If we observe biological phenomena, we areconfronted with various complex processes that often cannot be explained fromfirst principles and the outcome of which cannot reliably be foreseen fromintuition. Even if general biochemical principles are well established (e.g.,the central dogma of transcription and translation or the bio chemistry ofenzyme-catalyzed reactions), the bio chemistry of individual molecules andsystems is often unknown and can vary considerably between species. Experimentslead to biological hypotheses about individ ual processes, but it oftenremains unclear whether these hypotheses can be combined into a larger coherentpic ture because it is often difficult to foresee the global behavior of acomplex system from knowledge of its parts. Mathematical modeling and computersimulations can help us to understand the internal nature and dynamics of theseprocesses and to arrive at predictions about their future development and theeffect of interac tions with the environment.
如果我們觀察到生物現象，我們就會遇到各種複雜的過程，這些過程往往無法從第一原則中得到解釋，其結果也無法從直覺中可靠地預見。即使一般的生化原理（如轉錄和翻譯的中心教條或酶催化反應的生物化學）已經確立，單個分子和系統的生物化學往往是未知的，並且在物種之間可能有很大的差異。實驗導致了關於獨立過程的生物學假設，但往往仍不清楚這些假設是否可以結合成一個更大的連貫的圖片，因為它往往很難從對一個複雜系統的部分的知識中預測其全局行為。數學建模和計算機模擬可以幫助我們理解這些過程的內部性質和動態，並對它們的未來發展以及與環境的相互影響進行預測。
1.什麼是模型
The answer to this question willdiffer among communi ties of researchers. In a broad sense, a model is anabstract representation of objects or processes that explains features of theseobjects or processes (Figure 1.2). A biochemical reaction network can berepresented by a graphical sketch showing dots for metabolites and arrows forreactions; the same network could also be described by a system of differentialequations, which allows simulating and predicting the dynamic behavior of thatnetwork. If a model is used for simulations, it needs to be ensured that itfaithfully predicts the system’s behavior – at least those aspects that aresupposed to be covered by the model. Systems biology models are often based onwell-established physical laws that justify their general form, for instance,the thermodynamics of chemical reactions. Besides this, a computational modelneeds to make specific statements about a system of interest – which arepartially justified by experiments and biochemical knowledge, and partially bymere extrapolation from other systems. Such a model can summarize establishedknowledge about a system in a coherent mathematical formulation. Inexperimental biol ogy, the term 「model」 is also used to denote a species thatis especially suitable for experiments; for example, a geneti cally modifiedmouse may serve as a model for human genetic disorders.
這一問題的答案將在研究人員的共同體關係中有所不同。從廣義上講，模型是對象或過程的抽象表示，它解釋了這些對象或過程的特徵（圖1.2）。生化反應網絡可以用一個圖形草圖來表示，顯示代謝物的點和反應的箭頭；同樣的網絡也可以用一個微分方程組來描述，它允許模擬和預測該網絡的動態行為。如果一個模型被用於模擬，就需要確保它忠實地預測系統的行為——至少是模型應該涵蓋的那些方面。系統生物學模型往往基於公認的物理定律，這些定律證明了它們的一般形式，例如化學反應的熱力學。除此之外，一個計算模型需要對一個感興趣的系統做出具體的陳述——這在一定程度上是實驗和生化知識所證明的，在一定程度上只是從其他系統中推斷出來的。這樣的模型可以用一個連貫的數學公式來總結關於系統的既定知識。在實驗生物學中，「模型」一詞也被用來表示一個特別適合實驗的物種；例如，基因修飾小鼠可以作為人類遺傳疾病的模型。
2.模型的目的與價值
Modeling is a subjective andselective procedure. A model represents only specific aspects of reality but,if done properly, this is sufficient since the intention of modeling is toanswer particular questions. If the only aim is to predict system outputs fromgiven input signals, a model should display the correct input–output relation,while its interior can be regarded as a black box. How ever, if instead adetailed biological mechanism has to be elucidated, then the system’s structureand the relations between its parts must be described realistically. Somemodels are meant to be generally applicable to many similar objects (e.g.,Michaelis–Menten kinetics holds for many enzymes, the promoter–operator conceptis appli cable to many genes, and gene regulatory motifs are common), whileothers are specifically tailored to one particular object (e.g., the 3Dstructure of a protein, the sequence of a gene, or a model of deterioratingmitochondria during aging). The mathematical part can be kept as simple aspossible to allow for easy implemen tation and comprehensible results. Or itcan be modeled very realistically and be much more complicated. None of thecharacteristics mentioned above makes a model wrong or right, but theydetermine whether a model is appropriate to the problem to be solved. Thephrase 「essentially, all models are wrong, but some are useful」 coined by thestatistician George Box is indeed an appro priate guideline for modelbuilding.
建模是一個主觀的、選擇性的過程。模型只代表現實的特定方面，但如果做得好，這就足夠了，因為建模的目的是回答特定的問題。如果唯一的目標是預測給定輸入信號的系統輸出，那麼模型應該顯示正確的輸入-輸出關係，而其內部可以看作一個黑箱。然而，如果一個詳細的生物機制必須被闡明，那麼系統的結構和各部分之間的關係必須被現實地描述。一些模型通常適用於許多類似的對象（例如，許多酶的Michaelis-Menten動力學，啟動子-操作者概念適用於許多基因，基因調控基序是複合的），而另一些模型則專門針對一個特定的對象（例如，蛋白質的三維結構，基因序列，或衰老過程中線粒體退化的模式）。數學部分可以保持儘可能簡單，以便易於實現和理解的結果。或者它可以非常真實地建模，並且更加複雜。上面提到的所有特徵都不能使模型錯誤或正確，但它們決定了模型是否適合要解決的問題。統計學家George Box提出的「本質上，所有模型都是錯誤的，但有些模型是有用的」這句話確實是模型構建的一個適當的指導方針。
3.計算建模的優勢
Models gain their reference to reality fromcomparison with experiments, and their benefits therefore depend on the qualityof the experiments used. Nevertheless, model ing combined with experimentationhas a lot of advan tages compared with purely experimental studies:
模型從與實驗的比較中獲得對現實的參考，因此它們的好處取決於所使用的實驗的質量。然而，與單純的實驗研究相比，建模和實驗相結合有很多優點：
Modeling drives conceptual clarification. Itrequires verbal hypotheses to be made specific and conceptually rigorous.
建模推動概念澄清。它要求口頭上的假設是具體的，概念上是嚴謹的。
Modeling highlights gaps in knowledge orunderstanding. During the process of model formulation, unspecified componentsor interactions have to be determined.
建模突出了知識或理解上的差距。在模型制定過程中，必須確定未指定的組件或相互作用。
Modeling provides independence of the modeledobject.
建模提供了建模對象的獨立性。
Time and space may be stretched or compressed adlibitum.
時間和空間可以隨意拉伸或壓縮。
Solution algorithms and computer programs can beused independently of the concrete system.
求解算法和電腦程式可以獨立於具體系統使用。
Modeling is cheap compared with experiments.
與實驗相比，建模成本較低。
Models exert by themselves no harm on animals orplants and help to reduce ethical problems in experi ments. They do notpollute the environment.
模型本身不會對動植物造成傷害，有助於減少實驗中的倫理問題。它們不會汙染環境。
Modeling can assist experimentation. With anadequate model, one may test different scenarios that are not accessible byexperiment. One may follow time courses of compounds that cannot be measured inan experi ment. One may impose perturbations that are not feasi ble in thereal system. One may cause precise perturbations without directly changingother system components, which is usually impossible in real sys tems. Modelsimulations can be repeated often and for many different conditions.
建模可以輔助實驗。有了一個足夠的模型，人們可以測試不同的場景，這些場景通過實驗是無法訪問的。人們可以跟蹤無法在實驗中測量的化合物的時間進程。人們可能會施加在真實系統中不可能的擾動。在不直接改變其他系統部件的情況下，可能會引起精確的攝動，而這在實際系統中通常是不可能的。對於許多不同的條件，可以經常重複模型模擬。
Model results can often be presented in precisemathe matical terms that allow for generalization. Graphical representationand visualization make it easier to understand the system.
模型結果通常可以用精確的數學術語表示，以便於推廣。圖形表示和可視化使系統更容易理解。
Finally, modeling allows for making well-foundedand testable predictions.
最後，建模允許做出有充分依據且可測試的預測。
The attempt to formulate current knowledge and openproblems in mathematical terms often uncovers a lack of knowledge andrequirements for clarification. Further more, computational models can be usedto test whether proposed explanations of biological phenomena are feasi ble.Computational models serve as repositories of cur rent knowledge, bothestablished and hypothetical, about how systems might operate. At the sametime, they pro vide researchers with quantitative descriptions of thisknowledge and allow them to simulate the biological pro cess, which serves asa rigorous consistency test.
試圖用數學術語來表述當前的知識和未解決的問題，往往會暴露出缺乏知識和澄清的要求。此外，計算模型可以用來檢驗提出的對生物現象的解釋是否可行。計算模型充當關於系統可能如何運行的當前知識的儲存庫，既有已建立的，也有假設的。同時，它們為研究人員提供了對這些知識的定量描述，並允許他們模擬生物過程，這是一個嚴格的一致性測試。