TED@Merck KGaA, Darmstadt, Germany
Irina Kareva: Math can help uncover cancer's secrets
Filmed:
Readability: 5.8
1,223,313 views
Irina Kareva translates biology into mathematics and vice versa. She writes mathematical models that describe the dynamics of cancer, with the goal of developing new drugs that target tumors. "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," Kareva says. "It can help guide us to where we should keep looking, and where there may be a dead end." It all comes down to asking the right question and translating it to the right equation, and back.
Irina Kareva - Theoretical biologist
Irina Kareva is looking for answers to biological questions using mathematical modeling. Full bio
Irina Kareva is looking for answers to biological questions using mathematical modeling. Full bio
Double-click the English transcript below to play the video.
00:12
I am a translator.
0
549
1243
00:14
I translate from biology into mathematics
1
2514
3191
00:17
and vice versa.
2
5729
1150
00:19
I write mathematical models
3
7588
1790
00:21
which, in my case, are systems
of differential equations,
of differential equations,
4
9402
2847
00:24
to describe biological mechanisms,
5
12273
1947
00:26
such as cell growth.
6
14244
1158
00:28
Essentially, it works like this.
7
16122
1848
00:30
First, I identify the key elements
8
18573
2469
00:33
that I believe may be driving
behavior over time
behavior over time
9
21066
2777
00:35
of a particular mechanism.
10
23867
1539
00:38
Then, I formulate assumptions
11
26230
1891
00:40
about how these elements
interact with each other
interact with each other
12
28145
2886
00:43
and with their environment.
13
31055
1337
00:44
It may look something like this.
14
32916
1772
00:46
Then, I translate
these assumptions into equations,
these assumptions into equations,
15
34712
3317
00:50
which may look something like this.
16
38610
1824
00:53
Finally, I analyze my equations
17
41434
1890
00:55
and translate the results back
into the language of biology.
into the language of biology.
18
43348
3101
01:00
A key aspect of mathematical modeling
19
48156
2420
01:02
is that we, as modelers,
do not think about what things are;
do not think about what things are;
20
50600
3908
01:06
we think about what they do.
21
54532
1855
01:08
We think about relationships
between individuals,
between individuals,
22
56411
2489
01:10
whether they be cells, animals or people,
23
58924
2886
01:13
and how they interact with each other
and with their environment.
and with their environment.
24
61834
3048
01:17
Let me give you an example.
25
65639
1340
01:19
What do foxes and immune cells
have in common?
have in common?
26
67719
3803
01:24
They're both predators,
27
72793
1459
01:26
except foxes feed on rabbits,
28
74744
2723
01:29
and immune cells feed on invaders,
such as cancer cells.
such as cancer cells.
29
77491
3330
01:33
But from a mathematical point of view,
30
81273
2345
01:35
a qualitatively same system
of predator-prey type equations
of predator-prey type equations
31
83642
4156
01:39
will describe interactions
between foxes and rabbits
between foxes and rabbits
32
87822
3245
01:43
and cancer and immune cells.
33
91091
1774
01:45
Predator-prey type systems
have been studied extensively
have been studied extensively
34
93609
2708
01:48
in scientific literature,
35
96341
1269
01:49
describing interactions
of two populations,
of two populations,
36
97634
2378
01:52
where survival of one depends
on consuming the other.
on consuming the other.
37
100036
2775
01:55
And these same equations
provide a framework
provide a framework
38
103485
2620
01:58
for understanding
cancer-immune interactions,
cancer-immune interactions,
39
106129
2311
02:00
where cancer is the prey,
40
108464
1841
02:02
and the immune system is the predator.
41
110329
2372
02:04
And the prey employs all sorts of tricks
to prevent the predator from killing it,
to prevent the predator from killing it,
42
112725
4032
02:08
ranging from camouflaging itself
43
116781
1820
02:10
to stealing the predator's food.
44
118625
1839
02:13
This can have some very
interesting implications.
interesting implications.
45
121352
2562
02:15
For example, despite enormous successes
in the field of immunotherapy,
in the field of immunotherapy,
46
123938
4822
02:20
there still remains
somewhat limited efficacy
somewhat limited efficacy
47
128784
2461
02:23
when it comes solid tumors.
48
131269
1542
02:25
But if you think about it ecologically,
49
133423
2559
02:28
both cancer and immune cells --
50
136006
2090
02:30
the prey and the predator --
51
138120
1600
02:31
require nutrients
such as glucose to survive.
such as glucose to survive.
52
139744
3031
02:35
If cancer cells outcompete
the immune cells for shared nutrients
the immune cells for shared nutrients
53
143358
4789
02:40
in the tumor microenvironment,
54
148171
1793
02:41
then the immune cells will physically
not be able to do their job.
not be able to do their job.
55
149988
3414
02:46
This predator-prey-shared
resource type model
resource type model
56
154291
2868
02:49
is something I've worked on
in my own research.
in my own research.
57
157183
2297
02:51
And it was recently shown experimentally
58
159504
2724
02:54
that restoring the metabolic balance
in the tumor microenvironment --
in the tumor microenvironment --
59
162252
4054
02:58
that is, making sure
immune cells get their food --
immune cells get their food --
60
166330
3531
03:01
can give them, the predators, back
their edge in fighting cancer, the prey.
their edge in fighting cancer, the prey.
61
169885
5245
03:08
This means that if you abstract a bit,
62
176440
2339
03:10
you can think about cancer itself
as an ecosystem,
as an ecosystem,
63
178803
2955
03:13
where heterogeneous populations of cells
compete and cooperate
compete and cooperate
64
181782
4287
03:18
for space and nutrients,
65
186093
2017
03:20
interact with predators --
the immune system --
the immune system --
66
188134
2672
03:22
migrate -- metastases --
67
190830
2241
03:25
all within the ecosystem
of the human body.
of the human body.
68
193095
2467
03:28
And what do we know about most
ecosystems from conservation biology?
ecosystems from conservation biology?
69
196221
3869
03:32
That one of the best ways
to extinguish species
to extinguish species
70
200643
2852
03:35
is not to target them directly
71
203519
1952
03:37
but to target their environment.
72
205495
2439
03:40
And so, once we have identified
the key components
the key components
73
208880
3070
03:43
of the tumor environment,
74
211974
1644
03:45
we can propose hypotheses
75
213642
1948
03:47
and simulate scenarios
and therapeutic interventions
and therapeutic interventions
76
215614
3294
03:50
all in a completely safe
and affordable way
and affordable way
77
218932
3425
03:54
and target different components
of the microenvironment
of the microenvironment
78
222381
3369
03:57
in such a way as to kill the cancer
without harming the host,
without harming the host,
79
225774
3996
04:01
such as me or you.
80
229794
1570
04:05
And so while the immediate
goal of my research
goal of my research
81
233029
3002
04:08
is to advance research and innovation
82
236055
2266
04:10
and to reduce its cost,
83
238345
1896
04:12
the real intent, of course,
is to save lives.
is to save lives.
84
240265
2517
04:15
And that's what I try to do
85
243278
1771
04:17
through mathematical modeling
applied to biology,
applied to biology,
86
245073
2747
04:19
and in particular,
to the development of drugs.
to the development of drugs.
87
247844
2471
04:22
It's a field that until relatively
recently has remained somewhat marginal,
recently has remained somewhat marginal,
88
250895
4056
04:26
but it has matured.
89
254975
1452
04:28
And there are now very well-developed
mathematical methods,
mathematical methods,
90
256451
3149
04:31
a lot of preprogrammed tools,
91
259624
1899
04:33
including free ones,
92
261547
1496
04:35
and an ever-increasing amount
of computational power available to us.
of computational power available to us.
93
263067
4047
04:40
The power and beauty
of mathematical modeling
of mathematical modeling
94
268718
3399
04:44
lies in the fact
that it makes you formalize,
that it makes you formalize,
95
272141
2641
04:46
in a very rigorous way,
96
274806
2087
04:48
what we think we know.
97
276917
1465
04:50
We make assumptions,
98
278904
1444
04:52
translate them into equations,
99
280372
1568
04:53
run simulations,
100
281964
1311
04:55
all to answer the question:
101
283299
1773
04:57
In a world where my assumptions are true,
102
285096
2246
04:59
what do I expect to see?
103
287366
1570
05:01
It's a pretty simple conceptual framework.
104
289890
2086
05:04
It's all about asking the right questions.
105
292000
2226
05:06
But it can unleash numerous opportunities
for testing biological hypotheses.
for testing biological hypotheses.
106
294603
4095
05:11
If our predictions match our observations,
107
299696
2600
05:14
great! -- we got it right,
so we can make further predictions
so we can make further predictions
108
302320
3027
05:17
by changing this or that
aspect of the model.
aspect of the model.
109
305371
2560
05:20
If, however, our predictions
do not match our observations,
do not match our observations,
110
308733
3700
05:24
that means that some
of our assumptions are wrong,
of our assumptions are wrong,
111
312457
2585
05:27
and so our understanding
of the key mechanisms
of the key mechanisms
112
315066
2433
05:29
of underlying biology
113
317523
1439
05:30
is still incomplete.
114
318986
1270
05:32
Luckily, since this is a model,
115
320829
2362
05:35
we control all the assumptions.
116
323215
1889
05:37
So we can go through them, one by one,
117
325128
2140
05:39
identifying which one or ones
are causing the discrepancy.
are causing the discrepancy.
118
327292
3829
05:43
And then we can fill this newly
identified gap in knowledge
identified gap in knowledge
119
331637
3356
05:47
using both experimental
and theoretical approaches.
and theoretical approaches.
120
335017
2715
05:50
Of course, any ecosystem
is extremely complex,
is extremely complex,
121
338699
2821
05:53
and trying to describe all the moving
parts is not only very difficult,
parts is not only very difficult,
122
341544
3843
05:57
but also not very informative.
123
345411
1662
05:59
There's also the issue of timescales,
124
347518
2066
06:01
because some processes take place
on a scale of seconds, some minutes,
on a scale of seconds, some minutes,
125
349608
3668
06:05
some days, months and years.
126
353300
1948
06:07
It may not always be possible
to separate those out experimentally.
to separate those out experimentally.
127
355272
3199
06:11
And some things happen
so quickly or so slowly
so quickly or so slowly
128
359143
3384
06:14
that you may physically
never be able to measure them.
never be able to measure them.
129
362551
2720
06:17
But as mathematicians,
130
365295
2288
06:19
we have the power to zoom in
on any subsystem in any timescale
on any subsystem in any timescale
131
367607
5645
06:25
and simulate effects of interventions
132
373276
2124
06:27
that take place in any timescale.
133
375424
2701
06:31
Of course, this isn't the work
of a modeler alone.
of a modeler alone.
134
379942
2934
06:34
It has to happen in close
collaboration with biologists.
collaboration with biologists.
135
382900
3289
06:38
And it does demand
some capacity of translation
some capacity of translation
136
386213
3004
06:41
on both sides.
137
389241
1204
06:43
But starting with a theoretical
formulation of a problem
formulation of a problem
138
391550
3788
06:47
can unleash numerous opportunities
for testing hypotheses
for testing hypotheses
139
395362
3497
06:50
and simulating scenarios
and therapeutic interventions,
and therapeutic interventions,
140
398883
3239
06:54
all in a completely safe way.
141
402146
2070
06:56
It can identify gaps in knowledge
and logical inconsistencies
and logical inconsistencies
142
404977
5175
07:02
and can help guide us
as to where we should keep looking
as to where we should keep looking
143
410176
2839
07:05
and where there may be a dead end.
144
413039
1895
07:07
In other words:
145
415632
1247
07:08
mathematical modeling
can help us answer questions
can help us answer questions
146
416903
3494
07:12
that directly affect people's health --
147
420421
2388
07:15
that affect each
person's health, actually --
person's health, actually --
148
423942
2704
07:18
because mathematical modeling will be key
149
426670
2676
07:21
to propelling personalized medicine.
150
429370
1834
07:24
And it all comes down
to asking the right question
to asking the right question
151
432112
3067
07:27
and translating it
to the right equation ...
to the right equation ...
152
435711
2075
07:30
and back.
153
438670
1150
07:32
Thank you.
154
440533
1151
07:33
(Applause)
155
441708
3299
ABOUT THE SPEAKER
Irina Kareva - Theoretical biologistIrina Kareva is looking for answers to biological questions using mathematical modeling.
Why you should listen
Dr. Irina Kareva studies cancer as an evolving ecosystem, bringing in insights from various disciplines -- from evolutionary biology to paleontology to ergodic theory -- to understand how we can manage, if not cure, cancer like a chronic disease. She has authored more than 25 publications, including several papers with her parents, who are also mathematicians. The Kareva clan was featured in a Nature article entitled "Relationships: Scions of Science."
Kareva is a research scientist at EMD Serono Research Center near Boston Massachusetts, US. Her book, Understanding Cancer from a Systems Biology Point of View: From Observation to Theory and Back, was recently published by Elsevier, and a second book on mathematical modeling of the evolution of heterogeneous populations will be released in mid-2019.
In addition to her scientific studies and endeavors, Kareva also holds a degree in music and works actively as a professional opera singer. She is a member of the Boston Symphony Orchestra’s Tanglewood Festival Chorus, has performed solo roles in local productions, religious music performances, and can even occasionally be heard in pieces as varied as video game soundtracks and heavy metal recordings.
Irina Kareva | Speaker | TED.com