Classification of Single-Cell Gene Expression Trajectories from Incomplete and Noisy Data

Abstract

This paper studies classification of gene-expression trajectories coming from two classes, healthy and mutated (cancerous) using Boolean networks with perturbation (BNps) to model the dynamics of each class at the state level. Each class has its own BNp, which is partially known based on gene pathways. We employ a Gaussian model at the observation level to show the expression values of the genes given the hidden binary states at each time point. We use expectation maximization (EM) to learn the BNps and the unknown model parameters, derive closed-form updates for the parameters, and propose a learning algorithm. After learning, a plug-in Bayes classifier is used to classify unlabeled trajectories, which can have missing data. Measuring gene expressions at different times yields trajectories only when measurements come from a single cell. In multiple-cell scenarios, the expression values are averages over many cells with possibly different states. Via the central-limit theorem, we propose another model for expression data in multiple-cell scenarios. Simulations demonstrate that single-cell trajectory data can outperform multiple-cell average expression data relative to classification error, especially in high-noise situations. We also consider data generated via a mammalian cell-cycle network, both the wild-type and with a common mutation affecting p27.This paper studies classification of gene-expression trajectories coming from two classes, healthy and mutated (cancerous) using Boolean networks with perturbation (BNps) to model the dynamics of each class at the state level. Each class has its own BNp, which is partially known based on gene pathways. We employ a Gaussian model at the observation level to show the expression values of the genes given the hidden binary states at each time point. We use expectation maximization (EM) to learn the BNps and the unknown model parameters, derive closed-form updates for the parameters, and propose a learning algorithm. After learning, a plug-in Bayes classifier is used to classify unlabeled trajectories, which can have missing data. Measuring gene expressions at different times yields trajectories only when measurements come from a single cell. In multiple-cell scenarios, the expression values are averages over many cells with possibly different states. Via the central-limit theorem, we propose another model for expression data in multiple-cell scenarios. Simulations demonstrate that single-cell trajectory data can outperform multiple-cell average expression data relative to classification error, especially in high-noise situations. We also consider data generated via a mammalian cell-cycle network, both the wild-type and with a common mutation affecting p27.

Optimal Bayesian Transfer Learning

“…From (24) and (35), T l t = M l t,n . From (27) and (38), T l x = M l x . As a result, O OBTL (x|l) = O OBC (x|l), and consequently, Ψ OBTL (x) = Ψ OBC (x).…”

Scalable Optimal Bayesian Classification of Single-Cell Trajectories under Regulatory Model Uncertainty

“…Since the trajectories are assumed to be independent and drawn based on the dynamics of the true network, its steady-state distribution π ∞ θ * characterizes the probability of the system being at different states. It can be shown that the multiple-cell data are independent samples from the following measurement model [11]: where {x 1 , ..., x 2 n } denotes all the network states in the Boolean vector representation. However, we assume that the true network model θ * , is unknown, and is represented by a finite set of M possible network models {θ 1 , ..., θ M } with prior probability π(θ | c).…”

“…In [10] and [11], the maximum-likelihood (ML) based classification of single-cell trajectories has been developed. The method uses the ML-adaptive filter proposed in [7] for estimation of the unknown parameters, followed by the Bayes classifier tuned to the ML parameter estimates.…”

Gene regulatory network state estimation from arbitrary correlated measurements

“…We employ here an additive Gaussian noise observation model even though the methodology proposed in the paper is entirely general and could be applied in principle to any observation model satisfying constraints (3) and (4). A Gaussian model is appropriate for modeling gene-expression data from technologies such as cDNA microarrays [22] and live cell imaging-based assays [24], in which gene expression measurements are continuous and unimodal (within a single population of interest) [42][43][44][45]. Let Y k = (Y k (1), .…”