Design of experiment, application in biology 2012 Petr Císař

Faculty of fisheries and protection of waters Points of presentation Motivation Design of experiment Introduction Main steps Advantages Application in biology Process Method Results

Faculty of fisheries and protection of waters Motivation Experiment is one of the basic method of human understanding Experiment is a scientific method used for testing of hypothesis or existing theories It is a bridge between theory and reality Why the students do not use sophisticated methods of experiment realization and analysis? How to design the experiment? How to analyze the experiment?

Faculty of fisheries and protection of waters Classical approach One factor at a time (OFAT) Usually we change only factor – rest is fixed First we change X1 to get optimum and then we fix it and change X2 Real optimum Response surface Optimum found by OFAT method OFAT advantages: Simple OFAT disadvantages: Optimum need not to be found We do not know the relationship between factors and system response Impossible to understand to the mutual influence between factors Number of experiments? The OFAT experiment has to be repeated for each type of system response We do not know the system

Faculty of fisheries and protection of waters Motivation Is it possible to do it better? Measure everything under all conditions. NO Create optimal design of experiment and use statistics to understand to it Design of experiment (DOE).

Faculty of fisheries and protection of waters Design of experiment DOE – Design Of Experiment Set of tools for: Creation of experimental design Experiment realization Experiment analysis with optimal number of experiments Part of Six Sigma methodologies Industry standard for process improvement Used in industry since 1986 Planed experiment: active change of the process – controlled change of system factors Outputs: Minimal number of measurements List of important factors The level of influence of controlled and uncontrolled factors to the system response Interactions between factors Mathematical model of the system

Faculty of fisheries and protection of waters DOE - Main steps Identify variables of the system Identify factors Select design Define the levels of factors Randomize the order of measurements Realize measurements and record the results Analyze data Evaluate the results Verify results Experiment design Experiment analysis

Faculty of fisheries and protection of waters DOE - features Repetition – determine variance caused by noise Randomization – Avoid systematic influence of variables Block ordering – the same conditions inside the blocks (operator) Balanced design - explore the state space Central sample – determine response curvature factor Responce The influence of the factor

Faculty of fisheries and protection of waters DOE Problem definition: Aim determination Factors and their levels DOE response: Determination of the most important factors Determination of main factors influence and interactions, low number of factors Optimization of factors Optimization of high number of factors Experts discussion Impossible by DOE First screening Advanced screening Optimization DOE

Faculty of fisheries and protection of waters DOE – Statistical method The math behind DOE is relatively simple The students can learn the math by examples Tools: ANOVA – Analysis Of Variance – explore the sources of variance in the system – influence of the factors Regression model – determine mathematical description of the system Optimization methods - optimization using the mathematical model of system Everything can be show as pretty pictures We have to understand what is behind !!!

Faculty of fisheries and protection of waters DOE – Pretty pictures Experimental design table Experimental space Set of tools for:

Faculty of fisheries and protection of waters DOE – Pretty pictures Main factors plot Interaction plot

Faculty of fisheries and protection of waters DOE – ANOVA table

Faculty of fisheries and protection of waters Application in biology Biological experiments: Typical task: optimization of cultivation conditions High level of noise Impossible to know all influencing factors High number of factors Difficult to set experimental conditions to defined values Outliers – unpredictable results Time consuming experiments Repeatability of experiment by other experts

Faculty of fisheries and protection of waters Maximization of protein amount Aim to optimize production of fusion protein to obtain the highest amount of protein optimized protein: fusion protein (FP) - maltose binding protein (MBP) and parathyroid hormone (1-34) (PTH) Procedure 1.choose variable parameters and methods for measurement 2.create procedure for analysis of amount of fusion protein 3.use DOE for planning and analysis of experiments 4.locate optimum cultivation conditions 5.verify optimum by additionally experiments Authors: Martina Tesařová, Petr Císař, Zuzana Antošová, Oksana Degtjarik, Jost Ludwig and Dalibor Štys

Faculty of fisheries and protection of waters Process Growth of bacteria under cultivation conditions Extraction of the amount of the protein – expensive Factors and methods – based on expert knowledge Four factors : temperature25; 37; 42 °C starting OD0.1; 0.2 RPM of shaker150; 200 time of harvest1; 3; 6; 12; 24; 48 h Maximization of protein amount

Faculty of fisheries and protection of waters Extraction of the amount of protein Expensive and time consuming Estimation of the amount of protein Based on staining - electrophoresis gel Calibration based on extraction of protein and size of blob Blobs marked by manual annotation -> estimation of the amount of protein Problem of comparison of blobs between gels – usage of marker Maximization of protein amount

Faculty of fisheries and protection of waters DOE 1.Fractional factorial design – 3 repetitions Key factors – temperature, time of harvest Maximization of protein amount

Faculty of fisheries and protection of waters Maximization of protein amount DOE 1.Response surface Localized optimum - temperature: 36.6 °C, start OD: 0.1, RPM of shaker:150, time of harvest: 7.5 h

Faculty of fisheries and protection of waters Conclusion DOE Optimization of amount of protein Results 93% of the data are covered by the model – biological system Two key factors found: temperature and time of harvest Level of significance – 5% Localized optimum - temperature: 36.6 °C, start OD: 0.1, RPM of shaker:150, time of harvest: 7.5 h Optimum verified by 18 testing experiments DOE was successfully used for the optimization of biological experiment