Rob Phillips - "A Vision for Quantitative Biology"
Greetings. My name is Rob Phillips,
and I'm a professor of applied physics at the California Institute of Technology.
This morning, what I'm going to do is talk to you about a vision
for the role of biological numeracy.
What I'd like to do is try and address the question of
how quantitative thinking has been used as a tool
to sharpen the kinds of questions we can ask about biological phenomena.
Obviously, this is a very personal view, and if somebody else were to be standing here,
then their take on this would be different.
I'm going to use, as shown here,
the image of Archimedes as the icon of the kinds of things I'm thinking about.
He's known for carrying out his calculations with a stick in the sand,
and that's going to be the level of models I'm trying to advocate for.
So the way that I want to do this is to present four or so different arguments
which are rather philosophical and motivate the use of mathematics in biology,
and then I'll turn to a few words about how it is that we can try
to develop mathematic sophistication in biological students.
So my starting point is the idea that is inspired by this book by C. P. Snow, known as
The Two Cultures, where he argued that ignorance of the second law of thermodynamics
should be viewed as tantamount to ignorance of Hamlet.
This is related, in turn, to a very commonly held view, I would say, which is that,
in order to have a functioning democracy, we need to have an educated citizenry.
James Madison summarized this as follows:
"A popular government without popular information or the means of acquiring it
"is but a prologue to Farce or Tragedy or perhaps both.
"Knowledge will forever govern ignorance, and a people who mean to be their own Governors
"must arm themselves with the power knowledge gives."
So my take on this is that, in the same way that an educated citizenry
is a part of properly functioning democracy,
I think that scientists need to have some level of fluency
with not only the methods and techniques of mathematics,
but also with the potency and the ways that mathematics can be used, as I said before,
to sharpen the kinds of questions that we can ask about different problems of all kinds.
So, the second argument that I want to make for the role of biological numeracy
is best illustrated by one of my favorite scenes from the movie Apollo 13.
What happened after the explosion on Apollo 13
‚Äîthe astronauts were on their way to the moon‚Äî
is that they had to shuttle over into the lunar landing module
in order to basically survive while they went around the moon and came back to the Earth.
All this time, obviously, the engineers in Houston, at NASA, were
busily working to bring these astronauts back alive, and they were headed by Gene Krantz.
What he had to say really was, "Let's work the problem, people."
And his notion was that he didn't care whether they were rocket scientists or engineers
or physicists or chemists or mathematicians.
All he cared is that they brought their tools to bear on solving the key problems
that were faced in bringing the astronauts back.
One of the most important of which had to do with the rising CO2 levels in the lunar module.
It was not meant to hold three people for many days, and oddly the engineers had
designed circular and square scrubbers for the command module and the lunar module.
They poured out all the ingredients on the table
‚Äîeverything that was on the two spaceships‚Äî
and he told the engineers, "Figure out how to put the round peg in the square hole, or vice versa."
So, my thought here is that, in the context of biology,
one of the most useful tools that we can bring to bear is a bit of mathematical argumentation.
As Darwin put it, "People with an understanding of the great leading principles of mathematics
seem to have an extra sense."
And I think that this extra sense allows us to see biological problems in different ways.
It's another tool‚Äîone of many. It's not a unique tool, and it's not necessarily the best tool.
It's just another useful tool.
The next argument that I want to make has to do with a view
that was espoused by Darwin in a letter that he wrote, where he said,
"About thirty years ago, there was much talk that
"geologists ought only to observe and not theorize;
"and I well remember someone saying that at this rate
"a man might as well go into a gravel pit and count the pebbles and describe the colors.
"How odd is it that anyone should not see that
"all observation must be for or against some view to be of any service."
So my argument here is that mathematics provides us another way
of being for or against some view,
and often this way is different than one would be able to do
with purely verbal argumentation alone.
My fourth and final argument is less philosophical and has to do with the nature of biological data.
Whether we're thinking about the scale of individual bacteria or entire ecosystems,
the data is often quantitative, and this in turn demands quantitative modeling.
What I'm showing you here is an example of some data taken on the motility of bacteria
as they move towards particular chemical attractants.
The chemical attractant is added at a certain moment
then the bacteria are observed, in particular the rotation of their flagella,
and people can learn things. I'm not going to go into the details, but it's quite fascinating.
At a totally different scale, as shown at the bottom, Alfred Russel Wallace traveled
around what is now modern day Indonesia,
and in his travels, he noticed something quite peculiar.
Between the islands of Bali and Lombok,
he noticed that there was completely different flora and fauna
and this led to the elucidation of what is now known as the Wallace line
which separates these different classes of flora and fauna.
Most of us know, for example, that in Australia, there are marsupials,
and this is the kind of thing that he noticed.
In the modern hands of Robert MacArthur and E.O. Wilson,
this led to what they called the theory of island biogeography.
And one of the coolest things that you find in this book
is a simple, empirical relationship which relates species diversity to the area of islands.
They then proposed a simple mathematical equilibrium model
where they tried to balance rate of immigration, on the one hand,
and the rate of extinction on the other,
thus leading to a picture of the species-area relationship that I mentioned before.
But my main point here is just the idea that these very different scales,
very different kinds of problems both appeal to quantitative reasoning.
Of course, this idea of using quantitative analysis in biology is nothing new.
I'm saying nothing new at all.
And, there's classic examples that are very famous.
For example, the origins of classical genetics in the hands of Mendel and Morgan,
basically, by counting frequencies.
In the case of Mendel, looking at frequencies of things that we've all heard about
‚Äîthings like smoothness of peas and colors of flowers and so on‚Äî
he was able to elucidate the idea of these abstract elements of inheritance known as genes.
In the hands of Thomas Hunt Morgan and his student, Alfred Sturtevant,
they were able to actually figure out the position on the chromosome
of several different genes associated with a fruit fly.
The other example that I show you here is Hodgkin and Huxley,
who basically put together an idea of the propagation of electrical signals in cells,
which too had all sorts of interesting quantitative features
that they addressed in a quantitative fashion.
What I'm showing you here is a case study that I think is really compelling.
There's a classic video, taken by David Rogers, probably around fifty years ago
and what it shows is an individual white blood cell‚Äîa neutrophil‚Äî
as it hunts down a bacterium in a field of red blood cells.
And the idea that I wanted to put together here is just that,
it's often said that a picture is worth a thousand words, and this video has been,
in a certain sense, the seeds of a whole series of different research programs.
Why are people so amused and so interested in this video?
It tells many different stories, some of which can be couched in quantitative language.
To try and demonstrate that, I want to talk a little bit about bacterial chemotaxis.
So, I've already mentioned that bacteria express certain preferences.
They'll move towards attractants and from the mathematical model building perspective,
as shown here, we can take this cartoon, shown on the left column,
where what's depicted is the surface receptors that sit in the cell surface
and that actually capture the ligands which are seen as chemoattractants.
What's shown in the right column is basically a statistical calculation
of the probabilities of each of these different eventualities.
And what comes out of this is the ability to make at least a first cut at trying to
calculate how the rate of tumbling depends on the concentration of chemoattractant.
One of the things that I think is especially intriguing about this sort of quantitative bent is that
we can organize biological topics in different ways than we would
from the traditional biology point of view.
If you grab a very big molecular cell biology textbook,
you open up the subject of embryonic development
you open up the subject of bacterial chemotaxis,
they will be pages and pages apart from each other.
On the other hand, when viewed from the perspective that I'm trying to put forth here,
in both cases, we ask questions about chemical concentrations as a function of position
and then how cells actually count those concentrations in order to make decisions.
And so this proximity of topics in physical biology.
It's a different way of holding up a particular biological problem and viewing it differently.
My second example is shown here.
What's shown in the video is a dividing frog embryo.
Basically, we have a frog egg that's been fertilized,
and over time, what I want you to notice is the incredible synchrony of the cell divisions.
This is even better shown as the video goes on and we'll see three of them simultaneously.
So note that as the cells are dividing,
even the distinct embryos are dividing at this steady, rhythmic pace.
Now, the reason that I think this is amusing is that people have thought
very hard about how to write down mathematical descriptions of biological clocks.
Shown on the bottom are three different versions of genetic networks, and next to those
networks are equations, and if you look carefully, you'll see that they say things like dA/dt.
That's the rate of change of concentration of element A in the network.
And what I think is fun is that, of course,
many biological students are tortured by learning calculus at some stage in their careers.
But, at the same time, I think that if they were given a bit more motivation...
if they realized that this idea of calculating rates of changes
was going to be important to them in thinking about these amazing processes,
such as embryonic development, they might feel a better taste for learning mathematics.
And that brings me to my next point.
So, I haven't said much about how we can go about getting mathematical tools
in the hands of biological students, and I wanted to just give a few words
with the ultimate belief that I think that
nothing is so stimulating as having fantastic teachers.
But the first thing is this idea that was put forth in a book by Malcolm Gladwell called Outliers.
He elucidated what he called the ten thousand hour rule, and the basic idea is that
in order to get good at something like playing an instrument or good at soccer
or something like that, people that are really at the top of their game,
they've invested thousands and thousands of hours.
If you think about the length of a graduate student career, over the first couple of years,
let's assume that they're working 100 hours per week,
then that's going to come out to about 5,000 hours per year.
After a couple of years, they're practicing research at the very frontiers.
And so, although there's much to quibble with the presentation of Gladwell,
I think that this basic idea that in order to get good at something,
you really have to push should come as no surprise to anyone.
If you want to improvise as a jazz musician,
probably you're already very good at playing your scales.
If you want to learn how to do a slam dunk, you better know how to do a lay-up first.
I also wanted to show here that both Abraham Lincoln and Thomas Payne,
they studied Euclid's elements
‚Äîhere, I'm showing the Pythagorean theorem in Euclid's elements‚Äî
in order to sharpen their thinking.
And I think that this kind of idea of just putting in the effort,
the elbow grease to do mathematics... there's real payoffs.
Last point is, I just wanted to call people's attention to Bio 2010,
this report put together by the national academies
where they give other ideas about how to enhance biological numeracy
in the biological curriculum.
So, I'm going to make a point here that hearkens back to what I said earlier
about our shared scientific destiny.
So the world is faced with many different challenges, and I think people are looking to scientists
to be able to try and respond to those challenges,
and one of the most important of which is climate change.
Last week, in Science magazine, there was a letter submitted
by something on the order of one hundred people
about climate change and the integrity of science.
And one of the things that's very interesting about the list of people that signed this letter
is that some large fraction of them are biologists.
And what I'm getting across here is that I have no problem with biologists signing on to
expressing a scientific opinion about something like climate change,
but at the same time, we should not forget
that behind the scenes in this whole climate change discussion
is for sure some element of mathematical model building
which is an argument in favor of this notion of mathematical literacy.
So I'm going to close with the title of one of my favorite papers
from PLoS Biology by Joel Cohen, he asks:
"Is Mathematics Biology's Next Microscope, Only Better?
"Is Biology Mathematics' Next Physics, Only Better?"
Let's think about what those two things mean.
The top one -- mathematics is biology's next microscope, only better...
He's trying to say exactly what Darwin said before,
which is that people that have mathematics in their set of tools
seem to have an extra sense.
We can sharpen the questions we ask about biological problems using mathematics.
The second point‚Äîbiology is mathematics' next physics, only better...
That's merely to say that biology is bleeding over into other disciplines
in a huge way that makes an impact on those disciplines themselves.
It's not as though scientists from other fields moving into biology,
that's the proper direction of the flux.
Biology is also moving out into these other fields.
I'll close with a thought.
In his biography of Albert Einstein,
Abraham Pais said while speaking about Einstein's work on specific heats,
in order to recognize an anomaly, one needs a theory, a rule, or at least a prejudice.
And my thinking here is that mathematics gives us another way
to develop prejudices‚Äîoften prejudices that are inaccessible using strictly verbal descriptions.
And at the end of the day, my belief is that this interplay
between prejudice and expectation and experimentation
is the way that we improve our understanding of problems.