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Dynamics and Timing in Birdsong
Henry D. I. Abarbanel
Department of Physics
and
Marine Physical Laboratory (Scripps Institution of Oceanography)
Center for Theoretical Biological Physics
University of California, San Diego
Leif Gibb, Gabriel Mindlin, Misha Rabinovich, Sachin Talathi
Conversations with Michael Brainard, Allison Doupe, David Perkel
Green:
Pre-motor Pathway
NIf (?)HVcRA
Respiration/Syrinx
Song Production
Auditory Feedback
Red:
Anterior Forebrain Pathway (AFP)
HVcArea DLM
lMANArea X
HVc
Control and Song MaintenanceFrom Brainard and Doupe, 2002
Songbox
(Brainard and Doupe 2002)
Tutor sings during sensory period. Bird memorizes template Bird sings own song; learns
memorized song matching template-- sensorimotor period.
Song “matches” template and reaches crystallization
Auditory Feedback
Deafen Juvenile—song develops “incorrectly”
Lesion lMAN in juvenile---song mismatches template; crystallization occurs early.
Deafen adult—song slowly degrades
Lesion lMAN in adult--song stable
Deafen adult and lesion lMAN—song stable
Lesion HVc or RA—no song produced -------------------------
lMAN (and AFP) important in maintaining song when auditory feedback works—not deaf
When bird sings, HVc-->RA fires sparse bursts of spikes: one burst of 4.5 ± 2 spikes in 6.1 ± 2 ms in each motif. RA neurons fire 13 times more often, suggests one-to-many HVcRA connections
HVc acts as driver of song instructions. RA acts as “junction box” distributing commands to motor processes.
Song is group of motifs—about 1 sec each—composed of groups of syllables—about 100-300 ms.
Zebra Finch bout (song) is about 2-3 motifs
(Hahnloser, Kozhevnikov, and Fee 2002)
Auditory Feedback
Time difference in signal from HVcRA and HVcAFPRA is measured to be 50 ±10 ms.
AFP nuclei act as a population
Dynamics of AFP—X, DLM, lMAN is important
Kimpo, Theunissen, Doupe, 2003
We will discuss three topics:
plasticity at HVcRA connections. The alteration of these connections during song learning sets up
wiring in song “junction box” (RA).
This suggests a critical timing of about 40-50 ms.
dynamics of AFP and timing of signals from HVcAFPRA: origin of “40 ms”
RADLM connection to stabilize synaptic plasticity at HVcRA junction
We won’t be discussing:
connectivity of HVcRA in producing song syllables
A full theory, which we do not have, would connect HVc sparse bursts with auditory feedback and command signals from brain.
It would trace HVc signals to RA, directly and through AFP, and explain evaluation of produced song through auditory feedback to HVc.
At best we have the beginning of a quantitative picture of the timing issues in the neural part of this loop.
HVc
Area X
DLM
lMAN
RA
Motor Instructions Auditory Feedback
Motor Signaling
AFP
Excitation
Inhibition
HVcRA Plasticity
In adult zebra finch HVc signals arrive at dendritic location with about 1:1 NMDA to AMPA receptors.
In adult zebra finch lMAN signals arrive at RA dendritic locations with 10:1 NMDA to AMPA.
RA projection neurons (PNs) oscillate at 15-30 Hz “at rest”—i.e. no song. When singing begins, global inhibition in RA puts these PNs into small subthreshold variations. These are then driven by high frequency (500-600 Hz) HVc signals
We model “whole” RA with oscillations, etc.
Stark and Perkel, 1999
RA RAPN
From HVcFrom lMAN
RAIN
RAPN
To DLMIN
Excitation
InhibitionAt “rest” (no song) RA PN
oscillates at 15-30 Hz; RA IN is silent
We present bursts of NHVc spikes with fixed interspike intervals (ISIs) to RA neurons and ΔT later present NlMAN spikes. We determine VRA(t) from HH equations. Then using a calcium flux equation we determine from which, using a phenomenological connection between elevation over equilibrium intracellular Ca, we determine Δg for AMPA receptors.
2[ ]( )Ca t
2[ ]( )Ca t
The idea, following the observations of Yang, Tang, and Zucker, 1999 is that long term changes in Δg, LTP and LTD, can be induced by postsynaptic Ca changes alone. The mechanisms leading from Ca elevation to changes in Δg are not fully known.
NHVc NlMANΔT
Time
_ _
_ _
_ _
_ _
( )( ) ( ) ( )
( ) ( )
( ) ( ( )) ( , ( ))( ( ))
( ) ( , ( ))(
RAM ion currents HVc NMDA HVc AMPA
lMAN NMDA lMAN AMPA
HVc NMDA NH RA N HVc REV NMDA RA
HVc AMPA AH A HVc REV AMPA R
dV tC I t I t I t
dtI t I t
I t g B V t S t V t E V t
I t g S t V t E V
_ _
_ _
( ))
( ) ( ( )) ( , ( ))( ( ))
( ) ( , ( ))( ( ))
A
lMAN NMDA Nl RA N lMAN REV NMDA RA
lMAN AMPA Al A lMAN REV AMPA RA
t
I t g B V t S t V t E V t
I t g S t V t E V t
0
1 0
0
2+ 0.062 /
( , ( )) ( ( )) ( , ( ))
( ( ( )))
( ) is a "step function". 0, when V<0; 1, when V>0.
Magnesium block of NMDA receptors:
1 B(V)=
(1+0.288[Mg ] )
i pre pre i pre
i i pre
V mV
dS t V t S V t S t V t
dt S S V t
S V
e
0_ _
_ _
_ _
_ _
( ) ( )( ) ( )
( ) ( )
( ) ( ( )) ( , ( ))( ( ))
( ) ( , ( ))( ( ))
HVc NMDA HVc AMPAC
lMAN NMDA lMAN AMPA
HVc NMDA NC RA N HVc REV NMDA RA
HVc AMPA AC A HVc REV AMPA RA
lMA
dCa t C Ca tC t C t
dt
C t C t
C t g B V t S t V t E V t
C t g S t V t E V t
C
_ _
_ _
( ) ( ( )) ( , ( ))( ( ))
( ) ( , ( ))( ( ))
N NMDA NC RA N lMAN REV NMDA RA
lMAN AMPA AC A lMAN REV AMPA RA
t g B V t S t V t E V t
C t g S t V t E V t
Mg2+
NMDA Receptor
AMPA Receptor
Voltage Gated Calcium Channel
[Ca2+](t) = Ca(t)
Vpost(t)
Vpre(t) action potential leads to release of neurotransmitter--glutamate
Postsynaptic Membrane
Presynaptic Membrane
RA Neuron PN
From HVc or lMAN
0
0
0
0
( ) "puts" phosphates on AMPA driven by ( ) -
( ) "deletes" phosphates from AMPA drive n by ( ) -
( ) ( )( ( ) )(1 ( )) ( )
( ) ( )( ( ) )(1 ( ))
L
P P LP P
D
D
P t Ca t C
D t Ca t C
dP t P t xf Ca t C P t f x
dt x
dD t D tf Ca t C D t
dt
( )
( ) ( ( ) ( ) ( ) ( ) )
M
D MD
xf x
x
d g tP t D t D t P t
dt
Phenomenological Connection between Ca elevation and Δg
Spike Timing Induction Protocol
Time
pret ; 0 herepost pret t
Action potential arrives at presynaptic terminal
Action potential induced in postsynaptic neuron
We present bursts of NHVc spikes with fixed interspike intervals (ISIs) to RA neurons and ΔT later present NlMAN spikes. Using a simple voltage equation for RA membrane voltage, we determine VRA(t). Then using a calcium flux equation we determine from which, using a phenomenological connection between elevation over equilibrium intracellular Ca, we determine Δg for AMPA receptors.
2[ ]( )Ca t
2[ ]( )Ca t
NHVc NlMANΔT
Time
Crystallization of song gRA=0
Stable??
Lesion lMAN gRA=0
T
Dynamics of the Anterior Forebrain Pathway
Auditory Feedback
AFP:
HVc
XDLMlMANX
RA
HVc
Area X
DLM
lMAN
RA
Motor Instructions Auditory Feedback
Motor Signaling
AFPExcitation
Inhibition
Signal from HVc activates SN which inhibits AF allowing DLM to fire.
With no input SN cells are at rest;
AF cells fire periodically at 15-30 Hz.
Timing for signals to traverse the AFP depends on distribution of inhibition and excitation. In a coarse grained sense, the ratio RIE = gI/gE determines time delay
Burst of spikes arrives from HVc at X at t = 4000 ms
RIE = 4
48 msT
Burst of spikes arrives from HVc at X at t = 4000 ms
IE I ER = g /g
HVc
Area X
DLM
lMAN
RA
Motor Instructions Auditory Feedback
Motor Signaling
Now connect in RADLM link
With RADLM connection in we present N = 1,2 , … bursts from HVc to RA and to Area X. Each burst is 5 spikes with ISI = 2 ms.
Before spiking we have the HVcRA AMPA strength set at the initial condition gRA(0), then we compute gRA(1) = gRA(0)+ΔgRA(0), gRA(2) = gRA(1)+ΔgRA(1), .…, gRA(N) = gRA(N-1)+ΔgRA(N-1) .
This is a nonlinear map gRA(N) gRA(N+1). The results for large N depend on RIE and gRA(0), as ever with such maps.
Auditory Feedback
Can we change AFP time delay with neuromodulators??
Can we block GABA or decrease inhibition in AFP? or excitation?
Dopamine is known to modulate excitation in Area X.
Tests of properties of RA—DLM connection.
Plasticity not yet found at HVcRA PNs !!!
Where is tutor template?
How does auditory feedback work?
What are the dynamics of HVc? WLC???
