An inverse transformation algorithm to infer parameter distributions from population snapshot data

Abstract

Population snapshot data can be used to study heterogeneity in cell populations. Various approaches to integrating such data into computational models have been published, which enable new treatment strategies for cancer therapy, by exploiting the intra-tumor heterogeneity. A precision medicine approach for the cure of cancer could benefit from the combination of single-cell data and respective analytical methods. Here, we introduce the inverse transformation algorithm, which transforms population snapshot data to parameter distributions that are consistent with the underlying data given a dynamic model with distributed parameters. Therefore, it enables the assessment of the heterogeneity in and behavior of the whole underlying cell population. In contrast to the frequently used Approximate Bayesian Computation methods for population matching, our algorithm is a non-parametric likelihood-free approach. It directly computes a density function value for a single parameter based on density transformation methods. If the model can be described as a one-to-one map that invertibly maps parameters to measurable outputs, the inverse transformation algorithm asymptotically returns the true underlying parameter distribution.The inverse transformation algorithm is applied to snapshot data simulated via standard differential equation models for biochemical reaction networks. In particular, we evaluate our algorithm on two small test-bed models and discuss advantages and limitations in comparison to other existing approaches.