By Carolin Loos
Carolin bathrooms introduces novel techniques for the research of single-cell info. either ways can be utilized to review mobile heterogeneity and as a result strengthen a holistic figuring out of organic approaches. the 1st technique, ODE limited mix modeling, permits the id of subpopulation buildings and resources of variability in single-cell image information. the second one process 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 information.
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Extra resources for Analysis of Single-Cell Data. ODE Constrained Mixture Modeling and Approximate Bayesian Computation
Not only the mixture distribution can be exchanged. g. the linear noise approximation (Kampen, 2007, Chapter X). 4 can be incorporated into ODE-MMs. So far, the number of subpopulations needs to be predeﬁned and can be chosen by performing model selection for diﬀerent numbers of mixture components .
In the following we neglect the indices k for the time point, and j for the single-cells. The likelihood describes the probability of observing the measurement y¯e ∈ R as weighted sum of mixture probabilities p(¯ y |ϕes ) with parameters ϕes for subpopulation s in experiment e. Each of the ns subpopulations has a weight denoted by wse corresponding to its size. g. 1). The cells are stimulated with an experiment speciﬁc external stimulus denoted by ue . The time evolution of the moments xes of the system are described by a function f .
2014b). Nevertheless, modeling subpopulation dynamics by RREs gives no mechanistic description of the cell-to-cell variability within a subpopulation. A possibility to exploit higher order moments of the subpopulations is to describe the dynamics of a subpopulation by moment equations (MEs) (Engblom, 2006). 2. 1 a likelihood function for ODE-MMs with MEs to study univariate measurements y ∈ R. Additionally, we describe how the MEs can be linked to a normal and log-normal mixture distribution.