Synapse Calibration procedure

on ng-thalamu

There are 4 steps to the calibration:

1. gleak
2. Erev
3. txmt
4. tau_lpf

For gleak (Erev)

1. Arrange the board's xml file so the chip and synapse numbers you are looking to calibrate are first in the file
2. Match the chip and synapse numbers in syn_f_vs_g_sleak.py (f_vs_erev_sleak.py) to the desired chip and synapse numbers AND BE SURE TO SAVE.
3. In spring, run  syn_f_vs_g_sleak.py (f_vs_erev_sleak.py)
4. Set the chip and synapse numbers in calib_syn_f_vs_g_sleak.py (calib_f_vs_erev_sleak.py) to the desired chip and synapse numbers AND BE SURE TO SAVE.
5. Run calib_syn_f_vs_g_sleak.py (calib_f_vs_erev_sleak.py) in ipython --pylab
6. Execute extract_syn_param_g_lksoma.py (extract_syn_param_erev_lksoma.py) in ipython --pylab, and then call run_default with the appropriate bif file, board name, chip number, and synapse number.
7. Use median values in histogram as parameters in xml file

For txmt (tau_lpf)

1. In neuro-boa/apps/calibrate_neuron/calibrate_synapse/calibrate_pe/calibrate_pe.cpp (calibrate_vleakpf/calibrate_vleakpf.cpp):
1.  make sure the appropriate chip calibration is pushed back
• CALIBRATION_DAC_FILE.push_back(<check this>);
• CALIBRATION_ADC_FILE.push_back(<check this>);
2. make sure the appropriate chip number is pushed back
• selected_chips.push_back(<chip number>);
3. select the appropriate chip in the for loop around ~line 621
2. run make
3. run calibrate_pe (calibrate_vleakpf)
4. For txmt:
1. change pw_values.csv to pw_values_<board>_<chip>.csv
2. In fit_2d_1coeff.py
• change filename to match data
• select synapse
3. run fit_2d_1coeff.py
4. set C1 to median value
5. set C3 to 0
5. For tau_lpf:
1. change the data/ folder name to data<chip num>/
2. In fit_tau.py
1. change data folder to match chip number
3. run fit_tau.py
4. set tau_lpf to median value

Synaptic Pulse extender

On Neurogrid, the synaptic conductance, \(x\), is governed by
\[\tau \dot{x} = -x + g_{max}\sum_ip(t-t_i)\]
where \(p(t)\) is a square pulse of length \(t_{xmt}\) resulting from spikes arriving at time \(t_i\), \(g_{max}\) is the maximum synaptic conductance, and \(\tau\) is the synaptic time constant.

Let's analyze the steady state conductance induced by a Poisson spike train where the interarrival times of spikes are distributed exponentially with pdf \(f(t) = \lambda e^{-\lambda t}\).

At steady state, \(\dot{x} = 0\), and \(0 = -x + g_{max}p(t)\).
Therefore at steady state, \(x = g_{max}p(t)\) and on average \(\langle x \rangle=g_{max} \langle p(t) \rangle\).

There is one wrinkle in our analysis: when a spike arrives within \(t_{xmt}\) of the previous spike. The two resulting pulses do not add linearly.  The second pulse merely extends the previous pulse by the time between the spikes.

\[\langle p(t)\rangle=\langle \mathrm{spike\ rate}\rangle \langle \mathrm{average\ pulse\ value}\rangle\]

For a Poisson process, the rate is simply \(\lambda\).

For a full pulse, the area is simply \(t_{xmt}\).  For the pulse resulting from a collision, the area is \(t=\Delta t\). So

\[\langle \mathrm{average\ pulse\ value}\rangle = \int_0^{t_{xmt}} t \lambda e^{-\lambda t} dt + \int_{t_{xmt}}^\infty t_{xmt}\lambda e^{-\lambda t} dt\]

\[ = \left. t e^{-\lambda t}\right|_{t_{xmt}}^0 + \int_0^{t_{xmt}} e^{-\lambda t} dt + \left. t_{xmt}\lambda e^{-\lambda t} \right|_\infty^{t_{xmt}}\]
\[ = -t_{xmt} e^{-\lambda t_{xmt}} + \left. \frac{1}{\lambda} e^{-\lambda t} \right|_{t_{xmt}}^0 + t_{xmt}\lambda e^{-\lambda t_{xmt}} \]

\[ = \frac{1}{\lambda} (1-e^{-\lambda t_{xmt}})\]

\[\langle p(t)\rangle = \lambda \frac{1}{\lambda} (1-e^{-\lambda t_{xmt}})\]
\[\langle p(t)\rangle = (1-e^{-\lambda t_{xmt}})\]

The average synaptic conductance is then
\[\langle x \rangle = g_{max}(1-e^{-\lambda t_{xmt}})\]