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.
To kick start this, the organizers of this cooperation group have also organized a small workshop on mathematical modelling of cancer evolution. This being exactly the topic of my research for the last decade meant I was really excited to participate. The image at the top of this post shows many (but not all) of the participants.
Any interdisciplinary meeting will include people from at least two disciplines with the goal of the meeting being to establish some sort of bridge between them. In this case I could argue that the disciplines were mathematicians working on less applied topics vs those working on more applied ones (or biologists as one of them referred to us).
But where I stand, the more interesting gap to bridge was between those interested on the genetic aspects of cancer evolution and those (me and Indiana’s James Glazier) which focused instead on the role of selection. If you ask me (and by reading these lines you have implicitly done so) both genetic variation and selection are the two pillars of evolution and should be considered equally important. Nonetheless there seems to be a lot more work done in trying to understand genetic mutations and phylogenetic trees than in trying to see how the microenvironment and interactions between different cells determines which phenotypes will succeed and which ones will not. More importantly, selection is a key aspect of evolution that we need to understand if we want to have any success when applying treatments to anything from cancer to bacteria to viruses. Why are they (apparently) vastly more people working on genetic aspects rather than selection?
I think that this difference between workflows might partly explain why. There is a wealth of biological data, much of which is genetic in nature, which requires a comparatively modest degree of collaboration with experimentalists if you are a modeler. The process is described in the previous figure: use a mathematical model to find out what the data tells you and then generate hypotheses out of it.
Working on selection requires a different approach as there’s not much data available, especially data that could be easily slotted in a mechanistic model of cancer evolution. Here the mathematical model, built after much consultation with domain experts (that is, cancer biologists) is built to explore the biology and yield hypotheses, which, since we involved our experimental partners from the start, will be also explored in vivo or in vitro. This route is harder but also relatively unexplored, want to join?
A couple of months ago we got news that the NCI has awarded us a U01 grant to continue our work defining the bone ecosystem and how prostate cancer can come in and disrupt it. Of course this is something that cannot be done in a hurry so we are in this for the long-haul. We also need help. We have Conor Lynch and his lab as the willing partners for this work but we also need you.
And who are you, you might be (weirdly) asking yourself ? A lot of what we need was described in this post. Shall I start with a PhD in physics/maths/CS? the need to be able to think mathematically and (hopefully) be able to develop in a programming language like C++/Java/Python or others of the sort? Those are a must but not the most important quality to work in a place like ours.
Basically we want you to be a detective of cancer biology, able to work with other people, happy to discuss your ideas with either mathematicians, biologists and oncologists. Gregarious but also independent you want to try new ways to think about cancer treatment
Quite the title for the post, no? We just had a paper accepted in Nature Scientific Reports entitled Predictive computational modeling to define effective treatment strategies for bone metastatic prostate cancer and we thought we would share the news with you. This paper is part of our ongoing work with the Lynch lab at Moffitt to better understand the evolutionary dynamics of prostate cancer metastases in the bone. Continuing on our previous integrated computational platform [blog, description, paper] we decided to investigate a novel treatment which is not typically used in the clinic: the inhibition of the key signaling molecule TGF-Beta. If you know anything about prostate cancer research you will find TGF-Beta familiar. It has been studied to death and not much of clinical use has ever been found. The issue is that although we know a lot about it, cancer biologists have not found a model to integrate all those findings. We decided to use a computational agent-based model to integrate a lot of what we know of the biology of TGF-Beta in bone metastatic prostate cancer.
We took our previous model and worked carefully to make sure all the cell types responded to TGF-Beta to the best of the cancer biology community’s knowledge. We then went back and forth between this computational model and a mouse model in order to make sure that we could recapitulate TGF-Beta inhibition in the context of both: normal bone and cancerous bone. As you can see in the figure, one advantage of the computational model is that resolution of information about each cell type in any point of the tumor at any stage of the progression. This information can be contrasted with the relatively scarce experimental one to asses whether there are disagreements that need to be resolved.
Another advantage of the computational model is that, even if it is relatively complex like this one, it can test hypothesis at a much faster rate, for longer periods of time (and in a much cheaper and humane fashion) than mouse models. This allowed us to explore all kinds of schemes for the application of the TGF-Beta inhibitor. Once something promising is found we can then test those schemes experimentally to see how they fare with the mouse model.
What we found is that pre-application of the inhibitor is a much better option than application once the metastasis has established itself in the bone. What this could mean to a potential patient using a TGF-Beta inhibitor (which as said, is not a clinical option at the moment) is that we could give these treatments after the primary tumor has been identified in the prostate but before metastases have been found. It is important to understand though that this is the result of basic research and that this conclusion will have to remain hypothetical while we find how move our approach from a pre-clinical model to a clinical one. More importantly, what we have shown is that the integration of various sources of experimental data into a purposely made mechanistic mathematical model with the right amount of complexity (not too simple, not too complex) allows us to identify and explore novel treatments in ways (and at speeds) that would not be possible otherwise.