ApoE Modifier Alleles for Alzheimer's Disease Discovered by Information Theory Dependency Measures: MIST Software Package

Abstract

Information theory-based measures of variable dependency (previously published) have been implemented into a software package, MIST. The design of the software and its potential uses are described, and a demonstration is presented in the discovery of modifier alleles of the ApoE gene in affecting Alzheimer's disease (AD) by analyzing the UK Biobank dataset. The modifier genes uncovered overlap strongly with genes found to be associated with AD. Others include many known to influence AD. We discuss a range of uses of the dependency calculations using MIST that can uncover additional genetic effects in similar complex datasets, like higher degrees of interaction and phenotypic pleiotropy.

Keywords: Alzheimer's disease; ApoE modifier alleles; information theory dependency measures; software package.

FIG. 1.

A TupleSpace is composed of VG and GT. The GT act as templates defining the combination of variables drawn from the VG to form Variable Tuples. For example, the Variable at position 0 in the Variable Tuple will be chosen from the group at position 0 in the GT. In this figure, VG A and B are used in four TupleSpaces, each with a different GT. The generated Variable Tuples are displayed underneath each TupleSpace. Since each VG is a disjoint ordered set and each Variable Tuple is an ordered set, Variable Tuples can be determined by simply iterating through the VG. GT, Group Tuples; VG, Variable Groups.

FIG. 2.

MIST runtime as thread count increases over various N (top, left) and M (top, right) values. The speedup over single core performance (bottom) shows the diminishing returns of thread counts >60. Timings were taken on a server equipped with 4 Intel Xeon Gold 6148 CPUS (total 80 core, 160 threads) and 250GiB RAM. Each measurement was repeated q = 200 times and the mean is used.

FIG. 3.

(A, B) Runtime performance of randomly generated data consisting of N variables of length M. In most cases the bitset algorithm outperforms the vector algorithm. For data with a large number of value bins (B), the Vector algorithm is faster for some smaller variable sizes. Timings were taken on a workstation equipped with Intel Core i7-6850K and 62GiB RAM.

FIG. 4.

ApoE modifiers (ApoE is shown on Chr 19). Black lines mark the 10 top-scoring primary genes (top mutual information scores between SNPs and AD phenotype). The red lines indicate the top-scoring modifiers (Tables 3 and 4). AD, Alzheimer's disease; SNPs, single nucleotide polymorphisms.

FIG. 5.

Schematic diagrams of the use of the dependency measures in several analyses of genetic data. (A) The search for modifier alleles. (B) The search for gene interactions and for second-order modifier alleles. (C) The search for pleiotropic alleles.