Computational modeling of inhibitory signal transduction in urinary bladder PDGFRα+ cells

Abstract A crucial aspect of bladder function is the maintenance of a normo-active detrusor during bladder filling. The physiological mechanisms and pathways underlying this function are yet to be fully elucidated. Premature detrusor contractions are a key phenotype in detrusor overactivity, a common pathophysiological condition of the urinary bladder. Recent literature has identified PDFGRα+ cells as mediators in transducing inhibitory signals to detrusor smooth muscle cells via gap junctions. We employ computational modeling to study transduction pathways via which inhibitory signals are generated in PDFGRα+ cells in response to purinergic, nitrergic and mechanical stimuli. The key focus of our study here is to explore the effect of ATP, stretch and NO on the membrane potential of PDFGRα+ cells, which is driven to hyperpolarized potentials via the activation of SK3 channels. Our results indicate that purinergic, mechanical and nitrergic inputs can induce significant membrane hyperpolarizations of 20–35 mV relative to the resting membrane potential. Given the interconnections between PDFGRα+ cells and detrusor SMCs through gap junctions, these hyperpolarizations can have significant functional implications in the maintenance of a normo-active detrusor as also in departures from this state as seen in detrusor overactivity.


Introduction
Overactive Bladder (OAB) is a pathological condition of the urinary bladder and is defined as urgency, with or without urge incontinence, accompanied by nocturia and frequency (Abrams 2003).Further, OAB can be present with or without symptoms of detrusor overactivity (DO), which is a urodynamic observation characterised by involuntary detrusor contractions during bladder filling (Abrams 2003;Lee et al. 2014;Koh et al. 2018).In other words, the maintenance of relaxation in the detrusor smooth muscle during bladder filling, which is a crucial aspect of bladder function, is compromised.The various mechanisms and pathways that underlie the maintenance of a relaxed muscle tonus in the urinary bladder are yet to be thoroughly understood.A more comprehensive understanding of these pathways is essential for identifying pharmacological interventions for treating DO.
The urinary bladder wall has a heterogeneous tissue composition.The detrusor smooth muscle is the principal component of the bladder wall and its contractile apparatus.In addition to the detrusor smooth muscle cells (dSMCs), the bladder wall comprises specialized cell populations.These include sensory afferents, urothelial cells and bladder interstitial cells (ICs).ICs are thought to play a critical role in regulating the function of dSMCs (Koh et al. 2018).
Studies have identified a sub-population of bladder ICs which express the platelet-derived growth factor alpha (PDGFRa) receptor (Koh et al. 2012;Monaghan et al. 2012).These cells are found distributed within the bladder detrusor and the submucosa.Within the detrusor, they form close structural connections with neighbouring dSMCs via gap junctions and are in close apposition to nerve varicosities (Koh et al. 2012).
PDGFRaþ cells are thought to act as transducers mediating inhibitory regulation to the bladder detrusor smooth muscle in response to purinergic (Koh et al. 2018), nitrergic (Mamas et al. 2003) and stretch stimulation (Lee et al. 2017).Experimental investigations have reported that the application of exogenous adenosine triphosphate (ATP) results in a transient contraction followed by a sustained relaxation of the detrusor (Boland et al. 1993;Giglio et al. 2001).It is hypothesized that the mechanism underlying purinergic-mediated relaxation is the g-protein coupled purinergic receptor (P2Y) induced activation of the small conductance calcium-activated potassium (SK3) channel (Obara et al. 1998).Lee et al. (2013) demonstrated that the PDGFRaþ cells expressed an SK3 channel current density 100 times higher than the smooth muscle cells.This selective expression of SK3 channels in PDGFRaþ cells and the structural connection between PDGFRaþ cells and dSMCs is thought to play a critical role in mediating ATPinduced relaxation in the dSMCs.This hypothesis has gained further credence by functional studies demonstrating an increase in bladder overactivity in SK3 knockout mice (Herrera et al. 2003) and an increase in bladder contractility following the application of SK3 channel blocker apamin (Thorneloe et al. 2008).
In animal models, it has been demonstrated that nitric oxide (NO) induces dSMC relaxation, and the application of nitric oxide synthase (NOS) inhibitors reduced detrusor contractions (Mumtaz et al. 2000;Mamas et al. 2003).NO acts in target tissues via the nitric oxide-soluble guanyl cyclase-cyclic guanosine monophosphate (NO-sGC-cGMP) pathway.However, in isolated guinea pig bladder preparations, the application of the NO donor sodium nitroprusside did not raise cyclic guanosine monophosphate (cGMP) levels in the dSMCs suggesting the involvement of an indirect pathway for mediation of NO-induced relaxation (Gillespie and Drake 2004).This indirect pathway could be via NO action on PDGFRaþ cells, which express the nitric oxide sensitive soluble guanylyl cyclase (NO-sGC) and exhibit intense cGMP immunoreactivity (Blair et al. 2014).
The versatility of PDGFRaþ cells in regulating bladder function has been further demonstrated in murine detrusor PDGFRaþ cells, where interactions between mechanosensitive channelswhich mediate calcium (Ca 2þ ) entry into PDGFRaþ cellsand SK3 channels suppressed premature contractions of the bladder (Lee et al. 2017).A candidate channel for mediating stretch-induced Ca 2þ entry in PDGFRaþ cells is the stretch-activated Piezo1 channel, expressed abundantly in PDGFRaþ cells (Dalghi et al. 2019).
The above-mentioned functional studies indicate a likelihood for the participation of PDGFRaþ cells in maintaining a normo-active detrusor.However, they do not provide quantitative insights into the intracellular signals and intermediary secondary messengers participating in the transduction of purinergic, nitrergic and mechanical stimuli in PDGFRaþ cells.Elucidating these pathways is crucial to knowing how PDGFRaþ generate inhibitory potentials.Yeoh et al. (2016) described a mathematical model for purinergic signalling in PDGFRaþ cells of the GI tract.However, there is a dearth of quantitative data on the effect of activation of SK3 channels on the membrane voltage in bladder PDGFRaþ cells, particularly in response to mechanical stretch and NO.We address this gap by constructing a biophysically detailed and physiologically realistic computational model for the PDGFRaþ cells that details the following inhibitory pathways: (i) purinergic-activated P2Y receptor and SK3 channel kinetics; (ii) mechano-activated Piezo1 induced SK3 channel activation; (iii) NO activated cGMP pathway and SK3 channel activation.The primary objective behind constructing this PDGFRaþ cell model is to ascertain the impact of purinergic, nitrergic and mechanical stimulation on the membrane voltage in PDGFRaþ cells, thereby gaining a better mechanistic understanding of the cellular mechanisms that underlie inhibitory signals generated in these cells.

Methods
The PDGFRaþ cell model comprises the following three components: i. ATP-induced Ca 2þ dynamics ii.Ion Channels: SK3; Piezo1 channel; & non-specific cation channels (NSCC) iii.NO-induced SK3 channel activation The base framework of the PDGFRaþ cell model has been adapted from Yeoh et al. (2016), who described a mathematical model for purinergic signalling in PDGFRaþ cells of the GI tract.We modified this model to obtain a stable resting membrane potential (RMP) and to the Ca 2þ dynamics schema to obtain stable baseline levels of cytosolic calcium in the absence of purinergic input.We also tuned the SK3 channel kinetics to match the SK3 currents simulated by Yeoh et al. (2016).We added to this framework the mechanosensitive Piezo1 conductance (Gupta and Manchanda 2022) and a description of the NO-induced activation of SK3 conductance (adapted from Kapela et al. 2008).The integrated framework allows us to evaluate signal transduction associated with the generation of inhibitory potentials in PDGFRaþ cells.
We describe sequentially in the following sub-sections the ionic mechanisms that govern the inhibitory membrane responses in the PDGFRaþ cell model.
For each ionic mechanism, we mention here only the principal governing equations.The supporting component equations for each mechanism have been detailed in Section S3 of the Supplementary Material.Further, Table A.1 of the Supplementary Material contains the description and values of each of the model parameters.To note: the model description for the ATP-induced inositol triphosphate (IP3) production and the resultant IP3-mediated intracellular Ca 2þ dynamics, adapted from Yeoh et al. (2016), is described in detail in Section S2 of the Supplementary Material.The model has been implemented on MATLAB, and the rate equations have been computed using the forward Euler method with timestep for integration dt ¼ 0.001s.To visualize the different components of the model framework, Figure 1 depicts a schematic of the important components of the PDGFRaþ cell model and the interactions between its sub-components.

SK3 channels
SK3 channels are activated in response to an elevation in the cytosolic [Ca 2þ ] levels.The current through the SK3 channels is given by Equation (1) as described by Yeoh et al. (2016), who validated the SK3 channel kinetics against experimental data (Kurahashi et al. 2011).
Here, g SK3 is the maximum SK3 channel conductance (Kurahashi et al. 2011); P o represents the open channel probability; V m is the membrane voltage and E K represents the reversal potential for potassium (K þ) ions.The rate equation coding for the change in P o is given by Equation ( 2).
Here, s represents the activation time constant and P inf represents the steady state value of the SK3 open channel probability, described using a Hill equation (Equation (3)).
Here, EC 50 is the half-maximal effective concentration, and n represents the Hill coefficient describing the cooperativity of Ca 2þ binding to the SK3calmodulin complex associated with SK3 channel activation.Values of the constants associated with Equations ( 1)-( 3) can be found in Table A.1 of the Supplementary Material.

Piezo1 channels
Stretch-activated Ca 2þ influx has been reported in bladder PDGFRaþ cells (Lee et al. 2017), with the incoming Ca 2þ resulting in the subsequent activation of SK3 channels.A candidate channel activated by stretch found in bladder PDGFRaþ cells is the Piezo1 channel (Dalghi et al. 2019).We have previously described a mathematical model for stretch-activated Piezo1 channels (Gupta and Manchanda 2022), where we validated the Piezo1 channel kinetics against experimental data (Coste et al. 2010).We adopt this schema into the PDGFRaþ cell model to study interactions between the Piezo1-mediated Ca 2þ influx and SK3 channels.Equation (4) gives the governing equation for the Piezo1 current (I Pz ).Here the open channel probability of the Piezo1 channels is modelled as a product of two gating variables d Pz and f Pz where d Pz codes for the activation of Piezo1 channels and is a function of the tension developed in the membrane following membrane stretch, and f Pz is the timedependent gating variable coding for the inactivation of Piezo1 channels.
Here, G Pz represents the maximal Piezo1 channel conductance, V m is the membrane potential of the PDGFRaþ cell and E rev is the reversal potential for the Piezo1 current.Initial conditions, values of the different constants associated with Equation ( 4) and the component equations for the gating variables d Pz and f Pz can be found in Sections S1 and S3 of Supplementary Material.

NO-induced SK3 channel activation
A rise in NO stimulation results in the elevation of the secondary messenger cGMP, which regulates several crucial cellular mechanisms such as ionic conductances and pumps in the plasma and the endoplasmic reticulum membranes (Kapela et al. 2008).One such pathway/mechanism that can be activated by NO in PDGFRaþ cells are the SK3 channels.It has been shown that a rise in NO-activated cGMP results in an increase in K þ conductance (Koh et al. 1995).
Towards modelling the effects of NO on the SK3 conductance, we adopt the model description for cGMP formation by Condorelli and George (2001) and adapt the scheme described by Kapela et al. (2008) towards modelling NO-induced SK3 channel activation.The schema for the production of the secondary messenger cGMP by NO is detailed in Section S3 of the Supplementary Material.The governing equation for the NO-cGMP-activated SK3 current (I SKNO ) is given by Equation ( 5), where G SK3 is the maximal conductance of the SK3 channel; P oSKNO is the open channel probability of the SK3 channel following NO stimulation.
The rate equation coding for the change in the open channel probability P oSKNO is given by Equation ( 6).Here, s SKNO represents the activation time constant; P infNO given by Equation ( 7) represents the steady state value of P oSKNO following NO stimulation.
In Equation ( 8), V halfSKNO is the half-activation potential for the activation of SK3 channels following NO stimulation and is a function of Ca 2þ , NO and cGMP.It is represented by Equation ( 10), adapted from Kapela et al. (2008).
Here, V1 & V2, V3 and V4 represent voltage, cGMP and NO-dependent half-activation potentials, respectively.K cGMP and K NO represent dissociation constants for the regulatory effect of cGMP and NO on the half-activation potentials V3 and V4, respectively.Values and descriptions of the constants can be found in Table A.1 of the Supplementary Material.

Effect of ionic currents on V m
Equation ( 9) gives the governing equation describing the time dependence of the membrane potential V m , based on the classical Hodgkin-Huxley approach, where the membrane is represented as an equivalent electrical circuit comprising a capacitor in parallel with the various ionic currents that represent the ion channels.

Results
We have organized our results into three sections which detail the effects of ATP, stretch, and NO on the membrane potential (V m ) of the PDGFRaþ cell.We first present the ATP-induced activation of SK3 channels, which results in membrane hyperpolarization of the PDGFRaþ cell.These responses have been previously validated against experimental recordings (Kurahashi et al. 2011;Yeoh et al. 2016).We next describe the results of stretch-induced inhibitory signalling followed by NO-induced inhibitory signalling.

ATP-Induced inhibitory signalling
We provide two sets of stimulus inputs in line with the stimulation protocol employed by Yeoh et al. (2016).In the first simulation, we clamp the membrane potential at a holding potential of À50 mV: A train of ATP inputs of 0.1, 1, 10 and 1000 mM is given at 100, 200, 350 and 500 s, respectively, for a brief exposure of 20 s each.Figure 2 depicts the plots of the important read-outs from the model following purinergic stimulation.
We see from Figure 2a that the fraction of activated G-protein increases with an increase in the intensity of the ATP stimulus.This results in an enhancement in the production of IP 3 in the cytosol (Figure 2b).Elevated IP 3 releases Ca 2þ from the ER via the IP 3 R receptors, followed by the uptake of Ca 2þ from the cytosol back into the ER by the sarcoendoplasmic reticulum calcium ATPase (SERCA) pump.Due to the difference in the temporal response of the IP 3 R and the SERCA pump, Ca 2þ transients of varying amplitude are set up in the cytosol, as seen in Figure 2c.The Ca 2þ transients, in turn, activate the SK3 channels, resulting in outward hyperpolarizing potassium currents (I SK3 ).As seen in Figure 2d, the outward-flowing K þ currents match in amplitude with the peak values of the SK3 currents simulated by Yeoh et al. (2016), represented by black circles.The voltage clamp condition was removed to evaluate the effect of SK3 currents on the membrane voltage.Following the stimulus protocol employed by Yeoh et al. (2016), a train of ATP impulses of concentrations 0.1, 1, 10 and 1000 mM (lasting 0.5 s each) was given at 100, 300, 500 and 700 s. Figure 3 shows the resultant V m responses.
As seen in Figure 3a, the membrane hyperpolarizes in a concentration-dependent manner with increasing negative amplitudes as the ATP stimulus increases.This is due to the outward SK3 currents, which activate in response to the ATP-induced increase in cytosolic Ca 2þ levels.The peak amplitude of the hyperpolarization is $ 30 mV negative to the rest membrane potential of À 50 mV: Purinergic inhibitory junction potentials recorded in smooth muscle cells of the colon have reported a net hyperpolarization in the range of 20 À 30 mV negative to the resting membrane potential (RMP) (Gallego et al. 2008) which is similar to the range of hyperpolarization seen in the simulation (Figure 3a).Further, a recently published recording by Lee et al. 2022 shows a hyperpolarization of $ 20 mV amplitude relative to the RMP in detrusor PDGFRaþ cells following partial SK3 activation by SK3 channel activator CyPPA (Figure 3b).

Stretch-induced inhibitory signaling
As detailed in the methods, we incorporated a Piezo1 conductance into the PDGFRaþ cell model framework to explore interactions between stretch-mediated Ca 2þ input and SK3 channels.The kinetics of the Piezo1 current have been validated by us, as reported previously (Gupta and Manchanda 2022), against experimental data (Coste et al. 2010).We adopted this model and incorporated it into the PDGFRaþ cell model framework.As a first step towards evaluating the effect of Piezo1-mediated Ca 2þ entry on the SK3 channel activation, we provided a net-stretch input of 8 mm for a time period of 10 s at t ¼ 50 s, as seen in Figure 4a.
With this input as stimulus, a fast activating and rapidly inactivating Piezo1 current is observed at t ¼ 50 s, zoomed-in portion of the time axis in Figure 4b.It is to be noted that even though the input stimulus lasts for 10 s, the Piezo1 current inactivates rapidly (Figure 4b).The Piezo1 channels mediate Ca 2þ entry into the cell, as can be seen in the rise of Ca 2þ in the cytosol (Figure 4c).The Ca 2þ pump removes the excess intracellular Ca 2þ from the cytosol and into the extracellular space, albeit at a much slower rate, thereby setting up a Ca 2þ transient.Elevated cytosolic [Ca 2þ ] i activates the SK3 channels resulting in an outward K þ current (Figure 4d).
We next proceeded to study the effect of varying stretch inputs on the membrane voltage of the PDGFRaþ cell.We removed the clamp to make the membrane voltage a function of the various conductances.As input to the model, we provided varying net-stretches of 2, 4 and 8 mm at t ¼ 50 s, t ¼ 300 s and t ¼ 600 s, respectively.The stretch inputs were provided for a period of 10s.As can be seen in Figure 5, the membrane responses, i.e. membrane hyperpolarization's are stretch dependent, i.e. as the stretch levels increase, the membrane hyperpolarization also increases (Figure 5).Also, to be noted is the slight depolarization corresponding to the activation of Piezo1 channels which very briefly overpowers the SK3 currents, following which it inactivates rapidly ($15 ms).The maximum level of hyperpolarization induced in the PDGFRaþ cell is À35 mV relative to the RMP, corresponding to a stretch input of 8 mm.For stretch inputs between 4 mm and 8 mm, the net hyperpolarization induced is between $ 20 À 35 mV which is similar to the inhibitory response seen during purinergic signalling (Figure 3).

NO-induced inhibitory signaling
Gaseous nitric oxide derived neuronally or from the urothelium diffuses directly into the PDGFRaþ cell cytosol through the plasma membrane and activates the soluble guanyl cyclase-cyclic guanosine monophosphate (sGC-cGMP) pathway upregulating the production of the secondary messenger cGMP.Elevated cGMP levels in the cytosol have a cascading effect on several molecular mechanisms, including the endoplasmic reticulum (ER) and SK3 channels.Both cGMP and NO activate SK3 channels.Equation ( 8) captures the regulatory effect on the open channel probability of the SK3 channel by Ca 2þ , NO and cGMP.Since cGMP reduces cytosolic Ca 2þ to baseline levels, we took [Ca 2þ ] i as constant.We first evaluated the effect of NO on cGMP synthesis and then the overall effect of NO and cGMP on the SK3 currents.As input to the model, we provided varying [NO] of 0.01 mM, 0.1, 1 and 10 mM at t ¼ 100 s, t ¼ 400 s, t ¼ 700 s and t ¼ 1000s, respectively.The PDGFRaþ cell is clamped at À50 mV: As seen in Figure 6a, the concentration of cytosolic cGMP increases in a concentration-dependent manner in response to increasing NO.A combination of NO and cGMP activate SK3 channels which mediate an outward K þ current.NO and cGMP-activated SK3 current has an amplitude comparable to the ATPinduced Ca 2þ activated SK3 current (Figure 6b).
We next evaluated the effect of varying [NO] inputs on the membrane voltage of the PDGFRaþ cell.We removed the clamp voltage to make the membrane voltage a function of the various conductances.As input to the model, we provided varying [NO] of 0.01 mM, 0.1, 1 and 10 mM at t ¼ 100 s, t ¼ 400 s, t ¼ 700 s and t ¼ 1000s, respectively.Each [NO] input was provided for a period of 100s.With increasing NO input, the membrane hyperpolarization increases in a concentration-dependent manner (Figure 7).A maximum net-hyperpolarization of $ 35 mV negative to the RMP of À50 mV, corresponding to an NO input of 10 mM is observed from Figure 7. which in the range similar to the inhibitory response seen when the PDGFRaþ cell was presented with purinergic and stretch stimulation.

Discussion
Our model framework for the PDGFRaþ cell integrates signal transduction pathways for three modes of stimuli known to be relevant in bladder physiology: ATP, stretch and NO.The molecular machinery of the PDGFRaþ cell allows it to transduce these stimuli into inhibitory responses in the form of observable hyperpolarizations, which have been proposed/hypothesized to maintain a normo-active detrusor during bladder filling (Boland et al. 1993;Giglio et al. 2001;Koh et al. 2018).We have incorporated three signalling pathways into the model framework, namely: (i) the P2Y-SK3 pathway; (ii) Piezo1-SK3 pathway; (iii) NO-cGMP-SK3 pathway.The component models for the three aforementioned signaling pathways have been independently characterized and validated against experimental recordings (Kapela et al. 2008;Yeoh et al. 2016;Gupta and Manchanda 2022).We have further tuned the Ca 2þ dynamics schema and the background conductance to obtain stable baseline Ca 2þ levels and RMP that has been reported for PDGFRaþ cells.We integrated these mechanisms into the PDGFRaþ cell framework to predict the inhibitory responses generated by this cell type via our simulations.
From our simulations, the ATP-activated P2Y-SK3 pathway induces significant membrane hyperpolarization's negative to the RMP of the PDGFRaþ cell.A distinguishing feature of the PDGFRaþ cells is their lack of expression of active voltage conductances.This allows the membrane potential to produce passive hyperpolarized responses following the activation of SK3 channels.
As detailed in the introduction, Piezo1-SK3 interactions and NO-cGMP-SK3 interactions provide a pathway for mediating inhibitory signalling in PDGFRaþ cells.Accordingly, we expand our framework to explore interactions between the Piezo1 and SK3 channels.We see in our model simulations that Piezo1-mediated Ca 2þ entry activates SK3 channels to elicit membrane hyperpolarizations (Figure 5) that are comparable to those produced via purinergic-induced membrane hyperpolarization (Figure 3).Given the distribution of PDGFRaþ cells within detrusor smooth muscle bundles, which is a highly mechanical environment generating contractions, micro contractions and relaxations cycles, and the syncytial connections that the PDGFRaþ cells form with neighbouring dSMCs via gap-junctions, Piezo1 channels provide a transduction pathway for inducing inhibitory responses in dSMCs in response to stretch experienced in their localized surroundings.
While the application of NO agonist suppresses detrusor contractions in whole bladder preparations (Mumtaz et al. 2000;Mamas et al. 2003), it is noteworthy that in isolated guinea pig bladder preparations, NO did not have a significant impact on dSMCs.This observation underscores the point that while NO does induce inhibitory responses in dSMCs, it is not through direct signal transduction but via an intermediary entity.PDGFRaþ cells, in theory, have the molecular machinery to transduce NO-mediated inhibitory signalling and their interconnection with dSMCs provides a pathway for the inhibitory responses, which manifests as hyperpolarization of the membrane as seen in our model simulations (Figure 7).
The highly selective and high-density expression of SK3 in PDGFRaþ cells in comparison to other cell types found in the bladder wall has important pathological implications.Specifically, bladder overactivity has been linked to decreased expression of SK3 channels (Herrera et al. 2003;Thorneloe et al. 2008); Furthermore, interactions between mechanosensitive channels and SK3 suppressed premature bladder contractions (Lee et al. 2017).Also, the presence of the NO-sGC-cGMP pathway in these cells, which activates SK3 currents and the absence of this pathway in dSMCs points to their importance in transducing NO inputs to maintain a normo-active detrusor during bladder filling.This pathway, therefore, can be a novel pharmacological target for treating detrusor overactivity by enhancing SK3 currents which would hyperpolarize PDGFRaþ cells and, in turn, have an inhibitory effect on the neighbouring dSMCs via the gap junctional connections.Our findings indicate that alteration in SK3 expression in these cells or any breakdown in signal transduction in the Piezo1-SK3 or NO-cGMP-SK3 pathway can have important pathological consequences in relation to detrusor overactivity.Further, from a clinical perspective, the selective expression of SK3 in PDGFRaþ cells could provide a novel pharmacological target for treating conditions such as detrusor overactivity and detrusor underactivity.We propose that upregulating the activation of SK3 channels via SK3 activators will result in enhanced hyperpolarization of PDGFRaþ cells, which in turn will likely attenuate detrusor overactivity.Similarly, using highly specific SK3 blockers will have a reverse effect by counteracting the hyperpolarization induced by PDGFRaþ cells, and this could be effective in treating conditions where detrusor underactivity is observed.
While functional studies have pointed to a significant role of PDGFRaþ cells in bladder signaling by suppressing bladder contractions during the filling phase, as stated in the introduction and the results section, there is no quantitative data available for membrane hyperpolarization in response to ATP, NO and stretch.A possible reason for this shortage in quantitative experimental data stems from limitations in isolating these cells, given their low volume compared to the dSMCs.Further, interstitial cells are known to change phenotype in cultures, making it difficult to perform functional studies in isolation.Therefore, quantitative data from simulations where we have reconstructed the molecular mechanisms relevant to signal transduction in PDGFRaþ cells show that significant inhibitory responses can be generated in these cells, which can impact the RMP of the syncytial network of PDGFRaþ cells and dSMCs.Our model framework, in summary, shows that the unique molecular signature of PDGFRaþ cells allow them to respond to a variety of stimuli by generating inhibitory responses in the form of membrane hyperpolarizations.

Disclosure statement
No potential conflict of interest was reported by the authors.

Funding
This work is supported in part by the Department of Biotechnology (DBT), India (grant number BT/PR12973/ MED/122/47/2016) and in part by the Indian Institute of Technology Bombay.The funders had no role in study design, data collection and analysis, decision to publish, or manuscript preparation.

Figure 1 .
Figure 1.Schematic of the PDGFRaþ cell model.The model framework receives three kinds of inputs, namely (i) ATP; (ii) Stretch; and (iii) nitric oxide.The dashed lines represent the intercoupling between different components of the model.The solid lines represent the various fluxes and ionic currents, with the arrowheads depicting their respective directions.
9) Here I SK3 represents the Ca 2þ activated SK3 current (Equation (1)); I Pz represents the Piezo1 current (Equation (4)); I NSCC represents the NSCC current; and I CaPump represents the current generated by the Ca 2þ pump extruding Piezo1-mediated Ca 2þ back into the extracellular fluid.The component equations for the NSCC current and the I CaPump are given in Section S3 and Section S2 of the supplementary material.

Figure 2 .
Figure 2. (a) Fraction of activated G-protein following purinergic stimulation; (b) IP 3 production from PIP 2 following activation of G-protein via the PLC pathway; (c) IP 3 mediated Ca 2þ transients in the cytosol; (d) outward flowing Ca 2þ activated SK3 currents.The peak values of the SK3 currents simulated by Yeoh et al. (2016) is represented by the black circles in (d).Note: (i) a train of ATP inputs of 0.1, 1, 10 and 1000 mM was given at 100, 200, 350 and 500 s, respectively, for a brief exposure of 20 s each; (ii) Membrane potential was clamped at À50 mV:

Figure 3 .
Figure 3. (a) Simulation output of ATP-induced membrane hyperpolarization in PDGFRaþ cell via activation of outward flowing SK3 currents.(b) Experimental recording of membrane hyperpolarization in detrusor PDGFRaþ cells (adapted from 'Figure 4A: in detrusor PDGFRaþ cells from control bladders, CyPPA (10 lM) induced membrane hyperpolarization under current clamp (I ¼ 0, red dot line)' from Lee et al. 2022 is licensed under CC by 4.0).

Figure 4 .Figure 5 .
Figure 4. (a) A net-stretch of 8 mm at t ¼ 50s given as input to the model; (b) Piezo1 current profile (zoomed-in View of the time axis) showing a rapidly activating and fast inactivating Piezo1 current; (c) profile of the [Ca 2þ ] i following Ca 2þ influx via the Piezo1 channels; (d) Ca 2þ activated outward flowing SK3 currents.To be noted: the PDGFRaþ cell was clamped at À50 mV:

Figure 6 .Figure 7 .
Figure 6.(a) cGMP formation in the cytosol in response to NO stimulation; (b) SK3 current profile activated by cGMP and NO.Note: (i) [NO] input of 0.01 mM, 0.1, 1 and 10 mM was provided to the model at t ¼ 100 s, t ¼ 400 s, t ¼ 700 s and t ¼ 1000 s, respectively.(ii) the PDGFRaþ cell is clamped at À50 mV: