Research interview – Professor Sandy Anderson

By Dr. Jennifer Flegg

Jen talks with Professor Sandy Anderson from the Moffitt Cancer Center and SMB President-Elect, about his research in mathematical oncology.

Your research focuses on mathematical modelling of cancer across different spatial and temporal scales. How did you get into this field?
I’ve always been interested in space. Fractals were fascinating to me when I was younger because they were spatially very beautiful and complex and yet were produced from such simple rules. That interest in how simple rules can produce complex dynamics led me to Dundee to do an MSc in Mathematical Biology – ironically it was the fact that it had a focus on dynamical systems that drew me in not that it was relevant to biology. However, once I understood the potential power of mathematical models in describing biology there was no going back. I did my PhD with Brian Sleeman focused on nematode movement in heterogeneous environments. It was during that time that I developed the Hybrid Discrete Continuum (HDC) technique which generated individual based movement rules from PDEs. Nematodes can be solitary little worms and find their food through chemotaxis even in the heterogeneous environment of soil. Brian had supervised quite a few students before me, including a former SMB president – Mark Chaplain. When I finished my PhD, I approached Mark for a PostDoc as I could see the potential relevance of my nematode work to angiogenesis. Once I began working with Mark, I realised how fascinating and diverse the cancer problem really was and became completely hooked. Over the years my interested moved from blood vessels, to tumour invasion, the dialogue between the tumour and its environment and ultimately to understanding how cancers evolve through space and time. The cell is in many ways the fundamental unit of a tumour: within it, mutations and transformations happen, and it interacts with other cells to form larger masses. These masses in turn interact with normal tissue components that form an organ and can constrain or facilitate the tumour’s growth. It is clear that cancer is a process that bridges multiple scales and if we want to understand where the potential therapeutic points of intervention are, we need to understand how these scales interact and regulate one another.

What attracted you to mathematical oncology?
The major driver for my interest in oncology was that I could potentially impact patients’ lives. Another reason is that cancer is also a very diverse and complex disease with a huge array of treatment options and there is still a great deal to be understood. The more I worked on cancer, the more I realised that we (mathematical biologists) could have a real impact on its understanding and treatment. For me that ultimately meant leaving the comfort of my mathematics department office in Dundee and working directly where patients are treated.

What do you foresee as the biggest challenges in mathematical oncology?
Obtaining the right data. For example, right now much of oncology is focused on collecting and analysing data largely from the molecular scale. But cancer is a multiscale process where genetic changes alter signalling and, in turn, cellular behaviour. The cellular phenotype is a critical functional measure of how cells are behaving in a given tissue with specific mutations. Since cancers are evolving systems and evolution selects on the cellular phenotype (not the genotype), it’s important that we understand how phenotypes are changing through space and time. This data is very difficult to obtain, since it’s hard to quantify cell function in a tissue environment. Another example is in terms of quantifying individual patient tumour burden, right now we don’t have a very accurate means of monitoring how a patient’s tumour changes over time without very invasive procedures. The good news is that in both of these examples there are scientists actively working on ways to obtain more accurate and more functional measures of cell behaviour and tumour burden, but it’s early days.

What is your favourite research paper (by another mathematical biologist)?
That really is a tough question as there are so many great papers in our field. Perhaps I can reflect a little on the classics first! In my early years in the field I was blown away by the Hodgkin and Huxley model and the simplified version of that model by Fitzhugh and Nagumo. As I got more interested in reaction-diffusion I was drawn to the classic work on Turing pattern formation as well as Murray and Osters mechano-chemical approach to pattern formation. Activator-inhibitor systems in general have always held my interest and I was fortunate enough to see Hans Meinhardt present some of his seminal work. Spatio-temporal systems have driven much of my own research and have intrigued me scientifically for as long as I can remember. That means the PDE work of Lee Segal, Jim Murray and Philip Maini have dominated much of my early research career.  My interest in individual rather than population or density dynamics also drove me to the seminal works of Clifford Patlak or Pierre Bovet and Simon Benhamou on correlated random walks and the velocity jump processes discussed by Wolfgang Alt and Hans Othmer. But I guess I’m not exactly answering the question so let me try a bit harder. On the more mathematical side the paper by Hans Othmer and Angela Stevens, “The ABC’s of Taxis in Reinforced Random Walks” was an inspiration during my PhD. On the more biological side and more recent I’m a big fan of the work of Joao Xavier in PNAS, “Metabolic origins of spatial organization in the tumour microenvironment” – it’s a beautiful integrated piece where there is a nice feedback between experiment and model.

What is something exciting that you are currently working on?
I’m excited about everything I’m working on or else I wouldn’t work on it! But there are some projects that are distinct from others because we are trying to do something very different, one of those projects is on trying to bridge the divide between genetic mutation, cellular behaviour and tissue homeostasis in the early stages of skin cancer development. This has essentially led us to embed the entire genome inside simulated cells that generate a 3-dimensional homeostatic layer of skin then track the clonal dynamics over space and time.  This is a project led by Ryan Schenk (Oxford) and is in collaboration with Darryl Shibata (UCSF). Another one is in regards to dynamically changing treatment schedules based on treatment responses in animal models of metastatic melanoma. Using a simple system of ODEs, Eunjung Kim (Integrated Mathematical Oncology, IMO) fitted her model to the pre-treatment growth dynamics and predicted when the best time to treat next, for 10 different mice. This was repeated many times and led to tumour control for all of the mice. What is exciting here is that each of the mice ended up with very different treatments and they were far better off than any other standard or intermittent treatment strategy.

What impact has your research had outside of academia?
I’m very interested in communicating my science beyond the confines of academia and have participated in local events such as Pint of Science and the 2scientists podcasts. The podcasts, which are a lot of fun really, are run by scientists and have a broad scientific scope – check them out if you’re interested (2scientists.org). Since I work on a disease that directly impacts patients’ lives, it’s clear that the work I and the rest of the IMO are doing is important outside of academia. Right now, we have 4 clinical trials (2 in prostate, melanoma and thyroid cancer) that are active at Moffitt and are driven by mathematical model predictions. All of these trials are for treating patients with metastatic (and therefore incurable) cancer – some of the early results from these trials are very encouraging with us tripling the time to progression and halving the amount of drug given.

What is your favourite research paper that you have written?
This is a tough one, as it’s like asking a father to pick a favourite child! But for sure the most painful paper to write and one of my favourites is the one in Cell, titled “Tumor morphology and phenotypic evolution driven by selective pressure from the microenvironment”. My biological colleagues and I rewrote this paper 4 times and argued about the details every step of the way, and the review process was even more painful. In the end though, what emerged was something that I’m very proud of. In a similar vein the work I did on angiogenesis with Mark Chaplain was hated by reviewers on the first review – I clearly remember one of the reviewers stating: “Pretty pictures are not mathematical biology”. But fortunately, they considered a revision. This led to a very long and painful rebuttal and significant expansion of the paper, but in the end our paper was published in BMB in 1998 and has had a positive impact on the field. It’s ironic how the papers that sometimes cause the most pain turn out to be the most rewarding.

Have you encountered any surprising results in your research?
Yes, many times – it’s what makes doing research so exciting. Sometimes the surprise is that the model predicts a behaviour that is wrong and that forces you to relook at your assumptions and your data. Other times it’s when a model makes a prediction that seems counter intuitive but it turns out to be true.  Of course, it can also be that the surprising result is numerical error or a bad implementation.

Do you find the complexity of cancer biology daunting?
No! In fact, it’s the complexity of cancer that makes it so interesting and so amenable to mathematical modelling. I’ve been told by more than one biologist that cancer is too complex to model and therefore how can over simplified models provide any insights. Of course, that’s a pretty standard refrain from many who don’t fully understand the power of mathematical modelling. I always relish pointing out that cell culture and mice are models in their own right and oversimplify the real system. However, the important point here is that we should build models to answer specific questions and drive those models with specific experimental measurements. If it’s a useful model, it will do more than reproduce what you already know to be true, although that is a critical first step as it gives you confidence in your model. In cancer at least, models need to produce testable predictions and that can be achieved even with the simplest of models.

How have you found working with experimentalists?
I’ve been fortunate to work with some fantastic experimentalists over the years and it’s convinced me that there is no better way to understand cancer than through collaboration. But this doesn’t just apply to experimentalists, it’s part of a team science paradigm that’s become so important in cancer research (and I guess in many other fields as well). At IMO we have groups of scientists working on a specific problem and this can include, clinicians, experimentalists, imagining scientists, pathologists, bioinformaticians and more. It’s worth noting, though, that as the field becomes more integrated across disciplines there will be a temptation to build ever more complex models – this is a real danger, since as we know more we are encouraged to include more in our models. However, in my experience more complexity does not equal a better understanding – it’s often the opposite. So, we need to be cautious to only include what information is needed in a model to answer the question at hand. It’s a problem I deal with daily.

What is your vision for SMB during your time as president of the Society?
The society has been fortunate to have had some outstanding presidents recently, and they have enacted significant positive change for our society. I want to continue that trend and drive forward a more integrated society that is still true to its roots.  More specifically I see 3 areas where I hope to have an impact:

(i) Communication is key at the interface between mathematical, biological and clinical sciences. I’ve worked very hard to overcome the language barriers that exist, through hands on workshops that integrate scientists from all of these disciplines to learn in the most practical way possible – by building models together. As a society at the interface we need to address this issue through education via social media (Facebook, Twitter), our newsletter and by hosting such a workshop at our annual meeting – critically this will directly facilitate better biological participation.

(ii) Membership needs to have benefits beyond the reduced conference fee. Prizes are one area where SMB has historically done poorly especially for junior/mid- career scientists. A priority for me would be to continue to work on ways to make membership of SMB a must and this will include new prizes and new benefits.

(iii) The Bulletin is our journal and historically the place to publish important mathematical biology papers. I’m keen to help our society enrich and facilitate our journal’s success, both as a member of the editorial board and better integrating current trends through targeted calls.

What is one piece of advice you would give to a junior mathematical biologist?
Find a problem you’re passionate about and read all you can that’s relevant, then find a biologist who works on that problem and build models together. Ideally, those models should drive experiments and vice versa. It doesn’t need to be in that order but the point is, don’t work in isolation. In my experience, models that are developed in collaboration are more insightful and more rewarding to build. It also has the added benefit of developing a shared understanding – one of the biggest barriers to our progress is not being able to speak across disciplines.

What is the best part of being a mathematical biologist?
Working with a diverse group of scientists who are incredibly passionate about their science. Even better is that it’s an international group of scientists who are not only your colleagues and collaborators but also your friends that you can meet up with at some cool SMB conference in a bar you’ve never been to before to continue a discussion you started the previous year.

What is the best part of your job? What is the worst part of your job?
Doing what I love to do every day: Science!
Administration is a necessary evil that consumes a great deal of my time.

Finally, what do you do in your spare time?
I try to spend as much time with my family as I can. Other than that, I go see live music whenever I can, or listen to it at home. I drink some locally brewed IPAs. One of my daughters is in a band so I also sometimes get to do all of the above!