A biophysically comprehensive model of urothelial afferent neurons: implications for sensory signalling in urinary bladder.

The urothelium is the innermost layer of the bladder wall; it plays a pivotal role in bladder sensory transduction by responding to chemical and mechanical stimuli. The urothelium also acts as a physical barrier between urine and the outer layers of the bladder wall. There is intricate sensory communication between the layers of the bladder wall and the neurons that supply the bladder, which eventually translates into the regulation of mechanical activity. In response to natural stimuli, urothelial cells release substances such as ATP, nitric oxide (NO), substance P, acetylcholine (ACh), and adenosine. These act on adjacent urothelial cells, myofibroblasts, and urothelial afferent neurons (UAN), controlling the contractile activity of the bladder. There is rising evidence on the importance of urothelial sensory signalling, yet a comprehensive understanding of the functioning of the urothelium-afferent neurons and the factors that govern it remains elusive to date. Until now, the biophysical studies done on UAN have been unable to provide adequate information on the ion channel composition of the neuron, which is paramount to understanding the electrical functioning of the UAN and, by extension, afferent signalling. To this end, we have attempted to model UAN to decipher the ionic mechanisms underlying the excitability of the UAN. In contrast to previous models, our model was built and validated using morphological and biophysical properties consistent with experimental findings for the UAN. The model included all the channels thus far known to be expressed in UAN, including; voltage-gated sodium and potassium channels, N, L, T, P/Q, R-type calcium channels, large-conductance calcium-dependent potassium (BK) channels, small conductance calcium-dependent (SK) channels, Hyperpolarisation activated cation (HCN) channels, transient receptor potential melastatin (TRPM8), transient receptor potential vanilloid (TRPV1) channel, calcium-activated chloride(CaCC) channels, and internal calcium dynamics. Our UAN model a) was constrained as far as possible by experimental data from the literature for the channels and the spiking activity, b) was validated by reproducing the experimental responses to current-clamp and voltage-clamp protocols c) was used as a base for modelling the non-urothelial afferent neurons (NUAN). Using our models, we also gained insights into the variations in ion channels between UAN and NUAN neurons.

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

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.

Computational modeling of stretch induced calcium signaling at the apical membrane domain in umbrella cells.

The urinary bladder epithelium comprises a specialised population of superficially placed cells called the umbrella cells. The apical membrane domain of umbrella cells has several intriguing morphological properties and is the site for various signaling activities. A key function of umbrella cells is to sense mechanical stimuli as the bladder stretches in response to filling. More specifically, the mechanotransduction of stretch into subcellular signals is brought about by the activation of Piezo1 channels that mediate calcium into the cell interior. The incoming calcium is critical to several aspects of umbrella cell signaling, including regulation of exocytosis, ATP release and downstream purinergic signaling. We report here a computational framework that models stretch-induced mechanotransduction via Piezo1 channels and the resulting calcium signaling in umbrella cells factoring in morphological details of subcellular compartment volumes. Our results show the following: (i) activation of Piezo1 conductance in response to stretch; (ii) development of varying Piezo1 mediated [Ca2+] profiles in subcellular compartments, namely, the apical sub-plasma membrane space, cytosol and mitochondria. The varying calcium amplitudes and temporal profiles in the subcellular compartments indicate highly specialised roles for stretch-mediated calcium in umbrella cells, including its potential effect on the energetics of mitochondria and the regulation of exocytosis.

Difference in axon diameter and myelin thickness between excitatory and inhibitory callosally projecting axons in mice.

Synchronization of network oscillation in spatially distant cortical areas is essential for normal brain activity. Precision in synchronization between hemispheres depends on the axonal conduction velocity, which is determined by physical parameters of the axons involved, including diameter, and extent of myelination. To compare these parameters in long-projecting excitatory and inhibitory axons in the corpus callosum, we used genetically modified mice and virus tracing to separately label CaMKIIα expressing excitatory and GABAergic inhibitory axons. Using electron microscopy analysis, we revealed that (i) the axon diameters of excitatory fibers (myelinated axons) are significantly larger than those of nonmyelinated excitatory axons; (ii) the diameters of bare axons of excitatory myelinated fibers are significantly larger than those of their inhibitory counterparts; and (iii) myelinated excitatory fibers are significantly larger than myelinated inhibitory fibers. Also, the thickness of myelin ensheathing inhibitory axons is significantly greater than for excitatory axons, with the ultrastructure of the myelin around excitatory and inhibitory fibers also differing. We generated a computational model to investigate the functional consequences of these parameter divergences. Our simulations indicate that impulses through inhibitory and excitatory myelinated fibers reach the target almost simultaneously, whereas action potentials conducted by nonmyelinated axons reach target cells with considerable delay.

Effect of Variations in Gap Junctional Coupling on the Frequency of Oscillatory Action Potentials in a Smooth Muscle Syncytium.

Gap junctions provide pathways for intercellular communication between adjacent cells, allowing exchange of ions and small molecules. Based on the constituent protein subunits, gap junctions are classified into different subtypes varying in their properties such as unitary conductances, sensitivity to transjunctional voltage, and gating kinetics. Gap junctions couple cells electrically, and therefore the electrical activity originating in one cell can affect and modulate the electrical activity in adjacent cells. Action potentials can propagate through networks of such electrically coupled cells, and this spread is influenced by the nature of gap junctional coupling. Our study aims to computationally explore the effect of differences in gap junctional properties on oscillating action potentials in electrically coupled tissues. Further, we also explore variations in the biophysical environment by altering the size of the syncytium, the location of the pacemaking cell, as well as the occurrence of multiple pacemaking cells within the same syncytium. Our simulation results suggest that the frequency of oscillations is governed by the extent of coupling between cells and the gating kinetics of different gap junction subtypes. The location of pacemaking cells is found to alter the syncytial behavior, and when multiple oscillators are present, there exists an interplay between the oscillator frequency and their relative location within the syncytium. Such variations in the frequency of oscillations can have important implications for the physiological functioning of syncytial tissues.

Spontaneous synaptic drive in detrusor smooth muscle: computational investigation and implications for urinary bladder function.

The detrusor, a key component of the urinary bladder wall, is a densely innervated syncytial smooth muscle tissue. Random spontaneous release of neurotransmitter at neuromuscular junctions (NMJs) in the detrusor gives rise to spontaneous excitatory junction potentials (SEJPs). These sub-threshold passive signals not only offer insights into the syncytial nature of the tissue, their spatio-temporal integration is critical to the generation of spontaneous neurogenic action potentials which lead to focal contractions during the filling phase of the bladder. Given the structural complexity and the contractile nature of the tissue, electrophysiological investigations on spatio-temporal integration of SEJPs in the detrusor are technically challenging. Here we report a biophysically constrained computational model of a detrusor syncytium overlaid with spatially distributed innervation, using which we explored salient features of the integration of SEJPs in the tissue and the key factors that contribute to this integration. We validated our model against experimental data, ascertaining that observations were congruent with theoretical predictions. With the help of comparative studies, we propose that the amplitude of the spatio-temporally integrated SEJP is most sensitive to the inter-cellular coupling strength in the detrusor, while frequency of observed events depends more strongly on innervation density. An experimentally testable prediction arising from our study is that spontaneous release frequency of neurotransmitter may be implicated in the generation of detrusor overactivity. Set against histological observations, we also conjecture possible changes in the electrical activity of the detrusor during pathology involving patchy denervation. Our model thus provides a physiologically realistic, heuristic framework to investigate the spread and integration of passive potentials in an innervated syncytial tissue under normal conditions and in pathophysiology.

A computational model of large conductance voltage and calcium activated potassium channels: implications for calcium dynamics and electrophysiology in detrusor smooth muscle cells.

The large conductance voltage and calcium activated potassium (BK) channels play a crucial role in regulating the excitability of detrusor smooth muscle, which lines the wall of the urinary bladder. These channels have been widely characterized in terms of their molecular structure, pharmacology and electrophysiology. They control the repolarising and hyperpolarising phases of the action potential, thereby regulating the firing frequency and contraction profiles of the smooth muscle. Several groups have reported varied profiles of BK currents and I-V curves under similar experimental conditions. However, no single computational model has been able to reconcile these apparent discrepancies. In view of the channels' physiological importance, it is imperative to understand their mechanistic underpinnings so that a realistic model can be created. This paper presents a computational model of the BK channel, based on the Hodgkin-Huxley formalism, constructed by utilising three activation processes - membrane potential, calcium inflow from voltage-gated calcium channels on the membrane and calcium released from the ryanodine receptors present on the sarcoplasmic reticulum. In our model, we attribute the discrepant profiles to the underlying cytosolic calcium received by the channel during its activation. The model enables us to make heuristic predictions regarding the nature of the sub-membrane calcium dynamics underlying the BK channel's activation. We have employed the model to reproduce various physiological characteristics of the channel and found the simulated responses to be in accordance with the experimental findings. Additionally, we have used the model to investigate the role of this channel in electrophysiological signals, such as the action potential and spontaneous transient hyperpolarisations. Furthermore, the clinical effects of BK channel openers, mallotoxin and NS19504, were simulated for the detrusor smooth muscle cells. Our findings support the proposed application of these drugs for amelioration of the condition of overactive bladder. We thus propose a physiologically realistic BK channel model which can be integrated with other biophysical mechanisms such as ion channels, pumps and exchangers to further elucidate its micro-domain interaction with the intracellular calcium environment.

Electrophysiology of Syncytial Smooth Muscle.

As in other excitable tissues, two classes of electrical signals are of fundamental importance to the functioning of smooth muscles: junction potentials, which arise from neurotransmission and represent the initiation of excitation (or in some instances inhibition) of the tissue, and spikes or action potentials, which represent the accomplishment of excitation and lead on to contractile activity. Unlike the case in skeletal muscle and in neurons, junction potentials and spikes in smooth muscle have been poorly understood in relation to the electrical properties of the tissue and in terms of their spatiotemporal spread within it. This owes principally to the experimental difficulties involved in making precise electrical recordings from smooth muscles and also to two inherent features of this class of muscle, ie, the syncytial organization of its cells and the distributed innervation they receive, which renders their biophysical analysis problematic. In this review, we outline the development of hypotheses and knowledge on junction potentials and spikes in syncytial smooth muscle, showing how our concepts have frequently undergone radical changes and how recent developments hold promise in unraveling some of the many puzzles that remain. We focus especially on computational models and signal analysis approaches. We take as illustrative examples the smooth muscles of two organs with distinct functional characteristics, the vas deferens and urinary bladder, while also touching on features of electrical functioning in the smooth muscles of other organs.

Computational Model for Cross-Depolarization in DRG Neurons via Satellite Glial Cells using [K]o: Role of Kir4.1 Channels and Extracellular Leakage.

Satellite glial cells (SGCs) are glial cells found in the peripheral nervous system where they tightly envelop the somata of the primary sensory neurons such as dorsal root ganglion (DRG) neurons and nodose ganglion (NG) neurons. The somata of these neurons are generally compactly packed in their respective ganglia (DRG and NG). SGCs covering a neuron behave as an insulator of electrical activity from neighbouring neurons within the ganglion. Several studies have however shown that the somata show "cross-depolarization" (CD). Origin of CDs has been hypothesized to be chemical in nature: either from neurotransmitter release from both SGCs and somata or from elevation of extracellular potassium concentration ([K]o) in the vicinity of somata. Here, we investigate the role of Kir4.1 channels on SGC and diffusion/clearance factor (ß) of [K]o from the space between SGC and DRG neuron somata to the bulk extracellular space in ganglion. We show using two "Soma-SGC Units" interacting via gap junction that a combination of Kir4.1 and ß could be responsible for CD between DRG neuron somata in pathological conditions.

Effect of Gating Charges on Mediating the Dual Activation of BK Channels in Smooth Muscle Cells: A Computational Study.

This paper employs a computational model to study the dual gating modalities of BK channels in smooth muscles. These channels are gated by both membrane potential and intracellular calcium concentration. It has been previously reported that the sensors for these two stimuli are located at different regions of the channel. Thus, the two sensing modalities act independent of each other. Yet, they result in a concerted and synergistic opening of the channel pore. In this paper, we investigate the effects of these two gating mechanisms by computing the effective gating charges contributed by the channel's voltage and calcium sensors. Along with their independent contributions, we study and estimate the interplay and effect of these two modalities on the channel's activation. The voltage and calcium sensors appear to share the 'load' of the gating charges required to activate the channel based on the cytosolic calcium concentration and membrane potential. Thus, through our computational model, we demonstrate how the two independent sensors gate and coordinate the activation of the channel.

Cellular Environment in a Bundle Modulates SEJP Characteristics in Detrusor Smooth Muscle.

Smooth muscle that ensheathes the urinary bladder wall is known as the detrusor. The detrusor has a bundled syncytial architecture where groups of electrically coupled cells form discrete bundles. Electrical activity recorded from detrusor cells is varied. Among the electrical signals recorded from the detrusor, spontaneous excitatory junction potentials (SEJPs) are events that are sub-threshold for spike generation. SEJPs are caused by spontaneous random release of neurotransmitter molecules from varicosities of innervating nerves. SEJPs recorded from different cells of the detrusor vary in amplitude and/or kinetics, and the reasons for variability are obscure. Our hypothesis was that variety in SEJP characteristics may be attributed to the biophysical micro-environment of a cell (in a bundle), where it arises. With the help of computational models, we show how cellular environment factor, such as size of a bundle significantly alters the amplitude as well as kinetics of SEJPs. These findings are congruent with experimental observations. Our results also suggest that characteristically different SEJPs may be observed in identical detrusor cells, with the difference arising from their neighbourhood rather than the inherent nature of the cells. Consequently, SEJP characteristics might be indicative of the cellular environment of electrophysiological recording.

Investigation of the Syncytial Nature of Detrusor Smooth Muscle as a Determinant of Action Potential Shape.

Unlike most excitable cells, certain syncytial smooth muscle cells are known to exhibit spontaneous action potentials of varying shapes and sizes. These differences in shape are observed even in electrophysiological recordings obtained from a single cell. The origin and physiological relevance of this phenomenon are currently unclear. The study presented here aims to test the hypothesis that the syncytial nature of the detrusor smooth muscle tissue contributes to the variations in the action potential profile by influencing the superposition of the passive and active signals. Data extracted from experimental recordings have been compared with those obtained through simulations. The feature correlation studies on action potentials obtained from the experimental recordings suggest the underlying presence of passive signals, called spontaneous excitatory junction potentials (sEJPs). Through simulations, we are able to demonstrate that the syncytial organization of the cells, and the variable superposition of the sEJPs with the "native action potential", contribute to the diversity in the action potential profiles exhibited. It could also be inferred that the fraction of the propagated action potentials is very low in the detrusor. It is proposed that objective measurements of spontaneous action potential profiles can lead to a better understanding of bladder physiology and pathology.

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

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.

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

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.

A four-component model of the action potential in mouse detrusor smooth muscle cell.

BACKGROUND AND HYPOTHESIS: Detrusor smooth muscle cells (DSMCs) of the urinary bladder are electrically connected to one another via gap junctions and form a three dimensional syncytium. DSMCs exhibit spontaneous electrical activity, including passive depolarizations and action potentials. The shapes of spontaneous action potentials (sAPs) observed from a single DSM cell can vary widely. The biophysical origins of this variability, and the precise components which contribute to the complex shapes observed are not known. To address these questions, the basic components which constitute the sAPs were investigated. We hypothesized that linear combinations of scaled versions of these basic components can produce sAP shapes observed in the syncytium. METHODS AND RESULTS: The basic components were identified as spontaneous evoked junction potentials (sEJP), native AP (nAP), slow after hyperpolarization (sAHP) and very slow after hyperpolarization (vsAHP). The experimental recordings were grouped into two sets: a training data set and a testing data set. A training set was used to estimate the components, and a test set to evaluate the efficiency of the estimated components. We found that a linear combination of the identified components when appropriately amplified and time shifted replicated various AP shapes to a high degree of similarity, as quantified by the root mean square error (RMSE) measure. CONCLUSIONS: We conclude that the four basic components-sEJP, nAP, sAHP, and vsAHP-identified and isolated in this work are necessary and sufficient to replicate all varieties of the sAPs recorded experimentally in DSMCs. This model has the potential to generate testable hypotheses that can help identify the physiological processes underlying various features of the sAPs. Further, this model also provides a means to classify the sAPs into various shape classes.

Effects of location and extent of spine clustering on synaptic integration in striatal medium spiny neurons-a computational study.

The nucleus accumbens (NAc) is known widely for its role in the reward circuit, which is dysregulated in a number of psychological disorders. Recent evidence also suggests the contribution of this structure in spatial and gustatory memories. Because of its role in different types of memories, similar to the hippocampus, we assumed the formation of spine clusters, which are engrams of memory, to be present on dendrites of medium spiny neurons (MSNs). We found that the activation of clustered inputs resulted in sublinear summation when clusters were present on the same branch and also when inputs were distributed on different branches. The size, as well as the location of clusters, was found to affect the summation. With an increase in cluster size and distance from soma, the summation was increasingly sublinear. When the temporal integration window was measured for clustered spines, it was found to be narrower as compared to that for a single spine. Also, distally located clusters resulted in a wider temporal window, as compared to proximal clusters. Our results suggest that depending on the location of clusters, the modes of integration will differ in MSNs possessing clustered spines.

A Method for the Analysis of AP Foot Convexity: Insights into Smooth Muscle Biophysics.

Action potential (AP) profiles vary based on the cell type, with cells of the same type typically producing APs with similar shapes. But in certain syncytial tissues, such as the smooth muscle of the urinary bladder wall, even a single cell is known to exhibit APs with diverse profiles. The origin of this diversity is not currently understood, but is often attributed to factors such as syncytial interactions and the spatial distribution of parasympathetic nerve terminals. Thus, the profile of an action potential is determined by the inherent properties of the cell and influenced by its biophysical environment. The analysis of an AP profile, therefore, holds potential for constructing a biophysical picture of the cellular environment. An important feature of any AP is its depolarization to threshold, termed the AP foot, which holds information about the origin of the AP. Currently, there exists no established technique for the quantification of the AP foot. In this study, we explore several possible approaches for this quantification, namely, exponential fitting, evaluation of the radius of curvature, triangulation altitude, and various area based methods. We have also proposed a modified area-based approach (CX,Y) which quantifies foot convexity as the area between the AP foot and a predefined line. We assess the robustness of the individual approaches over a wide variety of signals, mimicking AP diversity. The proposed (CX,Y) method is demonstrated to be superior to the other approaches, and we demonstrate its application on experimentally recorded AP profiles. The study reveals how the quantification of the AP foot could be related to the nature of the underlying synaptic activity and help shed light on biophysical features such as the density of innervation, proximity of varicosities, size of the syncytium, or the strength of intercellular coupling within the syncytium. The work presented here is directed toward exploring these aspects, with further potential toward clinical electrodiagnostics by providing a better understanding of whole-organ biophysics.

A computational model of intracellular calcium oscillations in urinary bladder smooth muscle cells.

This paper presents a computational model for calcium (Ca2+) oscillations in detrusor smooth muscle (DSM) cells. The proposed model simulates the temporal profile of oscillations by incorporating various cellular and subcellular components. The cellular components include calcium influx via membrane and the plasma membrane calcium ATPase (PMCA) pump. The subcellular components include ryanodine receptors (RyRs), inositol 1, 4, 5 trisphosphate receptors (IP3Rs) and the sarco/endoplasmic reticulum calcium ATPase (SERCA) pump. The use of both cellular and subcellular components provides a better estimation of the origin and factors affecting these oscillations. Moreover, our work correlates these computational findings with associated physiology of the smooth muscle cell that aids our understanding of intracellular calcium oscillations and its inception in DSM. A deeper insight into calcium signalling in DSM cells is expected to provide a firmer basis for understanding the mechanical contractile activity.

Modeling extracellular fields for a three-dimensional network of cells using NEURON.

BACKGROUND: Computational modeling of biological cells usually ignores their extracellular fields, assuming them to be inconsequential. Though such an assumption might be justified in certain cases, it is debatable for networks of tightly packed cells, such as in the central nervous system and the syncytial tissues of cardiac and smooth muscle. NEW METHOD: In the present work, we demonstrate a technique to couple the extracellular fields of individual cells within the NEURON simulation environment. The existing features of the simulator are extended by explicitly defining current balance equations, resulting in the coupling of the extracellular fields of adjacent cells. RESULTS: With this technique, we achieved continuity of extracellular space for a network model, thereby allowing the exploration of extracellular interactions computationally. Using a three-dimensional network model, passive and active electrical properties were evaluated under varying levels of extracellular volumes. Simultaneous intracellular and extracellular recordings for synaptic and action potentials were analyzed, and the potential of ephaptic transmission towards functional coupling of cells was explored. COMPARISON WITH EXISTING METHOD(S): We have implemented a true bi-domain representation of a network of cells, with the extracellular domain being continuous throughout the entire model. This has hitherto not been achieved using NEURON, or other compartmental modeling platforms. CONCLUSIONS: We have demonstrated the coupling of the extracellular field of every cell in a three-dimensional model to obtain a continuous uniform extracellular space. This technique provides a framework for the investigation of interactions in tightly packed networks of cells via their extracellular fields.

A computational model of the [Formula: see text] transients and influence of buffering in guinea pig urinary bladder smooth muscle cells.

Many cellular events including electrical activity and muscle contraction are regulated and coordinated by intracellular [Formula: see text] concentration ([[Formula: see text]][Formula: see text]. In detrusor smooth muscle (DSM) cells, [[Formula: see text]]i is normally maintained at very low levels and rises transiently during signalling processes as a result of (i) influx from the extracellular space (mainly via L-type and T-type [Formula: see text] channels) and (ii) [Formula: see text] release from sarcoplasmic reticulum (SR) into the cytoplasm. Intracellular [Formula: see text] buffers, both fixed and diffusible, play a vital role in shaping the radial distribution of free [Formula: see text]. Our aim, in the work presented here, is to develop a mathematical model of [Formula: see text] buffering and diffusion and to generate [Formula: see text] transient in guinea pig DSM cells. The [Formula: see text] transient is generated using inward [Formula: see text] current that arises following voltage clamp and mediated by L-type and T-type [Formula: see text] channels. [Formula: see text] transient is obtained for different radial locations (or shells) of the DSM cytosol. This modeling study explores the levels of [[Formula: see text]]i achieved near the plasma membrane and in deeper locations. The [Formula: see text] transient generated in our model shows a high degree of similarity with experimental findings in terms of amplitude, duration and half-decay time. A number of different buffer properties such as concentration and mobility are tested for their effect on amplitude and shape of [Formula: see text] transient. The presence of fast buffer concentration in the cytosol markedly delays the rise of [[Formula: see text]]i in the core of the cell. Increase in the mobility of fast buffer slightly speeds up the redistribution of [Formula: see text]. To explore the model further, the role of plasma membrane [Formula: see text]-ATPase (PMCA) pump, sarcoplasmic/endoplasmic reticulum [Formula: see text]-ATPase (SERCA) pump and sodium calcium exchanger (NCX) on [Formula: see text] transient is studied and it is suggested that NCX may be of primary importance for the immediate lowering of [[Formula: see text]]i during the falling phase of a [Formula: see text] transient in DSM cells.