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Evidence-Based Complementary and Alternative Medicine
Volume 2013 (2013), Article ID 541436, 10 pages
Research Article

Optimizing Combinations of Flavonoids Deriving from Astragali Radix in Activating the Regulatory Element of Erythropoietin by a Feedback System Control Scheme

1State Key Laboratory of Analytical Chemistry for Life Science, Nanjing University, Nanjing, Jiangsu, China
2Department of Mechanical Engineering, The Hong Kong University of Science and Technology, Clear Water Bay Road, Hong Kong
3Division of Life Science and Center for Chinese Medicine, The Hong Kong University of Science and Technology, Clear Water Bay Road, Hong Kong
4School of Biomedical Engineering, Med-X Research Institute, Shanghai Jiao Tong University, Shanghai, China
5Center for Cell Control, Mechanical and Aerospace Engineering Department, Biomedical Engineering Department, University of California, Los Angeles, CA 90095-1597, USA

Received 4 February 2013; Accepted 22 March 2013

Academic Editor: Shao Li

Copyright © 2013 Hui Yu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Supplementary Material

Fig. 1S A typical DE/rand/1/bin strategy introduced in optimization of flavonoid combinations [21]. Initially, NP (number of population) combinations of the four flavonoids were generated. For each original combination xi, a mutation combination vi was generated following the formula in step 2, where r1, r2 and r3 are randomly generated integers in the range of 1~NP. Then the originals xi (black border) and mutations vi (orange border) were crossed to produce crossover combinations ui, controlled by the crossover constant CR in step 3. The crossover combinations were used as the trial combinations to compete with the original combinations. Combinations that derived better desired biological activities were carried over to the new generation xi,new. We decided to start with NP=6 and CR=0.5 to achieve fast convergence, and gradually increase to NP=18 and CR=0.9 to avoid being trapped by localized maximum responses. The brightness of the colors represented different concentration levels of each flavonoid

Fig. 2S The median effect equation for computerized simulation of synergism, additivism and antagonism of the effect of multiple drugs: in optimization of flavonoid combinations, the fraction affected fa was expressed as fa=C/T, where C was the control response, and T represented drug induced response [26].

Fig. 3S Benchmark test results of four functions for 50 times: (A) number of trials required to find the solutions of the four functions using DE algorithm and the exhaustive algorithm (Rand). Differential evolution (DE) solved the problems within only 58 ± 11, 53 ± 11, 131 ± 103 and 90 ± 46 trials for the four functions; (B) minimum value found by both algorithms in 60 trials; With DE, the minimum values were 0.42 ± 0.61, 0.38 ± 0.57, 25.48 ± 43.38, and 0.31 ± 0.23, and out of the 50 runs, there were 32, 33, 22, and 11 runs, that the minimum value 0 was found in 60 trials for the four functions, respectively.

  1. Supplementary Material