Math can help uncover cancer's secrets | Irina Kareva

74,501 views ・ 2018-04-25

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00:12
I am a translator.
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I translate from biology into mathematics
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and vice versa.
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I write mathematical models
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which, in my case, are systems of differential equations,
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to describe biological mechanisms,
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such as cell growth.
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Essentially, it works like this.
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First, I identify the key elements
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that I believe may be driving behavior over time
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of a particular mechanism.
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Then, I formulate assumptions
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about how these elements interact with each other
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and with their environment.
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It may look something like this.
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Then, I translate these assumptions into equations,
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which may look something like this.
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Finally, I analyze my equations
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and translate the results back into the language of biology.
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A key aspect of mathematical modeling
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is that we, as modelers, do not think about what things are;
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we think about what they do.
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We think about relationships between individuals,
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whether they be cells, animals or people,
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and how they interact with each other and with their environment.
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Let me give you an example.
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What do foxes and immune cells have in common?
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They're both predators,
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except foxes feed on rabbits,
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and immune cells feed on invaders, such as cancer cells.
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But from a mathematical point of view,
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a qualitatively same system of predator-prey type equations
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will describe interactions between foxes and rabbits
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and cancer and immune cells.
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Predator-prey type systems have been studied extensively
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in scientific literature,
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describing interactions of two populations,
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where survival of one depends on consuming the other.
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And these same equations provide a framework
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for understanding cancer-immune interactions,
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where cancer is the prey,
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and the immune system is the predator.
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And the prey employs all sorts of tricks to prevent the predator from killing it,
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ranging from camouflaging itself
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to stealing the predator's food.
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This can have some very interesting implications.
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For example, despite enormous successes in the field of immunotherapy,
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there still remains somewhat limited efficacy
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when it comes solid tumors.
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But if you think about it ecologically,
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both cancer and immune cells --
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the prey and the predator --
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require nutrients such as glucose to survive.
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If cancer cells outcompete the immune cells for shared nutrients
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in the tumor microenvironment,
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then the immune cells will physically not be able to do their job.
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This predator-prey-shared resource type model
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is something I've worked on in my own research.
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And it was recently shown experimentally
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that restoring the metabolic balance in the tumor microenvironment --
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that is, making sure immune cells get their food --
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can give them, the predators, back their edge in fighting cancer, the prey.
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This means that if you abstract a bit,
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you can think about cancer itself as an ecosystem,
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where heterogeneous populations of cells compete and cooperate
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for space and nutrients,
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interact with predators -- the immune system --
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migrate -- metastases --
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all within the ecosystem of the human body.
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And what do we know about most ecosystems from conservation biology?
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That one of the best ways to extinguish species
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is not to target them directly
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but to target their environment.
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And so, once we have identified the key components
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of the tumor environment,
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we can propose hypotheses
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and simulate scenarios and therapeutic interventions
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all in a completely safe and affordable way
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and target different components of the microenvironment
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in such a way as to kill the cancer without harming the host,
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such as me or you.
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And so while the immediate goal of my research
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is to advance research and innovation
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and to reduce its cost,
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the real intent, of course, is to save lives.
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And that's what I try to do
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through mathematical modeling applied to biology,
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and in particular, to the development of drugs.
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It's a field that until relatively recently has remained somewhat marginal,
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but it has matured.
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And there are now very well-developed mathematical methods,
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a lot of preprogrammed tools,
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including free ones,
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and an ever-increasing amount of computational power available to us.
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The power and beauty of mathematical modeling
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lies in the fact that it makes you formalize,
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in a very rigorous way,
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what we think we know.
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We make assumptions,
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translate them into equations,
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run simulations,
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all to answer the question:
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In a world where my assumptions are true,
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what do I expect to see?
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It's a pretty simple conceptual framework.
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It's all about asking the right questions.
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But it can unleash numerous opportunities for testing biological hypotheses.
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If our predictions match our observations,
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great! -- we got it right, so we can make further predictions
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by changing this or that aspect of the model.
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If, however, our predictions do not match our observations,
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that means that some of our assumptions are wrong,
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and so our understanding of the key mechanisms
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of underlying biology
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is still incomplete.
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Luckily, since this is a model,
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we control all the assumptions.
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So we can go through them, one by one,
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identifying which one or ones are causing the discrepancy.
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And then we can fill this newly identified gap in knowledge
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using both experimental and theoretical approaches.
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Of course, any ecosystem is extremely complex,
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and trying to describe all the moving parts is not only very difficult,
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but also not very informative.
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There's also the issue of timescales,
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because some processes take place on a scale of seconds, some minutes,
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some days, months and years.
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It may not always be possible to separate those out experimentally.
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And some things happen so quickly or so slowly
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that you may physically never be able to measure them.
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But as mathematicians,
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we have the power to zoom in on any subsystem in any timescale
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and simulate effects of interventions
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that take place in any timescale.
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Of course, this isn't the work of a modeler alone.
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It has to happen in close collaboration with biologists.
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And it does demand some capacity of translation
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on both sides.
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But starting with a theoretical formulation of a problem
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can unleash numerous opportunities for testing hypotheses
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and simulating scenarios and therapeutic interventions,
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all in a completely safe way.
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It can identify gaps in knowledge and logical inconsistencies
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and can help guide us as to where we should keep looking
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and where there may be a dead end.
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In other words:
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mathematical modeling can help us answer questions
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that directly affect people's health --
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that affect each person's health, actually --
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because mathematical modeling will be key
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to propelling personalized medicine.
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And it all comes down to asking the right question
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and translating it to the right equation ...
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and back.
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Thank you.
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(Applause)
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