1
Introduction

1. 1.1 Biology in Time and Space
2. 1.2 Models and Modeling
   1. What Is a Model?
   2. Purpose and Adequateness of Models
   3. Advantages of Computational Modeling
3. 1.3 Basic Notions for Computational Models
   1. Model Scope
   2. Model Statements
   3. System State
   4. Variables, Parameters, and Constants
   5. Model Behavior
   6. Model Classification
   7. Steady States
   8. Model Assignment Is Not Unique
4. 1.4 Networks
5. 1.5 Data Integration
6. 1.6 Standards
7. 1.7 Model Organisms
   1. Escherichia coli
   2. Saccharomyces cerevisiae
   3. Caenorhabditis elegans
   4. Drosophila melanogaster
   5. Mus musculus
8. References
9. Further Reading

1.1 Biology in Time and Space

Biological systems such as organisms, cells, or biomolecules are highly organized in their structure and function. They have developed during evolution and can only be fully understood in this context. To study them and to apply mathematical, computational, or theoretical concepts, we have to be aware of the following circumstances.

The continuous reproduction of cell compounds necessary for living and the respective flow of information is captured by the central dogma of molecular biology, which can be summarized as follows: genes code for mRNA, mRNA serves as template for proteins, and proteins perform cellular work. Although information is stored in the genes encoded by the DNA sequence, it is made available only through the cellular machinery that can decode this sequence and can translate it into structure and function. In this book, we will explain that from various perspectives.

A description of biological entities and their properties encompasses different levels of organization and different time scales. We can study biological phenomena at the level of populations, individuals, tissues, organs, cells, and compartments down to molecules and atoms. Length scales range from the order of meter (e.g., the size of whale or human) to micrometer for many cell types, down to picometer for atom sizes. Time scales include millions of years for evolutionary processes, annual and daily cycles, seconds for many biochemical reactions, and femtoseconds for molecular vibrations. Figure 1.1 gives an overview about scales.

Figure 1.1 Length and time scales in biology. (Data from the BioNumbers database at bionumbers.hms.harvard.edu.)

In a unified view of cellular networks, each action of a cell involves different levels of cellular organization, including genes, proteins, metabolism, or signaling pathways. Therefore, the current description of the individual networks must be integrated into a larger framework.

Many current approaches pay tribute to the fact that biological items are subject to evolution. The structure and organization of organisms and their cellular machinery has developed during evolution to fulfill major functions such as growth, proliferation, and survival under changing conditions. If parts of the organism or of the cell fail to perform their function, the individual might become unable to survive or replicate.

One consequence of evolution is the similarity of biological organisms of different species. This similarity allows for the use of model organisms and for the critical transfer of insights gained from one cell type to other cell types. Applications include, for example, prediction of protein function from similarity, prediction of network properties from optimality principles, reconstruction of phylogenetic trees, or the identification of regulatory DNA sequences through cross-species comparisons. However, the evolutionary process also leads to genetic variations within species. Therefore, personalized medicine and research is an important new challenge for biomedical research.

1.2 Models and Modeling

If we observe biological phenomena, we are confronted with various complex processes that often cannot be explained from first principles and the outcome of which cannot reliably be foreseen from intuition. Even if general biochemical principles are well established (e.g., the central dogma of transcription and translation or the biochemistry of enzyme-catalyzed reactions), the biochemistry of individual molecules and systems is often unknown and can vary considerably between species. Experiments lead to biological hypotheses about individual processes, but it often remains unclear whether these hypotheses can be combined into a larger coherent picture because it is often difficult to foresee the global behavior of a complex system from knowledge of its parts. Mathematical modeling and computer simulations can help us to understand the internal nature and dynamics of these processes and to arrive at predictions about their future development and the effect of interactions with the environment.

1.2.1 What Is a Model?

The answer to this question will differ among communities of researchers. In a broad sense, a model is an abstract representation of objects or processes that explains features of these objects or processes (Figure 1.2). A biochemical reaction network can be represented by a graphical sketch showing dots for metabolites and arrows for reactions; the same network could also be described by a system of differential equations, which allows simulating and predicting the dynamic behavior of that network. If a model is used for simulations, it needs to be ensured that it faithfully predicts the system's behavior - at least those aspects that are supposed to be covered by the model. Systems biology models are often based on well-established physical laws that justify their general form, for instance, the thermodynamics of chemical reactions. Besides this, a computational model needs to make specific statements about a system of interest - which are partially justified by experiments and biochemical knowledge, and partially by mere extrapolation from other systems. Such a model can summarize established knowledge about a system in a coherent mathematical formulation. In experimental biology, the term "model" is also used to denote a species that is especially suitable for experiments; for example, a genetically modified mouse may serve as a model for human genetic disorders.

Figure 1.2 Typical abstraction steps in mathematical modeling. (a) E. coli bacteria produce thousands of different proteins. If a specific protein type is labeled with a fluorescent marker, cells glow under the microscope according to the concentration of this marker. (Courtesy of M. Elowitz.) (b) In a simplified mental model, we assume that cells contain two enzymes of interest, X (red) and Y (blue), and that the molecules (dots) can freely diffuse within the cell. All other substances are disregarded for the sake of simplicity. (c) The interactions between the two protein types can be drawn in a wiring scheme: each protein can be produced or degraded (black arrows). In addition, we assume that proteins of type X can increase the production of protein Y. (d) All individual processes to be considered are listed together with their rates a (occurrence per time). The mathematical expressions for the rates are based on a simplified picture of the actual chemical processes. (e) The list of processes can be translated into different sorts of dynamic models, in this case, deterministic rate equations for the protein concentrations x and y. (f) By solving the model equations, predictions for the time-dependent concentrations can be obtained. If the predictions do not agree with experimental data, this indicates that the model is wrong or too much simplified. In both cases, the model has to be refined.

1.2.2 Purpose and Adequateness of Models

Modeling is a subjective and selective procedure. A model represents only specific aspects of reality but, if done properly, this is sufficient since the intention of modeling is to answer particular questions. If the only aim is to predict system outputs from given input signals, a model should display the correct input-output relation, while its interior can be regarded as a black box. However, if instead a detailed biological mechanism has to be elucidated, then the system's structure and the relations between its parts must be described realistically. Some models are meant to be generally applicable to many similar objects (e.g., Michaelis-Menten kinetics holds for many enzymes, the promoter-operator concept is applicable to many genes, and gene regulatory motifs are common), while others are specifically tailored to one particular object (e.g., the 3D structure of a protein, the sequence of a gene, or a model of deteriorating mitochondria during aging). The mathematical part can be kept as simple as possible to allow for easy implementation and comprehensible results. Or it can be modeled very realistically and be much more complicated. None of the characteristics mentioned above makes a model wrong or right, but they determine whether a model is appropriate to the problem to be solved. The phrase "essentially, all models are wrong, but some are useful" coined by the statistician George Box is indeed an appropriate guideline for model building.

1.2.3 Advantages of Computational Modeling

Models gain their reference to reality...