Modelling biochemical networks with intrinsic time delays: a hybrid semi-parametric approach

von Stosch, Moritz; Peres, Joana; de Azevedo, Sebastião Feyo; Oliveira, Rui

doi:10.1186/1752-0509-4-131

BMC Systems Biology

Table 3 Results for Case Study II

From: Modelling biochemical networks with intrinsic time delays: a hybrid semi-parametric approach

NN	Nlag	τ	BIC			MSE			NN	Nlag	τ	BIC			MSE
			train	valid	test	train	valid	test				train	valid	test	train	valid	test
3	0	0	-18561	-5147	-5000	0.0155	0.0187	0.0157	6	0	0	-18500	-5199	-5030	0.0148	0.0187	0.0154
4	0	0	-18514	-5164	-4994	0.0155	0.0187	0.0150	7	0	0	-18576	-5197	-4990	0.0153	0.0180	0.0144
5	0	0	-18531	-5186	-5011	0.0151	0.0189	0.0153	8	0	0	-18430	-5211	-5053	0.0146	0.0182	0.0158
2	1	2	-17144	-4697	-4475	0.0086	0.0098	0.0065	2	1	2.5	-16343	-4293	-4331	0.0077	0.0076	0.0067
3	1	2	-16981	-4588	-4470	0.0085	0.0108	0.0067	3	1	2.5	-17230	-4725	-4584	0.0186	0.0327	0.0183
4	1	2	-16877	-4581	-4484	0.0087	0.0117	0.0072	4	1	2.5	-16635	-4506	-4690	0.0154	0.0220	0.0170
5	1	2	-16792	-4544	-4490	0.0078	0.0093	0.0064	5	1	2.5	-16927	-4614	-4524	0.0086	0.0111	0.0072
6	1	2	-16911	-4643	-4544	0.0087	0.0119	0.0073	6	1	2.5	-16944	-4523	-4488	0.0082	0.0092	0.0066
7	1	2	-17197	-4632	-4505	0.0097	0.0151	0.0084	7	1	2.5	-17044	-4742	-4608	0.0082	0.0107	0.0075
8	1	2	-17181	-4530	-4496	0.0123	0.0155	0.0105	8	1	2.5	-16976	-4694	-4608	0.0084	0.0110	0.0076
2	2	2	-16466	-4512	-4525	0.0067	0.0079	0.0067	2	2	2.5	-17813	-4833	-4759	0.0130	0.0152	0.0129
3	2	2	-16856	-4656	-4535	0.0081	0.0116	0.0073	3	2	2.5	-16637	-4684	-4595	0.0079	0.0123	0.0079
4	2	2	-16788	-4616	-4525	0.0079	0.0111	0.0072	4	2	2.5	-16703	-4507	-4517	0.0073	0.0083	0.0064
5	2	2	-16734	-4430	-4446	0.0075	0.0088	0.0061	5	2	2.5	-16384	-4327	-4404	0.0068	0.0074	0.0063
6	2	2	-16573	-4271	-4353	0.0077	0.0081	0.0065	6	2	2.5	-16601	-4400	-4432	0.0071	0.0079	0.0062
7	2	2	-16704	-4569	-4541	0.0071	0.0089	0.0065	7	2	2.5	-16569	-4405	-4466	0.0068	0.0072	0.0061
8	2	2	-16921	-4728	-4632	0.0082	0.0132	0.0079	8	2	2.5	-16833	-4790	-4664	0.0080	0.0127	0.0079
2	3	2	-19006	-5136	-5080	0.0181	0.0177	0.0158	2	3	2.5	-16619	-4566	-4514	0.0077	0.0099	0.0071
3	3	2	-16811	-4692	-4549	0.0078	0.0119	0.0073	3	3	2.5	-16037	-4218	-4259	0.0064	0.0072	0.0058
4	3	2	-16737	-4474	-4466	0.0069	0.0089	0.0063	4	3	2.5	-16439	-4224	-4287	0.0068	0.0078	0.0057
5	3	2	-16519	-4357	-4408	0.0066	0.0076	0.0058	5	3	2.5	-16199	-4358	-4295	0.0063	0.0076	0.0056
6	3	2	-16832	-4506	-4415	0.0090	0.0107	0.0078	6	3	2.5	-16604	-4577	-4556	0.0072	0.0094	0.0067
7	3	2	-16565	-4385	-4439	0.0066	0.0072	0.0058	7	3	2.5	-16344	-4475	-4432	0.0064	0.0078	0.0060
8	3	2	-16758	-4672	-4569	0.0079	0.0117	0.0069	8	3	2.5	-16471	-4374	-4505	0.0066	0.0069	0.0061
2	4	2	-16655	-4365	-4504	0.0071	0.0107	0.0077	2	4	2.5	-16562	-4532	-4503	0.0079	0.0097	0.0073
3	4	2	-16377	-4301	-4431	0.0067	0.0078	0.0064	3	4	2.5	-16325	-4471	-4470	0.0072	0.0086	0.0066
4	4	2	-16215	-4183	-4316	0.0062	0.0067	0.0057	4	4	2.5	-16261	-4189	-4281	0.0064	0.0068	0.0058
5	4	2	-16611	-4481	-4484	0.0070	0.0101	0.0066	5	4	2.5	-15954	-4190	-4255	0.0056	0.0060	0.0052
6	4	2	-17503	-4762	-4597	0.0189	0.0374	0.0197	6	4	2.5	-16439	-4334	-4476	0.0064	0.0073	0.0060
7	4	2	-25835	-7171	-7226	10.160	9.2368	11.843	7	4	2.5	-25949	-7288	-7280	13.781	19.040	17.824
8	4	2	-16256	-4328	-4369	0.0058	0.0061	0.0052	8	4	2.5	-16296	-4326	-4381	0.0061	0.0065	0.0054

Results of the performance measures, BIC and MSE, over structure parameters, namely Numbers of Nodes in the hidden layer of the ANN, NN, Number of time lags, Nlag and the time lag, τ, for Pichia pastoris cells with distributed time delays using the structure of Fig. 4B. Integration of material balances along with the equations obtained from the sensitivity method is carried out using the linear approximation integration schema described in the Methods section. The times series were chosen such that one of the delays matched the maximum of the time delay of the weighting function of the simulation case (see Eqs. A 12).

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