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1.  Synaptic representation of locomotion in single cerebellar granule cells 
eLife  null;4:e07290.
The cerebellum plays a crucial role in the regulation of locomotion, but how movement is represented at the synaptic level is not known. Here, we use in vivo patch-clamp recordings to show that locomotion can be directly read out from mossy fiber synaptic input and spike output in single granule cells. The increase in granule cell spiking during locomotion is enhanced by glutamate spillover currents recruited during movement. Surprisingly, the entire step sequence can be predicted from input EPSCs and output spikes of a single granule cell, suggesting that a robust gait code is present already at the cerebellar input layer and transmitted via the granule cell pathway to downstream Purkinje cells. Thus, synaptic input delivers remarkably rich information to single neurons during locomotion.
eLife digest
Our voluntary movements, such as shaking hands and walking, are controlled by a region of the brain called the cerebellum. Inside this region is a layer of cells called granule cells, which are the smallest and also the most numerous type of neuron in the brains of mammals. Granule cells receive information from many other parts of the brain and respond by producing electrical signals that influence the motor system, which tells our muscles how to move. However, it is not clear how the granule cells interpret the information they receive and ensure that the right muscles are stimulated at the right time by the motor system.
Powell et al. have now used ‘patch-clamp electrodes’ to measure the electrical activity of individual granule cells in the cerebellum of mice, both at rest and as they walked. This is a powerful approach as it enables the recording of both the information received by each granule cell (input) and the electrical signals produced by it in response (output). Each mouse was placed on a treadmill with its head held still and given the choice to either rest or walk. These experiments show that when the mouse is resting, the granule cells are mostly inactive, producing only very low levels of fast electrical signals called ‘spikes’. When the mouse starts walking, the input to the granule cells triggers a strong increase in spiking in the granule cells.
Powell et al. used a computer model to understand how the granule cells represent movement. Remarkably, this model could be used to predict walking patterns of the mouse based on the activity of a single granule cell and its inputs. These findings suggest that even single neurons in the cerebellum contain rich information about the movement of the animal. The next challenge is to understand how this code interacts with the rest of the motor system to produce precisely coordinated movements. Furthermore, it will be important to determine whether a similar code is used in other parts of the brain that control movement.
PMCID: PMC4499793  PMID: 26083712
patch clamp; granule cells; cerebellum; locomotion; synaptic integration; mouse
2.  CaRuby-Nano: a novel high affinity calcium probe for dual color imaging 
eLife  null;4:e05808.
The great demand for long-wavelength and high signal-to-noise Ca2+ indicators has led us to develop CaRuby-Nano, a new functionalizable red calcium indicator with nanomolar affinity for use in cell biology and neuroscience research. In addition, we generated CaRuby-Nano dextran conjugates and an AM-ester variant for bulk loading of tissue. We tested the new indicator using in vitro and in vivo experiments demonstrating the high sensitivity of CaRuby-Nano as well as its power in dual color imaging experiments.
eLife digest
The movement of calcium ions within cells controls many vital biological processes, ranging from cell growth to muscle contraction and brain activity. These calcium signals are triggered by stimuli, such as nerve impulses, which drive calcium entry into cells or release calcium from internal stores. These changes in calcium levels can span several orders of magnitude, and can be either localized to very small parts of the cell or span the entire cell.
Scientists have developed numerous indicators or ‘probes’ that can detect even very low levels of calcium. One common method uses proteins that fluoresce when viewed under a fluorescence microscope each time the protein senses increases of calcium. Most of these probes fluoresce green, and so to view a second signal that occurs in the cell at the same time it's easier to use a probe that fluoresces with a different color, such as red. However, the red-shifted probes that are currently available either produce unreliable results because they tend to leak through cell membranes, or are not very sensitive to calcium ions. New types of red-shifted probes are therefore urgently needed.
In 2012, researchers developed a family of red fluorescent probes known as Calcium Ruby (CaRuby for short) that were more versatile than earlier red probes. Now, Collot, Wilms et al.—including several of the researchers involved in the 2012 research—have enhanced the properties of CaRuby by modifying the chemical structure of the probes. This increased the ability of CaRuby to bind calcium ions, making it more sensitive to small calcium changes. Testing the usefulness of the newly developed probes—called CaRuby Nano—in mouse nerve cells revealed the probes are highly sensitive and can even detect the calcium signal resulting from a single nerve impulse.
Collot, Wilms et al. then went on to demonstrate that CaRuby-Nano can be used alongside a green-fluorescing probe to record two signals at the same time. In one experiment, the release of chemical messengers known as neurotransmitters was stimulated, which caused calcium ions to flow into the observed nerve cells. The researchers succeeded in simultaneously detecting a green signal indicating an increase in neurotransmitter levels and a red signal produced by the corresponding release of calcium. Such dual-color imaging was not possible with previous probes. Finally, it was shown that CaRuby-Nano can also be used to produce dual-color images of the brain activity of live mice.
In summary, these results demonstrate that CaRuby-Nano is a highly sensitive and versatile indicator and can be used together with other probes to observe two simultaneous events in cells.
PMCID: PMC4379494  PMID: 25824291
calcium; two-photon imaging; click chemistry; fluorescence; mouse
3.  Reading out a spatiotemporal population code by imaging neighbouring parallel fibre axons in vivo 
Nature Communications  2015;6:6464.
The spatiotemporal pattern of synaptic inputs to the dendritic tree is crucial for synaptic integration and plasticity. However, it is not known if input patterns driven by sensory stimuli are structured or random. Here we investigate the spatial patterning of synaptic inputs by directly monitoring presynaptic activity in the intact mouse brain on the micron scale. Using in vivo calcium imaging of multiple neighbouring cerebellar parallel fibre axons, we find evidence for clustered patterns of axonal activity during sensory processing. The clustered parallel fibre input we observe is ideally suited for driving dendritic spikes, postsynaptic calcium signalling, and synaptic plasticity in downstream Purkinje cells, and is thus likely to be a major feature of cerebellar function during sensory processing.
The spatiotemporal pattern of synaptic inputs is critical for synaptic integration and plasticity in neurons but whether these inputs are structured or random is not clear. Here the authors use in vivo calcium imaging to monitor the presynaptic activity of cerebellar parallel fibre axons and find clustered patterns of axonal activity during sensory processing.
PMCID: PMC4366501  PMID: 25751648
4.  Target-Specific Effects of Somatostatin-Expressing Interneurons on Neocortical Visual Processing 
The Journal of Neuroscience  2013;33(50):19567-19578.
A diverse array of interneuron types regulates activity in the mammalian neocortex. Two of the most abundant are the fast-spiking, parvalbumin-positive (PV+) interneurons, which target the axosomatic region of pyramidal cells, and the somatostatin-positive (SOM+) interneurons, which target the dendrites. Recent work has focused on the influence of PV+ and SOM+ interneurons on pyramidal cells. However, the connections among PV+ and SOM+ interneurons are poorly understood and could play an important role in cortical circuitry, since their interactions may alter the net influence on pyramidal cell output. We used an optogenetic approach to investigate the effect of SOM+ interneurons on pyramidal cells and PV+ interneurons during visual stimulation in mouse primary visual cortex. We find that SOM+ interneuron activation suppresses PV+ cell spiking at least twice as potently as pyramidal cell spiking during visual stimulation. This differential effect of SOM+ cell stimulation is detectable even when only two to three SOM+ cells are activated. Importantly, the remaining responses to oriented gratings in PV+ cells are more orientation tuned and temporally modulated, suggesting that SOM+ activity unmasks this tuning by suppressing untuned input. Our results highlight the importance of SOM+ inhibition of PV+ interneurons during sensory processing. This prominent competitive inhibition between interneuron types leads to a reconfiguration of inhibition along the somatodendritic axis of pyramidal cells, and enhances the orientation selectivity of PV+ cells.
PMCID: PMC3858626  PMID: 24336721
5.  Synaptically Induced Long-Term Modulation of Electrical Coupling in the Inferior Olive 
Neuron  2014;81(6):1290-1296.
Electrical coupling mediated by gap junctions is widespread in the mammalian CNS, and the interplay between chemical and electrical synapses on the millisecond timescale is crucial for determining patterns of synchrony in many neural circuits. Here we show that activation of glutamatergic synapses drives long-term depression of electrical coupling between neurons of the inferior olive. We demonstrate that this plasticity is not triggered by postsynaptic spiking alone and that it requires calcium entry following synaptic NMDA receptor activation. These results reveal that glutamatergic synapses can instruct plasticity at electrical synapses, providing a means for excitatory inputs to homeostatically regulate the long-term dynamics of microzones in olivocerebellar circuits.
•Chemical synapses trigger long-term depression of inferior olive electrical coupling•Depression of electrical coupling requires NMDAR activation and calcium entry•Plasticity is not triggered by postsynaptic spiking alone and EPSPs remain unchanged•Excitatory inputs can thus homeostatically regulate synchrony patterns in the olive
The interplay between electrical and chemical synapses is crucial for determining patterns of synchrony in neuronal networks. Recording in the inferior olive, Mathy et al. show that coincident excitatory synaptic input and spiking can cause a sustained suppression of electrical coupling.
PMCID: PMC3988996  PMID: 24656251
6.  Structured Connectivity in Cerebellar Inhibitory Networks 
Neuron  2014;81(4):913-929.
Defining the rules governing synaptic connectivity is key to formulating theories of neural circuit function. Interneurons can be connected by both electrical and chemical synapses, but the organization and interaction of these two complementary microcircuits is unknown. By recording from multiple molecular layer interneurons in the cerebellar cortex, we reveal specific, nonrandom connectivity patterns in both GABAergic chemical and electrical interneuron networks. Both networks contain clustered motifs and show specific overlap between them. Chemical connections exhibit a preference for transitive patterns, such as feedforward triplet motifs. This structured connectivity is supported by a characteristic spatial organization: transitivity of chemical connectivity is directed vertically in the sagittal plane, and electrical synapses appear strictly confined to the sagittal plane. The specific, highly structured connectivity rules suggest that these motifs are essential for the function of the cerebellar network.
•Quadruple patch recordings from interneurons reveal highly nonrandom connectivity•Both chemical and electrical interneuron networks exhibit spatial clustering•Chemical synaptic connections are organized in transitive feedforward motifs•The electrical and chemical networks show specific overlap at the triplet level
Interneurons are connected by both chemical and electrical synapses, but the organization of this connectivity is unknown. With quadruple recordings from cerebellar interneurons, Rieubland et al. find that electrical and chemical interneuron networks exhibit highly structured nonrandom connectivity, including clustered and feedforward motifs.
PMCID: PMC3988957  PMID: 24559679
7.  How to build a grid cell 
Neurons in the medial entorhinal cortex fire action potentials at regular spatial intervals, creating a striking grid-like pattern of spike rates spanning the whole environment of a navigating animal. This remarkable spatial code may represent a neural map for path integration. Recent advances using patch-clamp recordings from entorhinal cortex neurons in vitro and in vivo have revealed how the microcircuitry in the medial entorhinal cortex may contribute to grid cell firing patterns, and how grid cells may transform synaptic inputs into spike output during firing field crossings. These new findings provide key insights into the ingredients necessary to build a grid cell.
PMCID: PMC3866442  PMID: 24366132
grid cell; entorhinal cortex; spatial navigation; patch clamp; neural circuit; path integration
8.  Inhibition dominates sensory responses in awake cortex 
Nature  2012;493(7430):97-100.
The activity of the cerebral cortex is thought to depend on the precise relationship between synaptic excitation and inhibition1-4. In visual cortex, in particular, intracellular measurements have related response selectivity to coordinated increases in excitation and inhibition5-9. These measurements, however, have all been performed during anaesthesia, which strongly influences cortical state10 and therefore sensory processing7,11-15. The synaptic activity evoked by visual stimulation during wakefulness is unknown. Here, we measured visually evoked responses – and the underlying synaptic conductances – in the visual cortex of anaesthetised and awake mice. Under anaesthesia, responses could be elicited from a large region of visual space16 and were prolonged in time. During wakefulness responses were more spatially selective and much briefer. Whole-cell patch-clamp recordings of synaptic conductances5,17 revealed a surprising difference in synaptic inhibition during the two conditions. Whereas under anaesthesia inhibition tracked excitation in amplitude and spatial selectivity, during wakefulness it was much stronger than excitation and exhibited extremely broad spatial selectivity. We conclude that during wakefulness cortical responses to visual stimulation are dominated by synaptic inhibition, restricting their spatial spread and temporal persistence. These results provide the first direct glimpse of synaptic mechanisms that control visual responses in the awake cortex.
PMCID: PMC3537822  PMID: 23172139
9.  A Preferentially Segregated Recycling Vesicle Pool of Limited Size Supports Neurotransmission in Native Central Synapses 
Neuron  2012;76(3-3):579-589.
At small central synapses, efficient turnover of vesicles is crucial for stimulus-driven transmission, but how the structure of this recycling pool relates to its functional role remains unclear. Here we characterize the organizational principles of functional vesicles at native hippocampal synapses with nanoscale resolution using fluorescent dye labeling and electron microscopy. We show that the recycling pool broadly scales with the magnitude of the total vesicle pool, but its average size is small (∼45 vesicles), highly variable, and regulated by CDK5/calcineurin activity. Spatial analysis demonstrates that recycling vesicles are preferentially arranged near the active zone and this segregation is abolished by actin stabilization, slowing the rate of activity-driven exocytosis. Our approach reveals a similarly biased recycling pool distribution at synapses in visual cortex activated by sensory stimulation in vivo. We suggest that in small native central synapses, efficient release of a limited pool of vesicles relies on their favored spatial positioning within the terminal.
► Native hippocampal synapses have a small spatially biased recycling vesicle pool ► Pool size is regulated and positioning near the active zone relies on actin turnover ► In vivo sensory-activated synapses in visual cortex share same organization ► Positional bias ensures effective transmission in central size-limited terminals
Using a functional-ultrastructural approach, Marra et al. demonstrate that recycling vesicles in native synapses form a small subset of the total vesicle population. The spatial bias of this functional pool toward the release site helps to support efficient neurotransmission.
PMCID: PMC3526798  PMID: 23141069
10.  Dendritic Calcium Signaling Triggered by Spontaneous and Sensory-Evoked Climbing Fiber Input to Cerebellar Purkinje Cells In Vivo 
The Journal of Neuroscience  2011;31(30):10847-10858.
Cerebellar Purkinje cells have one of the most elaborate dendritic trees in the mammalian CNS, receiving excitatory synaptic input from a single climbing fiber (CF) and from ∼200,000 parallel fibers. The dendritic Ca2+ signals triggered by activation of these inputs are crucial for the induction of synaptic plasticity at both of these synaptic connections. We have investigated Ca2+ signaling in Purkinje cell dendrites in vivo by combining targeted somatic or dendritic patch-clamp recording with simultaneous two-photon microscopy. Both spontaneous and sensory-evoked CF inputs triggered widespread Ca2+ signals throughout the dendritic tree that were detectable even in individual spines of the most distal spiny branchlets receiving parallel fiber input. The amplitude of these Ca2+ signals depended on dendritic location and could be modulated by membrane potential, reflecting modulation of dendritic spikes triggered by the CF input. Furthermore, the variability of CF-triggered Ca2+ signals was regulated by GABAergic synaptic input. These results indicate that dendritic Ca2+ signals triggered by sensory-evoked CF input can act as associative signals for synaptic plasticity in Purkinje cells in vivo and may differentially modulate plasticity at parallel fiber synapses depending on the location of synapses, firing state of the Purkinje cell, and ongoing GABAergic synaptic input.
PMCID: PMC3758548  PMID: 21795537
11.  Initiation of simple and complex spikes in cerebellar Purkinje cells 
The Journal of Physiology  2010;588(Pt 10):1709-1717.
Cerebellar Purkinje cells produce two distinct forms of action potential output: simple and complex spikes. Simple spikes occur spontaneously or are driven by parallel fibre input, while complex spikes are activated by climbing fibre input. Previous studies indicate that both simple and complex spikes originate in the axon of Purkinje cells, but the precise location where they are initiated is unclear. Here we address where in the axon of cerebellar Purkinje cells simple and complex spikes are generated. Using extracellular recording and voltage-sensitive dye imaging in rat and mouse Purkinje cells, we show that both simple and complex spikes are generated in the proximal axon, ∼15–20 μm from the soma. Once initiated, simple and complex spikes propagate both down the axon and back into the soma. The speed of backpropagation into the soma was significantly faster for complex compared to simple spikes, presumably due to charging of the somatodendritic membrane capacitance during the climbing fibre synaptic conductance. In conclusion, we show using two independent methods that the final integration site of simple and complex spikes is in the proximal axon of cerebellar Purkinje cells, at a location corresponding to the distal end of the axon initial segment.
PMCID: PMC2887989  PMID: 20351049
12.  Parallel processing of visual space by neighboring neurons in mouse visual cortex 
Nature neuroscience  2010;13(9):1144-1149.
Visual cortex exhibits smooth retinotopic organization on the macroscopic scale, but it is unknown how receptive fields are organized at the level of neighboring neurons. This information is crucial for discriminating among models of visual cortex. We used in vivo two-photon calcium imaging to independently map ON and OFF receptive field subregions of local populations of layer 2/3 neurons in mouse visual cortex. We found that receptive field subregions are often precisely shared among multiple neighboring neurons. Furthermore, large subregions appear to be assembled from multiple smaller, non-overlapping subregions of other neurons in the same local population. These experiments provide the first characterization of the diversity of receptive fields in a dense local network of visual cortex, and reveal elementary units of receptive field organization. Our results suggest that a limited pool of afferent receptive fields is available to a local population of neurons, and reveal new organizational principles for the neural circuitry of the mouse visual cortex.
PMCID: PMC2999824  PMID: 20711183
13.  Sensitivity to perturbations in vivo implies high noise and suggests rate coding in cortex 
Nature  2010;466(7302):123-127.
It is well known that neural activity exhibits variability, in the sense that identical sensory stimuli produce different responses, but it has been difficult to determine what this variability means. Is it noise, or does it carry important information – about, for example, the internal state of the organism? We address this issue from the bottom up, by asking whether small perturbations to activity in cortical networks are amplified. Based on in vivo whole-cell recordings in rat barrel cortex, we find that a perturbation consisting of a single extra spike in one neuron produces ~28 additional spikes in its postsynaptic targets, and we show, using simultaneous intra- and extra-cellular recordings, that a single spike produces a detectable increase in firing rate in the local network. Theoretical analysis indicates that this amplification leads to intrinsic, stimulus-independent variations in membrane potential on the order of ±2.2 - 4.5 mV – variations that are pure noise, and so carry no information at all. Therefore, for the brain to perform reliable computations, it must either use a rate code, or generate very large, fast depolarizing events, such as those proposed by the theory of synfire chains – yet in our in vivo recordings, we found that such events were very rare. Our findings are consistent with the idea that cortex is likely to use primarily a rate code.
PMCID: PMC2898896  PMID: 20596024
14.  Quantitative Comparison of Genetically Encoded Ca2+ Indicators in Cortical Pyramidal Cells and Cerebellar Purkinje Cells 
Genetically encoded Ca2+ indicators (GECIs) are promising tools for cell type-specific and chronic recording of neuronal activity. In the mammalian central nervous system, however, GECIs have been tested almost exclusively in cortical and hippocampal pyramidal cells, and the usefulness of recently developed GECIs has not been systematically examined in other cell types. Here we expressed the latest series of GECIs, yellow cameleon (YC) 2.60, YC3.60, YC-Nano15, and GCaMP3, in mouse cortical pyramidal cells as well as cerebellar Purkinje cells using in utero injection of recombinant adenoviral vectors. We characterized the performance of the GECIs by simultaneous two-photon imaging and whole-cell patch-clamp recording in acute brain slices at 33 ± 2°C. The fluorescent responses of GECIs to action potentials (APs) evoked by somatic current injection or to synaptic stimulation were examined using rapid dendritic imaging. In cortical pyramidal cells, YC2.60 showed the largest responses to single APs, but its decay kinetics were slower than YC3.60 and GCaMP3, while GCaMP3 showed the largest responses to 20 APs evoked at 20 Hz. In cerebellar Purkinje cells, only YC2.60 and YC-Nano15 could reliably report single complex spikes (CSs), and neither showed signal saturation over the entire stimulus range tested (1–10 CSs at 10 Hz). The expression and response of YC2.60 in Purkinje cells remained detectable and comparable for at least over 100 days. These results provide useful information for selecting an optimal GECI depending on the experimental requirements: in cortical pyramidal cells, YC2.60 is suitable for detecting sparse firing of APs, whereas GCaMP3 is suitable for detecting burst firing of APs; in cerebellar Purkinje cells, YC2.60 as well as YC-Nano15 is suitable for detecting CSs.
PMCID: PMC3182323  PMID: 21994490
genetically encoded Ca2+ indicators; adenovirus; two-photon imaging; patch-clamp recording; cortical pyramidal cell; cerebellar Purkinje cell; acute brain slice
15.  One Rule to Grow Them All: A General Theory of Neuronal Branching and Its Practical Application 
PLoS Computational Biology  2010;6(8):e1000877.
Understanding the principles governing axonal and dendritic branching is essential for unravelling the functionality of single neurons and the way in which they connect. Nevertheless, no formalism has yet been described which can capture the general features of neuronal branching. Here we propose such a formalism, which is derived from the expression of dendritic arborizations as locally optimized graphs. Inspired by Ramón y Cajal's laws of conservation of cytoplasm and conduction time in neural circuitry, we show that this graphical representation can be used to optimize these variables. This approach allows us to generate synthetic branching geometries which replicate morphological features of any tested neuron. The essential structure of a neuronal tree is thereby captured by the density profile of its spanning field and by a single parameter, a balancing factor weighing the costs for material and conduction time. This balancing factor determines a neuron's electrotonic compartmentalization. Additions to this rule, when required in the construction process, can be directly attributed to developmental processes or a neuron's computational role within its neural circuit. The simulations presented here are implemented in an open-source software package, the “TREES toolbox,” which provides a general set of tools for analyzing, manipulating, and generating dendritic structure, including a tool to create synthetic members of any particular cell group and an approach for a model-based supervised automatic morphological reconstruction from fluorescent image stacks. These approaches provide new insights into the constraints governing dendritic architectures. They also provide a novel framework for modelling and analyzing neuronal branching structures and for constructing realistic synthetic neural networks.
Author Summary
More than a century has passed since Ramón y Cajal presented a set of fundamental biological laws of neuronal branching. He described how the shape of the core elements of the neural circuitry – axons and dendrites – are constrained by physical parameters such as space, cytoplasmic volume, and conduction time. The existence of these laws enabled him to organize his histological observations, to formulate the neuron doctrine, and to infer directionality in signal flow in the nervous system. We show that Cajal's principles can be used computationally to generate synthetic neural circuits. These principles rigorously constrain the shape of real neuronal structures, providing direct validation of his theories. At the same time, this strategy provides us with a powerful set of tools for generating synthetic neurons, as well as a model-based approach for automated reconstructions of neuronal trees from confocal image stacks.
PMCID: PMC2916857  PMID: 20700495
16.  Traveling waves in developing cerebellar cortex mediated by asymmetrical Purkinje cell connectivity 
Nature neuroscience  2009;12(4):463-473.
Correlated network activity plays a critical role in the development of many neural circuits. Purkinje cells are among the first neurons to populate the cerebellar cortex, where they sprout exuberant axon collaterals. Here we use multiple patch-clamp recordings targeted with two-photon microscopy to characterize monosynaptic connections between Purkinje cells of juvenile mice. We show that Purkinje cell axon collaterals project asymmetrically in the sagittal plane, directed away from the lobule apex. Based on our anatomical and physiological characterization of this connection, we construct a network model that robustly generates waves of activity traveling along chains of connected Purkinje cells. Consistent with the model, we observe traveling waves of activity in Purkinje cells in sagittal slices from young mice that require GABAA receptor-mediated transmission and intact Purkinje cell axon collaterals. These traveling waves are absent in adult animals, suggesting they play a developmental role in wiring the cerebellar cortical microcircuit.
PMCID: PMC2912499  PMID: 19287389
17.  A New Approach for Determining Phase Response Curves Reveals that Purkinje Cells Can Act as Perfect Integrators 
PLoS Computational Biology  2010;6(4):e1000768.
Cerebellar Purkinje cells display complex intrinsic dynamics. They fire spontaneously, exhibit bistability, and via mutual network interactions are involved in the generation of high frequency oscillations and travelling waves of activity. To probe the dynamical properties of Purkinje cells we measured their phase response curves (PRCs). PRCs quantify the change in spike phase caused by a stimulus as a function of its temporal position within the interspike interval, and are widely used to predict neuronal responses to more complex stimulus patterns. Significant variability in the interspike interval during spontaneous firing can lead to PRCs with a low signal-to-noise ratio, requiring averaging over thousands of trials. We show using electrophysiological experiments and simulations that the PRC calculated in the traditional way by sampling the interspike interval with brief current pulses is biased. We introduce a corrected approach for calculating PRCs which eliminates this bias. Using our new approach, we show that Purkinje cell PRCs change qualitatively depending on the firing frequency of the cell. At high firing rates, Purkinje cells exhibit single-peaked, or monophasic PRCs. Surprisingly, at low firing rates, Purkinje cell PRCs are largely independent of phase, resembling PRCs of ideal non-leaky integrate-and-fire neurons. These results indicate that Purkinje cells can act as perfect integrators at low firing rates, and that the integration mode of Purkinje cells depends on their firing rate.
Author Summary
By observing how brief current pulses injected at different times between spikes change the phase of spiking of a neuron (and thus obtaining the so-called phase response curve), it should be possible to predict a full spike train in response to more complex stimulation patterns. When we applied this traditional protocol to obtain phase response curves in cerebellar Purkinje cells in the presence of noise, we observed a triangular region devoid of data points near the end of the spiking cycle. This “Bermuda Triangle” revealed a flaw in the classical method for constructing phase response curves. We developed a new approach to eliminate this flaw and used it to construct phase response curves of Purkinje cells over a range of spiking rates. Surprisingly, at low firing rates, phase changes were independent of the phase of the injected current pulses, implying that the Purkinje cell is a perfect integrator under these conditions. This mechanism has not yet been described in other cell types and may be crucial for the information processing capabilities of these neurons.
PMCID: PMC2861707  PMID: 20442875
18.  Predicting the synaptic information efficacy in cortical layer 5 pyramidal neurons using a minimal integrate-and-fire model 
Biological Cybernetics  2008;99(4-5):393-401.
Synaptic information efficacy (SIE) is a statistical measure to quantify the efficacy of a synapse. It measures how much information is gained, on the average, about the output spike train of a postsynaptic neuron if the input spike train is known. It is a particularly appropriate measure for assessing the input–output relationship of neurons receiving dynamic stimuli. Here, we compare the SIE of simulated synaptic inputs measured experimentally in layer 5 cortical pyramidal neurons in vitro with the SIE computed from a minimal model constructed to fit the recorded data. We show that even with a simple model that is far from perfect in predicting the precise timing of the output spikes of the real neuron, the SIE can still be accurately predicted. This arises from the ability of the model to predict output spikes influenced by the input more accurately than those driven by the background current. This indicates that in this context, some spikes may be more important than others. Lastly we demonstrate another aspect where using mutual information could be beneficial in evaluating the quality of a model, by measuring the mutual information between the model’s output and the neuron’s output. The SIE, thus, could be a useful tool for assessing the quality of models of single neurons in preserving input–output relationship, a property that becomes crucial when we start connecting these reduced models to construct complex realistic neuronal networks.
PMCID: PMC2798051  PMID: 19011927
Synaptic information efficacy; Linear integrate-and-fire model; Predicting every spike; Layer 5 cortical pyramidal neuron
19.  The Origin of the Complex Spike in Cerebellar Purkinje Cells 
Activation of the climbing fiber input powerfully excites cerebellar Purkinje cells via hundreds of widespread dendritic synapses, triggering dendritic spikes as well as a characteristic high-frequency burst of somatic spikes known as the complex spike. To investigate the relationship between dendritic spikes and the spikelets within the somatic complex spike, and to evaluate the importance of the dendritic distribution of climbing fiber synapses, we made simultaneous somatic and dendritic patch-clamp recordings from Purkinje cells in cerebellar slices. Injection of large climbing fiber-like synaptic conductances at the soma using dynamic clamp was sufficient to reproduce the complex spike, independently of dendritic spikes, indicating that neither a dendritic synaptic distribution nor dendritic spikes are required. Furthermore, we found that dendritic spikes are not directly linked to spikelets in the complex spike, and that each dendritic spike is associated with only 0.24 ± 0.09 extra somatic spikelets. Rather, we demonstrate that dendritic spikes regulate the pause in firing that follows the complex spike. Finally, using dual somatic and axonal recording, we show that all spikelets in the complex spike are axonally generated. Thus, complex spike generation proceeds relatively independently of dendritic spikes, reflecting the dual functional role of climbing fiber input: triggering plasticity at dendritic synapses and generating a distinct output signal in the axon. The encoding of dendritic spiking by the post-complex spike pause provides a novel computational function for dendritic spikes, which could serve to link these two roles at the level of the target neurons in the deep cerebellar nuclei.
PMCID: PMC2730632  PMID: 18650337
climbing fiber; Purkinje cell; cerebellum; dendritic spike; burst; axon
20.  Encoding of Oscillations by Axonal Bursts in Inferior Olive Neurons 
Neuron  2009;62(3):388-399.
Inferior olive neurons regulate plasticity and timing in the cerebellar cortex via the climbing fiber pathway, but direct characterization of the output of this nucleus has remained elusive. We show that single somatic action potentials in olivary neurons are translated into a burst of axonal spikes. The number of spikes in the burst depends on the phase of subthreshold oscillations and, therefore, encodes the state of the olivary network. These bursts can be successfully transmitted to the cerebellar cortex in vivo, having a significant impact on Purkinje cells. They enhance dendritic spikes, modulate the complex spike pattern, and promote short-term and long-term plasticity at parallel fiber synapses in a manner dependent on the number of spikes in the burst. Our results challenge the view that the climbing fiber conveys an all-or-none signal to the cerebellar cortex and help to link learning and timing theories of olivocerebellar function.
PMCID: PMC2777250  PMID: 19447094
21.  Cerebellar LTD and Pattern Recognition by Purkinje Cells 
Neuron  2007;54(1):121-136.
Many theories of cerebellar function assume that long-term depression (LTD) of parallel fiber (PF) synapses enables Purkinje cells to learn to recognize PF activity patterns. We have studied the LTD-based recognition of PF patterns in a biophysically realistic Purkinje-cell model. With simple-spike firing as observed in vivo, the presentation of a pattern resulted in a burst of spikes followed by a pause. Surprisingly, the best criterion to distinguish learned patterns was the duration of this pause. Moreover, our simulations predicted that learned patterns elicited shorter pauses, thus increasing Purkinje-cell output. We tested this prediction in Purkinje-cell recordings both in vitro and in vivo. In vitro, we found a shortening of pauses when decreasing the number of active PFs or after inducing LTD. In vivo, we observed longer pauses in LTD-deficient mice. Our results suggest a novel form of neural coding in the cerebellar cortex.
PMCID: PMC1885969  PMID: 17408582
22.  Initiation of simple and complex spikes in cerebellar Purkinje cells 
The Journal of Physiology  2010;588(10):1709-1717.
Cerebellar Purkinje cells produce two distinct forms of action potential output: simple and complex spikes. Simple spikes occur spontaneously or are driven by parallel fibre input, while complex spikes are activated by climbing fibre input. Previous studies indicate that both simple and complex spikes originate in the axon of Purkinje cells, but the precise location where they are initiated is unclear. Here we address where in the axon of cerebellar Purkinje cells simple and complex spikes are generated. Using extracellular recording and voltage-sensitive dye imaging in rat and mouse Purkinje cells, we show that both simple and complex spikes are generated in the proximal axon, ∼15–20 μm from the soma. Once initiated, simple and complex spikes propagate both down the axon and back into the soma. The speed of backpropagation into the soma was significantly faster for complex compared to simple spikes, presumably due to charging of the somatodendritic membrane capacitance during the climbing fibre synaptic conductance. In conclusion, we show using two independent methods that the final integration site of simple and complex spikes is in the proximal axon of cerebellar Purkinje cells, at a location corresponding to the distal end of the axon initial segment.
PMCID: PMC2887989  PMID: 20351049

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