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Time-scales of temporal response in regular and fast-spiking cortical neurons


Rauch,  A
Department Physiology of Cognitive Processes, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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La Camera, G., Rauch, A., Senn W, Fusi S, Thurbon, D., & Luescher, H. (2005). Time-scales of temporal response in regular and fast-spiking cortical neurons. Poster presented at Computational and Systems Neuroscience Meeting (COSYNE 2005), Salt Lake City, UT, USA.

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Recently, the use of a noisy input current to investigate single cell and network behavior in vitro and in cultures is becoming a standard and appreciated tool. Such an approach aims at describing the response of cortical neurons as if they were embedded in an intact brain, with the bonus that the input current can be manipulated, and the response easily recorded intracellularly, allowing quantitative modelling under in vivo-like conditions. We used this approach to study and compare the firing patterns of fast spiking (FS) and pyramidal neurons from rat somatosensory cortex on time scales of the order of tens of seconds. FS interneurons showed a pronounced sensitivity to input fluctuations, much larger than pyramidal neurons (50Hz vs 10Hz in response to a subthreshold noisy stimulus). Moreover, although no adaptation of the firing rate seems to occur in the first few hundred milliseconds, cellular processes are at play which reduce the firing rate over time in a slow fashion, as reported recently in somatosensory cortex (Reutimann et al, J. Neurosci. 24: 3295-3303, 2004) and in visual cortex (Descalzo et al, J. Neurophysiol, doi:10.1152/jn.00658.2004). The stationary response (both the firing rate and the variability of the interspike intervals) was characterized as a function of the average and the standard deviation (SD) of the input current, chosen as a Gaussian process. The firing rate in the final seconds of the stimulation interval (i.e. where it varies very slowly) could be fitted by a modified leaky integrate-and-fire model with 5 effective parameters (one representing spike frequency adaptation), as shown previously for pyramidal neurons (Rauch et al, J. Neurophysiol. 90: 1598-1612, 2003). The same model could reproduce well the statistics of the interspike intervals (ISIs), even though its parameters were tuned to fit the firing rates only. The temporal properties of the response are rich even though the stimuli were stationary. Several processes characterize the time course of the instantaneous frequency, which could be reduced to a small number (1 to 3) of phenomenological mechanisms. These mechanisms are to be interpreted as frequency-dependent modulations of the input current, either reducing (adapting) or increasing (facilitating) the neuron's firing rate. FS interneurons could be described either by a single adapting process (time constant of seconds), or by two adapting processes (time constants of hundreds of milliseconds and seconds respectively). For pyramidal neurons, a third process representing a strong initial adaptation, and an intermediate-duration process facilitating the firing rate, were also required. Slow adaptation was not disrupted by the presence of noise. An extended IF model including these processes provided an excellent fit to the data, providing a mechanistic description of the statistics of the temporal processes, i.e. their time constants and magnitudes. The parameters were usually input-dependent; for those which correlated with input current, we derived a model of their dependence. This makes it possible to build a time-dependent model out of data taken in stationary conditions, by allowing the current to change over time with its characteristic way, and letting e.g. the current-dependent parameters follow instantaneously the input dynamics. Such an approach has proved legitimate in very similar models (see e.g. La Camera et al, Neural Comp 16: 2101-2124, 2004). All the parameters describing the neural dynamics vary from cell to cell and the distribution is broad. The different adaptation mechanisms cover a wide range of time scales, ranging from initial adaptation (10-20 ms), to fast adaptation (50-200 ms), early facilitation (0.5-1 s), and slow (or late) adaptation (order of seconds). Although for single cells, the processes are usually distinct and their time scales well separated, populations of different neurons can practically cover all possible time scales, without any gap. Were our study extended to longer stimulation protocols, we would probably find other mechanisms operating on longer time scales. In conclusion, our results indicate that multiple time scales are at play in cortical neurons, even in response to stationary stimuli and in the presence of noise. The time-dependent processes and the distribution of their time scales across different neurons might partially explain the long range correlations in firing rate observed in vivo over many different time scales (S.B. Lowen, et al., Methods 24(4):377-394, 2001). Interestingly these correlations were present also in the absence of any sensory stimulus (the experiment was done in the darkness and the activity was recorded in the cat lateral geniculate nucleus), indicating that they are not a mere reflection of the complexity of the external world. Recently proposed computational consequences of multiple time scales (P.J. Drew, PhD thesis, Brandeis University) range from estimating the envelope of a signal, to discriminate between the responses to rare and common stimuli, to connect and link stimuli which are separated in time by intervals of a few seconds.