06-12-2012, 11:02 AM
Negatively correlated firing: the functional meaning of lateral inhibition within cortical columns
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Abstract
Lateral inhibition is a well documented
aspect of neural architecture in the main sensory systems.
Existing accounts of lateral inhibition focus on its
role in sharpening distinctions between inputs that are
closely related. However, these accounts fail to explain
the functional role of inhibition in cortical columns, such
as those in V1, where neurons have similar response
properties. In this paper, we outline a model of position
tracking using cortical columns of integrate-and-fire
and Hodgkin-Huxley-type neurons which respond optimally
to a particular location, to show that negatively
correlated firing patterns arise from lateral inhibition
in cortical columns and that this provides a clear benefit
for population coding in terms of stability, accuracy,
estimation time and neural resources.
Introduction
Understanding the functional meaning of particular
aspects of neural architecture is a central objective of
neuroscience. Inhibitory interneurons are very common
in the neocortex, and lateral inhibition has been shown
to play an important role in sharpening the distinctions
between similar inputs, where such inputs would otherwise
invoke nearly the same response in neurons that
have only slightly different response properties. However,
it is our belief (Nicol et al. 2005; Tate et al. 2005)
that inhibition also plays an important role in population
coding, stabilising the mean field potential (Eq. 1)
and greatly improving the ability of a group of neurons
to accurately represent a given stimulus, by creating
negatively correlated firing patterns. In this paper,
we will describe the principle on which this improvement
is based, showing how it extends the benefit of
population coding. We will then present a model and a
set of experiments using this model, which demonstrates
that pools of neurons operating with inhibitory connections
perform better on a stimulus-tracking task than the
same model with no inhibitory connections. The model
is designed to show how this can work in principle in
neural sensory coding, incorporating a number of realistic
aspects such as the use of spiking neurons, online
estimation and a simple filtering mechanism.
Inhibitory mechanisms in neocortex
Sensory neural processing is most often thought of in
terms of many interconnected circuits using excitatory
connections to propagate signals through layers of
increasingly abstract representation. Whilst there is
some truth in this necessarily simplified image, it
is also the case that a substantial fraction of neurons
in the brain are inhibitory. Inhibitory neurons can operate
in a variety of different ways, such as feedforward
inhibition, where excitatory and inhibitory connections
project from the same area to areas that are typically
opposite in function, and feedback inhibition, where
excitatory neurons suppress the activity of other
neurons in the same area through local inhibitory interneurons.
Much of the existing work on inhibitory mechanisms
in the context of cortical columns has focused on
the role of lateral inhibition in sharpening distinctions
between neurons with slightly different response
properties (Martin 1984; Ratliff 1972).
Methods
Network model
Ourmodel1 consists of a set ofNc = 10 cortical columns,
each containing Nn = 100 integrate-and-fire neurons,
which either are unconnected (control condition; an
effective synaptic strength of zero) or have a full set
of inhibitory connections to all other neurons in the
column (there were no recurrent connections back to
the originating neuron itself). There are no connections
across columns. Each neuron is parameterised by vthre
(firing threshold), vrest (resting and reset potential), τm
(membrane time constant), Cm (total membrane capacitance)
and xcol (stimulus position to which neurons
in the column respond most strongly). In the experiments
presented here, vrest was always set to 0 (using
a standard rescaling approach from realistic values, for
ease of analysis), Cm was always set to 1 nF and τm was
always set to 20ms. The
Experiments
A number of experiments have been conducted to
examine the effect of inhibitory connections in the network
on performance on the stimulus-tracking task.
Basic performance was measured using the mean
squared error (MSE), of the position estimate and the
actual stimulus position, at the end of each estimation
window period. Although a sliding estimation window
was used to produce a position estimate at the end of
every simulation step, in calculating the MSE we used
only the position at the end of a stimulus period (the
period of time during which the stimulus has been in
one location) in order to ensure that there were no
contamination effects from previous stimulus position
adversely affecting the current position estimate. In addition
to examining basic performance, correlation measures
(both across and within columns and estimate
autocorrelation) and firing rates have been shownwhere
appropriate.
Membrane time constant
As outlined in Sect. 4.1, the central difference between
the kinetic synaptic model used in the biophysical model
and the instantaneous current injection of the simple
model is that the former has a time trajectory (whose effect
is subject to further variation dependent on the state
of the postsynaptic membrane potential). The effect of
the synapse is not limited to the time at which the presynaptic
spike takes place but increases to a peak over
a short period of time and decays over a longer period.
The time course of the AMPA and GABAA synaptic
currents is shown on the left of Fig. 13. It is apparent
that most of the activity takes place over the first 20 ms,
for both synapse types. However, this is also modulated
by the rate at which external inputs affect the trajectory
of the membrane potential.