Rank order decoding of temporal parallel fibre input patterns in a complex Purkinje cell model
Introduction
It is widely believed that the patterns of neuronal firing rates and that of individual spike times are both important for the encoding of information in the brain (e.g. [1], [6]). In a simple temporal coding scheme, an analogue input vector is represented using the relative timing of spikes across an array of encoding neurons (e.g. [5], see Fig. 1). Compared to a rate code, such a temporal code allows for the transmission of more information in a shorter time window [9], [8].
The decoding of a temporal spike pattern requires a complex system of delay lines and coincidence detection. To simplify the decoding, Thorpe and Gautrais [8] have suggested a coding scheme where the precise timing of the spikes is thrown away and the only relevant information is the order in which the spikes arrive. Advantages of this rank order code are its invariance to changes in input intensity and contrast, and the existence of a simple decoding algorithm. Without any delay lines, a rank order-coded pattern of input spikes can be decoded by an array of different synaptic weights and a mechanism that desensitizes the decoding neuron depending on how many spikes have already arrived. The activation a of the decoding neuron is given bywhere wi is the synaptic weight of input is the firing order of neuron i in the input sequence, and 0<δ<1 is a desensitization factor. As a consequence of the desensitization, the activation of the decoding neuron is maximal when the inputs are ordered according to decreasing synaptic weights (oi<oj⇔wi>wj), and minimal for an input sequence with increasing weights (oi<oj⇔wi<wj).
Desensitization of the decoding neuron can be implemented by a number of mechanisms. In cerebellar Purkinje cells, the activation of a sufficient number of parallel fibre (PF) inputs leads to influx of Ca2+ into the dendritic tree and to an afterhyperpolarization (AHP) which is mediated by Ca2+ dependent channels (cf. [7]). The AHP is expected to reduce the Purkinje cell responsiveness to subsequent PF inputs and represents a possible desensitization mechanism. Here, we study the recognition of rank order-coded PF input patterns in a multi-compartmental Purkinje cell model with active dendrites. We use the model that has been described in detail in [3], [4]. The model receives excitatory input from 147,400 PFs which activate AMPA receptors on dendritic spines. To increase the computational efficiency, only 1% of the 147,400 spines is represented explicitly. Each of these 1474 spine compartments receives 100 PF inputs. All PFs are activated asynchronously with a frequency between 0.26 and , resulting in an asynchronous AMPA receptor activation in each spine compartment with a frequency of 26–. The background excitation is balanced by a tonic background inhibition, and the model fires simple spikes with an average frequency between 8 and .
In the original rank order coding scheme, a temporal pattern consists of a sequence of individual input spikes. In cerebellar Purkinje cells, the effect of a single PF input spike is not strong enough. Thus, the Purkinje cell model is presented with spatio-temporal PF input patterns consisting of the consecutive activation of a sequence of spatial PF patterns. Each of the spatial PF patterns consists of the synchronous activation of 1000 PFs. The PF inputs activate AMPA receptors on the Purkinje cell spines, with maximal conductances that are identical within a spatial pattern and different between the different spatial patterns in the sequence. All simulations are performed using the GENESIS simulator [2].
Section snippets
Simulation results
Fig. 2, Fig. 3 show simulation results for a Purkinje cell model that receives asynchronous PF background activation, resulting in simple spike firing with an average frequency of . The model is presented with all 3!=6 possible permutations of a sequence of three spatial PF input patterns {P1,P2,P3} with maximal AMPA receptor conductances . For a delay of between the three inputs in the sequence, the model fires an average number of 2.9 spikes
Conclusions
We have shown that a multi-compartmental model of a cerebellar Purkinje cell can implement rank order decoding of temporal parallel fibre (PF) input patterns, similar to the algorithm that was suggested by Thorpe and Gautrais [8] for simple integrate-and-fire neurons. Basis of the rank order decoding in the Purkinje cell model is the afterhyperpolarisation (AHP) that is caused by activation of KCa channels after PF input. Stronger PF inputs lead to a stronger AHP and to a weaker response to
Acknowledgements
Thanks to Arnaud Delorme and Rufin van Rullen for stimulating discussions. The work was supported by the FWO (Flanders) and a Human Frontier Science Program Organization long-term fellowship to VS.
Volker Steuber studied biochemistry at the University of Tübingen and the ETH Zürich. After graduating in 1993, he joined David Willshaw's group at the University of Edinburgh. In 1998, he received a Ph.D. for his work on “Computational Theories of Intracellular Signalling in Cerebellar Purkinje Cells”. He is currently a postdoctoral fellow in Erik De Schutter's group at the University of Antwerp, using computer simulations and in vivo recordings to study the function of cerebellar Purkinje
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Volker Steuber studied biochemistry at the University of Tübingen and the ETH Zürich. After graduating in 1993, he joined David Willshaw's group at the University of Edinburgh. In 1998, he received a Ph.D. for his work on “Computational Theories of Intracellular Signalling in Cerebellar Purkinje Cells”. He is currently a postdoctoral fellow in Erik De Schutter's group at the University of Antwerp, using computer simulations and in vivo recordings to study the function of cerebellar Purkinje cells.
Erik De Schutter (born 1959) received his medical degree from the University of Antwerp in 1984 where he went on to do a clinical residency in neuropsychiatry and a Ph.D. in medicine. In 1990 he became a postdoctoral Fellow at the California Institute of Technology. In 1994 he returned to the University of Antwerp to start the Theoretical Neurobiology group. He is a computational neuroscientist with a research focus on the function and operations of the cerebellar cortex. He played a seminal role in starting and directing a series of European summer schools on computational neuroscience (Crete, Trieste).