1.模型範圍
Systems biology models consist of mathematicalelements that describe properties of a biological system, for instance,mathematical variables describing the concentrations of metabolites. As a modelcan only describe certain aspects of the system, all other properties of thesystem (e.g., concentrations of other substances or the environment of a cell)are neglected or simplified. It is important – and, to some extent, an art – toconstruct models in such ways that the disregarded properties do not compromisethe basic results of the model.
系統生物學模型由描述生物系統特性的數學元素組成，例如描述代謝物濃度的數學變量。由於模型只能描述系統的某些方面，系統的所有其他特性（例如，其他物質的濃度或細胞的環境）都被忽略或簡化。重要的是——在某種程度上也是一門藝術——以這樣的方式構建模型，被忽視的屬性不會損害模型的基本結果。
2.模型陳述
Alongside the model elements,a model can contain vari ous kinds of statements and equations describingfacts about the model elements, most notably, their temporal behavior. Inkinetic models, the basic modeling paradigm considered in this book, thedynamics is determined by a set of ordinary differential equations describingthe sub stance balances. Statements in other model types may have the form ofequality or inequality constraints (e.g., in flux balance analysis), maximalitypostulates, stochastic processes, or probabilistic statements about quantitiesthat vary in time or between cells.
除了模型元素之外，模型還可以包含各種陳述和等式，這些陳述和方程式描述有關模型元素的事實，尤其是它們的時間行為。在動力學模型中，這是本書考慮的基本建模範例，動力學是由描述物質平衡的一組常微分方程確定的。其他模型類型中的語句可能具有等式或不等式約束的形式（例如在通量平衡分析中），極大值假設，隨機過程或有關隨時間或單元間變化的數量的概率性語句。
3.系統狀態
In dynamical systems theory, asystem is characterized by its state, a snapshot of the system at a given time.The state of the system is described by the set of variables that must be kepttrack of in a model: in deterministic models, it needs to contain enoughinformation to predict the behavior of the system for all future times. Eachmodeling framework defines what is meant by the state of the sys tem. Inkinetic rate equation models, for example, the state is a list of substanceconcentrations. In the corre sponding stochastic model, it is a probabilitydistribution or a list of the current number of molecules of a species. In aBoolean model of gene regulation, the state is a string of bits indicating foreach gene whether it is expressed (「1」) or not expressed (「0」). Also, thetemporal behavior can be described in fundamentally different ways. In adynamical system, the future states are determined by the current state, whilein a stochastic process, the future states are not precisely predetermined.Instead, each pos sible future history has a certain probability to occur.
在動力學系統理論中，系統的特徵在於其狀態，即給定時間的系統快照。系統狀態由在模型中必須跟蹤的一組變量描述：在確定性模型中，它需要包含足夠的信息以預測將來所有時間的系統行為。每個建模框架都定義了系統狀態的含義。例如，在動力學速率方程模型中，狀態是物質濃度的列表。在相應的隨機模型中，它是概率分布或物種當前分子數量的列表。在基因調控的布爾模型中，狀態是一串字符串，指示每個基因是被表達（「1」）還是未被表達（「0」）。同樣，可以以根本不同的方式描述時間行為。在動態系統中，未來狀態由當前狀態確定，而在隨機過程中，未來狀態未精確確定。相反，每個可能的未來歷史都有一定的發生概率。
4.變量、參數、常量
The quantities in a model can be classified asvariables, parameters, and constants. A constant is a quantity with a fixedvalue, such as the natural number e or Avogadro’s number (number of moleculesper mole). Parameters are quantities that have a given value, such as theKmvalue of an enzyme in a reaction. This value depends on the method used andon the experimental conditions and may change. Variables are quantities with achangeable value for which the model establishes relations. A subset ofvariables, the state variables, describes the system behavior completely. Theycan assume independent val ues and each of them is necessary to define thesystem state. Their number is equivalent to the dimension of the system. Forexample, the diameter d and volume V of a sphere obey the relation V=πd3/6,where π and 6 are constants, V and d are variables, but only one of them is astate variable since the relation between them uniquely determines the otherone.
模型中的量可以分為變量、參數和常數。常數是具有固定值的量，例如自然數e或阿伏加德羅的數（每摩爾的分子數）。參數是具有給定值的量，例如反應中酶的Km值。此值取決於所使用的方法和實驗條件，並可能發生變化。變量是具有可變值的量，模型為其建立關係。變量的子集，即狀態變量，完全描述了系統的行為。他們可以假定獨立的Values，每一個都是定義系統狀態所必需的。它們的數目相當於系統的維數。例如，球體的直徑d和體積V服從關係V=πd3/6，其中π和6是常數，V和d是變量，但其中只有一個是狀態變量，因為它們之間的關係唯一地決定了另一個變量。
Whether a quantity is avariable or a parameter depends on the model. In reaction kinetics, the enzymeconcentration appears as a parameter. However, the enzyme concentration itselfmay change due to gene expression or protein degradation, and in an extendedmodel, it may be described by a variable.
數量是變量還是參數取決於模型。在反應動力學中，酶濃度作為參數出現。但是，酶濃度本身可能會因基因表達或蛋白質降解而改變，在擴展模型中，可能會用一個變量來描述。
5.模型行為
Two fundamental factors thatdetermine the behavior of a system are (i) influences from the environment(input) and (ii) processes within the system. The system structure, that is,the relation among variables, parameters, and constants, determines howendogenous and exogenous forces are processed. However, different systemstructures may still produce similar system behavior (out put); therefore,measurements of the system output often do not suffice to choose betweenalternative models and to determine the system’s internal organization.
決定系統行為的兩個基本因素是(i)來自環境(輸入)的影響和(ii)系統內的過程。系統結構，即變量、參數和常量之間的關係，決定了如何處理內生力和外生力。但是，不同的系統結構仍可能產生相似的系統行為(輸出)；因此，對系統輸出的測量通常不足以在備選模型之間進行選擇，也不足以確定系統的內部組織。
6.模型分類
對於建模，根據一組標準對流程進行分類。
A structural or qualitativemodel (e.g., a network graph) specifies the interactions among model elements.A quantitative model assigns values to the elements and to their interactions,which may or may not change.
結構或定性模型（例如網絡圖）指定模型元素之間的相互作用。定量模型將值分配給元素及其相互作用，這些值可能會改變，也可能不會改變。
In a deterministic model, thesystem evolution through all following states can be predicted from the knowledge of the current state. Stochastic descriptions give instead a probabilitydistribution for the successive states.
在確定性模型中，可以從當前狀態的知識邊緣來預測所有隨後狀態的系統演化。相反，隨機描述給出了連續狀態的概率分布。
The nature of values that time, state, or space mayassume distinguishes a discrete model (where values are taken from a discreteset) from a continuous model (where values belong to a continuum).
時間，狀態或空間可能假定的值的性質將離散模型（其中值是從離散集合中獲取）與連續模型（其中值屬於連續體）區分開來。
Reversible processes can proceed in a forward and backward direction. Irreversibility means that only one direction is possible.
可逆過程可以向前和向後進行。不可逆性意味著只能有一個方向。
Periodicity indicates that the system assumes a series ofstates in the time interval {t, t+Δt} and again in the time interval {t+iΔt,t+(i+1)Δt} for i=1,2, . . . .
周期性表示對於i = 1,2，…，系統在時間間隔{t，t+Δt}中並在時間間隔{t+iΔt，t+(i+1)Δt}中再次呈現一系列狀態。
7.穩定狀態
The concept of stationary states is important for themodeling of dynamical systems. Stationary states (other terms are steady statesor fixed points) are determined by the fact that the values of all statevariables remain constant in time. The asymptotic behavior of dynamic systems,that is, the behavior after a sufficiently long time, is often stationary.Other types of asymptotic behavior are oscillatory or chaotic regimes.
穩態的概念對於動力學系統的建模很重要。固定狀態（其他術語是穩態或不動點）由以下事實決定：所有狀態變量的值都保持時間恆定。動態系統的漸近行為，即經過足夠長的時間後的行為通常是平穩的。其他類型的漸近行為是振蕩或混沌狀態。
The consideration of steady states is actually an abstraction that is based on a separation of time scales. In nature, everything flows.Fast and slow processes – ranging from formation and breakage of chemical bondswithin nano seconds to growth of individuals within years – are coupled in thebiological world. While fast processes often reach a quasi-steady state after ashort transition period, the change of the value of slow variables is oftennegligi ble in the time window of consideration. Thus, each steady state canbe regarded as a quasi-steady state of a system that is embedded in a largernonstationary envi ronment. Despite this idealization, the concept of stationary states is important in kinetic modeling because it points to typicalbehavioral modes of the system under study and it often simplifies themathematical problems.
穩態的考慮實際上是基於時間尺度分離的一種抽象。在自然界中，一切都會流動。快速和緩慢的過程-從納秒級的化學鍵形成和斷裂到數年之內的個體生長-都與生物界相關。儘管快速過程通常會在短暫的過渡期後達到準穩態，但在考慮的時間範圍內，慢變量值的變化通常可以忽略不計。因此，每個穩態都可以看作是嵌入較大的非平穩環境中的系統的準穩態。儘管有這種理想化，平穩狀態的概念在動力學建模中還是很重要的，因為它指出了所研究系統的典型行為模式，並且通常簡化了數學問題。
Other theoretical concepts in systems biology are onlyrough representations of their biological counterparts. For example, therepresentation of gene regulatory networks by Boolean networks, the descriptionof complex enzyme kinetics by simple mass action laws, or the representation ofmultifarious reaction schemes by black boxes proved to be helpfulsimplifications. Although being a simplification, these models elucidatepossible network properties and help to check the reliability of basicassumptions and to discover possible design principles in nature. Simplifiedmodels can be used to test mathematically formulated hypotheses about systemdynamics, and such models are easier to understand and to apply to differentquestions.
系統生物學中的其他理論概念僅是其生物學對應物的粗略表示。例如，通過布爾網絡表示基因調控網絡，通過簡單的質量作用定律表示複雜的酶動力學或通過黑盒表示多種反應方案被證明是有助於簡化的。儘管只是簡化，但這些模型闡明了可能的網絡屬性，並有助於檢查基本假設的可靠性並發現自然界中可能的設計原則。可以使用簡化的模型來測試關於系統動力學的數學公式化的假設，並且這種模型更易於理解並適用於不同的問題。
8.模型分配的不唯一性
Biologicalphenomena can be described in mathematical terms. Models developed during thelast few decades range from the description of glycolytic oscillations withordinary differential equations to population dynamics models with differenceequations, stochastic equations for signaling pathways, and Boolean networksfor gene expression. However, it is important to realize that a cer tainprocess can be described in more than one way: a biological object can beinvestigated with different exper imental methods and each biological processcan be described with different (mathematical) models. Some times, a modelingframework represents a simplified lim iting case (e.g., kinetic models aslimiting case of stochastic models). On the other hand, the same mathe maticalformalism may be applied to various biological instances: statistical networkanalysis, for example, can be applied to cellular transcription networks, thecircuitry of nerve cells, or food webs.
生物現象可以用數學術語來描述。在過去幾十年中發展起來的模型從用常微分方程描述糖酵解振蕩到具有差分方程的種群動力學模型、信號通路的隨機方程和基因表達的布爾網絡。然而，重要的是要認識到，一個CER過程可以用多種方式來描述：一個生物物體可以用不同的實驗方法來研究，每個生物過程可以用不同的（數學）模型來描述。有些時候，一個建模框架代表了一個簡化的lim&iting案例（例如，動力學模型作為隨機模型的限制情況）。另一方面，同樣的數學形式可以應用於各種生物學實例：例如，統計網絡分析可以應用於細胞轉錄網絡、神經細胞迴路或食物網。
The choice of a mathematical model or an algorithm todescribe a biological object depends on the problem, the purpose, and theintention of the investigator. Modeling has to reflect essential properties ofthe system and differ ent models may highlight different aspects of the samesystem. This ambiguity has the advantage that different ways of studying aproblem also provide different insights into the system. However, the diversityof modeling approaches makes it also very difficult to merge estab lishedmodels (e.g., for individual metabolic pathways) into larger supermodels (e.g.,models of complete cell metabolism).
描述生物學對象的數學模型或算法的選擇取決於研究者的問題，目的和意圖。建模必須反映系統的基本屬性，不同的模型可能會突出顯示同一系統的不同方面。這種歧義性的優點在於，研究問題的不同方法也可以提供對系統的不同見解。然而，建模方法的多樣性也使得很難將已建立的模型（例如，對於單個代謝途徑）合併成較大的超模型（例如，完全細胞代謝的模型）。