Examples of systems biology research1

One aspect of systems biology is the analysis of the structure of the molecular networks and its consequences for the cell. In much the same way as genome sequencing has lead to the emergence of the theoretical analysis of genomes (bioinformatics), has the availability of the entire metabolic, signaling, and gene networks of cells led to the development of theoretical analyses of networks [6, 54]. Many interesting properties of molecular networks haven been discovered [54-56]. Most noticeably are small world organization [57, 58], modularity [59, 60], motifs [61-63], flux balance analysis, extreme pathway and elementary mode analysis [6, 64-67]. All these methods analyze large-scale molecular networks and induce general information regarding their structure and functional consequences. This is one exciting branch of systems biology that is anticipated to develop further and discover many new insights into the molecular organization of cells. Reviews on this aspect of systems biology can be found elsewhere [6, 54].

Another aspect of systems biology is the construction of kinetic models of molecular network functioning as was introduced briefly in the previous section [12, 17, 20]. The history of kinetic model construction and analysis is already long. The first models of metabolism were created in the 1960s and 1970s [68, 69]. Those models suffered mostly from a lack of sufficient system data. The introduction of desktop computers, the development of theory for the analysis of dynamics of nonlinear systems (e.g., [70]), and the development of non-equilibrium thermodynamics (e.g., [71, 72]) lead to the analysis of simplified models - core models - illustrating complex dynamics of molecular networks [19, 73-76]. As understanding progressed, those core models were interchanged for detailed models describing com

1 The models mentioned in this section can all be investigated online at the JWS online website (www.jjj.bio.vu.nl)

plex dynamics, e.g., compare core models of glycolysis [74, 75] with detailed models [77, 78]. The more detailed models are of interest in bioengineering as they may facilitate rational approaches to optimization of product formation [10, 11, 51, 79].

Hoefnagel et al. [11] developed a kinetic model of pyruvate metabolism in Lactococcus lactis to optimize the production rate of acetoin by this organism. All the rate equations of enzymes, as they were characterized in the literature, were incorporated in a kinetic model. They showed that two enzymes (lactate dehydrogenase (LDH) and NADH oxidase (NOX)), previously not identified as important for acetoin production, had most control on the acetoin production flux. By deleting LDH and overexpressing NOX in experiment they were able to redirect carbon flux to acetoin; 49% of pyruvate consumption flux in the mutant versus ~0% in the wild type. This result was of importance for industry.

Glycolysis is a catabolic pathway (Fig. 1A) that is present in all kinds of cells. Teusink et al. [80, 81] constructed a kinetic model of yeast glycolysis that was quite helpful in solving the puzzle of an unexpected phenotype of a particular mutant strain and at the same time lead to a surprising new insight about glycolysis. Sac-charomyces cerevisiae strains with a lesion in the TPS1 gene, which encodes treha-lose-6-phosphate (Tre-6-P) synthase, cannot grow with glucose as the sole carbon and free energy source. Although this enzyme appeared to have little relevance to glycolysis - it was considered to function in the formation of storage carbohydrates and the acquisition of stress tolerance - it turned out to be crucial for growth on glucose. Using the detailed kinetic model of S. cerevisiae glycolysis it was shown that the turbo design of the glycolytic pathway (Fig. 1B), apart from being useful in allowing for rapid growth, also represents an inherent risk. A yeast cell investing ATP in the first part of glycolysis and producing a surplus of ATP in the downstream (lower) part of glycolysis runs the risk of an uncontrolled glycolytic flux. In the model, this resulted in the accumulation of hexose monophosphate and fructose-1,6-bisphosphate to levels that are considered toxic when established in the real yeast cell. The formation of trehalose-6-phosphate prevented glycolysis from going awry by inhibiting hexokinase (Fig. 2A), the first ATP-consuming step of glycolysis and thereby restricting the flux of glucose into glycolysis [80]. The importance of the trehalose branch of glycolysis for growth on glucose could only be discovered through the systems biological approach of combining experimental data with kinetic modeling as outlined above. Detailed models can also be used to calculate the outcome of experiments that are not yet achievable, too laborious or too costly to perform as a pilot experiment. Glycolysis in Trypanosoma brucei takes place in a special organel, the glycosome, except for the steps by which 3-phosphoglycerate is converted into pyruvate. In contrast to the situation described above for S. cerevi-siae, the first step catalyzed by hexokinase is not at all regulated in trypanosomes. The glycosome is surrounded by a membrane (Fig. 2B). Bakker et al. [13] were able to calculate the effect of the removal of the glycosomal membrane in T. brucei. At the time, this experiment could not be performed experimentally. However, they could remove the membrane in a detailed kinetic model that was validated earlier [7]. The removal of the membrane was of interest because the biological advantage

Phosphate Remove Scheme

Figure 1. The dangerous turbo design of glycolysis. (A) A simplified scheme of glycolysis. Solid lines represent reactions catayzed by a single enzyme; dashed lines represent multiple sequential reactions. Glc-6P, glucose 6-phosphate; Fru-1,6-BP, fructose 1,6 bisphosphate; DHAP, dihydroxyaceton phosphate; GA-3-P, glyceraldehyde 3-phosphate; 1,3-BPGA, 1,3-bis-phosphoglycerate; 3-PGA, 3-phosphoglycerate. (B) The turbo design of glycolysis. Generalized scheme for glycolysis in which the upper part from substrate S to intermediate I combines the ATP-consuming reactions and the lower part from I to product P combines the ATP-produ-cing reactions. The surplus of ATP produced in the lower part is depicted in bold capitals and the boosting effect on the upper part is indicated by thick lines.

Figure 1. The dangerous turbo design of glycolysis. (A) A simplified scheme of glycolysis. Solid lines represent reactions catayzed by a single enzyme; dashed lines represent multiple sequential reactions. Glc-6P, glucose 6-phosphate; Fru-1,6-BP, fructose 1,6 bisphosphate; DHAP, dihydroxyaceton phosphate; GA-3-P, glyceraldehyde 3-phosphate; 1,3-BPGA, 1,3-bis-phosphoglycerate; 3-PGA, 3-phosphoglycerate. (B) The turbo design of glycolysis. Generalized scheme for glycolysis in which the upper part from substrate S to intermediate I combines the ATP-consuming reactions and the lower part from I to product P combines the ATP-produ-cing reactions. The surplus of ATP produced in the lower part is depicted in bold capitals and the boosting effect on the upper part is indicated by thick lines.

of the glycosome was hypothesized by others to enable this organism to have an extremely high glycolytic flux. Bakker et al. [13] showed that yeast - which does not have glycosomes - can have fluxes as high as T. brucei. In addition, they showed that the removal of the glycosomal membrane did not cause a physiologically significant change in the glycolytic flux. Rather, the removal of the glycosome caused accumulation of glucose-6-phosphate and fructose-1,6-bisphosphate up to 100 mM. This would certainly represent a pathological situation for T. brucei involving phosphate depletion and possibly osmotic swelling. As it turned out, the glycosomal membrane makes sure that the upper part of glycolysis is not accelerated by the ATP produced by the lower part of glycolysis, because the surplus ATP producing step in the lower part of glycolysis (by pyruvate kinase) actually resides outside of the glycosome. Thus the glycosome is another implementation of a protective device

3bpga Structure

Figure 2. Two different solutions to the turbo design problem. (A) The trehalose branch in S. cerevisiae. The scheme is the same as the one shown in Figure 1A, except for the addition of the trehalose shunt in bold. Tre-6-P, trehalose 6-phosphate. The inhibition of hexokinase by Tre-6-P is indicated by a thick dashed line. (B) The glycosome in trypanosomes. Again, the scheme is the same as the one shown in Figure 1A, except for the addition of the glycosomal membrane in bold. The conversion of 3-PGA to pyruvate takes place outside of the glycosome.

Figure 2. Two different solutions to the turbo design problem. (A) The trehalose branch in S. cerevisiae. The scheme is the same as the one shown in Figure 1A, except for the addition of the trehalose shunt in bold. Tre-6-P, trehalose 6-phosphate. The inhibition of hexokinase by Tre-6-P is indicated by a thick dashed line. (B) The glycosome in trypanosomes. Again, the scheme is the same as the one shown in Figure 1A, except for the addition of the glycosomal membrane in bold. The conversion of 3-PGA to pyruvate takes place outside of the glycosome.

against the potentially dangerous 'turbo' design of glycolysis. These two examples of models of glycolysis demonstrate the power of (bottom-up systems biological) kinetic models; when precise and detailed knowledge of the kinetics of the molecular components is available, so-called computer experimentation can be carried out which serves as an adequate substitute for true experimentation.

Regulation of metabolic flux is governed by many different mechanisms. They may function at the level of metabolism, transcription, translation, or at the level of degradation of mRNA or protein. At the level of metabolism, contributions to the regulation of enzymatic conversion rates are made by substrates and products, by effectors through allosteric feedback or feedforward loops, or by covalent modification. Recently a quantitative mathematical tool has been developed in our laboratory, referred to as hierarchical regulation analysis, that allows for the quantitative determination of the importance of all those mechanisms that contribute to the regulation of flux, given experimental data [82-84].

The regulation of the ammonium-assimilation flux by Escherichia coli is governed by a complicated mechanism involving multiple covalent modifications, feedback, substrate/product effects, gene expression and targeted protein degradation [85, 86]. This system has for a long time been a paradigm of flux regulation by way of cova-lent modification. We have recently integrated all molecular data of this network into a detailed kinetic model describing the short-term metabolic regulation of ammonium assimilation [12]. We confirmed many of the hypotheses postulated in the literature on how this system should function. We identified that covalent modification of glutamine synthetase is the most important determinant of the ammonium assimilation flux upon sudden changes in ammonium availability using hierarchical regulation analysis. Removal of the covalent modification of glutamine synthetase caused accumulation of glutamine and severe impairment of growth as was shown experimentally by others [87]. It was confirmed that indeed gene expression of glutamine synthetase alone can lead to regulation of ammonium assimilation; the ammonium assimilation flux was not sensitive to changes made in the level of any of the other enzymes. Finally, we predicted that one advantage of all this complexity is to allow E. coli to keep its ammonium assimilation flux constant despite of changes in the ammonium concentration and to change from an energetically unfavorable mode of ammonium uptake to a more favorable alternative as the ammonium level is increased.

The analysis and construction of models incorporating signal transduction networks at a high level of molecular detail has recently been pioneered because of their high potential in drug design [8, 15, 52, 88-90]. We have investigated one of the largest and most complete model of a signal transduction network for its control properties [90]. We determined the control coefficients of all the processes in the network on three characteristics of the transient activation profile of extracellular signal regulated kinase (ERK), which is a member of the mitogen activating protein kinase (MAPK) family. The model contained 148 reactions and 103 variable concentrations and it is an enlarged version of the model published by Schoeberl et al. [89]. To our surprise, we found that less than 10% of the reactions had a large control on ERK activation. We identified RAF as a candidate oncogene and indeed it was found frequently mutated in tumors. To cope with the enormous size of signal transduction network some systems biologists are presently developing theoretical methods for model reduction [91-93]. Such strategies may greatly facilitate understanding, analysis, and experimental design.

In model-driven experimentation, usage of simplified models that illuminate principles of system functioning and guide experimentation (experimental design) are extremely helpful. This approach is nicely illustrated by a series of papers by the group of Ferrell and co-workers [94-97] and Alon and co-workers [98-102]. In Pomerening et al. [97], Ferrell and co-workers investigate the core oscillator driving the cell cycle inXenopus laevis. They study the entry into mitosis and the subsequent return to interphase by following the dynamics of the formation and degradation of the complex cdc2-cyclinB. The interphase-mitosis transition (mitosis: M-phase) is accompanied by synthesis and accumulation of cyclin-B and the subsequent formation of cdc2-cyclinB complex. The degradation of this complex is mediated by

APC-catalyzed degradation of cyclin-B and signals the exit of the M-phase and reentry into interphase. In addition, two net positive feedbacks play a role: via Myt1-Wee1 and cdc25. It was shown experimentally [103] that in the absence of the degradation of cyclin-B by APC the resulting network is bistable. In the presence of cyclin-B degradation, the network displays the oscillations characteristic for the cell cycle; more specifically, it functioned as a relaxation oscillator. Using a semi-detailed model (based on [18, 103]), the authors modeled the network in the absence and the presence of the degradation of cyclin-B and found bistability and oscillations, respectively. Then they investigated the effects of the two net positive feedbacks by inhibiting them. This caused the core oscillator to engage in damped oscillations rather than prolonged oscillations indicating the essentiality of the positive feedback for proper functioning of the cell cycle. The model they used was only quasi-detailed at best but still it had sufficient detail and reflection of reality facilitating model-driven experimentation. In our studies on MAPK signaling, we took a similar approach [45]. We used a simple core model of the MAPK pathway to investigate the difference between inhibition of phosphatases and kinases on the activation profile of ERK. We found that the core model could qualitatively predict the experimental data. It showed that phosphatases tend to control both the amplitude and duration of signaling whereas kinases tend to control only the amplitude. Those results were backed up by theory leading to new theorems in control analysis for signal transduction [45]. Another successful application of the use of simple models to drive experimentation is found in the work by Alon and co-workers [98-102]. They are characterizing the functional properties of motifs, small intracellular networks that occur more frequently in biological networks than in networks of similar size with a random structure. So far they focused mostly on gene circuitry and their activation by transcription factors. The reasoning behind the search and characterization for motifs is that if they occur significantly more frequently in biological networks their design is predicted to have a functional relevance for the cell. They have been successful in showing the functional significance of a number of these motifs. Synthetic biology takes the opposite approach. It tries to design new networks using simple models and implement those in cells to facilitate their analysis, as biosensors, and to endow them with new properties. One successful approach of synthetic biology has been the analysis of noise [104-111]. Noise occurs naturally in all physical systems. In cells noise, perceived as fluctuating copy numbers of molecules in cells, occurs because of fluctuating reaction rates due to local thermal fluctuations [40]. The magnitude of the fluctuations relative to the average copy number determines their influence and importance on intracellular dynamics. The effects of noise are most pronounced when the copy number of molecules are small, < 50 molecules/cell, but may become high even in systems with high average copy numbers, ~1,000s molecules/cell, if the system is sufficiently nonlinear [41, 112].

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