Inference on the structure of gene regulatory networks

In this paper, we conduct theoretical analyses on inferring the structure of gene regulatory networks. Depending on the experimental method and data type, the inference problem is classified into 20 different scenarios. For each scenario, we discuss the problem that with enough data, under what assumptions, what can be inferred about the structure. For scenarios that have been covered in the literature, we provide a brief review. For scenarios that have not been covered in literature, if the structure can be inferred, we propose new mathematical inference methods and evaluate them on simulated data. Otherwise, we prove that the structure cannot be inferred.

Joint analysis of binomial and continuous traits with a recursive model: a case study using mortality and litter size of pigs

This work presents a model for the joint analysis of a binomial and a Gaussian trait using a recursive parametrization that leads to a computationally efficient implementation. The model is illustrated in an analysis of mortality and litter size in two breeds of Danish pigs, Landrace and Yorkshire. Available evidence suggests that mortality of piglets increased partly as a result of successful selection for total number of piglets born. In recent years there has been a need to decrease the incidence of mortality in pig-breeding programs. We report estimates of genetic variation at the level of the logit of the probability of mortality and quantify how it is affected by the size of the litter. Several models for mortality are considered and the best fits are obtained by postulating linear and cubic relationships between the logit of the probability of mortality and litter size, for Landrace and Yorkshire, respectively. An interpretation of how the presence of genetic variation affects the probability of mortality in the population is provided and we discuss and quantify the prospects of selecting for reduced mortality, without affecting litter size.

Gene network inference via structural equation modeling in genetical genomics experiments

Our goal is gene network inference in genetical genomics or systems genetics experiments. For species where sequence information is available, we first perform expression quantitative trait locus (eQTL) mapping by jointly utilizing cis-, cis-trans-, and trans-regulation. After using local structural models to identify regulator-target pairs for each eQTL, we construct an encompassing directed network (EDN) by assembling all retained regulator-target relationships. The EDN has nodes corresponding to expressed genes and eQTL and directed edges from eQTL to cis-regulated target genes, from cis-regulated genes to cis-trans-regulated target genes, from trans-regulator genes to target genes, and from trans-eQTL to target genes. For network inference within the strongly constrained search space defined by the EDN, we propose structural equation modeling (SEM), because it can model cyclic networks and the EDN indeed contains feedback relationships. On the basis of a factorization of the likelihood and the constrained search space, our SEM algorithm infers networks involving several hundred genes and eQTL. Structure inference is based on a penalized likelihood ratio and an adaptation of Occam's window model selection. The SEM algorithm was evaluated using data simulated with nonlinear ordinary differential equations and known cyclic network topologies and was applied to a real yeast data set.

Analysis of litter size and average litter weight in pigs using a recursive model

An analysis of litter size and average piglet weight at birth in Landrace and Yorkshire using a standard two-trait mixed model (SMM) and a recursive mixed model (RMM) is presented. The RMM establishes a one-way link from litter size to average piglet weight. It is shown that there is a one-to-one correspondence between the parameters of SMM and RMM and that they generate equivalent likelihoods. As parameterized in this work, the RMM tests for the presence of a recursive relationship between additive genetic values, permanent environmental effects, and specific environmental effects of litter size, on average piglet weight. The equivalent standard mixed model tests whether or not the covariance matrices of the random effects have a diagonal structure. In Landrace, posterior predictive model checking supports a model without any form of recursion or, alternatively, a SMM with diagonal covariance matrices of the three random effects. In Yorkshire, the same criterion favors a model with recursion at the level of specific environmental effects only, or, in terms of the SMM, the association between traits is shown to be exclusively due to an environmental (negative) correlation. It is argued that the choice between a SMM or a RMM should be guided by the availability of software, by ease of interpretation, or by the need to test a particular theory or hypothesis that may best be formulated under one parameterization and not the other.