Gain Modulation

Huei-Ju Chen

Papers:

Chance, Abbott, and Reyes(2002)

E. Salinas & T. Sejnowski(2001)

E. Salinas & L.G. Abbott (1997, 1996)

Pouget & T. Sejnowski (2001)

Outline

• What is gain modulation?• Gain modulation in the parietal cortex

(coordinate transformations)• Gain modulation in Neglect• Invariant visual responses from attentional

gain fields• Gain modulation from background synaptic

Input

Introduction

• Gain modulation is a nonlinear way in which neurons combine information from two or more sources, which may be of sensory, motor, or cognitive origin.

• One input affects the gain of the neuron to the other input without modifying the neuron’s receptive field properties.– Salinas and Sejnowski, 2001

Salinas & Sejnowski, 2001

Gain Modulation In Neurons

Gain Fields: Gain Modulation Without Changing RF

: retinotopic position

: eye positionx

x

r

e

Gain Fields

• Response of one neuron

• The downstream response R

– e.g.

target

( ) ( ), f(t):weighted sum of input 1, g(t): input 2(modulator)

( ) ( )gaze

r f t g t

r f x a g x

1 target 2 gaze( )R F c x c x

target gazex x

Gain Modulation in Cognition

• Coordinate transformations– Modulatory quantity: gaze angle

• Translation-invariant object recognition and size constancy– Modulatory quantity: attention

• Motion processing

Gain Modulation In Coordinate

Transformations:Modulator: Gaze

Angle

Gain Modulation In Coordinate Transformations

Salinas and Abbott, 1996

A Model of Multiplicative Neural Responses in Parietal Cortex

• Synapse weights for recurrent connections

2

max 2

Total external input to the neuron i:

( ) ( )

( )( ) exp( )

2

( )

i

V Gi i i

V V ii

V

Gi i i i

h

h h x h y

x xh x h

h y m y b

2 2

2 2

( ) ( )exp( ) exp( )

2 2

The firing rate of neuron i

[ ] ,s:slope of firing rate function

i j i jij E I

E I

i i ij j thj

x x x xW A A

r s h W r h

Simulations

One Model of Neglect (A Coordinate Frame Syndrome)

• Neglect is a neurologic syndrome characterized by a conspicuous inability to react or respond to stimuli presented in the hemispace contralateral to the lesion.

One Model of Neglect (A Coordinate Frame Syndrome)

• Pouget & Sejnowski, 2001

20

20

2

2

4 41 41

1 1 1

1, 8 or 8 (two maps)

1 exp( ( ) / )

==> product form

( )exp

2

Ej

j

E Rij j ik i k

k

i i kik

i ijkl jkl jklj k l

ae e

a a w a

r rw

o w n a

1

2

ij r i e j

ij r i e j

N r e

N r e

One Model of Neglect (A Coordinate Frame Syndrome)

• The unilateral lesion is modeled by deleting the two right maps.

41

1,

is inversely proportional to RT.oij i

i ij ijj r r

i

s N a

s

Neglect (Contd.)

Neglect (Contd.)

Neglect (Contd.)

Salinas and Abbott, 1997

Invariant Visual Response From Attentional Gain Field

2 2

V4: ( ; ) ( ), G is a Gaussian function

IT: [ ] , is established by Hebbian learning

Translation Invariance

( ; ) [ ( ; )] [ ( ; )]

Scale Invariance

( ; ) [ ( ; )] ;

i i i i

i i ii

i i i i i i

Si i i i i

v F a I G y b

V Wv W

F a I S a I C a I

F a I S a I F

1 2 1 2

1 2 1 2

( ; ) [ ( ; )]

( ; ) ( ) ( ); ( ; ) ( ) ( )

( ) cos( / ) cos( / )sin{ [ cos( ) cos( )]}

( ) cos( / ) cos( / )cos{ [ cos( ) cos( )]}

Ci i i

S Ci i i i i i i i

Si i i i

Ci i i i

a I C a I

S a I dxI x f x a C a I dxI x f x a

f x h x h x k x x

f x h x h x k x x

Simulation of Model

Network for Images

Translated Across

Visual Field

Salinas and Abbott, 1997

Simulation: Images at

Different Scales

Chance, Abbott, and Reyes, 2002

Gain Modulation From Background Synaptic Input

• Chance, Abbott, and Reyes, 2002

• By introducing a barrage of excitatory and inhibitory synaptic conductance that mimics conditions encountered in vivo into pyramidal cells in rat cortex, the gain of a neuronal response to excitatory drive are shown to be modulated by varying the level of background synaptic input.

Changing the Level of

Background Input

Modulates Gain

Summary

• Gain modulation is a prominent feature of neuronal activity recorded in behaving animals, but the mechanism by which it occurs is still not clear.

• Gain modulation is very close to multiplicative. However, its essential feature is nonlinearity.

• Gain fields have been implicated in eye and reaching movements, spatial perception, attention, navigation, and object recognition.