Abstract
Biological systems are inherently complex systems, consisting of a large number of biological entities that interact and cooperate in an orchestrated fashion in order to produce robust and adaptive behaviors. At the same time, biological systems are characterized by a high degree of randomness and uncertainty, as these interactions occur in a probabilistic manner. System-level analysis of biological processes requires advanced experimental methods and sophisticated computational models, so as to fully describe the nature of biological phenomena. In this context, stochastic hybrid systems, that can efficiently describe complex processes that include continuous evolution and switch-like activation of their parts in a probabilistic manner, have already found important applications in systems biology modeling and set the basis for further investigation. This thesis concerns the applications of stochastic hybrid systems in the modeling of biological processes. Focus is given in two major ap ...
Biological systems are inherently complex systems, consisting of a large number of biological entities that interact and cooperate in an orchestrated fashion in order to produce robust and adaptive behaviors. At the same time, biological systems are characterized by a high degree of randomness and uncertainty, as these interactions occur in a probabilistic manner. System-level analysis of biological processes requires advanced experimental methods and sophisticated computational models, so as to fully describe the nature of biological phenomena. In this context, stochastic hybrid systems, that can efficiently describe complex processes that include continuous evolution and switch-like activation of their parts in a probabilistic manner, have already found important applications in systems biology modeling and set the basis for further investigation. This thesis concerns the applications of stochastic hybrid systems in the modeling of biological processes. Focus is given in two major applications: analysis of protein kinetics using Fluorescence Recovery After Photobleaching (FRAP) experiments and analysis of DNA re-replication.In the first part of the thesis, a complete workflow for the analysis of FRAP experimental data is proposed. We initially emphasized on the first steps of the analysis and developed the software easyFRAP, that enables the extraction of quantitative parameters from experimental FRAP recovery curves. We then present a stochastic hybrid model of FRAP experiments, based on a stochastic description of protein diffusion and binding at a particle level within a defined geometry representing the cell nucleus. Last, to infer kinetic parameters from FRAP experimental data, a novel parameter identification method was designed and implemented. The key idea behind the proposed method is the a priori construction of a mapping from the space of parameters associated with the recovery curves to the space of parameters of the underlying molecule kinetics. In this way, the method circumvents the repeated simulation of the model in the search of new estimates and provides interpolation within the range of parameters of the simulated curves. After validating the method in silico, parameter inference using experimental data on the proteins Cdt1-GFP, PCNA-GFP and GFPnls confirmed existing knowledge on the kinetic behavior of the proteins and provided additional insight on the cell-to-cell variability and identifiability of kinetic parameters.In the second part of the thesis, stochastic hybrid modeling is applied to the case of DNA re-replication, developed by refining existing work on normal DNA replication. The model accurately portrays the interplay between discrete dynamics, associated with different origin states, continuous dynamics, associated with the movement of the replication forks, and stochasticity, associated with random firing and re-firing events. Using input data from experimentally determined origin locations and efficiencies for the case of the fission yeast genome, the model allows the simulation of re-replication along the complete genome and thus the exploration of re-replication kinetics genome-wide. Comparison of in silico data for different model variations and sensitivity analysis on the model inputs has permitted insight into the parameters affecting re-replication dynamics. By comparing the simulated vs. the experimental amplification profiles at a population level, we observe that overall the simulated data reproduce the experimental re-replication pattern on a whole-genome scale, validating our approach. Striking differences regard specific regions, possibly attributed to location-specific cellular mechanisms. Analysis of simulated data at a single-cell level permits a more detailed insight into DNA re-replication. Amplification levels of individual loci were found to be affected by intrinsic properties in terms of firing efficiency, in cis effects from adjacent loci and in trans effects from distant loci. Overall, our analysis showed that, although re-replication profiles at the population level are robust, at the single-cell level they are characterized by a high degree of heterogeneity and can deviate significantly from the mean, since re-replication can, with varying probability, occur anywhere in the genome and generate many diverse genotypes within a population. Based on these observations we conclude that cell-to-cell variability is inherent in re-replication and can lead to a high degree of genome plasticity.
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