Figure 1.
Cross-talk in diploid autoregulators.
(a) Schematic representation of negative autoregulation when one (left) and two (right) copies of a gene are present in a cell. In the haploid the amount of negative autoregulation the gene experiences depends on on its own expression level. In the diploid, two gene copies are present (shown as light gray and dark gray), and the amount of negative autoregulation experienced by each gene depends on the expression level of both genes combined. If the two gene copies differ from one another in the strength of their transcription factor binding sites, complex dynamics can arise that are not observed in haploids. (b) IIllustration of variation in the repression function, , with protein concentration for different Hill coefficients,
(sold line),
(small dashes) and
(large dashes).
Figure 2.
Invasibility of autoregulatory binding sites.
The response time of mutant (a) homozygotes and (b) heterozygotes are shown. Different values of the binding strength of the resident allele, in units of (x-axis), are plotted against mutations to binding site strength
of different size (y-axis). Thus the graphs compare a resident allele,
with a mutant allele,
. Mutations falling into white region result in decreased response time in the carrier compared to resident genotype and are favoured by selection; mutations falling into the gray region result in increased response time and are not favoured by selection. Weak binding occurs when
[1], [2]. Response times were calculated by numerically integrating Eq. 1 from zero protein concentration to 90% of the equilibrium. The optimal binding strength in these graphs is
, corresponding to a background transcription rate
.
Figure 3.
Response times and allele expression.
This figure shows quantitative results for the contributions of different alleles to expression and to response time. (a) Expression level of the resident allele (black line) and the mutant allele (red line) in the heterozygote relative to the resident allele in the homozygote. As binding strength increases the resident allele is over-expressed. (b) Response times for individual alleles (time to return to of the equilibrium expression level) in the heterozygote. The response time of the resident allele (black line) and the mutant allele (red line) in the heterozygote are shown relative to the response time of the resident allele in the homozygote. The resident allele in the heterozygote shows an increased response time with increasing binding strength. Mutant alleles in these graphs have dissociation constant
, and the optimal binding strength in these graphs is
, corresponding to a background transcription rate
.
Figure 4.
Evolution of autoregulatory binding sites.
Distribution of binding site strength achieved in evolutionary simulations for haploids (gray) and diploids (white). Hapoids are able to evolve stronger binding than diploids. The histograms shows results of replicate simulations for each ploidy level. The simulation procedure is described in the main text and the Materials and Methods. The optimal binding strength used was
, corresponding to a a background transcription rate
.
Figure 5.
Intrinsic noise in gene expression.
The figure shows quantitative results for the intrinsic noise of autoregulating genes, as measured by the ratio of the variance to mean expression in protein concentration at equilibrium. (a) Percentage change in the noise of a heterozygote compared to the resident homozygote. These are shown for different Hill coefficients, (black),
(red) and
(blue). Mutations become deleterious in the heterozygote when
. (b) Percentage change in the noise of a mutant homozygote compared to the resident homozygote. Mutations become deleterious in the mutant homozygote when
is about
. The graphs show the results of stochastic simulations (see Materials and Methods) for parameter values typical for transcription factors [3],
,
,
,
and
. The resident homozygote has binding strength
(as indicated by the x-axis), mutations are of size
.