A biophysically constrained computational model of the action potential of mouse urinary bladder smooth muscle

Abstract

Urinary incontinence is associated with enhanced spontaneous phasic contractions of the detrusor smooth muscle (DSM). Although a complete understanding of the etiology of these spontaneous contractions is not yet established, it is suggested that the spontaneously evoked action potentials (sAPs) in DSM cells initiate and modulate the contractions. In order to further our understanding of the ionic mechanisms underlying sAP generation, we present here a biophysically detailed computational model of a single DSM cell. First, we constructed mathematical models for nine ion channels found in DSM cells based on published experimental data: two voltage gated Ca2+ ion channels, an hyperpolarization-activated ion channel, two voltage-gated K+ ion channels, three Ca2+-activated K+ ion channels and a non-specific background leak ion channel. The ion channels' kinetics were characterized in terms of maximal conductances and differential equations based on voltage or calcium-dependent activation and inactivation. All ion channel models were validated by comparing the simulated currents and current-voltage relations with those reported in experimental work. Incorporating these channels, our DSM model is capable of reproducing experimentally recorded spike-type sAPs of varying configurations, ranging from sAPs displaying after-hyperpolarizations to sAPs displaying after-depolarizations. The contributions of the principal ion channels to spike generation and configuration were also investigated as a means of mimicking the effects of selected pharmacological agents on DSM cell excitability. Additionally, the features of propagation of an AP along a length of electrically continuous smooth muscle tissue were investigated. To date, a biophysically detailed computational model does not exist for DSM cells. Our model, constrained heavily by physiological data, provides a powerful tool to investigate the ionic mechanisms underlying the genesis of DSM electrical activity, which can further shed light on certain aspects of urinary bladder function and dysfunction.

Fig 1. A DSM cell parallel conductance model.

It consists of voltage gated Ca²⁺ channels, Voltage gated K⁺ channels, Ca²⁺ activated K⁺ channels and leakage currents. Applying Kirchhoff’s current law after injecting stimulus current I_stim, we get the following differential equation describing changes in transmembrane potential V_m.

Fig 2. Detrusor smooth muscle I_CaL and I_CaT model.

(A) The holding potential (V_h) was set at ─90 mV, and the test potentials increased from ─70 mV to 50 mV in 10 mV steps to obtain the I_CaL current amplitude (B) Simulated (solid line) normalized I–V relationship of I_CaL and experimental (filled triangle) I–V data. (C) The holding potential (V_h) was set at ─90 mV,and the test potentials stepped from ─70 mV to 50 mV in 20 mV steps to obtain the I_CaT current amplitude. (D) Simulated (solid line) normalized I–V relationship of I_CaT and experimental (filled triangle) I–V data [56].

Fig 3. Detrusor I_Kv1 and I_Kv7 (KCNQ) model.

(A) Inactivation of I_Kv1 is illustrated in whole-cell currents elicited by 15s depolarizing pulses from a holding potential of ─80 mV to potentials between ─120 and +10 mV. (B) Normalized I_Kv1 current- voltage curve (solid line from simulation and experimental data in filled triangle from [61] of I_Kv1. (C) I_Kv7 (KCNQ) whole-cell currents elicited by 500 ms depolarizing pulses from a holding potential of ─80 mV to potentials between ─80 and +40 mV. (D) Normalized I_Kv7 current- voltage curve (solid line from simulation and experimental data in filled triangle from [64]).

Fig 4. DSM I_BK and I_IK model.

(A) DSM cell I_BK model. Fig 4A represents the normalized simulated current-voltage curve (solid line), where experimental data from murine DSM cell [80] are superimposed in filled square. Fig 4B represents the effects of intracellular Ca²⁺ concentration on shifting the current-voltage curve. The [Ca²⁺]_i is varied from the control value of 0.0001 mM (solid line) to 0.00001 mM (dashed line) and 0.001 mM (dot and dash line). (C) The solid line represents the normalized simulated I_IK current-voltage curve, where experimental data from mouse intestinal cell [81] are superimposed in filled triangle. (D) It represents open probability of α-subunits with respect to varying [Ca²⁺]_i in I_IK model.

Fig 5. DSM I_SK and K_ATP model.

(A) The normalized I_SK current with respect to Apamin in I_SK model. (B) The solid line represents the normalized simulated I_SK current-voltage curve, where experimental data from murine DSM cell [40] are superimposed (filled triangle). (C) The ATP dependent steady state activation parameter for K_ATP channel model. (D) The normalized K_ATP current-voltage relationship curve. The solid line represents result from our simulation where filled triangles are superimposed data from experiment [90].

Fig 6. DSM cell I_h current model.

(A) The simulated current due to voltage-clamp method: voltage steps of ─140 to ─20 mV from a holding potential of ─10mV. (B) The simulated normalized current-voltage relationship curve (solid line) with superimposed experimental data (filled triangle) from [91].

Fig 7. Passive and active membrane properties of DSM cell of the mouse bladder.

(A) Simulated current–voltage relationship is shown in solid line against superimposed experimental data (filled triangles) [21]. (B) Experimental overlaid traces show the membrane potential changes from an active response cell in the mouse bladder induced by intracellular current injection of +0.1 to ─0.1 nA for 100 ms (with permission from [21]). The resting membrane potential is ─50 mV. (C) The simulated relation between the amplitude of injected currents (─0.1 to 0.1 nA for 100 ms) and resultant membrane potential.

Fig 8. Current induced simulated AP and ionic currents.

(A) Simulated AP. (B) Total inward current (dotted line), L- type Ca²⁺ channel current (dashed line) and T- type Ca²⁺ channel current (solid line). (C) Total outward current (dotted line), BK channel current (dashed line) and Kv1 channel current (solid line) (D) Outward current KCNQ channel current (dotted line), SK channel current (solid line) and IK channel current (dashed line).

Fig 9. Simulated SDs with rapid rising phase and slower falling phase.

(A) The solid line represents the simulated SD after setting the maximum conductance to 0.01 μS. The experimental data (dotted line) are plotted against the simulated one (solid line). (B) SDs with varying maximum conductance: 0.01 μS (thick solid line), 0.006 μS (long dashed line) and 0.004 μS (short dashed line).

Fig 10. Synaptic input induced simulated AP and ionic currents.

(A) Simulated AP. The superimposed filled circles represent data from experimental recordings (B) Total inward current (dotted line), L- type Ca²⁺ channel current (dashed line) and T- type Ca²⁺ channel current (solid line). (C) Total outward current (dotted line), BK channel current (dashed line) and Kv1 channel current (solid line) (D) KCNQ channel current (dotted line), SK channel current (solid line) and IK channel current (dashed line).

Fig 11

Comparison of experimental & simulated spike-type APs of two different shapes produced by synaptic input with varying changes of conductance parameters (A and B). (A) Conductances of 0.006 μS (B) Conductances of 0.02 μS. AP in (A) generates AHP while AP in (B) generates the prominent ADP. (C) APs produced by our model which corresponds to each of the experimental signals tabulated.

Fig 12

Effects of inhibiting the inward currents I_CaT and I_CaL on the synaptic input based spikes (thick solid line, Fig 12A and Fig 12B) and total input current (thick solid line, Fig 12C and Fig 12D). Fig 12A and Fig 12C show the spike and inward current with L- type Ca²⁺ channel conductance of 0.0004 S/cm² (thick solid line), 0.0002 S/cm² (dotted line) and 0 (dashed line). Fig 12B and Fig 12D show the spike and inward current with T- type Ca²⁺ channel conductance of 0.0002 S/cm² (thick solid line), 0.0001 S/cm² (dotted line) and 0 (dashed line).

Fig 13. Effects of partially reducing conductance BK and KCNQ type K⁺ channels on the whole cell AP.

(A) Synaptic input induced AP (solid line), BK and KCNQ type K⁺ channels 20% blocked AP (dashed line). (B) Total outward current for whole cell AP (solid line), BK and KCNQ type K⁺ channels partially blocked outward current (dashed line).

Fig 14. Effects of reducing (50%) conductance SK type K⁺ channels on the whole cell AP.

(A) Synaptic input induced AP (solid line), SK type K⁺ channels blocked AP (dashed line). (B) Total outward current for whole cell AP (solid line), SK type K⁺ channels blocked outward current (dashed line).

Fig 15. Simulated Ca²⁺ transient during AP.

(A) Synaptic input induced simulated AP (Solid line) and superimposed experimental data (filled square). (B) Normalized simulated Ca²⁺ transient (Solid line) and extracted experimental data [93] (filled square).

Fig 16. Simplified model of 1-D cable.

(A) Unicellular compartmental 1-D cable with 111 segments. (B) Evoked AP at 11.1 mm (R0), propagated AP at 2λ (R1), and propagated AP at 4λ (R2). Inset shows the change in foot of propagated APs (long dashed line and short dashed line) due to spatial attenuation of the passive electrical activities.

Fig 17. Gap junction implementation in multicellular 1-D cable.

(A) three cells is connected by gap junction. (B) Evoked AP (V₀) at cell 0 (R0), propagated AP (V₁) at Cell 1 via one gap junction (R1), and propagated AP (V₂) via two gap junctions (R2).