Transcript High Conductances - New York University

Activity Dependent Conductances:
An “Emergent” Separation of Time-Scales
David McLaughlin
Courant Institute & Center for Neural Science
New York University
[email protected]
Input Layer of Primary Visual Cortex (V1)
for Macaque Monkey
Modeled at :
Courant Institute of Math. Sciences
& Center for Neural Science, NYU
In collaboration with:
Robert Shapley (Neural Sci)
Michael Shelley
Louis Tao
Jacob Wielaard
Visual Pathway: Retina --> LGN --> V1 --> Beyond
Our Model
• A detailed, fine scale model of a local patch of
input layer of Primary Visual Cortex;
• Realistically constrained by experimental data;
Refs: McLaughlin, Shapley, Shelley & Wielaard
--- PNAS (July 2000)
--- J Neural Science (July 2001)
Today  --- J Neural Science (submitted, 2001)
Equations of the Model
 = E,I
vj -- membrane potential
--  = Exc, Inhib
-- j = 2 dim label of location on
cortical layer
-- 16000 neurons per sq mm
(12000 Exc, 4000 Inh)
VE & VI -- Exc & Inh Reversal Potentials (Constants)
Conductance Based Model
 = E,I
Schematic of Conductances
gE(t) = gLGN(t) + gnoise(t) + gcortical(t)
Conductance Based Model
 = E,I
Schematic of Conductances
gE(t) = gLGN(t) + gnoise(t) + gcortical(t)
(driving term)
Conductance Based Model
 = E,I
Schematic of Conductances
gE(t) = gLGN(t) + gnoise(t) + gcortical(t)
(driving term)
(synaptic noise)
(synaptic time scale)
Conductance Based Model
 = E,I
Schematic of Conductances
gE(t) = gLGN(t) + gnoise(t) + gcortical(t)
(driving term)
(synaptic noise)
(synaptic time scale)
(cortico-cortical)
(LExc > LInh)
(Isotropic)
Conductance Based Model
 = E,I
Schematic of Conductances
gE(t) = gLGN(t) + gnoise(t) + gcortical(t)
(driving term)
(synaptic noise)
(synaptic time scale)
Inhibitory Conductances:
gI(t) = gnoise(t) + gcortical(t)
(cortico-cortical)
(LExc > LInh)
(Isotropic)
Integrate & Fire Model
 = E,I
Spike Times:
tjk = kth spike time of jth neuron
Defined by:
vj(t = tjk ) = 1,
vj(t = tjk + ) = 0
Conductances from Spiking Neurons

LGN & Noise


Spatial Temporal
Cortico-cortical
Here tkl (Tkl) denote the lth spike time of kth neuron
Elementary Feature Detectors
Individual neurons in V1 respond preferentially to
elementary features of the visual scene (color,
direction of motion, speed of motion, spatial
wave-length).
Elementary Feature Detectors
Individual neurons in V1 respond preferentially to
elementary features of the visual scene (color,
direction of motion, speed of motion, spatial
wave-length).
Three important features:
Elementary Feature Detectors
Individual neurons in V1 respond preferentially to
elementary features of the visual scene (color,
direction of motion, speed of motion, spatial
wave-length).
Three important features:
• Spatial location (receptive field of the neuron)
Elementary Feature Detectors
Individual neurons in V1 respond preferentially to
elementary features of the visual scene (color,
direction of motion, speed of motion, spatial
wave-length).
Three important features:
• Spatial location (receptive field of the neuron)
•
Spatial phase  (relative to receptive field center)
Elementary Feature Detectors
Individual neurons in V1 respond preferentially to
elementary features of the visual scene (color,
direction of motion, speed of motion, spatial
wave-length).
Three important features:
• Spatial location (receptive field of the neuron)
•
•
Spatial phase  (relative to receptive field center)
Orientation  of edges.
Grating Stimuli
Standing & Drifting
Two Angles:
Angle of orientation -- 
Angle of spatial phase -- 
(relevant for standing gratings)
Orientation Tuning Curves
(Firing Rates Vs Angle of Orientation)
Spikes/sec 
Terminology:
• Orientation Preference
• Orientation Selectivity
Measured by “ Half-Widths” or “Peak-to-Trough”
Orientation Preference
Orientation Preference
• Model neurons receive their
orientation preference
from convergent LGN input;
Orientation Preference
• Model neurons receive their
orientation preference
from convergent LGN input;
• How does the orientation preference k of the kth
cortical neuron depend upon the neuron’s
location k = (k1, k2) in the cortical layer?
Cortical Map of
Orientation Preference
• Optical Imaging
Blasdel, 1992
----
• Outer layers (2/3) of V1
----

500 

• Color coded for angle of
orientation preference
 right
eye
 left
eye
Pinwheel
Centers
4 Pinwheel Centers
1 mm x 1 mm
Active Model Cortex - High Conductances
When the model performs realistically, with respect to
biological measurements –
with proper
-- firing rates
-- orientation selectivity (tuning width & diversity)
-- linearity of simple cells
the numerical cortex resides in a state of high conductance,
with inhibitory conductances dominant!
The next few slides demonstrate this “cortical operating point”
\
Conductances Vs Time
• Drifting Gratings -- 8 Hz
• Turned on at t = 1.0 sec
• Cortico-cortical
excitation weak relative to LGN;
inhibition >> excitation
Distribution of Conductance
Within the Layer
Sec-1
<gT> = Time Average 
SD(gT) = Standard Deviation
Of Temporal Fluctuations 
Sec-1
Active Model Cortex - High Conductances
• Background Firing Statistics
====> gBack = 2-3 gslice
Active Model Cortex - High Conductances
• Background Firing Statistics
====> gBack = 2-3 gslice
• Active operating point
====> gAct = 2-3 gBack = 4-9 gslice
Active Model Cortex - High Conductances
• Background Firing Statistics
====> gBack = 2-3 gslice
• Active operating point
====> gAct = 2-3 gBack = 4-9 gslice
====> gInh >> gExc
Active Model Cortex - High Conductances
• Background Firing Statistics
====> gBack = 2-3 gslice
• Active operating point
====> gAct = 2-3 gBack = 4-9 gslice
====> gInh >> gExc
• Consistent with experiment
Hirsch, et al,
J. Neural Sci ‘98;
Borg-Graham, et al, Nature ‘98;
Anderson, et al, J. Physiology ‘00
Active Cortex - Consequences of High
Conductances
• Separation of time scales ;
Active Cortex - Consequences of High
Conductances
• Separation of time scales ;
• Activity induced g = gT-1 << syn (actually, 2 ms << 4 ms)
Conductance Based Model
 = E,I
dv/dt = - gT(t) [ v - VEff(t) ],
where gT(t) denotes the total conductance, and
VEff(t) = [VE gEE(t) - | VI | gEI(t) ] [gT(t)]-1
If [gT(t)] -1 << syn  v  VEff(t)
But the separation is only a factor of 2
(g = gT-1 = 2 ms;
syn =4 ms)
Is this enough for the time scales to be
“well separated” ?
Active Cortex - Consequences of High
Conductances
Membrane potential ``instantaneously’’ tracks
conductances on the synaptic time scale.
V(t) ~ VEff(t) =
[V
E
gEE(t) - | VI | gEI(t)
] [g (t)]
where gT(t) denotes the total conductance
T
-1
High Conductances in Active Cortex  Membrane Potential
Tracks Instantaneously “Effective Reversal Potential”
Active
Background
Effects of
Scale Separation
g = 2 syn
____(Red) = VEff(t)
____(Green) = V(t)
g = syn
g = ½ syn
Fluctuation-driven
spiking
(very noisy dynamics,
on the synaptic time scale)
Solid:
average
( over 72 cycles)
Dashed: 10 temporal
trajectories
Coarse-Grained Asymptotics
Coarse-Grained Asymptotics
• Using the spatial regularity of cortical maps (such as
orientation preference), we “coarse grain” the cortical layer
into local cells or “placquets”.
Cortical Map of
Orientation Preference
• Optical Imaging
Blasdel, 1992
----
• Outer layers (2/3) of V1
----

500 

• Color coded for angle of
orientation preference
 right
eye
 left
eye
Coarse-Grained Asymptotics
• Using the spatial regularity of cortical maps (such as
orientation preference), we “coarse grain” the cortical layer
into local cells or “placquets”.
Coarse-Grained Asymptotics
• Using the spatial regularity of cortical maps (such as
orientation preference), we “coarse grain” the cortical layer
into local cells or “placquets”.
• Using the separation of time scales which emerge from
cortical activity, g << syn
Coarse-Grained Asymptotics
• Using the spatial regularity of cortical maps (such as
orientation preference), we “coarse grain” the cortical layer
into local cells or “placquets”.
• Using the separation of time scales which emerge from
cortical activity, g << syn
Coarse-Grained Asymptotics
• Using the spatial regularity of cortical maps (such as
orientation preference), we “coarse grain” the cortical layer
into local cells or “placquets”.
• Using the separation of time scales which emerge from
cortical activity, g << syn
• Together with an averaging over the random cortical
maps (such as spatial phase, De Angelis, et al ‘99)
Coarse-Grained Asymptotics
• Using the spatial regularity of cortical maps (such as
orientation preference), we “coarse grain” the cortical layer
into local cells or “placquets”.
• Using the separation of time scales which emerge from
cortical activity, g << syn
• Together with an averaging over the irregular cortical
maps (such as spatial phase)
• we derive a coarse-grained description in terms of the
average firing rates of neurons within each placquet
[--- a form of Cowan – Wilson Eqs (1973)]

Uses of Coarse-Grained Eqs
Uses of Coarse-Grained Eqs
• Unveil mechanims for
(i) Better orientation selectivity near
pinwheel centers
(ii) Balances for simple and complex cells
• Input-output relations at high conductance
• Comparison of the mechanisms and performance
of distinct models of the cortex
• Most importantly, much faster to integrate;
• Therefore, potential parameterizations for more
global descriptions of the cortex.
Active Cortex - Consequences of High
Conductances
Cortical activity induces a separation of time scales
(with the synaptic time scale no longer the shortest),
Thus, cortical activity can convert neurons from integrators to
burst generators & coincidence detectors.
 For transmission of information:
“Input” temporal resolution -- synaptic time scale syn ;
“Output” temporal resolution -- g = gT-1
Summary: One Model of Local Patch of V1
• A detailed fine scale model -- constrained in its construction and
performance by experimental data ;
• Orientation selectivity & its diversity from cortico-cortical activity,
with neurons more selective near pinwheels;
• Linearity of Simple Cells -- produced by (i) averages over spatial
phase, together with cortico-cortical overbalance for inhibition;
• Complex Cells -- produced by weaker (and varied) LGN input,
together with stronger cortical excitation;
• Operates in a high conductance state -- which results from cortical
activity, is consistent with experiment, and makes integration
times shorter than synaptic times, a separation of temporal scales
with functional implications;
• Together with a coarse-grained asymptotic reduction -- which unveils
cortical mechanisms, and will be used to parameterize or
``scale-up’’ to larger more global cortical models.
Scale-up & Dynamical Issues
for Cortical Modeling
• Temporal emergence of visual perception
• Role of temporal feedback -- within and between cortical
layers and regions
• Synchrony & asynchrony
• Presence (or absence) and role of oscillations
• Spike-timing vs firing rate codes
• Very noisy, fluctuation driven system
• Emergence of an activity dependent, separation of time
scales
• But often no (or little) temporal scale separation
Distribution of Conductances Over Sub-Populations
“FAR” & “NEAR” Pinwheel Centers
<gT> = Time Average 
SD(gT) = Stand Dev of
Temporal Fluctuations 
One application of Coarse-Grained Equations
Why the Primary Visual Cortex?
Why the Primary Visual Cortex?
Elementary processing, early in visual pathway
Neurons in V1 detect elementary features of the visual scene,
such as spatial frequency, direction, & orientation
Why the Primary Visual Cortex?
Elementary processing, early in visual pathway
Neurons in V1 detect elementary features of the visual scene,
such as spatial frequency, direction, & orientation
Vast amount of experimental information about V1
Why the Primary Visual Cortex?
Elementary processing, early in visual pathway
Neurons in V1 detect elementary features of the visual scene,
such as spatial frequency, direction, & orientation
Vast amount of experimental information about V1
Input from LGN well understood (Shapley, Reid, …)
Anatomy of V1 well understood (Lund, Callaway, ...)
Why the Primary Visual Cortex?
Elementary processing, early in visual pathway
Neurons in V1 detect elementary features of the visual scene,
such as spatial frequency, direction, & orientation
Vast amount of experimental information about V1
Input from LGN well understood (Shapley, Reid, …)
Anatomy of V1 well understood (Lund, Callaway, ...)
The cortical region with finest spatial resolution --
Why the Primary Visual Cortex?
Elementary processing, early in visual pathway
Neurons in V1 detect elementary features of the visual scene,
such as spatial frequency, direction, & orientation
Vast amount of experimental information about V1
Input from LGN well understood (Shapley, Reid, …)
Anatomy of V1 well understood (Lund, Callaway, ...)
The cortical region with finest spatial resolution -Detailed visual features of input signal;
Why the Primary Visual Cortex?
Elementary processing, early in visual pathway
Neurons in V1 detect elementary features of the visual scene,
such as spatial frequency, direction, & orientation
Vast amount of experimental information about V1
Input from LGN well understood (Shapley, Reid, …)
Anatomy of V1 well understood (Lund, Callaway, ...)
The cortical region with finest spatial resolution -Detailed visual features of input signal;
Fine scale resolution available for possible representation;