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Foraging Strategies for Dictyostelium discoideum

Adviser: Ned S. Wingreen

Michael A. Gelbart


“A good adviser can always make a topic interesting and fun—and of course you will learn a lot from him or her in the process.”


I first worked with Professor Ned Wingreen on my spring-semester junior paper (JP). In the fall I had attended a talk of his about chemical gradient sensing in the amoeba Dictyostelium and I thought it was great. After the talk, I approached him and asked if he would advise a JP. I had some ideas about what I wanted the JP to be about—essentially extensions to the material discussed in his talk. Over the winter holidays, I thought hard and refined my ideas so that I was ready to clearly present them to him when we met for the first time. But when I got there in January, Professor Wingreen sat me down and told me a story about chromosome segregation in a bacterium called Caulobacter. After he had already spent an hour talking about my project on bacteria, I didn’t think it was a good time to introduce my crazy ideas. I hesitantly mentioned them anyway, but it was clear that I would work on the bacteria project for my JP.

At first I was quite disappointed by all this, partly because I really wanted to try out my own idea, and partly because I didn’t have any prior knowledge about (or interest in) bacterial chromosome segregation. But the project turned out to be really fun, and I learned a lot. Looking back, I consider that JP to be one of my favorite “classes” out of all those that I took at Princeton. At the end of the semester, I was feeling very positive and I thought that maybe I could go back to my original idea for the senior thesis—so that’s what I did.

As it turned out, my final thesis project didn’t have that much to do with my original idea. Sure, it was still about Dictyostelium and still involved some simulations and some game theory, but its focus was on foraging strategies, not on sensing chemical gradients as originally planned. This was probably a good thing: Looking back, I don’t think my original idea would really have led to a whole thesis worth of work. But it was a nice way to begin: I had a starting point that I felt was my own, and then I refined the question until I found something really worth addressing. This early stage of refining the questions took at least a month and was a very important part of the thesis for me. After all, one needs to find interesting questions in order to find interesting answers. Also, it was fun to meet with lots of new professors and others around campus, venturing into departments I had never set foot into (like ecology and evolutionary biology) and making new connections. In the end I decided to tackle the question of repulsion in Dictyostelium. Here’s the story, in brief: In the 1970s, biology professor John Bonner noticed that Dictyostelium amoebas repel each other, but it was never made clear why they do so, or why only some strains of amoeba repel while others don’t. Some people thought that repulsion might improve foraging efficiency (finding food more quickly), but that assumption was never quantified and it still didn’t explain why some strains don’t repel. My thesis was about understanding this phenomenon. 

I didn’t do any wet lab work for this project; it was all computer-based experiments (simulations). But, in the end, I managed to come up with a reasonable explanation for what Professor Bonner observed and suggest some possible experimental directions for this line of research. Actually, Professor Bonner is still around at Princeton (I think he turned 90 recently), and he was pretty excited about my work. It was a cool feeling to get to talk to him, since his observations from 30-plus years ago are what motivated my entire project.

Most of the actual work for my thesis was writing simulation code, something that I was pretty familiar with. I had to learn some strange programming tricks to get the code to run fast on Graphics Processing Units (GPUs), but in the end programming was not the main challenge for my thesis. Instead, the hard parts were making decisions about what direction to take the project in: Although Professor Wingreen gave me lots of guidance, he still wanted it to be my project and felt it important for me to choose where to go with it. This was one great thing about him as an adviser. Because of all this, in doing the thesis I learned much more about the general process of doing research than about the particular mathematical and computational methods involved (but I learned about these things too, of course). So perhaps I was lucky in this sense, since I didn’t need to spend that much time on the techniques. Instead, I was thinking a lot about exactly what questions I wanted to ask, because that determined which (computational) experiments I should run. 

The actual writing was a bit rushed at the end. I had to take a fairly lengthy break from the thesis in November and December to do my graduate school applications, so I felt I was a little behind schedule when January came and I didn’t have any results (even preliminary ones). But I was only taking two classes in the spring, so I had time to catch up. First, I showed that repulsion is beneficial, and then by doing evolution simulations I showed that the population can actually evolve heterogeneously, so that some cells repel and others don’t. I was pretty surprised that it worked out so well, but of course I was happy about it. Still, with about three weeks to go (or maybe even less? I don’t remember…), I hadn’t written more than a few sentences. I was a bit worried at the time but it turned out well, and writing was a lot of fun, too. For about 10 days, a few friends and I locked ourselves into Icahn Laboratory, Room 280, and just wrote nonstop. I would recommend making a thesis party out of it if you’re the kind of person that can concentrate with other people in the room. 

I started by talking about my adviser, and I think I’ll end that way, too. Doing my JP on a topic that I didn’t think I was interested in—and then loving it—taught me that the adviser is much more important than the topic. By senior year, we (or most of us) still don’t really have any idea of what we want to do. But a good adviser can always make a topic interesting and fun—and of course you will learn a lot from him or her in the process. So I would say the important part is to find a good adviser and allow yourself to become engaged with the topic. Try to come up with the questions on your own, so that you can experience what the process of doing research is like. As it turns out, it’s a lot of fun!

Foraging Strategies for Dictyostelium discoideum

Michael A. Gelbart

Ned S. Wingreen

Professor of Molecular Biology and the
Lewis-Sigler Institute for Integrative Genomics

“ other senior theses, Michael’s work has led my own research into new directions.”

For me, the senior thesis is a great opportunity for students to start doing real research. Every student who’s worked with me so far has pursued a topic that at least had the potential to contribute something new to human knowledge. Michael Gelbart’s thesis was no exception in this way, though it was exceptional in several others. What was exceptional? Well, first, Michael approached me with the topic he wanted to pursue. After a seminar I gave on campus, he came up to me and said, “I’d like to do my senior thesis on this [how well cells can sense chemical gradients], only I want to include game theory.” This was the second way in which Michael’s thesis was exceptional—I knew essentially nothing about the subject he was proposing to study. Fortunately, Michael knew quite a lot about game theory (from his excellent Princeton education!), and I knew something about how single cells can sense and follow chemical gradients. Michael’s idea was to weave these two strands together to ask how cells might compete or cooperate to find food. In fact, it took us some time to formulate a clear problem. Indeed, we worked together on a JP on a different topic before pursuing the senior thesis. Fortunately, we started talking about the senior thesis project in the spring and we had the whole summer to think things over. This is typical of theoretical research in my experience—at the early stages one has to do a lot of reading papers, talking, and ruminating to identify the question one really wants to ask. 

A critical lead came from an observation made in a 1977 paper by Princeton’s own John Bonner (professor emeritus in the Department of Ecology and Evolutionary Biology, or EEB). John was a pioneer in the study of the social amoeba Dictyostelium discoideum (Dicty), which are famous for alternating between a single-cell, foraging lifestyle, and a collective multicellular phase in which cells aggregate to form a slug and then a fruiting body. While Dicty were well known to attract each other in order to aggregate under bad conditions, John noticed that the same cells actually repelled each other under good conditions when food was abundant. This was exactly the behavior one might have expected for a cooperative foraging strategy: By avoiding each other, might cells be more efficient at group foraging?

Now that we understood the question, Michael set out to find an answer by developing a computer simulation of Dicty cells foraging on a lawn of bacteria. This “answering the question” stage of the senior thesis is one where I think students need to be given a lot of freedom. Once the question is formulated there are often many possible ways to go, and figuring out which way to attack a problem is an important part of the science experience. In this case, doing computer simulations made sense, but which features of Dicty behavior, other than some kind of repulsion, should the simulations try to capture? Processive motion, attraction to food, randomness, memory? And how to measure “fitness”? And how to implement the simulations? Some of the answers to these questions came from reading and talking to local Dicty experts, such as my colleague Professor Ted Cox from the Department of Molecular Biology and his postdoc Simon Norrelykke. Some answers came from trying to keep the simulations as simple as possible while still addressing the central conceptual question. And some just came from trying different things and seeing what worked. 

From the simulations, it became clear that, indeed, a group of Dicty cells could forage more efficiently with repulsion, but only within a range of repulsion strengths. Too little repulsion and the cells would cover each other’s territory, too much repulsion and the cells would freeze up like atoms in a crystal lattice. 

At this stage, Michael could have spent a lot of time trying out different variations of the simulations to explore this result. However, one of the things I like most about the senior thesis is that it has a definite end date. There’s no time in a senior thesis to do anything but go for the jugular. In Michael’s case that meant going for “game theory.” The idea of game theory is that competing players should ideally develop strategies that can’t be improved on, even if they know the strategies (though not the precise moves) to be employed by the other players. For Dicty, the game theoretic question was, “Could individual cells improve their own fitness (how many bacteria they got to eat) by adjusting their strategy (how much repellant they produced)?” 

The only way Michael was able to run the extensive simulations required to answer this question was with the help of Professor Iain Couzin (from the EEB department), an expert in collective animal behavior from insects to fish to humans. Iain and members of his group helped teach Michael to run simulations on their super-fast GPU computing system. With the ability to run large-scale simulations in minutes instead of months, Michael was able to let Dicty cells evolve according to survival of the fittest—whoever got to eat more bacteria in each run would have more offspring, with slight mutations in repulsion strength, in the next generation. I’ll leave it to Michael to describe the fascinating results of these simulations. Instead, I’ll just end by saying that like other senior theses, Michael’s work has led my own research into new directions. Importantly, it has started a new collaboration between my group and that of Iain Couzin. Our first task is to expand Michael’s thesis into a publication, and who knows where the science will take us from there? These are the kind of surprising developments that make senior thesis advising so rewarding!