Math can help uncover cancer's secrets | Irina Kareva

譯者: Lilian Chiu 審譯者: Helen Chang

I am a translator.

我翻譯，

I translate from biology into mathematics

從生物學翻譯成數學，

and vice versa.

也從數學譯回生物學。

I write mathematical models

我撰寫數學模型，

which, in my case, are systems of differential equations,

用微分方程系統

to describe biological mechanisms,

來描述生物的機制，

such as cell growth.

像是細胞的成長。

Essentially, it works like this.

基本上，它的運作如下。

First, I identify the key elements

我先要找出關鍵的元素，

that I believe may be driving behavior over time

那些我認為會隨著時間

of a particular mechanism.

驅動特定機制行為的元素。

Then, I formulate assumptions

接下來我做假設，

about how these elements interact with each other

臆測這些元素如何彼此互動、

and with their environment.

與環境互動。

It may look something like this.

看起來像圖示這樣。

Then, I translate these assumptions into equations,

然後我把這些假設翻譯成方程式，

which may look something like this.

看起來像這樣（右圖）。

Finally, I analyze my equations

最後，我分析方程式，

and translate the results back into the language of biology.

再把結果譯回生物學的語言。

A key aspect of mathematical modeling

建立數學模式的關鍵面向，

is that we, as modelers, do not think about what things are;

並非我們這些建模的人 設想東西「是」什麼，

we think about what they do.

而是「做」了什麼。

We think about relationships between individuals,

我們設想個體間的關係，

whether they be cells, animals or people,

不論是細胞、動物或人，

and how they interact with each other and with their environment.

設想他們如何彼此互動， 如何與環境互動。

Let me give you an example.

讓我舉個例子。

What do foxes and immune cells have in common?

狐狸和免疫細胞有什麼共通點？

They're both predators,

兩者都是捕食者，

except foxes feed on rabbits,

不過，狐狸吃兔子，

and immune cells feed on invaders, such as cancer cells.

免疫細胞吃癌細胞之類的入侵者。

But from a mathematical point of view,

但從數學的觀點來看，

a qualitatively same system of predator-prey type equations

用性質相同的 捕食者—獵物型方程式系統，

will describe interactions between foxes and rabbits

就能描述狐與兔間的互動，

and cancer and immune cells.

及癌症與免疫細胞間的互動。

Predator-prey type systems have been studied extensively

捕食者—獵物型方程式系統

已經在科學文獻中被廣泛研究，

in scientific literature,

describing interactions of two populations,

描述兩個族群間的互動，

where survival of one depends on consuming the other.

其中一個族群的生存 仰賴消費另一個族群。

And these same equations provide a framework

正是這些方程式提供架構

for understanding cancer-immune interactions,

來了解癌症—免疫間的互動，

where cancer is the prey,

癌症是獵物，

and the immune system is the predator.

免疫系統是捕食者。

And the prey employs all sorts of tricks to prevent the predator from killing it,

而獵物會採用各種詭計 避免遭捕食者獵殺，

ranging from camouflaging itself

詭計的範圍從偽裝自己，

to stealing the predator's food.

到偷竊捕食者的食物都有。

This can have some very interesting implications.

這意涵可能饒富興味。

For example, despite enormous successes in the field of immunotherapy,

例如，儘管免疫治療的領域 已取得巨大的成功，

there still remains somewhat limited efficacy

遇到實質固態瘤時功效仍然有限。

when it comes solid tumors.

But if you think about it ecologically,

如果從生態的角度來想，

both cancer and immune cells --

癌症和免疫細胞

the prey and the predator --

──捕食者和獵物──

require nutrients such as glucose to survive.

皆需葡萄糖之類的營養才能生存。

If cancer cells outcompete the immune cells for shared nutrients

在腫瘤微環境中競爭共同的養分時，

如果癌症細胞勝過了免疫細胞，

in the tumor microenvironment,

then the immune cells will physically not be able to do their job.

那麼免疫細胞將無法完成工作。

This predator-prey-shared resource type model

我研究這種捕食者—獵物 共享資源形式的模型。

is something I've worked on in my own research.

And it was recently shown experimentally

近期有實驗顯示，

that restoring the metabolic balance in the tumor microenvironment --

恢復腫瘤微環境的代謝平衡──

that is, making sure immune cells get their food --

亦即確保免疫細胞能獲取食物──

can give them, the predators, back their edge in fighting cancer, the prey.

能讓免疫細胞這捕食者取回優勢

來對抗癌症這獵物。

This means that if you abstract a bit,

意思是，可用抽象一點的方式，

you can think about cancer itself as an ecosystem,

把癌症本身設想像為生態系統，

where heterogeneous populations of cells compete and cooperate

那裡的各種細胞族群

彼此競爭和合作以取得空間和營養，

for space and nutrients,

interact with predators -- the immune system --

和免疫系統這捕食者互動，

migrate -- metastases --

遷移、轉移……

all within the ecosystem of the human body.

全都發生在人體這生態系統中。

And what do we know about most ecosystems from conservation biology?

我們從保育生物學的角度看， 對生態系統了解最多的是什麼？

That one of the best ways to extinguish species

我們知道滅絕物種的最佳方式，

is not to target them directly

不是直接針對物種，

but to target their environment.

而是針對物種的環境。

And so, once we have identified the key components

因此，一旦我們找出了

腫瘤環境的關鍵組成，

of the tumor environment,

we can propose hypotheses

我們就能提出假設、

and simulate scenarios and therapeutic interventions

模擬情境和干預治療，

all in a completely safe and affordable way

全都以安全和實惠的方式進行，

and target different components of the microenvironment

針對微環境中的不同組成成份，

in such a way as to kill the cancer without harming the host,

能夠殺死癌症卻不傷到宿主，

such as me or you.

不傷到我或你。

And so while the immediate goal of my research

所以，我研究的當前目標

is to advance research and innovation

是推動研究和創新，

and to reduce its cost,

並減少成本。

the real intent, of course, is to save lives.

當然，真正的目的是要拯救人命。

And that's what I try to do

那就是我試著在做的事，

through mathematical modeling applied to biology,

將數學建模應用到生物學，

and in particular, to the development of drugs.

特別是用在藥物的發展上。

It's a field that until relatively recently has remained somewhat marginal,

直到最近，這一直是個 邊緣、不被重視的領域，

but it has matured.

但它已經成熟了。

And there are now very well-developed mathematical methods,

現在有發展得非常好的數學方法，

a lot of preprogrammed tools,

有很多預編的程式工具，

including free ones,

也有很多免費的工具，

and an ever-increasing amount of computational power available to us.

我們能獲得的計算能力越來越多。

The power and beauty of mathematical modeling

數學建模的力與美在於

lies in the fact that it makes you formalize,

它能把我們的認知

in a very rigorous way,

以非常嚴謹的方式形式化。

what we think we know.

We make assumptions,

我們假設，

translate them into equations,

把假設翻譯為方程式，

run simulations,

進行模擬，

all to answer the question:

都是要解答這個問題：

In a world where my assumptions are true,

在假設能夠成立的世界裡，

what do I expect to see?

我預期看見什麼？

It's a pretty simple conceptual framework.

這是很簡單的概念性架構，

It's all about asking the right questions.

重點是要問對問題。

But it can unleash numerous opportunities for testing biological hypotheses.

它能夠解放出許多 測試生物假設的機會。

If our predictions match our observations,

如果我們的預測和觀察相吻合，

great! -- we got it right, so we can make further predictions

很棒！我們做對了。

我們就能改變模型來進一步預測。

by changing this or that aspect of the model.

If, however, our predictions do not match our observations,

然而如果預測和觀察不吻合，

that means that some of our assumptions are wrong,

那就表示有些假設是錯的，

and so our understanding of the key mechanisms

我們對於背後生物學的關鍵機制

of underlying biology

is still incomplete.

了解得還不夠完善。

Luckily, since this is a model,

幸運的是，因為這是模型，

we control all the assumptions.

我們能控制所有的假設，

So we can go through them, one by one,

所以能看過一個個假設，

identifying which one or ones are causing the discrepancy.

找出哪一個或哪幾個造成了不一致。

And then we can fill this newly identified gap in knowledge

接著就能把新辨識出來的知識落差，

using both experimental and theoretical approaches.

用實驗性和理論性的方式補起來。

Of course, any ecosystem is extremely complex,

當然，生態系統都極度複雜，

and trying to describe all the moving parts is not only very difficult,

試圖描述所有會動的部分，

不僅很困難，也無法提供很多資訊。

but also not very informative.

There's also the issue of timescales,

還有時間範圍的議題，

because some processes take place on a scale of seconds, some minutes,

因為有些過程的時間範圍 發生在秒上，有些在分上，

some days, months and years.

還有的是日、月、年。

It may not always be possible to separate those out experimentally.

未必都能在實驗裡分得開。

And some things happen so quickly or so slowly

有些發生得很快或很慢，

that you may physically never be able to measure them.

實際上根本不可能去量。

But as mathematicians,

但身為數學家，

we have the power to zoom in on any subsystem in any timescale

我們有能力放大 任何子系統的任何時間範圍，

and simulate effects of interventions

並模擬在任何時間範圍內

that take place in any timescale.

所發生的干預效果。

Of course, this isn't the work of a modeler alone.

當然，這不只是 建模者一個人的工作，

It has to happen in close collaboration with biologists.

一定要和生物學家密切合作才行。

And it does demand some capacity of translation

這確實會需要一些翻譯的能力，

on both sides.

雙方都要。

But starting with a theoretical formulation of a problem

從表述問題的理論開始，

can unleash numerous opportunities for testing hypotheses

就能帶出許多機會

來測試假設、

and simulating scenarios and therapeutic interventions,

模擬情景和干預治療措施，

all in a completely safe way.

全都以安全的方式進行。

It can identify gaps in knowledge and logical inconsistencies

它能夠辨視出知識的落差、

邏輯的不一致，

and can help guide us as to where we should keep looking

能引導我們應該持續探索的方向，

and where there may be a dead end.

指出哪裡可能是死胡同。

In other words:

換言之，

mathematical modeling can help us answer questions

數學建模能協助我們回答

直接影響人們健康的問題，

that directly affect people's health --

that affect each person's health, actually --

其實會影響每個人的健康，

because mathematical modeling will be key

因為數學建模將會是 推進個人化醫學的關鍵。

to propelling personalized medicine.

And it all comes down to asking the right question

而這全都涉及到：要問對問題，

and translating it to the right equation ...

要將問題翻譯成對的方程式，

and back.

和再翻譯回來。

Thank you.

謝謝。

(Applause)

（掌聲）