The term “mathematical biology” might have been considered an oxymoron more than a few decades ago: How could mathematics enrich the largely descriptive disciplines of biology? But Trachette Jackson of the University of Michigan has become a pioneer in this area, bringing deep mathematical insights to cancer therapeutics. In this episode, Jackson tells host Steve Strogatz how a tumor resembles a box of pencils, and how she came to appreciate the usefulness of mathematics for piercing biological mysteries.
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Trachette Jackson: I met the director of that program, who actually ended up changing my life by calling me into his office and saying, “How do you like engineering? You don’t, do you? You need to major in math.” And he sort of invited me to major in math, well, kinda ordered me to major in math, but that was a decision that changed the course of my life, and he sort of extended the invitation. He said, “You can contribute to this field, you are good,” and he — I mean he sort of, you know, let me know that there was a place for me in mathematics.
Steve Strogatz: You’re bringing a tear to my eye here, Trachette.
Jackson: Oh, really?
Strogatz: Come on, yes, it doesn’t… I hear you don’t have emotion in your voice as you tell it, but it’s a very powerful story you’re telling.
Jackson: Yeah, it is.
Steve Strogatz [narration]: From Quanta Magazine, this is The Joy of x. I am Steve Strogatz. In this episode, Trachette Jackson.
Jackson: I think I’m trying not to be at this point.
Strogatz: Okay, I’ll cry for you. I’m already choked up here. I mean the thing that started making me cry was when you said he — even repeating it is gonna get me going here — when he says you’re good. How important that is to hear that.
Jackson: Yeah, he did. It really was. It gave me the confidence to think, you know, maybe I could be good.
Strogatz: Trachette Jackson is a mathematical biologist who specializes in cancer research. Trachette is especially interested in what she calls targeted therapies, which is the attempt to use existing drugs or sometimes create new chemotherapy drugs that are targeting directly the cancer and not causing collateral damage with the rest of the body which is the thing that makes chemo so nasty. But there are all kinds of mathematical issues that arise like what dose to use, what timing should you leave between doses. So, there are quantitative issues where math really comes into play.
Strogatz: My mother had cancer, thyroid cancer actually, when I was 3 years old or so.
Jackson: Oh, wow.
Strogatz: And so, it didn’t mean… You know, I was too young to understand what was happening, but she used to have to go get radiation treatments at Yale New Haven Hospital, and they essentially… I mean, she was really scared of dying, so it was scary. I mean it was really scary, but fortunately, my mother did live years after that. I don’t know how relevant that is, just that cancer is such a… You know, we’re gonna be talking about it scientifically and mathematically, but it’s a real thing that really — people really suffer from.
Jackson: Yeah, right. It’s a personal thing, it really is, and yeah.
Jackson: Yeah. I lost both of my parents and both of my in-laws to cancer, so…
Strogatz: Oh, my God.
Strogatz: Oh, I’m so sorry to hear that.
Jackson: Yeah, yeah.
Strogatz: Really, oh, wow.
Jackson: And so, it just makes working in this field all the more personal for me, for sure.
Strogatz: Wow. How young were you?
Jackson: So, my mother passed away about 10 years ago. She was only 55. And my father just passed away last year on Father’s Day, unfortunately, yeah.
Strogatz: Oh, my — wow.
Strogatz: Yeah, I see.
Jackson: Yeah. So, I mean, it does make — it really hits home, to not just me, to a lot of people. Like you said, so many of us have been touched by this disease.
Strogatz: And it’s so mysterious in a way, that it’s something that our own cells start to do wrong.
Jackson: At its core, cancer is just the name given to a collection of diseases, and I think that’s important to note, that cancer isn’t just one disease. It’s over 200 different genetic diseases.
Strogatz: Wow, hmm.
Jackson: And they’re characterized by just the abnormal growth of cells. So, there is this article in Time Magazine that described cancer — I’m just gonna read a little bit of what they said because I really like this description. It says it’s an intricate and potentially lethal collaboration of genes gone awry, of growth inhibitors gone missing, of hormones and epigenomes changing, and rogue cells breaking free.
So, it’s kind of a colorful description, but it gets at some of the key features of cancer. It starts off as a normal cell. They acquire a series of mutations that give those cells or that single cell a selective advantage, allowing it to divide faster and ignore cues that tell it to die or to stop dividing. Instead, that cell begins to grow out of control, and that’s when you get a tumor.
Strogatz: Is it sort of like several things have to all go wrong?
Jackson: Yeah, so more than one thing has to go wrong. It’s a series of mutations has to happen that allow these cells to, sort of, do all of the bad things that they do. Your normal cells are really controlled and regulated, and when they should divide and how long they should live and do their job and… They pay close attention to cues from their environment, letting them know when they’re no longer needed. Cancer cells sort of bypass all of that machinery, and it takes several mutations and several steps and stages for all of those things to happen.
Strogatz: I see, I see. So, yeah, so it really is sort of like lightning having to strike not just once but a few times. Like you really have to get unlucky in a few different ways.
Jackson: Yeah. Yeah, you do, but it’s happening more and more often. I mean, it’s more and more common to have these mutations arising, and the cancer is the cause.
Strogatz: Oh, really?
Strogatz: Why? Is that because we’re living longer, or because of the environment, or what kinds of thing?
Jackson: Yeah, that’s a good question. I think it’s a combination of all of those things. Cancers are formed for different, environmental, oncogene reasons, and so I think there is a combination of all of those things. We live longer, our diets are different, our environments are different, we’re exposed to different things, all kinds of reasons.
Strogatz: Trachette knows so much about cancer and biology and math that I was surprised to learn that she didn’t start off in any of those fields. She went to college planning to be in engineering, and then the mentor that she was talking about convinced her to switch to math.
Strogatz: So, what happened then? You switched into math, and what was that like?
Jackson: They had a pure and applied sort of tracks in the major, and I didn’t really know the difference, so I was going along a pure track, and I started doing some research with a professor on a very pure topic. And, you know, it was okay, but I wasn’t really enjoying it. Luckily for me, in my junior year, Arizona State got an REU grant from the NSF to start having students do research, and connecting the research with science. So, I got involved with that, and that’s when I saw applied math as an option, and actually math biology as an option.
I started doing some research with a professor named Betty Tang, and we looked at the growth of bacteria in the gut, and we started to try to mathematically model it. And this really was the turning point for me, to know that this is a type of math I really like. I like applications. I like, you know, differential equations. And so, I sort of switched from the pure track to the applied track. And then I knew that going on to graduate school in that direction was what I wanted to do.
Strogatz: And help someone visualize what it means to be a mathematical biologist or a student.
Jackson: A student. So, at that time, the disciplines were pretty separate. I mean, either you liked math or you liked biology, and it was…
Jackson: Not many people, at least that I knew of, were integrating the two at the level of undergraduate education. So, when I found out that they were trying to do this for the first time, to get some undergraduate math students to come over to the biology side, I was very skeptical. I was doubtful that math could make any contribution. I didn’t see any connection. And it was really eye opening to, you know, really get my hands dirty, and start working in these areas.
But yeah, I approached it with a little bit of skepticism and a little bit of, like, concern. Like, people really think you can say something mathematical — you do math on these biological problems? But yeah, it was really eye opening.
And I had started this research project, and then maybe a semester later, Jim Murray had flyers — they were flyers about him coming, and they were all over the math department. And I thought, okay, really? His talk looked like it belonged in the biology department or the ecology department, because it was about leopards and spots, and there was really no math in the abstract, and you know, I… But I was working on a math biology project, so I said I’m going to go to this talk. And it was the very first talk I’d ever gone to as an undergraduate.
[RECORDING OF JIM MURRAY LECTURE PLAYING]
Strogatz: Well, it must have been a very startling and eye-opening experience for Trachette, that something as vivid as questions of how the leopard gets its spots or how butterflies get the patterns on their wings, how that can be translated into this invisible but very powerful world of abstract mathematics. You know, this age-old question of how the leopard got its spots can be answered with the help of calculus combined with chemistry combined with biology.
This is a very much, you know, late 20th-century discovery. People didn’t know how to do it until, really, starting in the 1950s with the work of Alan Turing, which then, in Jim Murray’s hands, and then in the hands of his students like Trachette Jackson, is now helping us understand all kinds of biological pattern formation, with implications not just for leopard spots but the patterns that, unfortunately, we see in cancer.
Jackson: But I came away with an even more profound understanding that mathematics can be really impactful. Not only in the type of biology problem that I was working on, this bacteria problem, but he was talking about developmental biology and medicine and all of these cool applications. It’s like it was a snowball effect — things started, and I saw math kind of making its way into biology, and then all of the sudden it snowballed, and I was seeing it everywhere.
Strogatz: So, Trachette started to see how these two disciplines, math and biology, could work together, and that’s a big deal. Mathematicians and biologists have completely different scientific cultures, different languages, different standards of evidence. We don’t talk to each other easily. Biologists are trained to love details and specifics. Mathematicians, on the other hand, love grand generalities, grand unifying theories And so as a result, there is a huge gulf between the two cultures. But eventually, Trachette started living in both of these scientific worlds by researching cancer treatments.
Jackson: I’d say I’ve been working in the field that’s now being called mathematical oncology for a long time. For over 20 years, and before the field even had a name, really. And that really started in graduate school. I didn’t realize I would end up working in cancer, per se, I just knew that I was interested in mathematical biology in general.
And in graduate school, I was at the University of Washington in Seattle, and they had what was called back then an applied math clinic, where they would have people come in from industries around Seattle and talk to us about problems. And we’d get in together in groups and try to work on them. And some scientists from a pharmaceutical company came, and they talked about developing a targeted strategy for cancer chemotherapy, and wanted some graduate students to work on it. And I sort of volunteered to take the lead, and that turned out to be my dissertation. Yeah.
Strogatz: What kind of company — who was it that you said came, again?
Jackson: His name was Peter Senter and he is with a company called, now, Seattle Genetics.
Jackson: It’s a pharmaceutical company out there. And they were designing these two-step drug targeting strategies. So, one of the biggest problems with traditional chemotherapy is that it will — it’s a drug that will attack cells that are dividing, and not just cancer cells divide, right? Some of our normal cells are actively dividing.
Strogatz: Sure. Yep.
Jackson: So, they wanted to figure out a way to get these drugs directly to the tumor site, so that it would have better efficacy and selectivity. And so, they designed this two-step process where first you would deliver a harmless pro-drug to the patient that would bind specifically to cancer cells, and then as a second step you would deliver an antibody-enzyme conjugate — that’s the pro-drug, and in the second step, you would deliver an actual drug that’s only activated when it came in contact with that enzyme.
Strogatz: There is an analogy that helped me understand what’s going on here. There is something called laser-guided weaponry, where the military will shoot a laser beam on a target and then that guides a missile to the spot. And so, the idea of laser-guided weaponry is, you just hit what you’re trying to hit.
So, cancer doctors have a similar issue: They want to put something like a laser-guided weapon on the cancer cell, and hit the cancer or the tumor, and not hit anything else that’s healthy surrounding it. And so, when Trachette talks about the antibody-enzyme complex, the antibody is sort of playing the role of the laser. It’s going on there and binding, attaching itself to the tumor cells and not to normal healthy cells.
The enzyme is a thing that is sitting there, waiting for what she calls the pro-drug, which is like the missile, except that it’s not deadly until it reaches the enzyme, and then the enzyme flips a switch and makes the pro-drug into a genuine drug. Now, what that does is, it sort of causes the medicine to be delivered right where you need it, to kill the cancer cells at the spot where they are.
Jackson: So, the idea was, that active drug would be enzymatically or catalytically created at the site of the tumor, and not anywhere else in the body, and therefore you would get selective and targeted benefit at the cancer site.
Strogatz: That’s very cool. I’m still trying to wrap my mind around this very clever strategy that… Because people know that when you say, take — have chemotherapy, you get really sick, aside from having cancer —.
Strogatz: It makes people super sick.
Jackson: It does.
Strogatz: Right. And that’s, I assume, because other cells are getting wiped out that shouldn’t be, or just all kinds of things are getting messed up as side effects.
Jackson: Exactly, exactly. All of the side effects are due to the fact that it’s not selective to cancer cells, and it’s impacting other cells in the body as well.
Strogatz: Okay, wow. So, there you are as a grad student. I’m picturing you in your 20s, maybe.
Jackson: Yeah, yep.
Strogatz: Wow. And so, you hear somebody from industry, from this pharmaceutical —was it a startup at that time or —?
Jackson: At that time, it was brand new, yeah, just starting, yep.
Strogatz: Huh. And I mean it’s just such a cool picture, thinking of this young, ambitious grad student. She is sitting there, and she is wondering, “What am I gonna do with my Ph.D.?”
Strogatz: I don’t — you know, and then — yeah, tell me, what was it like?
Jackson: That was exactly what it was like. I had no idea what I wanted to do specifically. I had fallen in love with mathematical biology late in my undergraduate training, so my biology background was very weak at the time. I had a lot of learning to do. And it was a little overwhelming to think about “which aspect of biology do I want to focus on?”
And this was a great way to hear important problems and questions from the people working on them, and to get a chance to kind of narrow down my interests and focus. And so, this fell into my lap, and it was really a great experience. I worked with great people. I was spoiled a little bit, because they would do experiments when I needed data. And I thought that was gonna be what the rest of my whole career would be like.
Strogatz: Yeah, maybe not, all right.
Strogatz: Wow. But still, what courage you must have had to think — or well, foolhardiness, something.
Strogatz: You know, because you said you didn’t have much bio background at that point.
Jackson: No, no, I didn’t. I was learning on the fly, learning as I go, as I went, I should say. Yeah.
Strogatz: Maybe more honest to say it the way you just said it.
Jackson: It is, actually.
Strogatz: We’re all learning as we go, all the time.
Jackson: Still learning as I go. I still am.
Strogatz: Yeah, we do.
Jackson: I still am, yeah.
Strogatz: No, that’s the fun of it. What helped you have the confidence to take that big dive? Was it the people around you or maybe just your natural self?
Jackson: I think I came into a very, very advanced cohort. These were very good people who came in, and I was from a state school and they were from MIT and Cal Tech, and so that was a bit of a knock to my confidence. But when I saw them stepping forward and, you know, volunteering to take leads on projects, when I heard something interesting to me, I just, you know, felt the urge to speak up and say, “You know what, let me give this a try. I think I could probably do this too.”
Jackson: “They’re all doing it, let me see if I can do it too.”
Strogatz: What was the question then that you tried to work on?
Jackson: So, they wanted to first of all determine how well the antibody-enzyme conjugate was targeting the tumor. So, we developed a model of, sort of, injection into the blood, diffusion into the tumor tissue, and looked at how far such a… The molecule itself is sort of large, so we wanted to know how far it would actually diffuse into tumor tissue, and is that a limiting factor to drug generation and questions like that.
And then they also wanted to know if we could say something about the timing of how long you should space out giving the thing that attaches and the pro-drug. So, we did some optimization simulations, and tried to figure out the best dosing schedule for giving the two-step process.
Strogatz: Okay. So, we give the pro drug, and then you said that one question was, how far is it likely to like penetrate the tumor, right? Maybe it just attaches on the surface, but ideally, you’d like it to kinda get in there and diffuse and —
Strogatz: All the way through the tumor.
Jackson: It would be nice but yeah.
Strogatz: Ideally, I suppose.
Jackson: It doesn’t. So, just to avoid confusion. So, the first step is the administration of the antibody-enzyme conjugate. So, the antibody is what’s going to attach to the markers on the tumor cells.
Strogatz: Okay. Yes.
Jackson: And there’s the switch, the enzyme that’s connected to that is what’s going to make the pro-drug active when we give it. So ideally, it would be lovely if that molecule was able to diffuse all the way through the tumor, and sort of attach uniformly to tumor cells, but of course, that doesn’t really happen. There’s all kinds of reasons that it doesn’t. It’s big, it’s bulky. And they did some work trying to — and one of the outcomes of the model was suggesting, figuring out ways to make it smaller, and they tried to make it smaller in certain ways, so that it could diffuse further into the tumor.
But then, there is this increased pressure within tumors that also blocks these things from getting in. So, there was all these impediments, from getting it all the way uniformly distributed into the center of a, you know, reasonably sized tumor mass.
Strogatz: So, as we’re putting the antibody, that’s the first one —.
Jackson: That’s the first one, yes.
Strogatz: That’s what I should be calling it?
Strogatz: Yeah. So, putting the antibody in, it’s gonna — like I’m picturing — I realize it’s wrong but just to have something in our head.
Jackson: No, yeah.
Strogatz: Like picture a big roast beef or something like that.
Strogatz: And we’re spraying it, or we’re somehow pasting — I don’t know, painting it or something with molecules which we’re hoping are gonna seep in there. These are the antibody, maybe they’re just sitting on the surface or maybe they’re seeping in, and then you mentioned pressure. Like there is something that’s pushing them back out.
Strogatz: In the tumor, it’s sort of resisting and saying, “You can’t come in here.”
Jackson: Right, right. So, if I could change our picture just a little bit.
Strogatz: Yeah, give me the better picture.
Jackson: Maybe just think about — this is how we actually modeled it — as concentric cylinders. So, a blood vessel is a cylinder and —
Jackson: It feeds a certain radius of tissue around it. And so, you would inject these molecules into the blood vessel, the inner cylinder, and you’d watch it diffuse out into the surrounding tissue that that blood vessel feeds. And you want to see how far — can it reach all the way through the distance of the tissue that that blood vessel is supposed to —?
Strogatz: Oh, okay, thank you.
Jackson: Yeah, does that make some sense?
Strogatz: That sounds more like a mathematical model, right. So, there is this cylinder and there is the stuff diffusing out radially —
Strogatz: From the cylinder.
Strogatz: Okay. Well, I wanted to have a picture.
Jackson: I like the roast beef too but…
Strogatz: Okay, now I have a little more of a picture. Well, because when you say “tumor,” I don’t know what to picture. What should I picture when you say —?
Jackson: Yeah. So, we — yeah, it is hard.
Strogatz: Actually, yeah, tell me how to think of that.
Jackson: It is challenging to figure out how to mathematically picture a tumor — and we had to make a choice on how to do it. So, we decided to view the whole tumor as a collection of these, what — they’re called Krogh cylinders, of capillaries fed — that feed certain regions of tissue. And there’s a whole bunch of those that make up the tissue of a vascular tumor.
Strogatz: Krogh is K-R-O-G-H. K-R-O-G-H is a Mr. Krogh, I think it’s August Krogh. Krogh was interested in the diffusion of oxygen out of capillaries into surrounding tissues, and so he thought of a capillary as like a cylinder. And, you know, he was interested in the spread of oxygen to neighboring tissues.
Now, what Trachette is doing is, she thinks of a tumor as a kind of tissue, and she thinks of it as being made up of cylinders, which you can picture as a box of pencils. This is an analogy that people use in this field. So, if you think of a box of pencils, in this analogy the pencil has a lead, that’s like the capillary going up the middle. The wood surrounding the lead would be like the tissue that’s being fed by that capillary. And the fact that you need a lot of pencils is because you’re describing a whole tumor. The tumor is — she conceives of as a box of pencils, all these cylinders, each being fed by their own capillaries and this, of course, is a bad thing. The feeding is the feeding the tumor, that’s what she was referring to as a vascular tumor. A tumor that’s being fed by blood vessels that have been hijacked to help the tumor, you know, stay alive and grow.
Strogatz: Just to say a little about the enterprise of what it means for a mathematician to be thinking about this, rather than a chemist or a biochemist or, you know, an oncologist. You’re going to use a computer, I suppose.
Strogatz: Or you might just use pencil and paper.
Strogatz: But tell us what that part looks like. If you say it’s the computer, it sounds like you are using computers.
Jackson: Yeah, so we definitely use computers. So, the first part, I guess, is the pen and paper part for us, is the actual writing down of the mathematical equations that we think describe the underlying mechanisms of, you know, whatever problem we’re working on. And that can be, you know, the hardest part. Well, one of the hardest parts is, you know, coming up with the actual mathematical formulation. Going from a biological question in words to first being able to wrap your mind around the complexity of the biological problem and simplify it down into something that you think you can model. And then actually going from words, something that you can articulate in words, into mathematical language is often one of the harder parts of the problem, and that’s the first step that we do.
And even before we go to the computer one of the — the second step and also a challenging part of the problem is determining parameter values that we need for our mathematical model. So, that also takes some time and some care and some attention. And then we’re ready to go to the computer.
So, we use the computer to solve these systems of… Usually, the kinds of models that I develop are differential equations, models, so either ordinary or partial. And so, then we go to the computer to solve that system of equations with parameters that we think connect to the experimental literature, or experiments that have been done in the lab directly for these — to answer these questions.
Strogatz: There’s still something missing, which is what these equations are describing.
Strogatz: That they’re, I’m guessing, things like, what’s the concentration of, of what? Of antibody as a function of position and time.
Jackson: Exactly, exactly.
Strogatz: Or something like that.
Jackson: So, for that particular example, it would be the concentration of the conjugate. We did do it in time and space because it was sort of radially diffusing out. The concentration of the pro-drug in time and space. And then, you know, we actually had a cellular component of the model. So, we had a rate of change of the number of cancer cells and that kind of thing.
Strogatz: Okay. So, it’s a lot of bookkeeping of how many cancer cells are here and there or somewhere else right now, and how much will there be later.
Strogatz: And how much antibody and how much enzyme and how much — you know, like it’s all that.
Jackson: All of it.
Strogatz: It’s a lot of bookkeeping of how much stuff is there in all the different places —
Jackson: It is.
Strogatz: At all the different times. And then, how will that predict how they will change over time as physical and chemical and biological things are happening to them as they’re —.
Jackson: Exactly, exactly.
Strogatz: Diffusing, as the drug is doing its thing against the cancer cells, et cetera, right? It’s — you’re trying to do a big simulation of what’s really happening —
Strogatz: In the tumor.
Jackson: Exactly. We’re trying to use all of the information that we can get about the biology of the tumor growing, and the biology and the chemistry of what the drugs are supposed to be doing, and how the cells are supposed to respond to that. And like you said, we try to incorporate all of that into some mathematical equations that can be predictive. To say, okay, if we give this amount at this time, and then we wait two days and give the drug, we’re going to generate X amount of active drug and kill Y amount of cancer cells.
Strogatz: But I mean if you didn’t have math and you’re just using words, you’d think, “Okay, I add some more drug, maybe I kill some more cells,” or “I kill some more cancer cells.” But this is a way of being much more precise.
Jackson: Precise and quantitative, yeah. Yeah, you can get, you know, depending on how well your parameters have been trained and adjusted, you can be pretty precise, and get some quantitative information about what should happen in terms of tumor reduction and drug generation, and all that kind of — yeah, cool stuff.
Strogatz: And the goal here was to help this company, it sounds like, optimize their drug, make their drug —?
Jackson: As possible, yeah.
Strogatz: As effective as it could be?
Jackson: Yes, yes.
Strogatz: I’m guessing that you couldn’t really see the payoff of what you did on patients. That would be way off in the future, is that right?
Jackson: Yes. This is — no, this was well before this process had been, you know, in clinical trials and things. They were doing experiments in mice, trying to, you know, get to the point of proposing a clinical trial and — yeah. So, this was very early. Most of my work is preclinical, it’s the very early stages.
Strogatz: I see. Well, very fundamental in that sense, maybe. But does this technique exist today? Is this something that people use?
Jackson: This technique does exist today. People have gone even further. They have done really good jobs at making… They have now actually made an enzyme that they can connect directly to a drug small enough and light enough, and figured out how to get it to penetrate the tumor better. So, these strategies have evolved, I’d say, and are still being researched and perfected.
Strogatz: So, the use of antibodies here makes me wonder if there is a connection to what people call cancer immunotherapy. That’s a different thing, is that right?
Jackson: That is a different thing. So, that is using your body’s own immune system, or trying to boost the immune system to fight cancer, and that is another very hot topic right now, something that’s of great interest. It has been around for a long time. It’s got this resurgence of interest lately, though. I am actually beginning to work… So, this is a new area for me, but I’m beginning to work with physician-scientists at the University of Chicago to develop a mathematical model to help us understand a little more about tumor immune dynamics in bladder cancer.
And so, we want to… So, my expertise has always been in, sort of, targeted therapeutics, but they want to look at these targeted therapies that I am familiar with in combination with some new immune therapies, because they think combination therapies are probably the way to go. And so, we’re developing a framework to model the integration or combination of immunotherapy and some of these receptor-targeted therapies.
Strogatz: Well, when you said that you think combination therapies may be the way to go, I am guessing that is because it might be harder for the cancer to become resistant to the therapies if you gave a combination —
Strogatz: Like in the way HIV —
Jackson: That is —.
Strogatz: Is that the argument in this case too?
Jackson: That is the argument, yep, combination therapies. So, there’s so many different molecular drivers of cancer. If one therapy inhibits one of those molecular targets, there are so many others. So, coming at cancer in a variety of different ways will hopefully reduce resistance and lead to better efficacy, and improve survival eventually of patients, yeah.
Strogatz: When we come back, Trachette uses math to target the most dangerous cancer cells.
[MUSIC PLAYS FOR BREAK]
Jackson: Over winter break, we just found out that a paper that we submitted to Cancer Research — which is one of the, sort of, big journals in my field. It’s an experimental journal that doesn’t typically look to mathematical approaches as their number one thing to publish, but —.
Strogatz: This is a very big understatement you’re making.
Strogatz: In other words, they don’t think mathematicians have that much to tell them.
Jackson: They’re learning about what we have to tell them, I think, and I think it’s changing a little bit.
Jackson: But we’re just excited that we got a paper accepted there. We just found out. And this work is dealing with cancer stem cells. Now, these are a population of cells that have been identified in a wide variety of cancer types, but they’re a small population of the cells. But they are really the drivers of tumor initiation, of tumor spreading. They play a big role in therapeutic evasion and recurrence. They really are the most important population in growing tumors.
So, when you think about it like that, conceptually, it makes sense: Well, let’s target this population. If we can get rid of that population, then we get rid of the driving force behind the whole cancer. But unfortunately, there just really aren’t that many therapies out there that are directed at these stem cells.
So, in this work, we looked at one particular target and developed a mathematical model for targeting the cancer stem cells along a particular pathway. And we looked at the targeted therapy in combination with chemotherapy, and did some optimization on how to schedule the dosing for those two drugs. Experimentally, they thought that they should just co-treat with the two drugs, give both drugs at the same time. Turns out the model predicts that that is antagonistic in almost all cases.
Jackson: But we were able to show that if you pretreat with a targeted drug, wait a week, give the chemotherapy, and then repeat that cycle, you will get a synergistic effect.
Strogatz: So, her therapy is to give two different drugs, one which will kill the stem cells and the other which will kill the bulk of the tumor, the other stuff. And what she found with her math — and this, I thought, was wonderful — she says that her mathematical model showed her that if you give the two drugs at the same time, they have an antagonistic effect on each other. They can kind of cancel each other out, which is not what you want, and which is what the doctors at first thought they should do.
But the math showed, no, it’s actually better to give the drugs on alternate weeks. Those two drugs given in this alternating week cycle will have, as she put it, a synergistic effect. They will actually cooperate. They will help each other. They’re better together than they would be separately.
Strogatz: And now you talked about targeting the stem cells.
Strogatz: These are the heads of the operation.
Strogatz: I mean these are the really bad guys —
Jackson: They are.
Strogatz: Because as you say, they have so much potential to help tumors evade treatment, to cause tumors to come back.
Strogatz: You know, recurrence, you mentioned. So yeah, if you could knock out these stem cells or at least — and you say part of the difficulty is there aren’t very many of them.
Jackson: They’re small.
Strogatz: So, I guess they’re hard to find.
Strogatz: Yeah, they’re small, there’s not too many. How do you look for them? How would — what is the technique to find, to target them and not someone else?
Jackson: That’s a really good question. About identifying stem cells, that’s a whole can of worms in itself. So, there are certain sets of markers that scientists believe identify stem cells, but there is some debate still about that. So, we have a set of markers that we believe identify the stem cells in the type of cancer that we’re working on, and we’re working on head and neck squamous cell carcinoma. And so, we have a set of markers that we believe identify the stem cell pool of that particular cancer, and we can isolate the cells with those particular markers. Well, not we. My collaborators can do the experimental stuff.
And in so doing, they found that a particular chemical mediator is really important to the growth of these cells, the self-renewal, the survival, and all of the potential bad things that these cells do. So, the target was actually this chemical that stimulates these stem cells.
Strogatz: What it is, is a thing called IL-6, that’s interleukin-6, and that’s an immune system molecule that occurs naturally in our bodies when we’re fighting either infections or injuries to our tissues. IL-6 is part of the inflammatory response, and so what her collaborators and others have been figuring out is that the stem cells that are responsible for these kinds of cancers, head and neck cancers, the IL-6 is helping them. This is like an accomplice, okay? If the cancer stem cells are the villain, IL-6 is an accomplice that is helping stimulate those cancer stem cells and feeding them.
And so, if you could knock out the accomplice, that’s the target. So, that’s what they’re actually doing. In her math model, when she talks about interfering with this chemical mediator, she is talking about blocking the action of the IL-6. And so that will cause the stem cells to wither.
Strogatz: What’s the future of cancer research? Or what do you think are the big areas for mathematicians to contribute to cancer research?
Jackson: So, I think the next horizon, which we’re just cracking the surface of right now in mathematical oncology, if you will, is precision medicine. We want to be able to make our models and our predictions patient-specific. So, we want to be able to take data from a particular patient’s physiology and molecular makeup in their particular cancer, because it… You know, cancer is over 200 different diseases, but it’s different in every person, you know. Even each type of cancer may be different in each person.
Jackson: So, if we can sort of move into personalized mathematical oncology, precision mathematical oncology, where we’re really able to take advantage of some of the molecular information we’re getting from each patient, I think that’s, you know, where we’re headed and what the future holds for us in the field, yeah.
Strogatz: Uh-huh. Is that something that’s happening right now? Or are we starting to make the first steps?
Jackson: I think it’s starting to.
Jackson: I think we’re starting to make the first steps in that. I know a few groups who are probably at the forefront of that, and I think there is lots of room to grow and lots of places to go in that area. And I think a lot more people are… A lot of people are trying to think about how they want to incorporate those aspects in their own research programs.
Strogatz: Okay, yeah. I guess it’s hard to talk about the future. It’s not here yet.
Jackson: Yeah, it’s hard. And I also hope that the future holds, you know, increased connection and collaboration between mathematicians and physician-scientists in the cancer field. I mean, cancer has been a hard nut to crack. I mean, you know, mathematics in neuroscience and mathematics in, you know, physics and mathematics in all these other, you know, areas of science seemed to have had an easier road than math and cancer for some reason.
But I think we’re cracking the surface. We’re seeing journals like Cancer Research publishing more and more quantitative papers. We’re seeing NIH sponsor centers for, you know, systems biology and cancer. Things like that are all promising signs that, you know, these connections between mathematicians and oncologists are real and promising and fruitful.
Strogatz: When I used to go to math biology conferences, we were a real fringe group back in the ’80s, let’s say. And today every big university has some kind of integrated biology or computational biology or systems biology, which brings techniques from engineering and physics and math and computers into biology and medicine. Like, that has really caught on, it seems.
Strogatz: But yet — but even having said that, you feel like cancer is one of the — is not picking it up as fast as, like, you mentioned neuroscience?
Jackson: Well, I think there’s been… There was, you know, a huge breakthrough in neuroscience. There was, you know, the Hodgkin-Huxley equations or, you know, things like — something huge to point to. And there’s lots of little great things to point to in mathematical oncology, but they’re not as well known as something like a set of equations you can point to that, you know, you think of when you think of neuroscience, or you think of fluid dynamics, or you think of — you know. Yeah.
Strogatz: That’s an interesting point you raise. So, like, if you had to ask yourself, what’s the greatest hit of math applied to cancer? It doesn’t have to be your work —
Strogatz: Maybe, what would you think is the most admirable achievement, or the best success story that we could tell? Is there one that we could tell?
Jackson: That’s a good question. That’s a good question. Like I said, there’s a lot of, you know, splashes in the pond. I think the work of Kristin Swanson in the Mayo Clinic in Scottsdale; she is doing some amazing work on glioblastoma, and she is on the forefront of personalized precision medicine with that. I think some of her work is probably what I would point to as a, you know, a bright light. Yeah.
Strogatz: To me, the big take-home message in Trachette’s work, and a real bright spot of her own making, is this interdisciplinary spirit that she is living — not just advocating, but really living it through her example. She is working with top oncologists on different kinds of cancers, head and neck. She says she is now starting to work on bladder cancer. This idea that it’s not going to be solved by the oncologists alone, that there are things that mathematicians and computer scientists can contribute — biomedical engineers, drug designers, pathologists, all kinds of people need to get in this fight and lend their expertise.
And so, to me, the bright spot is that there is now starting to be room at the table for what mathematicians and mathematical modelers have to offer. And she is demonstrating by her example that this may really lead to some exciting advances.
Next time on The Joy of x, computer scientist Melanie Mitchell tells us what it will really take ’til we have intelligent machines.
Melanie Mitchell: It’s a grand challenge to get a machine to have the common sense of an 18-month-old.
Strogatz: That’s good to remember next time you’re reading the big headline in the newspaper or, you know, one of those business magazines, that that’s the grand challenge: to produce an 18-month-old or something even close.
Strogatz: Probably even as smart as my dog.
Mitchell: No, nowhere near as smart as your dog or even, you know, in some sense, you know, even mice or things that we might think of as not very smart at all.
Strogatz: The Joy of x is a podcast project of Quanta Magazine. We’re produced by Story Mechanics. Our producers are Dana Bialek and Camille Peterson. Our music is composed by Yuri Weber and Charles Michelet. Ellen Horne is our executive producer. From Quanta, our editorial advisors are Thomas Lin and John Rennie. Our sound engineers are Charles Michelet and at the Cornell University Broadcast Studio, Glen Palmer and Bertrand Odom-Reed, who I like to call Bert.