Recent data on the cerebellum require new models and theories

The cerebellum has been a popular topic for theoretical studies because its structure was thought to be simple. Since David Marr and James Albus related its function to motor skill learning and proposed the Marr-Albus cerebellar learning model, this theory has guided and inspired cerebellar research. In this review, we summarize the theoretical progress that has been made within this framework of error-based supervised learning. We discuss the experimental progress that demonstrates more complicated molecular and cellular mechanisms in the cerebellum as well as new cell types and recurrent connections. We also cover its involvement in diverse non-motor functions and evidence of other forms of learning. Finally, we highlight the need to explain these new experimental findings into an integrated cerebellar model that can unify its diverse computational functions.journal articl

Climbing Fibers Provide Graded Error Signals in Cerebellar Learning

The cerebellum plays a critical role in coordinating and learning complex movements. Although its importance has been well recognized, the mechanisms of learning remain hotly debated. According to the classical cerebellar learning theory, depression of parallel fiber synapses instructed by error signals from climbing fibers, drives cerebellar learning. The uniqueness of long-term depression (LTD) in cerebellar learning has been challenged by evidence showing multi-site synaptic plasticity. In Purkinje cells, long-term potentiation (LTP) of parallel fiber synapses is now well established and it can be achieved with or without climbing fiber signals, making the role of climbing fiber input more puzzling. The central question is how individual Purkinje cells extract global errors based on climbing fiber input. Previous data seemed to demonstrate that climbing fibers are inefficient instructors, because they were thought to carry “binary” error signals to individual Purkinje cells, which significantly constrains the efficiency of cerebellar learning in several regards. In recent years, new evidence has challenged the traditional view of “binary” climbing fiber responses, suggesting that climbing fibers can provide graded information to efficiently instruct individual Purkinje cells to learn. Here we review recent experimental and theoretical progress regarding modulated climbing fiber responses in Purkinje cells. Analog error signals are generated by the interaction of varying climbing fibers inputs with simultaneous other synaptic input and with firing states of targeted Purkinje cells. Accordingly, the calcium signals which trigger synaptic plasticity can be graded in both amplitude and spatial range to affect the learning rate and even learning direction. We briefly discuss how these new findings complement the learning theory and help to further our understanding of how the cerebellum works

The Cellular Electrophysiological Properties Underlying Multiplexed Coding in Purkinje Cells

Neuronal firing patterns are crucial to underpin circuit level behaviors. In cerebellar Purkinje cells (PCs), both spike rates and pauses are used for behavioral coding, but the cellular mechanisms causing code transitions remain unknown. We use a well-validated PC model to explore the coding strategy that individual PCs use to process parallel fiber (PF) inputs. We find increasing input intensity shifts PCs from linear rate-coders to burst-pause timing-coders by triggering localized dendritic spikes. We validate dendritic spike properties with experimental data, elucidate spiking mechanisms, and predict spiking thresholds with and without inhibition. Both linear and burst-pause computations use individual branches as computational units, which challenges the traditional view of PCs as linear point neurons. Dendritic spike thresholds can be regulated by voltage state, compartmentalized channel modulation, between-branch interaction and synaptic inhibition to expand the dynamic range of linear computation or burst-pause computation. In addition, co-activated PF inputs between branches can modify somatic maximum spike rates and pause durations to make them carry analog signals. Our results provide new insights into the strategies used by individual neurons to expand their capacity of information processing

Role of CaMKII and PKA in early afterdepolarization of human ventricular myocardium cell: A Computational model study

Early afterdepolarization (EAD) plays an important role in arrhythmogenesis. Many experimental studies have reported that Ca2+/calmodulin-dependent protein kinase II (CaMKII) and β-adrenergic signaling pathway are two important regulators. In this study, we developed a modified computational model of human ventricular myocyte to investigate the combined role of CaMKII and β-adrenergic signaling pathway on the occurrence of EADs. Our simulation results showed that () CaMKII overexpression facilitates EADs through the prolongation of late sodium current’s () deactivation progress; () the combined effect of CaMKII overexpression and activation of β-adrenergic signaling pathway further increases the risk of EADs, where EADs could occur at shorter cycle length (2000 ms versus 4000 ms) and lower rapid delayed rectifier K+ current () blockage (77% versus 85%). In summary, this study computationally demonstrated the combined role of CaMKII and β-adrenergic signaling pathway on the occurrence of EADs, which could be useful for searching for therapy strategies to treat EADs related arrhythmogenesis

Firing rate-dependent phase responses of Purkinje cells support transient oscillations

Both spike rate and timing can transmit information in the brain. Phase response curves (PRCs) quantify how a neuron transforms input to output by spike timing. PRCs exhibit strong firing-rate adaptation, but its mechanism and relevance for network output are poorly understood. Using our Purkinje cell (PC) model, we demonstrate that the rate adaptation is caused by rate-dependent subthreshold membrane potentials efficiently regulating the activation of Na(+) channels. Then, we use a realistic PC network model to examine how rate-dependent responses synchronize spikes in the scenario of reciprocal inhibition-caused high-frequency oscillations. The changes in PRC cause oscillations and spike correlations only at high firing rates. The causal role of the PRC is confirmed using a simpler coupled oscillator network model. This mechanism enables transient oscillations between fast-spiking neurons that thereby form PC assemblies. Our work demonstrates that rate adaptation of PRCs can spatio-temporally organize the PC input to cerebellar nuclei

Exploring Impaired SERCA Pump-Caused Alternation Occurrence in Ischemia

Impaired sarcoplasmic reticulum (SR) calcium transport ATPase (SERCA) gives rise to Ca(2+) alternans and changes of the Ca2+release amount. These changes in Ca(2+) release amount can reveal the mechanism underlying how the interaction between Ca(2+) release and Ca(2+) uptake induces Ca(2+) alternans. This study of alternans by calculating the values of Ca(2+) release properties with impaired SERCA has not been explored before. Here, we induced Ca(2+) alternans by using an impaired SERCA pump under ischemic conditions. The results showed that the recruitment and refractoriness of the Ca(2+) release increased as Ca(2+) alternans occurred. This indicates triggering Ca waves. As the propagation of Ca waves is linked to the occurrence of Ca(2+) alternans, the "threshold" for Ca waves reflects the key factor in Ca(2+) alternans development, and it is still controversial nowadays. We proposed the ratio between the diastolic network SR (NSR) Ca content (Cansr) and the cytoplasmic Ca content (Ca i ) (Cansr/Ca i ) as the "threshold" of Ca waves and Ca(2+) alternans. Diastolic Cansr, Ca i , and their ratio were recorded at the onset of Ca(2+) alternans. Compared with certain Cansr and Ca i , the "threshold" of the ratio can better explain the comprehensive effects of the Ca(2+) release and the Ca(2+) uptake on Ca(2+) alternans onset. In addition, these ratios are related with the function of SERCA pumps, which vary with different ischemic conditions. Thus, values of these ratios could be used to differentiate Ca(2+) alternans from different ischemic cases. This agrees with some experimental results. Therefore, the certain value of diastolic Cansr/Ca i can be the better "threshold" for Ca waves and Ca(2+) alternans

26th Annual Computational Neuroscience Meeting (CNS*2017): Part 3 - Meeting Abstracts - Antwerp, Belgium. 15–20 July 2017

This work was produced as part of the activities of FAPESP Research,\ud Disseminations and Innovation Center for Neuromathematics (grant\ud 2013/07699-0, S. Paulo Research Foundation). NLK is supported by a\ud FAPESP postdoctoral fellowship (grant 2016/03855-5). ACR is partially\ud supported by a CNPq fellowship (grant 306251/2014-0)

Voltage- and Branch-Specific Climbing Fiber Responses in Purkinje Cells

Summary: Climbing fibers (CFs) provide instructive signals driving cerebellar learning, but mechanisms causing the variable CF responses in Purkinje cells (PCs) are not fully understood. Using a new experimentally validated PC model, we unveil the ionic mechanisms underlying CF-evoked distinct spike waveforms on different parts of the PC. We demonstrate that voltage can gate both the amplitude and the spatial range of CF-evoked Ca2+ influx by the availability of K+ currents. This makes the energy consumed during a complex spike (CS) also voltage dependent. PC dendrites exhibit inhomogeneous excitability with individual branches as computational units for CF input. The variability of somatic CSs can be explained by voltage state, CF activation phase, and instantaneous CF firing rate. Concurrent clustered synaptic inputs affect CSs by modulating dendritic responses in a spatially precise way. The voltage- and branch-specific CF responses can increase dendritic computational capacity and enable PCs to actively integrate CF signals. : Zang et al. find that the availability of K+ currents regulates Ca2+ influx and corresponding energy consumption during climbing fiber input in Purkinje cell dendrites. They systematically explore the mechanisms underlying variable somatic complex spikes and identify branchlet-specific computation in dendrites. Keywords: cerebellum, Purkinje cell, climbing fiber, complex spikes, dendritic spikes, dendritic excitability, biophysical model, energy consumptio