Comparison of simulated and experimental APs in Fig 9.

<p>Comparison of simulated and experimental APs in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006293#pcbi.1006293.g009" target="_blank">Fig 9</a>.</p

SK_Ca with IR: Role of SK_Ca inward rectification and SK_Ca and maximum conductance on inflammatory repetitive firing.

<p>Membrane potential, V_m (upper panel), intracellular calcium concentration, [Ca]_i (middle panel) and instantaneous SK_Ca conductance, <i>g</i> (lower panel) recorded against time for three maximum conductances () of the SK_Ca channel: 9*10⁻⁴ S/cm² (control) (A, D, G), 2.7*10⁻³ S/cm² (B, E, H) and 4.5*10⁻³ S/cm² (C, F, I). The neuron model used had SK_Ca channels endowed with inward rectification (SK_Ca with IR). Stimulus: 1000 ms, 0.12 nA rectangular current clamp.</p

Comparison of normalized experimental and simulated [Ca]_i and [Ca]_MT.

<p>The solid red line and solid blue line represent the simulated [Ca]_i and [Ca]_MT, respectively from the model (Sim.), obtained by evoking 20 APs at 10 Hz. APs were evoked by using rectangular current clamps of 1.25 nA and 1 ms. The red circles and blue triangles are experimental traces digitized (Expt.) [Ca]_i and [Ca]_MT for similar stimuli in small DRG neuron terminals obtained from [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006293#pcbi.1006293.ref106" target="_blank">106</a>]. The rising and falling dynamics of our bladder small DRG soma model output closely compares with those recorded experimentally. The S value for [Ca]_i and [Ca]_MT fits and their 5% thresholds (in brackets) are 0.12 (0.05) and 0.068 (0.05), respectively. Effects of calcium dye buffering were included in the simulations.</p

A biophysically detailed computational model of urinary bladder small DRG neuron soma

<div><p>Bladder small DRG neurons, which are putative nociceptors pivotal to urinary bladder function, express more than a dozen different ionic membrane mechanisms: ion channels, pumps and exchangers. Small-conductance Ca²⁺-activated K⁺ (SK_Ca) channels which were earlier thought to be gated solely by intracellular Ca²⁺ concentration ([Ca]_i) have recently been shown to exhibit inward rectification with respect to membrane potential. The effect of SK_Ca inward rectification on the excitability of these neurons is unknown. Furthermore, studies on the role of K_Ca channels in repetitive firing and their contributions to different types of afterhyperpolarization (AHP) in these neurons are lacking. In order to study these phenomena, we first constructed and validated a biophysically detailed single compartment model of bladder small DRG neuron soma constrained by physiological data. The model includes twenty-two major known membrane mechanisms along with intracellular Ca²⁺ dynamics comprising Ca²⁺ diffusion, cytoplasmic buffering, and endoplasmic reticulum (ER) and mitochondrial mechanisms. Using modelling studies, we show that inward rectification of SK_Ca is an important parameter regulating neuronal repetitive firing and that its absence reduces action potential (AP) firing frequency. We also show that SK_Ca is more potent in reducing AP spiking than the large-conductance K_Ca channel (BK_Ca) in these neurons. Moreover, BK_Ca was found to contribute to the fast AHP (fAHP) and SK_Ca to the medium-duration (mAHP) and slow AHP (sAHP). We also report that the slow inactivating A-type K⁺ channel (slow K_A) current in these neurons is composed of 2 components: an initial fast inactivating (time constant ∼ 25-100 ms) and a slow inactivating (time constant ∼ 200-800 ms) current. We discuss the implications of our findings, and how our detailed model can help further our understanding of the role of C-fibre afferents in the physiology of urinary bladder as well as in certain disorders.</p></div

SK_Ca w/o IR: Role of SK_Ca inward rectification and SK_Ca and maximum conductance on inflammatory repetitive firing.

<p>Membrane potential, V_m (upper panel), intracellular calcium concentration, [Ca]_i (middle panel) and instantaneous SK_Ca conductance, <i>g</i> (lower panel) was recorded against time for three maximum conductances of the SK_Ca channel: 9*10⁻⁴ S/cm² (control) (A, D, G), 2.7*10⁻³ S/cm² (B, E, H) and 4.5*10⁻³ S/cm² (C, F, I). The neuron model used had non-inward rectifying SK_Ca channels (SK_Ca w/o IR). Stimulus: 1000 ms, 0.12 nA rectangular current clamp.</p

K_A channel.

<p>(A) Voltage dependence of steady state activation (<i>n</i>_∞, solid line) and inactivation (<i>h</i>_∞, dashed line) of the modelled channel. Squares (<i>n</i>_∞) and triangles (<i>h</i>_∞) represent the experimental data for bladder small DRG neurons from [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006293#pcbi.1006293.ref007" target="_blank">7</a>]. (B) The activation time constant(<i>τ</i>_<i>n</i>) of the modelled channel. (C) The inactivation time constants of the channel: <i>τ</i>_{<i>h</i>,<i>slow</i>} (= slow time constant, solid line) and <i>τ</i>_{<i>h</i>,<i>fast</i>} (= fast time constant, dashed line). (D) The currents (<i>I</i>_<i>KA</i>) generated by the model (solid lines) and the currents reported in experiments (symbols, [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006293#pcbi.1006293.ref033" target="_blank">33</a>]) using rectangular voltage clamps. The holding potential was kept at −120 mV for 5 ms and test potentials of −20, −10 and 0 mV were applied for 300 ms. Experimental data for currents recorded is shown by triangles (= −20 mV), circles (= −10 mV) and squares (= 0 mV) along corresponding simulated currents (solid lines). (E) Peak I-V relationship from the model generated by recording the peak current at each test potential. Protocol: Rectangular voltage clamp steps were applied from −80 to 20 mV for 300 ms from a holding potential of −80 mV. Other model parameters: , E_K = −84.7 mV, RMP = −53.5 mV, membrane capacitance = 28 pF, soma diameter = 24 <i>μ</i>m. The S values for model fits and their 5% threshold values (given in brackets) are: <i>n</i>_∞ = 0.008 (0.05), <i>h</i>_∞ = 0.003 (0.05), for voltage clamp currents at: 0 mV = 0.157 nA (0.067 nA), −10 mV = 0.161 nA (0.059 nA) and −20 mV = 0.081 nA (0.045 nA).</p

Effects of SK_Ca channel inward rectification on AP and AHP properties.

<p>Comparison of RMP (A), AP Duration (B), AP overshoot (C), AHP Amplitude (D), Time to AHP Peak (E) and AHP_80% (F) in bladder small DRG neuron soma models having SK_Ca conductance endowed with inward rectification (SK_Ca with IR, filled squares) and without inward rectification (SK_Ca w/o IR, hollow squares). AP was generated by a current clamp of amplitude 0.18 nA and duration 15 ms. The was increased from 9*10⁻⁴ S/cm² to 4.5*10⁻³ S/cm² in steps of 4.5*10⁻⁴ S/cm². Parameters plotted are explained in the text. Incorporation of inward rectification diminished the effect of SK_Ca channel on the AP and AHP parameters.</p

Action potentials in the bladder small DRG neuron soma model for different stimuli.

<p>(A) AP generated by a current clamp of 0.16 nA and 50 ms duration for experiments by Hayashi et al. [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006293#pcbi.1006293.ref036" target="_blank">36</a>] (circles, Expt. AP) and simulated AP (solid line, Sim. AP). The standard error in regression, S for the fit and 5% threshold values (in brackets) are 4.43 mV (5.4 mV) indicating a good fit. (B) Response to long duration (800 ms) current clamp of amplitude 0.24 nA.</p

Role of PMCA, MCU, SERCA and MNCX in shaping the Ca²⁺ transient.

<p>(A) [Ca]_i levels for the response of the model to 20 APs generated by 1 ms, 1.25 nA rectangular current clamps given at 10 Hz. PMCA (red), MCU (orange), SERCA (blue) and MNCX (maroon) are blocked individually. Black curve is the control [Ca]_i (B) Magnified scale to show the effects of these components on the decay of Ca²⁺ transients.</p

BK_Ca channel.

<p>(A) Voltage (V_m)- and [Ca]_i-dependence of steady state activation (<i>n</i>_∞, solid lines) of the modelled channel (Sim. = Simulation). The symbols represent experimental data (Expt.) for open probability of the channel (P_open) for different [Ca]_i [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006293#pcbi.1006293.ref053" target="_blank">53</a>]: triangles ([Ca]_i = 0.1 <i>μ</i>M), squares ([Ca]_i = 1 <i>μ</i>M), circles ([Ca]_i = 10 <i>μ</i>M) and stars ([Ca]_i = 100 <i>μ</i>M). Intracellular Ca²⁺ concentration is represented in units of <i>μ</i>M. (B) Time constants of activation (<i>τ</i>_<i>n</i>) from the model (solid line). (C) Rectangular voltage clamp currents obtained from the model. Protocol: The holding potential was −53.5 mV. The test potentials from 30 to 60 mV, each of 500 ms duration were used in steps of 10 mV. Number above the current curves represent corresponding test potential. Other model parameters: , initial [Ca]_i = 1.36*10⁻⁴ mM, E_Ca ∼ 122 mV, E_K = −84.7 mV, RMP = −53.5 mV, total capacitance = 28 pF and soma diameter = 24 <i>μ</i>m. The S values for <i>n</i>_∞ for different [Ca]_i and their 5% threshold values (given in brackets) are: for 100 <i>μ</i>M = 0.070 (0.05), for 10 <i>μ</i>M = 0.121 (0.05), for 1 <i>μ</i>M = 0.079 (0.05) and for 0.1 <i>μ</i>M = 0.025 (0.05).</p