Physics and Biology — A Stable Marriage?

Introduction

Building a toy model, as intuitive as it sounds, gets ridiculously confounding when you’re trying to match the behaviour of a dynamical system. With all the complexities involved, a biological system is just like this. Recent advancements have allowed researchers to derive more information than ever before from such a system.

How do we make sense of all this data? How do we coalesce what we know into mathematical models that help us tell stories about the biological world? We will be discussing this question and more with Dr. Akshit Goyal, Simons Young Researcher, Ramanujan Fellow, at the International Centre for Theoretical Sciences (ICTS). Before joining ICTS as a Faculty Member, Akshit did a B.Sc (H) in Physics at St. Stephen’s College, UoD, then his PhD at the National Centre for Biological Sciences (NCBS), followed by a Postdoctoral Fellow position at the Massachusetts Institute of Technology (MIT), USA. Akshit’s work is primarily focused on understanding the collective dynamics of evolving ecosystems using concepts from dynamical systems, nonequilibrium statistical physics, data assimilation and information theory.

Can you give us a brief introduction of yourself, for the people who are not familiar with you?

My name is Akshit. I am a faculty member at the ICTS, which is the International Centre for Theoretical Sciences. I am a part of the Biological Physics unit here, which consists of a bunch of people with backgrounds in physics who try to understand different aspects of biology, including biomechanics, fluid dynamics, cell biology, neuroscience, etc. I am not associated with the above fields. I work more on the ecology and evolution side, and so primarily my interests are in understanding how large collections of species come together and have intriguing dynamics. Some of these dynamics are of the kind that allow a lot of species to coexist, which is what we can see in our daily lives. My other interest is in understanding how these species evolve in the milieu where multiple species coexist as part of an ecosystem. We address these questions by applying methods from theoretical physics and collaborating with experimentalists to obtain datasets from various kinds of ecosystems.

First Forays Into Theoretical Biology

Lovely! You did your bachelor’s in physics, so did you always plan on doing the kind of research that you do right now, which is broadly modelling and theoretical biology? Or was this some event that influenced you?

This answer will sound very similar to the ones people in theoretical biology give to the same question. In my undergrad days, I did not know about the existence of theoretical biology. I decided to pursue physics because of my interest in astronomy and astrophysics. When I asked people what I should study to pursue these interests, physics was mentioned more often, and that was my choice for the bachelor’s degree.

I did my first summer project at the NCRA (National Centre for Radio Astrophysics). Everything changed in my second year, when I was ready to continue working on problems in astronomy and astrophysics. Still, my professor encouraged me to try something completely different for one summer. He was the one who asked me to give biology a shot. I was confused about this suggestion in the beginning, especially since I had not studied biology since the 10th standard. Still, this professor was someone whom I respected, so I took his advice. That is what brought me to NCBS, doing a project under Prof. Sandeep Krishna, who later became my PhD advisor.

That really changed my mind about what research was like and what research could be like. Because that summer I was free to try lots of random things, and it felt like I was creating a video game of sorts when I was constructing these theoretical biology models. This is what made me explore the field of theoretical biology and continue doing research in it.

Why Biology needs Physics

That’s a really unique trajectory! Moving on, how do we get the intuition that maybe this mathematical or physical tool might help in solving this complex biological problem?

I believe that there is a lot of scope for creativity and out-of-the-box thinking precisely because it's not obvious when you look at something in biology and get an intuition that you could visualise this problem in terms of a mathematical or physical problem. Similarly, it is not obvious when you are learning a mathematical/ physical concept that it can be applied to a biological problem. This is something that makes this profession sort of fun because you learn these concepts independently, and the adventure is in making connections between the biological problem and the mathematical/ physical concepts. Once you spend enough time in the field, you do realise that there are problems in biology that do not have good models for understanding them, and you can think of some mathematical concept that can clearly be applied.

Yes, it is often not obvious, but if you look at history, some fundamental discoveries have come from merging or marrying two disciplines, like Einstein’s work in gravitation, which is based on differential geometry. So, combining ideas from independent disciplines happens very often in scientific research, but it is obvious in the case of theoretical biology.

The Stable Marriage Problem and Consumer Resource Models

Since you bring up the word “marriage”, this might be a good time to get an intro to your past research, including the “stable marriage problem” applied to biology and the consumer resource model. Can you tell us a bit about these two problems?

I will start with the stable marriage problem. This was one of the papers that I worked on during my PhD. The problem was focused on building an analogy for microbial communities using the concept in game theory and economics called the stable marriage problem. This is a good example for the earlier question because I was reading about the stable marriage problem independently and thinking about ecology in microbial communities and how microbes interact with each other through the consumption of resources. It sort of occurred to me that this biological problem could be thought of as a version of the stable marriage problem.

The idea of the stable marriage problem is that there were men and women who had different preferences with each other for getting married and even though you might think that it is not obvious on applying this to biology, we realised that when you think about different species of microbes and different nutrients that they consume, you can often find that different microbes prefer different nutrients. This analogy was quite fun to think about, but it had a practical implication, which is that there is this idea in the stable marriage problem that there could be multiple stable configurations. Because of the link between the two, we could figure out the stable configurations of different microbial ecosystems which was a hard problem in microbial ecology.

Talking about the consumer resource model, I think that’s a more standard idea which describes how in an ecosystem containing different species, interactions between species happen through resources. There are classical models by Robert MacArthur and others from the 60s called consumer resource models which describe a simple way to incorporate the fact that different microbes (different species of any kind) consume different resources by which they grow. And by the consumption of different resources, we can find that these different microbes can compete with each other in this regard. We can study these models to understand the kind of dynamics these species present. In the past 10 years or so, my work has involved extending these classical ideas to two different realms. One is the realm of highly diverse ecosystems where we have a very large number of species coexisting with each other. This is in contrast with the classical models which incorporated two or three species. To move from these two or three species to a large number of species, we used lots of tools from statistical physics. This is where my training in physics was useful. And the second big difference from the classical model is that the classical resource models only considered competition between different species as they consume resources. But there are many cases where cooperation is observed. So, we extended the classical models to allow the phenomenon of cooperation to happen via something called cross-feeding.

Thanks for sharing that! Onto a more specific question which is coming from my friend, Arhan from Fisher’s Fishes. Since problems in biological systems are mostly non-linear, what is your perspective on how you think about the role of linearity when you look at a biological problem? We wanted to ask this question because some of your models, like the consumer resource model, assume linear relationships

The linearity assumptions that we make are a bit nuanced. Consider an ecosystem with many different species. These species exist in some steady states wherein you know for certain that some species exist and some are dead/extinct. Some of the others have survived and are surviving at different abundances which are then fixed in time. This is some steady state. When we perturb this system, some things about the environment might change, or something about the species themselves. There might be removal of some species and emergence of others, these are the perturbations we are concerned with. Now, the state of the system changes. To predict the changes in the state, we will need to do some calculations with arbitrary precision based on the details of all the interactions between the different components of the ecosystem. This is quite difficult, and this is exactly why we make the linearity assumption, which is not a linearity assumption on the dynamics. The assumption says that the change in the ecosystem state from one condition to the next is small enough compared to the kind of change that would take the system to a completely different state with very different environmental conditions. This means that there are interactions between different species and different resources, and these resources will depend on the state of the ecosystem itself. We don’t know what state the ecosystem assumes in the future, so the perturbations act on the interactions in the state which you perturbed and not on the state which you reach after being perturbed.

Is this reasonable or not? Actually, it is. The reason that this approximation is reasonable is that it is often very valid in highly diverse ecosystems. In ecosystems which have a very small number of species, this is a really bad approximation. So, the scale that you’re working on is instrumental in deciding whether such a linearity assumption is indeed valid in your problem.

The Craft of Mathematical Modelling

Those are some very valuable inputs. Onto a more general and integral question in the field of mathematical modelling. Since there is no defined framework for addressing each and every problem, how do we get an intuition towards what parameters we should really consider and those which might be significant towards the question that we are asking?

Of course, this is a difficult question with no one-size-fits-all answer. Here are my takes on this.

One, when we make a model, we are not making it in abstraction; there will always be a purpose. For the same system, we can make very different models if we consider different purposes. So, the phenomenon you’re considering as important while writing down the equations should depend on the phenomenon you’re trying to address with the model for this system. For instance, when we consider the growth of a bacterial species, it might be very important to consider what nutrients are available and how these bacterial species take up the nutrients. These bacterial species will be subjected to all sorts of forces and surface tension from other bacteria surrounding them. While these forces are also important in nature, it might not be so relevant if your goal is to explain the rate at which bacterial collectives grow. When this is your goal and your system is well-mixed, these forces can be neglected while making the model. On the other hand, if your bacteria are on a rigid surface like an agar plate, where they’re far away from food and the only way to obtain the food is to push and pull at each other, a model that describes the growth of collectives should also include these forces.

Over time, you can gain a lot of experience and that kind of teaches you a lot about what will ultimately be the most important and least important factors when it comes to a particular system and purpose. It is sort of like we build an internal library about all the models you’ve built and all the approaches you’ve considered and what eventually worked out for the model.

Two, it also depends on the aesthetics, but as a physicist or as scientists in general and reductionist. We always find it aesthetically pleasing when something simple produces something complicated. So, we always kind of try to err on the side of the simplest possible model that is sufficient to explain the phenomena that we’re interested in.

The Reading Trap

I’m definitely keeping these in mind, especially the second point. Now, onto the next question for this session. For someone who is interested in the idea of understanding biology or biological systems from a theoretical and mathematical perspective, are there any key resources that could be kept in mind? Are there any key papers or books that helped you, especially in the initial phases where you were just getting started in the field?

I have a completely opposite perspective on this. I believe theoretical biology is one of the rare disciplines in science where the best way to get a feeling for it and to get started is to just do something. And this is opposed to a lot of other fields of physics, where you would often need to read books, papers, and learn a lot of things to get started and get a feeling for what it is like to do something new and interesting and research-worthy. You can actually get started in theoretical biology tomorrow because there are thousands of problems out there. You can pick up any decent set of papers or talk to anyone doing theoretical biology, and they will present you with 10 or more problems. Further, you can read a few things about these problems and come up with ideas that should be tried. So, it’s very simple and easy for you to get started on your own.

My strong recommendation to any student out there who wants to get started in theoretical biology is not to get stuck in the trap of reading. I think reading sort of paralyses and doing sort of catalyses. I feel that in theoretical biology, you should read after you do something. Because in the process, you get to know what your system is doing, how it’s behaving, and then you try maybe something else. So, only after you do something should you read what other people have done. This can help you understand what you’ve done fits into already established models. This is what I did in my first summer project, so maybe that’s why I’m biased, but I just played with some model of something, and I had a lot of fun doing it. And it’s only after that did I start to read the classic understanding of these kinds of phenomena. And what I found was that a lot of the things that people were talking about in the literature, I had kind of already realised myself by playing around with the model for just a month or two. So again, a lot of these things are accessible. They’re a lot of fun because they’re creative.

What I often find is that students read first and that paralyzes them because it sets them into one perspective or one framework of doing something. And this is not the field where it’s so rigid that all the frameworks are decided for you. You stand to make the biggest impact by actually not thinking like the way everyone thinks. If you think the way everyone thinks, you might become completely replaceable. But if you think about the problem from a different perspective, that’s when you’re going to be valuable and that’s also when you’re going to have fun because you’re going to have your own take on thinking about something.

The more you know, you might also become burdened by facts. And those facts, again, paralyze you because they give you the feeling that we as a species understand all these things. But the fact is that we don’t understand almost anything really, especially in biology. Many students think this is a bad thing. Especially, a lot of students in physics think that biology is bad because we don’t understand anything. But I would say, if you were a researcher, this is a goldmine. If we don’t understand anything now, we stand to understand so much. Also, when you’re studying physics now, you would wish that you were born in the 1800s so that you could have discovered all these things. From the perspective of biology, we are in the 1800s. If you really feel like you should have been born at some other point where something new was happening and we were in the midst of now knowing anything about a set of things about the world around us, then biology is really like that.

So, my advice to people would be to read about problems, talk to people about problems but you should try and do something on your own. Even if it's wrong, even if it’s simple, even if it’s silly, I think it will give you a lot of confidence and a lot of intuition and you will never get that intuition from years of reading.

The Long Road of Academia

You had a long journey, B.Sc, then PhD followed by a PostDoc and currently you’re a faculty member at ICTS. What was this journey like? And what helped you through the process of this?

I jumped into a PhD because I guess lots of people jump into a PhD or at least people around me were doing that. So, I thought, okay, fine. Research seems fine. Let’s do a PhD. But I didn’t really know what it meant to be a faculty member. No one in my family was really in academia so I didn’t really have a framework for what a career in academia looked like. So, for me, a real question about when I wanted to do a postdoc was okay, is an academic career something that I wanted to pursue? And to be honest, I wasn’t sure about that for a long part of my PhD. I think one thing that really helped me during my PhD to make a decision was that a lot of the work that I did, a lot of the recognition in the form of talks or papers coming out, gave me a lot of confidence. It made me feel that I’ve done something interesting that people find interesting. Throughout the process, even though I was having fun, I wasn’t sure whether this was something that other people would find interesting. So that gave me a boost to decide to go for a postdoc.

And from postdoc to faculty, when I decided to do that, the question was what is it that I want to do as a faculty member? Inherently, being a faculty member involves a very different mode of doing science, because you’re managing people alongside doing science. Being a theorist, I can do research myself, this is a rare situation. Whereas if I were an experimentalist, I would not be able to spend as much time at the bench. So, I really value and cherish that because as I said before, I think that a lot of the intuition about research comes from doing it. Spending time doing research by myself is something that I really enjoy, but I get less time for, these days. This kind of learning how to do all of this management is not something that I learned during my PhD or postdoc, but rather something that I’m kind of learning to do. The same goes for teaching as well.

Generally, I would say the thing that I have been enjoying the most, something that I didn’t realize before becoming a faculty member, is that the transition from a student to a postdoctoral faculty is really a transition from doing one project at a time to doing 2 projects at a time and eventually maybe 10 projects at a time. When you just have one project to do, your state of mind is very correlated with how that project is going. I don’t know if the same is the case for you. Weeks when the project was going well, I was happy. Weeks when the project was not going well, I was not very happy. When you’re doing 2 projects at a time, you kind of buffer that. When you’re doing 10 projects at once, it averages out. So, you kind of have one state of being. Because of this, in my perspective, I’m learning something new every day, not from the same project necessarily, but from different projects. So, currently I’m having a lot of fun.

This doesn’t mean that as a student, you should work on 10 projects at a time. You learn to manage 10 projects at a time only after you learn how to manage 1 project. So, I think you need to go through this process. I have kind of learnt to pick the positive elements of everything that I get to learn. So, if you are stuck in some subset of projects, you don’t really feel terrible because there will be another subset of projects that are going really well. You're actually thinking about a subset of projects every day. Those are the ones you're stuck on, but you feel motivated to do that because there's a bunch of other projects that are not stuck. So this power of averaging, much like this kind of thing that I was telling you, that things are much more predictable when there's high diversity, things are also much more kind of manageable when they're at a large diversity of projects. So that's something that I, no one told me about before, but also like I didn't realize, but it makes a lot of sense now that I've encountered it.