LECTURE 8
Neural coding (1)
I. Introduction
− Topographic Maps in Cortex
− Synesthesia
− Firing rates and tuning curves
Why Neural Coding?
• A way for us to understand high-level brain functions (in the
views of information theory and statistical inference)
• It answers:
– How external stimuli are represented in the form of neural
activities (internal representation)?
– How this internal representation is further read-out in
neural systems?
Encoding
Decoding
External Stimulus
Mental Operation
Neural Activity
(internal representation)
Different areas of the cerebral cortex carry
out different functions
(Gazzaniga et al., Cognitive Neuroscience)
‘Where’ and ‘What’ visual information
pathways in object recognition
‘Where’: the motion and spatial location
‘What’: form recognition and object representation (detailed features like
colour) and also long-term memory
(Gazzaniga et al., Cognitive Neuroscience)
Visual feature processing from simple to complex
(Gazzaniga et al., Cognitive Neuroscience)
Topographic maps in cortex
－ Each visual sensitive cell only responses to stimuli a limited region (receptive field)
－ Neighbouring cells have partially overlapping receptive fields
－ Neighboring points in a visual image evoke activity in neighboring regions of visual cortex.
－ In this manner, the visual system easily maintain the information of the spatial location
of stimulus
(Dayan and Abbott 2001)
Retinotopic Map
The tonotopic map in the auditory areas
The sound frequency is orderly mapped in the auditory cortex
(Gazzaniga et al., Cognitive Neuroscience)
The topographic maps in the
somatosensory and motor cortex
(Gazzaniga et al., Cognitive Neuroscience)
Examples of synesthesia
• When a man looks at printed black numbers, he sees them in color
• A girl sees blue when she listens to the note C played on the
piano; other notes evoke different hues
• People with synesthesia can provide valuable clues to understanding
the organization and function of the human brain
• Neural cross wiring may lie at the root of synesthesia
Tastes
experienced
by
synaesthete
E.S.
E.S.-- a 27-year-old
professional
musician
who is female,righthanded and of
average
intelligence
(Beeli, Esslen, Jäncke, 2005)
(Ramachandran and
Hubbard 2003)
• Rate coding:
Information is encoded in the firing rate.
• Temporal coding:
The fine structure of the pattern of inter-spike
intervals (ISIs) contains information
Tuning curve
Neuronal responses typically depend on many different properties of a
stimulus. Tuning curve of the average firing rate can be measured by
only considering one of the stimulus attributes
Gaussian
tuning curve
From a neuron in the primary visual cortex of a monkey
Recordings from the primary motor cortex of a monkey performing an
arm reaching task
Firing rate versus head direction plot
for a typical head direction cell
Irregularity of cortical neural responses
• Tuning curves allow us to predict the average firing rate, but
they do not describe how the spike-count firing rate varies
about its mean value from trial to trial
• While the map from stimulus to average response may be
described deterministically, it is likely that single-trial responses
can only be modeled in a probabilistic manner
• The Poisson process provides an extremely useful approximation
of stochastic neuronal firing
The probability that any sequence of n spikes occurs within a trial
of duration T obey the Poisson distribution:
Simulating Poisson spike sequences:
Comparison with data
From an MT neuron
responding to a moving
random dot image
Interspike interval histogram
generated from a Poisson
model
(Dayan and Abbott 2001)
Two cases
• The homogeneous Poisson process: the firing rate is constant over
time
• The inhomogeneous Poisson process: involves a time-dependent
firing rate
Where is the neural response variability from?
• Single neuron level:
－Unreliable release of neuro-transmitters
－ Stochasticity in channel gating
－ Fluctuations in the membrane potential
•
Network level:
－ Neurons are randomly connected with each other
－ Background stimuli from a changing environment to
neural systems
Key points:
1. Topographic maps in cortex
2. Tuning curve
3. Spike-train statistics