Fetal airway smooth muscle (ASM) exhibits phasic contractile behavior, which transitions to a more sustained “tonic” contraction after birth. The timing and underlying mechanisms of ASM transition from a phasic to a tonic contractile phenotype are yet to be established. We characterized phasic ASM contraction in preterm (128 day gestation), term (∼150 day gestation), 1–4 month, 1 yr, and adult sheep (5yr). Spontaneous phasic activity was measured in bronchial segments as amplitude, frequency, and intensity. The mechanism of phasic ASM contraction was investigated further with a computational model of ASM force development and lumen narrowing. The computational model comprised a two-dimensional cylindrical geometry of a network of contractile units and the activation of neighboring cells was dependent on the strength of coupling between cells. As expected, phasic contractions were most prominent in fetal airways and decreased with advancing age, to a level similar to the level in the 1–4 month lambs. Computational predictions demonstrated phasic contraction through the generation of a wave of activation events, the magnitude of which is determined by the number of active cells and the strength of cell–cell interactions. Decreases in phasic contraction with advancing age were simulated by reducing cell–cell coupling. Results show that phasic activity is suppressed rapidly after birth, then sustained at a lower intensity from the preweaning phase until adulthood in an ovine developmental model. Cell–cell coupling is proposed as a key determinant of phasic ASM contraction and if reduced could explain the observed maturational changes.

## Introduction

Smooth muscle in the fetal airway exhibits spontaneous phasic contractions that are identified in a variety of mammals including chickens, rats, guinea pigs, rabbits, dogs, pigs, and humans [15]. Phasic contractions occur when the muscle shortens rapidly to produce spontaneous contraction [6]. Such phasic activity of the airway smooth muscle (ASM) was first described more than 80 years ago and is thought to act as a developmental modulator, promoting lung growth through mechanotransduction pathways [7,8]. After birth, ASM produces predominately tonic force [911], a sustained contractile response [6], however, phasic ASM activity is also reported in adult animals and humans [11,12]. No data exist on when and to what extent ASM transitions from a phasic to a tonic contractile phenotype.

Compared with ASM contraction prior to birth, the functional significance (if any) of phasic ASM contraction after birth is less clear [13]. Peristaltic ASM movements to facilitate the movement of air and/or mucus from the lung have been proposed but remain disputed [14,15]. In the context of disease, the “postnatal reversion to prenatal phenotype hypothesis” attributes spontaneous bronchoconstriction in asthmatic patients to a phasic pattern of ASM contraction, albeit over a longer time-scale than in the prenatal lung [7]. That is, the expression of a phasic ASM phenotype in the airways of subjects with asthma may contribute to clinical symptoms and airflow limitation.

Physiological determinants of phasic smooth muscle contraction are well studied [16,17]. Phasic smooth muscle activity is typically more distinctive in single-unit musculature such as esophageal and intestinal smooth muscle where action potentials are generated [18]. Onset of phasic activity in ASM is not clearly understood but circumferential waves of calcium oscillations are documented in mature ASM [19,20]. While the frequency of calcium oscillation increases the amplitude of ASM contraction, the contractile response is predominantly tonic rather than phasic in nature [21]. There is evidence of spontaneously activated cells within the ASM layer [22] and also of gap junctions [23] that may propagate an activation signal. The presence of spontaneously active cells and gap junctions, therefore, provides a theoretical mechanistic framework for the emergence of phasic ASM contraction at any stage of life.

In this study, we examined phasic activity of pre- and postnatal ASM using an ovine developmental model. Mechanisms of phasic ASM contraction were investigated using a computational model of ASM force production and narrowing based upon probability of cell activation and cell–cell interactions. We further question to what extent the phasic contraction of ASM might be similar to a wave propagating through the airway wall. Findings demonstrate that the intensity of phasic ASM contraction reduces rapidly after birth, which is consistent with a fall in spontaneous ASM cell activation and/or “coupling” between cells.

## Materials and Methods

### Animals and Ethics Approval.

All animal experiments conformed to institutional ethics and animal care unit regulations and were approved by the Animal Ethics Committee (RA/3/100/1368), University of Western Australia. Five sheep groups were studied: preterm fetal lambs delivered via caesarean section at 128 day gestation (n = 10); term (∼150 day gestation, n = 8); 1–4 month lambs (n = 13); and sexually mature young adult (1 yr, n = 6) and adult (5 yr, n = 8) sheep. All animals were euthanized by intravenous sodium pentobarbitone overdose (150 mg kg−1) and subsequently exsanguinated. The lungs were removed and transported on ice for subsequent laboratory dissection.

### Airway Segment Preparation.

Bronchial segments were dissected, free of lung parenchyma, from the main stem bronchus of the right lower lobe, with all side branches ligated with surgical silk. The bronchial segments were cannulated at both ends and mounted horizontally in the organ bath containing gassed Krebs solution at 37 °C [2426]. The length of the bronchial segment in the organ bath was stretched to 120% of the relaxed length, to account for the recoil in length after dissection (determined in preliminary experiments).

The proximal end of the airway was connected to a reservoir filled with Krebs solution, which was used to flush the lumen between experiments. The reservoir was set at a height that would exert 5 cm H2O of transmural pressure (Ptm) on the airway wall. The distal end of the airway was connected to a servo-controlled syringe pump with pressure feedback as previously described [25,26]. All protocols were performed in a closed system, created by closure of a tap between the airway and the Krebs solution reservoir, and via the pressure-controlled syringe pump maintained a constant Ptm of 5 cm H2O by modifying lumen volume. Cyclical changes in lumen volume under constant pressure were used as an index of phasic ASM contraction. The system was leak-tested prior to each experiment and compliance was negligible.

### Experimental Protocol.

After dissection and mounting, airways were equilibrated for 1 h under static Ptm of 5 cm H2O, to simulate functional residual capacity in vivo. The Krebs solution in the organ bath was replaced every 10 min throughout the experiment to remove metabolites. Viability of the tissue was subsequently confirmed by parasympathetic nerve stimulation via electric field stimulation (60 V, 3 ms, 30 Hz for 10 s). Following 5 min recovery, airway segments were exposed to a single dose of acetylcholine (ACh; 10−4 M) and washed out. This stimulation protocol (agonist and electrical) is a conventional approach to equilibrate the airway to the new organ bath conditions [24].

Spontaneous phasic activity was examined up to ∼2 h after equilibration. Airways were fully relaxed to theophylline (10−2 M) at the end of the experiment and the volume of the airway at 5 cm H2O (V5) was determined by withdrawal of the syringe until closure [27]. Three parameters of phasic activity were assessed: frequency (the number of contractions/min), amplitude (the peak to trough volume change expressed as a percentage of V5), and intensity (the product of fractional amplitude and frequency; ΔV/V5 × contractions/min). The SD of intensity was also computed for each animal.

### Computational Model of Airway Contraction.

To aid the interpretation of the experimental data, we developed a simple computational model (Fig. 1) of an airway segment composed of identical ASM cells arranged in a rectangular array of size Nx by Ny, in the horizontal and vertical directions, respectively. The model has circular boundary conditions in the y direction so that the sheet can be considered as a tube. We assume that each cell has the ability to contract with a baseline probability per unit time denoted by pa. When contraction occurs, the cell is in the active state of duration Ta followed by a refractory state of duration Tr and the cell cannot be activated over this period. In addition to the spontaneous activity, cells interact with their neighbors, which alter their total probability p of being in the active state. The cell–cell interactions are taken into account by increasing p locally for a cell if any of its four neighbors are in the active state. Thus, if a cell is in the relaxed state, the probability that it becomes active is
$p=pa+gl+gr+gt+gb$
(1)

where gl, gr, gt, and gb denote the strength of interaction of the cell with its left, right, top, and bottom neighbor, respectively. If a neighbor cell is in the refractory state, the corresponding interaction is subtracted from p. When the interaction strengths are negligible, cells can become spontaneously active with probability pa. Additionally, we assume that a “neighbor-activated” cell will also attempt to synchronize its active cycle to the average neighbor activation by setting its clock to q = (t1 + t2 + t3 + t4)/4, where t1, …, t4 are between 1 and Ta and describe the clock state of each four neighbors. Therefore, a cell in the relaxed state will transition to the average active state of its neighbors with probability p.

Fig. 1
Fig. 1

The model is assumed to be under isobaric conditions with a baseline stiffness Kb. When a transmural pressure Ptm is applied across the wall, the volume of the airway at baseline is Vb = Ptm/Kb. When ASM cells contract, the pressure is maintained at Ptm, but the volume decreases from Vb to V and the expelled volume, ΔV=Vb − V, is equivalent to what is measured experimentally. Thus, the goal is to compute ΔV, or the relative change in volume, ΔV/Vb, as a function of the contractile state of all cells in the model and age.

To determine ΔV during contraction, we calculate it as
$ΔV=PtmKb−PtmK$
(2)
where K is the wall stiffness that is determined by the active and relaxed ASM cells in the wall, and K > Kb. To relate Kb and K to single cell level properties, we note that a computational network model of a single ASM cell suggested that cell stiffness (k) increases linearly with the magnitude of contractile force fc [28]. In our network model, each cell is modeled accordingly as follows:
$k=1+αfckb$
(3)
where kb is the baseline stiffness of a single cell in the absence of contraction and α is a proportionality constant to nondimensionalize force. For simplicity, we allow fc to take only two values, 0 in the relaxed state or 1 in the activated state. To scale the individual ASM cell stiffness to the entire wall, we further assume that cells are mechanically connected in the circumferential direction as springs in series, each having a k described in Eq. (3), and because the model is axially constrained, neighboring circumferential rings do not interact due to contraction. Consequently, K is the sum of the stiffness values of Nx rings in parallel each composed of Ny springs in series
$K=∑m=1Nx[∑n=1Ny11+αfcm,nkb]−1$
(4)
where fc(m, n) is the time varying contractile force (0 or 1) of the nth cell in the mth ring that depends on p. Note that if all cells are relaxed (fc(m, n) = 0), Eq. (4) reduces to the passive stiffness of the wall, Kb = (Nx/Ny)kb. Furthermore, by replacing fc(m, n) in Eq. (4) with its average value ⟨fc⟩, which is related to the fraction of activated cells, Eq. (4) can be simplified to the following:
$K=1+α⟨fc⟩kbNxNy=1+α⟨fc⟩Kb$
(5)
Equation (5) suggests that wall stiffness during contraction is proportional to the baseline stiffness and increases nearly linearly with the average contractile force which is consistent with the experimental results seen at the whole airway level [29]. Finally, substituting the right-hand side of Eq. (5) to Eq. (2), we obtain the relative change in volume as
$ΔVVb=α⟨fc⟩1+α⟨fc⟩$
(6)

Equation (6) provides the link between the relative volume displaced by the airway at isobaric conditions and the average microscopic force of the ASM cell.

In the computational simulations, Eq. (4) was calculated and substituted into Eq. (2) to predict relative volume changes during a simulation including 2,500,000 time steps for the following parameter combinations using matlab R2018a. The value of Ta was set to 100, while Tr was varied between 1 and 100. Cell–cell interactions were assumed to be isotropic with g = gl = gr = gt = gb and the value of g was varied between 0.002 and 0.256 for several values of pa ranging from 0.0005 to 0.05. The parameters Ta and Tr are completely arbitrary, and the g values are probabilities. These parameters were chosen after initial testing of the model followed by a broad sweep in the parameter space. The peaks in ΔV/Vb were identified with a peak detection algorithm from which we computed the mean and SD of amplitudes, contraction frequency defined as the inverse of the time between peaks and the intensity defined as the product of amplitude and frequency.

### Statistics.

Normally distributed data were analyzed using one-way analysis of variance, and all pairwise multiple comparison using sigmaplot (version 13.0, Chicago, IL). If data could not be normalized, one-way analysis of variance on ranks was used (sigmaplot). Data from the different age groups are expressed as mean ± SEM or median ± interquartile range (IQR) (graphpadprism, version 5.0; GraphPad Software, La Jolla, CA). Differences between groups were considered statistically significant at P <0.05.

## Results

### Animal and Bronchial Segment Characteristics.

The sex and mass of animals are shown in Table 1. Length, volume, and generation of bronchial segments are shown in Table 2. Immature airways were taken from a more proximal location of the main stem bronchus and had a lower lumen volume despite comparable lengths.

Table 1

Group characteristics

GroupSex (M:F)Body mass (kg)
Fetal (128 d gestation)7:33.3 ± 0.4
Term (150 d gestation)5:34.8 ± 0.3
1–4 month lambs9:422.6 ± 3.3
1-yr-old sheep6:039.0 ± 1.2
5-yr-old sheep0:866.6 ± 3.7
GroupSex (M:F)Body mass (kg)
Fetal (128 d gestation)7:33.3 ± 0.4
Term (150 d gestation)5:34.8 ± 0.3
1–4 month lambs9:422.6 ± 3.3
1-yr-old sheep6:039.0 ± 1.2
5-yr-old sheep0:866.6 ± 3.7

Data are mean  ±  SEM. M, male; F, female; and d, days. Body mass means were calculated based on n = 8, n = 11, and n = 6 for fetal, 1–4 month lambs, and 5-yr-old sheep, respectively, since weights of some animals were not available. Other groups had complete data.

Table 2

Length, volume, and generation of bronchial segments

GroupLength (mm)Volume (μL)Generation
Fetal (128 d gestation)22.9 ± 2.1486.8 ± 45.01–10
Term (150 d gestation)30.0 ± 0.6581.5 ± 35.54–10
1–4 month lambs29.2 ± 0.7885.7 ± 84.7a,b9–12
1-yr-old sheep31.0 ± 0.5a1103.9 ± 59.5 a,b11–13
5-yr-old sheep28.9 ± 1.61208.2 ± 174.5 a,b11–14
GroupLength (mm)Volume (μL)Generation
Fetal (128 d gestation)22.9 ± 2.1486.8 ± 45.01–10
Term (150 d gestation)30.0 ± 0.6581.5 ± 35.54–10
1–4 month lambs29.2 ± 0.7885.7 ± 84.7a,b9–12
1-yr-old sheep31.0 ± 0.5a1103.9 ± 59.5 a,b11–13
5-yr-old sheep28.9 ± 1.61208.2 ± 174.5 a,b11–14

Length is the stretched airway length in the organ bath. Volume is lumen volume at 5 cm H2O after theophylline. Data are mean  ±  SEM. Generation (mode for each distal and proximal end of the segment) was determined by counting the number of side-branches along the mainstem bronchus with trachea defined as Generation 0. Generation was not recorded for 3 airways in the fetal group.

a

Significantly different from fetal (P <0.05).

b

Significantly different from term (P <0.05), d: days.

### Phasic Airway Smooth Muscle Contraction in Sheep Bronchi.

Example traces of spontaneous phasic ASM contraction are provided in Fig. 2. Phasic activity was observed in all age groups before and after birth, but was most prominent in fetal and term groups, with a pronounced decrease in older animals. The amplitude of spontaneous volume oscillation in the 1–4 month old lamb group fell substantially compared with the term group (P =0.045; Fig. 3(a)). Frequency of spontaneous phasic contraction was significantly lower in 1- and 5-yr-old sheep compared with the fetal group (P <0.001; Fig. 3(b)). The frequency of spontaneous phasic contraction in 1-yr-old sheep was also lower compared with the term group (P =0.038; Fig. 3(b)). The intensity of phasic activity, expressed as a product of amplitude and frequency, was greatest in fetal and term groups compared with 1–4 month old lamb, 1- and 5-yr-old sheep (P <0.001; Fig. 3(c)). The duration of phasic activity (median ± IQR) varies within and between groups, with the duration higher in lamb (P =0.006), 1- (P <0.001) and 5-yr-old (P =0.002) sheep compared with the fetal group: fetal, 4.9 [1.7–8.7] min; term, 10.9 [5.8–25.2] min; lamb, 14.4 [8.7–25.6] min; 1-yr-old sheep, 37.4 [23.9–76.1] min; 5-yr-old sheep, 18.2 [13.7–27.0] min.

Fig. 2
Fig. 2
Fig. 3
Fig. 3

### Modeling the Transition From Phasic to Tonic Contraction.

Our computational model closely mimicked the characteristics of spontaneous phasic contraction observed in sheep bronchi and allowed us to empirically test the importance of the parameters involved in the transition of ASM with maturation. The model synchronized phasic contractions when the spontaneous activation parameter was set to a large value (pa = 0.05) with medium cell-cell interaction strength (g =0.05; Figs. 4(a)4(c), Supplementary Video 1, which is available under the “Supplemental Materials” tab for this paper on the ASME Digital Collection). In contrast, the model displayed sporadic contractions with isolated spikes that generated wave propagation of cellular contraction for low spontaneous activation (pa = 0.000002) coupled with strong cell–cell interactions (g =0.1; Figs. 4(d)4(f), Supplementary Video 2, which is available under the “Supplemental Materials” tab for this paper on the ASME Digital Collection).

Fig. 4
Fig. 4

Based on preliminary simulation results, we find that the three parameters broadly involved in the generation of phasic contractions are cell excitability (pa), Tr, the refractory period, and the strength of coupling between neighboring cells (g). In the absence of cell coupling (g =0), we observe a constant displaced volume due to contraction, even when g =0 is accompanied by high pa and Tr (Fig. 5(a), Supplementary Video 3, which is available under the “Supplemental Materials” tab for this paper on the ASME Digital Collection). A variety of behaviors including oscillations are observed when Tr is large but pa and g are low, as the model produces isolated clusters of active cells, but these clusters do not interact (Fig. 5(b)). The most interesting behavior is the sporadic oscillations with large Tr, but very low pa and medium g (Fig. 5(c)). The sporadic oscillations shown in Fig. 5(c) suggest that the system rarely reaches the threshold to initiate a measurable contraction because pa is low. However, synchronization occurs (albeit suboptimal) if a low pa is combined with a relatively strong g to produce a more coherent interaction among activated clusters, leading to a propagating contraction wave.

Fig. 5
Fig. 5

The decrease in phasic activity with age as seen in the sheep bronchi (Fig. 3) can be replicated by the model through gradual reduction in cell coupling. When g was set to decrease with age (g =1/age), g but not pa appears to impact the final amplitude (Fig. 6(a)), frequency (Fig. 6(b)), and intensity (Fig. 6(c)) of phasic contraction. Phasic contractions can be obtained with very low excitability (pa = 0.0005) and strong g; however the reverse, that is, high cell excitability (pa = 0.004) with weak g, will not produce phasic oscillation. This finding indicates that the propagation of spontaneous contractions and the production of volume oscillation are primarily determined by g.

Fig. 6
Fig. 6

The SD of intensity of ASM contraction measured in the sheep bronchi was significantly reduced in the 1–4 month lamb, 1- and 5-yr-old sheep compared with the fetal or term groups (P <0.05; Fig. 7(a)). Our computational model also reproduced this feature of the data; indeed, the model-predicted SD of the intensity decreased with age (Fig. 7(b)).

Fig. 7
Fig. 7

## Discussion

This study examined phasic activity from late gestation to adulthood using an ovine developmental model. Spontaneous phasic activity measured in isolated bronchial segments in vitro was most prominent in fetal airways. Some phasic activity was still observed in adult animals although intensity of this activity reduced markedly after birth. The experimentally identified transition from phasic to tonic ASM contraction was simulated in a computational model by gradually reducing the strength of cell to cell coupling.

The precise mechanism underlying the transition from phasic to tonic ASM contraction after birth is not known, but may intuitively reflect disruption of temporal and spatial distribution of ASM activation events. Phasic contraction in other smooth muscle types, involves spontaneous depolarization of pacemaker cells and the propagation of action potential via gap junctions to neighboring cells [30]. Pacemaker cells in the airway are not well established; however, some studies have suggested that spontaneous rhythmic activities are generated primarily from the proximal right lung [7,31]. Gap junctions identified in the airway presumably allow for coordinated phasic contractions [8,32].

We, therefore, devised a computational model of ASM force generation and subsequent airway narrowing to examine a potential mechanism facilitating phasic to tonic ASM transition. The two most important parameters in the model were the probability of cell activation and the strength of cell to cell coupling, which correspond, respectively, to spontaneous muscle activation and gap junctions. The degree of cell to cell coupling (g) appears to play a critical role in the generation of phasic activity, since phasic activity could be mimicked with very low cell excitation as long as cell to cell coupling was strong (Figs. 4(d)4(f)). These results suggest that the transition from a phasic to a tonic ASM phenotype with maturation could be simulated by gradually decreasing the strength of cell to cell coupling. If we assume that changes in coupling in the model are reflective of ASM gap junctions, a reduction in gap junction expression with age is a testable hypothesis that has a basis in other tissue types. For example, endothelial gap junctions are maximally expressed in rat aorta at birth, with gap junction expression declining within the first week of life [33].

The probability of cell activation (pa) was the other key parameter in the model. Cyclical activation of ASM cells is not purely restricted to intrinsic pacemaker activity, but may instead be pharmacologically mediated. For example, charybdotoxin-induced oscillatory contraction in guinea pig airways is regulated by activation of the cyclooxygenase two enzyme and downstream production of prostaglandins [34]. In murine airways, tetraethylammonium chloride induced oscillations in intracellular Ca2+ and force were produced cooperatively by L-type voltage-dependent Ca2+ channels, voltage-dependent Na+ channels, Ca2+-activated Cl channels, Na+–Ca2+ exchanger, Na+/K+ ATPase, release from Ca2+ stores mediated by inositol (1,4,5)-trisphosphate, and extracellular Ca2+ [35]. Whether phasic ASM contraction occurs appears dependent on the frequency of Ca2+ oscillation, wherein frequencies exceeding 40 cycles/min produce sustained (tonic) contraction [30] and phasic ASM contraction at much lower frequencies [31]. The frequency of contraction observed in the present study ranged from 0.5 to 5.3 contractions/min (Fig. 3) in sheep airways which in the future should be compared with direct measurements of intracellular Ca2+ over the same time period. Irrespectively, the model parameter (pa) should not be considered a specific representation of pacemaker activity, but any pathway that leads to spontaneous cell activation and thereafter latency.

Despite its overriding simplicity, our computational model exhibited a rich set of behaviors ranging from fully deterministic synchronized waves (Figs. 4(a)4(c), Supplementary Video 1, which is available under the “Supplemental Materials” tab for this paper on the ASME Digital Collection), which are similar in part to the contractions in the fetal airway (Fig. 2(a)), through more isolated sporadic waves (Figs. 4(d)4(f), Supplementary Video 2, which is available under the “Supplemental Materials” tab for this paper on the ASME Digital Collection) somewhat reminiscent to the contractions in the term airway (Fig. 2(b)), to a constant level of contraction (Fig. 5(a), Supplementary Video 3, which is available under the “Supplemental Materials” tab for this paper on the ASME Digital Collection) that may represent the tonic contraction with slow swings in the adult airway (Fig. 2(e)). While the biological mechanism associated with phasic contraction is the average single cell contractility that is responsible for the full airway contractility [31], the mechanism of contraction in our model is wave propagation (Fig. 4). This finding raises the possibility that phasic behavior is a network phenomenon arising from cell–cell interactions, rather than molecular mechanisms of single cell contractions. This idea of network behavior reproduced all of the measured data features, provided the cell–cell interaction parameter g decreased with age. In the absence of relevant data for ASM, we chose the simplest mathematical relation between g and age: g =1/age. While other forms could be explored, this simple relation produced behavior similar to the data (Fig. 3 versus Fig. 6). As the strength of cell–cell coupling is reduced with age, the probability that an activated cell induces a full wave is also reduced. Hence, both the frequency and amplitude, and hence, the intensity, of the waves decrease with age. It is noteworthy that the model also predicted that the SD of amplitude has a peak (data not shown) because with decreasing age, cell–cell coupling becomes stronger and all waves begin to be synchronized with similar amplitudes. Such a full synchronization is only rarely seen in the experimental data (see first 2 min in Fig. 2(a)). Nevertheless, the SD of intensity, being the product of amplitude and frequency, still shows a strong decrease with age, in agreement with the experimental data (Fig. 7).

An improved understanding regarding the physiology of phasic ASM contraction is potentially relevant to the pathogenesis of common obstructive diseases such as asthma. Jesudason draws a creative link between asthma and phasic ASM contraction [7]. Transient airflow limitation, which is a primary characteristic of asthma [36], is conceptually similar to the rhythmic mechanical response associated with phasic ASM contraction. The hypothesis proposed by Jesudason states that reversion to a prenatal ASM phenotype contributes to asthma onset [7]. Given the early life presentation of asthma, we further speculate that phasic ASM contraction may never completely transition in individuals at risk of asthma development. There is now an abundance of evidence to suggest that a number of prenatal factors contribute to asthma development including fetal growth kinetics [3739], preterm birth [40], and intrauterine infection [41]. Deficits in airway function at birth and in childhood are independent risk factors for the development of asthma [42,43]. Wheezing, an apparent symptomatic expression of airflow limitation, is common in infants [44]. Notably, wheezing phenotypes also include transient wheeze [45] which is perhaps most analogous to phasic ASM contraction. An unanswered question is whether the established associations between adverse events in early life and asthma are mediated by a direct effect on airway function that may include persistence of or regression to phasic ASM contraction.

There are limitations and assumptions in both biological and computational models used in the present study. Sex is a potential confounder, particularly in the older groups. Males were only available in the 1-yr-old group, while 5-yr-old females were studied as these were the mother ewes of the younger groups. Younger groups comprised both male and female lambs. Recent studies have raised the possibility of sex differences in ASM behavior and the role of sex hormones in the etiology of asthma is acknowledged [46]. Indeed, there is a sex-dependent shift in asthma prevalence from childhood to adulthood; the prevalence of asthma is greater in boys than girls during early childhood, but this trend is reversed after puberty [47]. It seems less likely that sex differences will be expressed at the level of the isolated airway in vitro, where normal regulation from external stimuli is lost. For example, while male sex hormones increase airway responsiveness to cholinergic stimulation via a vagus nerve-mediated reflex mechanism, contractile response of isolated tracheal and bronchial ring segments to carbachol are not different between males and females [48]. No obvious differences were observed between males and females in the present study, further, any sex differences cannot explain a decrease in phasic activity with age. Therefore, conclusions drawn from this study are not expected to be different if sex was controlled across groups.

The computational model is a simple statistical model devised to primarily investigate how the assembly of simple contractile units in the presence of varying neighbor interactions behave. We thus neglected all internal molecular mechanisms that participate in force generation. We also did not specify the nature of cell–cell interactions which might include information flowing through gap junctions, calcium waves, or mechanical force-induced signaling that can lead to cell activation [19,23,49]. For example, when a cell is in the activated state, it may release mediators as well as produce localized force that can affect the activation state of the neighbor cell. These processes may take time which may in part be represented by the period associated with the refractory period Tr. Nevertheless, to our knowledge, the ASM cell does not have a refractory period. To test the effect of Tr on model results, we carried out various complementary simulations and found that Tr = 0 was not different from Tr = 1 suggesting that the refractory period is not an essential component of the model. Another simplification is the assumption that axial forces do not contribute to the expelled volume during a full airway contraction. Finally, the effects of the extracellular matrix were also neglected. Contractile forces can propagate through the collagen fibers to neighboring as well as more distal cells potentially influencing their activation. However, as the extracellular matrix strengthens during maturation [50], its stiffness is expected to increase with potential effects on ASM phenotype and contractility. Despite all the simplicity of our minimal model, it was able to qualitatively reproduce the experimental data. Hence, we believe our minimal model captures some aspects of the transition of a full airway from phasic to tonic contractile phenotype.

## Conclusions

In conclusion, the intensity of phasic activity is greatest in fetal bronchi and while present after birth, decreases with age. Model simulations suggest that changes in cell–cell coupling account for the transition from a phasic to a tonic ASM phenotype which should be further tested in future experimental studies. Owing to the broad similarity in transient airflow obstruction in asthma and phasic ASM contraction activity, abnormalities in the normal phenotypic transition to tonic contraction may be of relevance to asthma pathogenesis.

## Acknowledgment

We would like to thank the assistance of Dr. Siavash A. Noorbakhsh in tissue collection.

## Funding Data

• National Health and Medical Research Council (NHMRC) of Australia (1077791 and 1057514, Funder ID. 10.13039/501100000925).

• National Institutes of Health (HL-11745 and U01 HL-139466, Funder ID. 10.13039/100000002).

• National Health and Medical Research Council Early Career Research Fellowship (1090888, Funder ID: 10.13039/501100000925)

• National Health and Medical Research Council Career Development Fellowship (1045824, Funder ID: 10.13039/501100000925).

• National Health and Medical Research Council Senior Research Fellowship (1077691, Funder ID: 10.13039/501100000925).

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