By Carolin Loos
Carolin bathrooms introduces novel techniques for the research of single-cell facts. either ways can be utilized to review mobile heterogeneity and for this reason strengthen a holistic figuring out of organic strategies. the 1st technique, ODE limited blend modeling, allows the id of subpopulation constructions and resources of variability in single-cell image info. the second one process estimates parameters of single-cell time-lapse facts utilizing approximate Bayesian computation and is ready to take advantage of the temporal cross-correlation of the information in addition to lineage information.
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Extra info for Analysis of Single-Cell Data. ODE Constrained Mixture Modeling and Approximate Bayesian Computation
6). 4 Simultaneous Analysis of Multivariate Measurements ⎛ σ 2,1 ⎜ 43 ⎞ 0 Γ=⎜ ⎝ 0 .. 0 0 0 . ⎟ 0 ⎟ ⎠. σ 2,d Other considerations, such as correlated behavior of the measurement noise for the different measurements, can also be included. Mixture of Multivariate Log-Normal Distributions For the log-normal distribution we use two diﬀerent parametrizations. If the mean obtained by the MEs describes the mean of the log-normal distribution, we use 1 my,i = eμi + 2 Σii , 1 Cy,ij = eμi +μj + 2 (Σii +Σjj ) (eΣij − 1) , for i, j = 1, .
A model that assumes a diﬀerent weighting under the conditions, which was motivated by the fact that the number of cells diﬀers signiﬁcantly under the two conditions, has been rejected based on the pooled data. Repeating model selection for the single replicates, the model, which assumes a higher phosphorylation of Erk in both subpopulations under condition 2, can not be rejected for any replicate neither by AIC nor by BIC. In the future, we will further analyze dose-response data to validate the results of the model selection.
The moments can be linked to the mixture parameters with function h. We also neglect the indices e and s in the following. g. 4) can be considererd separately. In this thesis, we consider second order moments. 3 Modeling Variability within a Subpopulation ⎛ x=⎝ ⎞ m ⎠, C m = (m1 , . . , mL ) , (C)ij = Cij , i, j = 1, . . , L . If we assume to have at most quadratic propensities ar (m) for the M reactions and if we neglect higher order moments, the MEs are (Engblom, 2006) dmi = dt dCij = dt M νir ar (m) + r=1 M νir r=1 l 1 2 l1 ,l2 ∂ 2 ar (m) Cl l ∂xl1 ∂xl2 1 2 ∂ar (m) Cjl + νjr ∂xl νir νjr 1 ar (m) + 2 l , ∂ar (m) Cil + ∂xl l1 ,l2 ∂ 2 ar (m) Cl l ∂xl1 ∂xl2 1 2 , with νij being the entries of the stochiometric matrix.
Analysis of Single-Cell Data. ODE Constrained Mixture Modeling and Approximate Bayesian Computation by Carolin Loos