Epistasis Across Chromosomes and Individuals 'Homozygous for Interactions'

Question

Apologies for any failures in nomenclature. I'm a mathematician who is making a foray into genetics for a masters thesis. Specifically, I'm generating artificial diploid genetic sequence data and phenotype data based on known epistatic interactions.

Primary Question

I am familiar with the concept that having multiple copies of a single allele (e.g. one from each parent) can actually increase expression and thereby change the quantitative phenotype (at least in some cases?). Can this also happen with epistatic effects? For example, consider the case that locus 1 ($L_1$) and locus 2 ($L_2$) exhibit some positive interaction ($\beta$) on the trait ($Y$). $$E[Y]=\mu+\beta(L_1L_2)$$ If both chromosomes contain the allele in question at both loci, then does this individual exhibit more of a trait increase than if he only had one chromosome with the epistatic alleles?

Secondary question

Can alleles interact epistatically even when they are present on different chromosomes? e.g. assume allele A at locus 1 interacts with allele B at locus 2. Individual has A at locus 1 and b at locus 2 on chromosome 1. He also has a at locus 1 and B at locus 2 on chromosome 2. Do A and B from the different chromosomes interact? My intuition is yes but I want verification.

Many thanks!!!

Answer 1

Question 1: The phenomena you describe in which it matters whether you have one or two copies of an allele (e.g., the AA phenotype being different than the Aa phenotype) are known as dominance effects. Dominance effects can interact with epistatic effects (in which the phenotypic effect of one locus depends on the genotype at the another locus).

One good example is the interaction between the Agouti locus and the Mc1R locus in the oldfield mouse (Peromyscus polionotus) in determining coat color. Dark-color homozygotes for the Agouti locus have dark coats irrespective of the allele at the Mc1R locus, whereas color in Agouti heterozygotes or light color homozygotes depends on genotype at the Mc1R locus. The figure below, from Steiner et al (2007), illustrates:

Question 2: Epistatically interacting loci need not be on the same chromosome. The loci discussed above provide a perfectly good example. Mc1R is on chromosome 1, where as Agouti is on chromosome 7, yet they interact epistatically.