Key Laboratory of Systems Biology, Shanghai Institutes for Biological Sciences (SIBS), Chinese Academy of Sciences (CAS), Shanghai, China

Shanghai Center for Bioinformatics Technology (SCBIT), Shanghai, China

Institute of Plant Physiology and Ecology, Shanghai Institutes for Biological Sciences (SIBS), Chinese Academy of Sciences (CAS), Shanghai, China

Abstract

Background

Comprehensive kinetic models of microbial metabolism can enhance the understanding of system dynamics and regulatory mechanisms, which is helpful in optimizing microbial production of industrial chemicals.

Results

We have developed an improved kinetic model featured with the incorporation of butyryl-phosphate, inclusion of net effects of complex metabolic regulations, and quantification of endogenous enzyme activity variations caused by these regulations. The simulation results of our model are more consistent with published experimental data than the previous model, especially in terms of reflecting the kinetics of butyryl-phosphate and butyrate. Through parameter perturbation analysis, it was found that butyrate kinase has large and positive influence on butanol production while CoA transferase has negative effect on butanol production, suggesting that butyrate kinase has more efficiency in converting butyrate to butanol than CoA transferase.

Conclusions

Our improved kinetic model of the ABE process has more capacity in approaching real circumstances, providing much more insight in the regulatory mechanisms and potential key points for optimization of solvent productions. Moreover, the modeling strategy can be extended to other biological processes.

Background

System modeling for metabolism of industrial microorganisms is important in metabolic engineering, as a comprehensive model can reveal relevant factors related to high yield of target products. Based on such analyses, system modeling can further enhance developing operation strategies, or help optimizing cultivation processes

The acetone-butanol-ethanol (ABE) pathway of

**The acetone-butanol-ethanol (ABE) pathway of C. acetobutylicum.** Reactions are represented by bold arrows and denoted by symbols from R1 to R21. The acidogenic reactions are R9 and R18 (catalyzed by PTA-AK and PTB-BK, respectively), generating acetate and butyrate respectively. The two acids are reassimilated through R7 and R17 (the reverse paths of R9 and R18), or directly converted to acetyl-CoA and butyryl-CoA through R8 and R15 (catalyzed by CoAT). The solventogenic reactions are R11, R16 and R19 (catalyzed by AAD, AADC and BDH, respectively), generating ethanol, acetate and butanol respectively. And R14 is a lumped reaction consisted of reactions catalyzed by BHBD, CRO and BCD

So far, multiple models have been established to simulate the ABE pathway, which mostly apply the metabolic flux analysis (MFA) and flux-balance analysis (FBA) approaches

To overcome the drawbacks of Shinto’s model, we developed an improved kinetic model for

Results

All the following results were based on our new model (Equation (1), section “Methods”), and they were compared with an experimental study (Zhao

Dynamical simulation

The initial value of our model was set according to the conditions described in the experiment by Zhao

Comparison of simulation results with the experimental observations of Zhao

**Comparison of simulation results with the experimental observations of Zhao et al.** A is the simulation results of BuP kinetics, in which data spots are concentrations and represented in blue. B is the experimental observation of BuP kinetics, in which data are concentrations and represented in black

In our simulation results, the first peak of BuP was shown to coincide with the onset of solvent production (Figure

Comparison of simualtion results of butyrate kinetics with Shinto’s model under Zhao

**Comparison of simualtion results of butyrate kinetics with Shinto’s model under Zhao et al’s conditions** A is the simulation results of butyrate kinetics based on our new model under Zhao

Perturbation analysis

Among the solvents (ethanol, acetone, butanol) produced in the ABE fermentation, butanol was considered to be the more valuable product, since it had advantageous properties over acetone and ethanol (e.g. better value for the heat of combustion)

**Results of single parameter perturbation tests with magnitude +5%.** The data entries included are numerical results obtained by increasing the value of every kinetic parameter by 5%. All parameters are traversed. There are 50 entries and the dataset is organized as a table in the format of *.xls (Excel worksheet). The first column is the index of the parameter perturbed, the second column is the parameter perturbed, and the third column is the

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**Results of single parameter perturbation tests with magnitude -5%.** The data entries included are numerical results obtained by decreasing the value of every kinetic parameter by 5%. All parameters are traversed. There are 50 entries and the dataset is organized as a table in the format of *.xls (Excel worksheet). The first column is the index, the second column is the parameter perturbed, and the third column is the

Click here for file

**Results of double parameter perturbation tests with respective magnitudes +5% and +5%.** The data entries included are numerical results obtained by increasing the values of every pair of kinetic parameters by 5% each. All 2-parameter combinations are traversed. There are 1225 entries and the dataset is organized as a table in the format of *.xls (Excel worksheet). The first column is the pair of indexes of the parameters perturbed, the second and third columns are the parameters perturbed, respectively, and the fourth column is the

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**Results of double parameter perturbation tests with respective magnitudes +5% and -5%.** The data entries included are numerical results obtained by altering the values of every pair of kinetic parameters, increasing the first parameter by 5% and decreasing the other one by 5%. All 2-parameter combinations are traversed. There are 1225 entries and the dataset is organized as a table in the format of *.xls (Excel worksheet). The first column is the pair of indexes of the parameters perturbed, the second and third columns are the parameters perturbed, respectively, and the fourth column is the

Click here for file

**Results of double parameter perturbation tests with respective magnitudes -5% and +5%.** The data entries included are numerical results obtained by altering the values of every pair of kinetic parameters, decreasing the first parameter by 5% and increasing the other one by 5%. All 2-parameter combinations are traversed. There are 1225 entries and the dataset is organized as a table in the format of *.xls (Excel worksheet). The first column is the pair of indexes of the parameters perturbed, the second and third columns are the parameters perturbed, respectively, and the fourth column is the

Click here for file

**Results of double parameter perturbation tests with respective magnitudes -5% and -5%.** The data entries included are numerical results obtained by decreasing the values of every pair of kinetic parameters by 5% each. All 2-parameter combinations are traversed. There are 1225 entries and the dataset is organized as a table in the format of *.xls (Excel worksheet). The first column is the pair of indexes of the parameters perturbed, the second and third columns are the parameters perturbed, respectively, and the fourth column is the

Click here for file

Part of the results of single parameter perturbation analysis.

P +5%

P -5%

P

Enz

Rd

P

Enz

Rd

Vmax19

BDH

0.0076

Vmax19

BDH

-0.0082

Vmax17

BK

0.0061

Vmax17

BK

-0.0063

Vmax18

PTB

-0.006

Vmax18

PTB

0.0063

Vmax14

B-C-B

0.0076

Vmax14

B-C-B

-0.0082

Vmax11

AAD

-0.0003

Vmax11

AAD

0.0003

Vmax7

AK

0.0054

Vmax7

AK

-0.0054

Vmax9

PTA

-0.0012

Vmax9

PTA

0.0012

Vmax15

CoAT^{a}

-0.0072

Vmax15

CoAT

0.0074

Vmax8

CoAT^{b}

-0.0002

Vmax8

CoAT

0.0002

Vmax1

PTS

0.0088

Vmax1

PTS

-0.0088

This table lists part of the results of perturbation tests on single kinetic parameters. Here “P” denotes the parameter perturbed. “Enz” denotes the corresponding enzyme. “+/- 5%” indicates up/down-shifting the parameter value by 5%. “B-C-B” stands for enzyme series BHBD-CRO-BCD. Subscripts “a” and “b” indicate there are 2 CoA transferases catalyzing R8 and R15 and here we took them in uniform.

Part of the results of double parameter perturbation analysis

P1+5%, P2+5%

P1-5%, P2-5%

P1

Enz1

P2

Enz2

Rd

P1

Enz1

P2

Enz2

Rd

Vmax14

B-C-B

Vmax19

BDH

0.0153

Vmax14

B-C-B

Vmax19

BDH

-0.0163

Vmax14

B-C-B

Vmax17

BK

0.0138

Vmax14

B-C-B

Vmax17

BK

-0.0145

Vmax15

CoAT

Vmax17

BK

-0.001

Vmax15

CoAT

Vmax17

BK

0.001

Vmax17

BK

Vmax19

BDH

0.0137

Vmax17

BK

Vmax19

BDH

-0.0146

Vmax18

PTB

Vmax19

BDH

0.0016

Vmax18

PTB

Vmax19

BDH

-0.0018

Vmax7

AK

Vmax8

CoAT

0.0053

Vmax7

AK

Vmax8

CoAT

-0.0053

Vmax9

PTA

Vmax11

AAD

-0.0014

Vmax9

PTA

Vmax11

AAD

0.0014

Vmax1

PTS

Vmax14

B-C-B

0.0163

Vmax1

PTS

Vmax14

B-C-B

-0.0171

Vmax1

PTS

Vmax19

BDH

0.0163

Vmax1

PTS

Vmax19

BDH

-0.0172

P1+5%, P2-5%

P1-5%, P2+5%

P1

Enz1

P2

Enz2

Rd

P1

Enz1

P2

Enz2

Rd

Vmax14

B-C-B

Vmax19

BDH

-0.0007

Vmax14

B-C-B

Vmax19

BDH

-0.0007

Vmax14

B-C-B

Vmax17

BK

0.0012

Vmax14

B-C-B

Vmax17

BK

-0.002

Vmax15

CoAT

Vmax17

BK

-0.0135

Vmax15

CoAT

Vmax17

BK

0.0136

Vmax17

BK

Vmax19

BDH

-0.0021

Vmax17

BK

Vmax19

BDH

0.0012

Vmax18

PTB

Vmax19

BDH

-0.0143

Vmax18

PTB

Vmax19

BDH

0.0138

Vmax7

AK

Vmax8

CoAT

0.0057

Vmax7

AK

Vmax8

CoAT

-0.0056

Vmax9

PTA

Vmax11

AAD

-0.0009

Vmax9

PTA

Vmax11

AAD

0.0009

Vmax1

PTS

Vmax14

B-C-B

0.0008

Vmax1

PTS

Vmax14

B-C-B

-0.0012

Vmax1

PTS

Vmax19

BDH

0.0008

Vmax1

PTS

Vmax19

BDH

-0.0011

This table lists part of the results of perturbation tests on double parameter pairs. Here “P1” and “P2” denote the parameters perturbed. “Enz1” and “Enz2” denote the corresponding enzymes. “+/- 5%” and “B-C-B” stand for the same meaning as in Table

Among all results, there were several interesting ones that might provide some insights for understanding the ABE process. Before examining the results, we could intuitively hypothesize that BK might be relatively important in solventogensis since it connected two important metabolites butyrate and BuP. Based on the analyses, we indeed found that shifting BK’s _{max}_{max}_{max}

Also, our computation results showed that CoAT, which also accepted butyrate as substrate, had a negative effect on butanol production as up-shifting its catalytic capacity (increasing _{max}_{m}_{max}_{m}_{max}_{m}

Illustration of the influences on butanol production originated from BK, CoAT and AK.

**Illustration of the influences on butanol production originated from BK, CoAT and AK.** The influence originated from BK is positive effect on butanol production, as indicated by the green arrow in the same direction with that of butanol production. The influence originated from CoAT is negative effect on butanol production, as indicated by the red arrow in the opposite direction with that of butanol production. The influence originated from AK is also positive effect on butanol production, but with a smaller magnitude than that of BK. It’s indicated by the blue arrow in the same direction with that of butanol production.

There were some places where our new model’s predictions differed from those of Shinto’s model. For instance, our model predicted that PTS had positive influence on butanol production, as increasing its _{max}_{m}

Discussion

Rational system modeling and comprehensive system analysis can serve as prior guidelines for understanding and deducing biological mechanisms. We can retrieve quantitative knowledge for assessing an organism’s metabolic capacity and use this knowledge for in-lab experiments to develop new strains with advantageous productivity

Model improvements

Since many studies related to

First, we have incorporated the key metabolite BuP, reflecting the relevant biological events that are specific to ABE kinetics

Second, we describe the regulatory effects of complex factors using a time division pattern. In Shinto’s model, the metabolic regulation beyond the level of substrate/product inhibition/activation is simply defined as the input of glucose. The shut-downs of several acidogenic/solventogenic enzymes (like PTB, BDH, etc) are solely due to the insufficiency of glucose. However, various evidences indicate that even with sufficient supply of glucose, the acidogenic enzymes are still shut down in the solventogenic phase, and the solventogenic enzymes are necessarily inactivated at the beginning of the acidogenic phase

Third, we introduce the “enzyme activity coefficient (EAC)” to quantify endogenous enzyme activity variations caused by metabolic regulations (see section “Methods” for EAC’s definition). For the quantification of enzyme activity curves, numerical interpolation (e.g. Lagrange, Legendre, etc.) should have been employed as to obtain fully continuous functions. But measurements in activity assays are usually not precise. If the errors are large, interpolation may result in huge errors or mistakes, causing the trouble of overfitting and distorting the original curve profile. On the contrary, the computation of EAC leaves the error just as the original error. Hence, using EAC will at least not amplify the error or distort the curve when the measurements are not precise. Moreover, our design of EAC is calculating a ratio instead of the particular value at each time instance, and this allows the error to be divided by a denominator, thus lowering the error level in computation.

Dynamical simulation and perturbation analysis

After the addition of BuP, 5 unknown parameters are introduced into the system. We have used Genetic Algorithm to estimate their values. In the process of parameter estimation, we used Shinto’s experimental observations of 16 metabolites to formulate the fitness function, but we didn’t employ any information about BuP. And in order to avoid the mistake of reasoning in a circle, we compare our results with observations of another experiment (Zhao

Simulations based on kinetic models can help develop in-lab strategies, thus increasing the success rate of metabolic engineering. In our work, we have simulated thousands of perturbed conditions to detect and assess potential spots that have large influences on butanol production. The magnitude of _{max}

In double parameter perturbation tests, we noticed that the net effect of combinatorial perturbation was equal to the sum of effects of individual perturbations, indicating that no crossover or nonlinear amplification originated from perturbations with mild magnitudes. This is probably because when the system is undergoing mild perturbation, it tries to maintain the normal status with minor alterations by means of system robustness. To demonstrate the hypothesis further, we implemented some three-parameter combinatorial perturbation tests. We randomly chose a number of three-parameter triplets and randomly decided their shift directions. For example, if we increased three parameters _{max14}, _{max19}, _{max17} by 5% each and re-computed our model (Equation (1)), we obtained _{m15b} and _{max19} by 5% and decreased _{max18} by 5%, we obtained

Significance

Traditional kinetic models cannot accommodate complex metabolic regulation effects (e.g. gene transcriptional control). Hence previous integrative modeling approaches for metabolic system are mainly based on the FBA method, in which the gene transcription regulations are described by Boolean logic and the metabolic level is expressed by flux balance equations. Since FBA based methods and Boolean logic cannot adequately reflect system dynamics, we have developed a new model as an attempt towards solving the problem. Actually, our modeling strategy is equivalent to extending the traditional BST, degenerating complex metabolic regulation effects to a form that is compatible with kinetic models. This strategy provides a way for integrating complex factors and knowledge from multiple levels into the framework of kinetic models. Moreover, our approach of describing metabolic regulation effects with a time division pattern and EAC is extendable. For instance, we can relate the enzyme activities to gene transcriptional level, build a formulism between them, and include the effects of other factors such as impulse and stochasticity. Our modeling method can be generalized and extended to the modeling of other bio-processes.

In this post-genomic era, massive information and experimental data have been accumulated. Therefore, it is important to develop methods or tools that are able to make use of existed information/data and capable of organizing, manipulating and interpreting them more comprehensively

Conclusions

We have developed a new kinetic model featured with major improvements over the previous one (Shinto’s model), with the information of BuP incorporated and the effects of complex metabolic regulatory factors included. The simulation results based on our model are highly consistent with published experimental data and have more superiority in precision and subtlety than the previous model. We have successfully simulated the right profile of BuP kinetics, which is not included in the previous model. And we can make more precise prediction on the kinetics of butyrate, another important intermediate in the ABE process. Through perturbation analysis, we predict that the path catalyzed by BK is more efficient over the one catalyzed by CoAT in converting butyrate to butanol during solventogenesis, although ATPs are consumed.

Methods

We made improvements to Shinto’s model with respect to three points: (i) incorporating key compound butyryl-phosphate (BuP); (ii) describing the net effects of complex ABE metabolic regulations with a time division pattern according to endogenous enzyme activity variations, and (iii) introducing the “enzyme activity coefficient” to quantify endogenous enzyme activity variations. After the model framework was established, parameter estimation was followed to obtain unknown parameter values. We then implemented perturbation analysis to detect sensitivities of reactions/enzymes.

Incorporating BuP

BuP was key intermediate in conversions between butyrate (But) and butyryl-CoA (BCoA). It was reported that BuP played a crucial role in solventogenesis, as the initial peak of its concentration marked the onset of solvent production

Time division pattern

We assumed endogenous enzyme activity variations were net effects of transcriptional control and other complex factors. As experimental studies suggested enzyme activities varied with time

Enzyme activity coefficient

We introduced EAC to quantify endogenous enzyme activity variations. EACs were formulated as time-dependent functions. At each time instance, the EAC value was the ratio of the current enzyme activity to its maximum activity. Here we employed the divided intervals in the time division pattern (see the previous paragraph) as markers of time. And for computation simplicity, we approximated EAC with a set of 0^{th} splines with respect to these markers. In other word, the EAC value remained constant within a divided interval and changed to another constant when stepping into another interval. The constant was the ratio of the average activity level in the interval to the maximum activity. We calculated all EACs of the considered enzymes and multiplied them to their corresponding rate equations to reflect endogenous activity variations. All enzyme activities data were collected from literatures

New Model

The new model contained 21 rate equations and 17 differential equations, involving 50 kinetic parameters. The model was built by integrating ABE kinetic features identified so far. Except for those included in Shinto’s model

where ** Y** was the vector of metabolites’ concentrations;

Unknown parameter estimation

We applied Genetic Algorithm (GA) to ** Y**(1:16) to match Shinto’s observations

**The values of kinetic parameters** There are 50 parameters in our kinetic model. The dataset is organized as a table in the format of *.xls (Excel worksheet). The first column contains the indexes of reactions, the second column contains the parameters involved in each reaction, and the third column contains the parameter values.

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**Description of the modeling method** This is the detailed description of the method of modeling, including the incorporation of BuP, the construction of time division pattern, the computation of EACs, parameter estimation procedure, and the computation of perturbation analysis. This file is in the format of * (Word document). This file contains 4 supplementary figures (Figure S1 - S4) and a supplementary table (Table S1).

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Perturbation analysis

We performed perturbation analysis to assess enzymes/reactions’ impacts on butanol production. By consecutively shifting the enzymes’ _{max}_{m}

where ** y** was the instantaneous butanol concentration in perturbed state, and

List of abbreviations

PTS: phosphotransferase system; AK: acetate kinase; PTA: phosphotransacetylase; CoAT: CoA transferase; AAD: alcohol/ aldehyde dehydrogenase; BHBD: β-hydroxybutyryl-CoA dehydrogenase; CRO: crotonase; BK: butyrate kinase; PTB: phosphotransbutyrylase; BDH: butanol dehydrogenase; BCD: butyryl-CoA dehydrogenase; AADC: acetoacetate decarboxylase; THL: thiolase

Competing interests

The authors declare that they have no competing interests.

Authors' contributions

Building the kinetic model: RDL and CR. Designing and performing numerical experiments: RDL and LYL. Data acquisition and analysis: RDL. Conceiving and designing the research: YYL, LL, YXL. Drafting the manuscript: RDL, YYL, LL.

Acknowledgements

This work was supported by National High-Tech R&D Program (863) (2007AA02Z330, 2007AA02Z331, 2007AA02Z332), National Basic Research Program of China (973) (2006CB0D1203, 2007CB707803), National Natural Science Foundation of China (30770497) and the Shanghai Commission of Science and Technology (08JC1416600, 08ZR1415800).

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