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PROFESSOR: Today what we want to do
is use the two papers that you read as kind of a backdrop
to try to think something about the regulation of genes
in response to changing environments.
So there's the Mitchell paper that
is talking about this idea of anticipatory regulation,
whereby if the environmental changes have
some typical pattern, then maybe the cells can take advantage
of that and start preparing for environment number two
when the cell sees environment number one.
But in other cases, it may be that the environment fluctuates
in ways that are really fundamentally unpredictable.
In that case, you can't use the sort of anticipatory regulation
strategy, but instead, there may be a way
that you can just stochastically switch
between the different strategies and implement what's known
as a bet hedging strategy.
And this is modeled largely on the work
that you just read about in the Kussell paper, Science
maybe May 2005.
I do want to stress, however, that if you observe
phenotypic heterogeneity in a clonal population,
that does not necessarily mean that the cell or the population
is implementing one of these bet hedging strategies.
In particular, I would argue rather strongly
that there are other possible evolutionary drivers
for such phenotypic heterogeneity
in the population.
First of all, just because you see
some phenomena does not mean it is necessarily selected for.
So it's possible that it's a side effect of something else.
However, if you're looking for an evolutionary kind
of explanation for something like this,
bet hedging is not the only one.
In particular, we'll talk about two
other possible explanations, and they both
have to do with kind of game dynamics
that we might illuminate or talk about.
But I guess our game theory talk was--
that was a week and a half ago, almost two weeks
ago now-- so maybe you've forgotten all the game
theory that we discussed.
But in particular, it could be that
the phenotypic heterogeneity might be the implementation
of a mixed strategy.
Or possibly it could be an example of some sort
of altruistic self-sacrifice.
And we'll try to explain the theory behind each
of these three things as well as possible biological examples
of each of the three.
In this case, we may think about bet hedging
as maybe an explanation for antibiotic persistence,
this idea that cells can switch into these slow-growing
persister states in which they're
resistant to antibiotics and other stresses.
Mixed strategies could be-- well,
we're going to argue it could be implemented
in the context of mixed sugar environments.
And altruistic self-sacrifice may
be the explanation behind colicin production in bacteria,
so it's a toxin.
So I want to start by thinking about this thing
about adaptive prediction of environmental changes
by Mitchell.
I think this is a very interesting paper
in a number of different ways.
One is, I think that it's sort of a big idea that
can be explored in these simple experiments.
I think that it's an exceptionally clear paper
in some ways, and that they really say,
oh, we're going to propose that this strategy should
be characterized by these three things.
And then they go and they try to show you the three things.
The figures, I think, are also very nice,
in the sense that in many of the cases
you could have shown the data just in the context of a table,
where you said, oh, for each of these strains, this
is the up regulation or so.
But if you had done that, it would've been much,
I think, less compelling, even though of course it's
the same data.
So I think this is a neat paper, in my opinion,
both from the standpoint of the ideas that are being explored,
but also because it highlights some of the things
that you should be thinking about when
you're writing your own papers.
You want to try to make the ideas as clear as possible.
You want to lay the groundwork so
that what you're about to show is
going to be-- the reader's going to feel
is a really important thing.
And then you want to take nice advantage of color
and some legends that are there.
So we'll kind of talk about all these issues as we go.
But before we get started, can somebody--
there's a very real sense that in this field of decision
making and systems biology that a lot of this research program
is kind of driven by following classic ideas
from other fields.
And what would be the corresponding classic idea
this paper is exploring?
AUDIENCE: Conditioning.
PROFESSOR: Conditioning.
Right.
And whose name do we associate with conditioning typically?
AUDIENCE: Pavlov.
PROFESSOR: Pavlov.
All right.
So I have not ever read these studies.
Pavlovian conditioning.
And I think that this is just-- it's good to highlight.
This is something that you might have
learned in your high school psychology class.
And it's, again, a big idea, but it's not the kind of thing--
we've all heard-- well, we're going
to talk about this in a moment.
Many of us, I think, have heard of this.
But this is an example of how you take something
that you learned in high school and you
make it useful to your daily life, or pseudo daily life.
Because I think you'll see that there are many kind of examples
of this throughout this literature,
where someone takes an idea that is, in some ways,
you open up a random textbook in introductory psychology,
and you can just march through and try
to see to what degree the ideas that were developed
in the context of humans or animals,
to what degree might they be relevant in the context of cell
decision making?
Can somebody just say what is this Pavlovian conditioning
idea?
Did you guys take high school psychology?
I'm sure somebody did.
No.
All right.
Well, incidentally, I recommend everybody
should take a solid introductory psychology
class if you have not done so.
We offer a class 900.
I'm sure that it's good and interesting.
Yes.
AUDIENCE: So there's two different events or stimuli,
and in Pavlovian conditioning you give one and then
always give the other one following.
PROFESSOR: That's right.
So there's some sense that what we might call--
there are two events of some sort.
One is following the other one, so it's A and then followed
by B. And people have done many different examples of this,
but what's the one that we typically--
what's the classic experiment that Pavlov did?
AUDIENCE: You ring a bell, and then you get food.
PROFESSOR: Yeah.
Right.
So you ring a bell and then you give-- and this is dogs,
at least in the version I remember.
So you have some dogs, you do this thing
where you ring the bell and then you give them the food.
And what's the response that you're supposed to get?
AUDIENCE: Drooling.
PROFESSOR: Yeah, right.
So the dog is supposed to start salivating.
OK.
So you might think your experiments
are gross, but-- right.
So ring a bell, and the idea is that you can train the dog
to start salivating in response to the bell, rather than,
of course, if you give the food they're
going to start salivating.
But here you can train the dog to start salivating
in response to the food.
So now, with training, this results in salivation.
And did Pavlov show there was a fitness benefit associated
with the salivation?
Not that I'm not I'm aware of.
But this is the classic story that we learned
in introductory psychology.
And the question is, can we apply a similar idea
in the case of microbial decision making?
Now was this-- can somebody say what
they think was the author's contribution
to the literature in the sense of-- via a vis this?
How much of what-- well, we can be maybe more concrete.
In the case of E. coli, what was known-- or maybe
we should describe the experiment once more
and then try to figure out what they did that was new new.
At least can somebody kind of summarize the basic idea
with E. coli?
AUDIENCE: We know that they have a certain metabolic life cycle
and that they exist in different environments.
PROFESSOR: OK.
So that E. coli existent in different environments.
And what environments are you referring to?
AUDIENCE: Gut and outside.
PROFESSOR: Gut and outside.
So if this is true-- then what is
going to be your next statement based on this?
AUDIENCE: Well, going through mammalian guts
there's always a certain sequence of events.
At the beginning, there's some acid, and then
less acid and more food, and stuff like that.
PROFESSOR: RIght.
So in the context of E. coli, there's this idea
that part of the life cycle of E. coli
and some other of these microbes is
to live inside the gut of mammals.
And we're going to focus in particular
on this aspect, the part of the life cycle that is in the gut.
So let's just imagine, so E. coli in gut or entering gut,
going through the gut, they might encounter
some sort of typical environmental cues,
or maybe orders of environmental exposure.
And actually, even before this paper,
there was another paper that was published by Saeed Tavazoie--
hard name to pronouce-- who was at Princeton at the time.
So he had published a Science paper just the year
before-- well, couple years before-- demonstrating
a related phenomenon.
What was it that this other paper had demonstrated?
Does anybody remember from the introduction?
So it wasn't the experiment that these guys did.
But in the introduction they spent
half of a paragraph describing this other experiment.
Another kind of environmental cue
that E. coli get when they enter the gut.
So what's-- yeah.
AUDIENCE: Isn't there a temperature increase and oxygen
decrease?
PROFESSOR: Temperature increase and oxygen decrease.
So temperature goes up and oxygen goes down.
And this makes sense.
The inside of our bodies typically
warmer than outside our body.
Also, it's a relatively anaerobic environment
inside the gut as compared to the ready availability
of oxygen outside.
So what is it that this other paper then showed?
Yes.
AUDIENCE: So I think they were trying
to show a symmetric response [INAUDIBLE].
If adaptation in one situation occurred,
then-- if it received one stimulus,
it would adapt to both.
PROFESSOR: Yes.
OK.
And the word adapt, we always have to be very careful,
because it could mean two very different things.
And in some cases, it might be that both-- possibly it
might be true, but when you say that it receives
one stimuluss-- so this we might call S1,
and this is S2-- so these are stimuli that the cell
senses-- are you saying that it might sense one,
and then it adapts to both.
When you say adapt, are you referring
to evolutionary adaptation or something else?
AUDIENCE: I'm referring to a single cell
implementing the appropriate metabolic--
PROFESSOR: That sort of cell level adaptation.
The sort of default thing is you might, say, well,
if you get the stimuli one and increase the temperature,
you should implement the program one or the response one that
corresponds to some set of genes that are required
to grow in high temperature.
Now similarly with stimulus 2-- well, we'll say this is R2.
So these could, in principal, have different gene network
responses to these two environmental changes.
But what they found is that actually, if you take E. coli
and you expose it to increase in temperature,
then not only does it activate the genes required
to handle high temperature, but also activates
the genes required handle low oxygen, and vice versa.
Now there's a question, though.
If you see this, it could just be the case
that you've mislabeled what really is R1, R2.
Maybe it's just a single R, single response
that allows the population to adapt to both
of those environmental changes.
Does anybody remember what the authors
did to show that that was maybe not what was going on?
You can look at your sheet of paper while I--I just want
to write down the reference in case anybody wants to look
at this more.
This is Tagkopoulos, Science 2008.
What would you do if you wanted to show
that this was a real regulatory strategy,
this so-called symmetric anticipatory regulation?
Yes.
AUDIENCE: Would it be you could measure
genes' pressure somehow, and then you
could get the function of each
PROFESSOR: Right.
So you could expose to this stimulus,
measure gene expression, expose to this stimulus, measures gene
expression, and try to figure out, maybe,
based on the difference which genes were more
or less-- but the argument was somehow
that in response to stimulus 1, there were some genes that
were really unnecessary.
So I guess you could go and you could
do knockouts of each of these 100 genes,
and then try to measure the effects.
And that would be a nice direct--
and it's related to something that they did in this paper
with the yeast.
They went and looked at the gene expression profiles.
What they did in this paper by Saeed
was that they took the E. coli that
displayed this, what they're arguing is a symmetric--
and based on some previous studies, I think,
saying that, oh, this had been annotated to be good
for temperature but not for oxygen and vice versa.
So there were already hints that this kind of made sense.
But what they did is they evolved the populations
in just one of these environments
and showed that they could decouple them.
So that's at least making you feel
that it's a little bit-- that maybe this was not
due to just some sense that it's the same genes that
are required for protection against these two environments,
but rather that because they had evolved in this environment
where, when they see an increase in temperature,
they often see a decrease in oxygen.
AUDIENCE: So when you say decoupled,
you mean you evolve them in high-temperature environments?
PROFESSOR: That's right.
AUDIENCE: You expose them to decreased oxygen,
and then they die?
PROFESSOR: No, no, no, no.
So just, they showed that if you evolve the population
so that it receives this stimulus without this stimulus,
then it removes this arrow, that it
stops activating these genes.
And then I think they also did look
at the functional consequences.
But the first order thing is just
that they saw that they could remove
one of these arrows, which is related to something that they
do here as well.
Now I think that it's worth thinking
about the question of whether this study, published
in Science in 2008, do you think that it's
a complete scoop of the paper that you just read,
which is Amir Mitchell's paper published in Nature in 2009?
No.
OK.
And on one level you say, well, they still
got it published in Nature, so therefore it was not a scoop.
But I can tell you that Amir was very worried,
because he had been working on this paper for many years.
And they really studied both E. coli and yeasts.
It was a major thing.
And then this paper came out, and I'm
sure that he was despondent.
And there will be times where you
feel despondent as a result of something
like this coming out, because it really is a very similar idea.
The E. coli stuff is very similar,
because it's same organism-- the idea is, in the gut.
So in what ways do you think that their paper is different,
and also, what strategies did they
follow in order to differentiate their paper?
Yeah.
AUDIENCE: Maybe potentially trying
to find differing regulation mechanisms, so they said, well,
there's a symmetric regulation mechanism
that someone talked about last year,
and we've got the asymmetric one.
PROFESSOR: That's right.
And I think that this is-- of course,
we cannot replay history.
But I think that they do a very nice thing in figure one
of laying the groundwork to make it very clear
that their work is different from Saeed's work.
And the thing is that if this had not been published,
they maybe would have framed their work differently.
They might not have had this difference
between a symmetrical anticipatory regulation
and the asymmetrical.
But by laying things out that way,
it clarifies that, oh yeah, these are different things.
And they're going to explore this one,
whereas Saeed's group had explored
a rather different mechanism.
But then, of course, depending on how you look at it,
they're either more or less similar.
But I think that they do a very nice job of kind of right
at the beginning setting out how their work is
going to be different.
So they explained that there's the simple direct sensing
mechanisms.
You'd say that you just have different stimuli that
lead to different responses.
That's fine.
They also have the stochastic switching, which
we're going to talk about more.
The idea here is that even though we
might be getting different stimuli at some rates,
we would still switch into these different responses.
And we'll talk about various reasons that this might happen.
Incidentally, these things don't have
to happen at the same rates.
So it could be that stimulus one it primarily does R1,
whereas stimulus 2 primarily does R2, for example.
If you'd like, these arrows could have different strengths.
But then what they do is they point out that there really
are-- well, this symmetric anticipatory regulation,
where it's crossed, maybe I'll just
write out the asymmetric one.
Can somebody say why it is that we
might want to do the asymmetrical as compared
to the symmetrical?
Yes.
AUDIENCE: If both of the stimuli are appearing at the same time,
then you might want to have a symmetric anticipatory
regulation?
PROFESSOR: Great.
So the important thin is here that this
is, because it's at the same time, the two stimuli kind
of come together, or very similar times, whereas this,
if there's a clear temporal order.
But you could think about this in some other way
as well, maybe.
Can somebody--
AUDIENCE: It's along the same lines,
but there's a cost to having S2 also performing.
Then if you ever use that--
PROFESSOR: Right.
So depending on the costs, it could
change what's sort of optimal, perhaps, right?
And I think it's also perhaps worth just saying
that it may also depend upon how frequent
these different environmental perturbations are,
because you can also imagine situations
where it's very common that the temperature goes up,
but it's very rare that oxygen goes down.
But there could be a sense in which this is, basically,
based on the logic I just said, this
would be then less predictive of this
than this would be of this.
Do you guys see what I'm saying?
Because it could be the case that any time that oxygen goes
down, then you really know that that means that you're entering
somebody's gut and you also better activate this,
whereas it could also be the case that if you sit out
in the sun, you get hot, it doesn't mean
that oxygen's going to go down.
So it could be that there is more or less information,
or that each of the stimuli have more or less information
about another stimuli.
So even if there's no temporal order,
it could be the case that something like that
could lead to a situation where this might be optimal.
AUDIENCE: So it seems people try to make
formal statements about information in this context,
just like they did in the context of stochastic theory.
PROFESSOR: So there's some of it.
I haven't seen anything that's quite as
clear and formal as what Edo Kussell did in that Science
paper you guys just read.
But for example, Amir did do a paper,
he wrote a PNAS paper basically laying out this model that's
sort of sketched at the end of this paper a little bit
in more detail in terms of explaining,
depending on the probability that something occurs
and the time, so kind of exploring
this a bit more, but not as formal
in terms of information as--
AUDIENCE: So it's not quite clear to me
why you would have a symmetric anticipatory regulation
comparing direct sensing.
If you have direct sensing, you can do the same thing.
PROFESSOR: That's right.
I think it's true.
But it could also be that because these things are
both fluctuating and they are measured
with some noise and the environment,
there could be a sense that-- because you can imagine
a world in which these two things are
both uncertain predictors of whether you're in the gut.
But if they both go, then that really
means something, in which case then it would make sense
to really look at both of them and activate both more strongly
as a result of seeing both.
AUDIENCE: But it could also make you
more susceptible to trigger a response that you
don't necessarily want.
PROFESSOR: That's true.
But if you say, oh, well this happens at a low rate
and this happens at a low rate, then
the probability that both of them happen at the same time
would be very small.
So your rate of false positive, in that sense,
would be-- you can really reduce the rate of false positives
by integrating both pieces of information.
And this paper, just to remind ourselves,
this paper is primarily exploring
the idea of asymmetrical anticipatory regulation.
And their argument is because there's
a typical temporal order to how E. Coli that are ingested
encounter different sugar.
And the claim in the paper is that bacteria will typically
see what before what?
AUDIENCE: Lactose before maltose.
PROFESSOR: Correct.
So the claim is that in the gut, the bacteria will see lactose
before they see maltose.
Now in order to evolve this asymmetrical anticipatory
regulation, does it have to be that you kind of always
see lactose before you see maltose?
So let's imagine that only 10% of the time that the bacteria
see lactose-- or sorry, only 10% of the time
that the bacteria encounter maltose that they actually saw
lactose before.
Since 10% is much less than 1, should that totally
scotch this whole mechanism?
No.
And can you say why not?
AUDIENCE: Every time they see lactose they see maltose.
PROFESSOR: That's right.
In some ways, that's not the right way
to think about it, but in terms of a cost-benefit type
argument, why is it that maybe it's OK in principle
that maltose is frequently observed without lactose?
AUDIENCE: There's no difference between the two strains
if you see maltose that way.
PROFESSOR: Right.
And I think this is a kind of an interesting, important point,
which is that if you imagine a competition between the strain
that just does, we can imagine, direct sensing versus we'll
call that AAR.
So direct sensing versus asymmetrical anticipatory
regulation.
Now if you imagine the situation where you encounter
maltose without encountering lactose, then these two
strategies behave essentially identically,
because they both just see the maltose,
they're both surprised.
They both activate the mall genes, everything's fine.
However, it's in this other direction
that you have to think about it.
So the real question is, when you encounter lactose,
you want to think about, well, what fraction of the time
and how long a delay is there before you encounter maltose?
Because if it's the case that you encounter lactose a lot,
and only infrequently do you then come on to maltose,
that's going to be a problem for evolving this
into asymmetrical anticipatory regulation,
or it would not necessarily be optimal to do so,
because in that case you're going to be activating
all those mall genes in advance, and frequently it
won't be useful.
And this is relevant, perhaps, just because what fraction
of the time do you think that E. coli going to the gut
will encounter lactose?
We should be able to make a reasonable estimate of this,
is my claim.
All right.
Where does lactose come from?
Lactose comes from milk.
Which animals drink milk?
Well, right, OK.
So we're thinking about mammals.
Just take a random mammal of your choice.
You might want to not choose humans
just because we're a little bit atypical in this regard,
although even there I think the numbers
end up being kind of the same.
But imagine a dog or a bear or your favorite mammal.
Which of them are drinking milk?
The young, right?
OK.
So there's some period of one's life where you drink milk,
and then as an adult you typically don't.
I guess all I'm saying is that if you
imagine the bacteria entering into a mammalian gut,
it might be 20%.
I don't know what, but it's basically
proportional to the years.
The kids, they may eat more dirty things.
So you have to wait or whatever.
The point is that they're going to encounter lactose
if they enter the gut of a baby or young child,
whereas if you enter an adult, then you won't see lactose,
and you'll just maybe then directly see the maltose.
But there's no real cost associated
with missing that signal vis a vis
the so-called direct strategy.
I think that they do lay out some other kind of conditions
that they think would be reasonable to demonstrate
if you want to do the asymmetrical anticipatory
regulation.
And once again, I think that this is both very clear
and also just lays the groundwork
for the reader in the sense that they tell you
what they would need to show in order for you to be convinced.
And then they go and they do those things.
Now in principle, you could argue
about one or the other things.
But I think they do such a nice job
of being clear about what would be needed that you don't even
think to object about any of it.
And of course they're not going to bring up the three things
that they would need to demonstrate
unless they actually were able to demonstrate those three
things.
So the three things that they claim
is that for this to have been an evolved trait that pre-exposure
to S1 increases the fitness under S2 or R2--
I guess in this case-- that's right.
So getting S1 helps you in S2.
So seeing lactose helps you in maltose.
Indeed they're going to show that.
Second, that there's some cost associated
with up regulating that, in this case
up regulating the mall genes.
And third, there's this idea of specificity.
Now the claim is that it's really
S1 that is activating this R2 response,
and that various other S's, in this case other sugar sources,
maybe should not pre-activate.
Now in figure 1, they basically are
exploring the difference between this arrow and this one.
So if you expose the cells to maltose
you activate the mall genes at a high level.
Is it required that exposure to lactose up
regulates the mall genes to the same level as maltose?
No.
Was it at the same level as maltose?
No.
But the idea is it up regulates it some, as compared
to other carbon sources.
Now they also made a comment about whether this arrow,
the so-called anticipatory regulation,
whether it was specific to their E. coli strain,
and their claim was that it was or was not?
Would it be good for it to be specific to their strain,
or bad?
Probably bad, although the fact that-- but then they
say, oh, it's not specific to our strain.
And then they cite another paper, which-- and this
is, again, a nice way of phrasing
it because they're adding strength to their paper
because they're saying, oh, it's not just our strain.
It's in other strains as well.
So you read that sentence and say yes, that's good.
Of course you could read that sentence
and say, oh, but somebody else already showed this?
But this is, again-- and I don't have
any real complaint about that, because I think what they've
done is they've really brought a set of measurements
together in one conceptual framework
that I think is rather compelling.
Now of course, you can always argue about
whether each of these examples really
did evolve for this purpose or not and so forth.
But just because somebody else had
seen that there was some cross-regulation of the mall
genes in response to lactose.
Doesn't mean that this paper is worthless.
But it is interesting to note that somebody else had already
seen this.
Moreover, in figure one they compare
this asymmetrical anticipatory regulation for their wild type
strain as compared to another strain.
And what other strain did they use?
Yes.
AUDIENCE: You didn't expose the cells to maltose
after the lactose [INAUDIBLE].
PROFESSOR: Right.
They evolved the cells in lactose for 500 generations.
And then what did they see?
AUDIENCE: The arrow.
PROFESSOR: That's right.
When they saw was that evolution-- and this
is in lactose-- removed that.
Now 500 generations, how long do you think
this is going to take them?
AUDIENCE: A few months.
PROFESSOR: A few months.
Have you guys ever heard of any other paper
where they evolved E. coli in lactose for 500 generations
in your extensive reading of the literature
that you've engaged in over this semester?
AUDIENCE: The cost-benefit paper.
PROFESSOR: The cost-benefit paper.
So it's fascinating to note that this sentence, they said,
"We have examined laboratory-evolved strains
of E. coli.
Did they say that they did the evolution?
No, they didn't.
And indeed, if you follow Citation 14 over here,
you can say, oh, right.
So it's another paper by Uri and company.
So I don't know if it was the exact same experiment,
but the idea is that-- so I think
what they did is, they took the strains that
were evolved for another purpose, and that's fine.
If somebody else already did the daily dilutions
for three months that is the exact same that you were going
to do, then you might as well just
analyze their evolved strains, right?
There's nothing that says you have to go and repeat the work.
You would get the same thing, maybe, presumably.
So this is just worth highlighting.
But it makes the paper much stronger
that they were able to do that.
So it's good to keep in mind that in some cases, what you
need to do to make your point has already been done
or has already been evolved and so forth.
So now what we have is a situation
where somebody else, maybe, has already seen
that lactose activates maltose.
Somebody else already did this evolution on lactose.
They didn't yet show that this regulation was removed.
So that was something that these guys had to do,
and indeed, it looks like it's removed.
But once again, I think there's a sense that they're really
looking at this problem from kind of a new, maybe
comprehensive way that allows them
to see the connections between all
these different experiments.
And then they are doing new measurements.
But the measurements themselves are perhaps relatively simple,
but the trick is knowing what measurements
you need to do in order to say something
that's very interesting.
So in figure three, what they went and they did is
they asked about this question of whether there really
is a fitness benefit associated with it.
Now I think this is another case where
you could have made this figure in the form of a table,
and it just would not be very compelling.
So you'd look at it and you just wouldn't be very excited by it,
whereas in this case, they have the figure, which
are these fitness advantages associated with whether you
take the strains, you first expose them to lactose and then
go to maltose, or you go from maltose
to lactose, or in this case GAL to maltose, sucrose to maltose.
What they showed was it was a selective benefit there,
that the cells really only gain the benefit of pre-exposure
to a sugar if it's lactose.
And they show that for the evolved strain,
not only does it no longer have that arrow
in the sense of the response, but it also no longer
has the benefit.
It's good to do both of those measurements
because it's possible you might have missed something.
Yeah.
AUDIENCE: So but like, it's for one protocol going from lactose
to maltose.
PROFESSOR: That's right.
Yep.
And this is the nature of science,
or in particular this kind of science, I think,
that you can collect data that is
consistent with this interpretation,
but it does not at all prove that this is not gut, either.
And so you could have imagined experiments
where you maybe mixed two strains that
follow this direct versus the AAR,
and you mix them together 50-50 in the gut.
And then you go and you do sequencing later.
And actually, people do such kinds of experiments,
and in some cases, amazingly, sometimes something
comes out the other end that is interesting.
I couldn't help myself.
Sorry about that.
So yes.
One other point on this paper, or this figure,
that they even color code the data points.
So they have their main thing in this black,
but then the other ones are red, yellow, blue.
it's telling us that this thing is directional.
It's S1, S2, S2, S1, specificity, extinction.
So they are even kind of telling us
what each of those data points mean.
And you might say, oh, that's kind of overkill.
But given that it's just so important that you're
keeping track of why we're doing each of these measurements
and what it's supposed to tell us about the big story,
I think that it's really just wonderful to be reminded,
OK, what is this controlling for, or what not.
Yes.
AUDIENCE: I like the colors too, but they don't stand out
very well in black and white.
PROFESSOR: Yes, well, OK.
So we can lead entire discussions about both
how to write a paper and how to read a paper.
How to read a paper is that you should just
get a color printer, OK?
So that's the advice.
In terms of how to write a paper,
I would say, though, that it's always
good-- you should take advantage of colors,
but you should choose the color scheme/scale such
that it is legible or compelling in both color
and black and white.
And actually there's a very nice set
of articles written by Wong, who's a graphic artist that
works at the Broad.
He wrote maybe 15 different kind of one- or two-page articles
for Nature Methods, basically just
about how to write figures.
And he talks about these different color scales.
You know, there's-- what do the words mean when
there's brightness?
Color, hue, saturation.
I can't remember what all these things mean anymore.
But that's why you should read the articles.
And it's fascinating stuff, actually.
So this is the basic argument they made in this paper,
that because E. coli are exposed to a typical order of carbon
sources in the mammalian gut, that that's
the possible explanation for why this thing evolved that they
can measure experimentally, which
is that when, these E. coli, they see lactose,
they start activating the mall genes but not vice versa.
Now, like always, you can't prove
that this is what's going on.
I think very interesting set of ideas.
Some of the people that study gut microbes just
think that it's implausible that this would actually work out
in the sense that the fitness cost benefits, et cetera,
would be relevant.
Do we know that the time scales even work out?
I don't know how-- so there are a bunch of things
that you could worry about.
And I would say I don't know enough about what
goes on in the gut to actually have an educated
opinion on that point.
But I think it's a very kind of clear exposition of the ideas.
Yeah.
AUDIENCE: Do you have a sense for what
fraction of E. coli bacteria are in the gut of animals?
Do you see what I mean?
Because it's just a very small fraction.
PROFESSOR: That's right.
Yeah, and I guess-- so I myself definitely
do not know what fraction of E.coli are in the gut as
compared to in the soil or in the--
it's not that E. coli are the dominant bacteria in our gut,
either.
It's just that they do enter the gut at some rate.
And then the question is, if we knew the answer,
I don't even know if it would tell us-- I mean,
it gives some guidance.
But there's also a question of where
is it that cells are actually dividing,
because it could be the case that the life cycle is
that they go in the gut, and that's where
they're dividing and happy.
And then they end up in some soil somewhere,
and they're in some stationary phase, and maybe most of them
are dying at some small rate.
Eventually some of them get uptaken again
and then they divide, divide, divide.
So it could be the cases that only 0.1% of all E. coli,
or 01% of the time.
It could be a very small amount of time or something,
and they're in the gut, but it could still
be the dominant event in their lives.
So I just don't know.
I think I'm maybe going to skip the second half of the talk,
or second half of the paper, where they discuss
this idea of the typical order of events in which yeast
in the context of fermentation and making wine
might encounter or experience different environmental
assaults.
And it's a similar kind of idea of cross-protection
against different assaults.
But in some ways, this is really sort
of two mini-papers that tie together
in this general thing of anticipatory regulation.
Are there any questions about this before we move on?
Yes.
AUDIENCE: I have a question about when
the baby males grow up.
Do they need this mechanism?
Do E. coli?
PROFESSOR: OK.
So your question is whether E. coli in the gut of adults
have this.
I don't know, but my feeling is that these things are probably
fairly transient in the sense that you probably
don't have-- well, certainly, from the standpoint of entering
the gut, the bacteria don't have any choice
about whose gut they enter.
So it probably is going to be the case that they
have to have a basic strategy that
is going to work across both adults and the kids,
although it's true that the gut communities in kids
are different from adults.
But it's hard to know what to make of that.
Yeah.
AUDIENCE: So here they decouple the two responses.
Are there any examples of researchers coupling them,
like Pavlov's?
PROFESSOR: Yeah.
That's a good question.
I know that I've heard people talking about it,
but I can't point to a specific example
of where it's been convincing.
That doesn't mean it's not out there, though.
It's a very important, interesting question.
So what we want to now is kind of switch gears
a little bit and switch to this topic of-- it's
going to be kind of partly about phenotypic heterogeneity,
but partly again about fluctuating environments.
And the way that those two topics are related
is via bet hedging, but I just want
to highlight that bet hedging is a way of using
phenotypic heterogeneity in order to survive fluctuating
environments, whereas it's not the only explanation
for this phenotypic heterogeneity.
So yeah, I think maybe we'll-- so first of all,
on the topic of phenotypic heterogeneity,
when we say that we are often referring to the fact that even
clonal populations can be remarkably heterogeneous
in a given environment.
So we'll say phenotypic heterogeneity
in clonal populations, because of course,
if there's a lot of genetic diversity in the population,
then it's not, perhaps, a surprise there would
be phenotypic heterogeneity.
What we're going to do is go through these three
different possible explanations and discuss, maybe,
canonical biological examples of each.
And the examples that we're going to give-- well,
the classic example is in the context of seed germination.
But more recently there's this question
of the persister cells, or the persistence phenotype.
Now in both of these cases, it's really
a way in which a clonal population can
send a small population of either seeds or cells
into a protected state that's protected against some assault.
So seed germination, this is a case
where the seed, if it doesn't germinate,
it's protected against draughts.
Draught.
And this one, maybe, is antibiotics.
What I want to do is just make sure
that we understand the seed germination idea.
And so this is, from the standpoint of ecology,
these ideas came out in the '70s, at least.
So what we can imagine is a situation where you are some,
maybe, desert annual.
And so you send out these seeds.
Now most of the time, you get enough rain,
the seeds are fine.
They can germinate, sprout the little seedlings,
and they'll be able to grow up just fine.
But at some rate there might be a severe drought
that would kill all the cells that actually germinated.
So the question is, what might be the optimal strategy?
So for example, let's just imagine
that we live in a world in which 75% of the time
there's rain, 25% of the time there's no rain.
Now if you germinate-- so a particular seed,
if it germinates, it pops out-- then
it will expect to send two seeds to the following year,
whereas as it germinates and there's no rain,
then it only has a 10% probability of surviving,
or that it could on average send 1/10 of a seed
to the next generation.
Now of course, you don't have to germinate.
If you don't germinate, then what happens
is that you just send one seed to the next year.
If you'd like, you can include some probability
that the seed doesn't survive, but for simplicity, we
can do that.
So the idea is that you don't know whether it's going to rain
or not.
But what you can do is you can either germinate or not
germinate.
And then this tells us how many seeds make it
to the following year.
Do you understand the framework?
So the question is, which one of these strategies
has a higher long term growth rate
in terms of the number of seeds that you
have in the population?
I'm going to give you 30 seconds just
to kind of think about this, play
with the numbers a little bit.
And the question is, should you just
have a strategy where you germinate or don't germinate?
And then what we're going to find,
maybe, is that the optimal strategy is
to do this probabilistically.
But it's useful to just play with such numbers
for a little bit.
The physics office, unfortunately,
is trying to steal our cards from us, so we don't have them.
But what we're going to instead do
is, if you think you want to germinate
you raise your left hand.
If you don't want to germinate, raise your right hand.
OK.
Ready, 3, 2, 1.
So we have a fair distribution of-- it really
is kind of 50-50.
That's interesting.
All right, let's go ahead and-- yeah, let's spend a minute.
Turn to your neighbor and try to convince them that it's either
better to germinate or not.
[SIDE CONVERSATIONS]
You can start with 100 of one, 100 of another, and then just--
AUDIENCE: Start with 100 and then you just go--
[SIDE CONVERSATIONS]
PROFESSOR: Let's say 10 to the 4.
So we're trying to not think about this--
[SIDE CONVERSATIONS]
So there's another question about short term
versus long term.
And we're actually trying to not worry about that.
So you can think about large populations, so it's really--
AUDIENCE: This is after one year.
You will maximize your expected value.
PROFESSOR: That's why I said the long term
growth of the population.
So if we just compare-- so why don't we reconvene.
Various people have been talking about the question
of how many seeds you're starting with,
what the population size is, because you
have to worry about extinction.
And that's another kind of interesting question
of short term versus long term payouts of fitness.
That's actually not the effect that we're
trying to get at right now.
So we can even think about this in the limit of just
large population sizes.
And we want to compare the two strategies.
And for any strategy you choose, including
the probabilistic strategies, there's
going to be a long term growth rate of the population.
So it will grow or shrink exponentially over time.
And what you want to do is you want
to find the strategy, in the context of bet hedging,
you want to find the strategy that maximizes this long term
growth rate of the population.
And this is essentially what Edo talks about in his paper,
but in a more mathematical, general-- because he's talking
about n different phenotypes and environments
and arbitrary switching rates.
And it's beautiful and general and he makes nice connections
to information theory.
But it's possible to read that paper and then not
actually understand what bet hedging,
or what any of these things are, quite.
So it's good to take the simple thing,
and then it's also good to know that somebody like Edo
has thought about this very deeply
and figured out all these beautiful things.
And I know that paper was hard, so don't-- but it's really like
a two-page paper if you look at the text.
So it shouldn't take too much time just
to get a sense of what he's thinking about.
But then it's good, also, to be concrete in a simple situation.
So what we want to know is that, over the long term--
then what you can do is you can just say,
well, the ratios of rain, no rain over the long term
will be 3 to 1, because it's over a long term.
It doesn't matter what order they come in
because over the long run it's all going to average out.
We're assuming we're a large population size,
so we don't have to worry about stochastic extinction.
The question is, since we don't have
to worry about stochastic extinction,
then can we just say that we just
calculate, for example, the mean weighted
by these fractions of these numbers?
And actually, the subtle possible thing
is that it's the geometric mean that is relevant,
not the normal mean.
And that's somehow tricky when given these numbers.
But it's sort of obvious if you just switch this to a 0.
Because if this is a 0, then is germinate
going to be a good strategy?
No, right?
Because what that would mean is that if everybody always
germinates, it may be that this number could be 1,000,
and it's wonderful except that if, at some low rate,
there's no rain and this is a 0, then the population's dead.
And you'll always encounter that eventually.
So that just highlights that it's
the geometric mean you want to be focusing on.
And in particular, we know that on average, over the long term,
there are going to be three of these years for each
of these years.
So we can just multiply the numbers.
So it's really going to be there's going to be three times
where you double for each one time that you divide by 10.
What you see is that over the long run,
this population shrinks, whereas in this case it's 1 times
1 times 1 times 1.
So the long term growth rate/shrinking
rate of these populations is that in the long run
this population does not change in size,
whereas over the long run, this population shrinks.
AUDIENCE: So in the geometric mean the expected change
in the log population, which is also the expected percentage
change in the population.
Is that right?
PROFESSOR: Yes.
So I think that if you take the logs,
it ends up being equivalent.
But you have to make sure you just do it all.
And I guess what I want to highlight in this case is that,
A, you have to be careful of taking averages, but B,
to get the intuition behind the situations
where bet hedging, I think, is really valuable,
it's situations where this thing gets very small
and this might become rather large.
So you can imagine that this could be 200
and this could be 10 to the minus 9.
Or if you'd like, you could say that's 0.
And it's clear that if this is 0, then
you can't germinate all the time,
because then the population's definitely
going to go extinct over the long run.
But this is also a situation where
there's real tension between long term and short term
situations if this probability is very small.
But it's in these situations that it
pays, in terms of the long run growth rate of the population,
to do this some fraction of the time.
And it could be very small.
It could be that only one in 10 to the 4 of the cells
enter this persister state that is resistant to antibiotics.
But it can maximize the long term growth
rate of the population.
There are various models that you
can write down for either seed germination or this or that.
But the relevant thing is, for example, in the persister case,
it might be that the rate of persister formation
might only be one cell in 10 to the 5 or 10 to the 6.
So a very small sub-population of the cells
are in this so-called persister state.
But those cells, they have a couple of properties.
One is that they are dividing slowly.
That means there really is a cost to entering that persister
state, but if it's only one of 10 to the 5,
that means that it's really a rather small cost in terms
of decreasing the growth of the population.
And those cells also could be resistant to antibiotics.
So you can select for them in the sense
that you add a bunch of antibiotics
and maybe only the persister cells are left after 12 hours.
But even though I say you selected for them,
it's not a true antibiotic resistance kind of mutation,
because if you take that persister population,
you let it grow back up, what you
find is that it is still sensitive to the antibiotic.
Now it's also possible that at some low rate, maybe one
in 10 to the 8, you evolve resistance to an antibiotic.
That's genetic resistance that stays with you,
whereas the persister kind of resistance, this
is something that is a phenotypic switch.
And when it grows back up, it kind of
reverts back to the original phenotype,
which is being sensitive to the antibiotic.
So that's the classic way that you distinguish
between genetic resistance and this persister-based or
phenotypic resistance.
Yes.
AUDIENCE: What would be the mechanism
of something like that?
PROFESSOR: That's right.
So people argue a fair amount about this.
And there's a thought that there are
these toxin, anti-toxin modules in bacteria that are normally
suppressed but can be triggered, and then
can lead to these states entering,
although this ends up kind of a muddy debate/subject somehow.
But the idea is that there's something in the cell that
is normally repressed, but then at some rate
activates and causes the cell to-- and of course,
you can always argue, OK, did it evolve for this purpose or not?
Because also, if you're dividing slowly,
then you're going to be resistant to many things.
But then there's also arguments that there are somehow
more specific persister-type states
against particular assaults or particular antibiotics.
So I think that there are many subtleties
to this whole debate.
Any other questions about this idea of bet hedging?
So I think that bet hedging is indeed
one possible way in which evolution
could select for phenotypic heterogeneity in a population.
So this is a population of seeds that are all, in principle,
identical.
You put them out and you plant them all
and they see the same environment.
They don't all germinate.
But it's not that all those seeds that didn't germinate
are dead, because actually, the following year, they still
go back and they can follow some stochastic strategy.
So I just want to stress that right now we're
considering the two extremes, but for bet hedging,
you say probability germinate, 1 minus p, don't germinate.
And those are, in general, going to be some probability p that
can be non-0 that maximizes long term growth
rate of the population.
But I do want to talk about two other possible explanations,
which is this idea of mixed strategies and altruism.
Now mixed strategies, in some ways,
is an obvious one, because we just
got done talking about mixed strategies in game theory,
where there is this notion that in a given game,
sometimes this Nash equilibrium was a pure strategy,
or the evolutionary stable state.
But sometimes at the equilibrium there
was coexistence of these two strategies,
and that could be either implemented
by two different genotypes, or by one genotype implementing
both phenotypes.
So this was the classic game that people talk about
in this area is this hawk dove game.
We talked about this just a little bit in class.
So this is a model of animal conflict.
And the idea is the animals can either
be-- so the idea is that there are two animals
and they come across some resource.
And the resource could be food or it could
be a mate or something else.
And the question is, should those animals
fight for the resource or should they back down?
Now the assumption in all this is
that the hawk is the strategy that fights and the dove
is the strategy that backs down.
Now the question is, how do we assign
some sort of costs and benefits to these various strategies?
Again, where this is the situation where
we take the two-player game and then
we'll kind of generalize it to the population.
Well, if two doves encounter each other,
then they don't need to fight at all,
and they just split the benefit.
So there's some benefit to the resource,
and they each get half of it.
Now of course, if a hawk meets a dove,
the hawk actually does better, because then the hawk gets
the entire benefit, doesn't have to pay the cost.
So already we can see from what I've said so far,
is dove a Nash equilibrium?
No, because you can already see that if your opponent is
a dove, it's better for you.
If you start in the situation where everybody's
a dove, so everybody's getting b over 2,
then one individual has the incentive
to change strategies and get the full benefit.
That hawk never has to fight anybody because they will all
back down.
Now of course this dove that fought
that hawk doesn't get any of the resource,
but also doesn't have to fight.
However, question is, what happens if two hawks meet?
And that's a situation where they really go at it.
And what you might say is, then, there's a 50-50 shot,
that each individual has a 50% chance of getting the benefit,
but then also has to pay this cost.
And then you can decide whether you
want to have-- so I think it's normally parameterized
to b minus c over 2.
The idea here is that you have a 50% chance of getting
the benefit, but you have a 50% chance of getting beaten up.
OK.
Very simple model.
Now the way that we normally parameterize
this is that-- let's say that we want the hawk-- wait,
hold on a second.
Under which circumstances will the hawk strategy
be a Nash equilibrium?
AUDIENCE: If b is larger than c.
PROFESSOR: That's right.
If b is larger than c, then the hawk
would be a Nash equilibrium, which is actually what
we don't want in this game.
So what we typically assume is that the benefit
is less than the cost.
So in that sense, it's somehow not worth fighting for.
And that means that neither strategy is a Nash equilibrium.
So neither the hawk nor the dove is a Nash equilibrium.
And indeed you can calculate what the Nash equilibrium is,
and the Nash equilibrium is to follow a mixed strategy
with some probability p star that is, I think, b over c.
So if there's a bigger benefit, p star
is the probability of following the hawk strategy.
But as the costs grow, then this Nash equilibrium probability
decreases.
So this is a case where it's a mixed strategy that
is this Nash equilibrium.
And so this is a situation that displays
what we call negative frequency dependent selection.
You can see that the rare strategies do better
than common strategies.
The key way to think about this is
that if you have a population of doves,
then a rare hawk does better.
However, if you have a population of hawks,
then it's a rare dove that does better.
And it's that kind of negative frequency of dependence
that pushes the population towards some equilibrium
between the phenotypes, or it could
be equilibrium between genotypes as well, because you could have
pure strategists of a hawk and a dove, so different genotypes
that just are different.
And the differences in fitness will naturally
lead to evolution to an equilibrium hawk
kind of frequency in the population
that is equal to this.
So this tells us either about the equilibrium frequency
of the genotype of hawk in the population.
Or it could be that it's a single genotype that
implements these two strategies with some frequency that
is b over c.
So I'd say that this is a simple idea from the context of game
theory, and the question is, what circumstances
might this actually arise in kind of real populations.
Oh, before I say anything else, I
do want to stress that all of you
have played mixed strategies before, because in the Rock
Paper Scissors game, which we're going to be talking about
more in the coming week or so-- you guys all know this,
that rock beats-- not paper-- but rock beats scissors,
scissors beats paper, paper beats rock--
so the Nash equilibrium of that game is to do 1/3 1/3, 1/3,
because if everybody's following that strategy,
nobody has the incentive to change strategies.
Definition of the Nash equilibrium.
Is that the optimal strategy against any opponent?
No.
And this is very important to point out,
because when you think about these Nash equilibrium
and everything in abstract terms,
it's easy to get confused about--
when we say that it's-- sometimes we say optimal,
or it's the solution to the game,
that doesn't mean that it's the best response to any given
strategy.
And you know that, because if you
know that your little brother is going to play rock, then
you know-- well, depending on whether you
want to make him happy or not, you decide what to do, right?
So it's clear that this 1/3, 1/3, 1/3 thing
is, it can be the solution to the game of the Nash
equilibrium without being the best response to any given
strategy.
So one of things that we're doing in my group,
actually, is we're arguing that in the case of yeasts that
are exposed to mixed sugar environments--
so yeast in environments that contain a little bit of glucose
and a little bit of galactose-- what we and actually
other people have found is that there's a bimodal response.
So if you look at the number of cells as a function of the GAL
operon expression, so GAL is the expression
of the genes required to break down galactose, what you see
is that some of the cells activate the GAL genes highly,
some don't activate it at all.
So the question is, what might be
an explanation for this phenotypic heterogeneity
observed in a clonal population?
And one way to think about this is
that it could be the implementation
of some sort of foraging game.
So you can imagine a population of animals that want
to go and eat some berries.
So there are two different food sources--
say there are blueberries and there are red berries.
You can imagine this is the kind of situation that
would lead to negative frequency dependence,
because if everybody else goes and eats--
I guess this was the blueberry-- so if everybody else goes
and eats the blueberries, then it's better for you
to eat the red berry because you don't have
to share with anyone, whereas if everyone else goes and eats
the red berries, then it's better for you
to eat the blueberries.
So that's the kind of situation that would naturally
lead to the so-called negative frequency dependent selection,
in which coexistence of the phenotypes
is somehow the equilibrium condition,
and that can be implemented either by different genotypes
or it can be implemented by a single genotype that
follows both phenotypes.
Incidentally, is this equilibrium--
does it maximize the fitness of the population?
No.
So what is it that would maximize
the fitness of the population?
If everybody were a dove, because-- and you can
you go ahead and do this calculation,
find out what the fitness of everybody is,
but what you'll see is that p star does not maximize fitness,
ford not maximize payoff.
So in these games, the equilibrium is not necessarily
fitness maximizing.
So so far what we've done is we've
given two examples of different evolutionary drivers
for phenotypic heterogeneity in a population.
And I just want to highlight what
I think is maybe the last big one, which would be altruism.
And sometimes people call it division of labor,
or sacrifice or so.
And a nice example of this is colicin production.
The idea is that in many bacteria,
they express these colicin, which are toxins.
And we're going to read more about this later.
So colicin is a toxin.
And the perhaps surprising thing is
that in many gram-negative bacteria, like E. coli, when
they make this colicin, the only way it's released
is cell lysis.
Now the question is, why would I possibly do this?
And the answer is, perhaps, that if there's
a plasmid that encodes the genes to make this toxin,
it also encodes an immunity protein.
What that means is that if one cell lyses--
so it bursts open and releases the colicin--
it will inhibit other bacteria, but not
the bacteria that are the clone mates that are related,
so not the bacteria that also carry that plasmid.
So it's important to note there that now when
we talk about kin selection or relatedness,
we're talking about the other cells that carry that gene.
So what's relevant is that the plasma that encodes this toxin
will inhibit other bacteria that do not encode the toxin.
Now you can see that this kind of lysis behavior
has to be stochastic, so there has
to be phenotypic heterogeneity.
And why is that?
AUDIENCE: Everyone always lyses.
PROFESSOR: That's right.
If this plasmid always makes everybody lyse,
then it's not going to get very far, right?
But you can kind of imagine situations
where, if you just 1% of the population
lyses but then inhibits the cells that
don't care that plasmid, then the plasmid
can spread in the population.
So this has to be stochastic.
So I think that this is another general explanation
for why there might be phenotypic heterogeneity
in the population.
All of these three explanations are both conceptually different
and they're experimentally different.
They make different falsifiable predictions
about what's driving that phenotypic heterogeneity.
In this field, I think often when people
see phenotypic heterogeneity, they immediately
assume that it's bet hedging, but these other two
explanations, I think, are just as general
and may be just as common.
So we really have to go and make measurements
to try to elucidate what's going on in each case.