Table 1.

Equations and parameter values for the model synaptic input.

Variable/parameter	Equation/value
Modified Bessel function of order n	$I_n(\kappa )=\frac{1}{2\pi }{\displaystyle \underset{-\pi }{\overset{\pi }{\int }}\text{exp}}\left(\kappa \cos (x)\right)\cos (nx)dx$
von-Mises distribution function with concentration parameter κ	$p_{\kappa }(t)=\frac{1}{2\pi I_0(\kappa )}\text{\hspace{0.17em}exp}\left(\kappa \cos (t)\right)=\frac{1}{2\pi }+\frac{1}{\pi }{\displaystyle \sum _{n=1}^{\infty }\frac{I_n(\kappa )}{I_0(\kappa )}}\cos (nt)$
Periodic intensity function for the inhomogeneous Poisson NM inputs	λ(t) = 2πλ0 pκ(2πfst)
Timing of the i-th spike of the m-th NM fiber	tmi
Unitary synaptic input conductance (alpha function) with time constant τ	α (t) = (Ht/τ) exp (1 − t/τ) (t ≥ 0)
Area between α(t) and the t-axis	S = eHτ
Fourier transform of α(t)	$\left|F_{\alpha }(f)\right|=\left|{\displaystyle \underset{0}{\overset{\infty }{\int }}\alpha }(t)\text{\hspace{0.17em}exp}(-2\pi ift)dt\right|=\frac{S}{1+{(2\pi f\tau )}^2}$
Total synaptic input conductance	$g_{\text{syn}}(t)={\displaystyle \sum _{m=1}^M{\displaystyle \sum _{i=1}^{I_m}\alpha }}\left(t-t_m{}^i\right)$
Linear membrane impedance	|Z(f)|
DC component of the input conductance (Equation 1)	DG = SMλ0
AC component of the input conductance (Equation 2)	$A_G=\frac{2r{D}_G}{1+{\left(2\pi f_s\tau \right)}^2}$
Noise component of the input conductance (Equation 3)	$N_G=\sqrt{M{\lambda }_0{\displaystyle \underset{-\infty }{\overset{\infty }{\int }}{\left|F_{\alpha }(f)\right|}^2}df}=\frac{D_G}{2\sqrt{M{\lambda }_0\tau }}$
AC component of the membrane potential (Equation 4)	$A_V=\frac{2r{D}_G}{1+{\left(2\pi f_s\tau \right)}^2}\left|E_{\text{syn}}-V_0\right|\left|Z\left(f_s\right)\right|$
Noise component of the membrane potential (Equation 5)	$N_V=\frac{D_G\left|E_{\text{syn}}-V_0\right|}{\sqrt{M{\lambda }_0}}\sqrt{{\displaystyle \underset{-\infty }{\overset{\infty }{\int }}\frac{{\left|Z(f)\right|}^2}{{\left(1+{(2\pi f\tau )}^2\right)}^2}}df}$
Equation for average potential V0	gL(EL − V0) + ḡK d∞(V0)(EK − V0) + DG(Esyn − V0) = 0
Stimulus sound frequency	fs (default: fs = 4000 Hz)
Mean spike rate of each NM fiber	λ0 (default: λ0 = 500 Hz)
Number of NM fibers converging onto one NL cell	M (default: M = 300 fibers)
Vector strength of phase-locked NM spikes	r = I1(κ)/I0(κ) (default: r = 0.6, κ = 1.516)
Half-peak-width of unitary input	W = 2.446τ (default: W = 0.1 ms; τ = 0.0409 ms)
Magnitude of unitary input	H = α (τ) (default: H = 1.3 nS)

The model equations and parameters are the same as those used in our previous (Funabiki et al., 2011) and accompanying (Ashida et al., 2013) papers. The number (M) and the mean spike rate (λ₀) of the NM fiber are taken from previous anatomical (Carr and Boudreau, 1993) and physiological (Peña et al., 1996) studies. Equations 1–5, obtained in the accompanying paper (Ashida et al., 2013), describe how each model parameter affects the formation of the sound analog synaptic input and membrane potential.