Helicobacter pylori and stem cells in the gastric crypt

November 24, 2014 by Artem Kaznatcheev

Last Friday, the 4th Integrated Mathematical Oncology Workshop finished here at Moffitt. The event drew a variety of internal and external participants — you can see a blurry photo of many of them above — and was structured as a competition between four teams specializing in four different domains: Microbiome, Hepatitis C, Human papillomavirus, and Helicobacter pylori. The goal of each team was to build mathematical models of a specific problem in their domain that were well integrated with existing clinical and biological resources, the reward was a start-up grant to the project that seemed most promising to the team of judges. As I mentioned earlier in the week, I was on team H. Pylori — lead by Heiko Enderling with clinical insights from Domenico Coppola and Jose M. Pimiento. To get a feeling for the atmosphere of this workshop, I recommend a video summary of 2013’s workshop made by Parmvir Bahia, David Basanta, and Arturo Araujo:

I want to use this post to summarize some of the modeling that we did for the interaction of H. Pylori and gastric cancer. This is a brief outline — a reminder of sorts — and concentrates only on the parts that I was closely involved in. Unfortunately, this means that I won’t cover all the perspectives that our team offered, nor all the great work that they did. I apologize for the content I omitted. Hopefully, I can convince some other team members to blog about their experience to give a more balanced perspective.

This post also won’t cover all that you might want to know about bacteria and gastric cancer. As we saw earlier, fun questions about H. Pylori span many length and temporal scales and it was difficult to pick one to focus on. Domenico pointed us toward Houghton et al.’s (2004) work on the effect of H. Pylori on stem cell recruitment (for a recent survey, see Bessede et al., 2014), and suggested we aim our modeling at a level where we can discuss stem cells quantitatively. The hope is to use the abundance of stem cells as a new marker for disease progression. In the few days of the workshop, we ended up building and partially integrating two complimentary models; one agent-based and one based purely on ODEs. In the future, we hope to refine and parametrize these models based on patient data from Moffitt for the non-H. Pylori related gastric cancers, and from our partners in Cali, Colombia for H. Pylori related disease.



Much like the small intestine, the stomach is lined with crypt structures, folds in the stomach wall that house the stem cells. However, unlike the intestinal crypt, where the stem cell is at the bottom, the gastric crypts have a bidirectional structure with stem cells in the middle of the crypt and one type of epithelial cells propagating quickly upwards toward the lumen, and another type of excretory cell propagating more slowly downward to the bottom of the crypt. You can see a cartoon of the structure on the left.

Before the workshop, I had no idea how the lining of the stomach was structured, but as soon as I learnt of the similarity to the intestine, two ideas immediately sprang to mind. First, we could take Bravo & Axelrod’s (2013) calibrated agent-based model of the intestinal crypt and add to it the bidirectionality that defined the gastric crypt. This would give us a beautiful visualization, and allow us to contribute a technical extension of the recent literature. Derek Park and Alicia Prieto Langarica started with Bravo & Axelrod’s publicly available NetLogo model, but quickly switched to a from-scratch approach in Matlab. Just in time for our presentation on Friday, they had a model that could generate and visualize all the stages of disease progression in an example gastric crypt. Second, we could adapt Baker et al. (2014) intestinal crypt imaging technique — that Trevor Graham presented at the MBI Workshop on the Ecology and Evolution of Cancer — to directly compare the dynamics of our agent-based model to the temporal dynamics we could infer from careful histological analysis of patients’ gastric crypts. In particular, Domenico has the samples necessary — both from Moffitt and Cali, Colombia — to carefully section z-stacks that we could then image, digitally combine, and unroll into cross-sections of the crypt that can be compared directly to our ABM. Most importantly, given the way the crypt renews itself, we had an opportunity that no other group had: we could turn the crypt’s spatial structure into temporal dynamics and thus have a much richer source of calibration for our model.

Of course, this is great for understanding normal stomach function and the structural effects of gastric cancer, but I’ve described nothing related to H. Pylori. Conveniently for us, the dynamics of H. Pylori in the stomach — although not the connection to cancer — have been relatively well modeled (Blaser & Kirschner, 1999; Joseph & Kirschner, 2004). Joseph & Kirschner (2004) present a particularly sophisticated — yet well parametrized from the literature — system of differential equations, combining the insights behind their early models of H. Pylori (Blaser & Kirschner, 1999) and gastric acid secretion (Joseph et al., 2003). This model already incorporates healthy stem cells, and would be a great launching point for a model of H. Pylori mediated gastric cancer — it is something I plan to play with in the future — but it was too detailed for us to modify during the time pressures of the workshop.

Instead, we went the route of coupling Blaser & Kirschner’s (1999) system of five ODEs to our own simple model of crypt homeostasis. The starting point was Heiko’s two carrying capacity system which he arrived at over a glass of wine at home and shared with me in a Beautiful Mind-esque scribble on the conference room window; it resembles a simplified version of Joseph & Kirschner’s (2004) approach to stem cells. From this sketch, Yougan Cheng, Hemachander Subramanian, and I modified the method for Goblet cell production, and added H. Pylori-mediated recruitment of stem cells from the bone marrow. This gave us a model that had six main qualitative features that we desired: (1) homeostasis in cell number without stress, (2) intestinal goblet cells appearing under extreme stress — the intestinal metaplasia observed in the progression to gastric cancer — and incorporated (3) H. Pylori dynamics that caused (4) smaller crypt size than from acid wash out, (5) an expansion of the stem cell niche, and (6) more and earlier-onset cancer than in the H. Pylori-independent case. Hema simulated the ODEs to show that our model could recreate the histological progression from gastritis, to metaplasia, to dysplasia and cancer; and I wrote a simple Mathematica script to let us look at the crypt dynamics and cancer risk as we infect (or treat) a virtual patient with H. Pylori of variable virulence.

Below is a sketch of the model:

Given the rich histological data that Domenico has available, we can combine the ODEs and agent-based approaches into a hybrid model, where the concentration of H.Pylori is described by Blaser & Kirschner’s (1999) equations, while the dynamics of the crypt are given by the ODE. The two models can feedback into each other by the ODE’s concentration of H. Pylori effectors determining the rate of random — i.e. not wash-out related — cell death in the ABM, and the number of Goblet cells in the ABM serving as a proxy for host response in the ODE. However, since H. Pylori is particularly prevalent in developing counties where pathologists might not be as patient as Domenico in analyzing crypt biopsies to inform the agent-based model, the ODEs provide an alternative that can allow clinicians to abduce the mechanism governing the progression of disease in individual patients. Exploring this approach to individual fitting can let us connect to the 2013 workshop’s theme of personalized medicine.

There are plenty of future directions to pursue and the workshop judges were kind enough to award our team the pilot grant to continue this exploration. During the workshop, our team outlined a hypothesis and two specific aims for the project, and I hope to convince Heiko to blog about these aspects and his plans for our work. I look forward to seeing where this project goes next; until then: congratulations team H. Pylori!

References

Baker A.M., Cereser B., Melton S., Fletcher A.G., Rodriguez-Justo M., Tadrous P.J., Humphries A., Elia G., McDonald S.A., Wright N.A., Simons B.D., Jansen M., & Graham T.A. (2014). Quantification of crypt and stem cell evolution in the normal and neoplastic human colon. Cell Reports, 8(4): 940-7.

Bessède, E., Dubus, P., Mégraud, F., & Varon, C. (2014). Helicobacter pylori infection and stem cells at the origin of gastric cancer. Oncogene.

Blaser, M. J., & Kirschner, D. (1999). Dynamics of Helicobacter pylori colonization in relation to the host response. Proceedings of the National Academy of Sciences, 96(15): 8359-8364.

Bravo, R., & Axelrod, D. E. (2013). A calibrated agent-based computer model of stochastic cell dynamics in normal human colon crypts useful for in silico experiments. Theoretical Biology and Medical Modelling, 10(1): 66.

Houghton, J., Stoicov, C., Nomura, S., Rogers, A.B., Carlson, J., Li, H., Cai, X., Fox, J.G., Goldenring, J.R., & Wang, T.C. (2004). Gastric cancer originating from bone marrow-derived cells. Science, 306 (5701), 1568-71 PMID: 15567866

Joseph, I. M., Zavros, Y., Merchant, J. L., & Kirschner, D. (2003). A model for integrative study of human gastric acid secretion. Journal of Applied Physiology, 94(4): 1602-1618.

Joseph, I.M., & Kirschner, D. (2004). A model for the study of Helicobacter pylori interaction with human gastric acid secretion. Journal of Theoretical Biology, 228(1): 55-80.