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Supplementary Materials for

Neural Correlates of a Magnetic Sense Le-Qing Wu and J. David Dickman*

*To whom correspondence should be addressed. E-mail: dickman@bcm.edu

Published 26 April 2012 on Science Express DOI: 10.1126/science.1216567

This PDF file includes:

Materials and Methods Fig. S1 References (25–30)

Other Supplementary Material for this manuscript includes the following: (available at www.sciencemag.org/cgi/content/full/science.1216567/DC1)

Movie S1

Supporting Online Materials

Materials and Methods:

Subjects and stimulation

All methods were approved by the Institutional Animal Care and Use Committee

and were in accordance with the National Institutes of Health Guidelines. Seven homing

pigeons (Columba livia) were surgically implanted with a plastic head restraint stud in

order to maintain a stable head position during stimulation (25). Single cell neural

recordings were obtained from vestibular brainstem neurons during magnetic field

stimulation while the pigeon was awake, in the dark (to reduce visual stimulation), and

placed head-fixed (to reduce vestibular stimulation) in the center of a magnetic field coil

system. An artificial magnetic field was delivered using a direct current source through

three pairs of Helmholtz coils (61 cm cube, 38 turns on each side of 1.09 mm copper wire)

driven by a computer interface (Power 1401; Cambridge Electronic Design) and custom

script software (Spike2). The ambient geomagnetic field was first measured (inclination

and amplitude) using a 3-axis magnetometer (HMC2003, Honywell) mounted directly

beneath the birds’ head, then was actively canceled to a net zero amplitude. An artificial

magnetic field vector of 100 µTesla (~2x intensity of the home laboratory) was then

generated and rotated through 360º at 10º steps (100 ms/step, total period = 3.6

s/revolution) along each of four different great planes (45 deg increments, Fig. 3).

Elevation and azimuth values were derived from Cartesian coordinates, where positive x,

y, and z axes corresponded to nasal, left ear, and vertex, respectively. Zero degrees

elevation and azimuth corresponded to a magnetic field vector directed along the positive

X axis; positive elevation and azimuth values corresponded to upward and leftward

angles, respectively (Fig. 3). Both CW (increasing direction angle, 0 – 360) and CCW

(decreasing angle, 360 – 0) magnetic vector rotation directions were alternated, with a

minimum of 10 repetitions for each presented. To examine intensity functions, four

different magnetic field amplitudes of the rotating magnetic vector including 20, 50, 100,

and 150 µT were also delivered in each of the great circle planes, for a subset of neurons.

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Neural recording and analyses

Single cell neural activity was obtained using epoxy-coated tungsten

microelectrodes (5 – 10 MΩ; FHC, Inc.) placed in guide tubes (28 gauge) and driven

vertically with a remote microdrive. All materials used for implants and recordings (head

stud, electrodes, guide-tubes) were non-magnetic to eliminate possible conductive

artifacts. Neural activity was band-pass filtered (100 – 5 KHz, Bessel), displayed on an

oscilloscope (Tektronix model 5311dn), then digitized (20KHz) and stored on computer.

From the stored data, single cells were identified by template match of waveform shape,

amplitude, and latency (Spike 2, CED, Cambridge England). Spike times were

temporally assorted into 100ms bins for each response to magnetic stimulation in each

great plane. To test for a significant response, the number of spikes per bin was compared

across all bins for the four stimulation great planes and two magnetic field rotation

directions (dependent variables). To be considered a response, the temporal modulation

in firing rate for at least one stimulation plane in either the CW or CCW rotation direction

must have been significantly different (ANOVA, p<.001) from baseline (26). Cells with

no significant modulation in any plane were considered non-responsive and not analyzed

further. As a final control, neural responses were recorded from: (1) a saline solution

substituted for a live pigeon and (2) a euthanized (non-live) pigeon brain while magnetic

stimulation was delivered, with no recorded electrical responses being observed.

Peri-stimulus time histograms (PSTHs) were made by calculating the mean firing

rate for each 100ms time bin for each stimulus plane (Fig. 3). The sensitivity and tuning

direction values for each MR cell were determined for the four great plane responses in

both the CW and CCW rotation directions. Cosine curve fits were applied to each

response using the form FR = Smax x cos(x1 • x2 + y1 • y2 + z1 • z2) + DC, where FR is

the firing rate of the cell, Smax is the maximum sensitivity response, x1;y1;z1 is the

measured response vector from which FR was obtained, x2;y2;z2 is the preferred vector,

and DC is the spontaneous firing rate. The 3D preferred direction was then calculated in

spherical coordinates from the cosine curve fits and plotted as unit vectors. A re-

sampling analysis was performed to assess whether the distribution of preferred

directions was significantly different from uniformity (27). First, the sum squared error

(across bins) between the measured distribution and an ideal uniform distribution were

2

calculated. Next, the sum squared error between the ideal distribution and a random re-

sampled (1000 repetitions) distribution was calculated. If the measured-ideal sum

squared error exceeded the 99% confidence interval of the re-sampled-ideal error, then

the measured distribution was considered to be significantly different from uniform. For

non-uniform distributions, a multimodality test was performed based on the kernel

density estimate to determine the number of modes. A von Mises method was used as

the kernel function for circular data and a Gaussian function for noncircular data. A

goodness-of-fit statistic was calculated to obtain the critical p value (Pk) of k modes

through a bootstrapping procedure (21). If Pk < 0.05 was obtained for k number of

modes, we considered the distribution to be significantly different from the next lowest

modality. As a control, the preferred directions obtained for 50 and 100 µT stimulation

amplitudes were found to be equivalent (pair-wise Sign test, p= 0.51).

The strength of the directional tuning for each neuron’s preferred response vector

was quantified using a direction discrimination index (DDI), of the

form: ( ) ( )( )MNSSESSSSDDI −÷+−÷−= 2minmaxminmax

where, Smax and Smin are the maximum and minimum cell responses from the

3D cosine fits, SSE is the sum of squared error for the mean response, N is the total

number of repetitions, and M = 8 for the four stimulation planes and CW and CCW

directions (28). DDI values range between 0 – 1, and compares the difference in the

cell’s firing rate between the preferred direction and the minimum (null) directions

against inherent variability. Values close to 1 indicate large response modulations

relative to noise, while values close to zero indicate no modulation.

For all responsive neurons, the sensitivity and tuning direction values were used

to plot Lambert cylindrical equal-area contour maps (29 - 30) illustrating cellular

sensitivity as a function of two stimulus angles: azimuth (0 – 360 degrees) and elevation

(-90 – 90 degrees). In addition, intensity functions were generated by presenting rotating

magnetic field vectors along all four great planes, for both CW and CCW directions, at

four amplitudes; 20, 50, 100, and 150µT for a subset of 9 MR cells. Intensity functions

were examined using a pairwise comparison repeated measures ANOVA and Tukey post-

hoc tests. Exponential curves of the form (f = A(1-exp(-B x X))c) were then fit to the

3

intensity function plots for each cell. Analyses were performed using MATLAB

(Mathworks Inc., Natick, MA) or PYTHON.

Histology

On the final experimental day for each of the seven birds, an electrolytic lesion

was made at the recording site location by passing DC constant current (20µA for 30s)

through the recording electrode. The animal experienced no discomfort during the

current delivery since (1) there are no pain receptors in brain tissue, (2) the lesions were

very small (<30µm diameter) made in regions distant to the dorsal column and

spinothalamic tracts, and (3) no outward signs of animal distress were exhibited. In one

bird, following the electrolytic lesion, magnetic field stimulation was delivered in order

to maximally activate the c-Fos transcription factor using a rotating field vector (150µT)

along each of 36 different elevation angles (12 each for X, Y, and Z axes; 10º increments).

Each magnetic field vector rotation required 2 minutes duration, for a total stimulation

period of 72 (2 x 36) minutes. All birds were then immediately euthanized (500 mg/kg

sodium pentobarbital i.m.) and perfused through the heart with 4% paraformaldehyde in

phosphate buffer. The brains were excised, cut into 50µm sections, and dehydrated with

a graded series of alcohols and xylene. Sections for the one c-Fos activated pigeon were

treated for dark reaction product immunohistochemistry, and were used in conjunction

with an earlier investigation (18). The sections were counterstained (Neutral red) and

photographed with a Nikon Eclipse 600 microscope.

Figure 1S. Neural responses from the representative MR cell shown in Fig. 3, to a single

cycle stimulation for four great circle plane magnetic vector (CW) rotations (gray

shaded), plotted as function of time. Each panel column shows the stimulation plane

(top), the instantaneous firing rate of the MR neuron (second panel, spikes/sec), the

amplified (1000x) and filtered (300 – 5K Hz) neural activity (third panel, MV =

millivolts), and the three magnetometer channels, Gz, Gy, and Gx (µT = micro Tesla).

Movie 1S. Neural activity to a single magnetic stimulation trial. Neural firing rate of

MR cell shown in Fig. 3 and 1S (top) in real time as the rotating magnetic vector (red

4

arrow) is presented in interleaved trials through CW and CCW directions through each of

four great circle planes (bottom, gray shaded). Audio consists of filtered (300 – 5K Hz)

neural activity.

Time (sec)0 1 2 3

Gy

(µT)

Gz

(µT)

−2000

200400600

MV

Firin

g ra

te (s

pks/

s)

0 1 2 3 0 1 2 3 0 1 2 3

10203040

−100

0

100

−100

0

100

−100

0

100

X

Z

YX

Z

YX

Z

YX

Z

Y

Gx

(µT)

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