Background: Given the complex mechanisms underlying biochemical processes systems biology researchers tend to build ever increasing computational models. However, dealing with complex systems entails a variety of problems, e.g. difficult intuitive understanding, variety of time scales or non-identifiable parameters. Therefore, methods are needed that, at least semi-automatically, help to elucidate how the complexity of a model can be reduced such that important behavior is maintained and the predictive capacity of the model is increased. The results should be easily accessible and interpretable. In the best case such methods may also provide insight into fundamental biochemical mechanisms. Results: We have developed a strategy based on the Computational Singular Perturbation (CSP) method which can be used to perform a "biochemically-driven" model reduction of even large and complex kinetic ODE systems. We provide an implementation of the original CSP algorithm in COPASI (a COmplex PAthway SImulator) and applied the strategy to two example models of different degree of complexity - a simple one-enzyme system and a full-scale model of yeast glycolysis. Conclusion: The results show the usefulness of the method for model simplification purposes as well as for analyzing fundamental biochemical mechanisms. COPASI is freely available at http://www.copasi.org.
Background: In order to replicate within their cellular host, many viruses have developed self-assembly strategies for their capsids which are sufficiently robust as to be reconstituted in vitro. Mathematical models for virus self-assembly usually assume that the bonds leading to cluster formation have constant reactivity over the time course of assembly (direct assembly). In some cases, however, binding sites between the capsomers have been reported to be activated during the self-assembly process (hierarchical assembly). Results: In order to study possible advantages of such hierarchical schemes for icosahedral virus capsid assembly, we use Brownian dynamics simulations of a patchy particle model that allows us to switch binding sites on and off during assembly. For T1 viruses, we implement a hierarchical assembly scheme where inter-capsomer bonds become active only if a complete pentamer has been assembled. We find direct assembly to be favorable for reversible bonds allowing for repeated structural reorganizations, while hierarchical assembly is favorable for strong bonds with small dissociation rate, as this situation is less prone to kinetic trapping. However, at the same time it is more vulnerable to monomer starvation during the final phase. Increasing the number of initial monomers does have only a weak effect on these general features. The differences between the two assembly schemes become more pronounced for more complex virus geometries, as shown here for T3 viruses, which assemble through homogeneous pentamers and heterogeneous hexamers in the hierarchical scheme. In order to complement the simulations for this more complicated case, we introduce a master equation approach that agrees well with the simulation results. Conclusions: Our analysis shows for which molecular parameters hierarchical assembly schemes can outperform direct ones and suggests that viruses with high bond stability might prefer hierarchical assembly schemes. These insights increase our physical understanding of an essential biological process, with many interesting potential applications in medicine and materials science.
We utilized the framework of mathematical modeling to gain insights into two distinct biological systems, the JAK/STAT1 signal transduction pathway and the regulation of cell cycle decisions in neuroblastoma.!! The family of JAK/STAT signaling pathways plays a key role in immunity. In several tumors dysregulation of the JAK/STAT pathways is observed. To investigate the functionality of this signal transduction pathway and eventually understand basic building principles, we establish a databased mathematical model of the JAK/STAT1 pathway by means of kinetic rate equations. We showed that pathway activation is coupled tightly to the receptor stimulus at the cost of signal strength. The nuclear signal is sustained by a combination of fast translocation rates and short nuclear residence times of activated STAT1 protein molecules. Model simulations reveal that STAT1 dimerization kinetics have a strong impact on both efficiency of signaling and response kinetics, implying that protein-protein interactions are evolutionary constrained to ensure network functionality. Measurements of STAT1 transport mutants validated the mathematical model and showed that STAT1 activation is robust against enhanced nuclear export. By the kinetic design of the pathway input noise is suppressed, the pathway can be efficiently activated and rapid relaxation after stimulus withdrawal is ensured.!! Neuroblastoma is the most common extracranial solid tumor of infants and children. Its course of illness varies between spontaneous regression and malignant, aggressive progression. Amplification of the MYCN oncogene is predictive for poor clinical outcome in neuroblastoma. MYCN-amplified cells proliferate strongly and exhibit impaired cell cycle arrest. To rationalize the impact of MYCN on the regulatory networks, governing cell cycle progression and DNA damage response, we established mathematical models of the regulatory modules, p53-MDM2 and E2F1-pRB, by means of mass action kinetics. The inherent regulation in the p53-MDM2 module leads to an universal form of the p53- MDM2 steady state and can account for several qualitatively different behaviors upon p53 activation. We show that it is plausible that the weak G1 arrest in the MYCN- overexpressing cells is due to a MYCN-induced protein level imbalance in the p53- MDM2 module. Furthermore we argue that the bifurcation diagram of the G1-S transition model can both theoretically as well as experimentally be used as an output to analyze the restriction point behavior in neuroblastoma. It shows that for cells with relatively high MYCN level and an enhanced CDK4 signal the bistable region is shifted to low stimuli and the model stays in an activated state even under DNA damage. A mathematical framework is provided, which potentially can serve as a future standard method to extract underlying cell cycle parameters from combined FACS-measured cell cycle phase distributions and cell growth rate measurements. Analysis of measurements in the SH-EP neuroblastoma cell line showed that conditionally upregulated MYCN mainly changes the length of the G1 phase.
Parameter estimation is central for the analysis of models in Systems Biology. Stochastic models are of increasing importance. However, parameter estimation for stochastic models is still in the early phase of development and there is need for efficient methods to estimate model parameters from time course data which is intrinsically stochastic, only partially observed and has measurement noise. The thesis investigates methods for parameter estimation for stochastic models presenting one efficient method based on integration of ordinary differential equations (ODE) which allows parameter estimation even for models which have qualitatively different behavior in stochastic modeling compared to modeling with ODEs. Further methods proposed in the thesis are based on stochastic simulations. One of the methods uses the stochastic simulations for an estimation of the transition probabilities in the likelihood function. This method is suggested as an addition to the ODE-based method and should be used in systems with few reactions and small state spaces. The resulting stochastic optimization problem can be solved with a Particle Swarm algorithm. To this goal a stopping criterion suited to the stochasticity is proposed. Another approach is a transformation to a deterministic optimization problem. Therefore the polynomial chaos expansion is extended to stochastic functions in this thesis and then used for the transformation. The ODE-based method is motivated from a fast and efficient method for parameter estimation for systems of ODEs. A multiple shooting procedure is used in which the continuity constraints are omitted to allow for stochasticity. Unobserved states are treated by enlarging the optimization vector or using resulting values from the forward integration. To see how well the method covers the stochastic dynamics some test functions will be suggested. It is demonstrated that the method works well even in systems which have qualitatively different behavior in stochastic modeling than in modeling with ODEs. From a computational point of view, this method allows to tackle systems as large as those tackled in deterministic modeling.
MicroRNAs (miRNAs) are a large family of small noncoding RNAs that extensively regulate gene expression in animals, plants and protozoa. The first miRNA was identified in the early 1990s, but it took almost a decade until miRNAs were recognized as key post-transcriptional regulators of gene expression. Despite the rapidly growing list of miRNA-regulated physiological and pathological processes, intracellular membrane trafficking has attracted little interest from scientific miRNA community. Membrane trafficking defines a complex network of pathways, including biosynthetic trafficking and endocytosis that are indispensable for normal cellular functions. Previous studies have analyzed a few miRNAs involved in insulin secretion, however, no systematic investigation of miRNAs as important regulators of membrane trafficking has been performed. The overall aim of this study was to identify miRNAs and their biologically relevant target genes involved in the regulation of membrane trafficking. As tools to modulate miRNA functions, we used synthetic miRNA mimics (pre-miRs) and inhibitors (anti-miRs) to enhance (gain-of-function) and to suppress (loss-of-function) the activity of cellular miRNAs, respectively. As proof of principle, we demonstrated that increased activity of miR-17 family miRNAs accelerates the biosynthetic cargo protein (ts-O45-G) transport and reduces the cellular internalization of DiI-LDL ligand. Taking the advantage of available technological platforms, we designed a gain-of-function large-scale screening to identify miRNAs that affect biosynthetic ts-O45-G transport rate. We showed that 44 out of 470 tested miRNAs induced significant changes in cargo trafficking. Using image analysis platform, we further identified eight miRNAs (miR-30b, -382, -432, -517a, -517b, -517c, -637 and -765) that also showed significant effects on Golgi complex integrity. Importantly, the majority of identified miRNAs are not endogenously expressed in HeLa cells, indicating the need for validation studies in other experimental systems. To identify functionally relevant target genes, we selected miR-17 and miR-517a and performed genome-wide transcriptome analysis 12h, 24h and 48h after transfection with the respective pre-miRs. We identified TBC1D2 and LDLR genes as novel functional miR-17 targets and confirmed that they exert the miR-17-mediated regulation of endocytosis. Further studies are needed to identify target genes responsible for the miR-17-governed acceleration of ts-O45-G to the plasma membrane. In case of miR-517a, we found a set of target genes with functions in 12 membrane trafficking system, however, their functional interplay with miR-517a remains to be confirmed. Bioinformatics analysis of transcriptome profiling data confirmed that the presence of miRNA seed binding site in the 3´UTRs of human mRNAs is an important determinant for functional miRNA:mRNA interaction. Additionally, we demonstrated that the sets of transcripts downregulated at early time points after transfection with pre-miRs have substantially higher fractions of transcripts with miRNA binding sites in their 3´UTRs compared to the transcripts downregulated at late time points. We believe that these findings could contribute to the development of more accurate miRNA target prediction tool, also allowing identification of nonconserved miRNA targets. In conclusion, we have established an experimental platform that consists of (i) a functional screening module to identify miRNAs that affect membrane trafficking, (ii) a microarray module to identify miRNA target genes, (iii) a statistics and bioinformatics module for data analysis and integration and (iv) a target validation module to validate functional links between targets and miRNAs. Using this platform, we identified numerous miRNAs with novel functions in membrane trafficking system. Moreover, we identified and confirmed TBC1D2 and LDLR genes as novel functional targets of miR-17.