title: Random phenotypic variation of yeast (Saccharomyces cerevisiae) single-gene knockouts fits a double pareto-lognormal distribution.
abstract: BACKGROUND
  Distributed robustness is thought to influence the buffering of random phenotypic variation through the scale-free topology of gene regulatory, metabolic, and protein-protein interaction networks. If this hypothesis is true, then the phenotypic response to the perturbation of particular nodes in such a network should be proportional to the number of links those nodes make with neighboring nodes. This suggests a probability distribution approximating an inverse power-law of random phenotypic variation. Zero phenotypic variation, however, is impossible, because random molecular and cellular processes are essential to normal development. Consequently, a more realistic distribution should have a y-intercept close to zero in the lower tail, a mode greater than zero, and a long (fat) upper tail. The double Pareto-lognormal (DPLN) distribution is an ideal candidate distribution. It consists of a mixture of a lognormal body and upper and lower power-law tails.
  
  
  OBJECTIVE
  If our assumptions are true, the DPLN distribution should provide a better fit to random phenotypic variation in a large series of single-gene knockout lines than other skewed or symmetrical distributions. We fit a large published data set of single-gene knockout lines in Saccharomyces cerevisiae to seven different probability distributions: DPLN, right Pareto-lognormal (RPLN), left Pareto-lognormal (LPLN), normal, lognormal, exponential, and Pareto. The best model was judged by the Akaike Information Criterion (AIC).
  
  
  RESULTS
  Phenotypic variation among gene knockouts in S. cerevisiae fits a double Pareto-lognormal (DPLN) distribution better than any of the alternative distributions, including the right Pareto-lognormal and lognormal distributions.
  
  
  CONCLUSIONS
  A DPLN distribution is consistent with the hypothesis that developmental stability is mediated, in part, by distributed robustness, the resilience of gene regulatory, metabolic, and protein-protein interaction networks. Alternatively, multiplicative cell growth, and the mixing of lognormal distributions having different variances, may generate a DPLN distribution.
authors.affiliation: Department of Biology, Berry College, Mount Berry, Georgia, USA. jgraham@berry.edu
authors.forename: John H
authors.initials: JH
authors.lastname: Graham
authors.forename: Daniel T
authors.initials: DT
authors.lastname: Robb
authors.forename: Amy R
authors.initials: AR
authors.lastname: Poe
mesh_terms: D030541:Databases, Genetic; D055786:Gene Knockout Techniques; D005800:Genes, Fungal; D010641:Phenotype; D011336:Probability; D012441:Saccharomyces cerevisiae / Q000166:cytology* / Q000235:genetics*; D016008:Statistical Distributions