Determining Physical Mechanisms of Gene Expression Regulation from Single Cell Gene Expression Data
Fig 9
Properties of two-state model and kinetic parameter estimation strategy.
Kinetic parameters control the shape of the gene expression distribution. Kinetic parameters are estimated by calculating the maximum likelihood from Eq 2. (A-B) In order to illustrate some properties of the two-state model, the likelihoods of various kinetic parameter sets were calculated for a toy example–specifically GFI1b gene expression data in hematopoietic stem cells (HSC). (A) For each possible Kon and Koff value, we calculated the maximum log likelihood across all possible Kt values. The overall log-maximum likelihood was 603.66 and only values that were within 0.5 of this value were coloured in, with the maximum value in dark red. (B) The maximum log likelihood of all possible Kon values were also calculated, as Koff and Kt were varied. There is a region in subfigure B where Koff and Kt can compensate for one another. (C) An example of parameter compensation was simulated: the original distribution (grey) has visible changes when Koff (blue) and Kt (red) are varied, but the distributions are barely distinguishable when both parameters are varied (purple). (D) Finally, we show our method’s estimates of Kon and ln(Koff/Kt) for each TF in each population of FACS cells.