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Leber et al (2016). Bistability analyses of CD4+ T follicular helper and regulatory cells during Helicobacter pylori infection.

November 2017, model of the month by Vincent Knight-Schrijver
Original model: BIOMD0000000625


Bistability is the property of a system to be in two different but stable states of equilibrium. In biological systems this can be observed in processes such as cell-fate decisions, certain mutually inhibitory gene regulatory networks, and signalling pathways [1, 2]. In this model of the month article, the model selected discusses the two possible stable population states of T-cells resulting from Helicobacter Pylori challenge in the gut microbiome of organisms [3].
Commensally dominant in half of the human population, the infection of H. Pylori can promote pathological conditions such as gut inflammation or cancer but only in a subset of those affected. On the other hand, dominant H. Pylori commensalism is also suggested to protect against certain diseases. It is thought that this dichotomy of beneficial and deleterious effects is partially attributed to the differential maintenance of T cell populations.
Thus, the model by Leber et al [3] delves into the mutual inhibition network of two T cell phenotypes, i.e. follicular helper T cells (Tfh) and follicular regulatory T cells (Tfr) - a type of regulatory T cell [4]. The high Tfh phenotype increases the severity of inflammatory responses by promoting the differentiation of T cells into the pro-inflammatory phenotypes TH1 and TH17 whilst inhibiting Tfr cell production. The high Tfr phenotype may restrict the activity of the Tfh population.


Before extending the structure into what is now the curated model, the authors began a top-down exploration of the T cell interplay and examined the bistability of this system. This was carried out using a two-ordinary differential equation model (ODE) for both T cell populations (figure 1A). Plotting the nullclines in a phase-plane portrait illustrates the ability to switch between two stable states, depending on the T cell class ratios (figure 1B). There appeared to be one unstable steady-state where the T cell populations are approximately equal. From this, the authors suggest that H. Pylori may force a stable chronic elevation of Tfh in some patients when both T cell populations are initially similar.

Figure 1

Figure 1. A, a two-ODE model of Tfh and Tfr interactions; B, the phase-plane portrait of steady-states in the small model. The colours in phase-plane portrait are d[Tfh] / dt = 0 (red) and d[Tfr] / dt = 0 (green). Figures adapted from [3].

In arriving at the curated model, the structure was extended to examine potential causes of the patient-selective H. Pylori-driven Tfh elevation. This included cytokines such as IL-2, IL-10 , IL-21, IL-6 and their downstream influence on STAT3 which control the expression of BLIMP-1 and BCL6, two major putative factors behind the Tfh and Tfr regulation (see figure 2).
Figure 2

Figure 2. The extended model network as a mutual inhibition model comprised of putative cytokine interactions between the Tfh and Tfr cell subsets. Figure taken from [3]/


Sensitivity analysis for both Tfh and Tfr indicated that a positive change in the number of Tfh cells was more sensitive to signalling parameters [3]. Furthermore, high sensitivity was seen towards TGIF1, a homeobox protein. TGIF1 was added to the model after observing its differential expression between Tfh and Tfr subsets experimentally. While Tfh was most sensitive to TGIF1 perturbation, the Tfr population remained relatively insensitive. This was largely apparent as a switch between the Tfr dominant and Tfh dominant states can be seen through small variations in the model's TGIF1 activiation parameter.

Figure 3

Figure 3. Parameter scan of the TGIF1 activation parameter showing the sensitivity and dynamic shift in T cell subset numbers. The extended time-course illustrates the attraction towards the two stable steady-states as well as the instability of the unstable steady-state as shown in figure 1. Simulations carried out in Copasi, figure plotted in R.

The model structure is constructed such that TGIF1 activation is catalysed by Tfh populations in an indirect positive feedback loop via the disinhibition of BCL6. The authors go on to suggest that an increased retinoid X receptor (RXR) activity could inhibit the deleterious effect of TGIF1 [3]. Using the model it is possible to simulate the effect of RXR pulses (figure 4), suggesting a therapeutic target in restoring the healthy stable conditions of Tfh and Tfr. Simulations with the curated model also predict that, to restore the healthy steady-state Tfh population, an extended dose period or certain dose-threshold might be required (figure 4). The simulation in figure 4 shows that a marked perturbation is required to reset the T cell populations.
Figure 3

Figure 4. Simulation of suggested agonistic targeting of RXR. Two different durations of high TGF-beta activity were simulated here (50 and 60 days). Simulations carried out in Copasi, figure plotted in R.


By combining multiple levels of structure, experimental data and parameter sensitivity analyses alongside simulations the authors expand upon hypotheses for the role of dysfunctional regulation of T cell populations in driving disease caused by H. Pylori infection. The presence of a bistable system agreed with experimental data from mouse-models of H. Pylori challenge. Furthermore, the model shows particular use in filtering the output of differential gene expression data for the highest impact genes in the control of T cell populations. Finally, the model demonstrates that predictive modelling is a cost-effective approach that can help direct further studies in targeted areas.


  1. Lai, K, Robertson, MJ, Schaffer, DV (2004). The sonic hedgehog signaling system as a bistable genetic switch.. Biophys. J., 86, 5:2748-57.
  2. Wu, M, Su, RQ, Li, X, Ellis, T, Lai, YC, Wang, X (2013). Engineering of regulated stochastic cell fate determination . Proc. Natl. Acad. Sci. U.S.A., 110, 26:10610-5.
  3. Leber, A, Abedi, V, Hontecillas, R, Viladomiu, M, Hoops, S, Ciupe, S, Caughman, J, Andrew, T, Bassaganya-Riera, J (2010). Bistability analyses of CD4+ T follicular helper and regulatory cells during Helicobacter pylori infection. J. Theor. Biol., 398:74-84.
  4. Sage, PT, Sharpe, AH (2016). T follicular regulatory cells. Immunol. Rev., 271, 1:246-59.