Matrix linear models for high-throughput chemical genetic screens

Abstract

We develop a exible and computationally ecient approach for analysing high throughput chemical genetic screens. In such screens, a library of genetic mutants is phenotyped in a large number of stresses. The goal is to detect interactions between genes and stresses. Typically, this is achieved by grouping the mutants and stresses into categories, and performing modied t-tests for each combination. This approach does not have a natural extension if mutants or stresses have quantitative or nonoverlapping annotations (eg. if conditions have doses, or a mutant falls into more than one category simultaneously). We develop a matrix linear model framework that allows us to model relationships between mutants and conditions in a simple, yet exible multivariate framework. It encodes both categorical and continuous relationships to enhance detection of associations. To handle large datasets, we develop a fast estimation approach that takes advantage of the structure of matrix linear models. We evaluate our method's performance in simulations and in an E. coli chemical genetic screen, comparing it with an existing univariate approach based on modied t-tests . We show that matrix linear models perform slightly better than the univariate approach when mutants and conditions are classied in non-overlapping categories, and substantially better when conditions can be ordered in dosage categories. Our approach is much faster computationally and is scalable to larger datasets. It is an attractive alternative to current methods, and provides a natural framework extensible to larger, and more complex chemical genetic screens. A Julia implementation of matrix linear models and the code used for the analysis in this paper can be found at https://bitbucket.org/jwliang/mlm_packages and https://bitbucket.org/jwliang/mlm_gs_supplement, respectively.

Sparse matrix linear models for structured high-throughput data

“…When λ = 1 (with an average of 78% zero interactions among the six plates), our auxotrophs had an 88% overlap with the Nichols et al auxotrophs. This is consistent with the 83% overlap found in our earlier work on least-squares t-statistics Liang, Nichols and Sen (2019). Figure 3 visualizes the distributions of each auxotroph's sparse interactions (λ = 1) across minimal media conditions.…”

“…If the rows are independent and identically distributed, but the columns are correlated, then we can transform the data so that the entries are uncorrelated. The estimation reduces to finding the least squares estimates, which have a closed-form solution that can be computed quickly even in high (Liang, Nichols and Sen, 2019) (Xiong et al, 2011). However, in many problems, B is expected to be sparse, or we may want to use a sparse B for prediction and interpretation.…”

“…To understand patterns across genes or gene groups, a second analysis across genes is performed, for example gene set enrichment analysis might be performed (Subramanian et al, 2005). By unifying the two steps into a single linear model, the analyst gains flexibilty in modeling (especially in the second step where the analysis can have noncategorical, or non-overlapping covariates), computational speed, as well as power to detect associations (Liang, Nichols and Sen, 2019). In this note we consider estimation of these models with a sparsity constraint.…”

High‐dimensional limit theorems for SGD: Effective dynamics and critical scaling

“…There has also been important work on scaling limits as the dimension tends to infinity for the specific problems of linear regression [55, 76], Online PCA [41, 76], and phase retrieval [71] from random starts, and teacher‐student networks [32, 64, 65, 73] and two‐layer networks for XOR Gaussian mixtures [60] from warm starts. We also note that the study of high‐dimensional regimes of gradient descent and Langevin dynamics have a history from the statistical physics perspective, for example, in [17, 21, 22, 45, 48, 67].…”