Parameters & Units

Parameters & Units#

ar004 · 14 May 2026 · pdf

All physical quantities in the codebase use the same unit system: ms for time, mV for voltage, nF for capacitance, μS for conductance, nA for current, Hz for rates. Time fields carry an explicit _ms suffix (sim_ms, ref_ms_E, tau_gaba); CLI flags follow the same convention (–t-ms 600). A Δt of 1 means 1 ms, not 1 s.

Quantities#

Quantity	Unit	Typical value	Variable
Integration step	ms	0.25	dt, DT_MS
Simulation length	ms	600	sim_ms
Membrane time constant	ms	20 (E), 5 (I)	tau_m_E, tau_m_I
Refractory period	ms	3 (E), 1.5 (I)	ref_ms_E, ref_ms_I
AMPA decay	ms	2	tau_ampa
GABA decay	ms	9	tau_gaba
Resting / leak potential	mV	−65	E_L
Spike threshold	mV	−50	V_th
Reset potential	mV	−65	V_reset
AMPA reversal	mV	0	E_e
GABA reversal	mV	−80	E_i
Membrane capacitance	nF	1.0 (E), 0.5 (I)	C_m_E, C_m_I
Leak conductance	μS	0.05 (E), 0.1 (I)	g_L_E, g_L_I
External drive	μS	0.0006 (async), 0.003 (PING)	t_e_async, t_e_ping
Input current (CUBA)	nA	20 per spike	input_scale
CUBA weight std	nA	32	W_STD_CUBA
Max input rate	Hz	25	max_rate_hz
Population firing rate	Hz	20–80	r_E, r_I
Gamma frequency	Hz	30–80	f_0

COBA / PING biophysical constants#

Used by COBA and PING. Values follow neuroscience conventions (cf. Dayan & Abbott, Gerstner Neuronal Dynamics); the E:I asymmetry in $𝜏_{𝑚}, 𝐶_{𝑚}, 𝑔_{𝐿}, 𝜏_{ref}$ produces the timescale separation that makes PING dynamics possible.

Parameter	E population	I population
$𝜏_{𝑚}$ (ms)	20	5
$𝐶_{𝑚}$ (nF)	1.0	0.5
$𝑔_{𝐿}$ (µS)	0.05	0.1
$𝜏_{ref}$ (ms)	3	1.5
$𝐸_{𝐿}$ (mV)	−65	−65
$𝑉_{th}$ (mV)	−50	−50
$𝑉_{reset}$ (mV)	−65	−65
$𝐸_{𝑒}$ (mV, reversal)	0	0
$𝐸_{𝑖}$ (mV, reversal)	−80	−80

Synapse time constants: $𝜏_{AMPA} = 2$ ms (excitation), $𝜏_{GABA} = 9$ ms (inhibition). These set the ceiling on PING’s Δt-stability: once $Δ 𝑡 ≳ 𝜏_{GABA}$ the E→I→E loop cannot complete within one step.

Internal consistency#

The chosen units are self-consistent — no conversion factors appear in the integration code. Two equations carry the whole system.

The membrane time constant is $𝜏 = 𝐶 / 𝑔$ . With $𝐶$ in nF and $𝑔$ in μS,

𝜏_{[ms]} = \frac{𝐶_{[nF]}}{𝑔_{[𝜇 S]}}

so $𝐶_{𝑚} = 1$ nF and $𝑔_{𝐿} = 0.05$ μS give $𝜏_{𝑚} = 20$ ms directly.

The LIF voltage update is $d 𝑣 = (Δ 𝑡 / 𝐶) (- 𝑔_{𝐿} (𝑣 - 𝐸_{𝐿}) + 𝐼)$ . With $Δ 𝑡$ in ms, $𝐶$ in nF, $𝑣, 𝐸$ in mV, $𝑔$ in μS, and $𝐼$ in nA,

d 𝑣_{[mV]} = \frac{Δ 𝑡_{[ms]}}{𝐶_{[nF]}} \cdot 𝐼_{[nA]}

because ms·nA / nF = mV exactly.

Conductance-current products share the same ledger: $𝑔 (𝑣 - 𝐸)$ is μS × mV = nA, so synaptic currents fold into $𝐼$ alongside any direct input current without a scale factor.

Why not SI?#

Pure SI (F, S, V, A, s) forces every value to a large negative exponent — $𝐶_{𝑚} = 10^{- 9}$ F, $𝑔_{𝐿} = 5 \times 10^{- 8}$ S, $Δ 𝑡 = 2.5 \times 10^{- 4}$ s. The neuroscience convention (ms, mV, nF, μS, nA) keeps every typical value between $10^{- 3}$ and $10^{2}$ , which makes numerical debugging and human intuition faster. The tradeoff is that readers have to trust the unit consistency rather than verify it by plugging into SI formulas — this page is here so that trust is auditable.