Reducing experimental variability in variance-based sensitivity analysis of biochemical reaction systems.

Sensitivity analysis is a valuable task for assessing the effects of biological variability on cellular behavior. Available techniques require knowledge of nominal parameter values, which cannot be determined accurately due to experimental uncertainty typical to problems of systems biology. As a consequence, the practical use of existing sensitivity analysis techniques may be seriously hampered by the effects of unpredictable experimental variability. To address this problem, we propose here a probabilistic approach to sensitivity analysis of biochemical reaction systems that explicitly models experimental variability and effectively reduces the impact of this type of uncertainty on the results. The proposed approach employs a recently introduced variance-based method to sensitivity analysis of biochemical reaction systems [Zhang et al., J. Chem. Phys. 134, 094101 (2009)] and leads to a technique that can be effectively used to accommodate appreciable levels of experimental variability. We discuss three numerical techniques for evaluating the sensitivity indices associated with the new method, which include Monte Carlo estimation, derivative approximation, and dimensionality reduction based on orthonormal Hermite approximation. By employing a computational model of the epidermal growth factor receptor signaling pathway, we demonstrate that the proposed technique can greatly reduce the effect of experimental variability on variance-based sensitivity analysis results. We expect that, in cases of appreciable experimental variability, the new method can lead to substantial improvements over existing sensitivity analysis techniques.

A comparison of approximation techniques for variance-based sensitivity analysis of biochemical reaction systems.

BACKGROUND: Sensitivity analysis is an indispensable tool for the analysis of complex systems. In a recent paper, we have introduced a thermodynamically consistent variance-based sensitivity analysis approach for studying the robustness and fragility properties of biochemical reaction systems under uncertainty in the standard chemical potentials of the activated complexes of the reactions and the standard chemical potentials of the molecular species. In that approach, key sensitivity indices were estimated by Monte Carlo sampling, which is computationally very demanding and impractical for large biochemical reaction systems. Computationally efficient algorithms are needed to make variance-based sensitivity analysis applicable to realistic cellular networks, modeled by biochemical reaction systems that consist of a large number of reactions and molecular species. RESULTS: We present four techniques, derivative approximation (DA), polynomial approximation (PA), Gauss-Hermite integration (GHI), and orthonormal Hermite approximation (OHA), for analytically approximating the variance-based sensitivity indices associated with a biochemical reaction system. By using a well-known model of the mitogen-activated protein kinase signaling cascade as a case study, we numerically compare the approximation quality of these techniques against traditional Monte Carlo sampling. Our results indicate that, although DA is computationally the most attractive technique, special care should be exercised when using it for sensitivity analysis, since it may only be accurate at low levels of uncertainty. On the other hand, PA, GHI, and OHA are computationally more demanding than DA but can work well at high levels of uncertainty. GHI results in a slightly better accuracy than PA, but it is more difficult to implement. OHA produces the most accurate approximation results and can be implemented in a straightforward manner. It turns out that the computational cost of the four approximation techniques considered in this paper is orders of magnitude smaller than traditional Monte Carlo estimation. Software, coded in MATLAB, which implements all sensitivity analysis techniques discussed in this paper, is available free of charge. CONCLUSIONS: Estimating variance-based sensitivity indices of a large biochemical reaction system is a computationally challenging task that can only be addressed via approximations. Among the methods presented in this paper, a technique based on orthonormal Hermite polynomials seems to be an acceptable candidate for the job, producing very good approximation results for a wide range of uncertainty levels in a fraction of the time required by traditional Monte Carlo sampling.

Probabilistic sensitivity analysis of biochemical reaction systems.

Sensitivity analysis is an indispensable tool for studying the robustness and fragility properties of biochemical reaction systems as well as for designing optimal approaches for selective perturbation and intervention. Deterministic sensitivity analysis techniques, using derivatives of the system response, have been extensively used in the literature. However, these techniques suffer from several drawbacks, which must be carefully considered before using them in problems of systems biology. We develop here a probabilistic approach to sensitivity analysis of biochemical reaction systems. The proposed technique employs a biophysically derived model for parameter fluctuations and, by using a recently suggested variance-based approach to sensitivity analysis [Saltelli et al., Chem. Rev. (Washington, D.C.) 105, 2811 (2005)], it leads to a powerful sensitivity analysis methodology for biochemical reaction systems. The approach presented in this paper addresses many problems associated with derivative-based sensitivity analysis techniques. Most importantly, it produces thermodynamically consistent sensitivity analysis results, can easily accommodate appreciable parameter variations, and allows for systematic investigation of high-order interaction effects. By employing a computational model of the mitogen-activated protein kinase signaling cascade, we demonstrate that our approach is well suited for sensitivity analysis of biochemical reaction systems and can produce a wealth of information about the sensitivity properties of such systems. The price to be paid, however, is a substantial increase in computational complexity over derivative-based techniques, which must be effectively addressed in order to make the proposed approach to sensitivity analysis more practical.

Hypoxia-inducible factor-1alpha induces the coronary collaterals for coronary artery disease.

BACKGROUND: Marked variability exists in coronary artery collaterals in patients with ischemic heart disease. Multiple factors are thought to play a role in collateral development; however, the contribution of hypoxia inducible factor-1alpha (HIF-1alpha), which is a transcriptional activator that functions as a master regulator of oxygen homeostasis, is not completely clear. It could play an important role in modulating collateral development. OBJECTIVE: The objective of this study is to investigate the changes and significance of expression of HIF-1alpha in patients with coronary artery collaterals. METHODS: Collateral vessels were determined in 98 patients with >or=70% narrowing of at least one coronary artery without earlier revascularization, 42 patients with coronary artery collaterals and 56 patients with no coronary artery collaterals. Extent of collaterals was expressed as scores according to the Rentrop scoring system. Another 50 cases with normal coronary arteries were selected as control. The levels of HIF-1alpha protein expression in monocyte and lymphocyte in the participants were tested by immunohistochemistry (IHC) and western blot; mRNA levels were measured using reverse transcriptase PCR technique. RESULTS: Compared with the control with normal coronary artery, the patients had higher expression of HIF-1alpha protein tested by IHC and western blot (52.6+/-10.2 vs. 13.7+/-6.2 by IHC, 50.8+/-4.5 vs. 6.5+/-1.8 by western blot); furthermore, significantly higher HIF-1alpha expression was observed in patients with collaterals compared with patients with no collaterals (81.5+/-11.8 vs. 20.7+/-9.4 by IHC; 87.2+/-6.5 vs. 9.5+/-1.4 by western blot). On the transcriptional levels of HIF-1alpha, the result was the same as the protein, there was significant difference of HIF-1alpha between the three groups. The patients with collaterals were the highest (127.3+/-23.9), followed by patients with no collaterals (35.7+/-12.3), and the control were the lowest (23.5+/-9.3). A highly positive correlation was observed between the expression/transcription of HIF-1alpha and collateral score (P<0.01, IHC: r1=0.78, reverse transcriptase PCR: r2=0.69, western blot: r3=0.84). CONCLUSION: These data suggest that higher inductions of HIF-1alpha are associated with coronary collaterals, thus implying that HIF-1alpha may promote coronary collateral formation. Detection of HIF-1alpha expression might be helpful to predict prognosis of patients with coronary artery disease.

DNA methylation dynamics during ex vivo differentiation and maturation of human dendritic cells.

BACKGROUND: Dendritic cells (DCs) are important mediators of innate and adaptive immune responses, but the gene networks governing their lineage differentiation and maturation are poorly understood. To gain insight into the mechanisms that promote human DC differentiation and contribute to the acquisition of their functional phenotypes, we performed genome-wide base-resolution mapping of 5-methylcytosine in purified monocytes and in monocyte-derived immature and mature DCs. RESULTS: DC development and maturation were associated with a great loss of DNA methylation across many regions, most of which occurs at predicted enhancers and binding sites for known transcription factors affiliated with DC lineage specification and response to immune stimuli. In addition, we discovered novel genes that may contribute to DC differentiation and maturation. Interestingly, many genes close to demethylated CG sites were upregulated in expression. We observed dynamic changes in the expression of TET2, DNMT1, DNMT3A and DNMT3B coupled with temporal locus-specific demethylation, providing possible mechanisms accounting for the dramatic loss in DNA methylation. CONCLUSIONS: Our study is the first to map DNA methylation changes during human DC differentiation and maturation in purified cell populations and will greatly enhance the understanding of DC development and maturation and aid in the development of more efficacious DC-based therapeutic strategies.

[Responses of Agriophyllum squarrosum phenotypic plasticity to the changes of soil nutrient and moisture contents and population density].

This paper studied the phenotypic plasticity of Agriophyllum squarrosum under effects of soil nutrient and moisture contents and population density. The results showed that with the increase of soil nutrient content, the root/shoot ratio of A. squarrosum was decreased from 0.135 to 0.073. However, soil moisture content and population density had less effect on the root/shoot ratio. The plasticity of reproductive allocation of A. squarrosum as responding to the changes of soil nutrient and moisture contents was a "real plasticity", and the allocation was negatively correlated with soil nutrient content but positively correlated with soil moisture content. When soil nutrient content was high or moisture content was low, the reproductive allocation of A. squarrosum changed larger with plant size. Population density had no effects on the reproductive allocation, while plant size conditioned the allocation. Among the three test affecting factors, soil nutrient content had the greatest effects on the morphological characters and biomass of A. squarrosum.