Least-squares methods for identifying biochemical regulatory networks from noisy measurements

BMC Bioinformatics

Table 4 p53 and mdm2 mRNA expression model: white noise with neglected kinetics

Samplings per Experiment	Algorithms	ε _M		ε _S		ε _F
		Mean	STD	Mean	STD	Mean	STD
4	LS	1.34	0.34	1.01	0.14	0.04	0.01
	TLS	1.34	0.34	1.01	0.14	0.04	0.01
	CTLS	1.34	0.34	1.01	0.14	0.04	0.01
8	LS	0.95	0.27	0.50	0.02	0.03	0.01
	TLS	25.03	196.73	1.01	0.15	1.06	8.42
	CTLS	0.44	0.12	0.50	0.00	0.02	0.00
12	LS	0.61	0.08	0.50	0.00	0.02	0.00
	TLS	47.53	241.86	0.92	0.31	2.49	13.07
	CTLS	0.49	0.06	0.50	0.02	0.02	0.00
16	LS	0.44	0.06	0.50	0.00	0.02	0.00
	TLS	50.96	833.28	1.02	0.20	3.11	50.06
	CTLS	0.49	0.05	0.50	0.02	0.02	0.00

The table shows the error comparisons in terms of the mean and the standard deviation (STD) for different number of data for each method based on 1000 Monte-Carlo Simulations. The measurements are taken every 2 hours and the states converge to steady states around the 16-th sample. ε_Mis the sum of two tems, i.e (1/N₁) Σ |α_{i j}| and (1/N₂) Σ |β_{i j}|, where α_{i j}and β_{i j}are the relative magnitude errors in the non-zero and zero elements of the true Jacobian, respectively, and N₁ and N₂ are the number of non-zero and zero elements in the true Jacobian, respectively. ε_Sis given by (1/n²) Σ |sign ( $\hat{f}$ _{i j}) - sign (f_{i j})|, i.e. the average sign differences, where $\hat{f}$ _{i j}and f_{i j}are the (i-th row, j-th column) elements of the estimated and the true Jacobian, respectively. ε_Fis the Frobenius norm of the difference between the estimated and the true Jacobian, i.e. || $\hat{F}$ - F||_F.

ISSN: 1471-2105