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  <cit> .
c. acetobutylicum is an extensively studied organism used for industrial-scale production of important solvents acetone and butanol, through the acetone-butanol-ethanol  pathway   <cit> .
the abe pathway of c. acetobutylicum comprises two distinct branches: acidogenesis and solventogenesis.
during acidogenesis, cells grow exponentially, acetate and butyrate are vigorously produced and the solvents  are not obviously generated.
while shifting to solventogenesis, the cells arrest their growth at stationary phase, solvents are produced and acids are reassimilated  <cit> .
so far, multiple models have been established to simulate the abe pathway, which mostly apply the metabolic flux analysis  and flux-balance analysis  approaches  <cit> .
although stoichiometric models can simulate the overall flux distributions based on limited kinetic data by using physicochemical constraints, they cannot appropriately reflect the dynamics in real-time scale.
in contrast, kinetics models integrated with biochemical information are more efficient in reflecting system dynamics.
by perturbing a kinetic model, system states that deviate from the normal state can be simulated and it is possible to reveal which reactions have potential impacts on target products’ productions.
to date, many experiments have explored the kinetic features of the abe process of c. acetobutylicum <cit>  and a kinetic model was recently developed by shinto et al.
<cit> .
however, as most current models did, this model did not integrate the metabolic regulatory effects of transcriptional control and other complex factors  <cit> .
moreover, shinto’s model did not include the information of some key metabolites, e.g.
butyryl-phoshate , which has proved to be important in solventogensis  <cit> .
to overcome the drawbacks of shinto’s model, we developed an improved kinetic model for c. acetobutylicum abe process.
the simulation results based on our model were consistent with published experimental observations and more comprehensive than those of shinto’s model.
furthermore, a series of perturbed circumstances were simulated as well, getting results which might provide insights for metabolic engineering aiming at increasing solvent productivity.
RESULTS
all the following results were based on our new model , section “methods”), and they were compared with an experimental study  that was independent of shinto’s model or our work.
the new model was established by integrating experimental information and knowledge not included in shinto’s model , and we applied some optimization methods to fix the unknown parameters introduced by integrating these information and knowledge.
the parameter fitting was done only under the conditions described in shinto’s work, only with respect to the metabolites contained in shinto’s model, and we didn’t use any information related to bup or the experimental study for comparison .
after these parameter values were derived, we first implemented dynamic simulation with respect to the conditions in zhao et al.’s work and compared the results with experimental observations.
we then carried out perturbation analysis to detect which reactions had large impacts on the overall butanol production in the system.
dynamical simulation
the initial value of our model was set according to the conditions described in the experiment by zhao et al.
<cit> , and the simulation results of metabolites’ kinetic profiles were shown in figure 2a and 2c.
since our model parameters were fitted under shinto’s experiment conditions, the metabolites’ kinetic profiles were naturally consistent with those in shinto’s experiment when shinto’s conditions were substituted in.
so the comparison with shinto’s experiment was not shown and we only focused on comparing with zhao et al.’s experiment here.
these simulation results were shown to be quite consistent with experimental observations .
the metric units in figure 2a and 2b were different , since the measurement of bup in zhao et al’s experiment accepted the unit of pmol/gdw.
it was impossible to exactly know the conversion between mm and pmol/gdw because there was no such relationship established in the si metric unit system.
but the quantity scale could be approximated given the size of an ordinary c. acetobutylicum cell, and this scale was consistent with that in our simulation results.
since bacteria cells might vary in their sizes, we could not give a general estimation that could represent all the others, so we just showed the original quantities on the vertical axis in figure 2b.
in our simulation results, the first peak of bup was shown to coincide with the onset of solvent production .
this was a phenomenon that was reported in experimental literatures and had biological implications  <cit> .
besides bup, we also demonstrated that we had a more precise simulation on butyrate, one crucial product in cell growth and solvent production  <cit>  .
in shinto’s model, when substituting in zhao et al.’s conditions, the quantity scale of butyrate curve  didn’t resemble precisely with the experimental curve in zhao et al.’s experiment .
this further demonstrated that our model had more capability in approaching real biological events.
perturbation analysis
among the solvents  produced in the abe fermentation, butanol was considered to be the more valuable product, since it had advantageous properties over acetone and ethanol   <cit> .
so we implemented a series of perturbation analyses to assess which enzymes/reactions had relatively large impacts on butanol production.
here we used rd values to measure the impacts .
we carried out perturbation tests both on single parameters and double parameter pairs, the magnitude was 5% and shift directions  were considered.
we traversed the entire parameter set.
the result set of single parameter perturbations included  entries .
and the result set of double parameter perturbations included  entries .
here table  <dig> and  <dig> showed some results with respect to the enzymes located on or close to acidogenic/solventogenic reactions in single and double parameter perturbations, respectively.
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  <dig> coa transferases catalyzing r <dig> and r <dig> and here we took them in uniform.
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  <dig>
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 vmax alone or in combination with other enzyme parameters  resulted in relatively large influences on butanol production .
actually, bk activity had positive effect on butanol production and the change in butanol quantity caused by shifting bk’s vmax ranked the 5th in the profile of single parameter shifts .
this suggested that bk, which coupled ptb to generate butyrate as well as catalyzing butyrate reassimilation, was important to butanol production as compared with other enzymes such as aad .
besides, ak also had positive effect on butanol production , indicating acetate reassimilation had similar influence as butyrate reassimilation in solventogenesis, but with less magnitude.
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  diminished butanol quantity .
because up-shifting the catalytic capacity of bk  or down-shifting the catalytic capacity of coat  would cause more butyrate molecules received by bk and the reverse operations would cause more butyrate received by coat, and given the fact that bk and coat both accepted butyrate as substrate, we could see that if more butyrate was received by bk, the butanol production would increase, i.e.
more butyrate molecules were converted and acid reassimilation was more efficient; and if more butyrate was received by coat, the situation would be on the contrary .
therefore we could conclude that bk had more efficiency than coat during acid reassimilation and solventogenesis.
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 vmax  resulted in amplified rd value.
while by shinto’s model, pts’s influence was negative.
given the fact that pts acted in nutrient uptake and many processes relating to the abe pathway were subjected to nutrient induction, our prediction might be more intuitively consistent with common sense  <cit> .
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  <cit> , or optimizing the cultivation process of existing strains  <cit> .
model improvements
since many studies related to c. acetobutylicum abe pathway have been reported , kinetic modeling of the abe pathway becomes feasible and enables us to simulate the system dynamics.
nevertheless, the previous kinetic model of c. acetobutylicum abe process  has several drawbacks as described in earlier context.
to overcome these drawbacks, we have established a new model featured with three improvements over the previous one.
first, we have incorporated the key metabolite bup, reflecting the relevant biological events that are specific to abe kinetics  <cit> .
the correspondence between bup concentration climax and solventogenesis onset is not merely a natural consequence of the fact that bup is the intermediate between butyryl-coa and butyrate.
there are implications on the genetic level as stated in zhao et al’s study  <cit> .
there are many important solventogenic genes, such as adhe <dig> , adhe <dig> , ctfa , ctfb , adc , bdha , bdhb , etc., having expression profiles that show a strictly correlated pattern with the kinetics of bup.
although the detailed mechanism of how bup acts to regulate abe process has not been very clear yet, its functional importance has been experimentally confirmed  <cit> .
our new model accounts for this knowledge and is successful in representing the phenomenon.
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  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  <cit> .
therefore, the metabolic regulations are not of the simple pattern as shinto suggested, but a significant 2-phase mode is shown .
in our work, this mode is approximated by considering endogenous enzyme activity variations, assuming enzymes are regulated by many factors  to exhibit different activity levels to fulfill conditional system requirements of different periods.
this assumption is equivalent to extending the application of biochemical system theory .
in bst, which is based on in vitro experiments, enzyme concentrations and endogenous enzyme activity levels are constant by default.
hence kinetic models based on bst are rigorously suitable for chemical simulations but may not entirely appropriate for in vivo conditions.
under in vivo conditions, the rate of a reaction does not solely depend on substrate/product concentrations, because the endogenous enzyme activity itself is regulated by many factors and its variation in turn affects the reaction rate  <cit> .
our model divides time into a set of periods according to the enzymes’ activity variations, allowing enzyme activities to vary throughout these periods.
third, we introduce the “enzyme activity coefficient ” to quantify endogenous enzyme activity variations caused by metabolic regulations .
for the quantification of enzyme activity curves, numerical interpolation  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,  <dig> 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  <dig> 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 .
it turns out that our results are significantly consistent with the observations and have shown some superiority over shinto’s model in reflecting the kinetics of bup and butyrate.
this indicates that shinto’s model is well fitted for its own condition but may not be suited well for other conditions.
in contrast, our model has more capacity in approaching real cases because of the improvements we have made.
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 in silico perturbations should not be too large because the system may exhibit alternative activations for other pathways when undergoing substantial fluctuations  <cit> .
when the system is encountering slight perturbations, its overall properties will not change substantially due to biological robustness  <cit> .
so it would be fairly assumed that when the perturbation magnitude on enzymatic parameters is 5%, the system will still survive and its functional normality is not interrupted or diverted.
in the computation, we have identified an interesting phenomenon that bk’s catalytic capacity exhibits positive influence on butanol production while coat has negative influences, as elevating bk activity results in increased rd value and uplifting coat activity diminishes the value.
and more convincingly, rd decreases when increasing the vmax values of bk and coat at the same time, which means the negative effect of coat can balance the positive effect of bk, confirming that coat has large effect in impairing butanol production.
based on this discovery, we propose a possible scenario that if more metabolites are received by bk as substrates, the overall acid  reassimilation efficiency will be benefited and butanol production is enhanced.
and if more metabolites are received by coat as substrates, the situation will be on the contrary.
it may not seem economical for the bacteria to use the bk-ptb path  to reassimilate butyrate since running through this path consumes atp.
nonetheless, based on our computation results and biochemical knowledge, we raise a predictive explanation for the underlying mechanism: in acidogenic phase, the metabolic flux actually runs in the direction of ptb-bk , thus this path generates atp for the growth of the bacteria; when the bacteria enters solventogenic phase, it doesn’t need to grow and atp has surplus, these surplus atps are utilized to proceed butyrate reassimilation.
it’s noteworthy that acids are severely poisonous to bacteria cells and it is a priority for the bacteria to convert acids to other forms .
in addition, enhanced butanol production means more acids are converted.
hence, although reactions through bk cost atp, but so far as bk’s efficiency is concerned, bk is still the preferred enzyme through which the bacteria reassimilates butyrate during solventogenesis.
therefore, the reason why the atp-costing path bk-ptb is more efficient over the path catalyzed by coat  in reassimilating butyrate is probably because of responding to severe poison stress, and the energetic basis for this process is the atp surplus generated during acidogenic phase.
our prediction is equivalent to considering the bacterial cellular behaviour to be related with biological robustness, as supposing that the bacteria is not seeking for its optimality when undergoing stress response, but seeking for sub-optimality.
in such case, certain costs or sacrifices are tolerated as long as it can survive   <cit> .
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 vmax <dig>  vmax <dig>  vmax <dig> by 5% each and re-computed our model ), we obtained rd= <dig> %, which exactly equalled the sum of individual effects of these perturbations.
again, if we increased km15b and vmax <dig> by 5% and decreased vmax <dig> by 5%, we obtained rd= <dig> %, still equalled to the sum of individual effects.
hence, we raise a hypothetic measure for increased butanol production: by slightly perturbing parameters in suitable directions and with appropriately mild magnitudes, we possibly can obtain a metabolic phenotype that can have amplified butanol production, and the strain can steadily and safely survive as well.
the amplification magnitudes of multiple parameter perturbations can be much greater than those in single parameter perturbations, if adequately many parameters are manipulated appropriately.
meanwhile, from an engineering point of view, multiple spot modifications can make the risks of system fluctuations or external impulsions more distributive than in the case that all alterations are concentrated on a single spot.
hence, this strategy provides a way that can make a more stable high-production system.
but this strategy requires high-precision genetic manipulation.
significance
traditional kinetic models cannot accommodate complex metabolic regulation effects .
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  <cit> .
our work just attempts to serve that goal by integrating existed information from multiple aspects and describing them mathematically.
nevertheless, the usage of “net effects of regulatory factors” in our modeling doesn’t seem to build direct links between the genetic level and metabolic level.
but if adequately more information about the regulatory factors on the genetic level is revealed, better formulism can be built to link the two levels and further studies on the control of bacteria cellular systems can be conducted.
CONCLUSIONS
we have developed a new kinetic model featured with major improvements over the previous one , 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.

 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. c. acetobutylicum is an extensively studied organism used for industrial-scale production of important solvents acetone and butanol, through the acetone-butanol-ethanol pathway. the abe pathway of c. acetobutylicum comprises two distinct branches: acidogenesis and solventogenesis. during acidogenesis, cells grow exponentially, acetate and butyrate are vigorously produced and the solvents are not obviously generated. while shifting to solventogenesis, the cells arrest their growth at stationary phase, solvents are produced and acids are reassimilated. so far, multiple models have been established to simulate the abe pathway, which mostly apply the metabolic flux analysis and flux-balance analysis approaches. although stoichiometric models can simulate the overall flux distributions based on limited kinetic data by using physicochemical constraints, they cannot appropriately reflect the dynamics in real-time scale. in contrast, kinetics models integrated with biochemical information are more efficient in reflecting system dynamics. by perturbing a kinetic model, system states that deviate from the normal state can be simulated and it is possible to reveal which reactions have potential impacts on target products’ productions. to date, many experiments have explored the kinetic features of the abe process of c. acetobutylicum and a kinetic model was recently developed by shinto et al.. however, as most current models did, this model did not integrate the metabolic regulatory effects of transcriptional control and other complex factors. moreover, shinto’s model did not include the information of some key metabolites, e.g. butyryl-phoshate, which has proved to be important in solventogensis. to overcome the drawbacks of shinto’s model, we developed an improved kinetic model for c. acetobutylicum abe process. the simulation results based on our model were consistent with published experimental observations and more comprehensive than those of shinto’s model. furthermore, a series of perturbed circumstances were simulated as well, getting results which might provide insights for metabolic engineering aiming at increasing solvent productivity.  all the following results were based on our new model, section “methods”), and they were compared with an experimental study that was independent of shinto’s model or our work. the new model was established by integrating experimental information and knowledge not included in shinto’s model, and we applied some optimization methods to fix the unknown parameters introduced by integrating these information and knowledge. the parameter fitting was done only under the conditions described in shinto’s work, only with respect to the metabolites contained in shinto’s model, and we didn’t use any information related to bup or the experimental study for comparison. after these parameter values were derived, we first implemented dynamic simulation with respect to the conditions in zhao et al.’s work and compared the results with experimental observations. we then carried out perturbation analysis to detect which reactions had large impacts on the overall butanol production in the system. dynamical simulation the initial value of our model was set according to the conditions described in the experiment by zhao et al., and the simulation results of metabolites’ kinetic profiles were shown in figure 2a and 2c. since our model parameters were fitted under shinto’s experiment conditions, the metabolites’ kinetic profiles were naturally consistent with those in shinto’s experiment when shinto’s conditions were substituted in. so the comparison with shinto’s experiment was not shown and we only focused on comparing with zhao et al.’s experiment here. these simulation results were shown to be quite consistent with experimental observations. the metric units in figure 2a and 2b were different, since the measurement of bup in zhao et al’s experiment accepted the unit of pmol/gdw. it was impossible to exactly know the conversion between mm and pmol/gdw because there was no such relationship established in the si metric unit system. but the quantity scale could be approximated given the size of an ordinary c. acetobutylicum cell, and this scale was consistent with that in our simulation results. since bacteria cells might vary in their sizes, we could not give a general estimation that could represent all the others, so we just showed the original quantities on the vertical axis in figure 2b. in our simulation results, the first peak of bup was shown to coincide with the onset of solvent production. this was a phenomenon that was reported in experimental literatures and had biological implications. besides bup, we also demonstrated that we had a more precise simulation on butyrate, one crucial product in cell growth and solvent production. in shinto’s model, when substituting in zhao et al.’s conditions, the quantity scale of butyrate curve didn’t resemble precisely with the experimental curve in zhao et al.’s experiment. this further demonstrated that our model had more capability in approaching real biological events. perturbation analysis among the solvents produced in the abe fermentation, butanol was considered to be the more valuable product, since it had advantageous properties over acetone and ethanol. so we implemented a series of perturbation analyses to assess which enzymes/reactions had relatively large impacts on butanol production. here we used rd values to measure the impacts. we carried out perturbation tests both on single parameters and double parameter pairs, the magnitude was 5% and shift directions were considered. we traversed the entire parameter set. the result set of single parameter perturbations included entries. and the result set of double parameter perturbations included entries. here table and showed some results with respect to the enzymes located on or close to acidogenic/solventogenic reactions in single and double parameter perturbations, respectively. 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 coa transferases catalyzing r and r and here we took them in uniform. 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 vmax alone or in combination with other enzyme parameters resulted in relatively large influences on butanol production. actually, bk activity had positive effect on butanol production and the change in butanol quantity caused by shifting bk’s vmax ranked the 5th in the profile of single parameter shifts. this suggested that bk, which coupled ptb to generate butyrate as well as catalyzing butyrate reassimilation, was important to butanol production as compared with other enzymes such as aad. besides, ak also had positive effect on butanol production, indicating acetate reassimilation had similar influence as butyrate reassimilation in solventogenesis, but with less magnitude. 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 diminished butanol quantity. because up-shifting the catalytic capacity of bk or down-shifting the catalytic capacity of coat would cause more butyrate molecules received by bk and the reverse operations would cause more butyrate received by coat, and given the fact that bk and coat both accepted butyrate as substrate, we could see that if more butyrate was received by bk, the butanol production would increase, i.e. more butyrate molecules were converted and acid reassimilation was more efficient; and if more butyrate was received by coat, the situation would be on the contrary. therefore we could conclude that bk had more efficiency than coat during acid reassimilation and solventogenesis. 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 vmax resulted in amplified rd value. while by shinto’s model, pts’s influence was negative. given the fact that pts acted in nutrient uptake and many processes relating to the abe pathway were subjected to nutrient induction, our prediction might be more intuitively consistent with common sense. 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, or optimizing the cultivation process of existing strains. model improvements since many studies related to c. acetobutylicum abe pathway have been reported, kinetic modeling of the abe pathway becomes feasible and enables us to simulate the system dynamics. nevertheless, the previous kinetic model of c. acetobutylicum abe process has several drawbacks as described in earlier context. to overcome these drawbacks, we have established a new model featured with three improvements over the previous one. first, we have incorporated the key metabolite bup, reflecting the relevant biological events that are specific to abe kinetics. the correspondence between bup concentration climax and solventogenesis onset is not merely a natural consequence of the fact that bup is the intermediate between butyryl-coa and butyrate. there are implications on the genetic level as stated in zhao et al’s study. there are many important solventogenic genes, such as adhe, adhe, ctfa, ctfb, adc, bdha, bdhb, etc., having expression profiles that show a strictly correlated pattern with the kinetics of bup. although the detailed mechanism of how bup acts to regulate abe process has not been very clear yet, its functional importance has been experimentally confirmed. our new model accounts for this knowledge and is successful in representing the phenomenon. 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 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. therefore, the metabolic regulations are not of the simple pattern as shinto suggested, but a significant 2-phase mode is shown. in our work, this mode is approximated by considering endogenous enzyme activity variations, assuming enzymes are regulated by many factors to exhibit different activity levels to fulfill conditional system requirements of different periods. this assumption is equivalent to extending the application of biochemical system theory. in bst, which is based on in vitro experiments, enzyme concentrations and endogenous enzyme activity levels are constant by default. hence kinetic models based on bst are rigorously suitable for chemical simulations but may not entirely appropriate for in vivo conditions. under in vivo conditions, the rate of a reaction does not solely depend on substrate/product concentrations, because the endogenous enzyme activity itself is regulated by many factors and its variation in turn affects the reaction rate. our model divides time into a set of periods according to the enzymes’ activity variations, allowing enzyme activities to vary throughout these periods. third, we introduce the “enzyme activity coefficient ” to quantify endogenous enzyme activity variations caused by metabolic regulations. for the quantification of enzyme activity curves, numerical interpolation 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, 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 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. it turns out that our results are significantly consistent with the observations and have shown some superiority over shinto’s model in reflecting the kinetics of bup and butyrate. this indicates that shinto’s model is well fitted for its own condition but may not be suited well for other conditions. in contrast, our model has more capacity in approaching real cases because of the improvements we have made. 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 in silico perturbations should not be too large because the system may exhibit alternative activations for other pathways when undergoing substantial fluctuations. when the system is encountering slight perturbations, its overall properties will not change substantially due to biological robustness. so it would be fairly assumed that when the perturbation magnitude on enzymatic parameters is 5%, the system will still survive and its functional normality is not interrupted or diverted. in the computation, we have identified an interesting phenomenon that bk’s catalytic capacity exhibits positive influence on butanol production while coat has negative influences, as elevating bk activity results in increased rd value and uplifting coat activity diminishes the value. and more convincingly, rd decreases when increasing the vmax values of bk and coat at the same time, which means the negative effect of coat can balance the positive effect of bk, confirming that coat has large effect in impairing butanol production. based on this discovery, we propose a possible scenario that if more metabolites are received by bk as substrates, the overall acid reassimilation efficiency will be benefited and butanol production is enhanced. and if more metabolites are received by coat as substrates, the situation will be on the contrary. it may not seem economical for the bacteria to use the bk-ptb path to reassimilate butyrate since running through this path consumes atp. nonetheless, based on our computation results and biochemical knowledge, we raise a predictive explanation for the underlying mechanism: in acidogenic phase, the metabolic flux actually runs in the direction of ptb-bk, thus this path generates atp for the growth of the bacteria; when the bacteria enters solventogenic phase, it doesn’t need to grow and atp has surplus, these surplus atps are utilized to proceed butyrate reassimilation. it’s noteworthy that acids are severely poisonous to bacteria cells and it is a priority for the bacteria to convert acids to other forms. in addition, enhanced butanol production means more acids are converted. hence, although reactions through bk cost atp, but so far as bk’s efficiency is concerned, bk is still the preferred enzyme through which the bacteria reassimilates butyrate during solventogenesis. therefore, the reason why the atp-costing path bk-ptb is more efficient over the path catalyzed by coat in reassimilating butyrate is probably because of responding to severe poison stress, and the energetic basis for this process is the atp surplus generated during acidogenic phase. our prediction is equivalent to considering the bacterial cellular behaviour to be related with biological robustness, as supposing that the bacteria is not seeking for its optimality when undergoing stress response, but seeking for sub-optimality. in such case, certain costs or sacrifices are tolerated as long as it can survive. 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 vmax vmax vmax by 5% each and re-computed our model ), we obtained rd= %, which exactly equalled the sum of individual effects of these perturbations. again, if we increased km15b and vmax by 5% and decreased vmax by 5%, we obtained rd= %, still equalled to the sum of individual effects. hence, we raise a hypothetic measure for increased butanol production: by slightly perturbing parameters in suitable directions and with appropriately mild magnitudes, we possibly can obtain a metabolic phenotype that can have amplified butanol production, and the strain can steadily and safely survive as well. the amplification magnitudes of multiple parameter perturbations can be much greater than those in single parameter perturbations, if adequately many parameters are manipulated appropriately. meanwhile, from an engineering point of view, multiple spot modifications can make the risks of system fluctuations or external impulsions more distributive than in the case that all alterations are concentrated on a single spot. hence, this strategy provides a way that can make a more stable high-production system. but this strategy requires high-precision genetic manipulation. significance traditional kinetic models cannot accommodate complex metabolic regulation effects. 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. our work just attempts to serve that goal by integrating existed information from multiple aspects and describing them mathematically. nevertheless, the usage of “net effects of regulatory factors” in our modeling doesn’t seem to build direct links between the genetic level and metabolic level. but if adequately more information about the regulatory factors on the genetic level is revealed, better formulism can be built to link the two levels and further studies on the control of bacteria cellular systems can be conducted.  we have developed a new kinetic model featured with major improvements over the previous one, 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. 
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. 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. 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. but this model did not integrate the metabolic regulatory effects of transcriptional control and other complex factors. 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. 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. up to date, only one kinetic model for c. acetobutylicum supported by experiment has been reported as far as we know. to systematically assess the potential of increased production of solvents, kinetic modeling has been applied to analyze the dynamics of this pathway and make predictive simulations. clostridium acetobutylicum produces solvents through the abe pathway.
 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. clostridium acetobutylicum produces solvents through the abe pathway. to systematically assess the potential of increased production of solvents, kinetic modeling has been applied to analyze the dynamics of this pathway and make predictive simulations. up to date, only one kinetic model for c. acetobutylicum supported by experiment has been reported as far as we know. but this model did not integrate the metabolic regulatory effects of transcriptional control and other complex factors. it also left out the information of some key intermediates.  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.  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. 9- september the 4th international conference on computational systems biology suzhou, p. r. china 