Dynamic modulation of spike timing-dependent calcium influx during corticostriatal upstates

Ion-channel degeneracy and heterogeneities in the emergence of signature physiological characteristics of dentate gyrus granule cells

Complex systems are neither fully determined nor completely random. Biological complex systems, including single neurons, manifest intermediate regimes of randomness that recruit integration of specific combinations of functionally specialized subsystems. Such emergence of biological function provides the substrate for the expression of degeneracy, the ability of disparate combinations of subsystems to yield similar function. Here, we present evidence for the expression of degeneracy in morphologically realistic models of dentate gyrus granule cells (GCs) through functional integration of disparate ion-channel combinations. We performed a 45-parameter randomized search spanning 16 active and passive ion channels, each biophysically constrained by their gating kinetics and localization profiles, to search for valid GC models. Valid models were those that satisfied 17 sub- and suprathreshold cellular-scale electrophysiological measurements from rat GCs. A vast majority (>99%) of the 15,000 random models were not electrophysiologically valid, demonstrating that arbitrarily random ion-channel combinations would not yield GC functions. The 141 valid models (0.94% of 15,000) manifested heterogeneities in and cross-dependencies across local and propagating electrophysiological measurements, which matched with their respective biological counterparts. Importantly, these valid models were widespread throughout the parametric space and manifested weak cross-dependencies across different parameters. These observations together showed that GC physiology could neither be obtained by entirely random ion-channel combinations nor is there an entirely determined single parametric combination that satisfied all constraints. The complexity, the heterogeneities in measurement and parametric spaces, and degeneracy associated with GC physiology should be rigorously accounted for while assessing GCs and their robustness under physiological and pathological conditions.NEW & NOTEWORTHY A recent study from our laboratory had demonstrated pronounced heterogeneities in a set of 17 electrophysiological measurements obtained from a large population of rat hippocampal granule cells. Here, we demonstrate the manifestation of ion-channel degeneracy in a heterogeneous population of morphologically realistic conductance-based granule cell models that were validated against these measurements and their cross-dependencies. Our analyses show that single neurons are complex entities whose functions emerge through intricate interactions among several functionally specialized subsystems.

A stochastic model of hippocampal synaptic plasticity with geometrical readout of enzyme dynamics

Discovering the rules of synaptic plasticity is an important step for understanding brain learning. Existing plasticity models are either (1) top-down and interpretable, but not flexible enough to account for experimental data, or (2) bottom-up and biologically realistic, but too intricate to interpret and hard to fit to data. To avoid the shortcomings of these approaches, we present a new plasticity rule based on a geometrical readout mechanism that flexibly maps synaptic enzyme dynamics to predict plasticity outcomes. We apply this readout to a multi-timescale model of hippocampal synaptic plasticity induction that includes electrical dynamics, calcium, CaMKII and calcineurin, and accurate representation of intrinsic noise sources. Using a single set of model parameters, we demonstrate the robustness of this plasticity rule by reproducing nine published ex vivo experiments covering various spike-timing and frequency-dependent plasticity induction protocols, animal ages, and experimental conditions. Our model also predicts that in vivo-like spike timing irregularity strongly shapes plasticity outcome. This geometrical readout modelling approach can be readily applied to other excitatory or inhibitory synapses to discover their synaptic plasticity rules.

Functional Dissection of Basal Ganglia Inhibitory Inputs onto Substantia Nigra Dopaminergic Neurons

Substantia nigra (SNc) dopaminergic neurons respond to aversive stimuli with inhibitory pauses in firing followed by transient rebound activation. We tested integration of inhibitory synaptic inputs onto SNc neurons from genetically defined populations in dorsal striatum (striosome and matrix) and external globus pallidus (GPe; parvalbumin- and Lhx6-positive), and examined their contribution to pause-rebound firing. Activation of striosome projections, which target "dendron bouquets" in the pars reticulata (SNr), consistently quiets firing and relief from striosome inhibition triggers rebound activity. Striosomal inhibitory postsynaptic currents (IPSCs) display a prominent GABA-B receptor-mediated component that strengthens the impact of SNr dendrite synapses on somatic excitability and enables rebounding. By contrast, GPe projections activate GABA-A receptors on the soma and proximal dendrites but do not result in rebounding. Lastly, optical mapping shows that dorsal striatum selectively inhibits the ventral population of SNc neurons, which are intrinsically capable of rebounding. Therefore, we define a distinct striatonigral circuit for generating dopamine rebound.

The microcircuits of striatum in silico

The basal ganglia play an important role in decision making and selection of action primarily based on input from cortex, thalamus, and the dopamine system. Their main input structure, striatum, is central to this process. It consists of two types of projection neurons, together representing 95% of the neurons, and 5% of interneurons, among which are the cholinergic, fast-spiking, and low threshold-spiking subtypes. The membrane properties, soma-dendritic shape, and intrastriatal and extrastriatal synaptic interactions of these neurons are quite well described in the mouse, and therefore they can be simulated in sufficient detail to capture their intrinsic properties, as well as the connectivity. We focus on simulation at the striatal cellular/microcircuit level, in which the molecular/subcellular and systems levels meet. We present a nearly full-scale model of the mouse striatum using available data on synaptic connectivity, cellular morphology, and electrophysiological properties to create a microcircuit mimicking the real network. A striatal volume is populated with reconstructed neuronal morphologies with appropriate cell densities, and then we connect neurons together based on appositions between neurites as possible synapses and constrain them further with available connectivity data. Moreover, we simulate a subset of the striatum involving 10,000 neurons, with input from cortex, thalamus, and the dopamine system, as a proof of principle. Simulation at this biological scale should serve as an invaluable tool to understand the mode of operation of this complex structure. This platform will be updated with new data and expanded to simulate the entire striatum.

Basal Ganglia Neuromodulation Over Multiple Temporal and Structural Scales-Simulations of Direct Pathway MSNs Investigate the Fast Onset of Dopaminergic Effects and Predict the Role of Kv4.2

The basal ganglia are involved in the motivational and habitual control of motor and cognitive behaviors. Striatum, the largest basal ganglia input stage, integrates cortical and thalamic inputs in functionally segregated cortico-basal ganglia-thalamic loops, and in addition the basal ganglia output nuclei control targets in the brainstem. Striatal function depends on the balance between the direct pathway medium spiny neurons (D1-MSNs) that express D1 dopamine receptors and the indirect pathway MSNs that express D2 dopamine receptors. The striatal microstructure is also divided into striosomes and matrix compartments, based on the differential expression of several proteins. Dopaminergic afferents from the midbrain and local cholinergic interneurons play crucial roles for basal ganglia function, and striatal signaling via the striosomes in turn regulates the midbrain dopaminergic system directly and via the lateral habenula. Consequently, abnormal functions of the basal ganglia neuromodulatory system underlie many neurological and psychiatric disorders. Neuromodulation acts on multiple structural levels, ranging from the subcellular level to behavior, both in health and disease. For example, neuromodulation affects membrane excitability and controls synaptic plasticity and thus learning in the basal ganglia. However, it is not clear on what time scales these different effects are implemented. Phosphorylation of ion channels and the resulting membrane effects are typically studied over minutes while it has been shown that neuromodulation can affect behavior within a few hundred milliseconds. So how do these seemingly contradictory effects fit together? Here we first briefly review neuromodulation of the basal ganglia, with a focus on dopamine. We furthermore use biophysically detailed multi-compartmental models to integrate experimental data regarding dopaminergic effects on individual membrane conductances with the aim to explain the resulting cellular level dopaminergic effects. In particular we predict dopaminergic effects on Kv4.2 in D1-MSNs. Finally, we also explore dynamical aspects of the onset of neuromodulation effects in multi-scale computational models combining biochemical signaling cascades and multi-compartmental neuron models.

T2N as a new tool for robust electrophysiological modeling demonstrated for mature and adult-born dentate granule cells

Compartmental models are the theoretical tool of choice for understanding single neuron computations. However, many models are incomplete, built ad hoc and require tuning for each novel condition rendering them of limited usability. Here, we present T2N, a powerful interface to control NEURON with Matlab and TREES toolbox, which supports generating models stable over a broad range of reconstructed and synthetic morphologies. We illustrate this for a novel, highly detailed active model of dentate granule cells (GCs) replicating a wide palette of experiments from various labs. By implementing known differences in ion channel composition and morphology, our model reproduces data from mouse or rat, mature or adult-born GCs as well as pharmacological interventions and epileptic conditions. This work sets a new benchmark for detailed compartmental modeling. T2N is suitable for creating robust models useful for large-scale networks that could lead to novel predictions. We discuss possible T2N application in degeneracy studies.

Reinforcement determines the timing dependence of corticostriatal synaptic plasticity in vivo

Plasticity at synapses between the cortex and striatum is considered critical for learning novel actions. However, investigations of spike-timing-dependent plasticity (STDP) at these synapses have been performed largely in brain slice preparations, without consideration of physiological reinforcement signals. This has led to conflicting findings, and hampered the ability to relate neural plasticity to behavior. Using intracellular striatal recordings in intact rats, we show here that pairing presynaptic and postsynaptic activity induces robust Hebbian bidirectional plasticity, dependent on dopamine and adenosine signaling. Such plasticity, however, requires the arrival of a reward-conditioned sensory reinforcement signal within 2 s of the STDP pairing, thus revealing a timing-dependent eligibility trace on which reinforcement operates. These observations are validated with both computational modeling and behavioral testing. Our results indicate that Hebbian corticostriatal plasticity can be induced by classical reinforcement learning mechanisms, and might be central to the acquisition of novel actions.

Spike timing dependent plasticity (STDP) has been studied extensively in slices but whether such pairings can induce plasticity in vivo is not known. Here the authors report an experimental paradigm that achieves bidirectional corticostriatal STDP in vivo through modulation by behaviourally relevant reinforcement signals, mediated by dopamine and adenosine signaling.

Calcium dynamics predict direction of synaptic plasticity in striatal spiny projection neurons

The striatum is a major site of learning and memory formation for sensorimotor and cognitive association. One of the mechanisms used by the brain for memory storage is synaptic plasticity - the long-lasting, activity-dependent change in synaptic strength. All forms of synaptic plasticity require an elevation in intracellular calcium, and a common hypothesis is that the amplitude and duration of calcium transients can determine the direction of synaptic plasticity. The utility of this hypothesis in the striatum is unclear in part because dopamine is required for striatal plasticity and in part because of the diversity in stimulation protocols. To test whether calcium can predict plasticity direction, we developed a calcium-based plasticity rule using a spiny projection neuron model with sophisticated calcium dynamics including calcium diffusion, buffering and pump extrusion. We utilized three spike timing-dependent plasticity (STDP) induction protocols, in which postsynaptic potentials are paired with precisely timed action potentials and the timing of such pairing determines whether potentiation or depression will occur. Results show that despite the variation in calcium dynamics, a single, calcium-based plasticity rule, which explicitly considers duration of calcium elevations, can explain the direction of synaptic weight change for all three STDP protocols. Additional simulations show that the plasticity rule correctly predicts the NMDA receptor dependence of long-term potentiation and the L-type channel dependence of long-term depression. By utilizing realistic calcium dynamics, the model reveals mechanisms controlling synaptic plasticity direction, and shows that the dynamics of calcium, not just calcium amplitude, are crucial for synaptic plasticity.

Control of Ca2+ Influx and Calmodulin Activation by SK-Channels in Dendritic Spines

The key trigger for Hebbian synaptic plasticity is influx of Ca²⁺ into postsynaptic dendritic spines. The magnitude of [Ca²⁺] increase caused by NMDA-receptor (NMDAR) and voltage-gated Ca²⁺ -channel (VGCC) activation is thought to determine both the amplitude and direction of synaptic plasticity by differential activation of Ca²⁺ -sensitive enzymes such as calmodulin. Ca²⁺ influx is negatively regulated by Ca²⁺ -activated K⁺ channels (SK-channels) which are in turn inhibited by neuromodulators such as acetylcholine. However, the precise mechanisms by which SK-channels control the induction of synaptic plasticity remain unclear. Using a 3-dimensional model of Ca²⁺ and calmodulin dynamics within an idealised, but biophysically-plausible, dendritic spine, we show that SK-channels regulate calmodulin activation specifically during neuron-firing patterns associated with induction of spike timing-dependent plasticity. SK-channel activation and the subsequent reduction in Ca²⁺ influx through NMDARs and L-type VGCCs results in an order of magnitude decrease in calmodulin (CaM) activation, providing a mechanism for the effective gating of synaptic plasticity induction. This provides a common mechanism for the regulation of synaptic plasticity by neuromodulators.

Hebbian or associative plasticity is triggered by postsynaptic Ca²⁺ influx which activates calmodulin and CaMKII. The influx of Ca²⁺ through voltage-dependent NMDA receptors and Ca²⁺ channels is regulated by Ca²⁺ -activated K⁺ channels (SK-channels) providing negative feedback regulation of postsynaptic [Ca²⁺]. Using 3-dimensional modeling of Ca²⁺ and calmodulin dynamics within dendritic spines we show that the non-linear relationship between Ca²⁺ influx and calmodulin activation endows SK-channels with the ability to “gate” calmodulin activation and therefore the induction of Hebbian synaptic plasticity. Since SK-channels are inhibited by several neuromodulator receptors including acetylcholine and noradrenaline, the gating of synaptic plasticity by SK-channels could represent a common mechanism by which neuromodulators control the induction of synaptic plasticity.

Granule cell excitability regulates gamma and beta oscillations in a model of the olfactory bulb dendrodendritic microcircuit

Odors evoke gamma (40-100 Hz) and beta (20-30 Hz) oscillations in the local field potential (LFP) of the mammalian olfactory bulb (OB). Gamma (and possibly beta) oscillations arise from interactions in the dendrodendritic microcircuit between excitatory mitral cells (MCs) and inhibitory granule cells (GCs). When cortical descending inputs to the OB are blocked, beta oscillations are extinguished whereas gamma oscillations become larger. Much of this centrifugal input targets inhibitory interneurons in the GC layer and regulates the excitability of GCs, which suggests a causal link between the emergence of beta oscillations and GC excitability. We investigate the effect that GC excitability has on network oscillations in a computational model of the MC-GC dendrodendritic network with Ca(2+)-dependent graded inhibition. Results from our model suggest that when GC excitability is low, the graded inhibitory current mediated by NMDA channels and voltage-dependent Ca(2+) channels (VDCCs) is also low, allowing MC populations to fire in the gamma frequency range. When GC excitability is increased, the activation of NMDA receptors and other VDCCs is also increased, allowing the slow decay time constants of these channels to sustain beta-frequency oscillations. Our model argues that Ca(2+) flow through VDCCs alone could sustain beta oscillations and that the switch between gamma and beta oscillations can be triggered by an increase in the excitability state of a subpopulation of GCs.

Calcium-dependent inactivation of calcium channels in the medial striatum increases at eye opening

Influx of calcium through voltage-gated calcium channels (VGCCs) is essential for striatal function and plasticity. VGCCs expressed in striatal neurons have varying kinetics, voltage dependences, and densities resulting in heterogeneous subcellular calcium dynamics. One factor that determines the calcium dynamics in striatal medium spiny neurons is inactivation of VGCCs. Aside from voltage-dependent inactivation, VGCCs undergo calcium-dependent inactivation (CDI): inactivating in response to an influx of calcium. CDI is a negative feedback control mechanism; however, its contribution to striatal neuron function is unknown. Furthermore, although the density of VGCC expression changes with development, it is unclear whether CDI changes with development. Because calcium influx through L-type calcium channels is required for striatal synaptic depression, a change in CDI could contribute to age-dependent changes in striatal synaptic plasticity. Here we use whole cell voltage clamp to characterize CDI over developmental stages and across striatal regions. We find that CDI increases at the age of eye opening in the medial striatum but not the lateral striatum. The developmental increase in CDI mostly involves L-type channels, although calcium influx through non-L-type channels contributes to the CDI in both age groups. Agents that enhance protein kinase A (PKA) phosphorylation of calcium channels reduce the magnitude of CDI after eye opening, suggesting that the developmental increase in CDI may be related to a reduction in the phosphorylation state of the L-type calcium channel. These results are the first to show that modifications in striatal neuron properties correlate with changes to sensory input.

A new framework for cortico-striatal plasticity: behavioural theory meets in vitro data at the reinforcement-action interface

A computational model yields new insights into the bewildering complexity of cortico-striatal plasticity and its rationale for supporting operant learning.

Operant learning requires that reinforcement signals interact with action representations at a suitable neural interface. Much evidence suggests that this occurs when phasic dopamine, acting as a reinforcement prediction error, gates plasticity at cortico-striatal synapses, and thereby changes the future likelihood of selecting the action(s) coded by striatal neurons. But this hypothesis faces serious challenges. First, cortico-striatal plasticity is inexplicably complex, depending on spike timing, dopamine level, and dopamine receptor type. Second, there is a credit assignment problem—action selection signals occur long before the consequent dopamine reinforcement signal. Third, the two types of striatal output neuron have apparently opposite effects on action selection. Whether these factors rule out the interface hypothesis and how they interact to produce reinforcement learning is unknown. We present a computational framework that addresses these challenges. We first predict the expected activity changes over an operant task for both types of action-coding striatal neuron, and show they co-operate to promote action selection in learning and compete to promote action suppression in extinction. Separately, we derive a complete model of dopamine and spike-timing dependent cortico-striatal plasticity from in vitro data. We then show this model produces the predicted activity changes necessary for learning and extinction in an operant task, a remarkable convergence of a bottom-up data-driven plasticity model with the top-down behavioural requirements of learning theory. Moreover, we show the complex dependencies of cortico-striatal plasticity are not only sufficient but necessary for learning and extinction. Validating the model, we show it can account for behavioural data describing extinction, renewal, and reacquisition, and replicate in vitro experimental data on cortico-striatal plasticity. By bridging the levels between the single synapse and behaviour, our model shows how striatum acts as the action-reinforcement interface.

A key component of survival is the ability to learn which actions, in what contexts, yield useful and rewarding outcomes. Actions are encoded in the brain in the cortex but, as many actions are possible at any one time, there needs to be a mechanism to select which one is to be performed. This problem of action selection is mediated by a set of nuclei known as the basal ganglia, which receive convergent “action requests” from all over the cortex and select the one that is currently most important. Working out which is most important is determined by the strength of the input from each action request: the stronger the connection, the more important that action. Understanding learning thus requires understanding how that strength is changed by the outcome of each action. We built a computational model that demonstrates how the brain's internal signal for outcome (carried by the neurotransmitter dopamine) changes the strength of these cortical connections to learn the selection of rewarded actions, and the suppression of unrewarded ones. Our model shows how several known signals in the brain work together to shape the influence of cortical inputs to the basal ganglia at the interface between our actions and their outcomes.