doi:10.1016/j.biosystems.2007.02.003
Copyright © 2007 Elsevier Ireland Ltd All rights reserved.
Steady state approach to model gene regulatory networks—Simulation of microarray experiments
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Subodh B. Rawoola, 
and K.V. Venkatesh
, a, ,
aBiosystems Engineering Lab., 136, Department of Chemical Engineering, Indian Institute of Technology, Bombay, Powai, Mumbai 400076, India
Received 14 September 2006;
revised 12 February 2007;
accepted 13 February 2007.
Available online 17 February 2007.
Abstract
Genetic regulatory networks (GRN) represent complex interactions between genes brought about through proteins that they code for. Quantification of expression levels in GRN either through experiments or theoretical modeling is a challenging task. Recently, microarray experiments have gained importance in evaluating GRN at the genome level. Microarray experiments yield log fold change in mRNA abundance which is helpful in deciphering connectivity in GRN. Current approaches such as data mining, Boolean or Bayesian modeling and combined use of expression and location data are useful in analyzing microarray data. However, these methodologies lack underlying mechanistic details present in GRN.
We present here a steady state gene expression simulator (SSGES) which sets up steady state equations and simulates the response for a given network structure of a GRN. SSGES includes mechanistic details such as stoichiometry, protein–DNA and protein–protein interactions, translocation of regulatory proteins and autoregulation. SSGES can be used to simulate the response of a GRN in terms of fractional transcription and protein expression. SSGES can also be used to generate log fold change in mRNA abundance and protein expression implying that it is useful to simulate microarray type experiments. We have demonstrated these capabilities of SSGES by modeling the steady state response of GAL regulatory system in Saccharomyces cerevisiae. We have demonstrated that the predicted data qualitatively matched the microarray data obtained experimentally by Ideker et al. [Ideker, T., Thorsson, V., Ranish, J.A., Christmas, R., Buhler, J., Eng, J.K., Bumgarner, R., Goodlett, D.R., Aebersold, R., Hood, L., 2001. Integrated genomic and proteomic analyses of a systematically perturbed metabolic network. Science 292, 929–934]. SSGES is available from authors upon request.
Keywords: Microarray modeling; Genetic regulatory network; Steady state modeling; GAL network; Saccharomyces cerevisiae
Fig. 1. Overview of working of SSGES. (A) The GRN—Gene1 is regulated by protein Pa1. Gene3 is positively autoregulated. Gene2 is regulated positively by product of Gene3 and negatively by a complex of the product of Gene1 and Pn. (B) Input file to SSGES—the text succinctly lists all genes, various proteins and interactions along with associated parameters for the GRN shown in (A). (C) SSGES generated MATLAB code files corresponding to the input file. (D) Graphical results—the graph shows probability of gene expression for GENE1, GENE2, GENE3 v/s Pa1 concentration. The profiles are consistent with respect to the underlying regulatory structure. With increase in Pa1 concentration, GENE3 shows sustained transcriptional probability, GENE1 shows ‘S’ shaped rise in transcriptional probability and GENE2 shows decrease in transcriptional probability.
Fig. 2. Interaction between various genes in the GAL regulatory network of S. cerevisiae. Circles indicate various genes. Different connectors signify different types of interactions.
Fig. 3. Comparison of SSGES LFT data with experimental data reported by Ideker et al. (2001). (A) GAL1 (B) GAL3 (C) GAL4. Solid lines with ‘○’ markers show data by Ideker et al. (2001). Dotted lines with ‘×’ markers show data generated by SSGES. Ticks on x axis - 1, 2, 3, 4, 5, 6, 7, 8 indicate following experimental conditions WT +gal, WT −gal, GAL3−+gal, GAL80−+gal, GAL4−+gal, GAL3−−gal, GAL80−−gal and GAL4−−gal respectively. ‘+gal’ indicates conditions wherein galactose is present, ‘−gal’ indicates condition wherein galactose is absent.
Fig. 4. Comparison of LFT data for wild type with that of mutants as predicted by SSGES. (A) Mutant 1: Gal80p translocation to nucleus was increased by a factor of 20 (B) mutant 2: Gal80p–Gal3p interaction affinity was reduced three-fold and (C) mutant 3: dimerization of Gal4p was eliminated, Gal4p operates as a monomer. Solid lines with ‘○’ markers show data generated by mutant models. Dotted lines with ‘×’ markers show data generated by WT model. The ticks 1, 2, 3, 4, 5, 6, 7 on x axis signify different genes, viz. GAL1, GAL2, GAL3, GAL4, GAL80, SUC2 and MEL1 under ‘gal+’ condition, i.e. when galactose is present.
Fig. 5. Simulated protein concentration profile for WT strain. (A) Gal1 profile, (B) Gal3 profile and (C) Gal80 profile.
Fig. C.1. Interactions in the GAL network under different environmental conditions. (A) Glucose medium: activated Mig1p translocates to nucleus causing repression. (B) Galactose medium: Gal80p is sequestered by Gal3p and remains preferably in the cytoplasm, thus Gal4p causes transcription initiation. (C) NINR (non-inducing non repressing medium) such as glycerol: Gal80p remains preferably in nucleus and binds to free or bound Gal4p, causing transcription repression. Bold arrow indicate preferred direction of equilibrium.
Table 1.
Simulation of log fold transcriptional gene expression data for the GAL network
WT: wild type; gl−/+: glucose absent/present condition; ga−/+: galactose absent/present condition; M1: MIG1− mutant; G8: GAL80− mutant; M1G8: MIG1−GAL80− double mutant; G3: GAL3− mutant; G4: GAL4− mutant; SM1: structural mutant wherein Gal80p translocation to nucleus was increased by a factor of 20; SM2: structural mutant wherein Gal80p–Gal3p interaction affinity was reduced three-fold; SM3: structural mutant wherein dimerization of Gal4p was eliminated, Gal4p operates as monomer.
Table A.1
Mathematical expressions for different regulatory modes
Same symbols as that of species symbol, indicate its concentration. O: operator site; I: inducer regulatory protein; symbol ‘K’ with different suffices indicate different dissociation constants; m: extent of cooperativity which indicates the degree to which binding to an operator site is enhanced when adjacent operator site is occupied by the transcriptional regulatory protein; R: repressor regulatory protein; a: co-response coefficient, 
indicates activated protein, subscript n indicates nuclear localization of the protein.
Corresponding author. Tel.: +91 22 2576 7223; fax: +91 22 2572 6895.
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