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This post was initially inspired by the Science Communication Marathon “2 minutes for science” on LinkedIn. The aim of this marathon is to fascinate the general, non-scientific audience for science by sharing the results of research studies published this year. The article describes why mathematics can be applied in oncology to answer current medical research questions and how we did so in Heidelberg, Germany this year. In the mathematical oncology community, we do not need to explain why mathematics is becoming an essential tool in modern cancer research. We want to stress the point that the spectrum of possible applications of mathematics in oncology is extremely broad and versatile. Mathematics can help at the intersection points with different fields of science from very fundamental to life-relevant questions not restricted to oncology or even medicine in general. Therefore, naming some examples of such non-mathematical scientific questions that could be answered with the help of mathematics may help to grasp its potential, spark new interests and inspire innovative research ideas.

Matter of our research: inherited bowel cancer

Interdisciplinary research is not a new concept: in fact, research is largely nurtured and strengthened by the input from different disciplines. As biologists and medics, we have been using general principles of physics and chemistry to design experiments and understand biological phenomena throughout the history of science. Now we also added mathematics to our research toolkit and use it to answer intriguing questions of cancer biology, which cannot be answered otherwise. Talking specifically about our research focus in Heidelberg, we applied mathematical modeling to understand cancer development in Lynch syndrome, the most common inherited bowel cancer syndrome¹.

The carriers of respective gene variants are at high risk of developing bowel cancer, as well as uterine cancer and less commonly cancer in other organs. Cancer screening tools, such as bowel exam (colonoscopy), allow detecting cancer at a low, sometimes even precancerous stage and contribute to reduced incidence and mortality in affected individuals. But these tools can only be implemented if the persons at risk are known. Strangely, though being similarly common as hereditary breast cancer, Lynch syndrome struggles to reach sufficient public attention so far. This limited public attention is directly reflected in the clinical management of Lynch syndrome carriers: limited Lynch syndrome awareness among healthcare professionals leads to Lynch syndrome carriers remaining undiscovered due to unclarified genetic background of the tumor. This hampers their participation at cancer prevention programs and leaves them with the high cancer risk. In addition to the limited awareness, detection of Lynch syndrome is hampered by its “incomplete penetrance”, meaning that not all individuals carrying the predisposing gene alteration will develop cancer during their life. In fact, the most recent calculations show a risk of about 50% for bowel cancer². Although this fact is good news for affected persons, it can make detection of Lynch syndrome carriers more complicated. Roughly put, half of the carriers do not get a disease manifestation. No clinical manifestation means no medical care. Importantly, the factors that may determine the tipping point between high and low cancer risk are mainly unknown. However, recent studies substantially advanced our understanding of this fragile balance and demonstrated that Lynch syndrome carriers can show distinctive immunological characteristics even without cancer manifestation³ providing hope for future, potentially tumor-independent Lynch syndrome diagnostics.

Lynch syndrome: Which questions can be answered by mathematics?

Back to the mathematical part of the mathematical oncology: how can we improve Lynch syndrome care using mathematics? As in all cancers, the first steps of progression to cancer are impossible to observe and study directly. However, exactly these initial steps are likely to contain the valuable information for clinical approaches to treat or even prevent cancer. And here mathematical approaches become indispensable: we can apply mathematical modeling and calibrate the models based on the existing biological knowledge. This can be performed both on a cell level and on a tissue level to model the possible steps of carcinogenesis and their likely molecular and clinical consequences. For example, by applying certain mathematical concepts, such as the Kronecker structure, we can model mutational processes, their dependencies and possible consequences for clinical disease presentation⁴. Lynch syndrome can be inherited via germline alterations in one of four different mismatch repair (MMR) genes, and previous studies demonstrated different clinical presentation (incidence of precancerous lesions, incidence of cancers, preventive effect of bowel exam) depending on the affected gene. By taking into consideration such biological factors as gene length or coding regions, it is possible to better understand the molecular steps of carcinogenesis capable of explaining these clinical differences and use this knowledge to optimize the cancer preventive approaches.

As tissue architecture is affected by carcinogenic processes, it is important to understand which rules underlie the malignant transformation of tissue and how these rules can be translated into mathematical equations. In our particular case, it is important to understand how cell clones with different genetic alterations behave in a cell population of a colonic crypt – a microscopic tissue unit of the human bowel. Crypts are the structures morphological transformation of which usually gives rise to precancerous and cancerous lesions in the bowel. Driven by genetic events, transformed crypts can become polyps, adenomas or cancer. But live-monitoring of this transformation is not possible and all what clinicians or researchers get to see is usually only a late snapshot during this transformation process. It means, we can analyze the material of the lesion, but we do not know, for example, how this lesion developed, how long it has been there or how long a certain mutation has been present in this lesion. Such timing questions are of crucial importance for Lynch syndrome, because carriers participate at regular bowel exams and the intervals between these exams are a matter of debate: some countries apply more strict intervals (every year) while others have more relaxed guidelines (every 3 years). Epidemiological evidence suggests that it is important to stratify clinical guidelines according to the affected MMR gene. This is paralleled by biological observations indicating that different pathogenic pathways underlying tumor development in Lynch syndrome are mainly determined by the type of driver mutations involved in the carcinogenic process⁵. Studying colonic crypt development by integrating the mutational processes into crypt dynamics shall help to gain knowledge on the duration of certain processes in the bowel tissue⁶. This can help in future to better estimate the optimal cancer surveillance intervals with highest preventive efficacy and lowest stress for affected individuals.

Armed with the great power of mathematical modeling, we now look forward to answer research questions of clinical relevance and improve medical care in Lynch syndrome. This work is part of the collaborative project "Mathematics in Oncology" of the Engineering Mathematics and Computing Lab (EMCL), Heidelberg University and the Applied Tumor Biology (ATB)), Heidelberg University Hospital.

References

1. Jasperson KW, Tuohy TM, Neklason DW, et al. Hereditary and familial colon cancer. Gastroenterology 2010;138:2044-58.
2. Dominguez-Valentin M, Sampson JR, Seppala TT, et al. Cancer risks by gene, age, and gender in 6350 carriers of pathogenic mismatch repair variants: findings from the Prospective Lynch Syndrome Database. Genet Med 2019.
3. Bohaumilitzky L, Kluck K, Hüneburg R et al. The different immune profiles of normal colonic mucosa in cancer-free Lynch syndrome carriers and Lynch syndrome colorectal cancer patients. Gastroenterology. 2021 Dec 1;S0016-5085(21)03805-1. doi: 10.1053/j.gastro.2021.11.029. Online ahead of print.
4. Haupt S, Zeilmann A, Ahadova A et al. Mathematical modeling of multiple pathways in colorectal carcinogenesis using dynamical systems with Kronecker structure. PLoS Comput Biol. 2021 May 18;17(5):e1008970.
5. Engel C, Ahadova A, Seppälä T et al. Associations of Pathogenic Variants in MLH1, MSH2, and MSH6 With Risk of Colorectal Adenomas and Tumors and With Somatic Mutations in Patients With Lynch Syndrome. Gastroenterology. 2020 Apr;158(5):1326-1333.
6. Haupt S, Gleim N, Ahadova A et al. A computational model for investigating the evolution of colonic crypts during Lynch syndrome carcinogenesis. Computational and Systems Oncology 1, e1020, doi:https://doi.org/10.1002/cso2.1020 (2021).