Table 2. Model equations and parameterization.

Equations	Parameters
The linear integrate and fire neuron follows the form $C_m\frac{\mathit{\text{dV}}}{\mathit{\text{dt}}}=I_{\mathit{\text{leak}}}+I_{\mathit{\text{syn}}}+I_{\mathit{\text{adapt}}}=(V_{\mathit{\text{rest}}}-V)/R_m+I_{\mathit{\text{syn}}}+I_{\mathit{\text{adapt}}}.$	Vrest = −65 mV
	Vap = 60 mV
	Vthresh = −50 mV
The dynamics of the neuron's membrane potential include contributions from membrane leak current, synaptic current and injected current to model adaptation. Using τm =CmRm, the equation can be rewritten as ${\tau }_m\frac{\mathit{\text{dV}}}{\mathit{\text{dt}}}=(V_{\mathit{\text{rest}}}-V)(1+R_m\cdot {\omega }_{\mathit{\text{ad}}})+R_m\overline{g}{g}_{\mathit{\text{syn}}}(E_{\mathit{\text{rev}}}-V).$	Erev_ex = 0 mV
	Erev_in = −80 mV
	dt = 0.1 ms
The properties of the excitatory and inhibitory synaptic currents were defined by the parameters selected for gpeak, Erev, τrise and τdecay. A scaling factor, ḡ, controlled the relative weight of each synapse.	τm = 10 ms
	Rm = 10 MΩ
	durrp = 1 ms
The change in synaptic conductance following a spike was modeled by gsyn(t)=ḡsynf(e−(t−t0)/τdecay− e−(t−t0)/τrise), which was represented by coupled, linear ordinary differential equations (Roth and van Rossum 2009), $\begin{array}{c}\frac{\mathit{\text{dg}}}{\mathit{\text{dt}}}=-\frac{g}{{\tau }_{\mathit{\text{decay}}}}+z(t)\text{and}\\ \frac{\mathit{\text{dz}}}{\mathit{\text{dt}}}=-\frac{z}{{\tau }_{\mathit{\text{rise}}}}+{\overline{g}}_{\mathit{\text{syn}}}u(t).\end{array}$	τr_ex = 0.9 ms
	τd_ex = 12.15 ms
	τr_in = 1.1 ms
	τd_in = 10 ms
	gpeak_ex = 0.28 mS/cm2
	gpeak_in = 1.5 mS/cm2
	ωad0 = 0.1
Neuronal adaptation was modeled by increasing the voltage threshold of the neuron following each spike. The adaptation variable decayed with time constant ωad. $\frac{d{\omega }_{\mathit{\text{ad}}}}{\mathit{\text{dt}}}=\frac{{\omega }_{\mathit{\text{ad}}}-{\omega }_{a{d}_0}}{{\tau }_{\mathit{\text{ad}}}}$	ωa_inc = 0.5
	τad = 35 ms
When a spike fired in the presynaptic neuron, ωad was incremented by ωa_inc and the membrane potential was reset $V_m(t)\ge V_{\mathit{\text{thresh}}}\{\begin{array}{c}{V}_m\to V_{\mathit{\text{rest}}}\\ {\omega }_{\mathit{\text{ad}}}\to {\omega }_{\mathit{\text{ad}}}+{\omega }_{a\_\mathit{\text{inc}}}\end{array}.$	ḡPel:INd = 0.45
	ḡPud:INd = 0.6
	ḡPud:INm+ = 0.44
Simulated bladder pressure (PB) was recurrently ḡ calculated using functions of bladder volume at the previous time step and SPN output firing rate in a sliding window. The SPN firing rate calculation was generated from a polynomial fit of prior experimental results (Sasaki 1998). $P_B(t)=f({\int }_{t-\mathit{\text{wl}}}^{t-1}F{R}_{\mathit{\text{SPN}}}(t)\mathit{\text{dt}})+f({\mathit{\text{Vol}}}_B(t-1))$	ḡPud:INm- = 0.7
	ḡINm-:SPN = 0.65
	ḡINm+:SPN= 0.6
where, f(FRSPN)=2×10−3FRSPN3 − 3.3×10−2FRSPN2 + 1.8FRSPN − 0.5 and f(VolB) = (1.5VolB − 10).
	ḡINd:SPN = 0.8
ḡPMC:INd = 0.33
Pelvic afferent firing rate was calculated from a polynomial fit of PB from recordings of the mean low threshold pelvic afferent response (Sengupta and Gebhart 1994) and fed back into the model. Negative firing rates generated by the polynomial were fixed at 0 spikes per second. FRpel(t) = f(PB(t−1)) = −3×10−8 PB5 + 1×10−5 PB4 −1.5×10−3 PB3 +7.9×10−2 PB2 −0.6PB	ḡFB:INd = 0.6
	ḡSPN:FB = 1.0
	FRpel_init = 1 spikes/s
	FRpud = 0 spikes/s
	FRPMC = 15 spikes/s
	VolDEC=13 mL
	wl =1000 ms