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I am a translator. I translate from biology into mathematics and vice versa.
我是一名翻译。我把生物学翻译成数学，反之亦然。
I write mathematical models which, in my case, are systems of differential equations,
我建造数学模型，用微分方程组
to describe biological mechanisms, such as cell growth. Essentially, it works like this.
来描述生物学机制，比如说细胞的生长。基本来说，运作过程如下。
First, I identify the key elements that I believe may be driving behavior over time of a particular mechanism.
首先，我找出关键的元素，那些我认为可能会随着时间的推移，影响某些特定机制运作的元素。
Then, I formulate assumptions about how these elements interact with each other and with their environment.
然后，我做出假设，猜测这些元素如何与彼此互动，与它们的环境互动。
It may look something like this. Then, I translate these assumptions into equations, which may look something like this.
可能看起来像这样。然后，我把这些假设翻译成方程，它看起来可能像这样。
Finally, I analyze my equations and translate the results back into the language of biology.
最后，我分析我的方程，并把结果翻译回生物学语言。
A key aspect of mathematical modeling is that we, as modelers, do not think about what things are; we think about what they do.
数学建模的一个关键点在于，我们作为建模者，不是想这些东西“是”什么，而是想它们“做”什么。
We think about relationships between individuals,
我们思考个体之间的关系，
whether they be cells, animals or people, and how they interact with each other and with their environment.
不管这些个体是细胞、动物还是人，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。
Let me give you an example. What do foxes and immune cells have in common?
让我来举个例子。狐狸和免疫细胞之间有什么共同点？
They're both predators, except foxes feed on rabbits, and immune cells feed on invaders, such as cancer cells.
它们都是捕食者，只不过狐狸吃兔子，而免疫细胞以入侵者为食，比如说癌细胞。
But from a mathematical point of view, a qualitatively same system of predator-prey type equations
但是从数学的角度来说，用本质上相同的捕食者--猎物方程系统，
will describe interactions between foxes and rabbits and cancer and immune cells.
就能描述狐狸与兔子之间的相互影响，还有癌细胞与免疫细胞之间的相互影响。
Predator-prey type systems have been studied extensively in scientific literature,
捕食者--猎物类型的方程系统，已经在科学文献中被广泛研究，
describing interactions of two populations, where survival of one depends on consuming the other.
它被用来描述两个种群之间的相互影响，其中一个种群吃掉另一个种群才能得以生存。
And these same equations provide a framework for understanding cancer-immune interactions,
也就是这些方程为我们提供了一个框架来了解癌细胞与免疫系统之间的相互影响，
where cancer is the prey, and the immune system is the predator.
在这套方程中，癌细胞是猎物，免疫系统是捕食者。
And the prey employs all sorts of tricks to prevent the predator from killing it,
猎物会采用一切诡计来防止被捕食者杀死，
ranging from camouflaging itself to stealing the predator's food.
从伪装自己到偷走捕食者的食物。
This can have some very interesting implications.
这可能会产生一些非常有趣的情况。
For example, despite enormous successes in the field of immunotherapy,
举例来说，尽管我们在免疫疗法领域取得了巨大的成就，
there still remains somewhat limited efficacy when it comes solid tumors.
但在面对实体恶性肿瘤时，其疗效还是十分有限的。
But if you think about it ecologically, both cancer and immune cells
但如果从生态学的观点来思考的话，不管是癌细胞和免疫细胞，
the prey and the predator -- require nutrients such as glucose to survive.
即猎物和捕食者，都需要营养（如葡萄糖）来生存。
If cancer cells outcompete the immune cells for shared nutrients in the tumor microenvironment,
如果癌细胞比免疫细胞摄入的共享养分更多，在肿瘤的微环境中，
then the immune cells will physically not be able to do their job.
免疫细胞就不能够完成它们的工作。
This predator-prey-shared resource type model is something I've worked on in my own research.
这种捕食者—猎物—共享资源类的模型，是我一直在研究的。
And it was recently shown experimentally that restoring the metabolic balance in the tumor microenvironment
最近的实验表明，恢复肿瘤微环境中的新陈代谢平衡，
that is, making sure immune cells get their food -- can give them, the predators, back their edge in fighting cancer, the prey.
也就是确保免疫细胞得到它们的食物--可以使免疫细胞（捕食者）在与癌细胞（猎物）对抗时找回优势。
This means that if you abstract a bit, you can think about cancer itself as an ecosystem,
意思就是，抽象一点来想，你可以把癌细胞自身想象成一个生态系统，
where heterogeneous populations of cells compete and cooperate for space and nutrients,
在这个系统中，多样的细胞种群相互竞争、相互合作来获取空间和营养，
interact with predators -- the immune system -- migrate -- metastases -- all within the ecosystem of the human body.
与捕食者--免疫细胞相互影响，迁移，也就是新陈代谢...这全都发生在人体这个生态系统之中。
And what do we know about most ecosystems from conservation biology?
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？
That one of the best ways to extinguish species is not to target them directly but to target their environment.
那就是，让一个物种灭绝的最佳方式之一，不是直接毁灭物种本身，而是破坏它们所生存的环境。
And so, once we have identified the key components of the tumor environment,
这样一来，一旦我们明确了肿瘤环境的关键成分，
we can propose hypotheses and simulate scenarios and therapeutic interventions all in a completely safe and affordable way
我们可以做出假设，模拟情景，然后进行干预治疗，这全部采用一种十分安全和实惠的方法，
and target different components of the microenvironment in such a way as to kill the cancer without harming the host, such as me or you.
之后以微环境中不同的成分为目标，在不危害宿主的情况下杀死癌细胞，宿主可以是你，或者是我。
And so while the immediate goal of my research is to advance research and innovation
所以，当前我研究的直接目标，是推动研究与创新的发展，
and to reduce its cost, the real intent, of course, is to save lives.
降低成本，当然，真实的目的是拯救生命。
And that's what I try to do through mathematical modeling applied to biology, and in particular, to the development of drugs.
这也是我一直在尝试的，将数学建模应用于生物学，特别是应用于药物的开发上。
It's a field that until relatively recently has remained somewhat marginal, but it has matured.
直到最近，这都还是一个有些边缘化的领域，但它已经成熟。
And there are now very well-developed mathematical methods, a lot of preprogrammed tools,
现在有很多开发成熟的数学方法，有很多预编工具，
including free ones, and an ever-increasing amount of computational power available to us.
包括很多免费的，我们能获取的计算能力在不断增多。
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.
数学建模的力与美在于它可以用最有力的方式，将我们的认知形式化。
We make assumptions, translate them into equations, run simulations, all to answer the question:
我们做出假设，把假设翻译成方程，模拟场景，全是为了回答一个问题：
In a world where my assumptions are true, what do I expect to see?
如果我的假设正确的话，我能看到什么？
It's a pretty simple conceptual framework. It's all about asking the right questions.
这是一个十分简单的概念框架。全在于问对问题。
But it can unleash numerous opportunities for testing biological hypotheses.
但这会释放出大量检验生物学假设的机会。
If our predictions match our observations, great!
如果我们的预测与观察相吻合，太好了！
we got it right, so we can make further predictions by changing this or that aspect of the model.
证明我们是对的，这样我们就能做出进一步的预测，通过改变模型的其他方面。
If, however, our predictions do not match our observations, that means that some of our assumptions are wrong,
但如果，我们的预测与我们的观察不符，这就意味着我们的假设出了错，
and so our understanding of the key mechanisms of underlying biology is still incomplete.
意味着我们对于生物学中潜在的关键机制理解得还不够完善。
Luckily, since this is a model, we control all the assumptions.
幸好，因为这只是个模型，我们能控制所有的假设。
So we can go through them, one by one, identifying which one or ones are causing the discrepancy.
所以我们可以一个一个的仔细检查，找出是哪个或哪些假设导致了偏差。
And then we can fill this newly identified gap in knowledge using both experimental and theoretical approaches.
然后我们就能通过实验与理论的方式，填补新发现的知识空白。
Of course, any ecosystem is extremely complex,
当然，任何生态系统都极其复杂，
and trying to describe all the moving parts is not only very difficult, but also not very informative.
尝试去描述这之中的所有运动不仅十分困难，而且也无法获得太多信息。
There's also the issue of timescales,
并且还有时间范围的问题，
because some processes take place on a scale of seconds, some minutes, some days, months and years.
因为有些过程发生的时间以秒为单位，有的以分为单位，还有的以天、月、年为单位。
It may not always be possible to separate those out experimentally.
把这些全部通过实验分开是不太可能的。
And some things happen so quickly or so slowly that you may physically never be able to measure them.
有的发生的太快，有的发生的太慢，以至于你不可能去测量它们。
But as mathematicians, we have the power to zoom in on any subsystem in any timescale
但是作为数学家，我们有能力在任何时间范围内放大任何子系统，
and simulate effects of interventions that take place in any timescale.
并模拟在任何时间范围中可能发生的干预效果。
Of course, this isn't the work of a modeler alone.
当然，这项工作光靠建模者是不行的。
It has to happen in close collaboration with biologists.
他们还得与生物学家密切合作才行。
And it does demand some capacity of translation on both sides.
这确实需要一些翻译能力，双方都需要。
But starting with a theoretical formulation of a problem can unleash numerous opportunities
但是从一个问题的理论构想开始，可以释放出大量的机会
for testing hypotheses and simulating scenarios and therapeutic interventions, all in a completely safe way.
去验证假设，去模拟场景和治疗干预，这都是在完全安全的情况下进行的。
It can identify gaps in knowledge and logical inconsistencies
这可以找出知识的空白、逻辑的不一致，
and can help guide us as to where we should keep looking and where there may be a dead end.
可以帮忙引导我们，让我们知道哪里值得继续寻找，哪里可能是个死胡同。
In other words: mathematical modeling can help us answer questions that directly affect people's health
换句话说：数学建模能帮助我们回答那些直接影响人们健康的问题，
that affect each person's health, actually -- because mathematical modeling will be key to propelling personalized medicine.
实际上，这会影响每个人的健康--因为数学建模，将会是推动个性化医疗的关键。
And it all comes down to asking the right question and translating it to the right equation ... and back. Thank you.
而这一切的关键在于问对问题，然后把它翻译成正确的方程，再翻译回去。谢谢。
