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WSEAS TRANSACTIONS on
BIOLOGY and BIOMEDICINE

Issue 11, Volume 4, November 2007
Print ISSN: 1109-9518
E-ISSN: 2224-2902

Title of the Paper: A functional representation of the simulation data of biochemical models based on molecular activity

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Authors: Simon Hardy, Pierre N. Robillard

Abstract: Interpreting the simulation data of a complex biochemical model to understand its dynamic behavior is a difficult task. Traditional data representations display simulation outputs as concentration plots. To study the dynamic behavior of a model from these plots, it is necessary to have in mind the topology of the modeled system, know the function of the individual elements of the system and be able to describe their activity. Only with this mental image of the model can the dynamic behavior be deciphered. In this paper, we suggest exploiting this knowledge to create a preprocessing filter for the simulation data. This data filter is based on the concept of molecular activity and transforms the simulation data from a concentration perspective to a molecular activity perspective. This is done in two steps: identify the functional groups of the system, and mathematically describe the molecular activity of these groups. In this paper, we demonstrate this new data representation approach with a complex model of the signal transduction system of long-term potentiation in the hippocampal post-synapse, a model exhibiting a bistable behavior. To facilitate viewing of the resulting data matrix, the preprocessed data are displayed with known visualization techniques, followed by the production of an animated and a spectral functional representation. One advantage of the functional data filter is that, once created, it can be applied to a large number of simulation runs while at the same time performing parametric and structural modifications on the model in order to quickly explore the impacts on the model’s behavior.

Keywords: biochemical modeling, simulation data, system dynamics, function, visualization

Title of the Paper: The Relationships Between the Diameter Growth and Distribution Laws

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Authors: Petras Rupsys

Abstract: The processes of growth play an important role in different fields of science, such as biology, medicine, forestry, ecology, economics. Usually, in applied sciences the averaged trend kinetics is represented by means of logistic laws (Verhulst, Gompertz, Mitscherlich, von Bertalanffy, Richards etc.). We used a generalized stochastic logistic model for predicting the tree diameter distribution of forestry stands. The purpose of this paper was to develop a diameter probability density function for even-aged and uneven-aged stands using the stochastic logistic law of diameter’s growth. The parameters of stochastic logistic growth law were estimated by the maximum likelihood procedure using a large dataset on permanent sample plots provided by Lithuanian National Forest Inventory. Subsequently, we numerically simulated the probability density function of diameter distribution for the Verhulst, Gompertz, Mitscherlich, von Bertalanffy, Richards stochastic growth laws. The exact solution (transition probability density function of diameter size) of the Fokker-Planck equation (the partial differential equation for evolving distribution of diameter size) was derived exclusively for the Gompertz stochastic growth law. The comparison of the goodness of fit among probability density functions was made by the normal probability plot and the p-value of the Kolmogorov-Smirnov and Cramer - von Mises tests. To model the diameter distribution, as an illustrative experience, is used a real data set from repeated measurements on permanent sample plots of pine stands in Dubrava district. The results are implemented in the symbolic computational language MAPLE.

Keywords: Diameter distribution, Stochastic differential equation, Density function, Fokker-Plank equation, Numerical solution.