Ca2+ dynamics in a population of smooth muscle cells: modeling the recruitment and synchronization

Multiphysics and multiscale modeling of uterine contractions: integrating electrical dynamics and soft tissue deformation with fiber orientation

The development of a comprehensive uterine model that seamlessly integrates the intricate interactions between the electrical and mechanical aspects of uterine activity could potentially facilitate the prediction and management of labor complications. Such a model has the potential to enhance our understanding of the initiation and synchronization mechanisms involved in uterine contractions, providing a more profound comprehension of the factors associated with labor complications, including preterm labor. Consequently, it has the capacity to assist in more effective preparation and intervention strategies for managing such complications. In this study, we present a computational model that effectively integrates the electrical and mechanical components of uterine contractions. By combining a state-of-the-art electrical model with the Hyperelastic Mass-Spring Model (HyperMSM), we adopt a multiphysics and multiscale approach to capture the electrical and mechanical activities within the uterus. The electrical model incorporates the generation and propagation of action potentials, while the HyperMSM simulates the mechanical behavior and deformations of the uterine tissue. Notably, our model takes into account the orientation of muscle fibers, ensuring that the simulated contractions align with their inherent directional characteristics. One noteworthy aspect of our contraction model is its novel approach to scaling the rest state of the mesh elements, as opposed to the conventional method of applying mechanical loads. By doing so, we eliminate artificial strain energy resulting from the resistance of soft tissues' elastic properties during contractions. We validated our proposed model through test simulations, demonstrating its feasibility and its ability to reproduce expected contraction patterns across different mesh resolutions and configurations. Moving forward, future research efforts should prioritize the validation of our model using robust clinical data. Additionally, it is crucial to refine the model by incorporating a more realistic uterus model derived from medical imaging. Furthermore, applying the model to simulate the entire childbirth process holds immense potential for gaining deeper insights into the intricate dynamics of labor.

Cellular communication among smooth muscle cells: The role of membrane potential via connexins

Communication via action potentials among neurons has been extensively studied. However, effective communication without action potentials is ubiquitous in biological systems, yet it has received much less attention in comparison. Multi-cellular communication among smooth muscles is crucial for regulating blood flow, for example. Understanding the mechanism of this non-action potential communication is critical in many cases, like synchronization of cellular activity, under normal and pathological conditions. In this paper, we employ a multi-scale asymptotic method to derive a macroscopic homogenized bidomain model from the microscopic electro-neutral (EN) model. This is achieved by considering different diffusion coefficients and incorporating nonlinear interface conditions. Subsequently, the homogenized macroscopic model is used to investigate communication in multi-cellular tissues. Our computational simulations reveal that the membrane potential of syncytia, formed by interconnected cells via connexins, plays a crucial role in propagating oscillations from one region to another, providing an effective means for fast cellular communication. Statement of Significance: In this study, we investigated cellular communication and ion transport in vascular smooth muscle cells, shedding light on their mechanisms under normal and abnormal conditions. Our research highlights the potential of mathematical models in understanding complex biological systems. We developed effective macroscale electro-neutral bi-domain ion transport models and examined their behavior in response to different stimuli. Our findings revealed the crucial role of connexinmediated membrane potential changes and demonstrated the effectiveness of cellular communication through syncytium membranes. Despite some limitations, our study provides valuable insights into these processes and emphasizes the importance of mathematical modeling in unraveling the complexities of cellular communication and ion transport.

A complete biomechanical model of Hydra contractile behaviors, from neural drive to muscle to movement

How does neural activity drive muscles to produce behavior? The recent development of genetic lines in Hydra that allow complete calcium imaging of both neuronal and muscle activity, as well as systematic machine learning quantification of behaviors, makes this small cnidarian an ideal model system to understand and model the complete transformation from neural firing to body movements. To achieve this, we have built a neuromechanical model of Hydra's fluid-filled hydrostatic skeleton, showing how drive by neuronal activity activates distinct patterns of muscle activity and body column biomechanics. Our model is based on experimental measurements of neuronal and muscle activity and assumes gap junctional coupling among muscle cells and calcium-dependent force generation by muscles. With these assumptions, we can robustly reproduce a basic set of Hydra's behaviors. We can further explain puzzling experimental observations, including the dual timescale kinetics observed in muscle activation and the engagement of ectodermal and endodermal muscles in different behaviors. This work delineates the spatiotemporal control space of Hydra movement and can serve as a template for future efforts to systematically decipher the transformations in the neural basis of behavior.

The Reversal Characteristics of GABAergic Neurons: A Neurovascular Model

Neurovascular coupling (NVC) is the ability to locally adjust vascular resistance as a function of neuronal activity. Recent experiments have illustrated that NVC is partially independent of metabolic signals. In addition, nitric oxide (NO) has been shown in some instances to provide an important mechanism in altering vascular resistance. An extension to the original model of NVC [1] has been developed to include the activation of both somatosensory neurons and GABAergic interneurons and to investigate the role of NO and the delicate balance of GABA and neuronal peptide enzymes (NPY) pathways. The numerical model is compared to murine experimental data that provides time-dependent profiles of oxy, de-oxy, and total-hemoglobin. The results indicate a delicate balance that exists between GABA and NPY when nNOS interneurons are activated mediated by NO. Whereas somatosensory neurons (producing potassium into the extracellular space) do not seem to be effected by the inhibition of NO. Further work will need to be done to investigate the role of NO when stimulation periods are increased substantially from the short pulses of 2 s as used in the above experiments.

Modeling and experimental approaches for elucidating multi-scale uterine smooth muscle electro- and mechano-physiology: A review

The uterus provides protection and nourishment (via its blood supply) to a developing fetus, and contracts to deliver the baby at an appropriate time, thereby having a critical contribution to the life of every human. However, despite this vital role, it is an under-investigated organ, and gaps remain in our understanding of how contractions are initiated or coordinated. The uterus is a smooth muscle organ that undergoes variations in its contractile function in response to hormonal fluctuations, the extreme instance of this being during pregnancy and labor. Researchers typically use various approaches to studying this organ, such as experiments on uterine muscle cells, tissue samples, or the intact organ, or the employment of mathematical models to simulate the electrical, mechanical and ionic activity. The complexity exhibited in the coordinated contractions of the uterus remains a challenge to understand, requiring coordinated solutions from different research fields. This review investigates differences in the underlying physiology between human and common animal models utilized in experiments, and the experimental interventions and computational models used to assess uterine function. We look to a future of hybrid experimental interventions and modeling techniques that could be employed to improve the understanding of the mechanisms enabling the healthy function of the uterus.

Pattern Formation in a Spatially Extended Model of Pacemaker Dynamics in Smooth Muscle Cells

Spatiotemporal patterns are common in biological systems. For electrically coupled cells, previous studies of pattern formation have mainly used applied current as the primary bifurcation parameter. The purpose of this paper is to show that applied current is not needed to generate spatiotemporal patterns for smooth muscle cells. The patterns can be generated solely by external mechanical stimulation (transmural pressure). To do this we study a reaction-diffusion system involving the Morris-Lecar equations and observe a wide range of spatiotemporal patterns for different values of the model parameters. Some aspects of these patterns are explained via a bifurcation analysis of the system without coupling - in particular Type I and Type II excitability both occur. We show the patterns are not due to a Turing instability and that the spatially extended model exhibits spatiotemporal chaos. We also use travelling wave coordinates to analyse travelling waves.

Engaging biological oscillators through second messenger pathways permits emergence of a robust gastric slow-wave during peristalsis

Peristalsis, the coordinated contraction—relaxation of the muscles of the stomach is important for normal gastric motility and is impaired in motility disorders. Coordinated electrical depolarizations that originate and propagate within a network of interconnected layers of interstitial cells of Cajal (ICC) and smooth muscle (SM) cells of the stomach wall as a slow-wave, underly peristalsis. Normally, the gastric slow-wave oscillates with a single period and uniform rostrocaudal lag, exhibiting network entrainment. Understanding of the integrative role of neurotransmission and intercellular coupling in the propagation of an entrained gastric slow-wave, important for understanding motility disorders, however, remains incomplete. Using a computational framework constituted of a novel gastric motility network (GMN) model we address the hypothesis that engaging biological oscillators (i.e., ICCs) by constitutive gap junction coupling mechanisms and enteric neural innervation activated signals can confer a robust entrained gastric slow-wave. We demonstrate that while a decreasing enteric neural innervation gradient that modulates the intracellular IP₃ concentration in the ICCs can guide the aboral slow-wave propagation essential for peristalsis, engaging ICCs by recruiting the exchange of second messengers (inositol trisphosphate (IP₃) and Ca²⁺) ensures a robust entrained longitudinal slow-wave, even in the presence of biological variability in electrical coupling strengths. Our GMN with the distinct intercellular coupling in conjunction with the intracellular feedback pathways and a rostrocaudal enteric neural innervation gradient allows gastric slow waves to oscillate with a moderate range of frequencies and to propagate with a broad range of velocities, thus preventing decoupling observed in motility disorders. Overall, the findings provide a mechanistic explanation for the emergence of decoupled slow waves associated with motility impairments of the stomach, offer directions for future experiments and theoretical work, and can potentially aid in the design of new interventional pharmacological and neuromodulation device treatments for addressing gastric motility disorders.

The coordinated contraction and relaxation of the muscles of the stomach, known as peristalsis is important for normal gastric motility and primarily governed by electrical depolarizations that originate and propagate within a network of interconnected layers of interstitial cells of Cajal (ICCs) and smooth muscle cells of the stomach wall as a slow-wave. Under normal conditions, a gastric slow-wave oscillates with a single period and uniform rostrocaudal lag, exhibiting network entrainment. However, the understanding of intrinsic and extrinsic mechanisms that ensure propagation of a robust entrained slow-wave remains incomplete. Here, using a computational framework, we show that in conjunction with an enteric neural innervation gradient along the rostrocaudal ICC chain, and intercellular electrical coupling, the intercellular exchange of inositol trisphosphate between ICCs prevents decoupling by extending the longitudinal entrainment range along the stomach wall, even when variability in intercellular coupling exists. The findings from our study indicate ways that ensure the rostrocaudal spread of a robust gastric slow-wave and provide a mechanistic explanation for the emergence of decoupled slow waves associated with motility impairments of the stomach.

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.

Multi-scale and multi-physics model of the uterine smooth muscle with mechanotransduction

Preterm labor is an important public health problem. However, the efficiency of the uterine muscle during labor is complex and still poorly understood. This work is a first step towards a model of the uterine muscle, including its electrical and mechanical components, to reach a better understanding of the uterus synchronization. This model is proposed to investigate, by simulation, the possible role of mechanotransduction for the global synchronization of the uterus. The electrical diffusion indeed explains the local propagation of contractile activity, while the tissue stretching may play a role in the synchronization of distant parts of the uterine muscle. This work proposes a multi-physics (electrical, mechanical) and multi-scales (cell, tissue, whole uterus) model, which is applied to a realistic uterus 3D mesh. This model includes electrical components at different scales: generation of action potentials at the cell level, electrical diffusion at the tissue level. It then links these electrical events to the mechanical behavior, at the cellular level (via the intracellular calcium concentration), by simulating the force generated by each active cell. It thus computes an estimation of the intra uterine pressure (IUP) by integrating the forces generated by each active cell at the whole uterine level, as well as the stretching of the tissue (by using a viscoelastic law for the behavior of the tissue). It finally includes at the cellular level stretch activated channels (SACs) that permit to create a loop between the mechanical and the electrical behavior (mechanotransduction). The simulation of different activated regions of the uterus, which in this first "proof of concept" case are electrically isolated, permits the activation of inactive regions through the stretching (induced by the electrically active regions) computed at the whole organ scale. This permits us to evidence the role of the mechanotransduction in the global synchronization of the uterus. The results also permit us to evidence the effect on IUP of this enhanced synchronization induced by the presence of SACs. This proposed simplified model will be further improved in order to permit a better understanding of the global uterine synchronization occurring during efficient labor contractions.

Importance of Altered Levels of SERCA, IP3R, and RyR in Vascular Smooth Muscle Cell

Calcium cycling between the sarcoplasmic reticulum (SR) and the cytosol via the sarco-/endoplasmic reticulum Ca-ATPase (SERCA) pump, inositol-1,4,5-triphosphate receptor (IP₃R), and Ryanodine receptor (RyR), plays a major role in agonist-induced intracellular calcium ([Ca²⁺]_cyt) dynamics in vascular smooth muscle cells (VSMC). Levels of these calcium handling proteins in SR get altered under disease conditions. We have developed a mathematical model to understand the significance of altered levels of SERCA, IP₃R, and RyR on the intracellular calcium dynamics of VSMC and to understand how variation in protein levels that arise due to diabetes contribute to different VSMC behavior and thus vascular disease. SR is modeled as a single continuous entity with homogeneous intra-SR calcium. Model results show that agonist-induced intracellular calcium dynamics can be modified by changing the levels of SERCA, IP₃R, and/or RyR. Lowering SERCA level will enable intracellular calcium oscillations at low agonist concentrations whereas lowered levels of IP₃R and RyR need higher agonist concentration for intracellular calcium oscillations. This research suggests that reduced SERCA level is the main factor responsible for the reduced intracellular calcium transients and contractility in VSMCs.

Signal Transduction at the Single-Cell Level: Approaches to Study the Dynamic Nature of Signaling Networks

Signal transduction, or how cells interpret and react to external events, is a fundamental aspect of cellular function. Traditional study of signal transduction pathways involves mapping cellular signaling pathways at the population level. However, population-averaged readouts do not adequately illuminate the complex dynamics and heterogeneous responses found at the single-cell level. Recent technological advances that observe cellular response, computationally model signaling pathways, and experimentally manipulate cells now enable studying signal transduction at the single-cell level. These studies will enable deeper insights into the dynamic nature of signaling networks.

An electro-mechanical multiscale model of uterine pregnancy contraction

Detecting preterm labor as early as possible is important because tocolytic drugs are much more likely to delay preterm delivery if administered early. Having good information on the real risk of premature labor also leads to fewer women who do not need aggressive treatment for premature labor threat. Currently, one of the most promising ways to diagnose preterm labor threat is the analysis of the electrohysterogram (EHG). Its characteristics have been related to preterm labor risk but they have not proven to be sufficiently accurate to use in clinical routine. One of the reasons for this is that the physiology of the pregnant uterus is insufficiently understood. Models already exist in literature that simulate either the electrical or the mechanical component of the uterine smooth muscle. Few include both components in a co-simulation of electrical and mechanical aspects. A model that can represent realistically both the electrical and the mechanical behavior of the uterine muscle could be useful for better understanding the EHG and therefore for preterm labor detection. Processing the EHG considers only the electrical component of the uterus but the electrical activity does not seem to explain by itself the synchronization of the uterine muscle that occurs during labor and not at other times. Recent studies have demonstrated that the mechanical behavior of the uterine muscle seems to play an important role in uterus synchronization during labor. The aim of the proposed study is to link three different models of the uterine smooth muscle behavior by using co-simulation. The models go from the electrical activity generated at the cellular level to the mechanical force generated by the muscle and from there to the deformation of the tissue. The results show the feasibility of combining these three models to model a whole uterus contraction on 3D realistic uterus model.

Intercellular ultrafast Ca(2+) wave in vascular smooth muscle cells: numerical and experimental study

Vascular smooth muscle cells exhibit intercellular Ca²⁺ waves in response to local mechanical or KCl stimulation. Recently, a new type of intercellular Ca²⁺ wave was observed in vitro in a linear arrangement of smooth muscle cells. The intercellular wave was denominated ultrafast Ca²⁺ wave and it was suggested to be the result of the interplay between membrane potential and Ca²⁺ dynamics which depended on influx of extracellular Ca²⁺, cell membrane depolarization and its intercel- lular propagation. In the present study we measured experimentally the conduction velocity of the membrane depolarization and performed simulations of the ultrafast Ca²⁺ wave along coupled smooth muscle cells. Numerical results reproduced a wide spectrum of experimental observations, including Ca²⁺ wave velocity, electrotonic membrane depolarization along the network, effects of inhibitors and independence of the Ca²⁺ wave speed on the intracellular stores. The numerical data also provided new physiological insights suggesting ranges of crucial model parameters that may be altered experimentally and that could significantly affect wave kinetics allowing the modulation of the wave characteristics experimentally. Numerical and experimental results supported the hypothesis that the propagation of membrane depolarization acts as an intercellular messenger mediating intercellular ultrafast Ca²⁺ waves in smooth muscle cells.

Electrical muscle stimulation in thomboprophylaxis: review and a derived hypothesis about thrombogenesis-the 4th factor

INTRODUCTION

Electrical muscle stimulation (EMS) is an FDA-approved thromboprophylactic method. Thrombus pathogenesis is considered to depend on factors related to components of the vessel wall, the velocity of blood, and blood consistency-collectively known as, the Virchow's triad.

OBJECTIVE

The testimony supporting the thromboprophylactic effects of the EMS is reviewed. An emphasis is placed on the fact that, EMS has demonstrated, in certain circumstances, an efficacy rate that cannot be fully explained by the Virchow's triad; also that, in reviewing relevant evidence and the theorized pathophysiological mechanisms, several findings collectively point to a potentially missed point. Remarkably, venous thromboembolic disease (VTE) is extremely more common in the lower versus the upper extremities even when the blood velocities equalize; EMS had synergistic effects with intermittent compressive devices, despite their presumed identical mechanism of action; sleep is not thrombogenic; non-peroperative EMS is meaningful only if applied ≥5 times daily; neural insult increases VTEs more than the degree expected by the hypomobility-related blood stasis; etc. These phenomena infer the presence of a 4th thrombogenetic factor: neural supply to the veins provides direct antithrombic effects, by inducing periodic vessel diameter changes and/or by neuro-humoral, chemically acting factors. EMS may stimulate or substitute the 4th factor. This evidence-based hypothesis is analyzed.

CONCLUSION

A novel pathophysiologic mechanism of thrombogenesis is supported; and, based on this, the role of EMS in thromboprophylaxis is expanded. Exploration of this mechanism may provide new targets for intervention.

Original Research: Combined model of bladder detrusor smooth muscle and interstitial cells

Although patients with lower urinary tract symptoms constitute a large and still growing population, understanding of bladder detrusor muscle physiology remains limited. Understanding the interactions between the detrusor smooth muscle cells and other bladder cell types (e.g. interstitial cells, IC) that may significantly contribute to coordinating and modulating detrusor contractions represents a considerable challenge. Computer modeling could help to elucidate some properties that are difficult to address experimentally; therefore, we developed in silico models of detrusor smooth muscle cell and interstitial cells, coupled through gap junctions. The models include all of the major ion conductances and transporters described in smooth muscle cell and interstitial cells in the literature. The model of normal detrusor muscle (smooth muscle cell and interstitial cells coupled through gap junctions) completely reproduced the experimental results obtained with detrusor strips in the presence of several pharmacological interventions (ryanodine, caffeine, nimodipine), whereas the model of smooth muscle cell alone (without interstitial cells) failed to reproduce the experimental results. Next, a model of overactive bladder, a highly prevalent clinical condition in both men and women with increasing incidence at older ages, was produced by modifying several processes as reported previously: a reduction of Ca(2+)-release through ryanodine receptors and a reduction of Ca(2+)-dependent K(+)-conductance with augmented gap junctional coupling. This model was also able to reproduce the pharmacological modulation of overactive bladder. In conclusion, a model of bladder detrusor muscle was developed that reproduced experimental results obtained in both normal and overactive bladder preparations. The results indicate that the non-smooth muscle cells of the detrusor (interstitial cells) contribute significantly to the contractile behavior of bladder detrusor muscle and should not be neglected. The model suggests that reduced Ca(2+)-release through ryanodine receptors and Ca(2+)-dependent K(+)-conductance together with augmented gap junctional coupling might play a major role in overactive bladder pathogenesis.

A generative modeling approach to connectivity-Electrical conduction in vascular networks

The physiology of biological structures is inherently dynamic and emerges from the interaction and assembly of large collections of small entities. The extent of coupled entities complicates modeling and increases computational load. Here, microvascular networks are used to present a novel generative approach to connectivity based on the observation that biological organization is hierarchical and composed of a limited set of building blocks, i.e. a vascular network consists of blood vessels which in turn are composed by one or more cell types. Fast electrical communication is crucial to synchronize vessel tone across the vast distances within a network. We hypothesize that electrical conduction capacity is delimited by the size of vascular structures and connectivity of the network. Generation and simulation of series of dynamical models of electrical spread within vascular networks of different size and composition showed that (1) Conduction is enhanced in models harboring long and thin endothelial cells that couple preferentially along the longitudinal axis. (2) Conduction across a branch point depends on endothelial connectivity between branches. (3) Low connectivity sub-networks are more sensitive to electrical perturbations. In summary, the capacity for electrical signaling in microvascular networks is strongly shaped by the morphology and connectivity of vascular (particularly endothelial) cells. While the presented software can be used by itself or as a starting point for more sophisticated models of vascular dynamics, the generative approach can be applied to other biological systems, e.g. nervous tissue, the lymphatics, or the biliary system.

Inherent rhythm of smooth muscle cells in rat mesenteric arterioles: An eigensystem formulation

On the basis of experimental data and mathematical equations in the literature, we remodel the ionic dynamics of smooth muscle cells (SMCs) as an eigensystem formulation, which is valid for investigating finite variations of variables from the equilibrium such as in common experimental operations. This algorithm provides an alternate viewpoint from frequency-domain analysis and enables one to probe functionalities of SMCs' rhythm by means of a resonance-related mechanism. Numerical results show three types of calcium oscillations of SMCs in mesenteric arterioles: spontaneous calcium oscillation, agonist-dependent calcium oscillation, and agonist-dependent calcium spike. For simple single and double SMCs, we demonstrate properties of synchronization among complex signals related to calcium oscillations, and show different correlation relations between calcium and voltage signals for various synchronization and resonance conditions. For practical cell clusters, our analyses indicate that the rhythm of SMCs could (1) benefit enhancements of signal communications among remote cells, (2) respond to a significant calcium peaking against transient stimulations for triggering globally oscillating modes, and (3) characterize the globally oscillating modes via frog-leap (non-molecular-diffusion) calcium waves across inhomogeneous SMCs.

On the roles of vascular smooth muscle contraction in cerebral blood flow autoregulation - a modeling perspective

We here review existing models of vascular smooth muscle cell, endothelial cell and cell-cell communication, which have been developed to better understand vascular tone and blood flow autoregulation. In particular, we discuss models that intended to explain modulation of myogenic tone by intraluminal pressure in resistance arterioles. Modeling efforts in the recent past have witnessed a shift from empirical models to models with mechanistic details that underscore different physical aspects of vascular regulation. Future models should synthesize mechanistic interactions in a hierarchy, from molecular regulation of ion channels to whole organ blood flow control.

A comprehensive mathematical framework for modeling intestinal smooth muscle cell contraction with applications to intestinal edema

The contraction of intestinal smooth muscle cells (ISMCs) involves many coordinated biochemical and mechanical processes. In this work, we present a framework for modeling ISMC contractility that begins with chemical models of calcium dynamics, continues with myosin light chain phosphorylation and force generation, and ends with a cell model of the ISMC undergoing contraction-relaxation. The motivation for developing this comprehensive framework is to study the effects of edema (excess fluid build-up in the muscle tissue) on ISMC contractility. The hypothesis is that more fluid equates to dilution of an external stimulis, eventually leading to reduced contractility. We compare our results to experimental data collected from normal versus edematous intestinal muscle tissue.

A multiscale model of the electrohysterogram the BioModUE_PTL project

The electrohysterogram (EHG) is a promising means of monitoring pregnancy and of detecting a risk of preterm labor. To improve our understanding of the EHG as well as its relationship with the physiologic phenomena involved in uterine contractility, we plan to model these phenomena in terms of generation and propagation of uterine electrical activity. This activity can be realistically modeled by representing the principal ionic dynamics at the cell level, the propagation of electrical activity at the tissue level and then the way it is reflected on the skin surface through the intervening tissue. We present in this paper the different steps leading to the development and validation of a biophysics based multiscale model of the EHG, going from the cell to the electrical signal measured on the abdomen.

Intercellular communication in the vascular wall: a modeling perspective

Movement of ions (Ca(2+) , K(+) , Na(+) , and Cl(-) ) and second messenger molecules like inositol 1, 4, 5-trisphosphate inside and in between different cells is the basis of many signaling mechanisms in the microcirculation. In spite of the vast experimental efforts directed toward evaluation of these fluxes, it has been a challenge to establish their roles in many essential microcirculatory phenomena. Recently, detailed theoretical models of calcium dynamics and plasma membrane electrophysiology have emerged to assist in the quantification of these intra and intercellular fluxes and enhance understanding of their physiological importance. This perspective reviews selected models relevant to estimation of such intra and intercellular ionic and second messenger fluxes and prediction of their relative significance to a variety of vascular phenomena, such as myoendothelial feedback, conducted responses, and vasomotion.

Multiple factors influence calcium synchronization in arterial vasomotion

The intercellular synchronization of spontaneous calcium (Ca(2+)) oscillations in individual smooth muscle cells is a prerequisite for vasomotion. A detailed mathematical model of Ca(2+) dynamics in rat mesenteric arteries shows that a number of synchronizing and desynchronizing pathways may be involved. In particular, Ca(2+)-dependent phospholipase C, the intercellular diffusion of inositol trisphosphate (IP(3), and to a lesser extent Ca(2+)), IP(3) receptors, diacylglycerol-activated nonselective cation channels, and Ca(2+)-activated chloride channels can contribute to synchronization, whereas large-conductance Ca(2+)-activated potassium channels have a desynchronizing effect. Depending on the contractile state and agonist concentrations, different pathways become predominant, and can be revealed by carefully inhibiting the oscillatory component of their total activity. The phase shift between the Ca(2+) and membrane potential oscillations can change, and thus electrical coupling through gap junctions can mediate either synchronization or desynchronization. The effect of the endothelium is highly variable because it can simultaneously enhance the intercellular coupling and affect multiple smooth muscle cell components. Here, we outline a system of increased complexity and propose potential synchronization mechanisms that need to be experimentally tested.

Criticality in intracellular calcium signaling in cardiac myocytes

Calcium (Ca) is a ubiquitous second messenger that regulates many biological functions. The elementary events of local Ca signaling are Ca sparks, which occur randomly in time and space, and integrate to produce global signaling events such as intra- and intercellular Ca waves and whole-cell Ca oscillations. Despite extensive experimental characterization in many systems, the transition from local random to global synchronous events is still poorly understood. Here we show that criticality, a ubiquitous dynamical phenomenon in nature, is responsible for the transition from local to global Ca signaling. We demonstrate this first in a computational model of Ca signaling in a cardiac myocyte and then experimentally in mouse ventricular myocytes, complemented by a theoretical agent-based model to delineate the underlying dynamics. We show that the interaction between the Ca release units via Ca-induced Ca release causes self-organization of Ca spark clusters. When the coupling between Ca release units is weak, the cluster-size distribution is exponential. As the interactions become strong, the cluster-size distribution changes to a power-law distribution, which is characteristic of criticality in thermodynamic and complex nonlinear systems, and facilitates the formation and propagation of Ca waves and whole-cell Ca oscillations. Our findings illustrate how criticality is harnessed by a biological cell to regulate Ca signaling via self-organization of random subcellular events into cellular-scale oscillations, and provide a general theoretical framework for the transition from local Ca signaling to global Ca signaling in biological cells.

Modeling Ca2+ signaling in the microcirculation: intercellular communication and vasoreactivity

A network of intracellular signaling pathways and complex intercellular interactions regulate calcium mobilization in vascular cells, arteriolar tone, and blood flow. Different endothelium-derived vasoreactive factors have been identified and the importance of myoendothelial communication in vasoreactivity is now well appreciated. The ability of many vascular networks to conduct signals upstream also is established. This phenomenon is critical for both short-term changes in blood perfusion as well as long-term adaptations of a vascular network. In addition, in a phenomenon termed vasomotion, arterioles often exhibit spontaneous oscillations in diameter. This is thought to improve tissue oxygenation and enhance blood flow. Experimentation has begun to reveal important aspects of the regulatory machinery and the significance of these phenomena for the regulation of local perfusion and oxygenation. Mathematical modeling can assist in elucidating the complex signaling mechanisms that participate in these phenomena. This review highlights some of the important experimental studies and relevant mathematical models that provide the current understanding of these mechanisms in vasoreactivity.

Calcium oscillations and pacemaking

Calcium plays important role in biological systems where it is involved in diverse mechanisms such as signaling, muscle contraction and neuromodulation. Action potentials are generated by dynamic interaction of ionic channels located on the plasma-membrane and these drive the rhythmic activity of biological systems such as the smooth muscle and the heart. However, ionic channels are not the only pacemakers; an intimate interaction between intracellular Ca(2+) stores and ionic channels underlie rhythmic activity. In this review we will focus on the role of Ca(2+) stores in regulation of rhythmical behavior.

Intercellular synchronization of diffusively coupled Ca(2+) oscillators

We examine the synchrony in the dynamics of localized [Ca(2 + )](i) oscillations among a group of cells exhibiting such complex Ca(2 + ) oscillations, connected in the form of long chain, via diffusing coupling where cytosolic Ca(2 + ) and inositol 1,4,5-triphosphate are coupling molecules. Based on our numerical results, we could able to identify three regimes, namely desynchronized, transition and synchronized regimes in the (T - k(e)) (time period-coupling constant) and (A - k(e)) (amplitude-coupling constant) spaces which are supported by phase plots (Δϕ verses time) and recurrence plots, respectively. We further show the increase of synchronization among the cells as the number of coupling molecules increases in the (T - k(e)) and (A - k(e)) spaces.

Complex activity patterns in arterial wall: results from a model of calcium dynamics

Using a dynamical model of smooth muscle cells in an arterial wall, defined as a system of coupled five-dimensional nonlinear oscillators, on a grid with cylindrical symmetry, we compare the admissible activity patterns with those known from the heart tissue. We postulate on numerical basis the possibility to induce a stable spiral wave in the arterial wall. Such a spiral wave can inhibit the propagation of the axial calcium wave and effectively stop the vasomotion. We also discuss the dynamics of the circumferential calcium wave in comparison to rotors in venous ostia that are a common source of supraventricular ectopy. We show that the velocity and in consequence the frequency range of the circumferential calcium wave is by orders of magnitude too small compared to that of the rotors. The mechanism of the rotor is not likely to involve the calcium-related dynamics of the smooth muscle cells. The calcium-related dynamics which is voltage-independent and hard to be reset seems to actually protect the blood vessels against the electric activity of the atria. We also discuss the microreentry phenomenon, which was found in numerical experiments in the studied model.

Toward a multiscale model of the uterine electrical activity

A comprehensive multiscale model of the uterine muscle electrical activity would permit understanding the important link between the genesis and evolution of the action potential at the cell level and the process leading to labor. Understanding this link can open the way to more effective tools for the prediction of labor and prevention of preterm delivery. A first step toward the realization of such a model is presented here. By using as starting point a previously published model of the generation of the uterine muscle action potential at the cell level, a significant reduction of the model complexity is here achieved in order to simulate 2-D propagation of the cellular activity at the uterine tissue level, for tissue strips of arbitrary dimension. From the obtained dynamic behavior of the electrical activity simulated at the tissue level, the use of a previously validated volume conductor model at the organ level permits us to simulate the electrohysterogram as recorded on the abdominal surface by an electrode array. Qualitative evaluation of the model at the cell level and at the organ level confirms the potential of the proposed multiscale approach for further refinement and extension aiming at clinical application.

Vasomotion - what is currently thought?

This minireview discusses vasomotion, which is the oscillation in tone of blood vessels leading to flowmotion. We will briefly discuss the prevalence of vasomotion and its potential physiological and pathophysiological relevance. We will also discuss the models that have been suggested to explain how a coordinated oscillatory activity of the smooth muscle tone can occur and emphasize the role of the endothelium, the handling of intracellular Ca(2+) and the role of smooth muscle cell ion conductances. It is concluded that vasomotion is likely to enhance tissue dialysis, although this concept still requires more experimental verification, and that an understanding at the molecular level for the pathways leading to vasomotion is beginning to emerge.

Smooth muscle modeling and experimental identification: application to bladder isometric contraction

This paper presents an original smooth muscle model based on the Huxley microscopic approach. This model is the main part of a comprehensive lower urinary track model. The latter is used for simulation studies and is assessed through experiments on rabbits, for which a subset of parameters is estimated, using intravesical pressure measurements in isometric conditions. Bladder contraction is induced by electrical stimulation that determines the onset and thus synchronizes simulation and experimental data. Model sensitivity versus parameter accuracy is discussed and allows the definition of a subset of four parameters that must be accurately identified in order to obtain good fitting between experimental and acquired data. Preliminary experimental data are presented as well as model identification results. They show that the model is able to follow the pressure changes induced by an artificial stimulus in isometric contractions. Moreover, the model gives an insight into the internal changes in calcium concentration and the ratio of the different chemical species present in the muscle cells, in particular the bounded and unbounded actin and myosin and the normalized concentration of intracellular calcium.

Calcium dynamics and signaling in vascular regulation: computational models

Calcium is a universal signaling molecule with a central role in a number of vascular functions including in the regulation of tone and blood flow. Experimentation has provided insights into signaling pathways that lead to or affected by Ca(2+) mobilization in the vasculature. Mathematical modeling offers a systematic approach to the analysis of these mechanisms and can serve as a tool for data interpretation and for guiding new experimental studies. Comprehensive models of calcium dynamics are well advanced for some systems such as the heart. This review summarizes the progress that has been made in modeling Ca(2+) dynamics and signaling in vascular cells. Model simulations show how Ca(2+) signaling emerges as a result of complex, nonlinear interactions that cannot be properly analyzed using only a reductionist's approach. A strategy of integrative modeling in the vasculature is outlined that will allow linking macroscale pathophysiological responses to the underlying cellular mechanisms.

Informational dynamics of vasomotion in microvascular networks: a review

Vasomotion refers to spontaneous oscillation of small vessels observed in many microvascular beds. It is an intrinsic phenomenon unrelated to cardiac rhythm or neural and hormonal regulation. Vasomotion is found to be particularly prominent under conditions of metabolic stress. In spite of a significant existent literature on vasomotion, its physiological and pathophysiological roles are not clear. It is thought that modulation of vasomotion by vasoactive substances released by metabolizing tissue plays a role in ensuring optimal delivery of nutrients to the tissue. Vasomotion rhythms exhibit a great variety of temporal patterns from regular oscillations to chaos. The nature of vasomotion rhythm is believed to be significant to its function, with chaotic vasomotion offering several physiological advantages over regular, periodic vasomotion. In this article, we emphasize that vasomotion is best understood as a network phenomenon. When there is a local metabolic demand in tissue, an ideal vascular response should extend beyond local microvasculature, with coordinated changes over multiple vascular segments. Mechanisms of information transfer over a vessel network have been discussed in the literature. The microvascular system may be regarded as a network of dynamic elements, interacting, either over the vascular anatomical network via gap junctions, or physiologically by exchange of vasoactive substances. Drawing analogies with spatiotemporal patterns in neuronal networks of central nervous system, we ask if properties like synchronization/desynchronization of vasomotors have special significance to microcirculation. Thus the contemporary literature throws up a novel view of microcirculation as a network that exhibits complex, spatiotemporal and informational dynamics.

Mechanisms of propagation of intercellular calcium waves in arterial smooth muscle cells

In rat mesenteric arteries, smooth muscle cells exhibit intercellular calcium waves in response to local phenylephrine stimulation. These waves have a velocity of approximately 20 cells/s and a range of approximately 80 cells. We analyze these waves in a theoretical model of a population of coupled smooth muscle cells, based on the hypothesis that the wave results from cell membrane depolarization propagation. We study the underlying mechanisms and highlight the importance of voltage-operated channels, calcium-induced calcium release, and chloride channels. Our model is in agreement with experimental observations, and we demonstrate that calcium waves presenting a velocity of approximately 20 cells/s can be mediated by electrical coupling. The wave velocity is limited by the time needed for calcium influx through voltage-operated calcium channels and the subsequent calcium-induced calcium release, and not by the speed of the depolarization spreading. The waves are partially regenerated, but have a spatial limit in propagation. Moreover, the model predicts that a refractory period of calcium signaling may significantly affect the wave appearance.

Evidence both L-type and non-L-type voltage-dependent calcium channels contribute to cerebral artery vasospasm following loss of NO in the rat

We recently found block of NO synthase in rat middle cerebral artery caused spasm, associated with depolarizing oscillations in membrane potential (E_m) similar in form but faster in frequency (circa 1 Hz) to vasomotion. T-type voltage-gated Ca²⁺ channels contribute to cerebral myogenic tone and vasomotion, so we investigated the significance of T-type and other ion channels for membrane potential oscillations underlying arterial spasm. Smooth muscle cell membrane potential (E_m) and tension were measured simultaneously in rat middle cerebral artery. NO synthase blockade caused temporally coupled depolarizing oscillations in cerebrovascular E_m with associated vasoconstriction. Both events were accentuated by block of smooth muscle BK_Ca. Block of T-type channels or inhibition of Na⁺/K⁺-ATPase abolished the oscillations in E_m and reduced vasoconstriction. Oscillations in E_m were either attenuated or accentuated by reducing [Ca²⁺]_o or block of K_V, respectively. TRAM-34 attenuated oscillations in both E_m and tone, apparently independent of effects against K_Ca3.1. Thus, rapid depolarizing oscillations in E_m and tone observed after endothelial function has been disrupted reflect input from T-type calcium channels in addition to L-type channels, while other depolarizing currents appear to be unimportant. These data suggest that combined block of T and L-type channels may represent an effective approach to reverse cerebral vasospasm.

A mathematical model of vasoreactivity in rat mesenteric arterioles: I. Myoendothelial communication

To study the effect of myoendothelial communication on vascular reactivity, we integrated detailed mathematical models of Ca(2+) dynamics and membrane electrophysiology in arteriolar smooth muscle (SMC) and endothelial (EC) cells. Cells are coupled through the exchange of Ca(2+), Cl(-), K(+), and Na(+) ions, inositol 1,4,5-triphosphate (IP(3)), and the paracrine diffusion of nitric oxide (NO). EC stimulation reduces intracellular Ca(2+) ([Ca(2+)](i)) in the SMC by transmitting a hyperpolarizing current carried primarily by K(+). The NO-independent endothelium-derived hyperpolarization was abolished in a synergistic-like manner by inhibition of EC SK(Ca) and IK(Ca) channels. During NE stimulation, IP(3) diffusing from the SMC induces EC Ca(2+) release, which, in turn, moderates SMC depolarization and [Ca(2+)](i) elevation. On the contrary, SMC [Ca(2+)](i) was not affected by EC-derived IP(3). Myoendothelial Ca(2+) fluxes had no effect in either cell. The EC exerts a stabilizing effect on calcium-induced calcium release-dependent SMC Ca(2+) oscillations by increasing the norepinephrine concentration window for oscillations. We conclude that a model based on independent data for subcellular components can capture major features of the integrated vessel behavior. This study provides a tissue-specific approach for analyzing complex signaling mechanisms in the vasculature.

Synchronization of Ca2+ oscillations: a coupled oscillator-based mechanism in smooth muscle

Entrained oscillations in Ca(2+) underlie many biological pacemaking phenomena. In this article, we review a long-range signaling mechanism in smooth muscle that results in global outcomes of local interactions. Our results are derived from studies of the following: (a) slow-wave depolarizations that underlie rhythmic contractions of gastric smooth muscle; and (b) membrane depolarizations that drive rhythmic contractions of lymphatic smooth muscle. The main feature of this signaling mechanism is a coupled oscillator-based synchronization of Ca(2+) oscillations across cells that drives membrane potential changes and causes coordinated contractions. The key elements of this mechanism are as follows: (a) the Ca(2+) release-refill cycle of endoplasmic reticulum Ca(2+) stores; (b) Ca(2+)-dependent modulation of membrane currents; (c) voltage-dependent modulation of Ca(2+) store release; and (d) cell-cell coupling through gap junctions or other mechanisms. In this mechanism, Ca(2+) stores alter the frequency of adjacent stores through voltage-dependent modulation of store release. This electrochemical coupling is many orders of magnitude stronger than the coupling through diffusion of Ca(2+) or inositol 1,4,5-trisphosphate, and thus provides an effective means of long-range signaling.

Using stochastic models calibrated from nanosecond nonequilibrium simulations to approximate mesoscale information

We demonstrate how the surrogate process approximation (SPA) method can be used to compute both the potential of mean force along a reaction coordinate and the associated diffusion coefficient using a relatively small number (10-20) of bidirectional nonequilibrium trajectories coming from a complex system. Our method provides confidence bands which take the variability of the initial configuration of the high-dimensional system, continuous nature of the work paths, and thermal fluctuations into account. Maximum-likelihood-type methods are used to estimate a stochastic differential equation (SDE) approximating the dynamics. For each observed time series, we estimate a new SDE resulting in a collection of SPA models. The physical significance of the collection of SPA models is discussed and methods for exploiting information in the population of estimated SPA models are demonstrated and suggested. Molecular dynamics simulations of potassium ion dynamics inside a gramicidin A channel are used to demonstrate the methodology, although SPA-type modeling has also proven useful in analyzing single-molecule experimental time series [J. Phys. Chem. B 113, 118 (2009)].

Smooth muscle model for functional electrical stimulation applications: simulation of realistic bladder behavior under FES

In this paper, we present a smooth muscle model which enables simulation of functional electrical stimulation (FES) induced contraction. The major novelty of this new version of our model is that it includes muscle cell calcium dynamics. We establish the relationship between calcium concentration and electrical potential of the membrane cell. Calcium concentration drives the microscopic mechanics of the muscle inducing contraction. We also refined the mechanical model: smooth muscles have slower dynamics than striated ones, it is therefore possible to neglect the second order terms in the differential equations. Validation of the model is achieved through the simulation of a well known example: the bladder electrical stimulation with a Finetech / Brindley implant. The obtained results are compared qualitatively with the experimental data available in the literature and show good consistency both in shape and time course. In order to obtain quantitative simulations, we need to perform the identification of the model through in-vivo testing on animals. Once this validation step is done, it will be possible to apply our methodology to human bladder neural stimulation.

Heterogeneity and weak coupling may explain the synchronization characteristics of cells in the arterial wall

Vascular smooth muscle cells (SMCs) exhibit different types of calcium dynamics. Static vascular tone is associated with unsynchronized calcium waves and the developed force depends on the number of recruited cells. Global calcium transients synchronized among a large number of cells cause rhythmic development of force known as vasomotion. We present experimental data showing a considerable heterogeneity in cellular calcium dynamics in the vascular wall. In stimulated vessels, some SMCs remain quiescent, whereas others display waves of variable frequency. At the onset of vasomotion, all SMCs are enrolled into synchronized oscillation. Simulations of coupled SMCs show that the experimentally observed cellular recruitment, the presence of quiescent cells and the variation in oscillation frequency may arise if the cell population is phenotypically heterogeneous. In this case, quiescent cells can be entrained at the onset of vasomotion by the collective driving force from the synchronized oscillations in the membrane potential of the surrounding cells. Partial synchronization arises with an increase in the concentration of cyclic guanosine monophosphate, but in a heterogeneous cell population complete synchronization also requires a high-conductance pathway that provides strong coupling between the cells.

A mathematical model of Ca2+ dynamics in rat mesenteric smooth muscle cell: agonist and NO stimulation

A mathematical model of calcium dynamics in vascular smooth muscle cell (SMC) was developed based on data mostly from rat mesenteric arterioles. The model focuses on (a) the plasma membrane electrophysiology; (b) Ca2+ uptake and release from the sarcoplasmic reticulum (SR); (c) cytosolic balance of Ca2+, Na+, K+, and Cl ions; and (d) IP3 and cGMP formation in response to norepinephrine(NE) and nitric oxide (NO) stimulation. Stimulation with NE induced membrane depolarization and an intracellular Ca2+ ([Ca2+]i) transient followed by a plateau. The plateau concentrations were mostly determined by the activation of voltage-operated Ca2+ channels. NE causes a greater increase in [Ca2+]i than stimulation with KCl to equivalent depolarization. Model simulations suggest that the effect of[Na+]i accumulation on the Na+/Ca2+ exchanger (NCX) can potentially account for this difference.Elevation of [Ca2+]i within a concentration window (150-300 nM) by NE or KCl initiated [Ca2+]i oscillations with a concentration-dependent period. The oscillations were generated by the nonlinear dynamics of Ca2+ release and refilling in the SR. NO repolarized the NE-stimulated SMC and restored low [Ca2+]i mainly through its effect on Ca2+-activated K+ channels. Under certain conditions, Na+-K+-ATPase inhibition can result in the elevation of [Na+]i and the reversal of NCX, increasing resting cytosolic and SR Ca2+ content, as well as reactivity to NE. Blockade of the NCX's reverse mode could eliminate these effects. We conclude that the integration of the selected cellular components yields a mathematical model that reproduces, satisfactorily, some of the established features of SMC physiology. Simulations suggest a potential role of intracellular Na+ in modulating Ca2+ dynamics and provide insights into the mechanisms of SMC constriction, relaxation, and the phenomenon of vasomotion. The model will provide the basis for the development of multi-cellular mathematical models that will investigate microcirculatory function in health and disease.

Calcium dynamics and vasomotion in arteries subject to isometric, isobaric, and isotonic conditions

In vitro, different techniques are used to study the smooth muscle cells' calcium dynamics and contraction/relaxation mechanisms on arteries. Most experimental studies use either an isometric or an isobaric setup. However, in vivo, a blood vessel is neither isobaric nor isometric nor isotonic, as it is continuously submitted to intraluminal pressure variations arising from heart beat. We use a theoretical model of the smooth muscle calcium and arterial radius dynamics to determine whether results may be considerably different depending on the experimental conditions (isometric, isobaric, isotonic, or cyclic pressure variations). We show that isobaric conditions appear to be more realistic than isometric or isotonic situations, as the calcium dynamics is similar under cyclic intraluminal pressure variations (in vivo-like situation) and under a constant pressure (isobaric situation). The arterial contraction is less pronounced in isotonic than in isobaric conditions, and the vasoconstrictor sensitivity higher in isometric than isobaric or isotonic conditions, in agreement with experimental observations. Interestingly, the model predicts that isometric conditions may generate artifacts like the coexistence of multiple stable states. We have verified this model prediction experimentally using rat mesenteric arteries mounted on a wire myograph and stimulated with phenylephrine.

Vasomotion dynamics following calcium spiking depend on both cell signalling and limited constriction velocity in rat mesenteric small arteries

Vascular smooth muscle cell contraction depends on intracellular calcium. However, calcium-contraction coupling involves a complex array of intracellular processes. Quantitating the dynamical relation between calcium perturbations and resulting changes in tone may help identifying these processes. We hypothesized that in small arteries accurate quantitation can be achieved during rhythmic vasomotion, and questioned whether these dynamics depend on intracellular signalling or physical vasoconstriction. We studied calcium-constriction dynamics in cannulated and pressurized rat mesenteric small arteries (∼300 μm in diameter). Combined application of tetra-ethyl ammonium (TEA) and BayK8644 induced rhythmicity, consisting of regular and irregular calcium spiking and superposition of spikes. Calcium spikes induced delayed vasomotion cycles. Their dynamic relation could be fitted by a linear second-order model. The dirac impulse response of this model had an amplitude that was strongly reduced with increasing perfusion pressure between 17 and 98 mmHg, while time to peak and relaxation time were the largest at an intermediate pressure (57 mmHg: respectively 0.9 and 2.3 sec). To address to what extent these dynamics reside in intracellular signalling or vasoconstriction, we applied rhythmic increases in pressure counteracting the vasoconstriction. This revealed that calcium-activation coupling became faster when vasoconstriction was counteracted. During such compensation, a calcium impulse response remained that lasted 0.5 sec to peak activation, followed by a 1.0 sec relaxation time, attributable to signalling dynamics. In conclusion, this study demonstrates the feasibility of quantitating calcium-activation dynamics in vasomoting small arteries. These dynamics relate to both intracellular sig-nalling and actual vasoconstriction. Performing such analyses during pharmacological intervention and in genetic models provides a tool for unravelling calcium-contraction coupling in small arteries.

Electrophysiological modelling of pulmonary artery smooth muscle cells in the rabbits--special consideration to the generation of hypoxic pulmonary vasoconstriction

In vascular smooth muscle cells, it has been suggested that membrane potential is an important component that initiates contraction. We developed a mathematical model to elucidate the quantitative contributions of major ion currents [a voltage-gated L-type Ca2+ current (ICaL), a voltage-sensitive K+ current (IKV), a Ca2+-activated K+ current (IKCa) and a nonselective cation current (INSC)] to membrane potential. In order to typify the diverse nature of pulmonary artery smooth muscle cells (PASMCs), we introduced parameters that are not fixed (variable parameters). The population of cells with different parameters was constructed and the cells that have the electrophysiological properties of PASMCs were selected. The contributions of each membrane current were investigated by sensitivity analysis and modification of the current parameters. Consequently, IKV and INSC were found to be the most important currents that affect the membrane potential. The occurrence of depolarisation in hypoxic pulmonary vasoconstriction (HPV) was also examined. In hypoxia, IKV and IKCa were reduced, but the consequent depolarisation in simulation was not enough to initiate contractions. If we add an increase of INSC (2.5-fold), the calculated membrane potential was enough to induce contraction. From the results, we conclude that the balance of various ion channel activities determines the resting membrane potential of PASMCs and our model was successful in explaining the depolarisation in HPV. Therefore, this model can be a powerful tool to investigate the various electrical properties of PASMCs in both normal and pathological conditions.

A model of smooth muscle cell synchronization in the arterial wall

Vasomotion is a rhythmic variation in microvascular diameter. Although known for more than 150 years, the cellular processes underlying the initiation of vasomotion are not fully understood. In the present study a model of a single cell is extended by coupling a number of cells into a tube. The simulated results point to a permissive role of cGMP in establishing intercellular synchronization. In sufficient concentration, cGMP may activate a cGMP-sensitive calcium-dependent chloride channel, causing a tight spatiotemporal coupling between release of sarcoplasmic reticulum calcium, membrane depolarization, and influx of extracellular calcium. Low [cGMP] is associated only with unsynchronized waves. At intermediate concentrations, cells display either waves or whole cell oscillations, but these remain unsynchronized between cells. Whole cell oscillations are associated with rhythmic variation in membrane potential and flow of current through gap junctions. The amplitude of these oscillations in potential grows with increasing [cGMP], and, past a certain threshold, they become strong enough to entrain all cells in the vascular wall, thereby initiating sustained vasomotion. In this state there is a rhythmic flow of calcium through voltage-sensitive calcium channels into the cytoplasm, making the frequency of established vasomotion sensitive to membrane potential. It is concluded that electrical coupling through gap junctions is likely to be responsible for the rapid synchronization across a large number of cells. Gap-junctional current between cells is due to the appearance of oscillations in the membrane potential that again depends on the entrainment of sarcoplasmic reticulum and plasma membrane within the individual cell.

Pacemaking through Ca2+ stores interacting as coupled oscillators via membrane depolarization

This study presents an investigation of pacemaker mechanisms underlying lymphatic vasomotion. We tested the hypothesis that active inositol 1,4,5-trisphosphate receptor (IP(3)R)-operated Ca(2+) stores interact as coupled oscillators to produce near-synchronous Ca(2+) release events and associated pacemaker potentials, this driving action potentials and constrictions of lymphatic smooth muscle. Application of endothelin 1 (ET-1), an agonist known to enhance synthesis of IP(3), to quiescent lymphatic smooth muscle syncytia first enhanced spontaneous Ca(2+) transients and/or intracellular Ca(2+) waves. Larger near-synchronous Ca(2+) transients then occurred leading to global synchronous Ca(2+) transients associated with action potentials and resultant vasomotion. In contrast, blockade of L-type Ca(2+) channels with nifedipine prevented ET-1 from inducing near-synchronous Ca(2+) transients and resultant action potentials, leaving only asynchronous Ca(2+) transients and local Ca(2+) waves. These data were well simulated by a model of lymphatic smooth muscle with: 1), oscillatory Ca(2+) release from IP(3)R-operated Ca(2+) stores, which causes depolarization; 2), L-type Ca(2+) channels; and 3), gap junctions between cells. Stimulation of the stores caused global pacemaker activity through coupled oscillator-based entrainment of the stores. Membrane potential changes and positive feedback by L-type Ca(2+) channels to produce more store activity were fundamental to this process providing long-range electrochemical coupling between the Ca(2+) store oscillators. We conclude that lymphatic pacemaking is mediated by coupled oscillator-based interactions between active Ca(2+) stores. These are weakly coupled by inter- and intracellular diffusion of store activators and strongly coupled by membrane potential. Ca(2+) store-based pacemaking is predicted for cellular systems where: 1), oscillatory Ca(2+) release induces depolarization; 2), membrane depolarization provides positive feedback to induce further store Ca(2+) release; and 3), cells are interconnected. These conditions are met in a surprisingly large number of cellular systems including gastrointestinal, lymphatic, urethral, and vascular tissues, and in heart pacemaker cells.

Interaction between Na+/K+-pump and Na+/Ca2+-exchanger modulates intercellular communication

Ouabain, a specific inhibitor of the Na(+)/K(+)-pump, has previously been shown to interfere with intercellular communication. Here we test the hypothesis that the communication between vascular smooth muscle cells is regulated through an interaction between the Na(+)/K(+)-pump and the Na(+)/Ca(2+)-exchanger leading to an increase in the intracellular calcium concentration ([Ca(2+)](i)) in discrete areas near the plasma membrane. [Ca(2+)](i) in smooth muscle cells was imaged in cultured rat aortic smooth muscle cell pairs (A7r5) and in rat mesenteric small artery segments simultaneously with force. In A7r5 coupling between cells was estimated by measuring membrane capacitance. Smooth muscle cells were uncoupled when the Na(+)/K(+)-pump was inhibited either by a low concentration of ouabain, which also caused a localized increase of [Ca(2+)](i) near the membrane, or by ATP depletion. Reduction of Na(+)/K(+)-pump activity by removal of extracellular potassium ([K(+)](o)) also uncoupled cells, but only after inhibition of K(ATP) channels. Inhibition of the Na(+)/Ca(2+)-exchange activity by SEA0400 or by a reduction of the equilibrium potential (making it more negative) also uncoupled the cells. Depletion of intracellular Na(+) and clamping of [Ca(2+)](i) at low concentrations prevented the uncoupling. The experiments suggest that the Na(+)/K(+)-pump may affect gap junction conductivity via localized changes in [Ca(2+)](i) through modulation of Na(+)/Ca(2+)-exchanger activity.

Permeation and gating in proteins: kinetic Monte Carlo reaction path following

We present a new Monte Carlo technique, kinetic Monte Carlo reaction path following (kMCRPF), for the computer simulation of permeation and large-scale gating transitions in protein channels. It combines ideas from Metropolis Monte Carlo (MMC) and kinetic Monte Carlo (kMC) algorithms, and is particularly suitable when a reaction coordinate is well defined. Evolution of transition proceeds on the reaction coordinate by small jumps (kMC technique) toward the nearest lowest-energy uphill or downhill states, with the jumps thermally activated (constrained MMC). This approach permits navigation among potential minima on an energy surface, finding the minimum-energy paths and determining their associated free-energy profiles. The methodological and algorithmic strategies underlying the kMCRPF method are described. We have tested it using an analytical model and applied it to study permeation through the curvilinear ClC chloride and aquaporin pores and to gating in the gramicidin A channel. These studies of permeation and gating in real proteins provide extensive procedural tests of the method.