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

Biophysical Mechanisms of Vaginal Smooth Muscle Contraction: The Role of the Membrane Potential and Ion Channels

The vagina is an essential component of the female reproductive system and is responsible for providing female sexual satisfaction. Vaginal smooth muscle contraction plays a crucial role in various physiological processes, including sexual arousal, childbirth, and urinary continence. In pathophysiological conditions, such as pelvic floor disorders, aberrations in vaginal smooth muscle function can lead to urinary incontinence and pelvic organ prolapse. A set of cellular and sub-cellular physiological mechanisms regulates the contractile properties of the vaginal smooth muscle cells. Calcium influx is a crucial determinant of smooth muscle contraction, facilitated through voltage-dependent calcium channels and calcium release from intracellular stores. Comprehensive reviews on smooth muscle biophysics are relatively scarce within the scientific literature, likely due to the complexity and specialized nature of the topic. The objective of this review is to provide a comprehensive description of alterations in the cellular physiology of vaginal smooth muscle contraction. The benefit associated with this particular approach is that conducting a comprehensive examination of the cellular mechanisms underlying contractile activation will enable the creation of more targeted therapeutic agents to control vaginal contraction disorders.

Review of cardiac-coronary interaction and insights from mathematical modeling

Cardiac-coronary interaction is fundamental to the function of the heart. As one of the highest metabolic organs in the body, the cardiac oxygen demand is met by blood perfusion through the coronary vasculature. The coronary vasculature is largely embedded within the myocardial tissue which is continually contracting and hence squeezing the blood vessels. The myocardium-coronary vessel interaction is two-ways and complex. Here, we review the different types of cardiac-coronary interactions with a focus on insights gained from mathematical models. Specifically, we will consider the following: (1) myocardial-vessel mechanical interaction; (2) metabolic-flow interaction and regulation; (3) perfusion-contraction matching, and (4) chronic interactions between the myocardium and coronary vasculature. We also provide a discussion of the relevant experimental and clinical studies of different types of cardiac-coronary interactions. Finally, we highlight knowledge gaps, key challenges, and limitations of existing mathematical models along with future research directions to understand the unique myocardium-coronary coupling in the heart. This article is categorized under: Cardiovascular Diseases > Computational Models Cardiovascular Diseases > Biomedical Engineering Cardiovascular Diseases > Molecular and Cellular Physiology.

The conducted vascular response as a mediator of hypercapnic cerebrovascular reactivity: A modelling study

It is well established that the cerebral blood flow (CBF) shows exquisite sensitivity to changes in the arterial blood partial pressure of CO2 ( [Formula: see text] ), which is reflected by an index termed cerebrovascular reactivity. In response to elevations in [Formula: see text] (hypercapnia), the vessels of the cerebral microvasculature dilate, thereby decreasing the vascular resistance and increasing CBF. Due to the challenges of access, scale and complexity encountered when studying the microvasculature, however, the mechanisms behind cerebrovascular reactivity are not fully understood. Experiments have previously established that the cholinergic release of the Acetylcholine (ACh) neurotransmitter in the cortex is a prerequisite for the hypercapnic response. It is also known that ACh functions as an endothelial-dependent agonist, in which the local administration of ACh elicits local hyperpolarization in the vascular wall; this hyperpolarization signal is then propagated upstream the vascular network through the endothelial layer and is coupled to a vasodilatory response in the vascular smooth muscle (VSM) layer in what is known as the conducted vascular response (CVR). Finally, experimental data indicate that the hypercapnic response is more strongly correlated with the CO2 levels in the tissue than in the arterioles. Accordingly, we hypothesize that the CVR, evoked by increases in local tissue CO2 levels and a subsequent local release of ACh, is responsible for the CBF increase observed in response to elevations in [Formula: see text] . By constructing physiologically grounded dynamic models of CBF and control in the cerebral vasculature, ones that integrate the available knowledge and experimental data, we build a new model of the series of signalling events and pathways underpinning the hypercapnic response, and use the model to provide compelling evidence that corroborates the aforementioned hypothesis. If the CVR indeed acts as a mediator of the hypercapnic response, the proposed mechanism would provide an important addition to our understanding of the repertoire of metabolic feedback mechanisms possessed by the brain and would motivate further in-vivo investigation. We also model the interaction of the hypercapnic response with dynamic cerebral autoregulation (dCA), the collection of mechanisms that the brain possesses to maintain near constant CBF despite perturbations in pressure, and show how the dCA mechanisms, which otherwise tend to be overlooked when analysing experimental results of cerebrovascular reactivity, could play a significant role in shaping the CBF response to elevations in [Formula: see text] . Such in-silico models can be used in tandem with in-vivo experiments to expand our understanding of cerebrovascular diseases, which continue to be among the leading causes of morbidity and mortality in humans.

A computational model predicts sex-specific responses to calcium channel blockers in mammalian mesenteric vascular smooth muscle

The function of the smooth muscle cells lining the walls of mammalian systemic arteries and arterioles is to regulate the diameter of the vessels to control blood flow and blood pressure. Here, we describe an in silico model, which we call the 'Hernandez-Hernandez model', of electrical and Ca2+ signaling in arterial myocytes based on new experimental data indicating sex-specific differences in male and female arterial myocytes from murine resistance arteries. The model suggests the fundamental ionic mechanisms underlying membrane potential and intracellular Ca2+ signaling during the development of myogenic tone in arterial blood vessels. Although experimental data suggest that KV1.5 channel currents have similar amplitudes, kinetics, and voltage dependencies in male and female myocytes, simulations suggest that the KV1.5 current is the dominant current regulating membrane potential in male myocytes. In female cells, which have larger KV2.1 channel expression and longer time constants for activation than male myocytes, predictions from simulated female myocytes suggest that KV2.1 plays a primary role in the control of membrane potential. Over the physiological range of membrane potentials, the gating of a small number of voltage-gated K+ channels and L-type Ca2+ channels are predicted to drive sex-specific differences in intracellular Ca2+ and excitability. We also show that in an idealized computational model of a vessel, female arterial smooth muscle exhibits heightened sensitivity to commonly used Ca2+ channel blockers compared to male. In summary, we present a new model framework to investigate the potential sex-specific impact of antihypertensive drugs.

A new model for evaluating pressure-induced vascular tone in small cerebral arteries

The capacity of small cerebral arteries (SCAs) to adapt to pressure fluctuations has a fundamental physiological role and appears to be relevant in different pathological conditions. Here, we present a new computational model for quantifying the link, and its contributors, between luminal pressure and vascular tone generation in SCAs. This is assembled by combining a chemical sub-model, representing pressure-induced smooth muscle cell (SMC) signalling, with a mechanical sub-model for the tone generation and its transduction at tissue level. The devised model can accurately reproduce the impact of luminal pressure on different cytoplasmic components involved in myogenic signalling, both in the control case and when combined with some specific pharmacological interventions. Furthermore, the model is also able to capture and predict experimentally recorded pressure-outer diameter relationships obtained for vessels under control conditions, both in a Ca2 + -free bath and under drug inhibition. The modularity of the proposed framework allows the integration of new components for the study of a broad range of processes involved in the vascular function.

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 computational model predicts sex-specific responses to calcium channel blockers in mammalian mesenteric vascular smooth muscle

The function of the smooth muscle cells lining the walls of mammalian systemic arteries and arterioles is to regulate the diameter of the vessels to control blood flow and blood pressure. Here, we describe an in-silico model, which we call the "Hernandez-Hernandez model", of electrical and C a 2+ signaling in arterial myocytes based on new experimental data indicating sex-specific differences in male and female arterial myocytes from murine resistance arteries. The model suggests the fundamental ionic mechanisms underlying membrane potential and intracellular C a 2+ signaling during the development of myogenic tone in arterial blood vessels. Although experimental data suggest that KV1.5 channel currents have similar amplitudes, kinetics, and voltage dependencies in male and female myocytes, simulations suggest that the KV1.5 current is the dominant current regulating membrane potential in male myocytes. In female cells, which have larger KV2.1 channel expression and longer time constants for activation than male myocytes, predictions from simulated female myocytes suggest that KV2.1 plays a primary role in the control of membrane potential. Over the physiological range of membrane potentials, the gating of a small number of voltage-gated K+ channels and L-type C a 2+ channels are predicted to drive sex-specific differences in intracellular C a 2+ and excitability. We also show that in an idealized computational model of a vessel, female arterial smooth muscle exhibits heightened sensitivity to commonly used C a 2+ channel blockers compared to male. In summary, we present a new model framework to investigate the potential sex-specific impact of anti-hypertensive drugs.

On the Ca2＋ elevation in vascular endothelial cells due to inositol trisphosphate-sensitive store receptors activation: A data-driven modeling approach

Agonist-induced Ca2+ signaling is essential for the regulation of many vital functions in endothelial cells (ECs). A broad range of stimuli elevate the cytosolic Ca2＋ concentration by promoting a pathway mediated by inositol 1,4,5 trisphosphate (IP3) which causes Ca2＋ release from intracellular stores. Despite its importance, there are very few studies focusing on the quantification of such dynamics in the vascular endothelium. Here, by using data from isolated ECs, we established a minimalistic modeling framework able to quantitatively capture the main features (averaged over a cell population) of the cytosolic Ca2＋ response to different IP3 stimulation levels. A suitable description of Ca2＋-regulatory function of inositol 1,4,5 trisphosphate receptors (IP3Rs) and corresponding parameter space are identified by comparing the different model variants against experimental mean population data. The same approach is used to numerically assess the relevance of cytosolic Ca2＋ buffering, as well as Ca2＋ store IP3-sensitivity in the overall cell dynamics. The variability in the dynamics' features observed across the population can be explained (at least in part) through variation of certain model parameters (such as buffering capacity or Ca2＋ store sensitivity to IP3). The results, in terms of experimental fitting and validation, support the proposed minimalistic model as a reference framework for the quantification of the EC Ca2＋ dynamics induced by IP3Rs activation.

Diversity of cells and signals in the cardiovascular system

This white paper is the outcome of the seventh UC Davis Cardiovascular Research Symposium on Systems Approach to Understanding Cardiovascular Disease and Arrhythmia. This biannual meeting aims to bring together leading experts in subfields of cardiovascular biomedicine to focus on topics of importance to the field. The theme of the 2022 Symposium was 'Cell Diversity in the Cardiovascular System, cell-autonomous and cell-cell signalling'. Experts in the field contributed their experimental and mathematical modelling perspectives and discussed emerging questions, controversies, and challenges in examining cell and signal diversity, co-ordination and interrelationships involved in cardiovascular function. This paper originates from the topics of formal presentations and informal discussions from the Symposium, which aimed to develop a holistic view of how the multiple cell types in the cardiovascular system integrate to influence cardiovascular function, disease progression and therapeutic strategies. The first section describes the major cell types (e.g. cardiomyocytes, vascular smooth muscle and endothelial cells, fibroblasts, neurons, immune cells, etc.) and the signals involved in cardiovascular function. The second section emphasizes the complexity at the subcellular, cellular and system levels in the context of cardiovascular development, ageing and disease. Finally, the third section surveys the technological innovations that allow the interrogation of this diversity and advancing our understanding of the integrated cardiovascular function and dysfunction.

Mathematical modeling of intracellular calcium in presence of receptor: a homeostatic model for endothelial cell

Calcium is a ubiquitous molecule and second messenger that regulates many cellular functions ranging from exocytosis to cell proliferation at different time scales. In the vasculature, a constant adenosine triphosphate (ATP) concentration is maintained because of ATP released by red blood cells (RBCs). These ATP molecules continuously react with purinergic receptors on the surface of endothelial cells (ECs). Consequently, a cascade of chemical reactions are triggered that result in a transient cytoplasmic calcium (Ca[Formula: see text]), followed by return to its basal concentration. The mathematical models proposed in the literature are able to reproduce the transient peak. However, the trailing concentration is always higher than the basal cytoplasmic Ca[Formula: see text] concentrations, and the Ca[Formula: see text] concentration in endoplasmic reticulum (ER) remains lower than its initial concentration. This means that the intracellular homeostasis is not recovered. We propose, herein, a minimal model of calcium kinetics. We find that the desensitization of EC surface receptors due to phosphorylation and recycling plays a vital role in maintaining calcium homeostasis in the presence of a constant stimulus (ATP). The model is able to capture several experimental observations such as refilling of Ca[Formula: see text] in the ER, variation of cytoplasmic Ca[Formula: see text] transient peak in ECs, the resting cytoplasmic Ca[Formula: see text] concentration, the effect of removing ATP from the plasma on Ca[Formula: see text] homeostasis, and the saturation of cytoplasmic Ca[Formula: see text] transient peak with increase in ATP concentration. Direct confrontation with several experimental results is conducted. This work paves the way for systematic studies on coupling between blood flow and chemical signaling, and should contribute to a better understanding of the relation between (patho)physiological conditions and Ca[Formula: see text] kinetics.

Modeling Reactive Hyperemia to Better Understand and Assess Microvascular Function: A Review of Techniques

Reactive hyperemia is a well-established technique for the non-invasive evaluation of the peripheral microcirculatory function, measured as the magnitude of limb re-perfusion after a brief period of ischemia. Despite widespread adoption by researchers and clinicians alike, many uncertainties remain surrounding interpretation, compounded by patient-specific confounding factors (such as blood pressure or the metabolic rate of the ischemic limb). Mathematical modeling can accelerate our understanding of the physiology underlying the reactive hyperemia response and guide in the estimation of quantities which are difficult to measure experimentally. In this work, we aim to provide a comprehensive guide for mathematical modeling techniques that can be used for describing the key phenomena involved in the reactive hyperemia response, alongside their limitations and advantages. The reported methodologies can be used for investigating specific reactive hyperemia aspects alone, or can be combined into a computational framework to be used in (pre-)clinical settings.

In silico Identification of Key Factors Driving the Response of Muscle Sensory Neurons to Noxious Stimuli

Nociceptive nerve endings embedded in muscle tissue transduce peripheral noxious stimuli into an electrical signal [i.e., an action potential (AP)] to initiate pain sensations. A major contributor to nociception from the muscles is mechanosensation. However, due to the heterogeneity in the expression of proteins, such as ion channels, pumps, and exchangers, on muscle nociceptors, we currently do not know the relative contributions of different proteins and signaling molecules to the neuronal response due to mechanical stimuli. In this study, we employed an integrated approach combining a customized experimental study in mice with a computational model to identify key proteins that regulate mechanical nociception in muscles. First, using newly collected data from somatosensory recordings in mouse hindpaw muscles, we developed and then validated a computational model of a mechanosensitive mouse muscle nociceptor. Next, by performing global sensitivity analyses that simulated thousands of nociceptors, we identified three ion channels (among the 17 modeled transmembrane proteins and four endoplasmic reticulum proteins) as potential regulators of the nociceptor response to mechanical forces in both the innocuous and noxious range. Moreover, we found that simulating single knockouts of any of the three ion channels, delayed rectifier voltage-gated K⁺ channel (Kv1.1) or mechanosensitive channels Piezo2 or TRPA1, considerably altered the excitability of the nociceptor (i.e., each knockout increased or decreased the number of triggered APs compared to when all channels were present). These results suggest that altering expression of the gene encoding Kv1.1, Piezo2, or TRPA1 might regulate the response of mechanosensitive muscle nociceptors.

Cellular and molecular effects of hyperglycemia on ion channels in vascular smooth muscle

Diabetes affects millions of people worldwide. This devastating disease dramatically increases the risk of developing cardiovascular disorders. A hallmark metabolic abnormality in diabetes is hyperglycemia, which contributes to the pathogenesis of cardiovascular complications. These cardiovascular complications are, at least in part, related to hyperglycemia-induced molecular and cellular changes in the cells making up blood vessels. Whereas the mechanisms mediating endothelial dysfunction during hyperglycemia have been extensively examined, much less is known about how hyperglycemia impacts vascular smooth muscle function. Vascular smooth muscle function is exquisitely regulated by many ion channels, including several members of the potassium (K+) channel superfamily and voltage-gated L-type Ca2+ channels. Modulation of vascular smooth muscle ion channels function by hyperglycemia is emerging as a key contributor to vascular dysfunction in diabetes. In this review, we summarize the current understanding of how diabetic hyperglycemia modulates the activity of these ion channels in vascular smooth muscle. We examine underlying mechanisms, general properties, and physiological relevance in the context of myogenic tone and vascular reactivity.

Electrical Propagation of Vasodilatory Signals in Capillary Networks

We have developed a computational model to study electrical propagation of vasodilatory signals and arteriolar regulation of blood flow depending on the oxygen tension and agonist distribution in the capillary network. The involving key parameters of endothelial cell-to-cell electrical conductivity and plasma membrane area per unit volume were calibrated with the experimental data on an isolated endothelial tube of mouse skeletal feeding arteries. We have estimated the oxygen saturation parameters in terms of erythrocyte ATP release from the data of a left anterior descending coronary blood perfusion of dog. Regarding the acetylcholine-induced upstream conduction, our model shows that spatially uniform superfusion of acetylcholine attenuates the electrical signal propagation, and blocking calcium-activated potassium channels suppresses that attenuation. On the other hand, a local infusion of acetylcholine induces enhanced electrical propagation that corresponds to physiological relevance. Integrating the electrophysiology of endothelial tube and the electrophysiology/mechanics of a lumped arteriole, we show mechanistically that endothelial purinergic oxygen sensing of ATP released from erythrocytes and local infusion of acetylcholine are individually effective to induce vasodilatory signals to regulate blood flow in arterioles. We have recapitulated the upstream vasomotion in arterioles from the elevated oxygen tension in the downstream capillary domain. This study is a foundation for characterizing effective pharmaceutical strategies for ascending vasodilation and oxygenation.

A mathematical model for persistent post-CSD vasoconstriction

Cortical spreading depression (CSD) is the propagation of a relatively slow wave in cortical brain tissue that is linked to a number of pathological conditions such as stroke and migraine. Most of the existing literature investigates the dynamics of short term phenomena such as the depolarization and repolarization of membrane potentials or large ion shifts. Here, we focus on the clinically-relevant hour-long state of neurovascular malfunction in the wake of CSDs. This dysfunctional state involves widespread vasoconstriction and a general disruption of neurovascular coupling. We demonstrate, using a mathematical model, that dissolution of calcium that has aggregated within the mitochondria of vascular smooth muscle cells can drive an hour-long disruption. We model the rate of calcium clearance as well as the dynamical implications on overall blood flow. Based on reaction stoichiometry, we quantify a possible impact of calcium phosphate dissolution on the maintenance of F0F1-ATP synthase activity.

Overview of mathematical modeling of myocardial blood flow regulation

The oxygen consumption by the heart and its extraction from the coronary arterial blood are the highest among all organs. Any increase in oxygen demand due to a change in heart metabolic activity requires an increase in coronary blood flow. This functional requirement of adjustment of coronary blood flow is mediated by coronary flow regulation to meet the oxygen demand without any discomfort, even under strenuous exercise conditions. The goal of this article is to provide an overview of the theoretical and computational models of coronary flow regulation and to reveal insights into the functioning of a complex physiological system that affects the perfusion requirements of the myocardium. Models for three major control mechanisms of myogenic, flow, and metabolic control are presented. These explain how the flow regulation mechanisms operating over multiple spatial scales from the precapillaries to the large coronary arteries yield the myocardial perfusion characteristics of flow reserve, autoregulation, flow dispersion, and self-similarity. The review not only introduces concepts of coronary blood flow regulation but also presents state-of-the-art advances and their potential to impact the assessment of coronary microvascular dysfunction (CMD), cardiac-coronary coupling in metabolic diseases, and therapies for angina and heart failure. Experimentalists and modelers not trained in these models will have exposure through this review such that the nonintuitive and highly nonlinear behavior of coronary physiology can be understood from a different perspective. This survey highlights knowledge gaps, key challenges, future research directions, and novel paradigms in the modeling of coronary flow regulation.

The effects of valve leaflet mechanics on lymphatic pumping assessed using numerical simulations

The lymphatic system contains intraluminal leaflet valves that function to bias lymph flow back towards the heart. These valves are present in the collecting lymphatic vessels, which generally have lymphatic muscle cells and can spontaneously pump fluid. Recent studies have shown that the valves are open at rest, can allow some backflow, and are a source of nitric oxide (NO). To investigate how these valves function as a mechanical valve and source of vasoactive species to optimize throughput, we developed a mathematical model that explicitly includes Ca²⁺ -modulated contractions, NO production and valve structures. The 2D lattice Boltzmann model includes an initial lymphatic vessel and a collecting lymphangion embedded in a porous tissue. The lymphangion segment has mechanically-active vessel walls and is flanked by deformable valves. Vessel wall motion is passively affected by fluid pressure, while active contractions are driven by intracellular Ca²⁺ fluxes. The model reproduces NO and Ca²⁺ dynamics, valve motion and fluid drainage from tissue. We find that valve structural properties have dramatic effects on performance, and that valves with a stiffer base and flexible tips produce more stable cycling. In agreement with experimental observations, the valves are a major source of NO. Once initiated, the contractions are spontaneous and self-sustained, and the system exhibits interesting non-linear dynamics. For example, increased fluid pressure in the tissue or decreased lymph pressure at the outlet of the system produces high shear stress and high levels of NO, which inhibits contractions. On the other hand, a high outlet pressure opposes the flow, increasing the luminal pressure and the radius of the vessel, which results in strong contractions in response to mechanical stretch of the wall. We also find that the location of contraction initiation is affected by the extent of backflow through the valves.

Adenylyl cyclase 5-generated cAMP controls cerebral vascular reactivity during diabetic hyperglycemia

Elevated blood glucose (hyperglycemia) is a hallmark metabolic abnormality in diabetes. Hyperglycemia is associated with protein kinase A (PKA)-mediated stimulation of L-type Ca2+ channels in arterial myocytes resulting in increased vasoconstriction. However, the mechanisms by which glucose activates PKA remain unclear. Here, we showed that elevating extracellular glucose stimulates cAMP production in arterial myocytes, and that this was specifically dependent on adenylyl cyclase 5 (AC5) activity. Super-resolution imaging suggested nanometer proximity between subpopulations of AC5 and the L-type Ca2+ channel pore-forming subunit CaV1.2. In vitro, in silico, ex vivo and in vivo experiments revealed that this close association is critical for stimulation of L-type Ca2+ channels in arterial myocytes and increased myogenic tone upon acute hyperglycemia. This pathway supported the increase in L-type Ca2+ channel activity and myogenic tone in two animal models of diabetes. Our collective findings demonstrate a unique role for AC5 in PKA-dependent modulation of L-type Ca2+ channel activity and vascular reactivity during acute hyperglycemia and diabetes.

SemGen: a tool for semantics-based annotation and composition of biosimulation models

SUMMARY

As the number and complexity of biosimulation models grows, so do demands for tools that can help users understand models and compose more comprehensive and accurate systems from existing models. SemGen is a tool for semantics-based annotation and composition of biosimulation models designed to address this demand. A key SemGen capability is to decompose and then integrate models across existing model exchange formats including SBML and CellML. To support this capability, we use semantic annotations to explicitly capture the underlying biological and physical meanings of the entities and processes that are modeled. SemGen leverages annotations to expose a model's biological and computational architecture and to help automate model composition.

AVAILABILITY AND IMPLEMENTATION

SemGen is freely available at https://github.com/SemBioProcess/SemGen.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Cardiovascular regulation in response to multiple hemorrhages: analysis and parameter estimation

Mathematical models can provide useful insights explaining behavior observed in experimental data; however, rigorous analysis is needed to select a subset of model parameters that can be informed by available data. Here we present a method to estimate an identifiable set of parameters based on baseline left ventricular pressure and volume time series data. From this identifiable subset, we then select, based on current understanding of cardiovascular control, parameters that vary in time in response to blood withdrawal, and estimate these parameters over a series of blood withdrawals. These time-varying parameters are first estimated using piecewise linear splines minimizing the mean squared error between measured and computed left ventricular pressure and volume data over four consecutive blood withdrawals. As a final step, the trends in these splines are fit with empirical functional expressions selected to describe cardiovascular regulation during blood withdrawal. Our analysis at baseline found parameters representing timing of cardiac contraction, systemic vascular resistance, and cardiac contractility to be identifiable. Of these parameters, vascular resistance and cardiac contractility were varied in time. Data used for this study were measured in a control Sprague-Dawley rat. To our knowledge, this is the first study to analyze the response to multiple blood withdrawals both experimentally and theoretically, as most previous studies focus on analyzing the response to one large blood withdrawal. Results show that during each blood withdrawal both systemic vascular resistance and contractility decrease acutely and partially recover, and they decrease chronically across the series of blood withdrawals.

The yin and yang of KV channels in cerebral small vessel pathologies

Cerebral SVDs encompass a group of genetic and sporadic pathological processes leading to brain lesions, cognitive decline, and stroke. There is no specific treatment for SVDs, which progress silently for years before becoming clinically symptomatic. Here, we examine parallels in the functional defects of PAs in CADASIL, a monogenic form of SVD, and in response to SAH, a common type of hemorrhagic stroke that also targets the brain microvasculature. Both animal models exhibit dysregulation of the voltage-gated potassium channel, K_V 1, in arteriolar myocytes, an impairment that compromises responses to vasoactive stimuli and impacts CBF autoregulation and local dilatory responses to neuronal activity (NVC). However, the extent to which this channelopathy-like defect ultimately contributes to these pathologies is unknown. Combining experimental data with computational modeling, we describe the role of K_V 1 channels in the regulation of myocyte membrane potential at rest and during the modest increase in extracellular potassium associated with NVC. We conclude that PA resting membrane potential and myogenic tone depend strongly on K_V 1.2/1.5 channel density, and that reciprocal changes in K_V channel density in CADASIL and SAH produce opposite effects on extracellular potassium-mediated dilation during NVC.

Coronary Smooth Muscle Cell Calcium Dynamics: Effects of Bifurcation Angle on Atheroprone Conditions

This work investigates the effect of arterial bifurcation angulation on atherosclerosis development through in-silico simulations of coupled cell dynamics. The computational model presented here combines cellular pathways, fluid dynamics, and physiologically-realistic vessel geometries as observed in the human vasculature. The coupled cells model includes endothelial cells (ECs) and smooth muscle cells (SMCs) with ion dynamics, hetero and homotypic coupling, as well as electro-diffusive coupling. Three arterial bifurcation surface models were used in the coupled cells simulations. All three simulations showed propagating waves of Ca²⁺ in both the SMC and EC layers, following the introduction of a luminal agonist, in this case ATP. Immediately following the introduction of ATP concentration Ca²⁺ waves propagate from the area of high ATP toward the areas of low ATP concentration, forming complex patterns where waves interact with eachother, collide and fade. These dynamic phenomena are repeated with a series of waves of slower velocity. The underlying motivation of this research was to examine the macro-scale phenomena, given that the characteristic length scales of atherosclerotic plaques are much larger than a single cell. The micro-scale dynamics were modeled on macro-scale arterial bifurcation surfaces containing over one million cells. The results of the simulations presented here suggest that susceptibility to atherosclerosis development depends on the bifurcation angulation. In conjunction with findings reported in the literature, the simulation results demonstrate that arterial bifurcations containing wider angles have a more prominent influence on the coupled cells pathways associated with the development of atherosclerosis, by means of disturbed flow and lower SMC Ca²⁺ concentrations. The discussion of the results considers the findings of this research within the context of the potential link between information transport through frequency encoding of Ca²⁺ wave dynamics and development of atheroprone conditions.

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.

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.

Predominant contribution of L-type Cav1.2 channel stimulation to impaired intracellular calcium and cerebral artery vasoconstriction in diabetic hyperglycemia

Enhanced L-type Ca²⁺ channel (LTCC) activity in arterial myocytes contributes to vascular dysfunction during diabetes. Modulation of LTCC activity under hyperglycemic conditions could result from membrane potential-dependent and independent mechanisms. We have demonstrated that elevations in extracellular glucose (HG), similar to hyperglycemic conditions during diabetes, stimulate LTCC activity through phosphorylation of Ca_V1.2 at serine 1928. Prior studies have also shown that HG can suppress the activity of K⁺ channels in arterial myocytes, which may contribute to vasoconstriction via membrane depolarization. Here, we used a mathematical model of membrane and Ca²⁺ dynamics in arterial myocytes to predict the relative roles of LTCC and K⁺ channel activity in modulating global Ca²⁺ in response to HG. Our data revealed that abolishing LTCC potentiation normalizes [Ca²⁺]_i, despite the concomitant reduction in K⁺ currents in response to HG. These results suggest that LTCC stimulation may be the primary mechanism underlying vasoconstriction during hyperglycemia.

Can endothelial hemoglobin-α regulate nitric oxide vasodilatory signaling?

We used mathematical modeling to investigate nitric oxide (NO)-dependent vasodilatory signaling in the arteriolar wall. Detailed continuum cellular models of calcium (Ca²⁺) dynamics and membrane electrophysiology in smooth muscle and endothelial cells (EC) were coupled with models of NO signaling and biotransport in an arteriole. We used this theoretical approach to examine the role of endothelial hemoglobin-α (Hbα) as a modulator of NO-mediated myoendothelial feedback, as previously suggested in Straub et al. (Nature 491: 473-477, 2012). The model considers enriched expression of inositol 1,4,5-triphosphate receptors (IP₃Rs), endothelial nitric oxide synthase (eNOS) enzyme, Ca²⁺-activated potassium (K_Ca) channels and Hbα in myoendothelial projections (MPs) between the two cell layers. The model suggests that NO-mediated myoendothelial feedback is plausible if a significant percentage of eNOS is localized within or near the myoendothelial projection. Model results show that the ability of Hbα to regulate the myoendothelial feedback is conditional to its colocalization with eNOS near MPs at concentrations in the high nanomolar range (>0.2 μM or 24,000 molecules). Simulations also show that the effect of Hbα observed in in vitro experimental studies may overestimate its contribution in vivo, in the presence of blood perfusion. Thus, additional experimentation is required to quantify the presence and spatial distribution of Hbα in the EC, as well as to test that the strong effect of Hbα on NO signaling seen in vitro, translates also into a physiologically relevant response in vivo.NEW & NOTEWORTHY Mathematical modeling shows that although regulation of nitric oxide signaling by hemoglobin-α (Hbα) is plausible, it is conditional to its presence in significant concentrations colocalized with endothelial nitric oxide synthase in myoendothelial projections. Additional experimentation is required to test that the strong effect of Hbα seen in vitro translates into a physiologically relevant response in vivo.

Synchronization and Random Triggering of Lymphatic Vessel Contractions

The lymphatic system is responsible for transporting interstitial fluid back to the bloodstream, but unlike the cardiovascular system, lacks a centralized pump-the heart–to drive flow. Instead, each collecting lymphatic vessel can individually contract and dilate producing unidirectional flow enforced by intraluminal check valves. Due to the large number and spatial distribution of such pumps, high-level coordination would be unwieldy. This leads to the question of how each segment of lymphatic vessel responds to local signals that can contribute to the coordination of pumping on a network basis. Beginning with elementary fluid mechanics and known cellular behaviors, we show that two complementary oscillators emerge from i) mechanical stretch with calcium ion transport and ii) fluid shear stress induced nitric oxide production (NO). Using numerical simulation and linear stability analysis we show that the newly identified shear-NO oscillator shares similarities with the well-known Van der Pol oscillator, but has unique characteristics. Depending on the operating conditions, the shear-NO process may i) be inherently stable, ii) oscillate spontaneously in response to random disturbances or iii) synchronize with weak periodic stimuli. When the complementary shear-driven and stretch-driven oscillators interact, either may dominate, producing a rich family of behaviors similar to those observed in vivo.

For decades, cardiovascular physiology has been an area of intense research, and we have a fundamental understanding of the mechanisms the heart uses to drive blood flow through the distributed network of vessels in the body. The lymphatic system is now receiving similar attention as more is learned about its functional role in disease processes. The importance of the lymphatic system in collecting excess fluid from tissues and returning it to the blood is well known, but how the lymph flow is regulated without a central pump is poorly understood. Each segment of collecting lymphatic vessel can independently contract yielding a network of distributed pump/conduits. This paper shows how the lymphatic muscle cells that squeeze fluid along the lymphatic vessels can be effectively regulated using only chemical and mechanical signals that they receive from their immediate microenvironment. Using stability theory and the tools of nonlinear dynamics we identify two complementary oscillators that respond to stretch of the vessel wall and shear of fluid flowing over the vessel wall. Numerical simulations of the combined oscillators show that they have characteristics well suited to the regulation of distributed systems in general and may have application in other biological and physical contexts.

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.

Stochastic model of endothelial TRPV4 calcium sparklets: effect of bursting and cooperativity on EDH

We examined the endothelial transient receptor vanilloid 4 (TRPV4) channel's vasodilatory signaling using mathematical modeling. The model analyzes experimental data by Sonkusare and coworkers on TRPV4-induced endothelial Ca(2+) events (sparklets). A previously developed continuum model of an endothelial and a smooth muscle cell coupled through microprojections was extended to account for the activity of a TRPV4 channel cluster. Different stochastic descriptions for the TRPV4 channel flux were examined using finite-state Markov chains. The model also took into consideration recent evidence for the colocalization of intermediate-conductance calcium-activated potassium channels (IKCa) and TRPV4 channels near the microprojections. A single TRPV4 channel opening resulted in a stochastic localized Ca(2+) increase in a small region (i.e., few μm(2) area) close to the channel. We predict micromolar Ca(2+) increases lasting for the open duration of the channel sufficient for the activation of low-affinity endothelial KCa channels. Simulations of a cluster of four TRPV4 channels incorporating burst and cooperative gating kinetics provided quantal Ca(2+) increases (i.e., steps of fixed amplitude), similar to the experimentally observed Ca(2+) sparklets. These localized Ca(2+) events result in endothelium-derived hyperpolarization (and SMC relaxation), with magnitude that depends on event frequency. The gating characteristics (bursting, cooperativity) of the TRPV4 cluster enhance Ca(2+) spread and the distance of KCa channel activation. This may amplify the EDH response by the additional recruitment of distant KCa channels.

Membrane potential and Ca2+ concentration dependence on pressure and vasoactive agents in arterial smooth muscle: A model

A mathematical model incorporating junctional and stretch-activated microdomains and 37 protein components describes the myogenic response in arterial smooth muscle cells.

Arterial smooth muscle (SM) cells respond autonomously to changes in intravascular pressure, adjusting tension to maintain vessel diameter. The values of membrane potential (V_m) and sarcoplasmic Ca²⁺ concentration (Ca_in) within minutes of a change in pressure are the results of two opposing pathways, both of which use Ca²⁺ as a signal. This works because the two Ca²⁺-signaling pathways are confined to distinct microdomains in which the Ca²⁺ concentrations needed to activate key channels are transiently higher than Ca_in. A mathematical model of an isolated arterial SM cell is presented that incorporates the two types of microdomains. The first type consists of junctions between cisternae of the peripheral sarcoplasmic reticulum (SR), containing ryanodine receptors (RyRs), and the sarcolemma, containing voltage- and Ca²⁺-activated K⁺ (BK) channels. These junctional microdomains promote hyperpolarization, reduced Ca_in, and relaxation. The second type is postulated to form around stretch-activated nonspecific cation channels and neighboring Ca²⁺-activated Cl⁻ channels, and promotes the opposite (depolarization, increased Ca_in, and contraction). The model includes three additional compartments: the sarcoplasm, the central SR lumen, and the peripheral SR lumen. It incorporates 37 protein components. In addition to pressure, the model accommodates inputs of α- and β-adrenergic agonists, ATP, 11,12-epoxyeicosatrienoic acid, and nitric oxide (NO). The parameters of the equations were adjusted to obtain a close fit to reported V_m and Ca_in as functions of pressure, which have been determined in cerebral arteries. The simulations were insensitive to ±10% changes in most of the parameters. The model also simulated the effects of inhibiting RyR, BK, or voltage-activated Ca²⁺ channels on V_m and Ca_in. Deletion of BK β1 subunits is known to increase arterial–SM tension. In the model, deletion of β1 raised Ca_in at all pressures, and these increases were reversed by NO.

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.

Mechanobiological oscillators control lymph flow

The ability of cells to sense and respond to physical forces has been recognized for decades, but researchers are only beginning to appreciate the fundamental importance of mechanical signals in biology. At the larger scale, there has been increased interest in the collective organization of cells and their ability to produce complex, "emergent" behaviors. Often, these complex behaviors result in tissue-level control mechanisms that manifest as biological oscillators, such as observed in fireflies, heartbeats, and circadian rhythms. In many cases, these complex, collective behaviors are controlled--at least in part--by physical forces imposed on the tissue or created by the cells. Here, we use mathematical simulations to show that two complementary mechanobiological oscillators are sufficient to control fluid transport in the lymphatic system: Ca(2+)-mediated contractions can be triggered by vessel stretch, whereas nitric oxide produced in response to the resulting fluid shear stress causes the lymphatic vessel to relax locally. Our model predicts that the Ca(2+) and NO levels alternate spatiotemporally, establishing complementary feedback loops, and that the resulting phasic contractions drive lymph flow. We show that this mechanism is self-regulating and robust over a range of fluid pressure environments, allowing the lymphatic vessels to provide pumping when needed but remain open when flow can be driven by tissue pressure or gravity. Our simulations accurately reproduce the responses to pressure challenges and signaling pathway manipulations observed experimentally, providing an integrated conceptual framework for lymphatic function.

Gap junctions suppress electrical but not [Ca(2+)] heterogeneity in resistance arteries

Despite stochastic variation in the molecular composition and morphology of individual smooth muscle and endothelial cells, the membrane potential along intact microvessels is remarkably uniform. This is crucial for coordinated vasomotor responses. To investigate how this electrical homogeneity arises, a virtual arteriole was developed that introduces variation in the activities of ion-transport proteins between cells. By varying the level of heterogeneity and subpopulations of gap junctions (GJs), the resulting simulations shows that GJs suppress electrical variation but can only reduce cytosolic [Ca(2+)] variation. The process of electrical smoothing, however, introduces an energetic cost due to permanent currents, one which is proportional to the level of heterogeneity. This cost is particularly large when electrochemically different endothelial-cell and smooth-muscle-cell layers are coupled. Collectively, we show that homocellular GJs in a passively open state are crucial for electrical uniformity within the given cell layer, but homogenization may be limited by biophysical or energetic constraints. Owing to the ubiquitous presence of ion transport-proteins and cell-cell heterogeneity in biological tissues, these findings generalize across most biological fields.

Linking the population pharmacokinetics of tenofovir and its metabolites with its cellular uptake and metabolism

Empirical pharmacokinetic models are used to explain the pharmacokinetics of the antiviral drug tenofovir (TFV) and its metabolite TFV diphosphate (TFV-DP) in peripheral blood mononuclear cells. These empirical models lack the ability to explain differences between the disposition of TFV-DP in HIV-infected patients vs. healthy individuals. Such differences may lie in the mechanisms of TFV transport and phosphorylation. Therefore, we developed an exploratory model based on mechanistic mass transport principles and enzyme kinetics to examine the uptake and phosphorylation kinetics of TFV. TFV-DP median C_max from the model was 38.5 fmol/10⁶ cells, which is bracketed by two reported healthy volunteer studies (38 and 51 fmol/10⁶ cells). The model presented provides a foundation for exploration of TFV uptake and phosphorylation kinetics for various routes of TFV administration and can be updated as more is known on actual mechanisms of cellular transport of TFV.

Neurovascular coupling and the influence of luminal agonists via the endothelium

A numerical model of neurovascular coupling (NVC) is presented based on neuronal activity coupled to vasodilation/contraction models via the astrocytic mediated perivascular K(+) and the smooth muscle cell Ca(2+) pathway. Luminal agonists acting on P2Y receptors on the endothelial cell surface provide a flux of IP3 into the endothelial cytosol. This concentration of IP3 is transported via gap junctions between endothelial and smooth muscle cells providing a source of sacroplasmic derived Ca(2+) in the smooth muscle cell. The model is able to relate a neuronal input signal to the corresponding vessel reaction. Results indicate that blood flow mediated IP3 production via the agonist ATP has a substantial effect on the contraction/dilation dynamics of the SMC. The resulting variation in cytosolic Ca(2+) can enhance and inhibit the flow of blood to the cortical tissue. IP3 coupling between endothelial and smooth muscle cells seems to be important in the dynamics of the smooth muscle cell. The VOCC channels are, due to the hyperpolarisation from K(+) SMC efflux, almost entirely closed and do not seem to play a significant role during neuronal activity. The current model shows that astrocytic Ca(2+) is not necessary for neurovascular coupling to occur in contrast to a number of experiments outlining the importance of astrocytic Ca(2+) in NVC, however this Ca(2+) pathway is not the only one mediating NVC. Importantly agonists in flowing blood have a significant influence on the endothelial and smooth muscle cell dynamics.

Agmatine induced NO dependent rat mesenteric artery relaxation and its impairment in salt-sensitive hypertension

l-Arginine and its decarboxylated product, agmatine are important mediators of NO production and vascular relaxation. However, the underlying mechanisms of their action are not understood. We have investigated the role of arginine and agmatine in resistance vessel relaxation of Sprague-Dawley (SD) and Dahl salt-sensitive hypertensive rats. Second or 3rd-order mesenteric arterioles were cannulated in an organ chamber, pressurized and equilibrated before perfusing intraluminally with agonists. The vessel diameters were measured after mounting on the stage of a microscope fitted with a video camera. The gene expression in Dahl rat vessel homogenates was ascertained by real-time PCR. l-Arginine initiated relaxations (EC50, 5.8±0.7mM; n=9) were inhibited by arginine decarboxylase (ADC) inhibitor, difluoromethylarginine (DFMA) (EC50, 18.3±1.3mM; n=5) suggesting that arginine-induced vessel relaxation was mediated by agmatine formation. Agmatine relaxed the SD rat vessels at significantly lower concentrations (EC50, 138.7±12.1μM; n=22), which was compromised by l-NAME (l-N(G)-nitroarginine methyl ester, an eNOS inhibitor), RX821002 (α-2 AR antagonist) and pertussis toxin (G-protein inhibitor). The agmatine-mediated vessel relaxation from high salt Dahl rats was abolished as compared to that from normal salt rats (EC50, 143.9±23.4μM; n=5). The α-2A AR, α-2B AR and eNOS mRNA expression was downregulated in mesenteric arterioles of high-salt treated Dahl hypertensive rats. These findings demonstrate that agmatine facilitated the relaxation via activation of α-2 adrenergic G-protein coupled receptor and NO synthesis, and this pathway is compromised in salt-sensitive hypertension.

Role of microprojections in myoendothelial feedback--a theoretical study

We investigated the role of myoendothelial projections (MPs) in endothelial cell (EC) feedback response to smooth muscle cell (SMC) stimulation using mathematical modelling. A previously developed compartmental EC-SMC model is modified to include MPs as subcellular compartments in the EC. The model is further extended into a 2D continuum model using a finite element method (FEM) approach and electron microscopy images to account for MP geometry. The EC and SMC are coupled via non-selective myoendothelial gap junctions (MEGJs) which are located on MPs and allow exchange of Ca(2+), K(+), Na(+) and Cl(-) ions and inositol 1,4,5-triphosphate (IP3). Models take into consideration recent evidence for co-localization of intermediate-conductance calcium-activated potassium channels (IKCa) and IP3 receptors (IP3Rs) in the MPs. SMC stimulation causes an IP3-mediated Ca(2+) transient in the MPs with limited global spread in the bulk EC. A hyperpolarizing feedback generated by the localized IKCa channels is transmitted to the SMC via MEGJs. MEGJ resistance (Rgj) and the density of IKCa and IP3R in the projection influence the extent of EC response to SMC stimulation. The predicted Ca(2+) transients depend also on the volume and geometry of the MP. We conclude that in the myoendothelial feedback response to SMC stimulation, MPs are required to amplify the SMC initiated signal. Simulations suggest that the signal is mediated by IP3 rather than Ca(2+) diffusion and that a localized rather than a global EC Ca(2+) mobilization is more likely following SMC stimulation.

Estimation of shear-stress-induced endothelial nitric oxide production from flow-mediated dilation

Vascular endothelial function assessment yields important diagnostic and prognostic information on patients with (or at risk of) cardiovascular diseases. Flow-mediated dilation (FMD) is the most widely used noninvasive method for assessing the endothelial function. In this method, the magnitude of FMD is used as a surrogate marker for the endothelial function. However, because vasodilation is affected by several other factors as well, the details of how this marker represents the endothelial function are not fully understood. Previously, we developed a mathematical model for vasodilation with intra- and intercellular pathways. In this study, we estimated the shear-stress-induced endothelial nitric oxide production from FMD measurements using the model. The results suggested that the accuracy of the estimated endothelial function obeys the characteristics of the shear stress added to the vascular wall. Furthermore, we showed that the FMD response describes not only the endothelial function but also vascular wall characteristics.

Systems biology of HBOC-induced vasoconstriction

Vasoconstriction is a major adverse effect of HBOCs. The use of a single drug for attenuating HBOC-induced vasoconstriction has been tried with limited success. Since HBOC causes disruptions at multiple levels of organization in the vascular system, a systems approach is helpful to explore avenues to counteract the effects of HBOC at multiple levels by targeting multiple sites in the system. A multi-target approach is especially appropriate for HBOC-induced vasoconstriction, because HBOC disrupts the cascade of amplification by NO-cGMP signaling and protein phosphorylation, ultimately resulting in vasoconstriction. Targeting multiple steps in the cascade may alter the overall gain of amplification, thereby limiting the propagation of disruptive effects through the cascade. As a result, targeting multiple sites may accomplish a relatively high overall efficacy at submaximal drug doses. Identifying targets and doses for developing a multi-target combination HBOC regimen for oxygen therapeutics requires a detailed understanding of the systems biology and phenotypic heterogeneity of the vascular system at multiple layers of organization, which can be accomplished by successive iterations between experimental studies and mathematical modeling at multiple levels of vascular systems and organ systems. Towards this goal, this article addresses the following topics: a) NO-scavenging by HBOC, b) HBOC autoxidation-induced reactive oxygen species generation and endothelial barrier dysfunction, c) NO- cGMP signaling in vascular smooth muscle cells, d) NO and cGMP-dependent regulation of contractile filaments in vascular smooth muscle cells, e) phenotypic heterogeneity of vascular systems, f) systems biology as an approach to developing a multi-target HBOC regimen.

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.

Multiscale modeling and data integration in the virtual physiological rat project

It has become increasingly evident that the descriptions of many complex diseases are only possible by taking into account multiple influences at different physiological scales. To do this with computational models often requires the integration of several models that have overlapping scales (genes to molecules, molecules to cells, cells to tissues). The Virtual Physiological Rat (VPR) Project, a National Institute of General Medical Sciences (NIGMS) funded National Center of Systems Biology, is tasked with mechanistically describing several complex diseases and is therefore identifying methods to facilitate the process of model integration across physiological scales. In addition, the VPR has a considerable experimental component and the resultant data must be integrated into these composite multiscale models and made available to the research community. A perspective of the current state of the art in model integration and sharing along with archiving of experimental data will be presented here in the context of multiscale physiological models. It was found that current ontological, model and data repository resources and integrative software tools are sufficient to create composite models from separate existing models and the example composite model developed here exhibits emergent behavior not predicted by the separate models.

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.

The nanostructure of myoendothelial junctions contributes to signal rectification between endothelial and vascular smooth muscle cells

Micro-anatomical structures in tissues have potential physiological effects. In arteries and arterioles smooth muscle cells and endothelial cells are separated by the internal elastic lamina, but the two cell layers often make contact through micro protrusions called myoendothelial junctions. Cross talk between the two cell layers is important in regulating blood pressure and flow. We have used a spatiotemporal mathematical model to investigate how the myoendothelial junctions affect the information flow between the two cell layers. The geometry of the model mimics the structure of the two cell types and the myoendothelial junction. The model is implemented as a 2D axi-symmetrical model and solved using the finite element method. We have simulated diffusion of Ca²⁺ and IP₃ between the two cell types and we show that the micro-anatomical structure of the myoendothelial junction in itself may rectify a signal between the two cell layers. The rectification is caused by the asymmetrical structure of the myoendothelial junction. Because the head of the myoendothelial junction is separated from the cell it is attached to by a narrow neck region, a signal generated in the neighboring cell can easily drive a concentration change in the head of the myoendothelial protrusion. Subsequently the signal can be amplified in the head, and activate the entire cell. In contrast, a signal in the cell from which the myoendothelial junction originates will be attenuated and delayed in the neck region as it travels into the head of the myoendothelial junction and the neighboring cell.

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.