title: Integrative analysis of transcriptomic and proteomic data of Desulfovibrio vulgaris: a non-linear model to predict abundance of undetected proteins.
abstract: BACKGROUND
  Gene expression profiling technologies can generally produce mRNA abundance data for all genes in a genome. A dearth of proteomic data persists because identification range and sensitivity of proteomic measurements lag behind those of transcriptomic measurements. Using partial proteomic data, it is likely that integrative transcriptomic and proteomic analysis may introduce significant bias. Developing methodologies to accurately estimate missing proteomic data will allow better integration of transcriptomic and proteomic datasets and provide deeper insight into metabolic mechanisms underlying complex biological systems.
  
  
  RESULTS
  In this study, we present a non-linear data-driven model to predict abundance for undetected proteins using two independent datasets of cognate transcriptomic and proteomic data collected from Desulfovibrio vulgaris. We use stochastic gradient boosted trees (GBT) to uncover possible non-linear relationships between transcriptomic and proteomic data, and to predict protein abundance for the proteins not experimentally detected based on relevant predictors such as mRNA abundance, cellular role, molecular weight, sequence length, protein length, guanine-cytosine (GC) content and triple codon counts. Initially, we constructed a GBT model using all possible variables to assess their relative importance and characterize the behavior of the predictive model. A strong plateau effect in the regions of high mRNA values and sparse data occurred in this model. Hence, we removed genes in those areas based on thresholds estimated from the partial dependency plots where this behavior was captured. At this stage, only the strongest predictors of protein abundance were retained to reduce the complexity of the GBT model. After removing genes in the plateau region, mRNA abundance, main cellular functional categories and few triple codon counts emerged as the top-ranked predictors of protein abundance. We then created a new tuned GBT model using the five most significant predictors. The construction of our non-linear model consists of a set of serial regression trees models with implicit strength in variable selection. The model provides variable relative importance measures using as a criterion mean square error. The results showed that coefficients of determination for our nonlinear models ranged from 0.393 to 0.582 in both datasets, providing better results than linear regression used in the past. We evaluated the validity of this non-linear model using biological information of operons, regulons and pathways, and the results demonstrated that the coefficients of variation of estimated protein abundance values within operons, regulons or pathways are indeed smaller than those for random groups of proteins.
  
  
  BACKGROUND
  Supplementary data are available at Bioinformatics online.
authors.affiliation: Department of Industrial, Systems and Operations Engineering, Tempe, AZ 85287-5906, USA. weiwen.zhang@asu.edu
authors.forename: Wandaliz
authors.initials: W
authors.lastname: Torres-García
authors.forename: Weiwen
authors.initials: W
authors.lastname: Zhang
authors.forename: George C
authors.initials: GC
authors.lastname: Runger
authors.forename: Roger H
authors.initials: RH
authors.lastname: Johnson
authors.forename: Deirdre R
authors.initials: DR
authors.lastname: Meldrum
mesh_terms: D001426:Bacterial Proteins / Q000737:chemistry* / Q000235:genetics*; D030562:Databases, Protein; D016969:Desulfovibrio vulgaris / Q000235:genetics* / Q000378:metabolism*; D020869:Gene Expression Profiling / Q000379:methods*; D017711:Nonlinear Dynamics; D040901:Proteomics / Q000379:methods*
chemical_list: D001426:Bacterial Proteins