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Stochastic modelling and simulations play a major role in Systems Biology because, at molecular level, biological systems exhibit noise coming both from within the cell (intrinsic) and from the environment (extrinsic). Stochastic modelling takes into account the effects of noise over the system dynamics, that can strongly affect the behavior of the system in conditions of relatively low amounts of molecular species. Stochastic simulations provide an effective way to describe the system dynamics, and can be applied on systems where specified chemical species are processed by a set of biochemical reactions, each one characterized by a stochastic constant. In the context of stochastic modelling, Parameter Sweep Applications (PSAs) can be a useful way to explore the huge spaces generated by the combinations of variables and parameters values in order to test their effects on systems dynamics. PSAs are common in the scientific community and are structured as sets of instances, each one characterized by a distinct parametrisation. A PSA that aims to sample such large spaces must involve a large number of instances and hence the problem becomes very time consuming. However, the independence of each instance of a particular PSA makes the distributed computing paradigm a very useful solution for large scale PSAs. In this work we present a grid based version of a multi-volume stochastic simulator, tau-DPP, implemented on the EGEE project platform. The aim of the proposed work is to exploit this platform for testing the reliability of PSAs over the grid, pointing out critical factors, bottlenecks and scalability by providing data about our experience in this kind of biological modelling and simulations. As a case study, we present a number of PSAs for a stochastic model of bacterial chemotaxis composed of 59 reactions and 31 chemical species.