According to the well-accepted paradigm, the underlying constituents of bi- ology are discrete molecules, with some being in very small copy numbers. It is therefore most precise to model the interaction of biological substances as discrete events connecting discrete states. Using this abstraction it is then natural to treat molecular interactions as being part of a computation and to perform formal analysis on them using the techniques of computer science. In this way it is possible to extract useful information about bio- logical systems in an automatic way. Membranes and membrane proteins are fundamental to the operation of biological cells, hence this thesis presents three new computational models designed to represent biological systems, based on models of membrane com- puting: Membrane Systems with Peripheral Proteins (MSPP), Membrane Systems with Peripheral and Integral Proteins (MSPIP) and Colonies of Synchronizing Agents (CSA). MSP(I)P is close to biologists’ prevailing view of the cell and hence is highly compatible with existing biochemical models. CSA is an hierarchical paradigm designed to represent complex systems such as populations of cells and tissues. This work extends the corpus of knowledge about biology and the theory of computation by prov- ing technical results related to these models. The MSPP, MSPIP and CSA models have associated software imple- mentations which allow the simulation of the temporal evolution of biologi- cal models by means of multiset rewriting under the control of a stochastic algorithm. One of these, Cyto-Sim (implementing the MSPP and MSPIP models), being most developed, is presented in detail with several examples. Stochastic simulation is inherently computationally intensive and hier- archical systems particularly so. This thesis presents a new state of the art stochastic simulation algorithm for hierarchical and agent-based systems (the Method of Partial Propensities) and uses this result to improve the state of the art of stochastic simulation algorithms for well stirred chemical systems (the Method of Arbitrary Partial Propensities). The noise evident in stochastic simulations is a potentially useful char- acteristic, containing information about the system being simulated. To extract detailed measures of stochasticity and the behaviour of a system, a new technique using Fourier analysis is presented and illustrated. With this it is possible to create a space of phenotype to characterise models and the performance of simulation algorithms.
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