Basic mevalonate pathway model with limonene synthesis: Construction and Ensemble analysis

This model serves as the preliminary MVA pathway framework that we have used as the foundation to debug and design improved MVA models. Although basic, this model was able to provide useful insights into the control of the MVA pathway and suggests strategies for possible engineering. The ensemble analysis carried out for this model have generated a total 8 model generations that have shown a significant improvement in their model scores after each reiteration. A step-by-step ensemble analysis that included scoring the models based on experimental data and identifying influential parameters have found that the proteins that are influential to the pathway are LIMS, MDC, GPPS and IDI. The analysis was also able to shed light on product inhibitions in the pathway that would influence the production of limonene, and also suggests an possible topological engineering design that could accelerate the pathway even more.

The simulation

Fig. 1: Overview of the basic MVA model simulation

Fig. 2: (Top) Plasmid used in our experiment, and (bottom) plasmid used in Weaver et. al. Right plot shows the measured OD readings in our experiment, with induction at timepoint 0 when cell cultures reached OD=0.75

Experiment

This simulation is based on an experiment on the DH10B strain of E. coli cell cultures that produces limonene that are sequestered into an organic layer. Brief description of the experimental method is as follows:

• • -The DH10B strain of E. coli was transformed with the limonene production plasmid pJBEI6410.
  • -Three 60 ml cultures (A, B and C), inoculated from individual colonies, were grown in flasks at 30 oC in a shaker incubator.
• -When cultures reached OD600 of 0.75 they were split into multiple 5 ml aliquots and 1 ml of dodecane overlay was added (timepoint zero). At this point some samples were Induced by the addition of IPTG (25 uM final concentration), other samples were left Uninduced. In addition controls were set-up with limonene added (500 ug/L) to one aliquot of each culture.
• -All cultures were then incubated at 30 oC in a shaker incubator until the designated timepoints.
• -At each timepoint (0, 2, 4, 8, 24 hr) samples were removed, OD600 was measured, the dodecane overlay was recovered for limonene quantification, and total RNA was prepared (but no RNAseq was performed on the 24hr samples as RNA quality was too low). The limonene control samples were analysed only at the 8 hr timepoint. The protein fraction of each sample was recovered and stored at -80oC.
• -The total RNA samples were treated to deplete ribosomal RNA (rRNA) and RNA integrity (RIN values) were determined for each sample prior to sending them for RNAseq

In silico simulation

To simulate the experiment described above, the model was simulated for 72 hours and E. coli was grown until OD_{600}= 5. For each model generation (iteration) 5000 ensemble models were generated, which means for each iteration, 5000 values were sampled from each distribution to describe the ensemble models. The concentration for input metabolites such as Acetyl coA along with the reductants (NADP, NADPH) and energy metabolites (ATP, ADP) were made constant in the model. The values for these concentrations were based on measured absolute concentrations in E. coli from (ref1=Park2006). The enzyme concentration in this model is also fixed, with the concentration values based on measured intercellular concentrations from (ref2=Weaver 2015). In that study, intercellular concentrations of enzymes of the bottom mevalonate pathway with amorphadiene (A different type of terpene) synthesis were measured, and these genes were from pbMIS plasmid that uses a the pTrc promoter for all of its bottom mevalonate pathway genes. This differs that what is used in our experiment in two ways: 1) We study limonene synthesis instead of amorphadiene; and 2) Our experiment used pjBEI-6410 plasmid that used pLac promoter for the upstream pathway genes, pTrc promoter for the bottom mevalonate pathway genes including for limonene synthesis ( Fig. 2). Therefore, there is a high level of uncertainty for the concentrations used for the enzymes in the pathway, especially for LIMS and GPPS (Fig. 1).

Parameters

Determining growth curve parameters

Fig. 3: Growth curve parameters were predicted from using the logistic equation. Table shows the initial and predicted parameters from this fitting

To identify the growth curve parameters required to simulate the cell growth, we’ve fitted the experimental OD₆₀₀ readings onto a logistic growth curve (Fig. 3). We have tried to fit with a more complex Baranyi (ref) growth with a lag-phase. Doing so gave a better fit however a test using Akaike Information Criterion (AIC) indicates that a less complex model is better; so we chose to proceed using this logistic growth curve to model the MVA pathway.

Kinetic parameters

Fig. 4: Heterologous mevalonate pathway with limonene synthesis with the source of genes highlighted in blue. The gene source is based on the genes in plasmid pjBEI-6410 (ref)

In this model, there is a total of 65 parameters. Table below lists the Mode, CI factor, mu and sigma used to generate the prior lognormal distributions used for its ensemble models.

index	Reaction	Parameter	Mode	CI	mu	sigma
1	AACT	Keq_AACT	7.80E-06	5.4983	-10.8582	0.6059
2	AACT	Km_acoa_AACT	333.3936	8.5216	6.522	0.8442
3	AACT	Km_aacoa_AACT	26.4941	7.0054	3.8928	0.7848
4	AACT	Km_coa_AACT	17.868	8.0717	3.5685	0.828
5	AACT	Kcat_AACT	5.21E+03	41.8813	10.1562	1.2642
6	HMGS	Keq_HMGS	6.27E+06	1.08E+02	17.8363	1.4783
7	HMGS	Km_acoa_HMGS	16.8418	9.4143	3.587	0.8736
8	HMGS	Km_aacoa_HMGS	1.325	8.9642	1.0196	0.8592
9	HMGS	Km_hmgcoa_HMGS	16.8418	9.4143	3.587	0.8736
10	HMGS	Km_coa_HMGS	1.325	8.9642	1.0196	0.8592
11	HMGS	Kcat_HMGS	261.0095	4.1687	5.9424	0.6147
12	HMGR	Keq_HMGR	0.0189	7.98E+02	-0.4531	1.8745
13	HMGR	kcatF_HMGR	232.1936	2.7395	5.6588	0.4595
14	HMGR	kcatR_HMGR	232.1936	2.7395	5.6588	0.4595
15	HMGR	Km_hmgcoa_HMGR	11.6277	8.7446	3.179	0.8519
16	HMGR	Km_nadph_HMGR	54.5006	5.1882	4.4728	0.6889
17	HMGR	Km_mev_HMGR	667.918	4.9009	6.953	0.6699
18	HMGR	Km_coa_HMGR	384.006	5.7179	6.4699	0.7206
19	HMGR	Km_nadp_HMGR	578.749	4.9418	6.8134	0.6727
20	MK	Keq_MK	5.00E+03	5.65E+04	15.1185	2.5691
21	MK	Km_mev_MK	65.452	10.6482	5.0079	0.9092
22	MK	Km_atp_MK	362.6772	10.7217	6.7237	0.9112
23	MK	Km_mevp_MK	65.452	10.6482	5.0079	0.9092
24	MK	Km_adp_MK	362.6772	10.7217	6.7237	0.9112
25	MK	kcat_MK	1.81E+03	4.1609	7.8778	0.614
26	PMK	Keq_PMK	8.5501	2.1771	2.2798	0.3659
27	PMK	Km_mevp_PMK	25.393	3.6469	3.5563	0.5673
28	PMK	Km_atp_PMK	67.5286	2.6683	4.4143	0.4491
29	PMK	Km_mevpp_PMK	38.1145	3.3212	3.9247	0.533
30	PMK	Km_adp_PMK	53.2536	3.215	4.2464	0.5209
31	PMK	kcat_PMK	224.2657	2.8912	5.6437	0.4805
32	MDC	Keq_MDC	4.18E+04	4.5814	11.0602	0.6472
33	MDC	Km_mevpp_MDC	28.1891	5.1085	3.8064	0.6837
34	MDC	Km_atp_MDC	77.174	5.1482	4.8171	0.6863
35	MDC	Km_ipp_MDC	28.1891	5.1085	3.8064	0.6837
36	MDC	Km_adp_MDC	77.174	5.1482	4.8171	0.6863
37	MDC	Km_pi_MDC	77.174	5.1482	4.8171	0.6863
38	MDC	Km_co2_MDC	77.174	5.1482	4.8171	0.6863
39	MDC	kcatF_MDC	315.0646	2.0572	5.8695	0.3417
40	MDC	kcatR_MDC	315.0646	2.0572	5.8695	0.3417
41	IDI	Km_ipp_IDI	1.83E+01	7.57E+01	4.8659	1.4
42	IDI	Km_dmapp_IDI	1.62E+01	8.84E+00	3.5183	0.8551
43	IDI	Kcat_IDI	1.99E+03	5.18E+02	10.8126	1.794
44	IDI	Keq_IDI	0.4801	14.3967	1.0219	0.9934
45	GPPS	Km_dmapp_gpps	376.3912	7.8616	6.603	0.82
46	GPPS	Km_ipp_gpps	7.4096	8.4234	2.7096	0.8407
47	GPPS	Km_gpp_gpps	20.2782	6.4021	3.5821	0.7566
48	GPPS	Km_pp_gpps	20.2782	6.4021	3.5821	0.7566
49	GPPS	Kcat_gpps	80.9145	6.8878	5.001	0.7795
50	GPPS	Keq_GPPS	3.46E+09	1.80E+04	27.71	2.4
51	LIMS	Km_gpp_LIMS	376.3912	7.8616	3.1693	1.0857
52	LIMS	Km_lim_LIMS	376.3912	7.8616	3.1693	1.0857
53	LIMS	Km_pp_LIMS	376.3912	7.8616	3.1693	1.0857
54	LIMS	Kcat_LIMS	376.3912	7.8616	1.5742	1.0982
55	LIMS	Keq_LIMS	376.3912	7.8616	49.7827	1.9157
56	constant	m_coa	1370	15.4949	8.2494	1.0133
57	constant	m_ATP	9630	1.1842	9.1797	0.0842
58	constant	m_ADP	555	1.2692	6.333	0.1184
59	constant	m_NADP	2.86	15.6513	2.0831	1.016
60	constant	m_NADPH	121	1.1037	4.7982	0.0493
61	constant	m_pi	23900	1.25	10.0939	0.1109
62	constant	m_ppi	23900	1.25	10.0939	0.1109
63	constant	m_co2	75.2	1.2503	4.3325	0.111
64	constant	m_acoa	606	1.1454	15.6218	0.0677
65	diffusion rate	D	23900	1.25	21.2956	0.7565

Acknowledgements

Special thanks to Dr. Christopher Robinson from the SynBioChem Centre University of Manchester for carrying out the experiment and supplying all of the OD readings and limonene titers for this simulation.