### NEURAL DYNAMICS IN CORTICAL NETWORKS: PRECISION AND VARIABILITY

Neurobiology and Biophysics, Institute of Biology III, Albert-Ludwigs-University
Sch\"{a}nzlestrasse 1, D-79104 Freiburg, Germany.

E-mail: aertsen@biologie.uni-freiburg.de

Studies of cortical function on the basis of multiple single-neuron recordings have revealed neuronal interactions which depend on stimulus and behavioral context. These interactions exhibit dynamics on different time scales, with time constants
down to the millisecond range. Mechanisms underlying such dynamic organization of the cortical network are investigated by experimental and theoretical approaches. Our recent work focuses on two interrelated aspects: {\it precision} and {\it variability} of cortical activity.

In a series of studies we investigated conditions for the occurrence of precise joint- spiking events in cortical activity [1]. Specifically, we tested the hypothesis that precise synchronization of action potentials among groups of neurons is supported by
cortical network activity, in spite of the fluctuating background [2]. Thus, we found evidence [3] that volleys of precisely synchronized spikes can propagate through the cortical network in a stable fashion with a temporal precision down to $\pm$1 ms,
consistent with experimental observations. These findings suggest that a combinatorial neural code, based on rapid associations of groups of neurons co- ordinating their activity at the single spike level, is biologically feasible.

In a separate study we assessed the trial-by-trial variability of spike trains from neurons in the monkey primary motor cortex. We found that Fano factors (ratio of variance and mean of spike counts across trials) of motor cortical discharges are widely distributed, covering a range from 0.2 to 6, and in rare cases reach even beyond [4]. More detailed analyses taking into account the time-resolved firing rate profiles [5] revealed that many of the recorded neurons exhibit systematic changes of variability throughout the trial. Our findings show that the spiking process of primary motor cortical neurons is not captured by a rate-modulated Poisson or gamma process. Instead, they indicate that a more elaborate point process model, possibly with time-dependent statistics, is required to adequately describe motor cortical unit activity.

How the findings from these two approaches can be reconciled into a single model of cortical function is still an open question, and the subject of current work.

1. Riehle A, Gr\"{u}n S, Diesmann M, Aertsen A (1997) Spike synchronization and rate modulation
differentially involved in motor cortical function. Science 278:1950-1953
2. Arieli A, Sterkin A, Grinvald A, Aertsen A (1996) Dynamics of ongoing activity: Explanation of
the large variability in evoked cortical responses. Science 273:1868-1871
3. Diesmann M, Gewaltig M-O, Aertsen A (1999) Stable propagation of synchronous spiking in cortical
neural networks. Nature 402: 529-533
4. Nawrot MP, Riehle A, Aertsen A, Rotter S (2000) Spike count variability in motor cortical neurons.
In: {\it Abstr Forum Europ Neurosci 2000} (Brighton), Europ J Neurosci 12, Suppl 11, p 506
5. Nawrot M, Aertsen A, Rotter S (1999) Single-trial estimation of neuronal firing rates - From single-ne
uron spike trains to population activity. J Neurosci Meth 94: 82-92

Funded by DFG, GIF and HFSP. Further information at http://www.brainworks.uni-freiburg.de

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