target current, which increases neuronal excitability. Output variability was lower in the presence of the neuropeptides, regardless of whether the neuropeptides significantly changed the mean of the corresponding parameter or not. However, the addition of the second neuropeptide did not add further to the reduction of variability. With a family of computational LP-like models, we explored how increased excitability and target variability contribute to output similarity and found two mechanisms: Saturation of the responses and a differential increase in baseline activity. Saturation alone can reduce the interindividual variability only if the population shares a similar ceiling for the responses. In contrast, reduction of variability due to the increase in baseline activity is independent of ceiling effects.Significance StatementThe activity of single neurons and neural circuits can be very similar across individuals even though the ionic currents underlying activity are variable. The mechanisms that compensate for the underlying variability and promote output similarity are poorly understood but may involve neuromodulation. Using an identified neuron, we show that neuropeptide modulation of excitability can reduce interindividual variability of response properties at a single-neuron level in two ways. First, the neuropeptide increases baseline excitability in a differential manner, resulting in similar response thresholds. Second, the neuropeptide increases excitability towards a shared saturation level, promoting similar maximal firing rates across individuals. Such tuning of neuronal excitability could be an important mechanism compensating for interindividual variability of ion channel expression.

Mechanisms Driving the Emergence of Neuronal Hyperexcitability in Fragile X Syndrome

Hyperexcitability is a shared neurophysiological phenotype across various genetic neurodevelopmental disorders, including Fragile X syndrome (FXS). Several patient symptoms are associated with hyperexcitability, but a puzzling feature is that their onset is often delayed until their second and third year of life. It remains unclear how and why hyperexcitability emerges in neurodevelopmental disorders. FXS is caused by the loss of FMRP, an RNA-binding protein which has many critical roles including protein synthesis-dependent and independent regulation of ion channels and receptors, as well as global regulation of protein synthesis. Here, we discussed recent literature uncovering novel mechanisms that may drive the progressive onset of hyperexcitability in the FXS brain. We discussed in detail how recent publications have highlighted defects in homeostatic plasticity, providing new insight on the FXS brain and suggest pharmacotherapeutic strategies in FXS and other neurodevelopmental disorders.

Compensatory variability in network parameters enhances memory performance in the Drosophila mushroom body

Neural circuits use homeostatic compensation to achieve consistent behavior despite variability in underlying intrinsic and network parameters. However, it remains unclear how compensation regulates variability across a population of the same type of neurons within an individual and what computational benefits might result from such compensation. We address these questions in the Drosophila mushroom body, the fly's olfactory memory center. In a computational model, we show that under sparse coding conditions, memory performance is degraded when the mushroom body's principal neurons, Kenyon cells (KCs), vary realistically in key parameters governing their excitability. However, memory performance is rescued while maintaining realistic variability if parameters compensate for each other to equalize KC average activity. Such compensation can be achieved through both activity-dependent and activity-independent mechanisms. Finally, we show that correlations predicted by our model's compensatory mechanisms appear in the Drosophila hemibrain connectome. These findings reveal compensatory variability in the mushroom body and describe its computational benefits for associative memory.

Ion Channel Degeneracy, Variability, and Covariation in Neuron and Circuit Resilience

The large number of ion channels found in all nervous systems poses fundamental questions concerning how the characteristic intrinsic properties of single neurons are determined by the specific subsets of channels they express. All neurons display many different ion channels with overlapping voltage- and time-dependent properties. We speculate that these overlapping properties promote resilience in neuronal function. Individual neurons of the same cell type show variability in ion channel conductance densities even though they can generate reliable and similar behavior. This complicates a simple assignment of function to any conductance and is associated with variable responses of neurons of the same cell type to perturbations, deletions, and pharmacological manipulation. Ion channel genes often show strong positively correlated expression, which may result from the molecular and developmental rules that determine which ion channels are expressed in a given cell type.

Intrinsic plasticity and birdsong learning

Although information processing and storage in the brain is thought to be primarily orchestrated by synaptic plasticity, other neural mechanisms such as intrinsic plasticity are available. While a number of recent studies have described the plasticity of intrinsic excitability in several types of neurons, the significance of non-synaptic mechanisms in memory and learning remains elusive. After reviewing plasticity of intrinsic excitation in relation to learning and homeostatic mechanisms, we focus on the intrinsic properties of a class of basal-ganglia projecting song system neurons in zebra finch, how these related to each bird's unique learned song, how these properties change over development, and how they are maintained dynamically to rapidly change in response to auditory feedback perturbations. We place these results in the broader theme of learning and changes in intrinsic properties, emphasizing the computational implications of this form of plasticity, which are distinct from synaptic plasticity. The results suggest that exploring reciprocal interactions between intrinsic and network properties will be a fruitful avenue for understanding mechanisms of birdsong learning.

Fragile X mental retardation protein modulates somatic D-type K+ channels and action potential threshold in the mouse prefrontal cortex

Axo-somatic K⁺ channels control action potential output in part by acting in concert with voltage-gated Na⁺ channels to set action potential threshold. Slowly inactivating, D-type K⁺ channels are enriched at the axo-somatic region of cortical pyramidal neurons of the prefrontal cortex, where they regulate action potential firing. We previously demonstrated that D-type K⁺ channels are downregulated in extratelencephalic-projecting (ET) L5 neurons in the medial prefrontal cortex (mPFC) of the Fmr1-knockout mouse model of fragile X syndrome (FX mice), resulting in a hyperpolarized action potential threshold. To test whether K⁺ channel alterations are regulated in a cell-autonomous manner in FXS, we used a virus-mediated approach to restore expression of fragile X mental retardation protein (FMRP) in a small population of prefrontal neurons in male FX mice. Outside-out voltage-clamp recordings revealed a higher D-type K⁺ conductance in FMRP-positive ET neurons compared with nearby FMRP-negative ET neurons. FMRP did not affect either rapidly inactivating A-type or noninactivating K⁺ conductance. ET neuron patches recorded with FMRP_1-298, a truncated form of FMRP that lacks mRNA binding domains, included in the pipette solution had larger D-type K⁺ conductance compared with heat-inactivated controls. Viral expression of FMRP in FX mice depolarized action potential threshold to near-wild-type levels in ET neurons. These results suggest that FMRP influences the excitability of ET neurons in the mPFC by regulating somatic D-type K⁺ channels in a cell-autonomous, protein-protein-dependent manner.NEW & NOTEWORTHY We demonstrate that fragile X mental retardation protein (FMRP), which is absent in fragile X syndrome (FXS), regulates D-type potassium channels in prefrontal cortex L5 pyramidal neurons with subcerebral projections but not in neighboring pyramidal neurons without subcerebral projections. FMRP regulates D-type potassium channels in a protein-protein-dependent manner and rescues action potential threshold in a mouse model of FXS. These findings have implications for how changes in voltage-gated channels contribute to neurodevelopmental disorders.

Training deep neural density estimators to identify mechanistic models of neural dynamics

Mechanistic modeling in neuroscience aims to explain observed phenomena in terms of underlying causes. However, determining which model parameters agree with complex and stochastic neural data presents a significant challenge. We address this challenge with a machine learning tool which uses deep neural density estimators-trained using model simulations-to carry out Bayesian inference and retrieve the full space of parameters compatible with raw data or selected data features. Our method is scalable in parameters and data features and can rapidly analyze new data after initial training. We demonstrate the power and flexibility of our approach on receptive fields, ion channels, and Hodgkin-Huxley models. We also characterize the space of circuit configurations giving rise to rhythmic activity in the crustacean stomatogastric ganglion, and use these results to derive hypotheses for underlying compensation mechanisms. Our approach will help close the gap between data-driven and theory-driven models of neural dynamics.

Modeling of lamprey reticulospinal neurons: multiple distinct parameter sets yield realistic simulations

For the lamprey and other vertebrates, reticulospinal (RS) neurons project descending axons to the spinal cord and activate motor networks to initiate locomotion and other behaviors. In the present study, a biophysically detailed computer model of lamprey RS neurons was constructed consisting of three compartments: dendritic, somatic, and axon initial segment (AIS). All compartments included passive channels. In addition, the soma and AIS had fast potassium and sodium channels. The soma included three additional voltage-gated ion channels (slow sodium and high- and low-voltage-activated calcium) and calcium-activated potassium channels. An initial manually adjusted default parameter set, which was based, in part, on modified parameters from models of lamprey spinal neurons, generated simulations of single action potentials and repetitive firing that scored favorably (0.658; maximum = 0.964) compared with experimentally derived properties of lamprey RS neurons. Subsequently, a dual-annealing search paradigm identified 4,302 viable parameter sets at local maxima within parameter space that yielded higher scores than the default parameter set, including many with much higher scores of approximately 0.85-0.87 (i.e., ~30% improvement). In addition, 5- and 2-conductance grid searches identified a relatively large number of viable parameters sets for which significant correlations were present between maximum conductances for pairs of ion channels. The present results indicated that multiple model parameter sets ("solutions") generated action potentials and repetitive firing that mimicked many of the properties of lamprey RS neurons. To our knowledge, this is the first study to systematically explore parameter space for a biophysically detailed model of lamprey RS neurons.NEW & NOTEWORTHY A computer model of lamprey reticulospinal neurons with a default parameter set produced simulations of action potentials and repetitive firing that scored favorably compared with the properties of these neurons. A dual-annealing search algorithm explored ~50 million parameter sets and identified 4,302 distinct viable parameter sets within parameter space that yielded higher/much higher scores than the default parameter set. In addition, 5- and 2-conductance grid searches identified significant correlations between maximum conductances for pairs of ion channels.

Homeostatic Intrinsic Plasticity Is Functionally Altered in Fmr1 KO Cortical Neurons

Cortical hyperexcitability is a hallmark of fragile X syndrome (FXS). In the Fmr1 knockout (KO) mouse model of FXS, cortical hyperexcitability is linked to sensory hypersensitivity and seizure susceptibility. It remains unclear why homeostatic mechanisms fail to prevent such activity. Homeostatic intrinsic plasticity (HIP) adjusts membrane excitability through regulation of ion channels to maintain activity levels following activity perturbation. Despite the critical role of HIP in the maturation of excitability, it has not been examined in FXS. Here, we demonstrate that HIP does not operate normally in a disease model, FXS. HIP was either lost or exaggerated in two distinct neuronal populations from Fmr1 KO cortical cultures. In addition, we have identified a mechanism for homeostatic intrinsic plasticity. Compromising HIP function during development could leave cortical neurons in the FXS nervous system vulnerable to hyperexcitability.

Fragile X syndrome (FXS) is characterized by cortical hyperexcitability, but the mechanisms driving hyperexcitability are poorly understood. Homeostatic intrinsic plasticity (HIP) regulates ion channel function to maintain appropriate activity levels. Bülow et al. show that HIP is functionally altered in FXS neurons, which may leave cortical neurons vulnerable to hyperexcitability.

Intrinsic neuronal properties represent song and error in zebra finch vocal learning

Neurons regulate their intrinsic physiological properties, which could influence network properties and contribute to behavioral plasticity. Recording from adult zebra finch brain slices we show that within each bird basal ganglia Area X-projecting (HVCX) neurons share similar spike waveform morphology and timing of spike trains, with modeling indicating similar magnitudes of five principal ion currents. These properties vary among birds in lawful relation to acoustic similarity of the birds' songs, with adult sibling pairs (same songs) sharing similar waveforms and spiking characteristics. The properties are maintained dynamically: HVCX within juveniles learning to sing show variable properties, whereas the uniformity rapidly degrades within hours in adults singing while exposed to abnormal (delayed) auditory feedback. Thus, within individual birds the population of current magnitudes covary over the arc of development, while rapidly responding to changes in feedback (in adults). This identifies network interactions with intrinsic properties that affect information storage and processing of learned vocalizations.

Molecular mechanisms of homeostatic plasticity in central pattern generator networks

Central pattern generator (CPG) networks rely on a balance of intrinsic and network properties to produce reliable, repeatable activity patterns. This balance is maintained by homeostatic plasticity where alterations in neuronal properties dynamically maintain appropriate neural output in the face of changing environmental conditions and perturbations. However, it remains unclear just how these neurons and networks can both monitor their ongoing activity and use this information to elicit homeostatic physiological responses to ensure robustness of output over time. Evidence exists that CPG networks use a mixed strategy of activity-dependent, activity-independent, modulator-dependent, and synaptically regulated homeostatic plasticity to achieve this critical stability. In this review, we focus on some of the current understanding of the molecular pathways and mechanisms responsible for this homeostatic plasticity in the context of central pattern generator function, with a special emphasis on some of the smaller invertebrate networks that have allowed for extensive cellular-level analyses that have brought recent insights to these questions.

Reduced intrinsic excitability of CA1 pyramidal neurons in human immunodeficiency virus (HIV) transgenic rats

The hippocampus is involved in key neuronal circuits that underlie cognition, memory, and anxiety, and it is increasingly recognized as a vulnerable structure that contributes to the pathogenesis of HIV-associated neurocognitive disorder (HAND). However, the mechanisms responsible for hippocampal dysfunction in neuroHIV remain unknown. The present study used HIV transgenic (Tg) rats and patch-clamp electrophysiological techniques to study the effects of the chronic low-level expression of HIV proteins on hippocampal CA1 pyramidal neurons. The dorsal and ventral areas of the hippocampus are involved in different neurocircuits and thus were evaluated separately. We found a significant decrease in the intrinsic excitability of CA1 neurons in the dorsal hippocampus in HIV Tg rats by comparing neuronal spiking induced by current step injections and by dynamic clamp to simulate neuronal spiking activity. The decrease in excitability in the dorsal hippocampus was accompanied by a higher rate of excitatory postsynaptic currents (EPSCs), whereas CA1 pyramidal neurons in the ventral hippocampus in HIV Tg rats had higher EPSC amplitudes. We also observed a reduction of hyperpolarization-activated nonspecific cationic current (Ih) in both the dorsal and ventral hippocampus. Neurotoxic HIV proteins have been shown to increase neuronal excitation. The lower excitability of CA1 pyramidal neurons that was observed herein may represent maladaptive homeostatic plasticity that seeks to stabilize baseline neuronal firing activity but may disrupt neural network function and contribute to HIV-associated neuropsychological disorders, such as HAND and depression.

Computational Analysis of Therapeutic Neuroadaptation to Chronic Antidepressant in a Model of the Monoaminergic Neurotransmitter and Stress Hormone Systems

The clinical practice of selective serotonin reuptake inhibitor (SSRI) augmentation relies heavily on trial-and-error. Unfortunately, the drug combinations prescribed today fail to provide relief for many depressed patients. In order to identify potentially more effective treatments, we developed a computational model of the monoaminergic neurotransmitter and stress-steroid systems that neuroadapts to chronic administration of combinations of antidepressant drugs and hormones by adjusting the strengths of its transmitter-system components (TSCs). We used the model to screen 60 chronically administered drug/hormone pairs and triples, and identified as potentially therapeutic those combinations that raised the monoamines (serotonin, norepinephrine, and dopamine) but lowered cortisol following neuroadaptation in the model. We also evaluated the contributions of individual and pairs of TSCs to therapeutic neuroadaptation with chronic SSRI using sensitivity, correlation, and linear temporal-logic analyses. All three approaches revealed that therapeutic neuroadaptation to chronic SSRI is an overdetermined process that depends on multiple TSCs, providing a potential explanation for the clinical finding that no single antidepressant regimen alleviates depressive symptoms in all patients.

Dimensions of control for subthreshold oscillations and spontaneous firing in dopamine neurons

Dopaminergic neurons (DAs) of the rodent substantia nigra pars compacta (SNc) display varied electrophysiological properties in vitro. Despite this, projection patterns and functional inputs from DAs to other structures are conserved, so in vivo delivery of consistent, well-timed dopamine modulation to downstream circuits must be coordinated. Here we show robust coordination by linear parameter controllers, discovered through powerful mathematical analyses of data and models, and from which consistent control of DA subthreshold oscillations (STOs) and spontaneous firing emerges. These units of control represent coordinated intracellular variables, sufficient to regulate complex cellular properties with radical simplicity. Using an evolutionary algorithm and dimensionality reduction, we discovered metaparameters, which when regressed against STO features, revealed a 2-dimensional control plane for the neuron’s 22-dimensional parameter space that fully maps the natural range of DA subthreshold electrophysiology. This plane provided a basis for spiking currents to reproduce a large range of the naturally occurring spontaneous firing characteristics of SNc DAs. From it we easily produced a unique population of models, derived using unbiased parameter search, that show good generalization to channel blockade and compensatory intracellular mechanisms. From this population of models, we then discovered low-dimensional controllers for regulating spontaneous firing properties, and gain insight into how currents active in different voltage regimes interact to produce the emergent activity of SNc DAs. Our methods therefore reveal simple regulators of neuronal function lurking in the complexity of combined ion channel dynamics.

Electrophysiological activity of the neuronal membrane and concomitant ion channel properties are highly variable within groups of neurons of the same type from the same brain region. Reconciliation of the mechanisms generating neuronal activity is challenging due to the complexity of the interactions between the channel currents involved. Here we present a set of mathematical analyses that uncover the low-dimensional intracellular parameter combinations capable of regulating features of subthreshold oscillations and spontaneous firing in empirically constrained models of nigral dopaminergic neurons. This method generates, from a naive starting point, linear combinations of ion channel properties that are surprisingly capable of reliably controlling a wide variety of emergent electrophysiological activity, thereby predicting drug effects and shedding light on unsuspected compensatory mechanisms that contribute to neuronal function.

The physiological variability of channel density in hippocampal CA1 pyramidal cells and interneurons explored using a unified data-driven modeling workflow

Every neuron is part of a network, exerting its function by transforming multiple spatiotemporal synaptic input patterns into a single spiking output. This function is specified by the particular shape and passive electrical properties of the neuronal membrane, and the composition and spatial distribution of ion channels across its processes. For a variety of physiological or pathological reasons, the intrinsic input/output function may change during a neuron's lifetime. This process results in high variability in the peak specific conductance of ion channels in individual neurons. The mechanisms responsible for this variability are not well understood, although there are clear indications from experiments and modeling that degeneracy and correlation among multiple channels may be involved. Here, we studied this issue in biophysical models of hippocampal CA1 pyramidal neurons and interneurons. Using a unified data-driven simulation workflow and starting from a set of experimental recordings and morphological reconstructions obtained from rats, we built and analyzed several ensembles of morphologically and biophysically accurate single cell models with intrinsic electrophysiological properties consistent with experimental findings. The results suggest that the set of conductances expressed in any given hippocampal neuron may be considered as belonging to two groups: one subset is responsible for the major characteristics of the firing behavior in each population and the other is responsible for a robust degeneracy. Analysis of the model neurons suggests several experimentally testable predictions related to the combination and relative proportion of the different conductances that should be expressed on the membrane of different types of neurons for them to fulfill their role in the hippocampus circuitry.

Biophysics of object segmentation in a collision-detecting neuron

Collision avoidance is critical for survival, including in humans, and many species possess visual neurons exquisitely sensitive to objects approaching on a collision course. Here, we demonstrate that a collision-detecting neuron can detect the spatial coherence of a simulated impending object, thereby carrying out a computation akin to object segmentation critical for proper escape behavior. At the cellular level, object segmentation relies on a precise selection of the spatiotemporal pattern of synaptic inputs by dendritic membrane potential-activated channels. One channel type linked to dendritic computations in many neural systems, the hyperpolarization-activated cation channel, HCN, plays a central role in this computation. Pharmacological block of HCN channels abolishes the neuron's spatial selectivity and impairs the generation of visually guided escape behaviors, making it directly relevant to survival. Additionally, our results suggest that the interaction of HCN and inactivating K⁺ channels within active dendrites produces neuronal and behavioral object specificity by discriminating between complex spatiotemporal synaptic activation patterns.

Activation mechanism of a neuromodulator-gated pacemaker ionic current

The neuromodulator-gated current (I_MI) found in the crab stomatogastric ganglion is activated by neuromodulators that are essential to induce the rhythmic activity of the pyloric network in this system. One of these neuromodulators is also known to control the correlated expression of voltage-gated ionic currents in pyloric neurons, as well as synaptic plasticity and strength. Thus understanding the mechanism by which neuromodulator receptors activate I_MI should provide insights not only into how oscillations are initiated but also into how other processes, and currents not directly activated by them, are regulated. To determine what specific signaling molecules are implicated in this process, we used a battery of agonists and antagonists of common signal transduction pathways. We found that the G protein inhibitor GDPβS and the G protein activator GTPγS significantly affect I_MI amplitude, suggesting that its activation is mediated by G proteins. Interestingly, when using the more specific G protein blocker pertussis toxin, we observed the expected inhibition of I_MI amplitude but, unexpectedly, in a calcium-dependent fashion. We also found that antagonists of calcium- and calmodulin-associated signaling significantly reduce I_MI amplitude. In contrast, we found little evidence for the role of cyclic nucleotide signaling, phospholipase C (PLC), or kinases and phosphatases, except two calmodulin-dependent kinases. In sum, these results suggest that proctolin-induced I_MI is mediated by a G protein whose pertussis toxin sensitivity is altered by external calcium concentration and appears to depend on intracellular calcium, calmodulin, and calmodulin-activated kinases. In contrast, we found no support for I_MI being mediated by PLC signaling or cyclic nucleotides.NEW & NOTEWORTHY Neuronal rhythmic activity is generated by either network-based or cell-autonomous mechanisms. In the pyloric network of decapod crustaceans, the activation of a neuromodulator-gated pacemaker current is crucial for the generation of rhythmic activity. This current is activated by several neuromodulators, including peptides and acetylcholine, presumably via metabotropic receptors. We have previously demonstrated a novel extracellular calcium-sensitive voltage-dependence mechanism of this current. We presently report that the activation mechanism depends on intracellular and extracellular calcium-sensitive components.

Homeostatic plasticity of excitability in crustacean central pattern generator networks

Plasticity of excitability can come in two general forms: changes in excitability that alter neuronal output (e.g. long-term potentiation of intrinsic excitability) or excitability changes that stabilize neuronal output (homeostatic plasticity). Here we discuss the latter form of plasticity in the context of the crustacean stomatogastric nervous system, and a second central pattern generator circuit, the cardiac ganglion. We discuss this plasticity at three levels: rapid homeostatic changes in membrane conductance, longer-term effects of neuromodulation on excitability, and the impacts of activity-dependent feedback on steady-state channel mRNA levels. We then conclude with thoughts on the implications of plasticity of excitability for variability of conductance levels across populations of motor neurons.

The transient potassium outward current has different roles in modulating the pyloric and gastric mill rhythms in the stomatogastric ganglion

The crustacean stomatogastric nervous system is a classic model for understanding the effects of modulating ionic currents and synapses at both the cell and network levels. The stomatogastric ganglion in this system contains two distinct central pattern generators: a slow gastric mill network that generates flexible rhythmic outputs (8-20 s) and is often silent, and a fast pyloric network that generates more consistent rhythmic outputs (0.5-2 s) and is always active in vitro. Different ionic conductances contribute to the properties of individual neurons and therefore to the overall dynamics of the pyloric and gastric mill networks. However, the contributions of ionic currents to different dynamics between the pyloric and gastric mill networks are not well understood. The goal of this study is to evaluate how changes in outward potassium current (I _A) in the stomatogastric ganglion affect the dynamics of the pyloric and gastric mill rhythms by interfering with normal I _A activity. We bath-applied the specific I _A blocker 4-aminopyridine to reduce I _A's effect in the stomatogastric ganglion in vitro and evaluated quantitatively the changes in both rhythms. We found that blocking I _A in the stomatogastric ganglion alters the synchronization between pyloric neurons, and consistently activates the gastric mill rhythm in quiescent preparations.

Genetic perturbations suggest a role of the resting potential in regulating the expression of the ion channels of the KCNA and HCN families in octopus cells of the ventral cochlear nucleus

Low-voltage-activated K⁺ (g_KL) and hyperpolarization-activated mixed cation conductances (g_h) mediate currents, I_KL and I_h, through channels of the Kv1 (KCNA) and HCN families respectively and give auditory neurons the temporal precision required for signaling information about the onset, fine structure, and time of arrival of sounds. Being partially activated at rest, g_KL and g_h contribute to the resting potential and shape responses to even small subthreshold synaptic currents. Resting g_KL and g_h also affect the coupling of somatic depolarization with the generation of action potentials. To learn how these important conductances are regulated we have investigated how genetic perturbations affect their expression in octopus cells of the ventral cochlear nucleus (VCN). We report five new findings: First, the magnitude of g_h and g_KL varied over more than two-fold between wild type strains of mice. Second, average resting potentials are not different in different strains of mice even in the face of large differences in average g_KL and g_h. Third, I_KL has two components, one being α-dendrotoxin (α-DTX)-sensitive and partially inactivating and the other being α-DTX-insensitive, tetraethylammonium (TEA)-sensitive, and non-inactivating. Fourth, the loss of Kv1.1 results in diminution of the α-DTX-sensitive I_KL, and compensatory increased expression of an α-DTX-insensitive, tetraethylammonium (TEA)-sensitive I_KL. Fifth, I_h and I_KL are balanced at the resting potential in all wild type and mutant octopus cells even when resting potentials vary in individual cells over nearly 10 mV, indicating that the resting potential influences the expression of g_h and g_KL. The independence of resting potentials on g_KL and g_h shows that g_KL and g_h do not, over days or weeks, determine the resting potential but rather that the resting potential plays a role in regulating the magnitude of either or both g_KL and g_h.

Consequences of degeneracy in network function

Often distinct elements serve similar functions within a network. However, it is unclear whether this network degeneracy is beneficial, or merely a reflection of tighter regulation of overall network performance relative to individual neuronal properties. We review circumstances where data strongly suggest that degeneracy is beneficial in that it makes network function more robust. Importantly, network degeneracy is likely to have functional consequences that are not widely appreciated. This is likely to be true when network activity is configured by modulators with persistent actions, and the history of network activity potentially impacts subsequent functioning. Data suggest that degeneracy in this context may be important for the creation of latent memories, and for state-dependent task switching.

Dynamic compensation mechanism gives rise to period and duty-cycle level sets in oscillatory neuronal models

Rhythmic oscillation in neurons can be characterized by various attributes, such as the oscillation period and duty cycle. The values of these features depend on the amplitudes of the participating ionic currents, which can be characterized by their maximum conductance values. Recent experimental and theoretical work has shown that the values of these attributes can be maintained constant for different combinations of two or more ionic currents of varying conductances, defining what is known as level sets in conductance space. In two-dimensional conductance spaces, a level set is a curve, often a line, along which a particular oscillation attribute value is conserved. In this work, we use modeling, dynamical systems tools (phase-space analysis), and numerical simulations to investigate the possible dynamic mechanisms responsible for the generation of period and duty-cycle levels sets in simplified (linearized and FitzHugh-Nagumo) and conductance-based (Morris-Lecar) models of neuronal oscillations. A simplistic hypothesis would be that the tonic balance between ionic currents with the same or opposite effective signs is sufficient to create level sets. According to this hypothesis, the dynamics of each ionic current during a given cycle are well captured by some constant quantity (e.g., maximal conductances), and the phase-plane diagrams are identical or are almost identical (e.g., cubic-like nullclines with the same maxima and minima) for different combinations of these maximal conductances. In contrast, we show that these mechanisms are dynamic and involve the complex interaction between the nonlinear voltage dependencies and the effective time scales at which the ionic current's dynamical variables operate.

Firing frequency and entrainment maintained in primary auditory neurons in the presence of combined BDNF and NT3

Primary auditory neurons rely on neurotrophic factors for development and survival. We previously determined that exposure to brain-derived neurotrophic factor (BDNF) and neurotrophin-3 (NT3) alters the activity of hyperpolarization-activated currents (Ih) in this neuronal population. Since potassium channels are sensitive to neurotrophins, and changes in Ih are often accompanied by a shift in voltage-gated potassium currents (IK), this study examined IK with exposure to both BDNF and NT3 and the impact on firing entrainment during high frequency pulse trains. Whole-cell patch-clamp recordings revealed significant changes in action potential latency and duration, but no change in firing adaptation or total outward IK. Dendrotoxin-I (DTX-I), targeting voltage-gated potassium channel subunits KV1.1 and KV1.2, uncovered an increase in the contribution of DTX-I sensitive currents with exposure to neurotrophins. No difference in Phrixotoxin-1 (PaTX-1) sensitive currents, mediated by KV4.2 and KV4.3 subunits, was observed. Further, no difference was seen in firing entrainment. These results show that combined BDNF and NT3 exposure influences the contribution of KV1.1 and KV1.2 to the low voltage-activated potassium current (IKL). Whilst this is accompanied by a shift in spike latency and duration, both firing frequency and entrainment to high frequency pulse trains are preserved.

Transient potassium channels augment degeneracy in hippocampal active dendritic spectral tuning

Hippocampal pyramidal neurons express an intraneuronal map of spectral tuning mediated by hyperpolarization-activated cyclic-nucleotide-gated nonspecific-cation channels. Modeling studies have predicted a critical regulatory role for A-type potassium (KA) channels towards augmenting functional robustness of this map. To test this, we performed patch-clamp recordings from soma and dendrites of rat hippocampal pyramidal neurons, and measured spectral tuning before and after blocking KA channels using two structurally distinct pharmacological agents. Consistent with computational predictions, we found that blocking KA channels resulted in a significant reduction in resonance frequency and significant increases in input resistance, impedance amplitude and action-potential firing frequency across the somato-apical trunk. Furthermore, across all measured locations, blocking KA channels enhanced temporal summation of postsynaptic potentials and critically altered the impedance phase profile, resulting in a significant reduction in total inductive phase. Finally, pair-wise correlations between intraneuronal percentage changes (after blocking KA channels) in different measurements were mostly weak, suggesting differential regulation of different physiological properties by KA channels. Our results unveil a pivotal role for fast transient channels in regulating theta-frequency spectral tuning and intrinsic phase response, and suggest that degeneracy with reference to several coexisting functional maps is mediated by cross-channel interactions across the active dendritic arbor.

Monoaminergic tone supports conductance correlations and stabilizes activity features in pattern generating neurons of the lobster, Panulirus interruptus

Experimental and computational studies demonstrate that different sets of intrinsic and synaptic conductances can give rise to equivalent activity patterns. This is because the balance of conductances, not their absolute values, defines a given activity feature. Activity-dependent feedback mechanisms maintain neuronal conductance correlations and their corresponding activity features. This study demonstrates that tonic nM concentrations of monoamines enable slow, activity-dependent processes that can maintain a correlation between the transient potassium current (I_A) and the hyperpolarization activated current (I_h) over the long-term (i.e., regulatory change persists for hours after removal of modulator). Tonic 5 nM DA acted through an RNA interference silencing complex (RISC)- and RNA polymerase II-dependent mechanism to maintain a long-term positive correlation between I_A and I_h in the lateral pyloric neuron (LP) but not in the pyloric dilator neuron (PD). In contrast, tonic 5 nM 5HT maintained a RISC-dependent positive correlation between I_A and I_h in PD but not LP over the long-term. Tonic 5 nM OCT maintained a long-term negative correlation between I_A and I_h in PD but not LP; however, it was only revealed when RISC was inhibited. This study also demonstrated that monoaminergic tone can also preserve activity features over the long-term: the timing of LP activity, LP duty cycle and LP spike number per burst were maintained by tonic 5 nM DA. The data suggest that low-level monoaminergic tone acts through multiple slow processes to permit cell-specific, activity-dependent regulation of ionic conductances to maintain conductance correlations and their corresponding activity features over the long-term.

Variability in State-Dependent Plasticity of Intrinsic Properties during Cell-Autonomous Self-Regulation of Calcium Homeostasis in Hippocampal Model Neurons

How do neurons reconcile the maintenance of calcium homeostasis with perpetual switches in patterns of afferent activity? Here, we assessed state-dependent evolution of calcium homeostasis in a population of hippocampal pyramidal neuron models, through an adaptation of a recent study on stomatogastric ganglion neurons. Calcium homeostasis was set to emerge through cell-autonomous updates to 12 ionic conductances, responding to different types of synaptically driven afferent activity. We first assessed the impact of theta-frequency inputs on the evolution of ionic conductances toward maintenance of calcium homeostasis. Although calcium homeostasis emerged efficaciously across all models in the population, disparate changes in ionic conductances that mediated this emergence resulted in variable plasticity to several intrinsic properties, also manifesting as significant differences in firing responses across models. Assessing the sensitivity of this form of plasticity, we noted that intrinsic neuronal properties and the firing response were sensitive to the target calcium concentration and to the strength and frequency of afferent activity. Next, we studied the evolution of calcium homeostasis when afferent activity was switched, in different temporal sequences, between two behaviorally distinct types of activity: theta-frequency inputs and sharp-wave ripples riding on largely silent periods. We found that the conductance values, intrinsic properties, and firing response of neurons exhibited differential robustness to an intervening switch in the type of afferent activity. These results unveil critical dissociations between different forms of homeostasis, and call for a systematic evaluation of the impact of state-dependent switches in afferent activity on neuronal intrinsic properties during neural coding and homeostasis.

Animal-to-Animal Variability in Neuromodulation and Circuit Function

Each animal alive in the world is different from all other individuals, while sharing most attributes of form and function with others of the same species. Still other attributes are shared within a phylum, and still others are common to most eukaryotic organisms. All animals have mechanisms that modulate the strength of their synapses or alter the intrinsic excitability of component neurons. What animal-to-animal variability in behavior arises from differences in neuronal structure, ion channel expression, or connectivity, and what variability arises from neuromodulation of brain states? Conversely, can robust behavior be maintained despite variability in circuit components by the action of neuromodulatory inputs? These are fundamental issues relevant to all nervous systems that have been illuminated by many years of study of the small, rhythmic motor circuits found in the crustacean stomatogastric nervous system.

Tonic 5nM DA stabilizes neuronal output by enabling bidirectional activity-dependent regulation of the hyperpolarization activated current via PKA and calcineurin

Volume transmission results in phasic and tonic modulatory signals. The actions of tonic dopamine (DA) at type 1 DA receptors (D1Rs) are largely undefined. Here we show that tonic 5nM DA acts at D1Rs to stabilize neuronal output over minutes by enabling activity-dependent regulation of the hyperpolarization activated current (I _h). In the presence but not absence of 5nM DA, I _h maximal conductance (G _max) was adjusted according to changes in slow wave activity in order to maintain spike timing. Our study on the lateral pyloric neuron (LP), which undergoes rhythmic oscillations in membrane potential with depolarized plateaus, demonstrated that incremental, bi-directional changes in plateau duration produced corresponding alterations in LP I _hG _max when preparations were superfused with saline containing 5nM DA. However, when preparations were superfused with saline alone there was no linear correlation between LP I _hG_max and duty cycle. Thus, tonic nM DA modulated the capacity for activity to modulate LP I _h G _max; this exemplifies metamodulation (modulation of modulation). Pretreatment with the Ca2+-chelator, BAPTA, or the specific PKA inhibitor, PKI, prevented all changes in LP I _h in 5nM DA. Calcineurin inhibitors blocked activity-dependent changes enabled by DA and revealed a PKA-mediated, activity-independent enhancement of LP I _hG _max. These data suggested that tonic 5nM DA produced two simultaneous, PKA-dependent effects: a direct increase in LP I _h G _max and a priming event that permitted calcineurin regulation of LP I _h. The latter produced graded reductions in LP I _hG _max with increasing duty cycles. We also demonstrated that this metamodulation preserved the timing of LP’s first spike when network output was perturbed with bath-applied 4AP. In sum, 5nM DA permits slow wave activity to provide feedback that maintains spike timing, suggesting that one function of low-level, tonic modulation is to stabilize specific features of a dynamic output.

QUANTITATIVE REEVALUATION OF THE EFFECTS OF SHORT- AND LONG-TERM REMOVAL OF DESCENDING MODULATORY INPUTS ON THE PYLORIC RHYTHM OF THE CRAB, CANCER BOREALIS

Neuromodulatory inputs are known to strongly influence the intrinsic excitability of individual neurons and the networks in which the targets of modulation are found. It is therefore important to understand how nervous systems respond to altered neuromodulatory environments.

The crustacean stomatogastric ganglion (STG) receives descending neuromodulatory inputs from three anterior ganglia: the paired commissural ganglia (CoGs), and the single esophageal ganglion (OG). In this paper, we provide the first detailed and quantitative analyses of the short- and long-term effects of removal of these descending inputs (decentralization) on the pyloric rhythm of the STG. Thirty minutes after decentralization, the mean frequency of the pyloric rhythm dropped from 1.20 Hz in control to 0.52 Hz. Whereas the relative phase of pyloric neuron activity was approximately constant across frequency in the controls, after decentralization this changed markedly. Nine control preparations kept for 5–6 d in vitro maintained pyloric rhythm frequencies close to their initial values. Nineteen decentralized preparations kept for 5–6 d dropped slightly in frequency from those seen at 30 min following decentralization, but then displayed stable activity over 6 d. Bouts of higher frequency activity were intermittently seen in both control and decentralized preparations, but the bouts began earlier and were more frequent in the decentralized preparations. Although the bouts may indicate that the removal of the modulatory inputs triggered changes in neuronal excitability, these changes did not produce obvious long-lasting changes in the frequency of the decentralized preparations.

Krüppel mediates the selective rebalancing of ion channel expression

Ion channel gene expression can vary substantially among neurons of a given type, even though neuron-type-specific firing properties remain stable and reproducible. The mechanisms that modulate ion channel gene expression and stabilize neural firing properties are unknown. In Drosophila, we demonstrate that loss of the Shal potassium channel induces the compensatory rebalancing of ion channel expression including, but not limited to, the enhanced expression and function of Shaker and slowpoke. Using genomic and network modeling approaches combined with genetic and electrophysiological assays, we demonstrate that the transcription factor Krüppel is necessary for the homeostatic modulation of Shaker and slowpoke expression. Remarkably, Krüppel induction is specific to the loss of Shal, not being observed in five other potassium channel mutants that cause enhanced neuronal excitability. Thus, homeostatic signaling systems responsible for rebalancing ion channel expression can be selectively induced after the loss or impairment of a specific ion channel.

Identifying crucial parameter correlations maintaining bursting activity

Recent experimental and computational studies suggest that linearly correlated sets of parameters (intrinsic and synaptic properties of neurons) allow central pattern-generating networks to produce and maintain their rhythmic activity regardless of changing internal and external conditions. To determine the role of correlated conductances in the robust maintenance of functional bursting activity, we used our existing database of half-center oscillator (HCO) model instances of the leech heartbeat CPG. From the database, we identified functional activity groups of burster (isolated neuron) and half-center oscillator model instances and realistic subgroups of each that showed burst characteristics (principally period and spike frequency) similar to the animal. To find linear correlations among the conductance parameters maintaining functional leech bursting activity, we applied Principal Component Analysis (PCA) to each of these four groups. PCA identified a set of three maximal conductances (leak current, _Leak; a persistent K current, _K2; and of a persistent Na+ current, _P) that correlate linearly for the two groups of burster instances but not for the HCO groups. Visualizations of HCO instances in a reduced space suggested that there might be non-linear relationships between these parameters for these instances. Experimental studies have shown that period is a key attribute influenced by modulatory inputs and temperature variations in heart interneurons. Thus, we explored the sensitivity of period to changes in maximal conductances of _Leak, _K2, and _P, and we found that for our realistic bursters the effect of these parameters on period could not be assessed because when varied individually bursting activity was not maintained.

Central pattern-generating networks (CPGs) must be remarkably robust, maintaining functional rhythmic activity despite fluctuations in internal and external conditions. Recent experimental evidence suggests that this robustness is achieved by the coordinated regulation of many membrane and synaptic current parameters. Experimental and computational studies showed that linearly correlated sets of such parameters allow CPG neurons to produce and maintain their rhythmic activity. However, the mechanisms that allow multiple parameters to interact, thereby producing and maintaining rhythmic single cell and network activity, are not clear. Here, we use a half-center oscillator (HCO) model that replicates the electrical activity (rhythmic alternating bursting of mutually inhibitory interneurons) of the leech heartbeat CPG to investigate potential relationships between parameters that maintain functional bursting activity in the HCOs and the isolated component neurons (bursters). We found a linearly correlated set of three maximal conductances that maintains functional bursting activity similar to the animal in burster model instances, therefore increasing robustness of bursting activity. In addition, we found that bursting activity was very sensitive to individual variation of these parameters; only correlated changes could maintain the activity type.

Ionic Current Variability and Functional Stability in the Nervous System

Identified neurons in different animals express ionic currents at highly variable levels (population variability). If neuronal identity is associated with stereotypical function, as is the case in genetically identical neurons or in unambiguously identified individual neurons, this variability poses a conundrum: How is activity the same if the components that generate it-ionic current levels-are different? In some cases, ionic current variability across similar neurons generates an output gradient. However, many neurons produce very similar output activity, despite substantial variability in ionic conductances. It appears that, in many such cells, conductance levels of one ionic current vary in proportion to the conductance levels of another current. As a result, in a population of neurons, these conductances appear to be correlated. Here, I review theoretical and experimental work that suggests that neuronal ionic current correlation can reduce the global ionic current variability and can contribute to functional stability.

The interplay of seven subthreshold conductances controls the resting membrane potential and the oscillatory behavior of thalamocortical neurons

The signaling properties of thalamocortical (TC) neurons depend on the diversity of ion conductance mechanisms that underlie their rich membrane behavior at subthreshold potentials. Using patch-clamp recordings of TC neurons in brain slices from mice and a realistic conductance-based computational model, we characterized seven subthreshold ion currents of TC neurons and quantified their individual contributions to the total steady-state conductance at levels below tonic firing threshold. We then used the TC neuron model to show that the resting membrane potential results from the interplay of several inward and outward currents over a background provided by the potassium and sodium leak currents. The steady-state conductances of depolarizing Ih (hyperpolarization-activated cationic current), IT (low-threshold calcium current), and INaP (persistent sodium current) move the membrane potential away from the reversal potential of the leak conductances. This depolarization is counteracted in turn by the hyperpolarizing steady-state current of IA (fast transient A-type potassium current) and IKir (inwardly rectifying potassium current). Using the computational model, we have shown that single parameter variations compatible with physiological or pathological modulation promote burst firing periodicity. The balance between three amplifying variables (activation of IT, activation of INaP, and activation of IKir) and three recovering variables (inactivation of IT, activation of IA, and activation of Ih) determines the propensity, or lack thereof, of repetitive burst firing of TC neurons. We also have determined the specific roles that each of these variables have during the intrinsic oscillation.

Homeostasis of functional maps in active dendrites emerges in the absence of individual channelostasis

The maintenance of ion channel homeostasis, or channelostasis, is a complex puzzle in neurons with extensive dendritic arborization, encompassing a combinatorial diversity of proteins that encode these channels and their auxiliary subunits, their localization profiles, and associated signaling machinery. Despite this, neurons exhibit amazingly stereotypic, topographically continuous maps of several functional properties along their active dendritic arbor. Here, we asked whether the membrane composition of neurons, at the level of individual ion channels, is constrained by this structural requirement of sustaining several functional maps along the same topograph. We performed global sensitivity analysis on morphologically realistic conductance-based models of hippocampal pyramidal neurons that coexpressed six well-characterized functional maps along their trunk. We generated randomized models by varying 32 underlying parameters and constrained these models with quantitative experimental measurements from the soma and dendrites of hippocampal pyramidal neurons. Analyzing valid models that satisfied experimental constraints on all six functional maps, we found topographically analogous functional maps to emerge from disparate model parameters with weak pairwise correlations between parameters. Finally, we derived a methodology to assess the contribution of individual channel conductances to the various functional measurements, using virtual knockout simulations on the valid model population. We found that the virtual knockout of individual channels resulted in variable, measurement- and location-specific impacts across the population. Our results suggest collective channelostasis as a mechanism behind the robust emergence of analogous functional maps and have significant ramifications for the localization and targeting of ion channels and enzymes that regulate neural coding and homeostasis.

Filamin A promotes dynamin-dependent internalization of hyperpolarization-activated cyclic nucleotide-gated type 1 (HCN1) channels and restricts Ih in hippocampal neurons

The actin-binding protein filamin A (FLNa) regulates neuronal migration during development, yet its roles in the mature brain remain largely obscure. Here, we probed the effects of FLNa on the regulation of ion channels that influence neuronal properties. We focused on the HCN1 channels that conduct Ih, a hyperpolarization-activated current crucial for shaping intrinsic neuronal properties. Whereas regulation of HCN1 channels by FLNa has been observed in melanoma cell lines, its physiological relevance to neuronal function and the underlying cellular pathways that govern this regulation remain unknown. Using a combination of mutational, pharmacological, and imaging approaches, we find here that FLNa facilitates a selective and reversible dynamin-dependent internalization of HCN1 channels in HEK293 cells. This internalization is accompanied by a redistribution of HCN1 channels on the cell surface, by accumulation of the channels in endosomal compartments, and by reduced Ih density. In hippocampal neurons, expression of a truncated dominant-negative FLNa enhances the expression of native HCN1. Furthermore, acute abrogation of HCN1-FLNa interaction in neurons, with the use of decoy peptides that mimic the FLNa-binding domain of HCN1, abolishes the punctate distribution of HCN1 channels in neuronal cell bodies, augments endogenous Ih, and enhances the rebound-response ("voltage-sag") of the neuronal membrane to transient hyperpolarizing events. Together, these results support a major function of FLNa in modulating ion channel abundance and membrane trafficking in neurons, thereby shaping their biophysical properties and function.

A codimension-2 bifurcation controlling endogenous bursting activity and pulse-triggered responses of a neuron model

The dynamics of individual neurons are crucial for producing functional activity in neuronal networks. An open question is how temporal characteristics can be controlled in bursting activity and in transient neuronal responses to synaptic input. Bifurcation theory provides a framework to discover generic mechanisms addressing this question. We present a family of mechanisms organized around a global codimension-2 bifurcation. The cornerstone bifurcation is located at the intersection of the border between bursting and spiking and the border between bursting and silence. These borders correspond to the blue sky catastrophe bifurcation and the saddle-node bifurcation on an invariant circle (SNIC) curves, respectively. The cornerstone bifurcation satisfies the conditions for both the blue sky catastrophe and SNIC. The burst duration and interburst interval increase as the inverse of the square root of the difference between the corresponding bifurcation parameter and its bifurcation value. For a given set of burst duration and interburst interval, one can find the parameter values supporting these temporal characteristics. The cornerstone bifurcation also determines the responses of silent and spiking neurons. In a silent neuron with parameters close to the SNIC, a pulse of current triggers a single burst. In a spiking neuron with parameters close to the blue sky catastrophe, a pulse of current temporarily silences the neuron. These responses are stereotypical: the durations of the transient intervals-the duration of the burst and the duration of latency to spiking-are governed by the inverse-square-root laws. The mechanisms described here could be used to coordinate neuromuscular control in central pattern generators. As proof of principle, we construct small networks that control metachronal-wave motor pattern exhibited in locomotion. This pattern is determined by the phase relations of bursting neurons in a simple central pattern generator modeled by a chain of oscillators.

Natural antisense transcripts regulate the neuronal stress response and excitability

Neurons regulate ionic fluxes across their plasma membrane to maintain their excitable properties under varying environmental conditions. However, the mechanisms that regulate ion channels abundance remain poorly understood. Here we show that pickpocket 29 (ppk29), a gene that encodes a Drosophila degenerin/epithelial sodium channel (DEG/ENaC), regulates neuronal excitability via a protein-independent mechanism. We demonstrate that the mRNA 3′UTR of ppk29 affects neuronal firing rates and associated heat-induced seizures by acting as a natural antisense transcript (NAT) that regulates the neuronal mRNA levels of seizure (sei), the Drosophila homolog of the human Ether-à-go-go Related Gene (hERG) potassium channel. We find that the regulatory impact of ppk29 mRNA on sei is independent of the sodium channel it encodes. Thus, our studies reveal a novel mRNA dependent mechanism for the regulation of neuronal excitability that is independent of protein-coding capacity.

DOI:http://dx.doi.org/10.7554/eLife.01849.001

Neurons communicate with one another via electrical signals known as action potentials. These signals are generated when a stimulus causes sodium and potassium ion channels in the cell membrane to open, leading to an influx of sodium ions, followed by an efflux of potassium ions. Changes in temperature affect the rate at which ion channels open and close, and thus affect how easy it is for a stimulus to trigger an action potential. In response to a sudden rise in temperature, neurons must adjust the number of ion channels in their membranes to ensure that they do not become hyperexcitable, which could result in epilepsy.

Now, Zheng et al. have revealed one possible mechanism for how neurons do this. In the fruit fly, Drosophila, a gene for a potassium channel is found on the same chromosomal location as a gene for a sodium channel, and some of the genetic elements that regulate the expression of these two genes even overlap. However, the genes are on opposite strands of the DNA double helix. This means that when the genes are transcribed to produce molecules of messenger RNA (mRNA), which is usually single stranded, some of the mRNA molecules will pair up to form double-stranded mRNA molecules. This is significant because such RNA ‘duplexes’ have been shown to inhibit the translation of conventional single-stranded mRNA molecules into proteins, or to lead to their complete degradation.

Zheng et al. found that flies with mutations in the potassium channel gene display seizures in response to sudden changes in temperature. However, insects with mutations in the sodium channel gene are not affected because, surprisingly, they have a higher than expected number of potassium channels. It turns out that the mutant sodium channel mRNA molecules are unable to form RNA duplexes with potassium channel mRNA molecules: these duplexes would normally limit the number of potassium channels so, in their absence, the number of potassium channels increases, and this protects the flies from seizures.

Zheng et al. also uncovered a novel mechanism by which mRNA molecules can regulate gene expression independent of their role as templates for proteins. Further work is required to determine whether this mechanism is also present in other organisms, including humans.

DOI:http://dx.doi.org/10.7554/eLife.01849.002

Correlated conductance parameters in leech heart motor neurons contribute to motor pattern formation

Neurons can have widely differing intrinsic membrane properties, in particular the density of specific conductances, but how these contribute to characteristic neuronal activity or pattern formation is not well understood. To explore the relationship between conductances, and in particular how they influence the activity of motor neurons in the well characterized leech heartbeat system, we developed a new multi-compartmental Hodgkin-Huxley style leech heart motor neuron model. To do so, we evolved a population of model instances, which differed in the density of specific conductances, capable of achieving specific output activity targets given an associated input pattern. We then examined the sensitivity of measures of output activity to conductances and how the model instances responded to hyperpolarizing current injections. We found that the strengths of many conductances, including those with differing dynamics, had strong partial correlations and that these relationships appeared to be linked by their influence on heart motor neuron activity. Conductances that had positive correlations opposed one another and had the opposite effects on activity metrics when perturbed whereas conductances that had negative correlations could compensate for one another and had similar effects on activity metrics.

Neurons within the same network independently achieve conserved output by differentially balancing variable conductance magnitudes

Biological and theoretical evidence suggest that individual neurons may achieve similar outputs by differentially balancing variable underlying ionic conductances. Despite the substantial amount of data consistent with this idea, a direct biological demonstration that cells with conserved output, particularly within the same network, achieve these outputs via different solutions has been difficult to achieve. Here we demonstrate definitively that neurons from native neural networks with highly similar output achieve this conserved output by differentially tuning underlying conductance magnitudes. Multiple motor neurons of the crab (Cancer borealis) cardiac ganglion have highly conserved output within a preparation, despite showing a 2-4-fold range of conductance magnitudes. By blocking subsets of these currents, we demonstrate that the remaining conductances become unbalanced, causing disparate output as a result. Therefore, as strategies to understand neuronal excitability become increasingly sophisticated, it is important that such variability in excitability of neurons, even among those within the same individual, is taken into account.

Ionic current correlations underlie the global tuning of large numbers of neuronal activity attributes

Ionic conductances in identified neurons are highly variable. This poses the crucial question of how such neurons can produce stable activity. Coexpression of ionic currents has been observed in an increasing number of neurons in different systems, suggesting that the coregulation of ionic channel expression, by thus linking their variability, may enable neurons to maintain relatively constant neuronal activity as suggested by a number of recent theoretical studies. We examine this hypothesis experimentally using the voltage- and dynamic-clamp techniques to first measure and then modify the ionic conductance levels of three currents in identified neurons of the crab pyloric network. We quantify activity by measuring 10 different attributes (oscillation period, spiking frequency, etc.), and find linear, positive and negative relationships between conductance pairs and triplets that can enable pyloric neurons to maintain activity attributes invariant. Consistent with experimental observations, some of the features most tightly regulated appear to be phase relationships of bursting activity. We conclude that covariation (and probably a tightly controlled coregulation) of ionic conductances can help neurons maintain certain attributes of neuronal activity invariant while at the same time allowing conductances to change over wide ranges in response to internal or environmental inputs and perturbations. Our results also show that neurons can tune neuronal activity globally via coordinate expression of ion currents.

Rapid homeostatic plasticity of intrinsic excitability in a central pattern generator network stabilizes functional neural network output

Neurons and networks undergo a process of homeostatic plasticity that stabilizes output by integrating activity levels with network and cellular properties to counter longer-term perturbations. Here we describe a rapid compensatory interaction among a pair of potassium currents, I(A) and I(KCa), that stabilizes both intrinsic excitability and network function in the cardiac ganglion of the crab, Cancer borealis. We determined that mRNA levels in single identified neurons for the channels which encode I(A) and I(KCa) are positively correlated, yet the ionic currents themselves are negatively correlated, across a population of motor neurons. We then determined that these currents are functionally coupled; decreasing levels of either current within a neuron causes a rapid increase in the other. This functional interdependence results in homeostatic stabilization of both the individual neuronal and the network output. Furthermore, these compensatory increases are mechanistically independent, suggesting robustness in the maintenance of neural network output that is critical for survival. Together, we generate a complete model for homeostatic plasticity from mRNA to network output where rapid post-translational compensatory mechanisms acting on a reservoir of channels proteins regulated at the level of gene expression provide homeostatic stabilization of both cellular and network activity.

Inactivating ion channels augment robustness of subthreshold intrinsic response dynamics to parametric variability in hippocampal model neurons

Voltage-gated ion channels play a critical role in regulating neuronal intrinsic response dynamics (IRD). Here, we computationally analysed the roles of the two inactivating subthreshold conductances (A and T), individually and in various combinations with the non-inactivating h conductance, in regulating several physiological IRD measurements in the theta frequency range. We found that the independent presence of a T conductance, unlike that of an h conductance, was unable to sustain an inductive phase lead in the theta frequency range, despite its ability to mediate theta frequency resonance. The A conductance, on the other hand, when expressed independently, acted in a manner similar to a leak conductance with reference to most IRD measurements. Next, analysing the impact of pair-wise coexpression of these channels, we found that the coexpression of the h and T conductances augmented the range of parameters over which they sustained resonance and inductive phase lead. Additionally, coexpression of the A conductance with the h or the T conductance elicited changes in IRD measurements that were similar to those obtained with the expression of a leak conductance with a resonating conductance. Finally, to understand the global sensitivity of IRD measurements to all parameters associated with models expressing all three channels, we generated 100,000 neuronal models, each built with a unique set of parametric values. We categorized valid models among these by matching their IRD measurements with experimental counterparts, and found that functionally similar models could be achieved even when underlying parameters displayed tremendous variability and exhibited weak pair-wise correlations. Our results suggest that the three prominent subthreshold conductances contribute differently to intrinsic excitability and to phase coding. We postulate that the differential expression and activity-dependent plasticity of these conductances contribute to robustness of subthreshold IRD, whereby response homeostasis is achieved by recruiting several non-unique combinations of these channel parameters.

Targeted deletion of Kcne2 impairs HCN channel function in mouse thalamocortical circuits

BACKGROUND

Hyperpolarization-activated, cyclic nucleotide-gated (HCN) channels generate the pacemaking current, I(h), which regulates neuronal excitability, burst firing activity, rhythmogenesis, and synaptic integration. The physiological consequence of HCN activation depends on regulation of channel gating by endogenous modulators and stabilization of the channel complex formed by principal and ancillary subunits. KCNE2 is a voltage-gated potassium channel ancillary subunit that also regulates heterologously expressed HCN channels; whether KCNE2 regulates neuronal HCN channel function is unknown.

METHODOLOGY/PRINCIPAL FINDINGS

We investigated the effects of Kcne2 gene deletion on I(h) properties and excitability in ventrobasal (VB) and cortical layer 6 pyramidal neurons using brain slices prepared from Kcne2(+/+) and Kcne2(-/-) mice. Kcne2 deletion shifted the voltage-dependence of I(h) activation to more hyperpolarized potentials, slowed gating kinetics, and decreased I(h) density. Kcne2 deletion was associated with a reduction in whole-brain expression of both HCN1 and HCN2 (but not HCN4), although co-immunoprecipitation from whole-brain lysates failed to detect interaction of KCNE2 with HCN1 or 2. Kcne2 deletion also increased input resistance and temporal summation of subthreshold voltage responses; this increased intrinsic excitability enhanced burst firing in response to 4-aminopyridine. Burst duration increased in corticothalamic, but not thalamocortical, neurons, suggesting enhanced cortical excitatory input to the thalamus; such augmented excitability did not result from changes in glutamate release machinery since miniature EPSC frequency was unaltered in Kcne2(-/-) neurons.

CONCLUSIONS/SIGNIFICANCE

Loss of KCNE2 leads to downregulation of HCN channel function associated with increased excitability in neurons in the cortico-thalamo-cortical loop. Such findings further our understanding of the normal physiology of brain circuitry critically involved in cognition and have implications for our understanding of various disorders of consciousness.

Progressive effect of beta amyloid peptides accumulation on CA1 pyramidal neurons: a model study suggesting possible treatments

Several independent studies show that accumulation of β-amyloid (Aβ) peptides, one of the characteristic hallmark of Alzheimer's Disease (AD), can affect normal neuronal activity in different ways. However, in spite of intense experimental work to explain the possible underlying mechanisms of action, a comprehensive and congruent understanding is still lacking. Part of the problem might be the opposite ways in which Aβ have been experimentally found to affect the normal activity of a neuron; for example, making a neuron more excitable (by reducing the A- or DR-type K⁺ currents) or less excitable (by reducing synaptic transmission and Na⁺ current). The overall picture is therefore confusing, since the interplay of many mechanisms makes it difficult to link individual experimental findings with the more general problem of understanding the progression of the disease. This is an important issue, especially for the development of new drugs trying to ameliorate the effects of the disease. We addressed these paradoxes through computational models. We first modeled the different stages of AD by progressively modifying the intrinsic membrane and synaptic properties of a realistic model neuron, while accounting for multiple and different experimental findings and by evaluating the contribution of each mechanism to the overall modulation of the cell's excitability. We then tested a number of manipulations of channel and synaptic activation properties that could compensate for the effects of Aβ. The model predicts possible therapeutic treatments in terms of pharmacological manipulations of channels' kinetic and activation properties. The results also suggest how and which mechanisms can be targeted by a drug to restore the original firing conditions.