The model parameters for the small-scale target network.

<p>The model parameters for the small-scale target network.</p

Inference of Vohradský's Models of Genetic Networks by Solving Two-Dimensional Function Optimization Problems

<div><p>The inference of a genetic network is a problem in which mutual interactions among genes are inferred from time-series of gene expression levels. While a number of models have been proposed to describe genetic networks, this study focuses on a mathematical model proposed by Vohradský. Because of its advantageous features, several researchers have proposed the inference methods based on Vohradský's model. When trying to analyze large-scale networks consisting of dozens of genes, however, these methods must solve high-dimensional non-linear function optimization problems. In order to resolve the difficulty of estimating the parameters of the Vohradský's model, this study proposes a new method that defines the problem as several two-dimensional function optimization problems. Through numerical experiments on artificial genetic network inference problems, we showed that, although the computation time of the proposed method is not the shortest, the method has the ability to estimate parameters of Vohradský's models more effectively with sufficiently short computation times. This study then applied the proposed method to an actual inference problem of the bacterial SOS DNA repair system, and succeeded in finding several reasonable regulations.</p></div

The precision versus the recall for the genetic network inference problems of 20 genes with 20 sets of time-series data.

<p>A solid line represents the performances of the proposed method. Dotted and dashed lines represent the performances of the least-squares approach with and , respectively.</p

The computation times of the proposed method for noisy experiments.

<p>Solid, dotted and dashed lines represents the averaged computation times required for solving the inference problems for 10, 20 and 30 genes, respectively.</p

The performances of the proposed method on the third problem of the DREAM3 in silico challenges [43].

<p>The performances were checked by changing the hyper-parameter of the proposed method, . FP, FN, TP and TN are the numbers of false-positive, false-negative, true-positive, true-negative regulations, respectively.</p

A sample of the parameters estimated by the proposed method in the experiment with actual gene expression data.

<p>The parameters written in boldface type correspond to biologically plausible regulations mentioned in the ‘Analysis of actual data’ section.</p

A sample of the parameters erroneously estimated by the proposed method in the experiment using the small-scale network.

<p>Note that the proposed method succeeded in estimating the parameter values with precision in 7 of the 10 trials.</p

Robustness analysis of the detailed kinetic model of an ErbB signaling network by using dynamic sensitivity

<div><p>The ErbB receptor signaling pathway plays an important role in the regulation of cellular proliferation, survival and differentiation, and dysregulation of the pathway is linked to various types of human cancer. Mathematical models have been developed as a practical complementary approach to deciphering the complexity of ErbB receptor signaling and elucidating how the pathways discriminate between ligands to induce different cell fates. In this study, we developed a simulator to accurately calculate the dynamic sensitivity of extracellular-signal-regulated kinase (ERK) activity (ERK*) and Akt activity (Akt*), downstream of the ErbB receptors stimulated with epidermal growth factor (EGF) and heregulin (HRG). To demonstrate the feasibility of this simulator, we estimated how the reactions critically responsible for ERK* and Akt* change with time and in response to different doses of EGF and HRG, and predicted that only a small number of reactions determine ERK* and Akt*. ERK* increased steeply with increasing HRG dose until saturation, while showing a gently rising response to EGF. Akt* had a gradual wide-range response to HRG and a blunt response to EGF. Akt* was sensitive to perturbations of intracellular kinetics, while ERK* was more robust due to multiple, negative feedback loops. Overall, the simulator predicted reactions that were critically responsible for ERK* and Akt* in response to the dose of EGF and HRG, illustrated the response characteristics of ERK* and Akt*, and estimated mechanisms for generating robustness in the ErbB signaling network.</p></div

Time course simulation of ERK* and Akt*.

<p>(A) Simulated and experimental time course of ERK*. (B) Simulated and experimental time course of Akt*. The HRG concentrations were 0.1, 0.5 and 10 nM, while the EGF concentration was set to 0.5 nM. The solid, dashed and dot-dash lines indicate the simulated results at 0, 0.5 and 10 nM HRG, respectively. The cross, circle and triangle indicate the experimental activity at 0.1, 0.5 and 10 nM HRG, respectively. The initial activities are set to zero by subtracting the background intensity from the measured activities and then the resultant activities are normalized so that the maximum intensity during time course is 1. The error bars denote the standard deviations of signal intensities in quadruplicate independent experiments.</p

Critical parameter shifts in the late stage in response to EGF at a low HRG concentration.

<p>Orange, blue and green colors indicates the Akt*-specific, ERK*-specific, and dual-specific critical reactions or parameters at 300s with (EGF, HRG) = (0.5nM, 0.5nM) and (EGF, HRG) = (10.0nM, 0.5nM).</p