Untitled - Laboratory of Neurophysics and Physiology

internally generated propagating waves provide a specific structure for the spatiotemporal activity in
visual cortex, uniquely encoding both stimulus identity and time of presentation in the amplitude and
phase of the population response [8]. With these results in mind, we go on to discuss the computational
paradigms towards which our observations point, elucidating these with numerical models and
further analysis.
Acknowledgements
Work supported by the CNRS and the European Community (BrainScales project, FP7-269921). LM is a PhD
fellow from Ècole des Neurosciences de Paris (ENP).
References
1. Xu W, Huang X, Takagaki K, Wu JY: Compression and reflection of visually evoked cortical waves.
Neuron 2007, 55:119-129.
2. Han F, Caporale N, Dan Y: Reverberation of recent visual experience in spontaneous cortical waves.
Neuron 2008, 60:321-327.
3. Ray S, Maunsell JH: Network rhythms influence the relationship between spike-triggered local field
potential and functional connectivity. J Neurosci 2011, 31:12674-12682.
4. Nauhaus I, Busse L, Ringrach DL, Carandini M: Robustness of traveling waves in ongoing activity of
visual cortex. J Neurosci 2012, 32:3088-3094.
5. Reynaud A, Takerkart S, Masson GS, Chavane F: Linear model decomposition for voltage-sensitive
dye imaging signals: Application in awake behaving monkey. Neuroimage 2011, 54:1196-1210.
6. Jancke D, Chavane F, Naaman S, Grinvald A: Imaging cortical correlates of illusion in early visual
cortex. Nature 2004, 428:423-426.
7. Reynaud A, Masson GS, Chavane F: Dynamics of local input normalization result from balanced
short- and long-range intracortical interactions in area V1. J Neurosci 2012, 32:12558-12569.
8. Ermentrout GB, Kleinfeld D: Traveling electrical waves in cortex: insights from phase dynamics and
speculation on a computational role. Neuron 2001, 29:33-44.
O9
Non-renewal spiking and neural dynamics – A simple theory of interspike interval
correlations in adapting neurons
Tilo Schwalger 1,2⋆ , Benjamin Lindner 1,2
1 Department of Physics, Humboldt-Universität zu Berlin, Berlin, 12489, Germany
2 Bernstein Center for Computational Neuroscience, Berlin, 10115, Germany
There is accumulating evidence that the spiking of many neurons is not a renewal process but is
characterized by correlations between interspike intervals (ISIs) [1]. These correlations are crucial for
understanding signal processing in single neurons, however, their origin and structure is still poorly
understood theoretically. Here, we present a simple theory of correlations in neural oscillators with
spike-triggered adaptation currents, which are a major source of non-renewal spiking. These currents
mediate spike-frequency adaptation and are commonly believed to result in negative correlations between
adjacent ISIs. For such adapting neurons, we show that the serial correlation coefficient (SCC)
is fundamentally related to the neuron’s phase response curve (PRC). The relation predicts possible
correlation patterns that characterize how correlations depend on the lag between ISIs. Different patterns
arise from the specific interplay between nonlinear neural dynamics and adaptation dynamics. In
particular, the correlation structure can be determined by a single parameter that includes the shape
of the PRC as well as the strength and time scale of the adaptation current (Fig. 1).
For a positive PRC (type I), the SCC is always negative at lag 1. At higher lags, we find either a
63