Regensburg 2010 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 2: Statistical Physics of Biological Systems I (joint session of BP + DY)

DY 2.5: Vortrag

Montag, 22. März 2010, 11:30–11:45, H45

Estimating molecule numbers based on fluctuations — •Andreas Ruttor and Manfred Opper — Technische Universität Berlin

Microarray experiments and other methods used to analyze biochemical systems are often not calibrated, so that results are given in arbitrary units. In this case the actual amount of molecules involved in the reactions remains unknown. However, fluctuations visible in the data set can be used to estimate it. For that purpose we use a diffusion model based on stochastic differential equations, which describe the dynamics of the reaction system. Here, two sources of fluctuations have to be taken into account: Observation noise, caused by the measurement process, is usually independent of the state of the system. But internal noise is the result of discrete reaction events occurring at random points in time. Therefore its size is directly related to the number of molecules per arbitrary unit, which is included in the model as a parameter. By solving the backward Fokker-Planck equation of the diffusion model in the weak noise limit, it is possible to calculate the likelihood of all observations. Maximizing this quantity with respect to the parameters leads to an estimate of the molecule numbers per arbitrary unit. Additionally, the uncertainty of this calibration can be obtained by calculating the Laplace approximation of the marginal posterior distribution.