By Carolin Loos
Carolin bogs introduces novel techniques for the research of single-cell information. either ways can be utilized to check mobile heterogeneity and as a result increase a holistic realizing of organic methods. the 1st approach, ODE limited combination modeling, permits the id of subpopulation constructions and assets of variability in single-cell image facts. the second one strategy estimates parameters of single-cell time-lapse facts utilizing approximate Bayesian computation and is ready to make the most the temporal cross-correlation of the knowledge in addition to lineage info.
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Additional info for Analysis of Single-Cell Data : ODE Constrained Mixture Modeling and Approximate Bayesian Computation
2. The total number of molecules N0 is assumed to be distributed with some mean μN0 and variance σN0 across the cells. Within an individual cell, the number of molecules is constant. , 2016) dmB dt dmA dt dmN0 dt dCB,B dt dC B,A dt CB,N0 dt CA,A dt CA,N0 dt CN0 ,N0 dt = (k1 + k3 )mA − k2 mB , = k2 mB − (k1 + k3 )mA , = 0, = (k1 + k3 )mB + k2 mA + 2(k1 + k3 )CB,A − 2k2 CB,B , = −(k1 + k3 )mB − k2 mA − (k1 + k2 + k3 )CB,A + k1 CA,A + k2 CB,B , = (k1 + k3 )CA,N0 − k2 CB,N0 , = (k1 + k3 )mA + k2 mB + 2k2 CB,A − 2(k1 + k3 )CA,A , = −(k1 + k3 )CA,N0 + k2 CB,N0 , = 0.
The true model MH2 has been selected correctly by AIC and BIC for both scenarios. (C, D) Proﬁles corresponding to the optimal model for Scenario 2 (C) and Scenario 3 (D). The true values of the parameters, which have been used to generate the data, are indicated by a green line. 4 Simultaneous Analysis of Multivariate Measurements In the previous section we presented ODE-MMs with MEs, which are able to capture variability within a subpopulation. However, correlations between the measurements can still not be detected and taken into account (Problem 4).
This yields 12 models that are tested with multi-start local optimization and model selection using AIC and BIC. 3 Modeling Variability within a Subpopulation 33 We perform parameter estimation with a toolbox that is internally used by the Datadriven Computational Modeling group of the Institute of Computational Biology at the Helmholtz Zentrum M¨ unchen. 3 for ODE-MMS with MEs. Both select the same optimal model, which detects the true diﬀerences between the subpopulations. 8A. 8B. All parameters are identiﬁable and the proﬁles are almost indistinguishable.
Analysis of Single-Cell Data : ODE Constrained Mixture Modeling and Approximate Bayesian Computation by Carolin Loos