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Covert et al. (2003): Identifying Constraints that Govern Cell Behavior: A Key to Converting Conceptual to Computational Models in Biology?
Cells "must abide" three types of constraints: "environmental", "physio-chemical" and "self-imposed" ones. Dealing with these constraints "has been helpful in converting conceptual models to computational models in biology", so the authors write in the abstract, and these models ought to be further refined.
What do the authors understand when they are talking about conceptual models on the one hand and computational models on the other? Quote:
Conceptual models describe a system in qualitative terms, whereas computational models can quantitatively simulate systemic properties to analyze, interpret, and predict cell behavior.
The reconstruction of "fairly complicated conceptual models of metabolic, regulatory, and signaling networks" has culminated "in the development of databases such as KEGG and MetaCyc", and the challenge now is to translate these models into "genome-scale computational models". According to the authors, the constraint-based approach may help achieve this goal:
In the constraint-based approach to analyzing metabolic networks, all possible behaviors of a system (e.g., flux distributions through the metabolic network) are considered[.] [...] By successively imposing constraints on conceptual models [...] the allowable range for each flux in the network is reduced dramatically. The problem of modeling complex biological systems shifts from experimental determination of kinetic and other fundamental parameters — as mentioned, currently an intractable problem — to continued identification of constraints that allow a more specific description of the system[.]
"Current constraint-based computational models have focused on microbial organisms" and are "at the genome-scale", which means they have "focused primarily on metabolism and associated transcriptional regulation, but are aimed at a complete representation of an organism and have already been used to simulate cell behavior under a variety of conditions" and "are instrumental in identifying and characterizing emergent properties of biological networks".
The next three chapters deal with the three types of constraints. The first is about external constraints:
External environments impose constraints on cells in terms of nutrients, physical factors, and neighboring influences. [...] Without adequate knowledge of the nutritional content of the external environment, significant constraints must be ignored or grossly approximated, resulting in incorrect or misleading predictions of cell behavior. [...] Physical characteristics of the external environment, such as temperature, pressure, pH, and exposure to light or water, can also limit possible cell behavior and survival. [...] The environmental conditions experienced by a cell generally change over time. [...] To account for such interactions in a model, the cellular community must therefore be accurately represented. [...] The intracellular environment of a cell also imposes constraints on cellular behavior, notably in terms of its internal components and the physical properties of its interior.
The second chapter is about physicochemical constraints:
Cells balance mass and energy, conform to the laws of thermodynamics and kinetics, and operate under limited enzyme turnover rates and activity of gene products. Physicochemical constraints are generally considered to be 'hard' constraints and are thought to remain unchanged. [...] Mass balance of reactions also imposes stoichiometric constraints on the network. [...] The requirement of mass balance exerts such a strong constraint on metabolic network function that flux balance analysis requires virtually only these constraints, with only a handful of strain-specific parameters, for detailed qualitative simulations. [...] The maximum throughput or enzyme capacity of biochemical reactions can also force the cell to exhibit more limited behaviors than otherwise. [...] The balance of osmotic pressure and maintenance of electroneutrality also impose constraints on cells.
The third chapter, finally, deals with self-imposed constraints:
Self-imposed constraints are different from other constraints because they respond to — and often change — internal or external environments. Unlike physicochemical constraints, they are time-dependent. Such adaptive constraints may entail regulation in the short term and evolution over longer time scales.
Moreover, this chapter lists two particular types of self-imposed constraints, namely "evolutionary constraints" and "regulatory constraints".
All of these constraints have been successfully applied to genome-scaled models:
As mentioned earlier, constraint-based approaches have enabled the development of genome-scale models of microorganisms. Thus far, the constraints that have been incorporated into genome-scale simulative models of metabolism, such as those that exist for E. coli, H. influenzae, H. pylori, and S. cerevisiae, have been stoichiometric, thermodynamic, enzyme capacity, and energy balance constraints. Transcriptional regulatory constraints have also recently been added to enable combined simulation of regulatory and metabolic networks.
How is this done in practice? The authors write:
A useful mathematical representation of all possible cell behaviors is one established geometrically as a solution space, which is effectively capped and reduced as constraints are incorporated. We are then left with a smaller solution space having general properties that can be studied, or in which certain points (i.e., cellular behaviors) may be examined in more detail.
Variants of this are "pathway analysis", "flux balance analysis", "energy balance analysis" and "regulatory flux balance analysis". The authors explain all of these variants, especially the last one.
In the appendix a couple of equations representing "certain physicochemical constraints in biology" are provided.
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