TED@Merck KGaA, Darmstadt, Germany
Irina Kareva: Math can help uncover cancer's secrets
艾瑞娜·卡瑞瓦: 数学有助于揭开癌症的奥秘
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艾瑞娜·卡瑞瓦把生物语言翻译成数学语言，再从数学翻译回生物。她建立描述癌症动态的数学模型，目的在于研制出治疗肿瘤的新型药物。“数学建模的力与美在于，它可以以最有力的方式，将我们的认知形式化。”艾瑞娜这样说。“数学模型可以引导我们，让我们知道哪里值得继续探索，哪里可能是死路。”这一切的关键在于问对问题、把问题翻译成对的方程式、再翻译回去。
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.
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我是一名翻译。
00:14
I translate from biology into mathematics
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我把生物学翻译成数学，
00:17
and vice versa.
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反之亦然。
00:19
I write mathematical models
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我建造数学模型，
00:21
which, in my case, are systems
of differential equations,
of differential equations,
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用微分方程组，
00:24
to describe biological mechanisms,
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来描述生物学机制，
00:26
such as cell growth.
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比如说细胞的生长。
00:28
Essentially, it works like this.
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基本来说，运作过程如下。
00:30
First, I identify the key elements
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首先，我找出关键的元素，
00:33
that I believe may be driving
behavior over time
behavior over time
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那些我认为
可能会随着时间的推移，
可能会随着时间的推移，
影响某些特定机制运作的元素。
00:35
of a particular mechanism.
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00:38
Then, I formulate assumptions
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然后，我做出假设，
00:40
about how these elements
interact with each other
interact with each other
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猜测这些元素
如何与彼此互动，
如何与彼此互动，
00:43
and with their environment.
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与它们的环境互动。
00:44
It may look something like this.
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可能看起来像这样。
00:46
Then, I translate
these assumptions into equations,
these assumptions into equations,
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然后，我把这些假设
翻译成方程，
翻译成方程，
00:50
which may look something like this.
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它看起来可能像这样。
00:53
Finally, I analyze my equations
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最后，我分析我的方程，
00:55
and translate the results back
into the language of biology.
into the language of biology.
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并把结果翻译回生物学语言。
01:00
A key aspect of mathematical modeling
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数学建模的一个关键点在于，
01:02
is that we, as modelers,
do not think about what things are;
do not think about what things are;
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我们作为建模者，
不是想这些东西“是”什么，
不是想这些东西“是”什么，
而是想它们“做”什么。
01:06
we think about what they do.
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我们思考个体之间的关系，
01:08
We think about relationships
between individuals,
between individuals,
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01:10
whether they be cells, animals or people,
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不管这些个体是细胞、动物还是人，
01:13
and how they interact with each other
and with their environment.
and with their environment.
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我们想它们如何与彼此相互影响、
与它们周围的环境相互影响。
与它们周围的环境相互影响。
01:17
Let me give you an example.
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让我来举个例子。
01:19
What do foxes and immune cells
have in common?
have in common?
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狐狸和免疫细胞之间
有什么共同点？
有什么共同点？
01:24
They're both predators,
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它们都是捕食者，
01:26
except foxes feed on rabbits,
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只不过狐狸吃兔子，
01:29
and immune cells feed on invaders,
such as cancer cells.
such as cancer cells.
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而免疫细胞以入侵者为食，
比如说癌细胞。
比如说癌细胞。
01:33
But from a mathematical point of view,
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但是从数学的角度来说，
01:35
a qualitatively same system
of predator-prey type equations
of predator-prey type equations
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用本质上相同的
捕食者——猎物方程系统，
捕食者——猎物方程系统，
01:39
will describe interactions
between foxes and rabbits
between foxes and rabbits
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就能描述狐狸与兔子
之间的相互影响
之间的相互影响
01:43
and cancer and immune cells.
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还有癌细胞与免疫细胞
之间的相互影响。
之间的相互影响。
01:45
Predator-prey type systems
have been studied extensively
have been studied extensively
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捕食者——猎物类型的方程系统，
01:48
in scientific literature,
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已经在科学文献中被广泛研究，
01:49
describing interactions
of two populations,
of two populations,
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它被用来描述
两个种群之间的相互影响，
两个种群之间的相互影响，
01:52
where survival of one depends
on consuming the other.
on consuming the other.
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其中一个种群吃掉另一个种群
才能得以生存。
才能得以生存。
01:55
And these same equations
provide a framework
provide a framework
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也就是这些方程为我们
提供了一个框架
提供了一个框架
01:58
for understanding
cancer-immune interactions,
cancer-immune interactions,
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来了解癌细胞与免疫系统
之间的相互影响，
之间的相互影响，
在这套方程中，癌细胞是猎物，
02:00
where cancer is the prey,
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02:02
and the immune system is the predator.
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免疫系统是捕食者。
02:04
And the prey employs all sorts of tricks
to prevent the predator from killing it,
to prevent the predator from killing it,
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猎物会采用一切诡计
来防止被捕食者杀死，
来防止被捕食者杀死，
02:08
ranging from camouflaging itself
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从伪装自己，
02:10
to stealing the predator's food.
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到偷走捕食者的食物。
02:13
This can have some very
interesting implications.
interesting implications.
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这可能会产生一些非常有趣的情况。
02:15
For example, despite enormous successes
in the field of immunotherapy,
in the field of immunotherapy,
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举例来说，尽管我们在免疫疗法领域
取得了巨大的成就，
取得了巨大的成就，
02:20
there still remains
somewhat limited efficacy
somewhat limited efficacy
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但在面对实体恶性肿瘤时，
02:23
when it comes solid tumors.
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其疗效还是十分有限的。
02:25
But if you think about it ecologically,
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但如果从生态学的观点来思考的话，
02:28
both cancer and immune cells --
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不管是癌细胞和免疫细胞——
02:30
the prey and the predator --
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即猎物和捕食者——
02:31
require nutrients
such as glucose to survive.
such as glucose to survive.
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都需要营养（如葡萄糖）来生存。
02:35
If cancer cells outcompete
the immune cells for shared nutrients
the immune cells for shared nutrients
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如果癌细胞比免疫细胞
摄入的共享养分更多，
摄入的共享养分更多，
02:40
in the tumor microenvironment,
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在肿瘤的微环境中，
02:41
then the immune cells will physically
not be able to do their job.
not be able to do their job.
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免疫细胞就不能够
完成它们的工作。
完成它们的工作。
02:46
This predator-prey-shared
resource type model
resource type model
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这种
捕食者—猎物—共享资源类的模型，
捕食者—猎物—共享资源类的模型，
02:49
is something I've worked on
in my own research.
in my own research.
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是我一直在研究的。
02:51
And it was recently shown experimentally
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最近的实验表明
02:54
that restoring the metabolic balance
in the tumor microenvironment --
in the tumor microenvironment --
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恢复肿瘤微环境中的
新陈代谢平衡——
新陈代谢平衡——
02:58
that is, making sure
immune cells get their food --
immune cells get their food --
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也就是确保免疫细胞
得到它们的食物——
得到它们的食物——
03:01
can give them, the predators, back
their edge in fighting cancer, the prey.
their edge in fighting cancer, the prey.
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可以使免疫细胞（捕食者）在
与癌细胞（猎物）对抗时找回优势。
与癌细胞（猎物）对抗时找回优势。
03:08
This means that if you abstract a bit,
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意思就是，抽象一点来想，
03:10
you can think about cancer itself
as an ecosystem,
as an ecosystem,
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你可以把癌细胞自身
想象成一个生态系统，
想象成一个生态系统，
03:13
where heterogeneous populations of cells
compete and cooperate
compete and cooperate
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在这个系统中，多样的细胞种群
相互竞争、相互合作
相互竞争、相互合作
03:18
for space and nutrients,
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来获取空间和营养，
03:20
interact with predators --
the immune system --
the immune system --
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与捕食者——免疫细胞相互影响，
03:22
migrate -- metastases --
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迁移，也就是新陈代谢……
03:25
all within the ecosystem
of the human body.
of the human body.
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这全都发生在人体
这个生态系统之中。
这个生态系统之中。
03:28
And what do we know about most
ecosystems from conservation biology?
ecosystems from conservation biology?
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那么，从生物保护的角度来看，
我 们对大多数生态系统有哪些了解？
我 们对大多数生态系统有哪些了解？
03:32
That one of the best ways
to extinguish species
to extinguish species
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那就是，让一个物种灭绝的
最佳方式之一，
最佳方式之一，
03:35
is not to target them directly
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不是直接毁灭物种本身，
03:37
but to target their environment.
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而是破坏它们所生存的环境。
03:40
And so, once we have identified
the key components
the key components
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这样一来，一旦我们明确了
03:43
of the tumor environment,
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肿瘤环境的关键成分，
03:45
we can propose hypotheses
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我们可以做出假设，
03:47
and simulate scenarios
and therapeutic interventions
and therapeutic interventions
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模拟情景，然后进行干预治疗，
03:50
all in a completely safe
and affordable way
and affordable way
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这全部采用一种十分安全
和实惠的方法
和实惠的方法
03:54
and target different components
of the microenvironment
of the microenvironment
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之后以微环境中不同的成分为目标
03:57
in such a way as to kill the cancer
without harming the host,
without harming the host,
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在不危害宿主的情况下
杀死癌细胞，
杀死癌细胞，
04:01
such as me or you.
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宿主可以是你，或者是我。
04:05
And so while the immediate
goal of my research
goal of my research
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所以，当前我研究的直接目标，
04:08
is to advance research and innovation
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是推动研究与创新的发展
04:10
and to reduce its cost,
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降低成本，
04:12
the real intent, of course,
is to save lives.
is to save lives.
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当然，真实的目的是拯救生命。
04:15
And that's what I try to do
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这也是我一直在尝试的，
04:17
through mathematical modeling
applied to biology,
applied to biology,
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将数学建模应用于生物学，
04:19
and in particular,
to the development of drugs.
to the development of drugs.
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特别是应用于药物的开发上。
04:22
It's a field that until relatively
recently has remained somewhat marginal,
recently has remained somewhat marginal,
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直到最近，
这都还是一个有些边缘化的领域，
这都还是一个有些边缘化的领域，
但它已经成熟。
04:26
but it has matured.
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04:28
And there are now very well-developed
mathematical methods,
mathematical methods,
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现在有很多开发成熟的数学方法，
04:31
a lot of preprogrammed tools,
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有很多预编工具，
包括很多免费的，
04:33
including free ones,
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04:35
and an ever-increasing amount
of computational power available to us.
of computational power available to us.
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我们能获取的计算能力在不断增多。
04:40
The power and beauty
of mathematical modeling
of mathematical modeling
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数学建模的力与美
04:44
lies in the fact
that it makes you formalize,
that it makes you formalize,
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在于它可以，
04:46
in a very rigorous way,
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用最有力的方式，
04:48
what we think we know.
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将我们的认知形式化。
04:50
We make assumptions,
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我们做出假设，
04:52
translate them into equations,
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把假设翻译成方程，
04:53
run simulations,
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模拟场景，
04:55
all to answer the question:
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全是为了回答一个问题：
04:57
In a world where my assumptions are true,
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如果我的假设正确的话，
04:59
what do I expect to see?
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我能看到什么？
05:01
It's a pretty simple conceptual framework.
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这是一个十分简单的概念框架。
05:04
It's all about asking the right questions.
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全在于问对问题。
05:06
But it can unleash numerous opportunities
for testing biological hypotheses.
for testing biological hypotheses.
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但这会释放出大量
检验生物学假设的机会。
检验生物学假设的机会。
05:11
If our predictions match our observations,
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如果我们的预测与观察相吻合，
05:14
great! -- we got it right,
so we can make further predictions
so we can make further predictions
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太好了！证明我们是对的，
这样我们就能做出进一步的预测，
这样我们就能做出进一步的预测，
05:17
by changing this or that
aspect of the model.
aspect of the model.
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通过改变模型的其他方面。
05:20
If, however, our predictions
do not match our observations,
do not match our observations,
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但如果，我们的预测
与我们的观察不符，
与我们的观察不符，
这就意味着我们的假设出了错，
05:24
that means that some
of our assumptions are wrong,
of our assumptions are wrong,
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05:27
and so our understanding
of the key mechanisms
of the key mechanisms
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意味着我们对于生物学中潜在的，
05:29
of underlying biology
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关键机制
05:30
is still incomplete.
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理解得还不够完善。
05:32
Luckily, since this is a model,
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幸好，因为这只是个模型，
我们能控制所有的假设。
05:35
we control all the assumptions.
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05:37
So we can go through them, one by one,
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所以我们可以一个一个的仔细检查，
05:39
identifying which one or ones
are causing the discrepancy.
are causing the discrepancy.
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找出是哪个或哪些假设导致了偏差。
05:43
And then we can fill this newly
identified gap in knowledge
identified gap in knowledge
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然后我们就能通过实验与理论的方式，
05:47
using both experimental
and theoretical approaches.
and theoretical approaches.
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填补新发现的知识空白。
05:50
Of course, any ecosystem
is extremely complex,
is extremely complex,
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当然，任何生态系统都极其复杂，
05:53
and trying to describe all the moving
parts is not only very difficult,
parts is not only very difficult,
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尝试去描述这之中的所有运动
不仅十分困难，
不仅十分困难，
05:57
but also not very informative.
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而且也无法获得太多信息。
05:59
There's also the issue of timescales,
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并且还有时间范围的问题，
06:01
because some processes take place
on a scale of seconds, some minutes,
on a scale of seconds, some minutes,
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因为有些过程发生的时间
以秒为单位，有的以分为单位，
以秒为单位，有的以分为单位，
还有的以天、月、年为单位。
06:05
some days, months and years.
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把这些全部通过实验分开
是不太可能的。
是不太可能的。
06:07
It may not always be possible
to separate those out experimentally.
to separate those out experimentally.
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06:11
And some things happen
so quickly or so slowly
so quickly or so slowly
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有的发生的太快，
有的发生的太慢，
有的发生的太慢，
06:14
that you may physically
never be able to measure them.
never be able to measure them.
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以至于你不可能去测量它们。
06:17
But as mathematicians,
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但是作为数学家，
06:19
we have the power to zoom in
on any subsystem in any timescale
on any subsystem in any timescale
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我们有能力在任何时间范围内
放大任何子系统，
放大任何子系统，
06:25
and simulate effects of interventions
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并模拟在任何时间范围中，
06:27
that take place in any timescale.
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可能发生的干预效果。
06:31
Of course, this isn't the work
of a modeler alone.
of a modeler alone.
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当然，这项工作光靠建模者是不行的。
06:34
It has to happen in close
collaboration with biologists.
collaboration with biologists.
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他们还得与生物学家密切合作才行。
这确实需要一些翻译能力，
06:38
And it does demand
some capacity of translation
some capacity of translation
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06:41
on both sides.
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双方都需要。
06:43
But starting with a theoretical
formulation of a problem
formulation of a problem
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但是从一个问题的理论构想开始
06:47
can unleash numerous opportunities
for testing hypotheses
for testing hypotheses
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可以释放出大量的机会
去验证假设
去验证假设
06:50
and simulating scenarios
and therapeutic interventions,
and therapeutic interventions,
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去模拟场景和治疗干预，
06:54
all in a completely safe way.
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这都是在完全安全的情况下进行的。
06:56
It can identify gaps in knowledge
and logical inconsistencies
and logical inconsistencies
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这可以找出知识的空白、
逻辑的不一致，
逻辑的不一致，
07:02
and can help guide us
as to where we should keep looking
as to where we should keep looking
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可以帮忙引导我们，
让我们知道哪里值得继续寻找，
让我们知道哪里值得继续寻找，
07:05
and where there may be a dead end.
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哪里可能是个死胡同。
07:07
In other words:
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换句话说：
数学建模能帮助我们回答
07:08
mathematical modeling
can help us answer questions
can help us answer questions
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那些直接影响人们健康的问题——
07:12
that directly affect people's health --
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07:15
that affect each
person's health, actually --
person's health, actually --
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实际上，这会影响每个人的健康——
07:18
because mathematical modeling will be key
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因为数学建模，
07:21
to propelling personalized medicine.
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将会是推动个性化医疗的关键。
07:24
And it all comes down
to asking the right question
to asking the right question
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而这一切的关键在于问对问题，
07:27
and translating it
to the right equation ...
to the right equation ...
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然后把它翻译成正确的方程，
07:30
and back.
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再翻译回去。
07:32
Thank you.
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谢谢。
07:33
(Applause)
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（掌声）
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