Interview with Dr. Alexander Anderson

Dr. Alexander R. A. “Sandy” Anderson is the Founding Richard O. Jacobson Distinguished Chair and Chair of the Integrated Mathematical Oncology (IMO) Department at Moffitt Cancer Center. His research focuses on developing mathematical and computational models that connect genetic, cellular, and tissue-scale processes in cancer, especially exploring how the tumor microenvironment acts as a selective force in tumor initiation, progression, and response to therapy. He holds an MSc and PhD in Mathematical Biology from the University of Dundee in the UK. Before coming to Moffitt in 2008, he worked on hybrid discrete‑continuum models of nematode movement, angiogenesis, tumor invasion, radiotherapy, and epithelial dynamics at Dundee University and Bath University. He is also Co‑Director of the Center of Excellence for Evolutionary Therapy at Moffitt, where his work aims to translate modeling into “eco‑evolutionary” treatment strategies that seek to control rather than eradicate cancer.

Isaac

Hello everybody and welcome to today's episode of High School Mathematical Oncology where we explore how science, mathematics, and medicine are coming together to create the future of cancer treatment. I'm thrilled to be joined today by Dr. Alexander Anderson, chair of Integrated Mathematical Oncology at Moffitt Cancer Center and one of the pioneers of adaptive therapy and mathematical oncology. Dr. Anderson's work is transforming how we treat cancer, not just by studying biology, but by using mathematical models to predict, personalize, and even outmaneuver this disease. Dr. Anderson, thank you so much for being here.

So, first question—let's start with your journey. A lot of students think about math and science, especially cancer treatment, as sort of different things. What inspired you to use mathematics to fight cancer, and how did you find your way into this field?

Dr. Anderson

That's a great question. When I was younger, I was always sort of impressed by the idea that mathematics could describe and help us understand biology. That drew me towards doing courses that linked mathematics and biology. Probably the first taste I got of that was through looking at fractals and understanding chaos—both of those are dynamical systems. The idea that you could get very complex structures out of very simple equations was impressive to me—mind-blowing even.

When I was doing my undergrad, for my honors project I focused on fractals and trying to understand if there were patterns in the structure and this whole concept of self-similarity. That ultimately led me down the route of dynamical systems towards chaos, and that's where I found a master's in mathematical biology at Dundee University. That was where I started to hear more about mathematics being applied to biology—including medical applications: modeling tumor growth, modeling neuronal firing, modeling population dynamics—the kind of complex interactions that very simple equations can capture.

From there, I did a PhD in mathematical biology, and that was actually on nematode movement. Nematodes are small worms, a real pest in crops in the UK—particularly potatoes. During that time, I developed a model, a technique I called the hybrid discrete-continuum technique, which essentially linked discrete agents with continuous chemical fields. It was like a PDE meets an agent-based model. That tool we’ve used throughout my cancer work.

I didn’t actually start working on cancer until I moved to my postdoc. My first postdoc was with Mark Chaplain at Bath University—he was at Bath at the time—and I worked on angiogenesis. But as soon as I started working on cancer, I realized there were so many interesting problems there and opportunities for mathematics and modeling. It really caught my attention. So that’s kind of the trajectory that took me there.

Isaac

So, going into those cancer models, you've used analogies comparing them to predicting a hurricane or an evolving ecosystem to understand how to treat cancer. How do these metaphors help both scientists and the public better understand what makes cancer so hard to treat?

Dr. Anderson

Another great question. These are two different metaphors, but both useful. One is the weather prediction idea—like the hurricane cone of uncertainty. In Florida, hurricane season is just beginning. One of the things you see in weather forecasts is the current eye of the hurricane, and then this cone that emerges from it. That cone is calculated from many mathematical model simulations that show where the hurricane might go next.

The reality is, it’s uncertain. Many factors can impact the direction of the hurricane—fluid, land, air, and stochastic interactions. So this idea that you might know the current state, and have some idea where it might go, but there's uncertainty—that’s very relevant to cancer.

When trying to understand the best way to treat a patient, there's no single best way, because we can’t be certain about every aspect of their disease. So we capture some aspect, account for the uncertainty, and try to design a treatment strategy that works within that uncertainty.

Sometimes the uncertainty is too large—then we have to wait for more information. Like with hurricanes, the more points you get on the trajectory, the narrower the cone becomes. Similarly, the more temporal and spatial data we get on a patient’s disease, the better we become at predicting its future.

The ecological metaphor is also important. Historically, cancer was viewed purely as a collection of mutated cells. But in reality, cancers are within functional organs. A person with lung cancer might have a lung heavily infiltrated by cancer, but they’re still breathing. A brain tumor might be large, but the person can still function. That interaction between tumor and non-tumor tissue is crucial.

And we’ve come to realize that the immune system is part of the "normal" environment—something we can exploit. But the tumor isn’t just interacting with the immune system. It’s interacting with fibroblasts, blood vessels, other cells, growth factors, nutrients. So we need to look at the ecological aspects—the collective interaction between tumor and non-tumor.

We’ve learned a lot about what separates hard-to-treat tumors from more treatable ones. For example, now we can take a pre-treatment biopsy and, based on the spatial orientation and number of immune and tumor cells, predict whether a patient will respond to immunotherapy. That pattern is already hardcoded in the tissue, and we couldn’t have done that without mathematical models and the data to feed them.

Isaac

I’d like to go back to the tumor vs. non-tumor idea. In your work, you've used adaptive therapy—the idea that sometimes you don't want to maximize the dose, because that kills off all the susceptible tumor cells, leaving resistant ones to grow and spread. Why might giving less drug be more effective than maximum doses in cancer therapy?

Dr. Anderson

I think you just said it! If you give the maximum tolerated dose and kill all the sensitive cells, all you leave behind are resistant cells. And if they're resistant, it doesn't matter how much drug you give—they’ll just grow.

This stems from a concept Bob Gatenby developed here at Moffitt. He’s a radiologist who’s also heavily involved in modeling. His idea was: instead of giving max dose and trying to eradicate everything, we leave behind some sensitive cells to compete with resistant ones.

That means you’re not curing the patient, but these are cancers we know aren’t curable—they’re metastatic. So instead of trying to cure the incurable, we try to control it. Adaptive therapy is a control strategy. The idea is to use sensitive cells to suppress resistant ones through competition.

You’re letting the tumor grow, shrinking it with drug, then letting it regrow and shrinking again. You adapt the therapy to the tumor’s individual dynamics—switching the drug on and off, or increasing and decreasing the dose.

We’ve used this across several cancers. An added advantage is that with less drug, patients often feel better, because the normal (non-tumor) tissue is exposed to less toxicity. Quality of life improves.

Of course, there’s a downside: you’re carrying a larger disease burden for longer. That might be painful or problematic for some patients. But if it extends life and improves quality of life for most, it’s a worthwhile strategy.

We’ve done this in about six different cancers and have nine active clinical trials, including skin, prostate, lung, and breast cancers. Within skin, we’re looking at melanoma and basal cell carcinoma.

To make this approach work, you need a way to measure the disease—ideally non-invasively. For example, with prostate cancer, you can measure PSA. With ovarian cancer, CA-125. But with breast or lung cancer, there aren’t always easy blood-based biomarkers. So you rely on imaging or emerging tools like ctDNA (circulating tumor DNA), which looks at fragmented tumor DNA in the bloodstream. It’s promising but sometimes hard to interpret.

Isaac

I guess knowing precisely what it means would be important because of that "Goldilocks window"—trying to get enough treatment to keep the tumor down but not so much that you kill all the sensitive cells. Could you explain how tumor metabolism plays a role in both immune evasion and treatment effectiveness—and how that plays into adaptive therapy?

Dr. Anderson

That's a lot to unpack, but it's an important point. Most cancers are glycolytic—they use the Warburg effect. That means they use both glucose and oxygen for energy, whereas most normal cells use a tiny amount of glucose and rely mostly on oxygen.

This glycolytic metabolism produces lactic acid, making the tumor environment acidic. That acidity is bad for normal tissue—it can kill healthy cells. But another big issue is that immune cells are silenced in acidic environments.

Your lymph nodes are actually quite acidic, possibly because we don’t want the immune system attacking its own home base. Tumors hijack this mechanism. Their acidity makes them more resistant to immune attacks.

So, we’ve hypothesized that you could buffer the acidity—neutralize it—to make the environment more favorable for immune cells and less favorable for tumors. One way might be giving a buffer like sodium bicarbonate (baking soda), or certain sports drinks. Bob Gatenby did preclinical experiments with mice, adding bicarb to their drinking water—and those mice didn’t get cancer, even though they were predisposed to it.

Now, drinking gallons of bicarb isn’t realistic for people. But newer delivery technologies might make that viable. You could imagine a therapy where you alternate between targeting the tumor and targeting its environment—buffering the acidity to support immune function, then applying treatment to suppress the tumor.

Often the more resistant cells are also more glycolytic—so buffering might help sensitive cells regrow and outcompete resistant ones. That leads to a form of adaptive therapy: alternating between hitting the tumor directly and modifying the environment to control it better.

Isaac

So going off that idea of switching between drugs—for a lot of people, it might feel more intuitive to just use both drugs at once and hit the tumor hard. But what if the mathematical model says that’s not the best strategy? How do you approach conversations with doctors or patients when the math says something that doesn’t seem intuitive?

Dr. Anderson

Yeah. So, I think what you’re saying is that cancer isn't intuitive—and it’s not linear. That’s something that’s hard for the public to grasp. There's this common idea that if I give more drug, I’ll kill more tumor.

But if you accept that there are cells that aren’t sensitive to that drug, then that logic falls apart.

Coming back to the idea of having two treatments—and say one of them is immunotherapy—timing becomes important.

Historically, when drugs are given in combination, they're almost always given simultaneously. There's usually no strategic planning—no consideration of whether one should come before the other.

But you could imagine a case where giving drug A first, then drug B, might be more effective—especially if drug A targets a population that leaves behind cells that are now more vulnerable to drug B. The sequence matters.

This is the hypothesis we've explored with immunotherapy. Giving immunotherapy before a targeted therapy might actually be more effective than giving them at the same time.

Isaac

Right. So it's not just about the drugs, but the order and timing?

Dr. Anderson

Exactly. You might have some overlap, but the key idea is that you're priming the immune response. You're waking up the immune system before you go in and start killing tumor cells.

As a result, when you destroy those cancer cells, the dead material can now educate the immune system you just activated, helping it go after the remaining tumor.

So yes, the sequence of drugs is something we need to better understand. Traditionally, clinicians have just given everything at once—but that may not be the best approach.

When it comes to explaining this to patients, you just have to show them the data and be as clear as possible.

A good example is our adaptive therapy trial for prostate cancer using abiraterone. The standard strategy is to give the maximum tolerated dose until the patient fails treatment—usually within a year. But the adaptive therapy strategy, developed by Bob Gatenby and Jin Seong Jang, with Joe Brown, took a different approach.

They used a simple rule we called AT50: reduce the tumor by 50%, then stop treatment. Wait until it returns to its original size, then start treatment again.

Isaac

Why 50% specifically?

Dr. Anderson

Good question. The models actually showed that the best way to control the tumor was to reduce it as little as possible—say 10%—then let it regrow. That way, you keep it at near-maximum density, maintaining competition between sensitive and resistant cells.

But practically, that’s hard to implement. Patients don’t like hearing, “We’re stopping treatment even though your tumor just started to respond.” Saying “We’ll stop at 50% shrinkage” feels more reasonable to both the clinician and patient. It’s a compromise—it may not be optimal, but it’s still better than max-dose treatment.

Isaac

In your research, you found that mice injected with genetically identical cancer cells still had very different responses. What causes that variability, and how can mathematical models help us understand it?

Dr. Anderson

Great question—and very timely. Are animals even the best models for studying cancer dynamics?

The experiment you’re referring to was done by a colleague here. They injected human melanoma cells into the mammary fat pad of mice. So first, you’re injecting human cells into mice, and second, you’re placing them in a location where melanoma cells don’t normally exist.

You inject the same number of genetically identical cells, but they grow very differently across animals. Why?

Well, even so-called “identical” cell lines are actually heterogeneous. Genetically, they may seem the same, but single-cell studies show that there are distinct epigenetic profiles within those lines. So, some populations are better at surviving or growing depending on the environment.

There’s no single winner, at least in the dish. But when you take a cell line and put it inside an animal, it creates a strong selection pressure. Whichever subpopulation gets an edge—whether by proliferating better or surviving in this difficult, distinct environment—that population will come out on top.

Depending on where exactly the cells are implanted, how many cells there are, and how the animal reacts to them, you can see very different dynamics emerge. This is well accepted when working with animals, as animal tumors can grow quite differently even without any treatment. That’s why there's a growing push toward non-animal models: mathematical models, organoids, and ex vivo systems like keeping patient-derived tissues alive in the lab.

Animals are still useful, but we now know they can give us misleading signals. Many drugs have cured cancer in mice—but failed completely in humans.

Isaac

Could that variability also be due to tumor shape or spatial structure? Like in your “carpet patch” hypothesis?

Dr. Anderson

Absolutely. How well-mixed tumor subpopulations are—and whether they’re clustered or dispersed—can drastically affect dynamics.

We once published a simple model: take 100 cells and seed them randomly vs. placing them in a tight cluster in the center of a domain. The clustered cells compete immediately and grow slowly. The scattered cells don’t compete at first and grow exponentially.

So, spatial interactions influence not just growth, but also migration, nutrient access, and response to therapy.

Isaac

Yeah, I’ve seen that in VisualPDE—it’s helped me understand how space matters in tumors. I’d love to ask about the evolutionary tumor board. How is that different from a traditional cancer care team?

Dr. Anderson

This is one of the more exciting initiatives we’ve done. Normally, to change clinical practice, you need a clinical trial. But trials take years—we have trials in years 5, 6, even 7 right now.

Tumor boards, on the other hand, are routine clinical meetings. A group of oncologists, radiologists, pathologists, and others meet to discuss complex patient cases and make decisions in real time.

Our idea was: what if we added mathematical oncologists and evolutionary biologists to that team? We could build a mathematical model for a specific patient to forecast their disease and optimize treatment.

Unlike trials, we only have a week to gather data and make a recommendation. It’s fast.

One major challenge was getting access to temporal clinical data—what treatments the patient received, when, and how their tumors responded. Clinicians often don’t have that at their fingertips.

So, we developed a visual timeline—a plot showing tumor burden, metastases, and treatments over time. This was a revelation for clinicians and essential for our modeling.

We then use historical data from similar patients to build virtual cohorts. These help us match our real patient to a digital twin, which we use to simulate different treatment strategies.

We’ve now done this for around 25 patients across different cancer types. Once you’ve done all that work for one disease site—building models, collecting data—you can reuse it for future patients.

Isaac

We’re almost out of time. One quick question about the high school internship program at Moffitt: What inspired you to start it, and what do you hope students take away from it?

Dr. Anderson

The idea actually came from Heiko Enderling, who used to be at IMO. One of my PhD students, Derek Park, had been a high school intern in a program Heiko ran back in Boston. That experience eventually led him to pursue a PhD in mathematical oncology.

So, we thought—why not try this at Moffitt?

Our goal was to catch students early, while they’re still deciding what to major in, and show them that math and biology can go together. Traditionally, students in the life sciences avoid math—but we wanted to change that.

We started with local students, but the demand grew, and we expanded it nationally. It’s an 8-week research project, and it’s real science—not just shadowing. Some high school interns have even been co-authors on publications.

It’s intense for both students and mentors, but it’s been incredibly successful. We now get over 200 applications for just 15 spots.

Isaac

Last question: What do you hope to see in the next five years of mathematical oncology?

Dr. Anderson

I’d love to see more departments dedicated to mathematical oncology. Right now, we’re the only full department in the country. But we’ve worked hard to build community and share resources.

Check out mathematicaloncology.org. We run a weekly newsletter, do YouTube lectures, create art, and host an annual conference and workshop. It’s all about growing the field.

Ultimately, I hope that every cancer center in the US has at least one mathematical oncologist on staff—not just as an add-on, but integrated into patient care. That’s how we’ll really start making faster, smarter progress in cancer research.

Isaac

Dr. Anderson, thank you so much for sharing your insights today. It's been really interesting hearing how math and medicine can come together to tackle cancer.

For everyone watching—if you're curious about math, biology, or cancer research, I encourage you to explore Dr. Anderson’s lab or apply to Moffitt’s high school internship program. Links will be in the description. Thanks for watching!