Alla Borisyuk
Department of Mathematics and
Neuroscience graduate program
University of Utah

• Steve Odom (U. of Utah, Mathematics)
• Gary Rose (U. of Utah, Biology)
• Christopher Leary (U. of Mississippi, Biology)
• NSF,NIH

Rise time discrimination is important in auditory processing
Human data
J. Hämäläinen et al. Brain and Language, 2005

Hyla versicolor
Hyla chrysoscelis
Tetraploid
Long calls
Slow rise time
Similar looking
Share habitat
Diploid
Short calls
Fast rise time http://species.wikimedia.org

• Behaviorally: prefer sounds with conspecific envelope
• Electrophysiology:
Cells in Hyla versicolor midbrain prefer conspecific (slow rise) calls

Cells in Hyla versicolor midbrain prefer conspecific (slow rise) calls

Where in the brain is the recording?
Richards et al. Front. Syn. Neurosci. (2010)
8 th nerve
Superior Olive
Inferior Colliculus
Cochlear Nucleus

What are the mechanisms of the slow rise-time selectivity?
• Does it arise in the inferior colliculus or is it inherited from the lower level structures?
• Is it a network or a single-cell property?

What are the mechanisms of the slow rise-time selectivity?
• Does it arise in the inferior colliculus or is it inherited from the lower level structures?
• Is it a network or a single-cell property?
• We don’t know
• I will show preliminary data and suggested possible mechanisms realized in computational models

What information can we gain from data?
• In vivo , intracellular, current clamp
• Record responses to slow rise and fast rise
• Hyperpolarizing current injections, record voltage in response to stimulus
I
1
→ V
1
(t)
I
2
→ V
2
(t)
• Assume: no active currents at these voltages

I
1
→ V
1
(t)
I
2
→ V
2
(t)
C V'=-g(V-V
L
)-g
E
(V-V
E
)-g
I
(V-V
I
)+I
1
C V'=-g(V-V
L
)-g
E
(V-V
E
)-g
I
(V-V
I
)+I
• Assume: we can estimate C, g, V
E
, V
I
• For every time step the equations become
2
A
1 g
E
+B
1 g
I
=C
1
A
2 g
E
+B
2 g
I
=C
2
Priebe and Ferster, Neuron, 2005

g
I
A
1 g
E
+B
1 g
I
=C
1
A
1 g
E
+B
1 g
I
=C
1
Checks: a) More current levels b)Block active current c) Predict voltage without current clamp g
E
Priebe and Ferster, Neuron, 2005

Example of E and I conductance reconstruction, I

Example of E and I conductance reconstruction, II

Detour: How do you reconstruct with three input conductances?
C V’=-g(V-V
L
)-g
1
(V-V
1
)-g
2
(V-V
2
) )-g
3
(V-V
3
)+I
Record with I
1,
I
2,
I
3
Solve the system for g
1, g
2,
The matrix is degenerate
 g
3
Odom, Borisyuk, in preparation

Detour: How do you reconstruct with three input conductances?
Idea: use stochastic version of the equation
I
1
→ V
1
(t)
Δt
Use relationships between means and variances of voltage distribution from one time step to another
Odom, Borisyuk, in preparation

Detour: How do you reconstruct with three input conductances?
C (V n+1 -V n )/(Δt)=-g(V n -V
L
)-Σg i n (1+ξ i
)(V
•
Superscript n refers to the n-th time step n -V i
) +I
•
Subscript i refers to the i-th conductance
• ξ i are independent, Normally distributed with 0 mean and standard deviation
σ i

Detour: How do you reconstruct with three input conductances?
Constraints on conductances:

From the means (same as before): g
2= g
2
( g
1
)
, g
3=

Condition on variances: g
3
( g
1
)
σ(
V n+1
)=
σ(
V n
,
ξ g1,
ξ g2
, ξ g3
)
Odom, Borisyuk, in preparation

Detour: Example of 3 conductance reconstruction from a model
Odom, Borisyuk, in preparation

Relaxing the assumptions (towards reconstructing with real data)
Error of reconstruction = mean(| g rec
-g actual
|)

Mechanisms of slow rise time selectivity
• 3 hypotheses (computational models):
- Fast rise sensitive inhibition
- Slowly inactivating inhibition
- Interval counting with adaptation

Mechanisms of slow rise time selectivity
• 3 hypotheses (computational models):
- Fast rise sensitive inhibition
- Slowly inactivating inhibition
- Interval counting with adaptation
• For each model:
- Compatibility with data
- Supporting evidence (mostly indirect)
• Predictions that will support/falsify models, and distinguishes between models (in progress)

Hypothesis 1:
Fast rise sensitive inhibition
E
IC
I
Fast-rise sensitive

• Appropriately timed (delayed and fast onset) negative feedback. Possibly:
- local negative feedback loop (as in the electric fish [Rose and Heiligenberg, 1985])
E
IC
I
I

• Appropriately timed (delayed and fast onset) negative feedback. Possibly:
- local negative feedback loop (as in the electric fish [Rose and Heiligenberg, 1985])
- intracellular (e.g. in the form of low voltage potassium current, KLT, as in mammalian and avian cochlear nucleus [Manis and Marx
1991])

Realization of fast rise sensitive inhibition mechanism
CV’=-I
L
-I
Na
-I
KHT
-I h
-I
KLT
+S(t)
Rothman and Manis 2003

Realization of fast rise sensitive inhibition mechanism
E
IC
I

Realization of fast rise sensitive inhibition mechanism
E
IC
I

(Indirect) evidence for the fast rise sensitivity of inhibition, I
• Some aCN neurons respond much stronger to fast rising stimulus than the slowly rising stimulus
Schematic

(Indirect) evidence for the fast rise sensitivity of inhibition, II
• Evidence for differential inhibition in the conductances reconstruction

Hypothesis 2:
Inactivation of inhibition
I
E
I
IC on at rest slow

Realization of inactivating inhibition mechanism
τ
E r
E
’=-r
E
+w
E f(S)
Exponential I&F
E
I1 IC
τ
I1 r
I1
’=-r
I1
+w
I1 f(S)
I2 slow
τ
I2 r
I2
’=-r
I2
+R
12
-w
I12 f(r
1
) on at rest

I
1
E
I
2
C
I

(Indirect) evidence for slow inactivating inhibition, I
• Local release of glutamate in aIC sometimes results in pronounced slow hyperpolarization
– possible source of inhibition
• In most reconstructions the inhibitory conductances goes negative – indicates presence of tonic inhibition at rest
Reconstructed conductance = deviation from rest level

fast
Depends on time scale of slow inhibition inactivation
• Distinguishes between fast and slow if τ
I is in the right range
• Responds if the slope is low enough
Prediction slow

Hypothesis 3: interval counting in IC + adaptation in CN
Adaptation
E
Interval counting
IC

• Responds after a certain number of interpulse intervals of correct length
• An interval that is too short or too long resets counting
Edwards, Leary, Rose, 2007

Hypothesis 3: interval counting in IC + adaptation in CN
Adaptation
E
Interval counting
IC

Hypothesis 3: interval counting in IC + adaptation in CN
Adaptation
E
Interval counting
IC

V'=-g(V-V
L
)+I
0
-a+S(t)
τ a a'=-a
At reset: a(t+)=a(t-)+Δa
S(t)
E IC
Interval counting postulated

• Interval counting neurons are there
• Adaptation is there
• Time scales are feasible
• In some voltage recordings from slow rise sensitive cells it does look like voltage increases in discrete increments

• Depends on time constant of adaptation relative to the input slope
Prediction : responses for a range of slopes, but not for lower or higher slope fast
Can be used to distinguish between hypotheses experimentally slow

• Slow rise-time selectivity in Hyla versicolor midbrain
• Inputs can be reconstructed from current-clamp data
• Three conductance reconstruction can be done using relationship between voltage and conductance variances
• Three proposed mechanisms for slow rise-time sensitivity:
Fast rise sensitive inhibition
Inactivation of inhibition
Interval counting with adaptation
• Predictions: model responses as a function of input slope differ from one another
• To do: more model predictions and then more experiments