Quantification of microtubule-guided peroxisome migration using a hidden Markov chain model

www.leibniz-hki.de References Quantification of microtubule-guided peroxisome migration using a hidden Markov chain model Carl-Magnus Svensson1, Katharina Reglinski2,3,4, Wolfgang Schliebs5, Ralf Erdmann5, Christian Eggeling2,3,4, Marc Thilo Figge1,6 1Applied Systems Biology, Leibniz Institute for Natural Product Research and Infection Biology – Hans Knöll Institute, Jena, Germany 2Leibniz-Institute of Photonic Technologies, Jena, Germany 3Institute of Applied Optics and Biophysics, Friedrich-Schiller University Jena, Jena, Germany 4MRC Human Immunology Unit, Weatherall Institute of Molecular Medicine, University of Oxford, Oxford, United Kingdom 5Institute of Biochemistry and Pathobiochemistry, Systems Biochemistry, Ruhr-University Bochum, Bochum, Germany 6Institute of Microbiology, Faculty of Biological Sciences, Friedrich-Schiller University Jena, Jena, Germany [1] Svensson et al. (2023) Quantitative analysis of peroxisome tracks using a Hidden Markov Model . Sci. Rep. 13(1), 19694 [2] Baum LE et al. (1970) A Maximization Technique Occurring in the Statistical Analysis of Probabilistic Functions of Markov Chains . Ann. Math. Stat. 41(1):164–171 [3] Churbanov and Winters-Hilt (2008) Implementing EM and Viterbi algorithms for Hidden Markov Model in linear memory. BMC Bioinformatics 9:224 Peroxisome role and movement Hidden Markov Model Results •Oganelles present in eukaryotic cells •Functions in the cell •Metabolism of hydrogen peroxide •Fatty acid oxidation •Removal of reactive oxygen species •Interacts with the microtubule to provide active transport •Peroxisome tracks from HEK 293 cells •Δ𝑡 = 0.1s •Three different conditions •Untreated cells, norm condition, 193 cells •Nocodazole treated cells, noc condition, 130 cells •Cells with knocked out PEX14 gene, KO PEX14 condition, 131 cells •In noc condition the microtubular structure is destroyed •PEX14 play an important role in tubulin binding •Find and quantify directed peroxisome movement [1] •Directed migration is expected to be a couple of precent of the movement [email protected] Funded by the German Federal Ministry of Education and Research within the funding program Photonics Research Germany, Project Leibniz Center for Photonics in Infection Research, Subproject LPI-BT3, contract number 13N15709 States of the the model 𝑠1:Brownian motion 𝑠2:Directed motion along microtubili Observables: 𝜄𝑡:Speed of the peroxisome at time 𝑡 𝛼𝑡:Relative turning angle between 𝑡and 𝑡 + 1 Conditional independence of observables: 𝒐𝑡= [𝜄𝑡, 𝛼𝑡] 𝑝 𝒐𝑡𝑠𝑘= 𝑝 𝜄𝑡𝑠𝑘𝑝 𝛼𝑡𝑠𝑘 •KO PEX has a lower attachment probability than normal cells •Nocodazole tracks spend more time in 𝑠2, but only for short periods •The destroyed network in the noc condition causes the apparent loss of directed motion in the noc condition (𝑥𝑡, 𝑦𝑡) (𝑥𝑡+1, 𝑦𝑡+1) (𝑥𝑡+2, 𝑦𝑡+2) (𝑥𝑡+3, 𝑦𝑡+3) 𝜄𝑡 𝜄𝑡+1 𝜄𝑡+2 𝛼𝑡 𝛼𝑡+1 𝑠1𝑠2 𝜄𝑡𝛼𝑡 𝑇𝑠1,𝑠1𝑇𝑠1,𝑠2 𝑇𝑠2,𝑠1 𝑇𝑠2,𝑠2 Brownian motion 𝑝 𝜄𝑡𝑠𝑘= 𝑙𝑜𝑔𝑛𝑜𝑟𝑚(𝜇𝑠1, 𝜎𝜄,𝑠1) 𝑝 𝛼𝑡𝑠𝑘= 𝑢𝑛𝑖𝑓𝑜𝑟𝑚(−𝜋, 𝜋) •Fits parameters using an efficient Expectation Maximization method •Can fit all or a selection of parameters 𝜃 = {𝝁𝜄, 𝝈𝜄, 𝜎𝛼,𝑠2, 𝑻, 𝝅} •Created simulated data for validation of the methods Scaled Baum-Welch (BW) algorithm [2] GT track •Find the most likely states given a set of observations •Bayesian approach: 𝑎𝑟𝑔𝑚𝑎𝑥𝑠𝑘𝑝(𝑠𝑘|𝒐𝑡) ~𝑝 𝒐𝑡𝑠𝑘𝑝 𝑠𝑘 •Prior: 𝑝 𝑠𝑘= 𝜋𝑠𝑘 Viterbi algorithm [3] (𝑥𝑁𝑡, 𝑦𝑁𝑡) [𝑠1, 𝑠1, … , 𝑠1, 𝑠2, … , 𝑠2, 𝑠2] Model fitting •Manually select 52 tracks with mixed migration modes •We set 𝜎𝛼,𝑠2= 0.45 and fit the rest of the parameters using Baum-Welch Training data Directed motion •𝑝 𝜄𝑡𝑠𝑘= 𝑙𝑜𝑔𝑛𝑜𝑟𝑚(𝜇𝑠2, 𝜎𝜄,𝑠2) •𝑝 𝛼𝑡𝑠𝑘= 𝑛𝑜𝑟𝑚𝑎𝑙(0, 𝜎𝛼,𝑠2) norm noc