Analysis of Single-Cell Data : ODE Constrained Mixture by Carolin Loos

By Carolin Loos

Carolin bathrooms introduces novel techniques for the research of single-cell info. either methods can be utilized to check mobile heterogeneity and hence boost a holistic figuring out of organic techniques. the 1st procedure, ODE limited mix modeling, permits the id of subpopulation constructions and resources of variability in single-cell photograph 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 details.

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10: Scatterplot and marginals of measurands A and B with (A) positive correlation and (B) negative correlation. The measurements are given in arbitrary units. 4 Simultaneous Analysis of Multivariate Measurements For a simpler notation, we further neglect the indices e, k and j, corresponding to the experiment, time point and single-cell, respectively. 5) gives the probability to observe a multivariate vector ¯ ∈ Rd . The ns subpopulations with parameters ψ s and weights ws are simulated with an y external stimulus u.

2 pErk rk pErrk pEr pErk pEr Trk Trk F TrkA NG Trk NGF F NG NGF NGF TrkA TrkA NGF TrkA NGF NGF TrkA NGF TrkA Trk Trk F TrkA NG Trk NGF F NG TrkA subpop. 2 NGF NGF subpop. 1 NGF NGF NGF condition 1 NGF subpop. 1 NGF NGF NGF NGF pErrk pEr pErk pEr condition 2 pErk rk Erk TrkA NGF pErrk pEr pErk pEr pErrk pEr pErk pEr NGF subpop. 2 Trk Er NGF NGF pErk subpop. 2 Trk NGF N Trk Trk T kA A NG Trk A NG N FF Erk Er Er TrkA NGF TrkA NGF pErrk pEr pErk pEr Trk Trk TrkA NG F Trk NGF F NG Erk Er Er NGF NGF TrkA NGF TrkA NGF NGF NGF subpop.

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 .

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