Activity Dependent Conductances: An

1
Activity Dependent ConductancesAn Emergent
Separation of Time-Scales

• David McLaughlin
• Courant Institute Center for Neural Science
• New York University
• dmac_at_courant.nyu.edu

2
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

3
Visual Pathway Retina --gt LGN --gt V1 --gt Beyond
4
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)
• --- J Neural Science (submitted, 2001)

Today ?
5
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)


6
Conductance Based Model
? E,I
Schematic of Conductances

g?E(t) gLGN(t) gnoise(t)
gcortical(t)
7
Conductance Based Model
? E,I
Schematic of Conductances

g?E(t) gLGN(t) gnoise(t)
gcortical(t) (driving term)

8
Conductance Based Model
? E,I
Schematic of Conductances

g?E(t) gLGN(t) gnoise(t)
gcortical(t) (driving term)
(synaptic noise)
(synaptic time scale)

9
Conductance Based Model
? E,I
Schematic of Conductances

g?E(t) gLGN(t) gnoise(t)
gcortical(t) (driving term)
(synaptic noise) (cortico-cortical)
(synaptic time scale)
(LExc gt LInh) (Isotropic)
10
Conductance Based Model
? E,I
Schematic of Conductances

g?E(t) gLGN(t) gnoise(t)
gcortical(t) (driving term)
(synaptic noise) (cortico-cortical)
(synaptic time scale)
(LExc gt LInh)
(Isotropic) Inhibitory Conductances g?I(t)
gnoise(t) gcortical(t)
11
Integrate Fire Model
? E,I
Spike Times tjk kth spike time of jth
neuron Defined by vj?(t tjk ) 1, vj?(t
tjk ?) 0
12
Conductances from Spiking Neurons
?
?
?
LGN Noise Spatial Temporal
Cortico-cortical
Here tkl (Tkl) denote the lth spike time of
kth neuron
13
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).

14
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

15
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)

16
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)

17
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.

18

Grating Stimuli Standing Drifting
Two Angles Angle of orientation -- ? Angle
of spatial phase -- ? (relevant for standing
gratings)
19
Orientation Tuning Curves(Firing Rates Vs Angle
of Orientation)
Spikes/sec ?

• Terminology
• Orientation Preference
• Orientation Selectivity
• Measured by Half-Widths or Peak-to-Trough

20
Orientation Preference

21
Orientation Preference

• Model neurons receive their
• orientation preference
• from convergent LGN input

22
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 neurons
• location k (k1, k2) in the cortical layer?

23
Cortical Map of Orientation Preference

• Optical Imaging
• Blasdel, 1992
• Outer layers (2/3) of V1
• Color coded for angle of
• orientation preference

---- ? 500 ? ? ----
? right eye ? left eye
24
Pinwheel Centers
25
4 Pinwheel Centers
1 mm x 1 mm
26
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 \
27

• Conductances Vs Time
• Drifting Gratings -- 8 Hz
• Turned on at t 1.0 sec
• Cortico-cortical
• excitation weak relative to LGN
• inhibition gtgt excitation

28
Distribution of Conductance Within the
Layer ltgTgt Time Average ? SD(gT)
Standard Deviation Of Temporal Fluctuations ?
Sec-1
Sec-1
29
(No Transcript)
30
Active Model Cortex - High Conductances

• Background Firing Statistics
• gt gBack 2-3 gslice

31
Active Model Cortex - High Conductances

• Background Firing Statistics
• gt gBack 2-3 gslice
• Active operating point
• gt gAct 2-3 gBack 4-9 gslice

32
Active Model Cortex - High Conductances

• Background Firing Statistics
• gt gBack 2-3 gslice
• Active operating point
• gt gAct 2-3 gBack 4-9 gslice
• gt gInh gtgt gExc

33
Active Model Cortex - High Conductances

• Background Firing Statistics
• gt gBack 2-3 gslice
• Active operating point
• gt gAct 2-3 gBack 4-9 gslice
• gt gInh gtgt gExc
• Consistent with experiment
• Hirsch, et al, J. Neural Sci 98
• Borg-Graham, et al, Nature 98
• Anderson, et al, J. Physiology 00

34
Active Cortex - Consequences of High Conductances

• Separation of time scales

35
Active Cortex - Consequences of High Conductances

• Separation of time scales
• Activity induced ?g gT-1 ltlt ?syn (actually, 2
  ms ltlt 4 ms)

36
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 ltlt ?syn ? v ? VEff(t)


37
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 ?
38
Active Cortex - Consequences of High Conductances

• Membrane potential instantaneously tracks
  conductances on the synaptic time scale.
• V(t) VEff(t) VE gEE(t) - VI gEI(t)
  gT(t)-1
• where gT(t) denotes the total conductance

39
High Conductances in Active Cortex ? Membrane
Potential Tracks Instantaneously Effective
Reversal Potential
Active
Background
40
Effects of Scale Separation
?g 2 ?syn ?g ?syn ?g ½ ?syn
____(Red) VEff(t) ____(Green) V(t)
41
Fluctuation-driven spiking
(very noisy dynamics, on the synaptic time scale)
Solid average ( over 72
cycles) Dashed 10 temporal trajectories
42
Coarse-Grained Asymptotics
43
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.

44
Cortical Map of Orientation Preference

• Optical Imaging
• Blasdel, 1992
• Outer layers (2/3) of V1
• Color coded for angle of
• orientation preference

---- ? 500 ? ? ----
? right eye ? left eye
45
(No Transcript)
46
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.

47
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 ltlt ?syn

48
(No Transcript)
49
(No Transcript)
50
(No Transcript)
51
(No Transcript)
52
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 ltlt ?syn

53
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 ltlt ?syn
• Together with an averaging over the random
  cortical maps (such as spatial phase, De Angelis,
  et al 99)

54
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 ltlt ?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)

55
?
56
Uses of Coarse-Grained Eqs
57
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.

58
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

59
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.

60
(No Transcript)
61
Scale-up Dynamical Issuesfor 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

62
(No Transcript)
63
Distribution of Conductances Over
Sub-Populations FAR NEAR Pinwheel Centers
ltgTgt Time Average ? SD(gT) Stand
Dev of Temporal Fluctuations ?
64
One application of Coarse-Grained Equations
65
(No Transcript)
66
(No Transcript)
67
(No Transcript)
68
(No Transcript)
69
(No Transcript)
70
(No Transcript)
71
(No Transcript)
72
(No Transcript)
73
(No Transcript)
74
(No Transcript)
75

• Why the Primary Visual Cortex?

76

• 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

77

• 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

78

• 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,
  ...)

79

• 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 --

80

• 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

81

• 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

82
(No Transcript)
83
(No Transcript)
84
(No Transcript)
85
(No Transcript)