article: 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+ (SKCa) 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 SKCa inward rectification on the excitability of these neurons is unknown. Furthermore, studies on the role of KCa 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 SKCa is an important parameter regulating neuronal repetitive firing and that its absence reduces action potential (AP) firing frequency. We also show that SKCa is more potent in reducing AP spiking than the large-conductance KCa channel (BKCa) in these neurons. Moreover, BKCa was found to contribute to the fast AHP (fAHP) and SKCa to the medium-duration (mAHP) and slow AHP (sAHP). We also report that the slow inactivating A-type K+ channel (slow KA) 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.
  The sensory component of the reflex pathway of the bladder is formed by the dorsal root ganglion (DRG) neurons. Afferent signals such as bladder pressure, volume, temperature, pH, presence of irritants and pain are transmitted to the spinal cord via these neurons. Urinary incontinence—the involuntary voiding of urine from the body—is a major group of disorders including overactive bladder in some of which sensory neuron pathophysiology has been implicated [1–6]. Biophysical changes at the axon terminals in the bladder and at the spinal cord as well as the alterations in the soma located in the DRG are major factors that may under certain conditions contribute to urinary bladder pathophysiology. Two types of DRG neurons have been found to supply the human, rat and feline urinary bladder [3,7]: the unmyelinated C-fibre neurons and myelinated A-δ fibre neurons. In rats, the C-fibre neurons have small soma diameter (∼24 μm) and are therefore called small DRG neurons while the A-δ fibres have a somewhat larger soma diameter range (30-35 μm) and are referred to as medium-sized or medium-diameter DRG neurons [3,8]. The small DRG neurons are generally considered nociceptors i. e. they convey information related to pain. They may also take up the function of A-δ fibres (viz. sensing non-nociceptive stimuli; detrusor pressure, stretch, volume) in bladder dysfunction [3]. Significant changes in bladder small DRG neurons have been reported in various conditions such as bladder inflammation (interstitial cystitis), spinal cord injury (SCI), bladder overactivity, bladder outlet obstruction and hyperexcitability [3,5, 9,10]. The somata of these sensory neurons are located within the DRG and do not lie in the direct path of information propagation from the bladder to the spinal cord, the said path being constituted by the axon of the pseudounipolar DRG neuron. Historically, the DRG neuron somata were thought to play a purely metabolic role, for example in providing nutrition to the neurons, and synthesizing ion channels and various other proteins that are subsequently transported to axons and terminals. Recently, however, somata and the T-junction of the DRG neuron (the three-way junction where the axon bifurcates into two axon branches: the peripheral branch which innervates the sensory organ, and the central branch which conveys the electrical signals to the spinal cord) were found to be important players in filtering the signals from sensory branch of the axon [11–13], and in generating ectopic activity during nerve injury [14]. Moreover, the interaction within the ganglia between the DRG neuron somata and the satellite glial cells (SGCs) that sheath the DRG neuron soma has been implicated in the genesis of gastrointestinal pain [15]. Electrical stimulation of DRG, which is emerging as a new therapeutic strategy for pain alleviation [16] suggests a role for DRG neuron somata in regulating the electrical activity of the sensory neurons. For these reasons, the DRG neuron soma merits exploration in its own right. In-vivo electrophysiological studies on individual somata are difficult to perform since DRG neuron somata are tightly packed with other somata in the dorsal root ganglia, as well as enveloped by the closely investing SGCs, blood vessels and extracellular matrix. A simple in-silico alternative to experiments which are otherwise much difficult to perform in-vivo is by the use of computational models and simulations. A comprehensive electrophysiological model of a DRG neuron soma would be a good starting point for such models. While a few models have been published for DRG neurons, e. g. for the GIT (Gastro-Intestinal Tract), others are for non-specific DRG neurons [13,17–23]. None so far, however, is specific to bladder small DRG neurons. Furthermore, most existing models have been developed for medium- or other large-diameter DRG neurons and moreover, do not incorporate the effects of mitochondrial and endoplasmic reticulum calcium release and uptake mechanisms. In order to address these questions, we therefore set out to build a biophysically detailed electrophysiological model of bladder small DRG neuron soma. Our aim was to build a model as tightly constrained as possible by available physiological data. Towards this end, we incorporated all the major membrane mechanisms known to exist in these neurons, including ion channels, pumps and Na+/Ca2+ exchanger. Although we adapted a number of models from existing reports, most of these models had not previously been validated, and we validated each such model individually. For instance, the simulated ionic currents were validated against the corresponding experimentally recorded currents, both in respect to their temporal dynamics and their current-voltage (I-V) relationship. We also incorporated intracellular Ca2+ dynamics including buffering, diffusion, endoplasmic reticulum (ER) and mitochondrial mechanisms. We then validated the action potentials and Ca2+ transients obtained from our physiologically constrained model against experimental data on bladder small DRG neuron action potentials and Ca2+ transients so as to be able to place confidence in our model’s robustness. We proceed to employ our validated model in order to address certain questions important in the regulation of bladder small DRG neuron functions such as the following. (1) One of the Ca2+-activated K+ (KCa) channels, the small-conductance KCa (SKCa) channel which was earlier thought be activated by intracellular Ca2+ only, has been recently shown to exhibit inward rectification in addition to Ca2+ dependence [24–26]. Since the range of voltages over which rectification occurs (positive values of membrane potential, Vm, [27,28]), the rectifying SKCa channel would pass a smaller outward current, we hypothesized that incorporation of rectification should result in an increase of excitability of the bladder small DRG soma. Prior studies have also shown that inward rectification influences neuronal excitability markedly in other neurons [29]. Since the effects of SKCa current rectification on the excitability of bladder small DRG neurons or in any other excitable/non-excitable cell have not been studied yet, we first built a model of SKCa channel incorporating rectification (see Methods), included this channel in our soma model, and finally employed the soma model to address our hypothesis. (2) SKCa along with BKCa (large-conductance KCa) channels can govern the excitability of the neurons by contributing to the afterhyperpolarization (AHP) of the action potentials (APs). The origins and function of the AHPs observed in bladder DRG neuron AHPs is not clearly delineated [30]. The genesis of the AHPs has been proposed to be different in different neurons. For instance, in vagal sensory neurons, BKCa channels are thought to underlie medium duration AHP (mAHP) [31] while in several central nervous system neurons, the mAHP is controlled by SKCa channels [32]. In the face of these conflicting proposals, and in view of the importance of AHPs in governing neuronal excitation (especially frequency), we thought to resolve the role of KCa channels underlying the AHPs in bladder sensory neurons. (3) The A-type K+ (KA) channels found in the bladder DRG neurons are important regulators of excitability of neurons in conditions such as bladder cystitis and spinal cord injury [3]. KA channels have faster activation time constants than KDR channels, and can alter the depolarizing phase of an AP. The KA channels expressed in bladder DRG neurons are of 2 types: the rapidly-inactivating KA (fast KA) which are present in medium-diameter neurons and a slow-inactivating KA (slow KA) found in small DRG neurons [3,7, 33–35]. Both these currents have a transient rising phase and a fast or slow inactivating phase when recorded under rectangular voltage clamps. Even though several studies have been carried out to decipher the molecular components giving rise to this KA current [34–36], the question is as yet unresolved. (4) Another unresolved issue pertains to the relative importance of BKCa and SKCa channels in regulating firing rate in these neurons during repetitive firing. We used our model to shed light on both these unsettled biological questions, i. e. (3) and (4). Using our validated model, we show that incorporation of rectifying as opposed to non-rectifying SKCa channels increases the excitability of the bladder small DRG neurons. It was also found from conductance-based studies that SKCa channels are more potent than BKCa channels in controlling the firing rate of these neurons. By exercising our detailed model, we are able to propose that the fast afterhyperpolarization (fAHP) in bladder small DRG neurons may result primarily from BKCa channels while SKCa may contribute primarily to the mAHP and the slow AHP (sAHP). Furthermore, we found the SKCa channel to be a more potent regulator of repetitive firing than the BKCa channel. By the use of channel modelling and optimization, we found that the slow inactivating A-type K+ (slow KA) current in bladder small DRG neurons is composed of two inactivating components: a relatively fast and a relatively slower component. This could arise from contributions of two different molecular constituents of the channel or because of interactions between two different inactivation states of Kv1. 4. In sum, having developed and validated a detailed and physiologically constrained model of the bladder small DRG neuron, we employed in order to illuminate questions of the type that computational models are ideally suited for: (1) hypothesis testing, in regard to our prediction that the inward rectifying SKCa channel would render the neuron more excitable; (2) taking into account previous conflicting contentions and resolving them in regard to the relative contributions of KCa channels to the AHP; (3) shedding light on an open biological question, as regards the probable subunit composition of the slow KA channel in these neurons and assessing the relative contributions of SKCa and BKCa channels in governing repetitive firing. We discuss the implications of our findings in the framework of bladder small DRG neuron functioning and of bladder physiology as modulated by these afferents. Initial studies related to this work were published in Mandge et al. [37,38] and Aruljothi et al. [39].
  Passive parameters such as total membrane capacitance (Cm) and specific membrane resistance (Rm) along with other model specifications are given in Table 1. Input resistance (Rin) of the model was found to be 316. 05 MΩ. It was found by using a long duration hyperpolarizing current clamp of −0. 01 nA and calculated by dividing the change observed in membrane potential, Vm (between the resting membrane potential, RMP and the steady state Vm) and the current amplitude. The observed Rin from the model is in range of values reported in literature for dissociated bladder small DRG neurons i. e. 175 MΩ-581 MΩ [7,41] and is also close to the value reported for intact bladder DRG neurons (332 MΩ) [42]. A passive channel was added to the model to incorporate the currents through voltage-independent channels reported in small DRG neurons such as the K2P channels: TREK1, TREK2, TRAAK [47]. The channel current was calculated as follows: I p a s = g p a s (V m - E p a s) (2) Where gpas = 1/Rm = 1/ (10000 Ω-cm2) = 1*10−4 S/cm2 and Epas was set to −41. 583 mV to have a stable RMP of −53. 5 mV. Twenty-two ionic membrane mechanisms including ion channels, pumps and exchangers were built/ adapted, validated for their parameters such as time constants and steady state of (in) activation as well as for voltage clamp currents and I-V relationships, and were then incorporated into the bladder small DRG neuron soma model (see S1 Fig). All the known membrane ion channels reported for bladder small DRG neurons along with membrane mechanisms described essential in other small DRG neuron functioning were added. Table 2 shows the plasma membrane mechanisms added to the model along with their data source and animal species from which the data was obtained. General modelling formalisms used for the mechanisms are explained in S1 Text. Validation of individual model mechanisms are explained ahead and in S2 Text. The ionic concentrations, RMP, membrane capacitance and maximum density (or conductance or permeability) used for validating individual mechanisms were fixed as per the experimental protocol reported for that mechanism and may be different from parameters used for the complete model (Table 1). These and other experimental parameters used for validating individual mechanisms are provided along with their respective descriptions in the text and figures. The maximum densities were tuned for the complete soma model to give experimentally reported action potential (AP) properties such AP amplitude, AP overshoot and AP duration, and Ca2+ transients (see Results). Tuning was done in accordance with the densities reported in experiments, for instance, conductance of Nav1. 8 channels was higher than Nav1. 9 and TTX-sensitive Na+ channels as reported in [7] and [51]. S1 Table has the membrane mechanism densities, maximum conductances and maximum permeabilities used for the complete model. Standard error of the regression (S) also called the root mean squared error (RMSE) was used to test the goodness-of-fit for channel parameters, channel currents, action potentials and intracellular and mitochondrial Ca2+ concentrations as R2 is not good estimate of the goodness of fits for such nonlinear models [80]. S gives the standard deviation of residuals between the model fit curve and the experimental points. The lower the value of S, the better is the fit [81]. The value of threshold below which the fit is good was chosen as 5% of the difference between the maximum and minimum values taken by that parameter e. g. for the steady state activation/inactivation parameters (m∞ and h∞), the value is 0. 05 (5% of 1). The threshold values for parameters of membrane mechanisms, APs and Ca2+ concentrations are given along with their respective figures in captions. S value is given by: S = Σ (Y e x p t - Y f i t) 2 v (3) where Yexpt is the experimental value, Yfit is the corresponding value from the curve fit, v is the residual degrees of freedom which is the difference in number of data points, n and the number of parameters used to fit the curve. For instance, m∞ in Boltzmann equation has 2 fit parameters: half-activation potential and slope factor and hence, v = n − 2. For AP and Ca2+ concentrations goodness-of-fits, v was taken as n − 1. S value was not calculated for parameters with v < 4. The remaining part of the section describes the modelling and validation of individual mechanisms and Ca2+ dynamics of the bladder small DRG neuron model. The soma was divided into 12 concentric shells for encoding Ca2+ diffusion, tuning [Ca]i and in creating separate Ca2+ concentration pools in the neuron [48]. Each shell has a separate intracellular Ca2+ concentration ([Ca]i), endoplasmic reticulum (ER) Ca2+ concentration ([Ca]ER), and mitochondrial Ca2+ concentration ([Ca]MT) representing a separate pool for each component in each shell (see S1 and S2 Figs). Mitochondrial volume in rat glabrous skin small-diameter DRG neurons has been estimated close to 7% (∼ 6. 96%) of total cytoplasmic volume by [92]. ER can occupy >10% of the total cytosolic volume in eukaryotic cells [93]. Accordingly, we made mitochondria volume 7%, ER volume 12% and cytoplasmic volume to 81% of the total volume in each shell (S2 Fig). The number of shells were tuned to get a proper [Ca]i transient in the outermost (towards plasma membrane) shell. The cytoplasmic, mitochondrial and ER Ca2+ concentrations in the outermost shell were considered [Ca]i, [Ca]MT and [Ca]ER, respectively of the bladder small DRG neuron soma model as the outermost shell receives Ca2+ from plasma membrane mechanisms and will have the maximum change in the concentrations. The outermost [Ca]i concentration defines the electrochemical gradient for movement of Ca2+ ions across the cell membrane via the Ca2+ permeable channels and also activates the membrane Ca2+-activated K+ channels (BKCa and SKCa), plasma membrane NCX and plasma membrane Ca2+-ATPase (PMCA) pump. Ca2+-activated Cl- channels (CaCC) are activated by Vm and by local Ca2+ concentration release from inositol triphosphate receptors (IP3Rs) present on ER [72] in the outermost shell. The rate of change of [Ca]i in the outermost shell was given by the algebraic sum of Ca2+ flux from soma membrane Ca2+ permeable channels and exchanger (JMembrane), plasma membrane Ca2+ ATPase (JPMCA) pump, endoplasmic reticulum (ER) (JER), mitochondria (JMT) and intracellular Ca2+ diffusion (JDiffusion): ∂ [ C a ] i ∂ t = 1 1 + β (J M e m b r a n e - J P M C A + J E R + J M T) + J D i f f u s i o n (35) β is the buffer binding ratio of for the cell (discussed ahead) and codes for buffering of [Ca]i. For shells below the outermost shell, JMembrane and JPMCA are absent. The changes in [Ca]ER was modelled as: d [ C a ] E R d t = 1 1 + β E R (J S E R C A - J I P 3 R - J C I C R - J L e a k) (36) where βER is the buffering component of ER, JSERCA is the flux through sarco-endoplasmic reticulum Ca2+ ATPase pump, JIP3R is the flux due to IP3 receptor, JCICR is the Ca2+ induced Ca2+ release (CICR) flux via the ryanodine receptors and JLeak is the flux through leak channels on the ER. A negative flux sign denotes the decrease in [Ca]ER with time as result of release of Ca2+ ions into cytoplasm and vice versa. Individual components of ER are discussed ahead. The changes in the [Ca]MT were modelled as: d [ C a ] M T d t = 1 1 + β M T (J M C U - J M N C X) (37) where JMCU is the mitochondria uniporter flux and JMNCX is the flux due to mitochondrial Na+/Ca2+ exchanger (MNCX) and βMT is the Ca2+ buffering component of mitochondria and was added to prevent the depletion of mitochondrial Ca2+ during high neuron firing. MNCX being a mitochondrial release mechanism, JMNCX is negative and signifies a decrease in mitochondrial Ca2+.
  KCa channels have been shown to affect the AHP phase in sensory neurons [31,120] and hence, neurons excitability. The AHPs have 3 phases: the fast AHPs (fAHP) which have a fast rise and last for about a few 10’s of milliseconds, medium-duration AHPs (mAHP) which start within a few milliseconds of the AP and lasts for some 100’s of ms and the slow AHPs (sAHP) that can sustain upto 10’s of seconds [32]. The channels underlying different AHPs may be different for central nervous system (CNS) neurons and peripheral sensory neurons. mAHP is modulated by SKCa channels in CNS neurons [121] while in vagal primary sensory neurons, BKCa channels are thought to underlie mAHP [120]. Here, we conducted a systematic study on the role of BKCa and SKCa channels on the AP and AHP properties, and the excitability of bladder small DRG neurons. The conductance of KCa channels increases with increasing [Ca]i and could play an important role in shaping the APs and the excitability of the neurons. The effect of blocking KCa channels was minimal on a single AP (generated by rectangular current clamp of 0. 18 nA, 15 ms, [10]) due to their small current contributions (Fig 21). As can be seen in Fig 21, the block of BKCa decreased the AHP Amplitude while SKCa block resulted in decreasing the AHP duration. In order to quantify the changes in the AHP and AP properties, we stepped the g ¯ of the BKCa and SKCa channels from the control value of 9*10−4 (for both BKCa and SKCa) to 4. 5*10−3 S/cm2 in multiples of 4. 5*10−4 S/cm2. As expected from the blocking studies, an elevated BKCa conductance resulted in increase in AHP Amplitude (Fig 22D) whereas elevated SKCa conductance led to a slower decay of the AHP (Fig 22F). BKCa conductance increase resulted in larger AHP amplitude (Fig 22D) than SKCa. Hence, BKCa may contribute to the fAHP. The change in AHP80% is larger for a change in SKCa conductance than for the same change in BKCa conductance. The greater sensitivity to SKCa shows that it may regulate the later part of the AHP and may underlie medium-duration AHP (mAHP, which decay within few 100’s of ms) and the slow AHP (lasting a few seconds) in bladder DRG neurons. In order to test the sensitivity of AP firing to the KCa channels, we altered the conductance of channels individually in the range of 9*10−4 (control) to 4. 5*10−3 S/cm2 to a model that shows inflammatory repetitive firing for a long duration rectangular current clamp of amplitude 0. 12 nA and 1000 ms duration, as used in Fig 18. We recorded the number of spikes generated by the model and peak [Ca]i. Spikes were counted whenever Vm crossed 0 mV from a negative to a positive Vm. The graphs in Fig 23A show that the SKCa channel is more likely to change the firing rate than the BKCa channel when channel conductance is elevated. A decremental trend is seen in maximum [Ca]i (Fig 23B). The decrement is greater for enhanced SKCa channel conductance compared to BKCa conductance. This parallels the reduction in the number of APs recorded. It can be inferred from Fig 23B that [Ca]i is more sensitive to SKCa than to BKCa at raised conductance values. Thus, while both SKCa and BKCa channels affect the firing frequency of the bladder DRG neurons, SKCa is more effective than BKCa in this respect. A reason for this is the strong effect of SKCa on the slow AHP (See Fig 22F for AHP80%). AHP80%, which indicates the recovery time from AHP towards RMP, is relatively higher at larger conductances for SKCa channel than BKCa channels. Hence, a larger depolarization is required to bring Vm from slow AHP potential to the AP threshold. This will reduce the firing frequency of the neuron.
  The model of SKCa channel presented here incorporates both inward rectification and [Ca]i-dependence. Our working hypothesis was that since rectification gives rise to smaller outward currents over the relevant range of membrane voltage [27,28], incorporation of rectification should result in an increase of excitability of the bladder small DRG soma. Our simulations show that SKCa channels have marked effects on the electrical activity of the bladder small DRG neuron. We show that inward rectification of SKCa channels can regulate the afterhyperpolarization, RMP and AP properties of these neurons. The DRG neuron model endowed with SKCa inward rectification exhibited a higher firing rate compared to the model in which SKCa was endowed just with [Ca]i-dependence (Fig 18A). This is expected as the reduced outward current for potentials more depolarized than the Nernst potential of K+ prevents the generation of a larger AHP (Fig 14B and 14E) and leads to greater excitability. We propound therefore that, SKCa channel rectification may play a significant part in shaping and regulating the flow of the electrical sensory signals from the bladder, not only in the DRG soma but also at the DRG neuron terminals in the spinal cord where SKCa channels could be involved along with Ca2+ channels in regulating neurotransmitter release [87,89]. Another site at which SKCa channels could play a role in regulating the release of neurotransmitter is the DRG neuron soma since these somata have also been shown to release such neurotransmitters as adenosine triphosphate (ATP) and glutamate which could be involved in intercellular communication between neighbouring somata via the satellite glial cells surrounding them [15]. The presence of rectification has been shown in recombinant cell lines expressing SKCa channels such as in HEK-293 [24,25] and Xenopus oocytes [26,28] but rectification in endogenous DRG neurons is not yet studied. Even though the intracellular milieu including the Ca2+ release and uptake mechanisms might be different in recombinant cells as compared to DRG neurons, the evidence that rectification is an intrinsic property of the SKCa channel [26] suggests that this feature might also be present in DRG neurons. Rectification is caused by the presence of charged amino acids in the transmembrane domain S6 of the SKCa channel [26]. Jenkins et al. [122] found that serine-507 and alanine-532 residues in the inner pore region when substituted by threonine and valine, respectively reduced the rectification in human KCa 2. 3 (hSK3) channels. In addition, in view of the finding that SKCa inward rectification is an outcome of block by intracellular divalent cations like Ba2+ and Mg2+ [24,25], it is highly likely that it is also found in the native DRG neuron including the bladder DRG neurons. The effect of this property on the electrical activity of neurons therefore merits considerable attention. The role of different KCa (BKCa, SKCa and IKCa) channels in shaping the AP is not studied in detail in the bladder DRG neurons while there are numerous studies on other somatic and non-bladder DRG (sensory) neurons such as the cutaneous DRG neurons and vagal sensory neurons [54,120,123]. Pharmacological studies using blockers and openers of BKCa, SKCa and IKCa channels in bladder small DRG neurons have been reported to change their electrical excitability [30,52]. Hougaard et al. [30] tested the effects of SKCa blocker (apamin) and opener/positive modulator (1-EBIO and NS4591) on bladder small DRG neurons. The SKCa channel positive modulator NS4591 at concentration of 1 μM hyperpolarized the RMP. In our simulation, application of channel opener was mimicked by augmenting the conductance of the SKCa channel which also resulted in hyperpolarized RMP (See Fig 22A). Apamin decreased the amplitude of the AHP recorded after one AP [30], an effect similar to that seen in simulations by removing SKCa channels from the model (Fig 21B), the change being very small (∼0. 1 mV). Similarly, minimal increase (<0. 1 mV) in AHP amplitude with increasing SKCa conductance in our simulation (Fig 22D) is in line with the experimental observation that AHP amplitude does not change on applying 1-EBIO and NS4591 [30]. The application of these drugs (NS4591 and 1-EBIO) reduced the number of APs recorded during a 500 ms long current clamp stimulus from 8 to 2 APs. This effect may be correlated with our studies on the effect of SKCa on a train of APs where an elevated SKCa conductance decreases firing rate in the neuron (See Fig 23A). Unlike our observations of an enhanced AHP decay time (AHP80%) with raised SKCa conductance (Fig 22F, Filled triangles and Fig 15F, SKCa with IR), Hougaard et al. [30] did not observe significant change in AHP decay time on application of SKCa openers in bladder small DRG neurons. The difference in AHP decay time in experiments and our simulations of DRG model with SKCa endowed IR (Fig 22F, Filled triangles) can arise because of the hyperpolarized holding potentials (−70 mV, −62 mV) used in the experimental work before applying blockers and openers while the RMP is close to −50 mV. The RMP reported for L6-S1 spinal level rat bladder small DRG neuron is generally between −48 to −53. 5 mV [5,10,34] whereas the hyperpolarized holding potential used by [30] could lead to activation of channels currents such as slow KA, Nav1. 9 and HCN channels. These channels have activation parameters that operate at more hyperpolarized potentials compared to those of other channels (See Fig 3A for n∞ of slow KA and Figs Aa and Ga in S2 Text for m∞ of Nav1. 9 and HCN). These channels could affect the amplitude of the AHP as well as recovery from it to the RMP. Some neurons tested by Hougaard et al. , [30] also fired tonically to a 500 ms suprathreshold current clamp. Bladder small DRG neurons usually fire just a single AP for such a stimulus (Fig 9B) while the medium-diameter bladder DRG neurons show tonic firing with many spikes [3,34,49]. A BKCa channel blocker, A-272651 increased the AP duration in L6-S1 spinal level capsaicin-sensitive small DRG neurons from rats [52], some of which supply the bladder [3,85,86]. The effect of BKCa channel block in our model did not result in an appreciable increase in AP duration (Fig 21D). A probable reason for this inconsistency could be that the neurons tested represent a different subpopulation of bladder small DRG neurons. Our model reproduced the behaviour obtained by BKCa block of Isolectin B4 (IB4) -negative cutaneous small DRG neurons (Fig 8B of [54]). Compared to IB4-positive neurons, IB4-negative neurons have fewer Nav1. 9 and KA channels and have a less negative RMP [35,124,125]. Bladder small DRG neurons, most of which are IB4-negative (∼75%, [3]) have a depolarized RMP (−53. 5 mV, [10]) than the RMP of small DRG neurons studied in [52] (< −60 mV). The expression of Nav1. 9 and KA channels also is far less than that in other non-bladder DRG neurons [35,51]. Moreover, bladder small DRG neurons generate a single AP for a long duration rectangular clamp similar to cutaneous IB4-negative small DRG neurons reported by [54] whereas neurons investigated by [52] gave rise to more than one AP for similar stimulus as also seen for IB4-positive cutaneous DRG neurons [54]. The firing frequency for IB4-positive cutaneous DRG neurons increased by using BKCa blocker while it did not for IB4-negative DRG neurons. In the light of these observations, it could be reasoned that neurons in Shieh et al. [52] are IB4-positive which probably have higher BKCa expression than IB4-negative bladder small DRG neurons. Taking this into consideration, our BKCa channel and bladder small DRG neuron models possibly represents model of IB4-negative bladder small DRG neurons. The two categories IB4-positive and IB4-negative neurons could be explored further through simulations by altering the conductances for Nav1. 9, KA and BKCa channels of our model as per the above observations and could also be explored experimentally by studying the ion channel expressions and electrophysiological properties of IB4-positive and IB4-negative bladder small DRG neurons. Although, IB4-positive bladder small DRG neurons represent smaller subpopulation (∼ 15-20%) [90] compared to IB4-negative, both seem to be significant in nociception [3,126,127]. Electrophysiological and ion channel expression differences in these two subpopulations of bladder small DRG neurons could be important regulators of excitability as shown in non-specific small DRG neurons [125,128], and also merit further experimental exploration. The precise genesis of the AHP in the bladder small DRG neuron and AHP effects on the excitability of bladder small DRG neurons [30] is not clear. In rabbit vagal sensory ganglion neurons, fAHPs generally last a few ms (∼ 30 ms) and were Ca2+-independent, mAHPs could last for 300 ms while sAHP rise in about 100 ms and can last or 2-15 s [120]. Both mAHPs and sAHPs were Ca2+-dependent. In enteric ganglia neurons, BKCa contributes to the fast AHP [17]. Some differences have been reported for the role of KCa channels in central neurons and peripheral sensory neurons. mAHPs were blocked by picomolar concentrations of apamin (SKCa blocker) in CNS neurons [32]. Apamin, even at millimolar levels did not block the mAHPs in vagal sensory neurons [31], in which and BKCa channels were predicted to underlie mAHP. SKCa channels, in contrast, were shown to contribute to sAHPs [31,121]. Based on the above lines of evidence and to clarify the contributions of KCa channels to different AHPs, we hypothesized that the fAHPs receive contributions chiefly from the BKCa conductance while SKCa channels contribute to mAHPs and sAHPs. It was found that BKCa can regulate the fAHP as they contribute to the fast rise of AHP (< 3 ms) and the AHP amplitude is augmented on increasing the BKCa conductance. SKCa channels contribute more strongly to the AHP phase after the fAHP peak, and hence may underlie the mAHP and sAHP. Bladder small DRG neurons obtained from rats with bladder inflammation and spinal cord injury were found to be more excitable than corresponding neurons from controls [1,5, 9,10,35,49]. DRG neuron somata in the former undergo hypertrophy [3] and exhibit plasticity in ion channel expression such as for TTX-S, Nav1. 8, slow KA and KDR channels [5,9, 10,34] leading to lower AP threshold and thus, greater excitability. Given these observations, we thought to test the effects of BKCa and SKCa channels on regulating the firing rate of the bladder small DRG neurons. It was found that increasing the conductance of BKCa and SKCa channels, which would mimic application of pharmacological channel openers to bladder small DRG neurons, reduced the spiking induced by changing channel densities of Nav1. 8, slow KA and KDR channels. We replicated the firing frequency (∼20 Hz) as seen in bladder small DRG neuron obtained from rats with inflammatory cystitis [10] (Fig 17A). Enhancement of SKCa conductance lead to a larger reduction in spiking than commensurate enhancement of BKCa conductance, suggesting that SKCa activators could be more effective in controlling hyperexcitability of bladder small DRG neurons than the BKCa activators. Slow KA currents are found in bladder small DRG neurons while the medium diameter bladder DRG neurons express fast KA currents [7,49]. Slow KA currents appear to be important currents in bladder small DRG neurons, as a drop in their current density in spinal transected rats [34] as well as in rats with chronic bladder inflammation [10,36] has been reported to augment the excitability of the neurons. Though several studies have been carried out to investigate the molecular components of these slow KA currents [34–36], the contribution of different Kv components to the slow KA current is not clear. We showed by optimization of our slow KA current model that the inactivating phase of experimental slow KA currents under voltage clamp in bladder small DRG neurons were best fit by a biexponential decay, comprising of a fast-decaying exponential (τh, fast) and a slow-decaying exponential (τh, slow). This could indicate the existence of at least 2 current components which in turn could mean 2 separate molecular components. The molecular identity of the slow KA channels expressed in these neurons is still not clear. KA channels in some non-bladder DRG neurons can form both homomers and heteromers [129]. In non-bladder DRG neurons, expression of Kv1. 1,1. 2,1. 4,4. 1 and 4. 3 KA channel forming subunits has been reported [35,36,129]. Yunoki et al. [35] showed that phrixotoxin 2, a Kv4 channel blocker was able to block the KA currents in IB4 (isolectin B4) -positive non-peptidergic somatic DRG neurons and not in the IB4-negative peptidergic bladder DRG neurons. From these data we conclude that Kv4 subunits are highly unlikely to contribute to bladder slow KA currents. Moreover, the steady state half-inactivation parameters of Kv4. 1,4. 2 and 4. 3 subunits (−44, −44 and −32 mV, respectively) expressed in Chinese hamster ovary cells [35] are more depolarized than that of bladder slow KA channel (−74. 2 mV) [10]. Hayashi et al. [36] reported a preferential expression of Kv1. 4 α subunits in bladder small DRG neurons. Takahashi et al. [34] and Hayashi et al. , [36] also suggested that Kv1. 1 or Kv1. 2 could form heteromers with Kv1. 4 to form slow KA currents in bladder small DRG neurons. Kv1 subunits expressed in HEK-293 cell lines showed different current inactivation profiles [130]. The Kv1. 2 channels exhibited a slow inactivation with an inactivation time constant close to that of the slow component modelled in our study (200-800 ms, τh, slow Fig 3C) while the Kv1. 1 channel expressing cells do not seem to inactivate discernibly within 1000 ms. Kv1. 4 expressing HEK cells showed an inactivation which is much faster than Kv1. 2 and is close to the value for the fast component of the KA channel model in our study (25-100 ms, τh, fast, Fig 3C). The similarity of values of inactivation time constants of Kv1. 2 and Kv1. 4 to those of our model suggests that the subunits most likely to form the slow KA channels found in the bladder small DRG neurons are heteromers of Kv1. 2 and Kv1. 4. Another possible reason for two different phases in the inactivation of slow KA currents of bladder small DRG neurons can be the existence of dual inactivation mechanism as mediated by the same molecular unit comprising the slow KA current. Kv1. 4 subunits could show such phenomena [131], displaying two inactivation mechanisms: (i) N-type, a fast inactivation (50-350 ms) which is caused by binding and blocking of channel pore with N-terminal ball, and (ii) C-type, a slower inactivation (2-3 s) which is believed to be caused by intracellular and conformational changes of the channel [131]. Bett et al. [131] showed that the coupling between N-type and C-type inactivation in Kv1. 4 channels can explain experimentally recorded Kv1. 4 currents in inactivation time constants with intermediate values of fast and slow inactivation. A similar coupling could also explain the biexponential decay found in the slow KA currents of the bladder DRG neuron. Considering all the arguments above, a more detailed molecular analysis of slow KA channels of bladder neurons will shed light on the unresolved questions. Contributions HCN, KCNQ/M and slow KA channels to different AHPs were not studied as we only focussed on the contribution of BKCa and SKCa channels. Moreover, the expression and the contribution of HCN and KCNQ/M channels in the bladder small DRG neurons comparatively smaller [8,42] than other currents and may have minor effects on AHP. The effect of neurotransmitters such as ATP and certain channels such as TRP (transient receptor potential) vanilloid 1 and ASIC (acid-sensing) channels were not added to the model. These mechanisms are activated by specific stimuli (such as capsaicin and abnormal pH) which assume greater importance in pathological conditions. Likewise, the effect of the satellite glial cells (SGCs) on the soma were omitted for similar reasons. On the morphological level, a complete model with axon and its sensory terminals in the bladder (including various receptors e. g. for noxious stimuli) can provide a finer-grained understanding of sensory information transmission from the bladder. Few studies have reported effects of the geometry of the T-junction of the DRG neuron and ion channel densities in stem axon and soma on the electrical activity [11–13]. Taking these considerations into account, conduction of sensory information can be understood in greater depth. We have commenced work on several of these fronts such as modelling the TRPV1 channels [39] and SGC interactions with the DRG neuron soma [38], and they will be taken up in future studies. Our detailed and biophysically constrained computational model of bladder small DRG neuron soma presented here was able to reproduce experimentally observed signals such as the action potential and cytoplasmic Ca2+ transients. By exercising our model in appropriate ways we were able to (i) corroborate our hypothesis concerning the effect of inwardly rectifying SKCa channels on neuronal excitability; (ii) gain several insights into the roles of BKCa and SKCa channels in bladder small DRG neuron such as the contributions of these channels to the genesis of different types of AHP and the relative efficacies of BKCa and SKCa channels in the regulation of repetitive firing in these neurons, thus casting light on hitherto unresolved biological questions. In addition, we suggest a difference in expression of BKCa in IB4-negative and IB4-positive populations of bladder small DRG neurons which could determine the repetitive firing similar to that seen in cutaneous small DRG neurons [54]. We also suggest that the slow KA currents could be made up of 2 components; a fast inactivating and a slow inactivating current which could either be a result of heteromeric KA channel formed by Kv1. 4 and Kv1. 2 subunits (both found in bladder small DRG neurons, [34,36] or a result of interaction between 2 different inactivation states exhibited by Kv1. 4 subunits (C-type and N-type). These insights can be tested experimentally, for instance by the use of drugs to remove the inward rectification of the SKCa channel. The consequent reduction in spiking frequency may in some conditions hold promise as a potential intervention such as in mitigating hyperexcitability of bladder small DRG neurons, thus having implications for certain types of pathology. Our work thus provides heuristic predictions that can lead to a deeper understanding of bladder small DRG neuron function, its role in the regulation of bladder physiology and its possible involvement in pathophysiology.
summary: The small dorsal root ganglion (DRG) neurons of the bladder carry information related to pain from the bladder to the spinal cord. The level of electrical activity of these neurons is generally low but rises in abnormal conditions such as bladder inflammation and spinal cord injury. In order to investigate the reasons for this hyperactivity, we constructed a model of the bladder small DRG neuron soma including its membrane ion channels and intracellular Ca2+ dynamics. One of the channels, the small-conductance Ca2+-activated K+ (SKCa) channel present in these neurons which was earlier thought to be activated solely by intracellular Ca2+ concentration was recently shown to exhibit inward rectification with respect to the neuron’s membrane potential. It was found that SKCa inward rectification can alter the repetitive firing of the bladder small DRG neurons. We also delineated the role SKCa and BKCa (large-conductance Ca2+-activated K+) channels to the complex afterhyperpolarization (AHP) of the neuron’s action potentials, shedding light on the mechanisms that govern repetitive firing in these sensory neurons. Our findings have implications for the normal biophysics and dysfunctional states of urinary bladder arising from changes in sensory axon function, and these are discussed.
keywords: medicine and health sciences
  action potentials
  membrane potential
  bladder
  endoplasmic reticulum
  cell processes
  electrophysiology
  neuroscience
  ion channels
  mitochondria
  bioenergetics
  cellular structures and organelles
  animal cells
  proteins
  biophysics
  cell membranes
  physics
  biochemistry
  cellular neuroscience
  cell biology
  anatomy
  secretory pathway
  physiology
  neurons
  biology and life sciences
  cellular types
  renal system
  energy-producing organelles
  potassium channels
  physical sciences
  neurophysiology
title: A biophysically detailed computational model of urinary bladder small DRG neuron soma