Studying cancer using the lens of Darwinian evolution and mathematical modelling
Author: David Basanta
I am a mathematical modeler studying cancer from a Darwinian evolution perspective. I use mathematical and computational tools and work with my talented colleagues at Moffitt's Integrated Mathematical Oncology department and with cancer biologists and doctros.
While she has been at the CancerEvo group at Moffitt’s IMO for over a month now, I finally found time to update the website so please welcome Dr. Anna Miller. Anna just finished her PhD in mathematical biology at the University of Utah under the supervision of Fred Adler.
At Utah, Anna worked on mathematical models of HPV, work that she is likely to continue here at Moffitt. But her skills will also be used to study cancer, where multiple myeloma, a cancer in the bone, will be focus of much of her work. Stay tuned!
This is the title of our latest pre-print that, while submitted to a special issue of BMB edited by Philip Maini and Sandy Anderson, can also be found on biRXiv too. We used the agent-based model we described here and here to do something different this time.
Exploring the early stages of metastasis in the bone is very hard using animal models or clinical data. During those early stages, the metastases are too small to be detectable and thus subjected to analyses. Mathematical models do not have these constraints so we decided to use it and see what happens when prostate tumor cells extravasate and try to colonize the bone ecosystem.
The figure embedded in the post shows how certain key aspects of prostate cancer to bone metastases change when we imagine clusters of metastatic cells of different sizes. For each case (1, 10, 100, 250, 500 and 750) we show the impact on the number of tumor cells and on the amount of bone at two different timepoints: early (day 125) and late (day 250). You can see that some of the circles are bigger than others: that reflects the variability of the results. More interestingly, the fraction at the top-right corner in each plot shows how many of the simulations led to the establishment of a successful metastasis (as opposed to one in which the seeding tumor cells do not grow).
These results show that, while seeding a handful of prostate cancer cells in the bone is better than seeding one, the rule the more the merrier is not always true. Having more seeding cells can help the metastasis as the tumor cells together can produce enough disruption in the process of bone homeostasis. Beyond a threshold the more cells the more competition for the limited resources that need to be shared not only between the tumor cells but also between the stromal cells that are co-opted by the metastasis to support the growth.
Let us know what you think if you read the pre-preprint.
I usually start our papers on prostate cancer to bone metastases by explaining how common prostate cancer is and how little can we do for a patient when the disease metastasizes. But the good news is that only about 1 in 10 patients die of prostate cancer. One of the questions when dealing with a new prostate cancer patient is not how to treat the cancer but whether treatment should be given.
To make this decision, pathologists look at tissue sections (see the featured image) and decide, based on the size and shape of the cancer cells and whether tissue architecture seems to be destroyed. With that information (and two representative examples) they produce a Gleason score with values ranging from 2 (no tumor) to 10 (most aggressive one). One thing that is generally overlooked is the prostate ecosystem. Prostate cancer cells emerge from epithelial cells whose work is supported by smooth muscle cells, fibroblasts and others. These stromal cells can produce an environment that is permisive to the tumor (in the case of reactive stroma). Why haven’t we used information about stroma before? This week we have released a bioRxiv preprint that shows how this can be done. This manuscript constitutes a substantial body of work including a sophisticated computational model (Sandy Anderson, Ziv Frankenstein and yours truly) to explore our hypothesis that led to a clinical biomarker tested on historical clinical data (Gustavo Ayala) and in vivo validation (Simon Hayward, Omar Franco and Doug Strand).
Using a computational model we can explore how the interactions between a heterogeneous cancer population (more or less aggressive cancer cells) and an also heterogeneous stroma (more or less permissive stromal cells) can lead to vastly different evolutionary paths and thus, clinical outcomes. Here’s an example where we look at the tumor growing, starting from one of the glands and gradually taking over the prostate:
We can also see the tumor phenotypes leading the charge:
Using this model we learned the impact that a permissive stroma has on the evolutionary dynamics of prostate cancer.
Highlighting the importance of computationally driven approaches (which can study vastly more scenarios more efficiently and cheaply than any experimental model) is the fact that this dialogue can lead to rather counterintuitive outcomes. For instance that less permissive microenvironments (with more reactive stroma) can, paradoxically, select for tumor cells that are (relatively) less aggressive.
With these insights in mind, we propose an Integrated Cancer Biomarker (ICB) which we tested using a cohort of historical data from 870 patients.
Clearly , integrating pathological information from both the tumor and the stroma allows us to better predict how the tumor will turn to be from the clinical perspective. Adding further credence to the results is that we decided to validate the biological mechanism we used to build the computational model with an animal model.
I am excited about this paper because it shows what a mathematical model can do when mathematicians, biologists and clinical researchers work together. If you want to know the details, check out the bioRxiv version here.
Congratulations to Jake who has just passed his viva and, pending minor revisions, will receive a DPhil in mathematics for the work he developed while working under the supervision of Prof. Jon Chapman at Oxford’s Mathematical Institute, Mason Porter at UCLA and yours truly here at Moffitt.
During his doctoral studies Jake worked with collaborators of this group like Conor Lynch and Andriy Marusyk to understand cancer biology through network modeling. Together with Conor, Jake developed a model of osteocyte growth which allows us to understand how tumor cells can disrupt this process and lead to pathological bone. Together with Andriy, Jake developed a technique he named simulated ablation to study the signaling impact of cells to other cells in their environment.
Along the way Jake was awarded the Lee Segel prize for his previous work on velocity jump processes.
So congratulations Jake, we are eager to see what will you revolutionize next!
The March for Science will be taking place this Saturday and our organization Scientists Inc is one of the supporters. Our science festival will be next week and in this medium blog post I explain why it’s on us, scientists, to bridge the gap between experts and the public and how festivals like taste of science are a valuable tool to do so.
Niccolò is a trained physician that realized that there are more ways to contribute to medicine other than seeing patients. As a result, he started a PhD at the University of Turin, Italy, working with Marco Beccuti, Francesca Cordero and Gianfranco Balbo, developing mathematical models of tumor metabolism.
After coming to Tampa last November to attend the 5th IMO Workshop, he decided that it would pay to spend more time here. So for the next half year Niccolò and us will be working together on an agent-based model of metabolic heterogeneity in cancer. Stay tuned.
One more year one more IMO Workshop. This year our group worked on CMML or Chronic MyeloMonocytic Leukemia, a relatively rare blood cancer. As usual in IMO workshops our team included clinical (physician and malignant hematology specialist Eric Padron), cancer biologists (Andriy Marusyk and Daria Miroshnychenko) and mathematical modelers from Moffitt, Cleveland Clinic, Oxford, Yale and Harvard. A crack team of interdisciplinary researchers that I was lucky to be part of.
The JAK pathway is considered a driver of CMML and fortunately a drug known as ruxolitinibruxolitinib can target cells whose growth is driven by JAK. Unfortunately, as it is the case with most targeted treatments, ruxolitinib quickly leads to the emergence of resistance and relapse. While this is not entirely surprising, the interesting bit is that neither allele frequency nor tumor burden are impacted by the treatment. What exactly drives ruxolitinib resistance?
Team member Artem Kaznatcheev has written about the basis of our project before so please start by taking a look there. Our group produced a suite of models where we consider three distinct possibilities: that there is a subtle Darwinian selection force impacting proliferation rates, that a (provocatively named) Lamarckian force is driving resistance or that non cell-autonomous mechanisms are in place. We clearly thought of something that resonated with the workshop judges as we were awarded a pilot grant to test this experimentally so stay tuned.