Math can help uncover cancers secrets Irina Kareva
I am a translator.
I translate from biology into mathematics
and vice versa.
I write mathematical models
which, in my case, are systems
of differential equations,
to describe biological mechanisms,
such as cell growth.
Essentially, it works like this.
First, I identify the key elements
that I believe may be driving
behavior over time
of a particular mechanism.
Then, I formulate assumptions
about how these elements
interact with each other
and with their environment.
It may look something like this.
Then, I translate
these assumptions into equations,
which may look something like this.
Finally, I analyze my equations
and translate the results back
into the language of biology.
A key aspect of mathematical modeling
is that we, as modelers,
do not think about what things are;
we think about what they do.
We think about relationships
between individuals,
whether they be cells, animals or people,
and how they interact with each other
and with their environment.
Let me give you an example.
What do foxes and immune cells
have in common?
They’re both predators,
except foxes feed on rabbits,
and immune cells feed on invaders,
such as cancer cells.
But from a mathematical point of view,
a qualitatively same system
of predator-prey type equations
will describe interactions
between foxes and rabbits
and cancer and immune cells.
Predator-prey type systems
have been studied extensively
in scientific literature,
describing interactions
of two populations,
where survival of one depends
on consuming the other.
And these same equations
provide a framework
for understanding
cancer-immune interactions,
where cancer is the prey,
and the immune system is the predator.
And the prey employs all sorts of tricks
to prevent the predator from killing it,
ranging from camouflaging itself
to stealing the predator’s food.
This can have some very
interesting implications.
For example, despite enormous successes
in the field of immunotherapy,
there still remains
somewhat limited efficacy
when it comes solid tumors.
But if you think about it ecologically,
both cancer and immune cells –
the prey and the predator –
require nutrients
such as glucose to survive.
If cancer cells outcompete
the immune cells for shared nutrients
in the tumor microenvironment,
then the immune cells will physically
not be able to do their job.
This predator-prey-shared
resource type model
is something I’ve worked on
in my own research.
And it was recently shown experimentally
that restoring the metabolic balance
in the tumor microenvironment –
that is, making sure
immune cells get their food –
can give them, the predators, back
their edge in fighting cancer, the prey.
This means that if you abstract a bit,
you can think about cancer itself
as an ecosystem,
where heterogeneous populations of cells
compete and cooperate
for space and nutrients,
interact with predators –
the immune system –
migrate – metastases –
all within the ecosystem
of the human body.
And what do we know about most
ecosystems from conservation biology?
That one of the best ways
to extinguish species
is not to target them directly
but to target their environment.
And so, once we have identified
the key components
of the tumor environment,
we can propose hypotheses
and simulate scenarios
and therapeutic interventions
all in a completely safe
and affordable way
and target different components
of the microenvironment
in such a way as to kill the cancer
without harming the host,
such as me or you.
And so while the immediate
goal of my research
is to advance research and innovation
and to reduce its cost,
the real intent, of course,
is to save lives.
And that’s what I try to do
through mathematical modeling
applied to biology,
and in particular,
to the development of drugs.
It’s a field that until relatively
recently has remained somewhat marginal,
but it has matured.
And there are now very well-developed
mathematical methods,
a lot of preprogrammed tools,
including free ones,
and an ever-increasing amount
of computational power available to us.
The power and beauty
of mathematical modeling
lies in the fact
that it makes you formalize,
in a very rigorous way,
what we think we know.
We make assumptions,
translate them into equations,
run simulations,
all to answer the question:
In a world where my assumptions are true,
what do I expect to see?
It’s a pretty simple conceptual framework.
It’s all about asking the right questions.
But it can unleash numerous opportunities
for testing biological hypotheses.
If our predictions match our observations,
great! – we got it right,
so we can make further predictions
by changing this or that
aspect of the model.
If, however, our predictions
do not match our observations,
that means that some
of our assumptions are wrong,
and so our understanding
of the key mechanisms
of underlying biology
is still incomplete.
Luckily, since this is a model,
we control all the assumptions.
So we can go through them, one by one,
identifying which one or ones
are causing the discrepancy.
And then we can fill this newly
identified gap in knowledge
using both experimental
and theoretical approaches.
Of course, any ecosystem
is extremely complex,
and trying to describe all the moving
parts is not only very difficult,
but also not very informative.
There’s also the issue of timescales,
because some processes take place
on a scale of seconds, some minutes,
some days, months and years.
It may not always be possible
to separate those out experimentally.
And some things happen
so quickly or so slowly
that you may physically
never be able to measure them.
But as mathematicians,
we have the power to zoom in
on any subsystem in any timescale
and simulate effects of interventions
that take place in any timescale.
Of course, this isn’t the work
of a modeler alone.
It has to happen in close
collaboration with biologists.
And it does demand
some capacity of translation
on both sides.
But starting with a theoretical
formulation of a problem
can unleash numerous opportunities
for testing hypotheses
and simulating scenarios
and therapeutic interventions,
all in a completely safe way.
It can identify gaps in knowledge
and logical inconsistencies
and can help guide us
as to where we should keep looking
and where there may be a dead end.
In other words:
mathematical modeling
can help us answer questions
that directly affect people’s health –
that affect each
person’s health, actually –
because mathematical modeling will be key
to propelling personalized medicine.
And it all comes down
to asking the right question
and translating it
to the right equation …
and back.
Thank you.
(Applause)