Modeling of Hysteresis in Gene Regulatory Networks

Hysteresis, observed in many gene regulatory networks, has a pivotal impact on biological systems, which enhances the robustness of cell functions. In this paper, a general model is proposed to describe the hysteretic gene regulatory network by combining the hysteresis component and the transient dynamics. The Bouc-Wen hysteresis model is modified to describe the hysteresis component in the mammalian gene regulatory networks. Rigorous mathematical analysis on the dynamical properties of the model is presented to ensure the bounded-input-bounded-output (BIBO) stability and demonstrates that the original Bouc-Wen model can only generate a clockwise hysteresis loop while the modified model can describe both clockwise and counter clockwise hysteresis loops. Simulation studies have shown that the hysteresis loops from our model are consistent with the experimental observations in three mammalian gene regulatory networks and two E.coli gene regulatory networks, which demonstrate the ability and accuracy of the mathematical model to emulate natural gene expression behavior with hysteresis. A comparison study has also been conducted to show that this model fits the experiment data significantly better than previous ones in the literature. The successful modeling of the hysteresis in all the five hysteretic gene regulatory networks suggests that the new model has the potential to be a unified framework for modeling hysteresis in gene regulatory networks and provide better understanding of the general mechanism that drives the hysteretic function.     

Axonemal dynein expression in human fetal tracheal epithelium

Ciliogenesis in human fetal airway epithelium occurs from 11 to 24 gestational weeks. Using genetic and antigenic markers specific for human axonemal dynein heavy chain 9, we characterized temporal aspects of axonemal dynein expression associated with large airway epithelial ciliogenesis during human fetal development. Late in the first trimester, an undifferentiated columnar epithelium is characteristic of the large airways, and immunocytochemical studies exhibited focal localization of axonemal dynein antigen on luminal epithelial cell borders at sites consistent with emergent ciliary beds. From 12 to 22 wk, immunocytochemical labeling of new ciliary beds was prominent, and localization within the cytoplasm of epithelial cells suggested avid synthesis of axonemal dynein in advance of ciliogenic events. Quantitative RT-PCR of tracheal RNA and in situ hybridization studies compared favorably with immunocytochemical findings with the earliest expression of axonemal dynein at 9-10 wk gestation. These studies have documented that axonemal dynein is expressed early in human fetal life during airway epithelial maturation and well before histological or ultrastructural evidence of ciliogenesis is apparent.     

Relaxin stimulates bronchial epithelial cell PKA activation,migration, and ciliary beating

Relaxin is an insulin-like serum protein secreted during pregnancy and found in many tissues, including the lung. Relaxin is reported to stimulate epithelial cell proliferation, but the effects of relaxin on airway epithelium are unknown. We tested the hypothesis that relaxin would stimulate the increased migration of bronchial epithelial cells (BEC) in response to wounding. Using monolayers of BEC in a wound-healing model, relaxin augmented wound closure with maximal closure occurring at 12 hr (1 micro M). Unlike cytokines, relaxin did not stimulate increased BEC interleukin-8 (IL-8) release. Relaxin caused a significant stimulation of ciliary beat frequency (CBF) in BEC. Because protein kinase (PKA) activation increases CBF and relaxin can elevate intracellular cAMP levels, we measured PKA activity in BEC treated with relaxin. Relaxin increased PKA activity 3-4 fold by approximately 4 hr, with a return to baseline levels by 8-10 hr. Relaxin-stimulated PKA activity differs temporally from the rapid (1 hr) beta-adrenergic activation of PKA in BEC. These data suggest that relaxin augments epithelial repair by increasing airway cell migration and CBF via PKA-dependent mechanisms.     

Intracellular calcium oscillations regulate ciliary beat frequency of airway epithelial cells

The effect of ATP-induced Ca2+ oscillations on ciliary activity was examined in airway epithelial cells by simultaneously measuring the ciliary beat frequency (CBF) and the intracellular Ca2+ concentration ([Ca2+]i) near the base of the cilia. Exposure to extracellular ATP (ATPo) induces a rapid and large increase in both [Ca2+]i and CBF, followed by oscillations in [Ca2+]i and a sustained elevation in CBF. After each Ca2+ oscillation, the [Ca2+]i returned to near basal values. By contrast, the CBF remained elevated during these Ca2+ oscillations, although each Ca2+ oscillation induced small variations in CBF. During Ca2+ oscillations, increases in CBF closely followed the rising phase of increases in [Ca2+]i, but declines in CBF lagged behind declines in [Ca2+]i. Higher frequency Ca2+ oscillations reduced variations in CBF, producing a stable and sustained elevation in CBF. The maximal CBF was induced by Ca2+ oscillations and was 15% greater than the CBF induced by the substantially larger initial [Ca2+]i increase. These data demonstrate that the rate of CBF is not directly dependent on the absolute [Ca2+]i, but is dependent on the differential changes in [Ca2+]i and suggest that CBF in airway epithelial cells is regulated by frequency-modulated Ca2+ signaling.     

Decreased Soluble Adenylyl Cyclase Activity in Cystic Fibrosis Is Related to Defective Apical Bicarbonate Exchange and Affects Ciliary Beat Frequency Regulation

Human airway cilia contain soluble adenylyl cyclase (sAC) that produces cAMP upon HCO₃⁻/CO₂ stimulation to increase ciliary beat frequency (CBF). Because apical HCO₃⁻ exchange depends on cystic fibrosis transmembrane conductance regulator (CFTR), malfunctioning CFTR might impair sAC-mediated CBF regulation in cells from patients with cystic fibrosis (CF). By Western blot, sAC isoforms are equally expressed in normal and CF airway epithelial cells, but CBF decreased more in CF than normal cells upon increased apical HCO₃⁻/CO₂ exposure in part because of greater intracellular acidification from unbalanced CO₂ influx (estimated by 2′,7′-bis(2-carboxyethyl)-5(6)-carboxyfluorescein (BCECF) fluorescence). Importantly, ciliated cell-specific cAMP production (estimated by FRET fluorescence ratio changes of tagged cAMP-dependent protein kinase (PKA) subunits expressed under a ciliated cell-specific promoter) in response to increased apical HCO₃⁻/CO₂ perfusion was higher in normal compared with CF cells. Inhibition of bicarbonate influx via CFTR (CFTR_inh172) and inhibition of sAC (KH7) and PKA activation (H89) led to larger CBF declines in normal cells, now comparable with changes seen in CF cells. These inhibitors also reduced FRET changes in normal cells to the level of CF cells with the expected exception of H89, which does not prevent dissociation of the fluorescently tagged PKA subunits. Basolateral permeabilization and subsequent perfusion with HCO₃⁻/CO₂ rescued CBF and FRET changes in CF cells to the level of normal cells. These results suggest that CBF regulation by sAC-produced cAMP could be impaired in CF, thereby possibly contributing to mucociliary dysfunction in this disease, at least during disease exacerbations when airway acidification is common.     

Connexins Induce and Maintain Tight Junctions in Epithelial Cells

Connexins (Cx) are considered to play a crucial role in the differentiation of epithelial cells and to be associated with adherens and tight junctions. This review describes how connexins contribute to the induction and maintenance of tight junctions in epithelial cells, hepatic cells and airway epithelial cells. Endogenous Cx32 expression and mediated intercellular communication are associated with the expression of tight junction proteins of primary cultured rat hepatocytes. We introduced the human Cx32 gene into immortalized mouse hepatic cells derived from Cx32-deficient mice. Exogenous Cx32 expression and the mediated intercellular communication by transfection could induce the expression and function of tight junctions. Transfection also induced expression of MAGI-1, which localized at adherens and tight junction areas in a gap junctional intercellular communication (GJIC)–independent manner. Furthermore, expression of Cx32 was related to the formation of single epithelial cell polarity of the hepatic cells. On the other hand, Cx26 expression, but not mediated intercellular communication, contributed to the expression and function of tight junctions in human airway epithelial cells. We introduced the human Cx26 gene into the human airway epithelial cell line Calu-3 and used a model of tight junction disruption by the Na⁺/K⁺-ATPase inhibitor ouabain. Transfection with Cx26 prevented disruption of both tight junction functions, the fence and barrier, and the changes of tight junction proteins by treatment with ouabain in a GJIC–independent manner. These results suggest that connexins can induce and maintain tight junctions in both GJIC-dependent and –independent manners in epithelial cells.     

The type III toxins of Pseudomonas aeruginosa disrupt epithelial barrier function

The type III secreted toxins of Pseudomonas aeruginosa are important virulence factors associated with clinically important infection. However, their effects on bacterial invasion across mucosal surfaces have not been well characterized. One of the most commonly expressed toxins, ExoS, has two domains that are predicted to affect cytoskeletal integrity, including a GTPase-activating protein (GAP) domain, which targets Rho, a major regulator of actin polymerization; and an ADP-ribosylating domain that affects the ERM proteins, which link the plasma membrane to the actin cytoskeleton. The activities of these toxins, and ExoS specifically, on the permeability properties of polarized airway epithelial cells with intact tight junctions were examined. Strains expressing type III toxins altered the distribution of the tight junction proteins ZO-1 and occludin and were able to transmigrate across polarized airway epithelial monolayers, in contrast to DeltaSTY mutants. These effects on epithelial permeability were associated with the ADP-ribosylating domain of ExoS, as bacteria expressing plasmids lacking expression of the ExoS GAP activity nonetheless increased the permeation of fluorescent dextrans, as well as bacteria, across polarized airway epithelial cells. Treatment of epithelial cells with cytochalasin D depolymerized actin filaments and increased permeation across the monolayers but did not eliminate the differential effects of wild-type and toxin-negative mutants on the epithelial cells, suggesting that additional epithelial targets are involved. Confocal imaging studies demonstrated that ZO-1, occludin, and ezrin undergo substantial redistribution in human airway cells intoxicated by ExoS, -T, and -Y. These studies support the hypothesis that type III toxins enhance P. aeruginosa's invasive capabilities by interacting with multiple eukaryotic cytoskeletal components.     

Modeling the oscillation dynamics of activated airway smooth muscle strips

When strips of activated airway smooth muscle are stretched cyclically, they exhibit force-length loops that vary substantially in both position and shape with the amplitude and frequency of the stretch. This behavior has recently been ascribed to a dynamic interaction between the imposed stretch and the number of actin-myosin interactions in the muscle. However, it is well known that the passive rheological properties of smooth muscle have a major influence on its mechanical properties. We therefore hypothesized that these rheological properties play a significant role in the force-length dynamics of activated smooth muscle. To test the plausibility of this hypothesis, we developed a model of the smooth muscle strip consisting of a force generator in series with an elastic component. Realistic steady-state force-length loops are predicted by the model when the force generator obeys a hyperbolic force-velocity relationship, the series elastic component is highly nonlinear, and both elastic stiffness and force generation are adjusted so that peak loop force equals isometric force. We conclude that the dynamic behavior of airway smooth muscle can be ascribed in large part to an interaction between connective tissue rheology and the force-velocity behavior of contractile proteins.     

A Computational Model of Dynein Activation Patterns that Can Explain Nodal Cilia Rotation

Normal left-right patterning in vertebrates depends on the rotational movement of nodal cilia. In order to produce this ciliary motion, the activity of axonemal dyneins must be tightly regulated in a temporal and spatial manner; the specific activation pattern of the dynein motors in the nodal cilia has not been reported. Contemporary imaging techniques cannot directly assess dynein activity in a living cilium. In this study, we establish a three-dimensional model to mimic the ciliary ultrastructure and assume that the activation of dynein proteins is related to the interdoublet distance. By employing finite-element analysis and grid deformation techniques, we simulate the mechanical function of dyneins by pairs of point loads, investigate the time-variant interdoublet distance, and simulate the dynein-triggered ciliary motion. The computational results indicate that, to produce the rotational movement of nodal cilia, the dynein activity is transferred clockwise (looking from the tip) between the nine doublet microtubules, and along each microtubule, the dynein activation should occur faster at the basal region and slower when it is close to the ciliary tip. Moreover, the time cost by all the dyneins along one microtubule to be activated can be used to deduce the dynein activation pattern; it implies that, as an alternative method, measuring this time can indirectly reveal the dynein activity. The proposed protein-structure model can simulate the ciliary motion triggered by various dynein activation patterns explicitly and may contribute to furthering the studies on axonemal dynein activity.     

The effect of intracellular calcium oscillations on fluid secretion in airway epithelium

Airway epithelium has been shown to elicit fluid secretion after a rise in intracellular calcium. This rise in intracellular calcium has been shown to display complex oscillations in many species after the binding of particular agonists to extracellular receptors.Fluid secreted by the airway epithelium is used to maintain the depth of the periciliary liquid (PCL) above the apical membrane of the epithelial cells lining the bronchial airways. Previous mathematical models have been published which separately consider the electrophysiology involved in regulating periciliary liquid depth, and the transmission of intracellular calcium waves in airway epithelial tissue. In this paper we present a mathematical model that combines these previous models and allows the effect of oscillations in intracellular calcium on fluid secretion by airway epithelial cells to be investigated. We show that an oscillatory calcium response produces different fluid secretion properties to that elicited by a tonic rise in intracellular calcium. These differences are shown to be due to saturation of the Ca²⁺ activated ion channels.     

Temporal Monitoring of Differentiated Human Airway Epithelial Cells Using Microfluidics

The airway epithelium is exposed to a variety of harmful agents during breathing and appropriate cellular responses are essential to maintain tissue homeostasis. Recent evidence has highlighted the contribution of epithelial barrier dysfunction in the development of many chronic respiratory diseases. Despite intense research efforts, the responses of the airway barrier to environmental agents are not fully understood, mainly due to lack of suitable in vitro models that recapitulate the complex in vivo situation accurately. Using an interdisciplinary approach, we describe a novel dynamic 3D in vitro model of the airway epithelium, incorporating fully differentiated primary human airway epithelial cells at the air-liquid interface and a basolateral microfluidic supply of nutrients simulating the interstitial flow observed in vivo. Through combination of the microfluidic culture system with an automated fraction collector the kinetics of cellular responses by the airway epithelium to environmental agents can be analysed at the early phases for the first time and with much higher sensitivity compared to common static in vitro models. Following exposure of primary differentiated epithelial cells to pollen we show that CXCL8/IL–8 release is detectable within the first 2h and peaks at 4–6h under microfluidic conditions, a response which was not observed in conventional static culture conditions. Such a microfluidic culture model is likely to have utility for high resolution temporal profiling of toxicological and pharmacological responses of the airway epithelial barrier, as well as for studies of disease mechanisms.     

Integrin-β4 regulates the dynamic changes of phenotypic characteristics in association with epithelial-mesenchymal transition (EMT) and RhoA activity in airway epithelial cells during injury and repair

Background: In airway disease such as asthma a hyperactive cellular event of epithelial-mesenchymal transition (EMT) is considered as the mechanism of pathological airway tissue remodeling after injury to the airway epithelium. And the initiation of EMT in the airways depends on the epithelial disruption involving dissolution and/or destabilization of the adhesive structures between the cells and ECM. Previously, we have shown that integrin-β4, an epithelial adhesion molecule in bronchial epithelium is an important regulator of cell proliferation and wound repair in human airway epithelial cells. Therefore, in this study we aimed to investigate whether integrin-β4 also regulates EMT phenotypes during injury and repair in airway epithelial cells of both wild type/integrin-β4^-/- mice in vivo and cultured cells treated with integrin-β4/nonsense siRNA in vitro.Methods: We induced injury to the airway epithelial cells by either repeated exposure to ozone and mechanical scratch wound, and subsequently examined the EMT-related phenotypic features in the airway epithelial cells including biomarkers expression, adhesion and cytoskeleton reorganization and cell stiffness.Results: The results show that in response to injury (ozone exposure/scratch wound) and subsequent spontaneous repair (ozone withdrawal/wound healing) both in vivo and in vitro, the airway epithelial cells underwent dynamic changes in the epithelial and mesenchymal biomarkers expression, adhesion and cytoskeleton structures as well as cell stiffness, all together exhibiting enhanced EMT phenotypic features after injury and reversal of the injury-induced effects during repair. Importantly, these injury/repair-associated EMT phenotypic changes in airway epithelial cells appeared to be dependent on integrin-β4 expression. More specifically, when integrin-β4 was deficient in mice (integrin-β4^-/-) the repair of ozone-injured airway epithelium was impaired and the recovery of ozone-enhanced EMT biomarkers expression in the airway epithelium was delayed. Similarly, in the scratch wounded airway epithelial cells with integrin-β4 knockdown, the cells were impaired in all aspects related to EMT during wound and repair including cell proliferation, wound closure rate, adhesion and cytoskeleton protein expression (vinculin and vimentin), mesenchymal-like F-actin reorganization, cell stiffness and RhoA activation.Conclusion: Taken together, these results suggested that integrin-β4 may be essential in regulating the effects of injury and repair on EMT in airway epithelial cells via influencing both the cell adhesion to ECM and cells'' physical phenotypes through RhoA signaling pathway.     

Toxic effects of sulfur mustard on respiratory epithelial cells in culture

Sulfur mustard (SM) is known to induce cutaneous injury and to cause acute damage to the respiratory tract. Although skin vesication has been demonstrated on human epidermal keratinocytes in culture, no study has been carried out to analyze the effects of SM on the ultrastructural and functional activity of surface respiratory epithelial cells. To evaluate this SM toxicity, we developed an in vitro model of respiratory epithelial cells in primary culture. The study was performed on surface epithelial cells from rabbit trachea cultured according to the explant-outgrowth technique. The functional activity of the cultures was evaluated by measuring the ciliary beating frequency (CBF) of the ciliated cells with a videomicroscopic method. The morphological aspects of the cells were analyzed by light and electron microscopy. Addition of 0.1 mM SM directly into the culture medium produced a sudden and irreversible CBF inhibition, first observed after 2 hr on the ciliated cells of the outgrowth periphery. The arrest of the ciliary beating progressively reached the whole surface of the outgrowth and was simultaneously observed with a detachment of the outgrowth cells. It began at the outgrowth border, leading to the exfoliation of cell sheets, and then to the whole culture after 48 hr. Morphological damage was expressed by intense vacuolisation and disorganization of cytoplasmic and nuclear structures. These findings suggest that the detachment of the respiratory epithelial cells from the matrix represents a major toxic effect of 0.1 mM SM. SM dramatically affects the viability of respiratory epithelial cells in culture. Moreover, the sudden CBF inhibition is more likely due to the death of the ciliated cells than to a specific ciliotoxic effect of SM.Abbreviations CBF ciliary beating frequency - HEPES N2-hydroxyethylpiperazine-N'2ethanesulfonic acid - PBS phosphate buffer saline - SM sulfur mustard - TEM transmission electron microscopy     

Effects of local anaesthetics (lidocaine) on the structure and function of ciliated respiratory epithelial cells

Summary— Sampling for nasal or bronchial ciliated cells requires the use of anaesthetic agents, but such drugs may interfere with the morphological or functional results. Lidocaine is the most frequently used local anaesthetic. In order to study the morphological and functional effects of lidocaine hydrochloride, we designed an experimental study on ciliated cells from guinea pig and bovine trachea. On guinea pig tracheal specimens, different lidocaine concentrations (0.05, 0.25 and 1%) were tested. Tracheal rings were immersed in either culture medium alone (control) or in different lidocaine concentrations. Measurements of ciliary beat frequency (CBF) were performed by the stroboscopic method. Tracheal rings were consecutively incubated in culture medium alone and a second set of measurements was performed. Tracheal rings were studied by light microscopy after incubation in either 1% lidocaine or in culture medium alone. On bovine tracheal specimens, a coton wool swab impregnated with different lidocaine concentrations (0, 0.25, 1, 2.5 and 5%) was placed in contact with the tracheal mucosa. Three different kinds of samples were collected: the first one was used to study CBF, the second one (0.1 and 5%) was studied by scanning electron microscope (SEM) and the third (0.1 and 5%) by transmission electron microscopy (TEM). The results on guinea pig specimens show a significant but reversible CBF diminution for concentrations of 0.25 and 1% lidocaine and cellular lesions for the concentration of 1%. On bovine specimens a diminution in CBF for concentrations of 2.5 and 5% lidocaine was shown and the SEM study demonstrated obvious lesions on the epithelial surface treated with the 5% concentration. The TEM study showed morphological alterations on respiratory epithelium (deciliated areas, cytoplasmic vacuoles and mitochondrial swelling) for 5% lidocaine concentration. However the axonemal structure of cilia was normal for control and 5% concentration. We concluded that in vitro lidocaine can inhibit the CBF and that high concentrations of lidocaine can damage the respiratory epithelium but without modifications of the axonemal ultrastructure.     

The degradation of airway tight junction protein under acidic conditions is probably mediated by transient receptor potential vanilloid 1 receptor

Acidic airway microenvironment is one of the representative pathophysiological features of chronic inflammatory respiratory diseases. Epithelial barrier function is maintained by TJs (tight junctions), which act as the first physical barrier against the inhaled substances and pathogens of airway. As previous studies described, acid stress caused impaired epithelial barriers and led the hyperpermeability of epithelium. However, the specific mechanism is still unclear. We have showed previously the existence of TRPV (transient receptor potential vanilloid) 1 channel in airway epithelium, as well as its activation by acidic stress in 16HBE cells. In this study, we explored the acidic stress on airway barrier function and TJ proteins in vitro with 16HBE cell lines. Airway epithelial barrier function was determined by measuring by TER (trans-epithelial electrical resistance). TJ-related protein [claudin-1, claudin-3, claudin-4, claudin-5, claudin-7 and ZO-1 (zonula occluden 1)] expression was examined by western blotting of insoluble fractions of cell extraction. The localization of TJ proteins were visualized by immunofluorescent staining. Interestingly, stimulation by pH 6.0 for 8 h slightly increased the epithelial resistance in 16HBE cells insignificantly. However, higher concentration of hydrochloric acid (lower than pH 5.0) did reduce the airway epithelial TER of 16HBE cells. The decline of epithelial barrier function induced by acidic stress exhibited a TRPV1-[Ca²⁺]_i-dependent pathway. Of the TJ proteins, claudin-3 and claudin-4 seemed to be sensitive to acidic stress. The degradation of claudin-3 and claudin-4 induced by acidic stress could be attenuated by the specific TRPV1 blocker or intracellular Ca²⁺ chelator BAPTA/AM [1,2-bis-(o-aminophenoxy)ethane-N,N,N'',N''-tetra-acetic acid tetrakis(acetoxymethyl ester)].     

Analytical modeling of the hysteresis phenomenon in guinea pig ventricular myocytes

In the present study, we have demonstrated hysteresis phenomena in the excitability of single, enzymatically dissociated guinea pig ventricular myocytes. Membrane potentials were recorded with patch pipettes in the whole-cell current clamp configuration. Repetitive stimulation with depolarizing current pulses of constant cycle length and duration but varying strength led to predictable excitation (1:l) and non-excitation (1:0) patterns depending on current strength. In addition, transition between patterns depended on the direction of current intensity change and stable hysteresis loops were obtained in stimulus:response pattern vs. current intensity plots in 14 cells. Increase of pulse duration and decrease of stimulation rate contributed to a reduction in hysteresis loop areas. Changes in amplitude and shape of the subthreshold responses during the transitions from one stable pattern to the other, suggested that activity led to an increase in membrane resistance, particularly in the voltage domain between resting potential, and threshold. Therefore, we modelled the dynamic behaviour of the single cells as a function of diastolic membrane resistance, using previously published analytical solutions. Numerical iteration of the analytical model equations closely reproduced the experimental hysteresis loops in both qualitative and quantitative ways. In particular, the effect of stimulation frequency on the model was similar to the experimental findings. The overall study suggests that the excitability pattern of guinea pig ventricular myocytes accounts for hysteresis and bistabilities when current intensity is allowed to fluctuate around threshold levels.