Hybrid stochastic simulations of intracellular reaction-diffusion systems.

With the observation that stochasticity is important in biological systems, chemical kinetics have begun to receive wider interest. While the use of Monte Carlo discrete event simulations most accurately capture the variability of molecular species, they become computationally costly for complex reaction-diffusion systems with large populations of molecules. On the other hand, continuous time models are computationally efficient but they fail to capture any variability in the molecular species. In this study a hybrid stochastic approach is introduced for simulating reaction-diffusion systems. We developed an adaptive partitioning strategy in which processes with high frequency are simulated with deterministic rate-based equations, and those with low frequency using the exact stochastic algorithm of Gillespie. Therefore the stochastic behavior of cellular pathways is preserved while being able to apply it to large populations of molecules. We describe our method and demonstrate its accuracy and efficiency compared with the Gillespie algorithm for two different systems. First, a model of intracellular viral kinetics with two steady states and second, a compartmental model of the postsynaptic spine head for studying the dynamics of Ca+2 and NMDA receptors.

Forecasting cost based on a stochastic utilization plan and a fixed cost function

The application of Markov processes is very useful to health-care problems. The objective of this study is to provide a structured methodology of forecasting cost based upon combining a stochastic model of utilization (Markov Chain) and deterministic cost function. The perspective of the cost in this study is the reimbursement for the services rendered. The data to be used is the OneCare database of claim records of their enrollees over a two-year period of January 1, 1996–December 31, 1997. The model combines a Markov Chain that describes the utilization pattern and its variability where the use of resources by risk groups (age, gender, and diagnosis) will be considered in the process and a cost function determined from a fixed schedule based on real costs or charges for those in the OneCare claims database. The cost function is a secondary application to the model. Goodness-of-fit will be used checked for the model against the traditional method of cost forecasting. ^