I translate from biology into mathematics

我翻譯，

and vice versa.

從生物學翻譯成數學，

I write mathematical models

也從數學譯回生物學。

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

我撰寫數學模型，

to describe biological mechanisms,

用微分方程系統

such as cell growth.

來描述生物的機制，

Essentially, it works like this.

像是細胞的成長。

First, I identify the key elements

基本上，它的運作如下。

that I believe may be driving behavior over time

我先要找出關鍵的元素，

of a particular mechanism.

那些我認為會隨著時間

Then, I formulate assumptions

驅動特定機制行為的元素。

about how these elements interact with each other

接下來我做假設，

and with their environment.

臆測這些元素如何彼此互動、

It may look something like this.

與環境互動。

Then, I translate these assumptions into equations,

看起來像圖示這樣。

which may look something like this.

然後我把這些假設翻譯成方程式，

Finally, I analyze my equations

看起來像這樣（右圖）。

and translate the results back into the language of biology.

最後，我分析方程式，

A key aspect of mathematical modeling

再把結果譯回生物學的語言。

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

建立數學模式的關鍵面向，

we think about what they do.

並非我們這些建模的人 設想東西「是」什麼，

We think about relationships between individuals,

而是「做」了什麼。

whether they be cells, animals or people,

我們設想個體間的關係，

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

不論是細胞、動物或人，

Let me give you an example.

設想他們如何彼此互動， 如何與環境互動。

What do foxes and immune cells have in common?

讓我舉個例子。

They're both predators,

狐狸和免疫細胞有什麼共通點？

except foxes feed on rabbits,

兩者都是捕食者，

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

不過，狐狸吃兔子，

But from a mathematical point of view,

免疫細胞吃癌細胞之類的入侵者。

a qualitatively same system of predator-prey type equations

但從數學的觀點來看，

will describe interactions between foxes and rabbits

用性質相同的 捕食者—獵物型方程式系統，

and cancer and immune cells.

就能描述狐與兔間的互動，

Predator-prey type systems have been studied extensively

及癌症與免疫細胞間的互動。

in scientific literature,

捕食者—獵物型方程式系統

describing interactions of two populations,

已經在科學文獻中被廣泛研究，

where survival of one depends on consuming the other.

描述兩個族群間的互動，

And these same equations provide a framework

其中一個族群的生存 仰賴消費另一個族群。

for understanding cancer-immune interactions,

正是這些方程式提供架構

where cancer is the prey,

來了解癌症—免疫間的互動，

and the immune system is the predator.

癌症是獵物，

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

免疫系統是捕食者。

ranging from camouflaging itself

而獵物會採用各種詭計 避免遭捕食者獵殺，

to stealing the predator's food.

詭計的範圍從偽裝自己，

This can have some very interesting implications.

到偷竊捕食者的食物都有。

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

這意涵可能饒富興味。

there still remains somewhat limited efficacy

例如，儘管免疫治療的領域 已取得巨大的成功，

when it comes solid tumors.

遇到實質固態瘤時功效仍然有限。

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，

in the tumor microenvironment,

如果癌症細胞勝過了免疫細胞，

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.

近期有實驗顯示，

And it was recently shown experimentally

恢復腫瘤微環境的代謝平衡──

that restoring the metabolic balance in the tumor microenvironment --

亦即確保免疫細胞能獲取食物──

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

能讓免疫細胞這捕食者取回優勢

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

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

for space and nutrients,

彼此競爭和合作以取得空間和營養，

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

of the tumor environment,

腫瘤環境的關鍵組成，

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.

我們假設，

We make assumptions,

把假設翻譯為方程式，

translate them into equations,

進行模擬，

run simulations,

都是要解答這個問題：

all to answer the question:

在假設能夠成立的世界裡，

In a world where my assumptions are true,

我預期看見什麼？

what do I expect to see?

這是很簡單的概念性架構，

It's a pretty simple conceptual framework.

重點是要問對問題。

It's all about asking the right questions.

它能夠解放出許多 測試生物假設的機會。

But it can unleash numerous opportunities for testing biological hypotheses.

如果我們的預測和觀察相吻合，

If our predictions match our observations,

很棒！我們做對了。

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

我們就能改變模型來進一步預測。

by changing this or that aspect of the model.

然而如果預測和觀察不吻合，

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

那就表示有些假設是錯的，

that means that some of our assumptions are wrong,

我們對於背後生物學的關鍵機制

and so our understanding of the key mechanisms

了解得還不夠完善。

of underlying biology

幸運的是，因為這是模型，

is still incomplete.

我們能控制所有的假設，

Luckily, since this is a model,

所以能看過一個個假設，

we control all the assumptions.

找出哪一個或哪幾個造成了不一致。

So we can go through them, one by one,

接著就能把新辨識出來的知識落差，

identifying which one or ones are causing the discrepancy.

用實驗性和理論性的方式補起來。

And then we can fill this newly identified gap in knowledge

當然，生態系統都極度複雜，

using both experimental and theoretical approaches.

試圖描述所有會動的部分，

Of course, any ecosystem is extremely complex,

不僅很困難，也無法提供很多資訊。

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

還有時間範圍的議題，

but also not very informative.

因為有些過程的時間範圍 發生在秒上，有些在分上，

There's also the issue of timescales,

還有的是日、月、年。

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

未必都能在實驗裡分得開。

some days, months and years.

有些發生得很快或很慢，

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

實際上根本不可能去量。

And some things happen so quickly or so slowly

但身為數學家，

that you may physically never be able to measure them.

我們有能力放大 任何子系統的任何時間範圍，

But as mathematicians,

並模擬在任何時間範圍內

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

所發生的干預效果。

and simulate effects of interventions

當然，這不只是 建模者一個人的工作，

that take place in any timescale.

一定要和生物學家密切合作才行。

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

這確實會需要一些翻譯的能力，

It has to happen in close collaboration with biologists.

雙方都要。

And it does demand some capacity of translation

從表述問題的理論開始，

on both sides.

就能帶出許多機會

But starting with a theoretical formulation of a problem

來測試假設、

can unleash numerous opportunities for testing hypotheses

模擬情景和干預治療措施，

and simulating scenarios and therapeutic interventions,

全都以安全的方式進行。

all in a completely safe way.

它能夠辨視出知識的落差、

It can identify gaps in knowledge and logical inconsistencies

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

that directly affect people's health --

直接影響人們健康的問題，

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.

而這全都涉及到：要問對問題，

And it all comes down to asking the right question

要將問題翻譯成對的方程式，

and translating it to the right equation ...

和再翻譯回來。

and back.

謝謝。

Thank you.

（掌聲）

(Applause)