Modeling and Biology

Biologists and Engineers often use the same term, but actually mean differnt things. If you encounter such problems visit the Systems Biology Glossary to understand what the other side might mean.
The complexity of biology can not only be seen on the global level, but already becomes apparent when a pathway elicited by a single signaling molecule is looked at. A system is not just an assembly of genes and proteins. Therefore, its properties cannot be fully understood merely by drawing diagrams of their interconnections (Kitano 2002). Model aided understanding should introduce new ideas into biology, as it has introduced into engineering, economy or ecology. Biologists are using "conceptiol" models describing their pictured view of the events involved. Those models are in general purely qualitative. The models that will be introduced now are from an engineers point of view. They introduce mathematics, trying to elucidate the underlying mechanism on a quantitative basis to gain systems-level understanding, not just a pictured view.

Advanced technologies and biology have extremely different physical implementations, but they are far more alike in systems-level organization than is widely appreciated. Convergent evolution in both domains produces modular architectures that are composed of elaborate hierarchies of protocols and layers of feedback regulation, are driven by demand for robustness to uncertain environments, and use often imprecise components. This complexity may be largely hidden in idealized laboratory settings and in normal operation, becoming conspicuous only when contributing to rare cascading failures. These puzzling and paradoxical features are neither accidental nor artificial, but derive from a deep and necessary interplay between complexity and robustness, modularity, feedback, and fragility (Csete and Doyle 2002).

Modeling in Biology

The idea of modeling in biology is not new (see also). There are several books available giving an overview over model applications in biology (e.g. Murray 1990; Keener and Sneyd 1998; Lauffenburger and Linderman 1993). In signal transduction modeling, the MAPK cascade and the EGF receptor, that, among others, activates this pathway, stand out as used model objects (Huang and Ferrell 1996; Schöberl et al. 2002). There is a wealth of data, both qualitative and quantitative and easy model systems (e.g. Xenopus oocytes, which are thousand times larger than a normal cell, making experiments on the single cell possible) are available for these pathways, but, for example, also caspase function has been modeled (Fussenegger et al. 2000). However, only isolated parts of signal transduction have been modeled so far. Only very recently models have been introduced that integrate whole pathways (Schöberl 2002). Modeling in biology is much better established for metabolic networks, and the area of metabolic engineering has emerged (Heinrich and Rapoport 1977; Stephanopoulos et al. 1998). Many of the ideas developed on metabolic networks, could, in principle, be applied to protein networks as well. However, in metabolic control analysis usually stationary states and linearized models are considered and the insight gained is restricted to those stationary points (local analysis). No conclusions can be drawn concerning the global behavior of the non-linearized model. Signal transduction, for example, is far from being linear, and, unlike in metabolic networks, stationary points are of less interest.

Model, System and more Definitions

The word model derives from the Latin language and refers (the way it is used here) to the simplified representation of a real system. Here the representation is via mathematics and the system is the TNF signaling network. Mathematical models can correlate experimental data. They are an aid to evaluate complex sets of data and point out connections and properties maybe hidden otherwise. The words model and system are often used as synonyms. The word system derives from the Greek language and means the out of parts combined and structured whole. Systems and models are often structured and hierarchically build. On the cellular level, for example, usually the metabolic, gene, and protein networks are distinguished, although, of course, interconnected, and organs and then the organism form the next higher levels.

Types of models

Different types of models can be distinguished. Models can be based on a priori knowledge about system elements, e.g. physical laws, or be based on a behavior seen, e.g. curve fitting, where the correlation between input and output is then usually treated as a black box. In a static system all output signals only depend on the input signal at the same time, e.g. Ohm s law u(t) = R " i(t). Here only the topology is relevant for the behavior. Otherwise the model is dynamic, where the system behavior also depends on the past. This implies storage in the system. The state of all system variables (storages) describes the system. The number of state variables is called order. Biology is highly dynamic and dynamic effects have to be taken into account to understand the systems behavior. Models can be deterministic, i.e. for a certain input and certain initial conditions of the state variables, there is one output or models can be probabilistic, i.e. the output is predicted within a range of values, and each value has an assigned probability. Certainly probabilistic models are useful in biology, and are necessary if small numbers of molecules are involved. However, probabilistic models are more complicated and also more demanding in terms of computer performance to be solved.

Features and analysis of models

The most important features of protein networks are non-linearities and feedback. Feedback means that the information on which the decision is based, is influenced by the measurement of the output. Two of the most common responses to external stimuli are amplification and adaptation. Adaptation allows cells to return to their original steady state, without the input signal needing to return to its prestimulation value. Models can be analyzed for system behavior, either analytically (i.e. explicitly solving mathematical equations) or numerically (calculating the result for different input values using computers). Analytic analysis for large systems are often problematic, and one prerequisite in general is usually linearity. Therefore, numeric solutions are often the method of choice. Numeric solutions are obtained by simulation, which means computer aided numeric integration of differential equation systems. Sensitivity and robustness are important features of networks. Sensitivity analysis shows how a change in one parameter effects the overall behavior. If a system is sensitive to a certain parameter, small changes in its value will have large effects on the system performance. This links sensitivity to robustness, which defines whether or not the system settles to its solution space when excited over a broad range of input conditions. So, a robust system has a low sensitivity towards the input. With metabolic control analysis, metabolic engineering provides a theoretical approach to flux control and sensitivity. However, the dynamics and non-linearity make our system unsuitable for applying this approach. Sensitivity in a biological sense is used differently and means a measure for the minimal strength of a certain stimulus required for a reaction (Haubelt 2002).

Modeling - an Iterative Process

Modeling is an iterative process. For biological systems, one has to consider the questions the model is supposed to answer, and clearly define the model system, e.g. which cell line is to be modeled. Then experiments have to be performed to gain information. Certainly, literature can already provide a lot of information, although this information often is only qualitative not quantitative and often obtained on different model systems. However, this often is sufficient to define the structure of the model, i.e. what molecules are there and who interacts. Of course, before modeling, the type of model has to be considered (see above) and how detailed it should be, again this depends on the questions the model should be able to answer. After the structure of the model has been defined, it has to be implemented kinetically (if a dynamic model approach is chosen, as is the case here), i.e. the kinetic parameters have to be adjusted, so that the model can explain the experimental data. The operating model resulting thereof has then to be verified by testing model predictions and comparing those with literature or new own experimental data that have not already been used in the model implementation. Also, negative tests can be performed, i.e. is the model not doing what it should not do? The experiments have to be designed to distinguish a right from a wrong model. With new data at hand, the model can be refined, maybe only by adjusting parameters, but maybe also by changing the structure, thus starting the next iteration round.

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