The intense research activity in hybrid systems has led to powerful methods for modeling, analysis and control of many man-made systems. The main aim of the Systems Biology group is to adapt and exploit these recent advances for the in silico modeling and analysis of biological systems.
- DNA replication control in the fission yeast cell cycle
- DNA repair
- Identification of Genetic Regulatory Networks: A Stochastic Hybrid Approach
DNA replication, the process of duplication of the cell's genetic material, is central to the life of every living cell, and is always carried out prior to cell division to ensure that the cell's genetic information is maintained. Replication takes place during a specific stage in the life cycle of a cell (the cell cycle). The cell cycle can be subdivided in four phases: G1, a growth phase in which the cell increases its mass; S (synthesis), when DNA replication takes place; G2, a second growth phase, and finally M phase (mitosis), during which the cell divides into two daughter cells.
Cell cycle events are regulated by the periodic fluctuations in the activity of protein complexes called CDKs (Cyclin Dependent Kinases). CDKs are the master regulators of the cell cycle. There are two identified thresholds in CDK activity. Threshold 1 defines entry into S phase and threshold 2 defines entry into mitosis. Complex models have already been developed for the biochemical network regulating the fluctuation of CDK activity during the cell cycle.
During S-phase, every base of the genome must be replicated once and only once, so that genetic information is preserved: daughter cells must have the same genetic information as their progenitor. Because genomes of eukaryotic cells are large in size and the speed of replication is limited, DNA replication initiates from multiple points along the genome, called origins of replication. Following initiation from a given origin, replication continues bidirectionally along the genome, giving rise to two replication forks moving in opposite directions.
Initial models, influenced by the replication of bacterial genomes, postulated that defined regions in the genome would act as origins of replication in every cell cycle. Indeed, initial work from the budding yeast (Saccharomyces cerevisiae) identified specific sequences which acted as origins of replication with high efficiency. This simple deterministic model of origin selection however is reappraised following more recent findings which show that, especially in higher eukaryotes, a large number of potential origins exist, and active origins are stochastically selected during each S phase.
Schizosaccharomyces pombe (S. pombe, fission yeast) is a very attractive model organism for the study of the cell cycle because it is a simple unicellular eukaryote amenable to genetic and biochemical analysis. It has conserved many genes affecting cell cycle control that are typically found in higher organisms and its origin selection appears more similar to higher eukaryotes. Furthermore, and because it is very distantly related to budding yeast, the study of fission yeast can serve as a very promising complementary model system to compare global data sets of these two widely manipulated eukaryotes. In S. pombe (as well as in mammalian cells) no specific consensus sequences have been characterized that can function as an origin. Many potential origins have been mapped, but their pattern of firing shows an astonishing heterogeneity among cells in the population. This stochastic feature appears to be totally independent of successive replication events; there is no epigenetic regulation causing an origin that has fired in a cell cycle to preferentially fire or not in the next. The firing origins are not the same for every cell so, out of the pool of all possible origins, a semi-random sample will be active in a specific replication event. [7]
Our groups has been developing stochastic hybrid models to capture the DNA replication in S. Pombe. Based on these models we have been able to draw interesting and sometimes surprising conclusions about the regulation mechanisms controling this complex process.
Nucleotide excision repair after damage is a biochemical mechanism that provides maintenance of DNA sequences in living cells. It is divided into several steps such as recognition of the lesion, excision of damaged nucleotides and replication of the missing strand. This involves the concerted action of several copies of different polypeptides that are recruited to the site under repair. Several qualitative or semi-quantitative models of the repair dynamics are being considered in the biology research community and are empirically tested based on macroscopic experimental data. However, the improvement of experimental techniques and the tremendous computational speed-up of modern computers are laying the basis for simulation and verification of quantitative models of the microscopical particle dynamics involved in this process.
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Among the aspects of excision repair that are not yet well understood are diffusion of protein complexes and the dynamics of protein binding to DNA sites or to other proteins and intracellular structures. The currently dominating approach is to express the evolution of macroscopical observables of the system (e.g. spatially averaged protein concentrations) directly in terms of paramaters such as overall diffusion coefficients and average binding times. The quality of a model is then evaluated based on the comparison of model predictions with typical experimental curves. In particular, tagging repair agents with the Green-Fluoresce Protein (GPF) and measurement of the speed of diffusion-induced recovery after photobleaching (Fluorescence Recovery After Photobleaching, FRAP) are readily available techniques for generating data to support model analysis and validation.
We believe that these and other experimental methods shall contribute more to the study of DNA repair if used in conjunction with individual modeling of the repair agents. Each protein complex taking part to the process undergoes a combination of continuous dynamics - which determine random motion through the cell - and discrete dynamics - that expresses e.g. binding and unbinding. Coexistence of several such individuals gives rise to a high dimensional stochastic hybrid model which cannot be manipulated analytically. It can, however, be simulated by powerful computing systems. First results in this direction are shown in [8], where fluorescence data drawn from biological experiments on mammalian cancerous cells are compared to synthetic data simulated from a dynamical model of the cell at the particle level. Our work aims at exploiting Markov Chain Monte Carlo (MCMC) techniques to draw a detailed analysis of both microscopic and macroscopic behavior of the system. Using temporal and spatial information on the system dynamics, we plan to identify parameters such as stochastic diffusion rates and probabilities of binding of several repair agents, and to validate the model by comparison of experimental and synthetic data sets. We hope, that approach will offer deeper insight into DNA-related processes and help biologists to gain better understanding of the excision repair mechanism.
Genetic regulatory networks govern the synthesis of proteins and other essential molecules in the living cell, and are thus responsible for fundamental cell functions such as metabolism, development, and replication. Thorough understanding of genetic networks is fundamental in that it determines our ability to interact with the basic biological mechanisms and to reproduce them. This has a major impact on the design of modern medical therapies, contributes to enhancing industrial procedures for the synthesis of biochemical products, and paves the way for the implementation of artificial biological circuitry. Modeling and identification methods for such systems have been developed in the framework of deterministic nonlinear systems. However, it appears that certain systems are more naturally described by hybrid models that explicitly account for both continuous and discrete phenomena. Further, it is increasingly being recognized that stochasticity plays a fundamental role in the regulation of gene expression.
In our current research, we are exploring techniques for stochastic hybrid modeling and identification of genetic regulatory networks. One such example is a piecewise deterministic model where deterministic protein synthesis is induced by the random activation of gene expression. In turn, gene expression follows the laws of a finite state Markov chain whose transition rates depend on current protein concentration levels. This stochastic hybrid modelling framework is able to explain phenomena that are not captured by deterministic models. In the case of the bistable switch network, for instance, the coexistence of two different equilibria can be explained in terms of a multimodal stationary distribution of the system state.
Under the assumption that the topology of the network is known, we established an identification procedure that allows for a very efficient estimation of several unknown parameters of the model. Current simulation results have been promising for low order models (two-state Bistable switch), as well as for higher order problems (six-state nutrients response model for the bacterium Escherichia coli, see [9]). We intend to apply this hybrid stochastic modeling and identification technique to experimental data through our work in the YeastX project .
The more challenging problem of identifying the network of interactions among genes is being addressed within the same modelling framework.