In this talk,
I discussed two types of electrical activities of cortical
neurons. One is neuronal oscillations of the gamma (40 Hz),
and theta (8 Hz) types. The other is spike adaptation and
its functions in the real-time input-output computation
of cortical neurons. Both topics are concerned with the
main objective of my research, namely to study how the behavior
of neurons and neural networks is organized in time.
Brain rhythms
are interesting both because they are manifestations of
synchronous activity of large neural populations, and because
in principle they can carry temporal (phasic) information.
We have been interested in the cellular and network mechanisms
underlying the generation of various neural oscillations
and the network synchronization. Recently, I proposed the
first ionic conductance models for the neocortical fast
(gamma, or 40 Hz) oscillations. The mechanism is based on
a persistent sodium conductance and a slowly inactivating
potassium conductance, that are located on the dendrite
and electronically separated from the spike generating sites
near the soma. We show that a similar mechanism may generate
the theta rhythm in pacemaker neurons for the hippocampal
theta wave. At the network level, we discovered that synaptic
inhibition, not excitation, is often responsible for synchronizing
large neural populations. We are currently pursuing detailed
network modeling of these various neural waves, and of their
possible roles in the sequential coordination of behavior.
More recently,
we started to look at other forms of complex temporal dynamics
of neurons and networks. One set of projects is to develop
theoretical tools to analyse several very different time
scales involved in a nervous system. Problems include the
calcium dynamics of neurons and its control of the neural
responses to time-varying inputs; variabilities in neural
firing and neural coding of random inputs; and adaptation.
Based on data from recent dendritic recording and calcium
imaging experiments, and by computer simulations of a two-compartment
conductance model, we investigated the interplay between
voltage-dependent electrical activity and the intracellular
calcium dynamics in cortical pyramidal neurons. A main characteristic
of these cells is spike adaptation when subject to a constant
stimulus. The time course of spike adaptation can often
be approximated by a mono-exponential law, f(t)=A+B*exp(-t/tau_adap),
where f(t) is the instantaneous firing rate. By assuming
that the spike adaptation is produced mainly by a calcium-dependent
potassium conductance (g_AHP), we derive this exponential
law semi-analytically, and relate the adaptation time constant
(tau_adap) with cellular parameters such as g_AHP and the
calcium decay time constant. By the same token, we introduce
the notion of "calcium modes" when the calcium conductance's
are distributed over a multi-compartmental dendrite.
The spike adaptation
property endows the pyramidal neurons with interesting computational
functions. With our model three phenomena are demonstrated
here. (1) When the input consists of a periodic train of
pulses, the response of the cell is sharply tuned to the
lower input frequencies, similar to the observed contrast
adaptation in the visual cortical neurons. (2) If an input
is random and correlated in time, the signal is decorrelated
in the cell's output ("efficient coding" and "novelty detection").
(3) In the presence of two or several inputs of slightly
different amplitudes, the cell can selectively respond to
the strongest input and suppresses the others ("selective
attention").
