A microarray data-based semi-kinetic method for predicting quantitative dynamics of genetic networks

Abstract

Background: Elucidating the dynamic behaviour of genetic regulatory networks is one of the most significant challenges in systems biology. However, conventional quantitative predictions have been limited to small networks because publicly available transcriptome data has not been extensively applied to dynamic simulation.

Results: We present a microarray data-based semi-kinetic (MASK) method which facilitates the prediction of regulatory dynamics of genetic networks composed of recurrently appearing network motifs with reasonable accuracy. The MASK method allows the determination of model parameters representing the contribution of regulators to transcription rate from time-series microarray data. Using a virtual regulatory network and a Saccharomyces cerevisiae ribosomal protein gene module, we confirmed that a MASK model can predict expression profiles for various conditions as accurately as a conventional kinetic model.

Conclusion: We have demonstrated the MASK method for the construction of dynamic simulation models of genetic networks from time-series microarray data, initial mRNA copy number and first-order degradation constants of mRNA. The quantitative accuracy of the MASK models has been confirmed, and the results indicated that this method enables the prediction of quantitative dynamics in genetic networks composed of commonly used network motifs, which cover considerable fraction of the whole network.

Figure 1

Validation results of the MASK method using the virtual genetic network. (a) Part of the virtual genetic network shown in Ref. [21]. The regulation of gene G by gene C was employed to compare the MASK method and conventional kinetic model. (b) A log-log scatter plot of the R values of gene C and G. (c) The training data used in estimating the MASK model parameters. (d) The test data used for the validation of the MASK model. Applied to the same gene C expression time series, the MASK model calculated the time course of gene G as accurately as the original kinetic model. The model parameters were not changed.

Figure 2

Validation results of the MASK method using yeast RP genes. (a) A genetic regulatory module of yeast RP genes described in Ref.[22]. Our model included 13 target genes of this module. (b) A comparison of the training microarray data [27] and a time course calculated by the MASK model. The mean relative error of RPL40A time series was 11.4%. (c) A comparison of the test data [28] and a calculated time series. The mean relative error of the RPL40A time series was 12.1%.

Figure 3

A prediction of RP gene transcription in the fhl1Δ strain. (a) The R value of FHL1 was changed to realize depletion of Fhl1 mRNA. The transcription rates of the other two regulators were unchanged. (b) Calculated RP mRNA levels in the wild-type (WT) and fhl1Δ strains. The 40–60% decrease is in agreement with a previous observation [29].

Figure 4

A reaction mechanism postulated by Eq.(1). (a) Variation of transcription rate defined by Eq,(1). Transcript rate is saturated as RNA polymerase increases. The R value determines maximum transcription rate. (b) A reaction scheme of RNA synthesis.

Figure 5

Procedure for estimating the parameters of Eqs. (2) and (4). The time derivative of an RNA level is the sum of the transcription rate and the degradation rate of RNA (top centre). The degradation rate is the product of the RNA level and the first-order degradation constant (centre left). Subtracting the degradation rate from the time derivative of microarray data, results in the RNA synthesis rate (centre). The time-series of R values are yielded by normalizing the synthesis rate as R(t = 0) = 1 (centre right). Eq. (3) is a mathematical representation of this procedure. Provided the time-series of the R values of regulators and target genes, the time delay τ_i between the regulators and the target genes are calculated using the local clustering method[24]. Finally, a regression analysis of the time delay-corrected R time-series (bottom right) provides least-squares estimate of the coefficients in Eqs. (2) and (4) (bottom left).