Modelling Cell Cycle using Different Levels of Representation

Understanding the behaviour of biological systems requires a complex setting of in vitro and in vivo experiments, which attracts high costs in terms of time and resources. The use of mathematical models allows researchers to perform computerised simulations of biological systems, which are called in silico experiments, to attain important insights and predictions about the system behaviour with a considerably lower cost. Computer visualisation is an important part of this approach, since it provides a realistic representation of the system behaviour. We define a formal methodology to model biological systems using different levels of representation: a purely formal representation, which we call molecular level, models the biochemical dynamics of the system; visualisation-oriented representations, which we call visual levels, provide views of the biological system at a higher level of organisation and are equipped with the necessary spatial information to generate the appropriate visualisation. We choose Spatial CLS, a formal language belonging to the class of Calculi of Looping Sequences, as the formalism for modelling all representation levels. We illustrate our approach using the budding yeast cell cycle as a case study

Efficient Stochastic Simulation of Biological Systems with Multiple Variable Volumes

The application of concurrent calculi to the formalisation of biological systems constitutes a promising approach to the analysis in silico of biological phenomena. The Gillespie algorithm is one of the main models exploited for their stochastic simulation. While the original algorithm considers only one fixed-volume compartment, the simulation of biological systems often requires multi-compartment semantics. In this paper we present an enhanced formulation of an extended version of the algorithm which handles multiple compartments with varying volumes. The presented algorithm is used as basis for the implementation of an extension of the stochastic π-Calculus, called Sπ@, which allows an intuitive and concise formalisation of such systems. The algorithm is also efficient in presence of a high number of compartments and reactions, therefore Sπ @ represents the starting point for the development of an effective tool for the simulation of biological systems with dynamical structure even in presence of computationally expensive phenomena like diffusion.

Dynamics of Genetic Circuits with Molecule Partitioning Errors in Cell Division and RNA-RNA Interactions

Many signaling and regulatory molecules within cells exist in very few copies per cell. Any process affecting even limited numbers of these molecules therefore has the potential to affect the dynamics of the biochemical networks of which they are a part. This sensitivity to small copy-number changes is what allows stochasticity in gene expression to introduce a degree of randomness in what cells do. While this randomness can be suppressed, it does not appear to be so in many biological systems, at least not to the maximum degree possible. This suggests that this randomness is not necessarily detrimental to cell populations, as it can produce qualitatively new behaviours in genetic networks which may be utilized by cells.In this thesis, two other mechanisms are investigated which, through their interaction with low copy-number molecules, are able to produce qualitatively different dynamics in genetic networks: the stochastic partitioning of molecules in cell division, and the direct interaction of two low copy-number molecules. For this, a novel simulator of chemical kinetics is first presented, designed to simulate the dynamics of genetic circuits inside growing populations of cells. It is then used to study a genetic switch where one repressive link is formed by direct interaction between RNA molecules. This arrangement was found to decouple the stability of the two noisy attractors of the network and the speeds of the state transitions. In other words, it allows the network to have two equally-stable noisy attractors, but differing state transition speeds.Next, the cell-to-cell diversity in RNA numbers (as quantified by the normalized variance) of a single gene over time in a growing model cell population was studied as a function of the division synchrony. In the model, synchronous cell divisions introduce transient increases in the cell-to-cell diversity in RNA numbers of the population, a prediction which was verified using single-molecule measurements of RNA numbers. Finally, the effects of the stochastic partitioning of regulatory molecules in cell division on the dynamics of two genetic circuits, a switch and a clock, were studied. Of these two circuits, the switch has the most dramatic changes in its dynamics, brought on by the inevitable negative correlation in molecule numbers that sister cells inherit. This negative correlation can allow a cell population to partition the phenotypes of the individual cells with less variance than a binomial distribution.These results advance our understanding of the different behaviours that can be produced in genetic circuits due to these two mechanisms. Since they produce unique behaviours, these mechanisms, and combinations thereof, are expected to be used for specialized purposes in natural genetic circuits. Further, since the downstream effects of these mechanisms may be more predictable than, e.g., modifying promoter sequences, they may also be useful in the design and implementation of future synthetic genetic circuits with specific behaviours.<br/

Effects of Intracellular and Partitioning Asymmetries in Escherichia coli

Cell divisions in Escherichia coli are, in general, morphologically symmetric. However, in a few cases, significant asymmetries between sister cells exist. These asymmetries between sister cells result in functional differences between them. For example, cells inheriting the older pole, over generations, accumulate more unwanted protein aggregates than their sister and, consequently, have a reduced growth rate. The reduced ability of these cells to reproduce shows that even these unicellular organisms are susceptible to the effects of aging. To understand senescence in these organisms, it is critical to investigate the sources as well as the functional consequences of asymmetries in division.In this thesis, we characterize mechanisms responsible for functional and morphological asymmetries in division in E. coli cells, using live, single-cell, single-molecule imaging techniques and detailed stochastic models. First, to understand the functional asymmetries due to the heterogeneous spatial distribution of large, inert protein complexes, we study the kinetics of segregation and retention of such complexes by observing these events, one event at a time. For that, we track individual MS2-GFP tagged RNA complexes, as they move in the cell cytoplasm, and characterize the mechanisms responsible for their long-term spatial distribution and resulting partitioning. Next, to understand the morphological asymmetries, we study the difference in cell sizes between sister cells at division under different environmental conditions. Finally, we present the models and simulators developed to characterize and mimic these processes, as well as to explore their functional consequences.Our results suggest that functional and morphological asymmetries in division, in the growth conditions studied, appear to be mostly driven by the nucleoid. In particular, we find that the fluorescent complexes are retained at the poles due to nucleoid occlusion. Further, the positioning of the point of division is also regulated by the degree of proximity between the two replicated nucleoids in the cell at the moment preceding division. Finally, based on simulation results of the models in extreme conditions, we suggest that asymmetries in these processes in division can enhance the mean vitality of E. coli cell populations. Overall, the results suggest that nucleoid occlusion contributes, in different ways, to heterogeneities in E. coli cells that ultimately generate phenotypic differences between sister cells