The cellular and molecular interactions in the current model
To understand the complex cellular and molecular responses to HP infection, we have summarized the currently prevailing hypotheses regarding HP infection and host responses into a wiring diagram. As a visualization aid, the wiring diagram is further divided into four modules (Fig. 1): the transcription changes, atrophy, Hedgehog singling, and the restriction point. The biological justifications for these modules are described in the method section.
Similar to experimental models, a mathematical model must be able to mimic the biological systems we wish to study. To fulfill this requirement, we first test whether our model is able to recapture experimental observations.
Modeling host transcriptional changes following HP infection
Under normal conditions, NF-κB is held in its inactive state by its inhibitor IkB proteins, with IkBα being the dominant one. Upon infection with HP, gastric cells lose their IkBα expression within 2 h. This loss results in an increase in Nf-kB expression and a corresponding increase in downstream genes [6].
IkBα itself is a target gene of NF-κB, after its activation, Nf-κB promotes the expression of IkBα. This negative feedback has been incorporated into our current model (Fig. 1). Prior to HP infection, the model simulation shows a high level of IkBα (black curve, Fig. 2a) and a low level of NF-κB (blue curve, Fig. 2a). Following infection by HP (applied at t = 5 h in Fig. 2a), IkBα is degraded and its level quickly decreases. Due to the degradation of its inhibitors, NF-κB is activated. Activated NF-kB leads to the transcription of target genes (red curve, Fig. 2a). Because IkBα is downstream of Nf-κb, IkBα level gradually increases and again brings down the level of NF-κB.
Despite the function of the negative feedback, NF-κB activity is sustained for some time following HP infection. It was previously reported that NF-κB transcription activity can still be observed 24 h after HP infection [6]. Our model simulation is consistent with this experimentally observed activation of NF-κB transcription activity even in the presence of the re-accumulated IkBα (see Fig. 4A and B, Schumacher et al., 2015, [6]). The residual activity of NF-kB is able to sustain the transcription of its target genes for more than 20 h post HP infection (Fig. 2a).
In addition to NF-κB, HP infection also activates other transcriptional enhancers and factors such as β-catenin and AP1. In turn, these factors lead to increased CyclinD production and enhanced cell proliferation [9]. Such enhanced proliferation will be discussed below.
The current model recaptures HP induced gastric atrophy
In the weeks following HP infection, elevated expression of IL-1 can be detected in infected mice [10]. This gradual increase in IL-1 is recaptured in our model simulation (blue curve, Fig. 2b). The increase in IL-1 is able to repress the secretion of acid as well as the production of Shh (see Fig. 5A and B, Waghray et al. 2009) [10]. After the level of IL-1 increases to a threshold point, both acid secretion and Shh expression are lost (Fig. 2b), consistent to the experimentally observed atrophy.
As illustrated in the wiring diagram (Fig. 1), a positive feedback between acid secretion and Shh production maintains high levels of both acid and Shh in healthy cells. After the increase of IL-1, Shh is inhibited and this positive feedback is blocked, leading to an atrophic state where upon gastric cells lose production of both Shh and acid (Fig. 2b).
Shh reemerges in the presence of high IL-1
During chronic HP infection, elevated levels of inflammatory cytokines (e.g. INF-γ, TGF-β) recruit bone marrow derived mesenchymal stem cells (BMMSCs) to the site of gastritis [11, 12]. These BMMSCs express and secrete high levels of Shh [13]. This forms an autocrine loop in which Shh promotes the expression of Cyclin D1 in MSCs to promote MSC proliferation. Cyclin D1 represses the cell cycle inhibitors Rb and p27, leading to an increase in the percentage of MSCs in the S/G2/M stages. Through a paracrine loop, Shh also promotes the proliferation of epithelial cells, including CD44 positive tumor stem cells [14].
This reemergence of Shh is mimicked in our model. As shown by the black curve in Fig. 2c, Shh level is decreased 10 weeks post HP infection. Later, the increased level of TGFβ (blue curve, Fig. 2c) recruits BMMSCs to the site of infection (red curve, Fig. 2c), (see Fig. 1, Houghton et al. 2004, [11] and Fig. 3, Varon et al. 2012, [12]). In turn, these MSCs can raise the Shh level months after HP infection.
Gastric atrophy is likely controlled by a bi-stable Shh switch
Under normal physiological conditions, acid secreted by parietal cells along with Shh forms a positive feed-forward loop as shown in Fig. 1. Shh promotes the expression of proton pumps in parietal cells, thus increasing the secretion of acid. In return, the H+ secreted by parietal cells promotes the processing and activation of Shh. This mutual activation between Shh and acid sustains a healthy environment with both a high level of acid and Shh.
Following HP infection, the accumulation of inflammatory factors such as IL-1 results in the reduction of both Shh and acid (Fig. 2b). To better understand the time dependent change of Shh and its control by IL-1, we have computed the steady state of Shh at varying IL-1 levels (black curve, Fig. 2d). The time dependent change of Shh and IL-1 are also plotted (red curve, Fig. 2d).
In healthy cells, IL-1 level is low and Shh level remains high. Following HP infection, IL-1 begins to accumulate. Before IL-1 reaches the critical threshold (θ1, Fig. 2d), the high Shh level is maintained. After the level of IL-1 accumulates higher than the critical threshold, the steady state with high Shh level collapses with the intermediate, unstable, steady state and is lost. Following the loss of the high Shh state, Shh is attracted by the remaining steady state with low Shh. This remaining state may correspond to gastric atrophy.
If the positive feedback indeed functions as described, our model predicts that a bistable switch controls the conversion of the healthy state to the atrophy state. Furthermore, this bistability predicts that a lower level of IL-1 is necessary to maintain the atrophy state once atrophy is induced. In the extreme case indicated by the blue dashed arrow in Fig. 2d, the atrophy state might be maintained even after IL-1 disappears. In this way, the model predicts that a transient IL-1 increase might be sufficient to cause permanent gastric atrophy in infected patients.
Shh reemergence is controlled by additional positive feedback
The upward movement of the red trajectory at high levels of IL-1 cannot be explained by the computed steady state of Shh (Fig. 2d). Rather, this late activation of Shh is caused by the accumulation of TGF-β, triggering an additional positive feedback (Fig. 3a). This feedback defines a second threshold for TGF-β (θ2, Fig. 3a). After TGF-β accumulates higher than this second threshold, the stable attractor with low Shh disappears and Shh level rises. The increase of Shh promotes the recruitment of BMMSCs, which secrete additional Shh. The mutual activation between Shh and BMMSC results in the reemergence of a high Shh steady state at high level of TGF-β. Note that the elevation of Shh and BMMSC are quite slow as shown by the red, time dependent trajectory. These components do not begin to increase until the level of TGF-β has passed over θ2 for quite some time (Fig. 3a).
The interplay between the positive feedbacks that control Shh
The level of Shh is controlled by two independent elements IL-1 and TGF-β.The combined effect of these two control elements can be illustrated on the plane of IL-1 and TGF-β. In Fig. 3b, the thresholds of Shh activation and inactivation (black curves) divide the IL-1-TGF-β plane into three distinct areas: the left area is characterized by inactive Shh; the right area by activated Shh; in the middle bistable area, Shh could be either low or high depending on the system’s history.
The red, time dependent trajectory in Fig. 3b illustrates the comprehensive trajectory of Shh. In healthy cells, Shh level is active due to the positive feedback between Shh and acid secretion. After HP infection, the accumulation of IL-1 brings the system across the Shh inactivation threshold and results in a low level of Shh. Later, the accumulation of TGF-β brings the system across the Shh activation threshold and Shh accumulates once again. Compared with the isolated views that only considers IL-1 (Fig. 2d) or TGF-β (Fig. 3a), the IL-1 and TGF-β plane (Fig. 3b) might provide a satisfactory explanation for why Shh first decreases and then increases.
The current model mimics the observed activation of Ihh
During the atrophy stages following HP infection, parietal cells are lost and Shh is repressed. This condition is mimicked in a parietal cell specific Shh knockout mouse. In these mice, reduction in Shh expression and acid production results in a decrease in somatostatin (SST) production by D cells; the reduced SST levels lead to elevated gastrin production (by G cells) and plasma gastrin. Circulating gastrin binds to gastrin receptors on gastric Pit cells, resulting in the expression of Ihh in these cells. After its production and secretion, Ihh binds to its trans-membrane receptor Pth located on mesenchyme cells, activating the downstream transcription factor Gli (in mesenchyme cells). Gli, in turn, elevates the expression of its transcription targets (i.e. Wnt). After Wnt is produced and secreted (in mesenchyme cells), it binds to receptors and stabilizes β-catenin in epithelial cells. Stabilized β-catenin results in elevated proliferation of epithelial cells [15].
The activation of Ihh is recaptured in our model simulation (black curve, Fig. 3c). The elevation of Ihh follows the elevation of the Gli target gene Wnt after the positive feedback Ihh is fully activated (red curve, Fig. 3c) (see Figs. 3, 5, 6 of Feng et al. 2014, [15]).
As described above, the elevation of TGF-β could cause an increase of Shh months after the initial the HP infection. Because decreased Shh might be responsible for the increase in gastrin, the reemergence of Shh should cause a decrease in gastrin, as simulated with the blue curve in Fig. 3c.
Despite the transient increase of gastrin, our model simulation suggests that the elevated levels of both Ihh and Wnt might be sustained (red and black curves, Fig. 3c). This is due to the activation of a positive feedback between Pit cells and Ihh. Pit cells secrete an elevated level of Ihh, while increased Ihh promotes the proliferation of more Pit cells. Due to this mutual activation, elevated Ihh levels can be sustained even after gastrin level decreases (the red trajectory, Fig. 3d). A model of this multi-scale feedback was elegantly illustrated by Feng et al. [15].
The current model mimics HP induced proliferation
In the stomach, Lgr5+ stem cells reside at the base of antral glands. This stem cell pool continuously self-renews and differentiates into other functional cells. After HP enters the stomach, the bacteria colonizes the gastric glands resulting in enhanced proliferation of gastric stem cells.
Lgr5-eGFPIRES-CreERT2 and Rosa26-TdTomato mouse lines were crossed. Upon treatment with tamoxifen, the Lgr5+ cells and their progenitors expressed TdTomato [16]. After uninfected, control cells are treated with tamoxifen for 5 days, only a small portion of the antral gland is TdTomato+. At this low rate of proliferation, it took 10–15 days for the TdTomato + cells to replace the antral gland. In contrast, mice infected with HP show an increase in the accumulation rate of TdTomato + cells. Moreover, this enhanced proliferation correlates with the HP number in the antral gland, indicating that HP infection enhances the proliferation of Lgr5+ stem cells (i.e. the more bacteria, the stronger the proliferation) [16]. This increase in proliferation can be detected as soon as 24 h post infection [17].
Mammalian cells make the decision on whether or not to enter the cell cycle at their restriction point [18, 19]. At this point in the G1 phase of the cell cycle, the Rb activity in a cell is either lost or sustained high. In cells with sustained Rb activity proliferation is arrested. Conversely, cells with inactive Rb enter active proliferation.
The mitotic signals received by cells set their Rb and Cdk activities. In the absence of mitotic stimulation due to infection, Cdk activity is low (blue solid curve in Fig. 4a) and Rb is active (black solid curve in Fig. 4a). This cell would arrest in the quiescent state. In HP infected cells, the mitotic signal from the bacteria activates the transcription factor cMyc (the black dashed line in Fig. 4b), which then induces the expression of CyclinD and the activation of Cdk (green and blue curves in Fig. 4b). Rb is then inactivated (black curve, Fig. 4b) resulting in active proliferation.
The mutually antagonistic switch between Cdk and Rb controls the decision on the restriction point [19]. By inhibiting the transcription factor E2F and actively recruiting histone deacetylases, Rb represses the transcription of Cyclin A and Cyclin E. In this way, Rb can inhibit Cdk activity because both Cyclins A and E are activating partners of Cdk. This inhibitory regulation is illustrated by the Cdk balance curve (blue curve, Fig. 4c). At low levels of Rb, Cdk activity is high; when Rb activity increases, Cdk activity is brought down. On the other hand, Cdk phosphorylates Rb and represses Rb activity. Hence the Rb balance curve shows high Rb activity only when Cdk activity is low. As Cdk activity increases, Rb is inactivated (black curve, Fig. 4c).
The three intersections between the Rb balance curve and the Cdk balance curve correspond to the three steady states of the restriction point control system. Two of these are stable attractors (black circles, Fig. 4c), and their coexistence has been shown by the response of cells to transient growth factor stimulation [18]. The intermediate intersection (black rectangle, Fig. 4c) corresponds to an unstable steady state. Due to its instability, it cannot be observed experimentally. However it must exist for the two stable attractors to coexist. This is because the unstable steady state serves as the origin of a separatrix (red dashed lines, Fig. 4c). The separatrix is necessary for dividing the plane into two attracting regions: the top, left part is the attracting region of the left attractor; and the bottom, right part is the attracting region of the right attractor.
In the absence of HP, the cell resides in the attracting region of the right attractor. Hence, as time goes by, this cell moves to the right attractor, characterized by high Rb activity and low Cdk2 activity (red dashed trajectory, Fig. 4c). Once reaching this stable attractor, the cell must remain near the attractor and cannot progress through the cell cycle.
Following HP infection, transcriptional activators such as β-catenin are activated [20]. These factors induce cell cycle promoters such as Cyclin D, which inhibit Rb. As Rb is repressed by these cell cycle promoters, less Cdk activity is required to bring down Rb activity. On the phase plane, this event is reflected by the left shift of the Rb balance curve (compare the black curves, Fig. 4c and d). This left movement of the Rb balance curve results in the loss of the right attractor corresponding to a resting cell (with high Rb and low Cdk activity). Consequently, the cell has to move to the left attractor that corresponds to a proliferating cell (characterized by low Rb and high Cdk activity). In this way, HP infection can result in enhanced cell proliferation.
