A Primer on Modeling and Measurement of Signaling Outcomes Affecting Decision Making in Cells: Methods for Determining Optimal and Incorrect Outcomes in Noisy Biochemical Dynamics

Characterization of decision makings in a cell in response to received signals is of high importance for understanding how cell fate is determined. The problem becomes multi-faceted and complex when we consider cellular heterogeneity and dynamics of biochemical processes. In this paper, we present a unified set of decision-theoretic and statistical signal processing methods and metrics to model the precision of signaling decisions, given uncertainty, using single cell data. First, we introduce erroneous decisions that may result from signaling processes, and identify false alarm and miss event that are associated with such decisions. Then, we present an optimal decision strategy which minimizes the total decision error probability. The optimal decision threshold or boundary is determined using the maximum likelihood principle that chooses the hypothesis under which the data are most probable. Additionally, we demonstrate how graphing receiver operating characteristic curve conveniently reveals the trade-off between false alarm and miss probabilities associated with different cell responses. Furthermore, we extend the introduced signaling outcome modeling framework to incorporate the dynamics of biochemical processes and reactions in a cell, using multi-time point measurements and multi-dimensional outcome analysis and decision making algorithms. The introduced multivariate signaling outcome modeling framework can be used to analyze several molecular species measured at the same or different time instants. We also show how the developed binary outcome analysis and decision making approach can be extended to include more than two possible outcomes. To show how the overall set of introduced models and methods can be used in practice and as an example, we apply them to single cell data of an intracellular regulatory molecule called Phosphatase and Tensin homolog (PTEN) in a p53 system, in wild-type and abnormal, e.g., mutant cells. These molecules are involved in tumor suppression, cell cycle regulation and apoptosis. The unified signaling outcome modeling framework presented here can be applied to various organisms ranging from simple ones such as viruses, bacteria, yeast, and lower metazoans, to more complex organisms such as mammalian cells. Ultimately, this signaling outcome modeling approach can be useful for better understanding of transition from physiological to pathological conditions such as inflammation, various cancers and autoimmune diseases. Brief Summary Cells are supposed to make correct decisions, i.e., respond properly to various signals and initiate certain cellular functions, based on the signals they receive from the surrounding environment. Due to signal transduction noise, signaling malfunctions or other factors, cells may respond differently to the same input signals, which may result in incorrect cell decisions. Modeling and quantification of decision making processes and signaling outcomes in cells have emerged as important research areas in recent years. Here we present univariate and multivariate data-driven statistical models and methods for analyzing dynamic decision making processes and signaling outcomes. Furthermore, we exemplify the methods using single cell data generated by a p53 system, in wild-type and abnormal cells.