A quantitative description of the contraction of blood vessels following the release of noradrenaline from sympathetic varicosities

Predictive analytics identifies key factors driving hyperalgesic priming of muscle sensory neurons

Hyperalgesic priming, a form of neuroplasticity induced by inflammatory mediators, in peripheral nociceptors enhances the magnitude and duration of action potential (AP) firing to future inflammatory events and can potentially lead to pain chronification. The mechanisms underlying the development of hyperalgesic priming are not well understood, limiting the identification of novel therapeutic strategies to combat chronic pain. In this study, we used a computational model to identify key proteins whose modifications caused priming of muscle nociceptors and made them hyperexcitable to a subsequent inflammatory event. First, we extended a previously validated model of mouse muscle nociceptor sensitization to incorporate Epac-mediated interaction between two G protein-coupled receptor signaling pathways commonly activated by inflammatory mediators. Next, we calibrated and validated the model simulations of the nociceptor's AP response to both innocuous and noxious levels of mechanical force after two subsequent inflammatory events using literature data. Then, by performing global sensitivity analyses that simulated thousands of nociceptor-priming scenarios, we identified five ion channels and two molecular processes (from the 18 modeled transmembrane proteins and 29 intracellular signaling components) as potential regulators of the increase in AP firing in response to mechanical forces. Finally, when we simulated specific neuroplastic modifications in Kv1.1 and Nav1.7 alone as well as with simultaneous modifications in Nav1.7, Nav1.8, TRPA1, and Kv7.2, we observed a considerable increase in the fold change in the number of triggered APs in primed nociceptors. These results suggest that altering the expression of Kv1.1 and Nav1.7 might regulate the neuronal hyperexcitability in primed mechanosensitive muscle nociceptors.

Biochemical Assessment of Pheochromocytoma and Paraganglioma

Pheochromocytoma and paraganglioma (PPGL) require prompt consideration and efficient diagnosis and treatment to minimize associated morbidity and mortality. Once considered, appropriate biochemical testing is key to diagnosis. Advances in understanding catecholamine metabolism have clarified why measurements of the O-methylated catecholamine metabolites rather than the catecholamines themselves are important for effective diagnosis. These metabolites, normetanephrine and metanephrine, produced respectively from norepinephrine and epinephrine, can be measured in plasma or urine, with choice according to available methods or presentation of patients. For patients with signs and symptoms of catecholamine excess, either test will invariably establish the diagnosis, whereas the plasma test provides higher sensitivity than urinary metanephrines for patients screened due to an incidentaloma or genetic predisposition, particularly for small tumors or in patients with an asymptomatic presentation. Additional measurements of plasma methoxytyramine can be important for some tumors, such as paragangliomas, and for surveillance of patients at risk of metastatic disease. Avoidance of false-positive test results is best achieved by plasma measurements with appropriate reference intervals and preanalytical precautions, including sampling blood in the fully supine position. Follow-up of positive results, including optimization of preanalytics for repeat tests or whether to proceed directly to anatomic imaging or confirmatory clonidine tests, depends on the test results, which can also suggest likely size, adrenal vs extra-adrenal location, underlying biology, or even metastatic involvement of a suspected tumor. Modern biochemical testing now makes diagnosis of PPGL relatively simple. Integration of artificial intelligence into the process should make it possible to fine-tune these advances.

Identification of key factors driving inflammation-induced sensitization of muscle sensory neurons

Sensory neurons embedded in muscle tissue that initiate pain sensations, i.e., nociceptors, are temporarily sensitized by inflammatory mediators during musculoskeletal trauma. These neurons transduce peripheral noxious stimuli into an electrical signal [i.e., an action potential (AP)] and, when sensitized, demonstrate lower activation thresholds and a heightened AP response. We still do not understand the relative contributions of the various transmembrane proteins and intracellular signaling processes that drive the inflammation-induced hyperexcitability of nociceptors. In this study, we used computational analysis to identify key proteins that could regulate the inflammation-induced increase in the magnitude of AP firing in mechanosensitive muscle nociceptors. First, we extended a previously validated model of a mechanosensitive mouse muscle nociceptor to incorporate two inflammation-activated G protein-coupled receptor (GPCR) signaling pathways and validated the model simulations of inflammation-induced nociceptor sensitization using literature data. Then, by performing global sensitivity analyses that simulated thousands of inflammation-induced nociceptor sensitization scenarios, we identified three ion channels and four molecular processes (from the 17 modeled transmembrane proteins and 28 intracellular signaling components) as potential regulators of the inflammation-induced increase in AP firing in response to mechanical forces. Moreover, we found that simulating single knockouts of transient receptor potential ankyrin 1 (TRPA1) and reducing the rates of G_αq-coupled receptor phosphorylation and G_αq subunit activation considerably altered the excitability of nociceptors (i.e., each modification increased or decreased the inflammation-induced fold change in the number of triggered APs compared to when all channels were present). These results suggest that altering the expression of TRPA1 or the concentration of intracellular G_αq might regulate the inflammation-induced increase in AP response of mechanosensitive muscle nociceptors.

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.

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.

Respiratory modulated sympathetic activity: a putative mechanism for developing vascular resistance?

KEY POINTS

Sympathetic activity exhibits respiratory modulation that is amplified in hypertensive rats. Respiratory modulated sympathetic activity produces greater changes in vascular resistance than tonic stimulation of the same stimulus magnitude in normotensive but not hypertensive rats. Mathematical modelling demonstrates that respiratory modulated sympathetic activity may fail to produce greater vascular resistance changes in hypertensive rats because the system is saturated as a consequence of a dysfunctional noradrenaline reuptake mechanism. Respiratory modulated sympathetic activity is an efficient mechanism to raise vascular resistance promptly, corroborating its involvement in the ontogenesis of hypertension.

ABSTRACT

Sympathetic nerve activity (SNA) exhibits respiratory modulation. This component of SNA is important - being recruited under cardiorespiratory reflex conditions and elevated in the spontaneously hypertensive (SH) rat - and yet the exact influence of this modulation on vascular tone is not understood, even in normotensive conditions. We constructed a mathematical model of the sympathetic innervation of an arteriole, and used it to test the hypothesis that respiratory modulation of SNA preferentially increases vasoconstriction compared to a frequency-matched tonic pattern. Simulations supported the hypothesis, where respiratory modulated increases in vasoconstriction were mediated by a noradrenergic mechanism. These predictions were tested in vivo in adult Wistar rats. Stimulation of the sympathetic chain (L3) with respiratory modulated bursting patterns, revealed that bursting increases vascular resistance (VR) more than tonic stimulation (57.8 ± 3.3% vs. 44.8 ± 4.2%; P < 0.001; n = 8). The onset of the VR response was also quicker for bursting stimulation (rise time constant = 1.98 ± 0.09 s vs. 2.35 ± 0.20 s; P < 0.01). In adult SH rats (n = 8), the VR response to bursting (44.6 ± 3.9%) was not different to tonic (37.4 ± 3.5%; P = 0.57). Using both mathematical modelling and in vivo techniques, we have shown that VR depends critically on respiratory modulation and revealed that this pattern dependency in Wistar rats is due to a noradrenergic mechanism. This respiratory component may therefore contribute to the ontogenesis of hypertension in the pre-hypertensive SH rat - raising VR and driving vascular remodelling. Why adult SH rats do not exhibit a pattern-dependent response is not known, but further modelling revealed that this may be due to dysfunctional noradrenaline reuptake.

Modelling the vascular response to sympathetic postganglionic nerve activity

This paper explores the influence of burst properties of the sympathetic nervous system on arterial contractility. Specifically, a mathematical model is constructed of the pathway from action potential generation in a sympathetic postganglionic neurone to contraction of an arterial smooth muscle cell. The differential equation model is a synthesis of models of the individual physiological processes, and is shown to be consistent with physiological data.

The model is found to be unresponsive to tonic (regular) stimulation at typical frequencies recorded in sympathetic efferents. However, when stimulated at the same average frequency, but with repetitive respiratory-modulated burst patterns, it produces marked contractions. Moreover, the contractile force produced is found to be highly dependent on the number of spikes in each burst. In particular, when the model is driven by preganglionic spike trains recorded from wild-type and spontaneously hypertensive rats (which have increased spiking during each burst) the contractile force was found to be 10-fold greater in the hypertensive case. An explanation is provided in terms of the summative increased release of noradrenaline. Furthermore, the results suggest the marked effect that hypertensive spike trains had on smooth muscle cell tone can provide a significant contribution to the pathology of hypertension.

•

We model the sympathetic-driven contraction of a vascular smooth muscle cell.

•

The cell is unresponsive to tonic stimulation at typical sympathetic frequencies.

•

We quantify the force produced by the cell in response to sympathetic bursting.

•

The response of the cell is strongly dependent on burst amplitude and duration.

•

Recordings from hypertensive animals produce significant contractile forces.

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.

Neurogenic responses in rat and porcine large pulmonary arteries

Pharmacological differences between neurogenic sympathetic responses in rat and pig isolated pulmonary arteries were examined in strip preparations. Electrical field stimulation in the range of 0.6 to 40 Hz resulted in frequency-dependent contractions in terms of amplitude and rate of rise. Responses in the rat declined sharply from pulmonary trunk to main artery; in contrast, in the pig they continued into the third-order vessels. Contractions were inhibited in the presence of tetrodotoxin, prazosin or WB-4101 and hence neurogenic in origin. Cocaine enhanced field stimulated contractions in both rat and porcine tissues; however, the effect in the former was of significantly greater magnitude in terms of either area under the mechanogram or height of contraction. In addition, the rate of rise, time to peak and duration of peak were all increased in the rat but less so or not in the pig. Field stimulated contractions were virtually abolished by guanethidine (1×10(-6) M) in rat but not in porcine pulmonary arteries in which a ten-fold higher concentration significantly reduced neurogenic contractions and abolished them in 2 out of 4 tissues tested. The effect of guanethidine (1×10(-6) M) observed in blood vessels of rat exceeded about five-fold that observed in porcine tissues. Thus, neurogenic responses appear to be entirely mediated by extra-junctional α(1)-adrenoceptors in both species, and in contrast to the rat, pig tissues seem to have a noradrenaline re-uptake that is either less efficient or operating near saturation.

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.

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.

Smooth muscle contraction: Mechanochemical formulation for homogeneous finite strains

Chemical kinetics of smooth muscle contraction affect mechanical properties of organs that function under finite strains. In an effort to gain further insight into organ physiology, we formulate a mechanochemical finite strain model by considering the interaction between mechanical and biochemical components of cell function during activation. We propose a new constitutive framework and use a mechanochemical device that consists of two parallel elements: (i) spring for the cell stiffness; (ii) contractile element for the sarcomere. We use a multiplicative decomposition of cell elongation into filament contraction and cross-bridge deformation, and suggest that the free energy be a function of stretches, four variables (free unphosphorylated myosin, phosphorylated cross-bridges, phosphorylated and dephosphorylated cross-bridges attached to actin), chemical state variable driven by Ca2+-concentration, and temperature. The derived constitutive laws are thermodynamically consistent. Assuming isothermal conditions, we specialize the mechanical phase such that we recover the linear model of Yang et al. [2003a. The myogenic response in isolated rat cerebrovascular arteries: smooth muscle cell. Med. Eng. Phys. 25, 691-709]. The chemical phase is also specialized so that the linearized chemical evolution law leads to the four-state model of Hai and Murphy [1988. Cross-bridge phosphorylation and regulation of latch state in smooth muscle. Am. J. Physiol. 254, C99-C106]. One numerical example shows typical mechanochemical effects and the efficiency of the proposed approach. We discuss related parameter identification, and illustrate the dependence of muscle contraction (Ca2+-concentration) on active stress and related stretch. Mechanochemical models of this kind serve the mathematical basis for analyzing coupled processes such as the dependency of tissue properties on the chemical kinetics of smooth muscle.

Origins of blood volume change due to glutamatergic synaptic activity at astrocytes abutting on arteriolar smooth muscle cells

The cellular mechanisms that couple activity of glutamatergic synapses with changes in blood flow, measured by a variety of techniques including the BOLD signal, have not previously been modelled. Here we provide such a model, that successfully accounts for the main observed changes in blood flow in both visual cortex and somatosensory cortex following their stimulation by high-contrast drifting grating or by single whisker stimulation, respectively. Coupling from glutamatergic synapses to smooth muscle cells of arterioles is effected by astrocytes releasing epoxyeicosatrienoic acids (EETs) onto them, following glutamate stimulation of the astrocyte. Coupling of EETs to the smooth muscle of arterioles is by means of potassium channels in their membranes, leading to hyperpolarization, relaxation and hence an increase in blood flow. This model predicts a linear increase in blood flow with increasing numbers of activated astrocytes, but a non-linear increase with increasing glutamate release.