Background synaptic activity modulates the response of a modeled purkinje cell to paired afferent input

Purkinje cell models: past, present and future

The investigation of the dynamics of Purkinje cell (PC) activity is crucial to unravel the role of the cerebellum in motor control, learning and cognitive processes. Within the cerebellar cortex (CC), these neurons receive all the incoming sensory and motor information, transform it and generate the entire cerebellar output. The relatively homogenous and repetitive structure of the CC, common to all vertebrate species, suggests a single computation mechanism shared across all PCs. While PC models have been developed since the 70's, a comprehensive review of contemporary models is currently lacking. Here, we provide an overview of PC models, ranging from the ones focused on single cell intracellular PC dynamics, through complex models which include synaptic and extrasynaptic inputs. We review how PC models can reproduce physiological activity of the neuron, including firing patterns, current and multistable dynamics, plateau potentials, calcium signaling, intrinsic and synaptic plasticity and input/output computations. We consider models focusing both on somatic and on dendritic computations. Our review provides a critical performance analysis of PC models with respect to known physiological data. We expect our synthesis to be useful in guiding future development of computational models that capture real-life PC dynamics in the context of cerebellar computations.

Human Purkinje cells outperform mouse Purkinje cells in dendritic complexity and computational capacity

Purkinje cells in the cerebellum are among the largest neurons in the brain and have been extensively investigated in rodents. However, their morphological and physiological properties remain poorly understood in humans. In this study, we utilized high-resolution morphological reconstructions and unique electrophysiological recordings of human Purkinje cells ex vivo to generate computational models and estimate computational capacity. An inter-species comparison showed that human Purkinje cell had similar fractal structures but were larger than those of mouse Purkinje cells. Consequently, given a similar spine density (2/μm), human Purkinje cell hosted approximately 7.5 times more dendritic spines than those of mice. Moreover, human Purkinje cells had a higher dendritic complexity than mouse Purkinje cells and usually emitted 2-3 main dendritic trunks instead of one. Intrinsic electro-responsiveness was similar between the two species, but model simulations revealed that the dendrites could process ~6.5 times (n = 51 vs. n = 8) more input patterns in human Purkinje cells than in mouse Purkinje cells. Thus, while human Purkinje cells maintained spike discharge properties similar to those of rodents during evolution, they developed more complex dendrites, enhancing computational capacity.

Diverse Neuron Properties and Complex Network Dynamics in the Cerebellar Cortical Inhibitory Circuit

Neuronal inhibition can be defined as a spatiotemporal restriction or suppression of local microcircuit activity. The importance of inhibition relies in its fundamental role in shaping signal processing in single neurons and neuronal circuits. In this context, the activity of inhibitory interneurons proved the key to endow networks with complex computational and dynamic properties. In the last 50 years, the prevailing view on the functional role of cerebellar cortical inhibitory circuits was that excitatory and inhibitory inputs sum spatially and temporally in order to determine the motor output through Purkinje cells (PCs). Consequently, cerebellar inhibition has traditionally been conceived in terms of restricting or blocking excitation. This assumption has been challenged, in particular in the cerebellar cortex where all neurons except granule cells (and unipolar brush cells in specific lobules) are inhibitory and fire spontaneously at high rates. Recently, a combination of electrophysiological recordings in vitro and in vivo, imaging, optogenetics and computational modeling, has revealed that inhibitory interneurons play a much more complex role in regulating cerebellar microcircuit functions: inhibition shapes neuronal response dynamics in the whole circuit and eventually regulate the PC output. This review elaborates current knowledge on cerebellar inhibitory interneurons [Golgi cells, Lugaro cells (LCs), basket cells (BCs) and stellate cells (SCs)], starting from their ontogenesis and moving up to their morphological, physiological and plastic properties, and integrates this knowledge with that on the more renown granule cells and PCs. We will focus on the circuit loops in which these interneurons are involved and on the way they generate feed-forward, feedback and lateral inhibition along with complex spatio-temporal response dynamics. In this perspective, inhibitory interneurons emerge as the real controllers of cerebellar functioning.

Synaptic Activation of a Detailed Purkinje Cell Model Predicts Voltage-Dependent Control of Burst-Pause Responses in Active Dendrites

The dendritic processing in cerebellar Purkinje cells (PCs), which integrate synaptic inputs coming from hundreds of thousands granule cells and molecular layer interneurons, is still unclear. Here we have tested a leading hypothesis maintaining that the significant PC output code is represented by burst-pause responses (BPRs), by simulating PC responses in a biophysically detailed model that allowed to systematically explore a broad range of input patterns. BPRs were generated by input bursts and were more prominent in Zebrin positive than Zebrin negative (Z+ and Z-) PCs. Different combinations of parallel fiber and molecular layer interneuron synapses explained type I, II and III responses observed in vivo. BPRs were generated intrinsically by Ca-dependent K channel activation in the somato-dendritic compartment and the pause was reinforced by molecular layer interneuron inhibition. BPRs faithfully reported the duration and intensity of synaptic inputs, such that synaptic conductance tuned the number of spikes and release probability tuned their regularity in the millisecond range. Interestingly, the burst and pause of BPRs depended on the stimulated dendritic zone reflecting the different input conductance and local engagement of voltage-dependent channels. Multiple local inputs combined their actions generating complex spatio-temporal patterns of dendritic activity and BPRs. Thus, local control of intrinsic dendritic mechanisms by synaptic inputs emerges as a fundamental PC property in activity regimens characterized by bursting inputs from granular and molecular layer neurons.

Modeling the Cerebellar Microcircuit: New Strategies for a Long-Standing Issue

The cerebellar microcircuit has been the work bench for theoretical and computational modeling since the beginning of neuroscientific research. The regular neural architecture of the cerebellum inspired different solutions to the long-standing issue of how its circuitry could control motor learning and coordination. Originally, the cerebellar network was modeled using a statistical-topological approach that was later extended by considering the geometrical organization of local microcircuits. However, with the advancement in anatomical and physiological investigations, new discoveries have revealed an unexpected richness of connections, neuronal dynamics and plasticity, calling for a change in modeling strategies, so as to include the multitude of elementary aspects of the network into an integrated and easily updatable computational framework. Recently, biophysically accurate “realistic” models using a bottom-up strategy accounted for both detailed connectivity and neuronal non-linear membrane dynamics. In this perspective review, we will consider the state of the art and discuss how these initial efforts could be further improved. Moreover, we will consider how embodied neurorobotic models including spiking cerebellar networks could help explaining the role and interplay of distributed forms of plasticity. We envisage that realistic modeling, combined with closed-loop simulations, will help to capture the essence of cerebellar computations and could eventually be applied to neurological diseases and neurorobotic control systems.

The 40-year history of modeling active dendrites in cerebellar Purkinje cells: emergence of the first single cell "community model"

The subject of the effects of the active properties of the Purkinje cell dendrite on neuronal function has been an active subject of study for more than 40 years. Somewhat unusually, some of these investigations, from the outset have involved an interacting combination of experimental and model-based techniques. This article recounts that 40-year history, and the view of the functional significance of the active properties of the Purkinje cell dendrite that has emerged. It specifically considers the emergence from these efforts of what is arguably the first single cell "community" model in neuroscience. The article also considers the implications of the development of this model for future studies of the complex properties of neuronal dendrites.

Reevaluation of the beam and radial hypotheses of parallel fiber action in the cerebellar cortex

The role of parallel fibers (PFs) in cerebellar physiology remains controversial. Early studies inspired the "beam" hypothesis whereby granule cell (GC) activation results in PF-driven, postsynaptic excitation of beams of Purkinje cells (PCs). However, the "radial" hypothesis postulates that the ascending limb of the GC axon provides the dominant input to PCs and generates patch-like responses. Using optical imaging and single-cell recordings in the mouse cerebellar cortex in vivo, this study reexamines the beam versus radial controversy. Electrical stimulation of mossy fibers (MFs) as well as microinjection of NMDA in the granular layer generates beam-like responses with a centrally located patch-like response. Remarkably, ipsilateral forepaw stimulation evokes a beam-like response in Crus I. Discrete molecular layer lesions demonstrate that PFs contribute to the peripherally generated responses in Crus I. In contrast, vibrissal stimulation induces patch-like activation of Crus II and GABAA antagonists fail to convert this patch-like activity into a beam-like response, implying that molecular layer inhibition does not prevent beam-like responses. However, blocking excitatory amino acid transporters (EAATs) generates beam-like responses in Crus II. These beam-like responses are suppressed by focal inhibition of MF-GC synaptic transmission. Using EAAT4 reporter transgenic mice, we show that peripherally evoked patch-like responses in Crus II are aligned between parasagittal bands of EAAT4. This is the first study to demonstrate beam-like responses in the cerebellar cortex to peripheral, MF, and GC stimulation in vivo. Furthermore, the spatial pattern of the responses depends on extracellular glutamate and its local regulation by EAATs.

Model-founded explorations of the roles of molecular layer inhibition in regulating purkinje cell responses in cerebellar cortex: more trouble for the beam hypothesis

For most of the last 50 years, the functional interpretation for inhibition in cerebellar cortical circuitry has been dominated by the relatively simple notion that excitatory and inhibitory dendritic inputs sum, and if that sum crosses threshold at the soma the Purkinje cell generates an action potential. Thus, inhibition has traditionally been relegated to a role of sculpting, restricting, or blocking excitation. At the level of networks, this relatively simply notion is manifest in mechanisms like "surround inhibition" which is purported to "shape" or "tune" excitatory neuronal responses. In the cerebellum, where all cell types except one (the granule cell) are inhibitory, these assumptions regarding the role of inhibition continue to dominate. Based on our recent series of modeling and experimental studies, we now suspect that inhibition may play a much more complex, subtle, and central role in the physiological and functional organization of cerebellar cortex. This paper outlines how model-based studies are changing our thinking about the role of feed-forward molecular layer inhibition in the cerebellar cortex. The results not only have important implications for continuing efforts to understand what the cerebellum computes, but might also reveal important features of the evolution of this large and quintessentially vertebrate brain structure.

Dendritic excitability modulates dendritic information processing in a purkinje cell model

Using an electrophysiological compartmental model of a Purkinje cell we quantified the contribution of individual active dendritic currents to processing of synaptic activity from granule cells. We used mutual information as a measure to quantify the information from the total excitatory input current (I_Glu) encoded in each dendritic current. In this context, each active current was considered an information channel. Our analyses showed that most of the information was encoded by the calcium (I_CaP) and calcium activated potassium (I_Kc) currents. Mutual information between I_Glu and I_CaP and I_Kc was sensitive to different levels of excitatory and inhibitory synaptic activity that, at the same time, resulted in the same firing rate at the soma. Since dendritic excitability could be a mechanism to regulate information processing in neurons we quantified the changes in mutual information between I_Glu and all Purkinje cell currents as a function of the density of dendritic Ca (g_CaP) and Kca (g_Kc) conductances. We extended our analysis to determine the window of temporal integration of I_Glu by I_CaP and I_Kc as a function of channel density and synaptic activity. The window of information integration has a stronger dependence on increasing values of g_Kc than on g_CaP, but at high levels of synaptic stimulation information integration is reduced to a few milliseconds. Overall, our results show that different dendritic conductances differentially encode synaptic activity and that dendritic excitability and the level of synaptic activity regulate the flow of information in dendrites.

The functional equivalence of ascending and parallel fiber inputs in cerebellar computation

At the center of the computational cerebellar circuitry are Purkinje cells, which integrate synaptic inputs from >150,000 granule cell inputs. Traditional theories of cerebellar function assume that all granule cell inputs are comparable. However, it has recently been suggested that the two anatomically distinct granule cell inputs, ascending and parallel fiber, have different functional roles. By systematically examining the efficacy of patches of granule cells with photostimulation, we found no differences in the efficacy of the two inputs in driving the activity of, or in producing postsynaptic currents in, Purkinje cells in cerebellar slices in vitro. We also found that the activity of Purkinje cells was significantly increased upon stimulation of lateral granule cells in vivo. Moreover, when we estimated parallel fiber and ascending apparent unitary EPSC amplitudes using photostimulation in cerebellar slices in vitro, we found them to be indistinguishable. These results are inconsistent with differential functional roles for these two inputs. Instead, our data support theories of cerebellar computation that consider granule cell inputs to be functionally comparable.

The functional architecture of the shark's dorsal-octavolateral nucleus: an in vitro study

Learning to predict the component in the sensory information resulting from the organism's own activity enables it to respond appropriately to unexpected stimuli. For example, the elasmobranch dorsal octavolateral nucleus (DON) can apparently extract the unexpected component (i.e. generated by nearby organisms) from the incoming electrosensory signals. Here we introduce a novel and unique experimental approach that combines the advantages of in vitro preparations with the integrity of in vivo conditions. In such an experimental system one can study, under control conditions, the cellular and network mechanisms that underlie cancellation of expected sensory inputs. Using extracellular and intracellular recordings we compared the dynamics and spatiotemporal organization of the electrosensory afferent nerve and parallel fiber inputs to the DON. The afferent nerve has a low threshold and high conduction velocity; a stimulus that recruits a small number of fibers is sufficient to activate the principal neurons. The excitatory postsynaptic potential in the principal cells evoked by afferent nerve fibers has fast kinetics that efficiently reach the threshold for action potential. In contrast, the parallel fibers have low conduction velocity, high threshold and extensive convergence on the principal neurons of the DON. The excitatory postsynaptic response has slow kinetics that provides a wide time window for integration of inputs. The highly efficient connection between the afferent nerve and the principal neurons in the DON indicates that filtration occurring in the DON cannot be mediated simply by summation of the parallel fibers' signals with the afferent sensory signals. Hence we propose that the filtering may be mediated via secondary neurons that adjust the principal neurons' sensitivity to afferent inputs.

Firing dynamics of cerebellar purkinje cells

Knowledge of intrinsic neuronal firing dynamics is a critical first step to establishing an accurate biophysical model of any neuron. In this study we examined cerebellar Purkinje cells to determine the bifurcations likely to underlie firing dynamics within a biophysically realistic and experimentally supported model. We show that Purkinje cell dynamics are consistent with a system undergoing a saddle-node bifurcation of fixed points in the transition from rest to firing and a saddle homoclinic bifurcation from firing to rest. Our analyses account for numerous observed Purkinje cell firing properties that include bistability, plateau potentials, specific aspects of the frequency-current (F-I) relationship, first spike latency, and the ability for climbing fiber input to induce state transitions in the bistable regime. We also experimentally confirm new properties predicted from our model and analysis that include the presence of a depolarizing afterpotential (DAP), the ability to fire at low frequencies (<50 Hz) and with a high gain in the F-I relationship, and a bistable region limited to low-frequency firing. Purkinje cell dynamics, including bistability, prove to arise from numerous biophysical factors that include the DAP, fast refractory dynamics, and a long membrane time constant. A hyperpolarizing activated cation current (I(H)) is shown not to be directly involved in establishing bistable dynamics but rather reduces the range for bistability. A combined electrophysiological and modeling approach thus accounts for several properties of Purkinje cells, providing a firm basis from which to assess Purkinje cell output patterns.

Feedforward inhibition controls the spread of granule cell-induced Purkinje cell activity in the cerebellar cortex

Synapses associated with the parallel fiber (pf) axons of cerebellar granule cells constitute the largest excitatory input onto Purkinje cells (PCs). Although most theories of cerebellar function assume these synapses produce an excitatory sequential "beamlike" activation of PCs, numerous physiological studies have failed to find such beams. Using a computer model of the cerebellar cortex we predicted that the lack of PCs beams is explained by the concomitant pf activation of feedforward molecular layer inhibition. This prediction was tested, in vivo, by recording PCs sharing a common set of pfs before and after pharmacologically blocking inhibitory inputs. As predicted by the model, pf-induced beams of excitatory PC responses were seen only when inhibition was blocked. Blocking inhibition did not have a significant effect in the excitability of the cerebellar cortex. We conclude that pfs work in concert with feedforward cortical inhibition to regulate the excitability of the PC dendrite without directly influencing PC spiking output. This conclusion requires a significant reassessment of classical interpretations of the functional organization of the cerebellar cortex.

Modeling single-neuron dynamics and computations: a balance of detail and abstraction

The fundamental building block of every nervous system is the single neuron. Understanding how these exquisitely structured elements operate is an integral part of the quest to solve the mysteries of the brain. Quantitative mathematical models have proved to be an indispensable tool in pursuing this goal. We review recent advances and examine how single-cell models on five levels of complexity, from black-box approaches to detailed compartmental simulations, address key questions about neural dynamics and signal processing.

Correlations Between Purkinje Cell Single-Unit Activity and Simultaneously Recorded Field Potentials in the Immediately Underlying Granule Cell Layer

Evidence from both anatomical and physiological studies suggests that the ascending segment of the granule cell axon provides a large, driving input to overlying Purkinje cells. In the current experiments, we used dual recording electrodes to simultaneously record spike activity of Purkinje cells and multiunit field potential activity in the directly underlying granule cell layer. These dual recordings were performed both during periods of spontaneous (“background”) firing and also after peripheral tactile stimulation. The results demonstrate that in the large majority of cases, there is a strong positive correlation between spontaneous Purkinje cell simple spikes and spontaneous activity in the immediately underlying granule cell layer. The strength of this correlation was dependent on both the firing rate of the Purkinje cell as well as on the rate of granule cell layer multiunit activity. In addition, for any given pair of recordings, the correlation seen during spontaneous activity accurately predicted the magnitude and time course of responses evoked by peripheral tactile stimulation. These results provide additional evidence that the synapses associated with the ascending segment of the granule cell axon have a substantial influence on Purkinje cell output. This relationship is considered in the context of our ongoing reevaluation of the physiological relationship between cerebellar granule and Purkinje cells.

Dynamic spatiotemporal synaptic integration in cortical neurons: neuronal gain, revisited

Gain modulation is a ubiquitous phenomenon in cortical neurons, providing flexibility to operate under changing conditions. The prevailing view is that this modulation reflects a change in the relationship between mean input and output firing rate brought about by variation in neuronal membrane characteristics. An alternative mechanism is proposed for neuronal gain modulation that takes into account the capability of cortical neurons to process spatiotemporal synaptic correlations. Through the use of numerical simulations, it is shown that voltage-gated and leak conductances, membrane potential, noise, and input firing rate modify the sensitivity of cortical neurons to the degree of temporal correlation between their synaptic inputs. These changes are expressed in a change of the temporal window for synaptic integration and the range of input correlation over which response probability is graded. The study also demonstrates that temporal integration depends on the distance between the inputs and that this interplay of space and time is modulated by voltage-gated and leak conductances. Thus, gain modulation may reflect a change in the relationship between spatiotemporal synaptic correlations and output firing probability. It is further proposed that by acting synergistically with the network, dynamic spatiotemporal synaptic integration in cortical neurons may serve a functional role in the formation of dynamic cell assemblies.