Deciphering the neural code: neuronal discharge variability is preferentially controlled by the temporal distribution of afferent impulses☆
Introduction
We report the results of a detailed study that explored the discharge behavior of a realistic one-compartment Purkinje cell (PC) model when the properties of the activation process were varied, including the temporal distribution and frequency of afferent impulses, afferent fiber number (effective convergence), and presence of paired-pulse facilitation (PPF). We show that activation by a sequence of impulses displaying a non-Poissonian temporal pattern leads to novel cell discharge behavior that eliminates a requirement for temporal averaging that is present in rate-based models.
Section snippets
The model
Simulations employed a cell based on a previously reported composite model PC [3] that now incorporates a dynamic potassium equilibrium potential [6], [4], and PPF [1].
Rate-coded afferent excitation was modelled as a Poisson process. Alternatively, temporally coded activation was described by a Gaussian distribution of impulses in time such that the Gaussian envelope was symmetric about an assumed mean stimulus time [2]. Impulse timing within this “pulsed Gaussian” stimulation was controlled by
Results
A near logarithmic relation between the effective convergence and the mean PC discharge frequency was exhibited under both stimulation paradigms. Generally, the PC discharge frequency exhibited only weakly linear scaling with the product of impulse number and mean impulse frequency.
Under Poisson stimulation, facilitation had little influence on the PC current/frequency (f/i) relation. The slope was (−PPF condition) or (+PPF condition), cf. (calculated from Fig. 5B, [5]
Conclusions
The novel features of PC discharge behavior that occurred under pulsed Gaussian stimulation, but not Poissonian, stimulation, were associated with the timing of the afferent impulses rather than simply their rate. Only under pulsed Gaussian stimulation could convergence be tuned to achieve a relation between the mean frequency of stimulation and the mean PC discharge frequency, a condition that was associated with a significantly reduced PC discharge CV.
The emergence of periodic discharge
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This work was supported by Neurosciences Research Foundation.