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.

Dominance of the proximal coordinate frame in determining the locations of hippocampal place cell activity during navigation.

The place-specific activity of hippocampal cells provides downstream structures with information regarding an animal's position within an environment and, perhaps, the location of goals within that environment. In rodents, recent research has suggested that distal cues primarily set the orientation of the spatial representation, whereas the boundaries of the behavioral apparatus determine the locations of place activity. The current study was designed to address possible biases in some previous research that may have minimized the likelihood of observing place activity bound to distal cues. Hippocampal single-unit activity was recorded from six freely moving rats as they were trained to perform a tone-initiated place-preference task on an open-field platform. To investigate whether place activity was bound to the room- or platform-based coordinate frame (or both), the platform was translated within the room at an "early" and at a "late" phase of task acquisition (Shift 1 and Shift 2). At both time points, CA1 and CA3 place cells demonstrated room-associated and/or platform-associated activity, or remapped in response to the platform shift. Shift 1 revealed place activity that reflected an interaction between a dominant platform-based (proximal) coordinate frame and a weaker room-based (distal) frame because many CA1 and CA3 place fields shifted to a location intermediate to the two reference frames. Shift 2 resulted in place activity that became more strongly bound to either the platform- or room-based coordinate frame, suggesting the emergence of two independent spatial frames of reference (with many more cells participating in platform-based than in room-based representations).

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. ^