Appendix

A program written for Simnon to model Arenivaga CNS positional unit behavior is listed below. The program's file name is ARENcns3.T. (The *.T is not used in the program text below.) Comment and space lines begin with quotes, ". The actual *.txt program is case insensitive, and should not have boldface characters; they were used here for emphasis. If Microsoft Word is used to prepare the program, it should be saved as a "text only" file named ARENcns3.T, not ARENcns3.txt.(Simnon does not recognize the *.txt extension.) 10 point, Courier New type should be used.

Continuous system ARENcns3 " Simnon program. V. 2/27/99 " Use EULER integration with delT = tau.

" Neural model to simulate enhancement of positional orientation

" by protocerebral PPI units, as recorded by Willey, 1981.

" There are 47 states.

STATE r1 r2 r3 r4

STATE v1 v2 v3 v4 v5 v6 v7

STATE p1 q1 p2 q2 p3 q3 p4 q4 p5 q5 p6 q6 p7 q7 p8 q8 p9 q9 STATE p10 q10 p11 q11 p12 q12 p13 q13 p14 q14 p15 q15 STATE p16 q16 p17 q17 p18 q18

DER dr1 dr2 dr3 dr4

DER dv1 dv2 dv3 dv4 dv5 dv6 dv7

DER dp1 dq1 dp2 dq2 dp3 dq3 dp4 dq4 dp5 dq5 dp6 dq6 dp7 dq7 dp8 dq8

dp 9 dq9

DER dp10 dq10 dp11 dq11 dp12 dq12 dp13 dq13 dp14 dq14 dp15 dq15

DER dp16 dq16 dp17 dq17 dp18 dq18

" ANALOG DRIVES FOR 4 VNC PIs: (Theta can range 0 to 360 deg.)

frcpi =(maxF1/2)*(1 + cos(2*(theta - 45)/R)) "Choose theta in deg. rcpi is +

rcpi1 = IF THETA > 135 THEN 1 ELSE 0 " Suppresses rcpi for theta rcpi2 = IF THETA < 315 THEN 1 ELSE 0 " between 135 - 315°. rcpi3 = rcpi1*rcpi2

rcpi = IF rcpi3 > 0 THEN 0 ELSE frcpi fripi = (maxF2/2)*(1 + cos(2*(theta - 135)/R)) " cos arg must be in rads. ripi1 = IF theta > 225 THEN 1 ELSE 0 ripi2 = IF theta < 45 THEN 1 ELSE 0 ripi3 = ripi1 + ripi2

ripi = IF ripi3 > 0 THEN 0 ELSE fripi flipi = (maxF2/2)*(1 + cos(2*(theta - 225)/R)) l ipi 1 = IF theta > 315 THEN 1 ELSE 0

lipi2 = IF theta < 135 THEN 1 ELSE 0 lipi3 = lipil + lipi2

lipi = IF lipi3 > 0 THEN 0 ELSE flipi flcpi = (maxFl/2)* (1 + cos(2*(theta - 315)/R)) lcpil = IF theta > 45 THEN 1 ELSE 0 lcpi2 = IF theta < 225 THEN 1 ELSE 0 lcpi3 = lcpi1*lcpi2

lcpi = IF lcpi3 > 0 THEN 0 ELSE flcpi

" IPFM VFCs TO GENERATE INPUT SPIKES: Driven by analog f(theta)s above. dr1 = rcpi - zi1

wi 1 = IF r1 > phi 2 THEN 1 ELSE 0 si 1 = DELAY (wi1, tau) xi1 = wi1 - si1

b1 = IF xi1 > 0 THEN xi1 ELSE 0 z i1 = b1*phi2/tau uRCPI = zi1*Do " Pulse train emulating VNC positional interneuron, RCPI.

wi2 = IF r2 > phi2 THEN 1 ELSE 0 si2 = DELAY (wi2, tau) xi2 = wi2 - si2

b2 = IF xi2 > 0 THEN xi2 ELSE 0 zi2 = b2 *phi2 / tau uRIPI = zi2*Do " Pulse train emulating VNC positional interneuron, RIPI.

wi3 = IF r3 > phi 2 THEN 1 ELSE 0 si3 = DELAY (wi3, tau) xi3 = wi3 - si3

b3 = IF xi3 > 0 THEN xi3 ELSE 0 zi3 = b3 *phi2 / tau uLIPI = zi3*Do " Pulse train emulating VNC positional interneuron, LIPI.

wi4 = IF r4 > phi2 THEN 1 ELSE 0 si4 = DELAY (wi4, tau) xi4 = wi4 - si4

b4 = IF xi4 > 0 THEN xi4 ELSE 0 zi4 = b4*phi2 / tau uLCPI = zi4*Do " Pulse train emulating VNC positional interneuron, LCPI.

" THE 3 OUTPUT RPFM NEURONS

dv1 = -co*v1 + co*e1 - z 1 " RPFM Output Neuron # 1 @45°. z1 resets v1 to 0.

z1 = y1*phi/tau " e1 is sum of e- & i- psps to N1. w1 = IF v1 > phi THEN 1 ELSE 0 s 1 = DELAY (w1, tau)

xi = w1 - si y1 = IF xi > 0 THEN xi ELSE 0 " + pulse generator when vi > phi.

ui = yi*Doo/tau el = gei*qi - gii*q2 " Sum of epsps - ipsps for Ni.

dv2 = -co*v2 + co*e2 - z2 " Output Neuron 2 @ 90°.

u2 = y2*Doo/tau e2 = ge2* (q7 + q8) - gi2*(q6 + q9)

dv3 = -co*v3 + co*e3 - z3 " Output Neuron 3 @ i35°.

" 4 INHIBITORY INTERNEURONS:

" SYNAPTIC BALLISIC FILTER ODEs. (There are 14 synapses)

c1 = uRCPI

dq1 = -ae*qi + pi ci is spike input to BF. q1 is BF analog output, > 0.

c5 = uLCPI

c7 = uRIPI

c10 = uLIPI

c14 = uRIPI

c15 = uRCPI

c16 = uLIPI

c17 = uRIPI

c18 = uLCPI

OFFSET SCALED SPIKE OUTPUTS FOR PLOTTING:

VNC INPUTS set by theta.

"

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