Cracking Complex Systems


Luis Amaral, Northwestern University professor of chemical and biological engineering, studies complex systems: sociological, biological and technological constructs made up of countless interconnected components that adapt and change with time.

If you think this sounds complicated, you’re not alone. They’re called complex systems for a reason, and for much of our history, their study has been limited to simply observation of the whole and only detailed investigation of the parts. But with advancements across the sciences, accumulation of new sets of data, and faster computers that can store and help analyze these data, scientists are learning more and more about how these systems work. We asked Amaral for the details.

Luis AmaralLuis AmaralYour research group focuses on complex systems. What do you mean by “complex systems,” and what are some examples?
For a long time, science was concerned with relatively simple systems. Physics started with Galileo looking at objects dropping or rolling on inclined planes. These are [considered] simple because the objects that are being studied remain the same—they have no free will, no capability of adapting, or adjusting to the environment.

But people have always been interested in understanding human societies: how families work, how individuals make decisions, why these kinds of organizations emerge. If you look at the history of humanity, you go from people living in extended family tribes and then starting to have higher levels of organization. When you are working in a small clan or tribe, everybody has to do almost everything. Now we have very specialized jobs. That is the result of us organizing into different functions, enabling us to survive as societies, because of the interactions and coordination between different individuals.

I’ve giving examples from society, but I could equally be giving examples from biology or from ecology. If you think about natural systems, they are as complex as human society. You have different species and the species specialize. Sometimes people think about them living together as being in equilibrium, which we know not to be true. There are always fluctuations and changes.

That actually makes it very hard to make quantitative predictions, or to understand how these systems emerge, how they survive, or to understand the characteristics that make them effective. So there are lots of questions that we are trying to answer, and these questions are in biological systems, social systems, and in technological systems.

There are many areas of inquiry that have these characteristics: many parts that interact in time-dependent and sometimes surprising ways, and give rise to very interesting and very intriguing organizations. Complex systems [research] is interested in trying to study and understand those types of systems.   

How do you tackle these complicated, changing systems from a quantitative perspective?
Our lab does computational research. We are able to do this because the environment has changed. It’s easy to get computers, it’s easy to get computers that are able to do many calculations and store lots and lots of data.

The other thing that has changed [is that] the amounts of data that are now available to us in all sorts of contexts is growing exponentially. [For example], the scientific community has [sequenced] the genetic information of [thousands of] organisms that people can study. The most famous was the Human Genome Project.

So there is all this information that [is available], and that is a great opportunity for someone who does computational research. We look at large amounts of data and we try to find patterns. When we find patterns, we try to build models that include the crucial mechanisms we suspect that give rise to those patterns. Then we see if it’s true or not by running that model on a computer. By implementing the model in the computer, we observe in the computer the same kind of patterns that we observe in the world.

Can you give me an example?
There is a worm called C. Elegans, and C. Elegans is relatively sensitive to the temperature at which it lives. Usually it likes to live at around 15 to 20 degrees Celsius. If you place it in an environment in which the temperature is around 30 degrees, you kill it.

There have been a lot of studies about placing these worms in inhospitable environments—where it is very hot, or where there is lots of radiation—and you see how the worm breaks down, what are the things that fail. But what if we put the worm in temperatures where it wouldn’t kill the worm, but where it would be uncomfortable?

Why is this relevant? We are worried about global warming. If the temperature were to increase by a couple of degrees Celsius, would that affect basic, physiologic functioning of organisms on Earth?

One of the things that has the greatest consequence for survival of a species is reproduction. Organisms have developed reproductive strategies over millions of years or more, and they’ve come upon a strategy that has enabled them to survive. If there is something that disrupts and makes that strategy not optimal, that could have dire consequences.

We made a mathematical model of how the reproduction rate was affected by temperature. You could put the worm at 28 degrees for three hours and then bring it back to 25 and then do something different [and see what happens]. We developed a model that was able to reproduce the outcomes we were observing in the experiments. That gave us an understanding of the pattern of how the egg-laying rate changed over time depending on the temperature, and we were able to reproduce those behaviors.

What we found is that even small changes in temperature could have very dramatic effects on organisms that are unable to regulate their body temperature, [like] unicellular organisms, or very small animals that are not warm-blooded. [They] don’t have that many resources to control their internal temperature, so they could be affected even by small changes.

And that could travel all the way up the food chain, correct?
That’s the thing about complex systems. You make a change in one part of the system, and because things are interconnected and interdependent, you can have consequences that seem extraordinarily large when compared to what you [thought was] a small change. It’s one of the dangerous aspects of complex system—they are robust, but at the same time there are small perturbations that could completely destroy them.

You’ve used computational modeling to study the evolutionary rates of different species. How can you track the speed at which a species evolves?
The way in which organisms evolve is that they acquire new genes. Sometimes the way they acquire these new genes is by taking a gene that exists, duplicating it in the genome, and then letting mutations occur, so that copy of the gene can actually be used to starting doing something new.

Most of the genes in the genome code for proteins, [like] a blueprint. You can go into an organism and identify protein families. The number of families that you have and how large the families are will both depend on the mutation rate—the duplication of genes and the mutation of those duplicated genes. If you have an organism that has a very large mutation rate, that organism is going to have many more families and many more proteins inside each family than an organism that mutates very little. There was a hypothesis that different species, and different groups of species, have different mutation rates, or different evolution rates.

How is this measured?
[Researchers have] found that the distributions [of protein families in organisms] were well approximated by power laws (a kind of mathematical relationship). One example of power law distribution is income, or wealth. You can have an individual like Warren Buffet, or Bill Gates, who is worth tens of billions of dollars. The mean (average) income in the US is nowhere close to a billion dollars, but there are individuals with worth in the billions, [making the distribution of incomes very broad].

In protein families, it is the same. Because it’s a power law, you can observe families with very, very large sizes. [In the mathematical formula], power laws are characterized by an exponent (a mathematical quantity that represents the power to which another number should be raised). In this case, the value of the exponent is dependent on the mutation rate. The higher the mutation rate, the smaller this exponent is.

When [other researchers] measured this for different organisms, they were coming up with different estimates of the value of [the exponent, and therefore different mutation rates]. What we observed was, because you have small amount of data for each [species], you cannot estimate this parameter perfectly.

Imagine that I have a ruler that doesn’t have inches, only has feet, and I’m trying to estimate your height. I would say “five-something.” I wouldn’t be able to give a very precise result. There are many situations in which you are trying to measure something but you are not able to measure it perfectly, either because you don’t have enough data, or the instrument you have to measure it with is not perfect.

Can you give me an example?
Let’s imagine for one species that [the exponent] is equal to 2.1, and for another species [the exponent] is equal to 1.7. Since the second number is smaller, you would say the mutation rate is greater. So one species has a lower mutation rate, and [the other] has a higher mutation rate. That’s assuming that one number is exactly 2.1 and the other number is exactly 1.7. But what if what I really know is that [the first number] is 1.7 plus or minus .3? Then [the true value] could be anything from 1.4 to 2. And the second number is 2.1 plus or minus .4, which means that it could be anywhere from 1.7 to 2.5. So how confident are you now that these two numbers are different? The first one can be anything from 1.4 to 2, and the second one can be anything from 1.7 to 2.5. There is a lot of overlap. They could be exactly the same.

That’s what we tried to test. We looked at thousands of species and the estimates of the exponents, and we asked if the fluctuations could actually be due the fact that we make an error when we estimated the value. What we found out is that [the differences] were perfectly explicable by fluctuations. Essentially, we say that there is no way, from this data, to prove the exponents are different. That would suggest that, in fact, the evolution rates of all these different species were the same. There were all these people that were trying to make statements based on different evolution rates, when there is no evidence that there are different evolution rates.

That’s why, when you are looking at data, you have to be very careful. When you make a measurement, you have a value. That value is not the whole truth. You also have to know what the uncertainty is on that value. Having uncertainty does not mean that you do not understand what’s going on. It just means that your measurement tool is not perfect.

For example, going back to another big topic, global warming: scientists say warming could be anywhere from two degrees Celsius to six degrees Celsius. People say, “Well, is it two or six?” What we are saying is that we don’t know. But we know that it’s not zero, which means that there is global warming.





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