Date Published: January 23, 2011
Publisher: Hindawi Publishing Corporation
Author(s): Dagmar Iber.
Biological functionality arises from the complex interactions of simple components. Emerging behaviour is difficult to recognize with verbal models alone, and mathematical approaches are important. Even few interacting components can give rise to a wide range of different responses, that is, sustained, transient, oscillatory, switch-like responses, depending on the values of the model parameters. A quantitative comparison of model predictions and experiments is therefore important to distinguish between competing hypotheses and to judge whether a certain regulatory behaviour is at all possible and plausible given the observed type and strengths of interactions and the speed of reactions. Here I will review a detailed model for the transcription factor σF, a regulator of cell differentiation during sporulation in Bacillus subtilis. I will focus in particular on the type of conclusions that can be drawn from detailed, carefully validated models of biological signaling networks. For most systems, such detailed experimental information is currently not available, but accumulating biochemical data through technical advances are likely to enable the detailed modelling of an increasing number of pathways. A major challenge will be the linking of such detailed models and their integration into a multiscale framework to enable their analysis in a larger biological context.
The success of modern physics came about by a fruitful combination of theory and experiment. Models in physics succeed, in general, in predicting experimental results quantitatively. Where applicable, concepts from physics and chemistry have also greatly helped to understand biological mechanisms, the generation of ATP by coupling phosphorylation to an electrochemical concentration gradient , the emergence of action potentials based on changes in membrane conductivity , and the kinetics of enzymatic reactions , among many others. However, in most cases it is the regulatory structure that emerges from a complex network of protein and gene interactions that determines biological functionalities and appearances. Jacob and Monod were the first to recognize the regulatory logic of a gene regulatory network , a network that has since attracted numerous computational studies and has led to the discovery of many important concepts in molecular biology . Further theoretical studies have established the basic requirements for a range of qualitative properties of the regulatory system, that is, its ability to show transient, sustained, or oscillatory responses, or to be sensitive or robust to molecular noise [6, 7]. While the basic requirements are now mostly understood, their functioning in the complex setting of a cell has remained hazy.
Sporulation in B. subtilis is one of the best understood examples for cell differentiation and development and has provided a paradigm for asymmetric cell division and differential cell fate decisions in genetically identical sister cells . In response to starvation, B. subtilis can initiate a cellular program that leads to asymmetric cell division and to the subsequent differentiation of the smaller compartment (prespore or forespore) into an endospore that can withstand and survive particularly harsh conditions (Figure 1(a)). The larger sister cell develops into an altruistic mother cell that supports the development of the prespore. The different fates of the two compartments are sealed when the transcription factor σF is activated in the smaller but not in the larger compartment [10–12]. The network that controls σF activity is simple (Figure 1(b)) and has been known for a long time . Yet how compartment-specific activation of σF is achieved has long remained elusive.
The regulatory system was particularly amenable to a quantitative analysis because all network components could be purified and the network could therefore be reconstituted in the test tube [44, 45]. This permitted us to develop a comprehensive differential equation model that would include all states and reactions of the test tube network [46, 47]. As we intended to create a quantitative, predictive model, it was important to move away from phenomenological descriptions to a detailed, mechanistic model that considered all binding reactions and conformational changes explicitly. Figure 1(c) shows a contact map of all possible regulatory interactions in the network. Accordingly, all parameter values corresponded to a physical entity and could be determined from experimental in vitro data. The detailed model for the small regulatory network with only four components (plus the RNA polymerase and the housekeeping transcription factor σA for the cellular model) eventually comprised more than 150 reactions that gave rise to a set of about 50 differential equations. The reaction kinetics depended on about 30 independent parameter values that we measured in experiments. While we took great care to validate the model with experimental data, there always remain concerns with regard to the estimated parameter values. Does the optimized parameter set represent biological reality or are conclusions misguided by errors in the data and limitations in the parameter estimation? Parameter estimation procedures for such large systems are prone to be trapped in a local parameter optimum. To address such concerns, we have recently conducted a wider parameter screen where we searched within a larger parameter space for parameter combinations that would capture the in vitro data (Iber, unpublished results). We noticed that about 20–30% of the parameter sets that fitted the in vitro behaviour reasonably well captured also the in vivo behaviour. Only when we required a very accurate fit to the experimental data did we obtain a 100% success rate in our predictions of the in vivo behaviour. This stresses the importance of high quality, quantitative data to extract meaningful insight from a model.
Based on the fully parameterized and validated model, we predicted that the difference in cell size would be sufficient to determine cell fate . A 2.5-fold increase in the phosphatase concentration was sufficient to trigger the appearance of micromolar concentrations of RNA polymerase-σF holoenzyme in the model (Figure 2). The model was not only validated with in vitro data but also succeeded in predicting the phenotypes of all mutants for which quantitative data was available [46, 47]. This was important because it enabled us to show that also those experiments that had led to alternative proposals could be reproduced with our model, and that the other proposed mechanisms would not contribute significantly to the control of σF release under physiological conditions (i.e., for physiologically realistic parameter values). Thus neither the proposed temporal imbalance in gene expression  nor AB degradation [41, 42] is relevant on the time scale on which σF becomes active [46, 47]. Equally the same response is attained for the entire range of physiological ATP concentrations. A lower starvation-induced ATP concentration, therefore, does not play a role in σF activation . Once we had shown that the regulatory interactions in Figures 1(b) and 1(c) were sufficient to explain septation-dependent σF activation, the model could be used to explain how this extraordinary high sensitivity to changes in the phosphatase concentration could be achieved. We realised that a combination of allosteric effects and enzyme saturation enables this high sensitivity with a small 3-component network.
(Molecular) biology has been incredibly successful in uncovering the regulatory principles and foundations of life while remaining largely a descriptive science. The key cellular machineries as well as the principles of cellular regulation have been revealed. Entire genomes have been sequenced, and the proteomes of important model organisms are currently being determined and quantified. Many interaction partners have been characterized [75, 76], and this has led to detailed wiring diagrams that describe the regulatory interactions in many important signalling pathways. The generation of large amount of data has necessitated the development of powerful bioinformatic tools to organize, analyse, store, and disseminate the available information and computational approaches are well established in these biological disciplines. In spite of huge amounts of data and powerful computational algorithms, it has remained difficult to predict biological functionalities and dependencies from the available data.