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 (?)  HVc  RA  Respiration/Syrinx Song Production Auditory Feedback Red: Anterior Forebrain Pathway (AFP) HVc  Area  DLM  lMAN  Area X HVc Control and Song Maintenance From 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 HVc  RA 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 ms. Zebra Finch bout (song) is about 2- 3 motifs (Hahnloser, Kozhevnikov, and Fee 2002)

Auditory Feedback Time difference in signal from HVc  RA and HVc  AFP  RA 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 HVc  RA connections. The alteration of these connections during song learning sets up wiring in song “junction box” (RA). This suggests a critical timing of about ms.  dynamics of AFP and timing of signals from HVc  AFP  RA: origin of “40 ms”  RA  DLM connection to stabilize synaptic plasticity at HVc  RA junction We won’t be discussing:  connectivity of HVc  RA 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

HVc  RA 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 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 ( Hz) HVc signals We model “whole” RA with oscillations, etc. Stark and Perkel, 1999

RA RA PN From HVc From lMAN RA IN RA PN To DLM IN Excitation Inhibition At “rest” (no song) RA PN oscillates at Hz; RA IN is silent

We present bursts of N HVc spikes with fixed interspike intervals (ISIs) to RA neurons and ΔT later present N lMAN spikes. We determine V RA (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. 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. N HVc N lMAN ΔT Time

Mg 2+ NMDA Receptor AMPA Receptor Voltage Gated Calcium Channel [Ca 2+ ](t) = Ca(t) V post (t) V pre (t) action potential leads to release of neurotransmitter-- glutamate Postsynaptic Membrane Presynaptic Membrane RA Neuron PN From HVc or lMAN

Phenomenological Connection between Ca elevation and Δg

Spike Timing Induction Protocol Time Action potential arrives at presynaptic terminal Action potential induced in postsynaptic neuron

We present bursts of N HVc spikes with fixed interspike intervals (ISIs) to RA neurons and ΔT later present N lMAN spikes. Using a simple voltage equation for RA membrane voltage, we determine V RA (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. N HVc N lMAN ΔT Time

Crystallization of song Δg RA =0 Stable?? Lesion lMAN Δg RA =0

Dynamics of the Anterior Forebrain Pathway

Auditory Feedback AFP: HVc  X  DLM  lMAN  X  RA

HVc Area X DLM lMAN RA Motor Instructions Auditory Feedback Motor Signaling AFP Excitation 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 Hz.

Timing for signals to traverse the AFP depends on distribution of inhibition and excitation. In a coarse grained sense, the ratio R IE = g I /g E determines time delay

Burst of spikes arrives from HVc at X at t = 4000 ms R IE = 4

Burst of spikes arrives from HVc at X at t = 4000 ms

HVc Area X DLM lMAN RA Motor Instructions Auditory Feedback Motor Signaling Now connect in RA  DLM link

With RA  DLM 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 HVc  RA AMPA strength set at the initial condition g RA (0), then we compute g RA (1) = g RA (0)+Δg RA (0), g RA (2) = g RA (1)+Δg RA (1),.…, g RA (N) = g RA (N-1)+Δg RA (N-1). This is a nonlinear map g RA (N)  g RA (N+1). The results for large N depend on R IE and g RA (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 HVc  RA PNs !!! Where is tutor template? How does auditory feedback work? What are the dynamics of HVc? WLC???