Patent Application: US-201113210484-A

Abstract:
a method for determining candidates for gene deletions and additions using a model of a metabolic network associated with an organism , the model includes a plurality of metabolic reactions defining metabolite relationships , the method includes selecting a bioengineering objective for the organism , selecting at least one cellular objective , forming an optimization problem that couples the at least one cellular objective with the bioengineering objective , and solving the optimization problem to yield at least one candidate .

Description:
the ability to investigate the metabolism of single - cellular organisms at a genomic scale , and thus systemic level , motivates the need for novel computational methods aimed at identifying strain engineering strategies . the present invention includes a computational framework termed optknock for suggesting gene deletion strategies leading to the overproduction of specific chemical compounds in e . coli . this is accomplished by ensuring that the production of the desired chemical becomes an obligatory byproduct of growth by “ shaping ” the connectivity of the metabolic network . in other words , optknock identifies and subsequently removes metabolic reactions that are capable of uncoupling cellular growth from chemical production . the computational procedure is designed to identify not just straightforward but also non - intuitive knockout strategies by simultaneously considering the entire e . coli metabolic network as abstracted in the in silico e . coli model of palsson and coworkers ( edwards and palsson , 2000 ). the complexity and built - in redundancy of this network ( e . g ., the e . coli model encompasses 720 reactions ) necessitates a systematic and efficient search approach to combat the combinatorial explosion of candidate gene knockout strategies . the nested optimization framework shown in fig1 is developed to identify multiple gene deletion combinations that maximally couple cellular growth objectives with externally imposed chemical production targets . this multi - layered optimization structure involving two competing optimal strategists ( i . e ., cellular objective and chemical production ) is referred to as a bilevel optimization problem ( bard ; 1998 ). problem formulation specifics along with an elegant solution procedure drawing upon linear programming ( lp ) duality theory are described in the methods section . the optknock procedure is applied to succinate , lactate , and 1 , 3 - propanediol ( pdo ) production in e . coli with the maximization of the biomass yield for a fixed amount of uptaken glucose employed as the cellular objective . the obtained results are also contrasted against using the minimization of metabolic adjustment ( moma ) ( segre et al ., 2002 ) as the cellular objective . based on the optknock framework , it is possible identify the most promising gene knockout strategies and their corresponding allowable envelopes of chemical versus biomass production in the context of succinate , lactate , and pdo production in e . coli . a preferred embodiment of this invention describes a computational framework , termed optknock , for suggesting gene deletions strategies that could lead to chemical production in e . coli by ensuring that the drain towards metabolites / compounds necessary for growth resources ( i . e ., carbons , redox potential , and energy ) must be accompanied , due to stoichiometry , by the production of the desired chemical . therefore , the production of the desired product becomes an obligatory byproduct of cellular growth . specifically , optknock pinpoints which reactions to remove from a metabolic network , which can be realized by deleting the gene ( s ) associated with the identified functionality . the procedure was demonstrated based on succinate , lactate , and pdo production in e . coli k - 12 . the obtained results exhibit good agreement with strains published in the literature . while some of the suggested gene deletions are quite straightforward , as they essentially prune reaction pathways competing with the desired one , many others are at first quite non - intuitive reflecting the complexity and built - in redundancy of the metabolic network of e . coli . for the succinate case , optknock correctly suggested anaerobic fermentation and the removal of the phosphotranferase glucose uptake mechanism as a consequence of the competition between the cellular and chemical production objectives , and not as a direct input to the problem . in the lactate study , the glucokinase - based glucose uptake mechanism was shown to decouple lactate and biomass production for certain knockout strategies . for the pdo case , results show that the entner - doudoroff pathway is more advantageous than emp glycolysis despite the fact that it is substantially less energetically efficient . in addition , the so far popular tpi knockout was clearly shown to reduce the maximum yields of pdo while a complex network of 15 reactions was shown to be theoretically possible of “ leaking ” flux from the ppp pathway to the tca cycle and thus decoupling pdo production from biomass formation . the obtained results also appeared to be quite robust with respect to the choice for the cellular objective . the present invention contemplates any number of cellular objectives , including but not limited to maximizing a growth rate , maximizing atp production , minimizing metabolic adjustment , minimizing nutrient uptake , minimizing redox production , minimizing a euclidean norm , and combinations of these and other cellular objectives . it is important to note that the suggested gene deletion strategies must be interpreted carefully . for example , in many cases the deletion of a gene in one branch of a branched pathway is equivalent with the significant up - regulation in the other . in addition , inspection of the flux changes before and after the gene deletions provides insight as to which genes need to be up or down - regulated . lastly , the problem of mapping the set of identified reactions targeted for removal to its corresponding gene counterpart is not always uniquely specified . therefore , careful identification of the most economical gene set accounting for isozymes and multifunctional enzymes needs to be made . preferably , in the optknock framework , the substrate uptake flux ( i . e ., glucose ) is assumed to be 10 mmol / gdw · hr . therefore , all reported chemical production and biomass formation values are based upon this postulated and not predicted uptake scenario . thus , it is quite possible that the suggested deletion mutants may involve substantially lower uptake efficiencies . however , because optknock essentially suggests mutants with coupled growth and chemical production , one could envision a growth selection system that will successively evolve mutants with improved uptake efficiencies and thus enhanced desired chemical production characteristics . where there is a lack of any regulatory or kinetic information within the purely stoichiometric representation of the inner optimization problem that performs flux allocation , optknock is used to identify any gene deletions as the sole mechanism for chemical overproduction . clearly , the lack of any regulatory or kinetic information in the model is a simplification that may in some cases suggest unrealistic flux distributions . the incorporation of regulatory information will not only enhance the quality of the suggested gene deletions by more appropriately resolving flux allocation , but also allow us to suggest regulatory modifications along with gene deletions as mechanisms for strain improvement . the use of alternate modeling approaches ( e . g ., cybernetic ( kompala et al ., 1984 ; ramakrishna et al ., 1996 ; varner and ramkrishna , 1999 ), metabolic control analysis ( kacser and burns , 1973 ; heinrich and rapoport , 1974 ; hatzimanikatis et al ., 1998 )), if available , can be incorporated within the optknock framework to more accurately estimate the metabolic flux distributions of gene - deleted metabolic networks . nevertheless , even without such regulatory or kinetic information , optknock provides useful suggestions for strain improvement and more importantly establishes a systematic framework . the present invention naturally contemplates future improvements in metabolic and regulatory modeling frameworks . the maximization of a cellular objective quantified as an aggregate reaction flux for a steady state metabolic network comprising a set ={ 1 , . . . , n } of metabolites and a set ={ 1 , . . . , m } of metabolic reactions fueled by a glucose substrate is expressed mathematically as follows , where s ij is the stoichiometric coefficient of metabolite i in reaction j , v j represents the flux of reaction j , v glc — uptake is the basis glucose uptake scenario , v atp — main is the non - growth associated atp maintenance requirement , and v biomass t arg et is a minimum level of biomass production . the vector v includes both internal and transport reactions . the forward ( i . e ., positive ) direction of transport fluxes corresponds to the uptake of a particular metabolite , whereas the reverse ( i . e ., negative ) direction corresponds to metabolite secretion . the uptake of glucose through the phosphotransferase system and glucokinase are denoted by v pts and v glk , respectively . transport fluxes for metabolites that can only be secreted from the network are members of secr — only . note also that the complete set of reactions is subdivided into reversible rev , and irreversible irrev reactions . the cellular objective is often assumed to be a drain of biosynthetic precursors in the ratios required for biomass formation ( neidhardt and curtiss , 1996 ). the fluxes are reported per 1 gdw · hr such that biomass formation is expressed as g biomass produced / gdw · hr or 1 / hr . the modeling of gene deletions , and thus reaction elimination , first requires the incorporation of binary variables into the flux balance analysis framework ( burgard and maranas , 2001 ; burgard et al ., 2001 ). these binary variables , assume a value of one if reaction j is active and a value of zero if it is inactive . the following constraint , ensures that reaction flux v j is set to zero only if variable y j is equal to zero . alternatively , when y j is equal to one , v j is free to assume any value between a lower v j min and an upper v j max bound . in this study , v j min and v j max are identified by minimizing and subsequently maximizing every reaction flux subject to the constraints from the primal problem . the identification of optimal gene / reaction knockouts requires the solution of a bilevel optimization problem that chooses the set of reactions that can be accessed ( y j = 1 ) so as the optimization of the cellular objective indirectly leads to the overproduction of the chemical or biochemical of interest ( see also fig1 ). using biomass formation as the cellular objective , this is expressed mathematically as the following bilevel mixed - integer optimization problem where k is the number of allowable knockouts . the final constraint ensures that the resulting network meets a minimum biomass yield , v biomass t arg et . the direct solution of this two - stage optimization problem is intractable given the high dimensionality of the flux space ( i . e ., over 700 reactions ) and the presence of two nested optimization problems . to remedy this , we develop an efficient solution approach borrowing from lp duality theory which shows that for every linear programming problem ( primal ) there exists a unique optimization problem ( dual ) whose optimal objective value is equal to that of the primal problem . a similar strategy was employed by ( burgard and maranas , 2003 ) for identifying / testing metabolic objective functions from metabolic flux data . the dual problem ( ignizio and cavalier , 1994 ) associated with the optknock inner problem is where λ i stoich is the dual variable associated with the stoichiometric constraints , glc is the dual variable associated with the glucose uptake constraint , and μ j is the dual variable associated with any other restrictions on its corresponding flux v j in the primal . note that the dual variable μ j acquires unrestricted sign if its corresponding flux in the optknock inner problem is set to zero by enforcing y j = 0 . the parameters μ j min and μ j max are identified by minimizing and subsequently maximizing their values subject to the constraints of the dual problem . if the optimal solutions to the primal and dual problems are bounded , their objective function values must be equal to one another at optimality . this means that every optimal solution to both problems can be characterized by setting their objectives equal to one another and accumulating their respective constraints . thus the bilevel formulation for optknock shown previously can be transformed into the following single - level milp an important feature of the above formulation is that if the problem is feasible , the optimal solution will always be found . in this invention , the candidates for gene knockouts included , but are not limited to , all reactions of glycolysis , the tca cycle , the pentose phosphate pathway , respiration , and all anaplerotic reactions . this is accomplished by limiting the number of reactions included in the summation ( i . e ., problems containing as many as 100 binary variables were solved in the order of minutes to hours using cplex 7 . 0 accessed via the gams modeling environment on an ibm rs6000 - 270 workstation . it should be understood , however , that the present invention is not dependent upon any particular type of computer or environment being used . any type can be used to allow for inputting and outputting the information associated with the methodology of the present invention . moreover , the steps of the methods of the present invention can be implemented in any number of types software applications , or languages , and the present invention is not limited in this respect . it will be appreciated that other embodiments and uses will be apparent to those skilled in the art and that the invention is not limited to these specific illustrative examples . which reactions , if any , that could be removed from the e . coli k - 12 stoichiometric model ( edwards and palsson , 2000 ) so as the remaining network produces succinate or lactate whenever biomass maximization is a good descriptor of flux allocation were identified . a prespecified amount of glucose ( 10 mmol / gdw · hr ), along with unconstrained uptake routes for inorganic phosphate , oxygen , sulfate , and ammonia are provided to fuel the metabolic network . the optimization step could opt for or against the phosphotransferase system , glucokinase , or both mechanisms for the uptake of glucose . secretion routes for acetate , carbon dioxide , ethanol , formate , lactate and succinate are also enabled . note that because the glucose uptake rate is fixed , the biomass and product yields are essentially equivalent to the rates of biomass and product production , respectively . in all cases , the optknock procedure eliminated the oxygen uptake reaction pointing at anaerobic growth conditions consistent with current succinate ( zeikus et al ., 1999 ) and lactate ( datta et al ., 1995 ) fermentative production strategies . table i summarizes three of the identified gene knockout strategies for succinate overproduction ( i . e ., mutants a , b , and c ). the anaerobic flux distributions at the maximum biomass yields for the complete e . coli network ( i . e ., wild - type ), mutant b , and mutant c are illustrated in fig2 a - c . the results for mutant a suggested that the removal of two reactions ( i . e ., pyruvate formate lyase and lactate dehydrogenase ) from the network results in succinate production reaching 63 % of its theoretical maximum at the maximum biomass yield . this knockout strategy is identical to the one employed by stols and donnelly ( stols and donnelly , 1997 ) in their succinate overproducing e . coli strain . next , the envelope of allowable succinate versus biomass production was explored for the wild - type e . coli network and the three mutants listed in table i . note that the succinate production limits , shown in fig3 a , revealed that mutant a does not exhibit coupled succinate and biomass formation until the yield of biomass approaches 80 % of the maximum . mutant b , however , with the additional deletion of acetaldehyde dehydrogenase , resulted in a much earlier coupling of succinate with biomass yields . a less intuitive strategy was identified for mutant c which focused on inactivating two pep consuming reactions rather than eliminating competing byproduct ( i . e ., ethanol , formate , and lactate ) production mechanisms . first , the phosphotransferase system was disabled requiring the network to rely exclusively on glucokinase for the uptake of glucose . next , pyruvate kinase was removed leaving pep carboxykinase as the only central metabolic reaction capable of draining the significant amount of pep supplied by glycolysis . this strategy , assuming that the maximum biomass yield could be attained , resulted in a succinate yield approaching 88 % of the theoretical maximum . in addition , fig3 a revealed significant succinate production for every attainable biomass yield , while the maximum theoretical yield of succinate is the same as that for the wild - type strain . the optknock framework was next applied to identify knockout strategies for coupling lactate and biomass production . table i shows three of the identified gene knockout strategies ( i . e ., mutants a , b , and c ) and the flux distribution of mutant c at the maximum biomass yield is shown in fig2 d . mutant a redirects flux toward lactate at the maximum biomass yield by blocking acetate and ethanol production . this result is consistent with previous work demonstrating that an adh , pta mutant e . coli strain could grow anaerobically on glucose by producing lactate ( gupta and clark , 1989 ). mutant b provides an alternate strategy involving the removal of an initial glycolysis reaction along with the acetate production mechanism . this results in a lactate yield of 90 % of its theoretical limit at the maximum biomass yield . the vertical red line for mutant b in fig3 b indicates that the network could avoid producing lactate while maximizing biomass formation . this is due to the fact that optknock does not explicitly account for the “ worst - case ” alternate solution . it should be appreciated that upon the additional elimination of the glucokinase and ethanol production mechanisms , mutant c exhibited a tighter coupling between lactate and biomass production . biomass and chemical yields for various gene knockout strategies identified by optknock . the reactions and corresponding enzymes for each knockout strategy are listed . the maximum biomass and corresponding chemical yields are provided on a basis of 10 mmol / hr glucose fed and 1 gdw of cells . the rightmost column provides the chemical yields for the same basis assuming a minimal redistribution of metabolic fluxes from the wild - type ( undeleted ) e . coli network ( moma assumption ). for the 1 , 3 - propanediol case , in addition to devising optimum gene knockout strategies , optknock was used to design strains where gene additions were needed along with gene deletions such as in pdo production in e . coli . although microbial 1 , 3 - propanediol ( pdo ) production methods have been developed utilizing glycerol as the primary carbon source ( hartlep et al ., 2002 ; zhu et al ., 2002 ), the production of 1 , 3 - propanediol directly from glucose in a single microorganism has recently attracted considerable interest ( cameron et al ., 1998 ; biebl et al ., 1999 ; zeng and biebl , 2002 ). because wild - type e . coli lacks the pathway necessary for pdo production , the gene addition framework was first employed ( burgard and maranas , 2001 ) to identify the additional reactions needed for producing pdo from glucose in e . coli . the gene addition framework identified a straightforward three - reaction pathway involving the conversion of glycerol - 3 - p to glycerol by glycerol phosphatase , followed by the conversion of glycerol to 1 , 3 propanediol by glycerol dehydratase and 1 , 3 - propanediol oxidoreductase . these reactions were then added to the e . coli stoichiometric model and the optknock procedure was subsequently applied . optknock revealed that there was neither a single nor a double deletion mutant with coupled pdo and biomass production . however , one triple and multiple quadruple knockout strategies that can couple pdo production with biomass production was identified . two of these knockout strategies are shown in table i . the results suggested that the removal of certain key functionalities from the e . coli network resulted in pdo overproducing mutants for growth on glucose . specifically , table i reveals that the removal of two glycolytic reactions along with an additional knockout preventing the degradation of glycerol yields a network capable of reaching 72 % of the theoretical maximum yield of pdo at the maximum biomass yield . note that the glyceraldehyde - 3 - phosphate dehydrogenase ( gapa ) knockout was used by dupont in their pdo - overproducing e . coli strain ( nakamura , 2002 ). mutant b revealed an alternative strategy , involving the removal of the triose phosphate isomerase ( tpi ) enzyme exhibiting a similar pdo yield and a 38 % higher biomass yield . interestingly , a yeast strain deficient in triose phosphate isomerase activity was recently reported to produce glycerol , a key precursor to pdo , at 80 - 90 % of its maximum theoretical yield ( compagno et al ., 1996 ). the flux distributions of the wild - type e . coli , mutant a , and mutant b networks that maximize the biomass yield are available in fig4 . not surprisingly , further conversion of glycerol to glyceraldehyde was disrupted in both mutants a and b . for mutant a , the removal of two reactions from the top and bottom parts of glycolysis resulted in a nearly complete inactivation of the pentose phosphate and glycolysis ( with the exception of triose phosphate isomerase ) pathways . to compensate , the entner - doudoroff glycolysis pathway is activated to channel flux from glucose to pyruvate and glyceraldehyde - 3 - phosphate ( gap ). gap is then converted to glycerol which is subsequently converted to pdo . energetic demands lost with the decrease in glycolytic fluxes from the wild - type e . coli network case , are now met by an increase in the tca cycle fluxes . the knockouts suggested for mutant b redirect flux toward the production of pdo by a distinctly different mechanism . the removal of the initial pentose phosphate pathway reaction results in the complete flow of metabolic flux through the first steps of glycolysis . at the fructose bisphosphate aldolase junction , the flow is split into the two product metabolites : dihydroxyacetone - phosphate ( dhap ) which is converted to pdo and gap which continues through the second half of the glycolysis . the removal of the triose - phosphate isomerase reaction prevents any interconversion between dhap and gap . interestingly , a fourth knockout is predicted to retain the coupling between biomass formation and chemical production . this knockout prevents the “ leaking ” of flux through a complex pathway involving 15 reactions that together convert ribose - 5 - phosphate ( r5p ) to acetate and gap , thereby decoupling growth from chemical production . next , the envelope of allowable pdo production versus biomass yield is explored for the two mutants listed in table i . the production limits of the mutants along with the original e . coli network , illustrated in fig5 , reveal that the wild - type e . coli network has no “ incentive ” to produce pdo if the biomass yield is to be maximized . on the other hand , both mutants a and b have to produce significant amounts of pdo if any amount of biomass is to be formed given the reduced functionalities of the network following the gene removals . mutant a , by avoiding the tpi knockout that essentially sets the ratio of biomass to pdo production , is characterized by a higher maximum theoretical yield of pdo . the above described results hinge on the use of glycerol as a key intermediate to pdo . next , the possibility of utilizing an alternative to the glycerol conversion route for 1 , 3 - propandediol production was explored . applicants identified a pathway in chloroflexus aurantiacus involving a two - step nadph - dependant reduction of malonyl - coa to generate 3 - hydroxypropionic acid ( 3 - hpa ) ( menendez et al ., 1999 ; hugler et al ., 2002 ). 3 - hpa could then be subsequently converted chemically to 1 , 3 propanediol given that there is no biological functionality to achieve this transformation . this pathway offers a key advantage over pdo production through the glycerol route because its initial step ( acetyl - coa carboxylase ) is a carbon fixing reaction . accordingly , the maximum theoretical yield of 3 - hpa ( 1 . 79 mmol / mmol glucose ) is considerably higher than for pdo production through the glycerol conversion route ( 1 . 34 mmol / mmol glucose ). the application of the optknock framework upon the addition of the 3 - hpa production pathway revealed that many more knockouts are required before biomass formation is coupled with 3 - hpa production . one of the most interesting strategies involves nine knockouts yielding 3 - hpa production at 91 % of its theoretical maximum at optimal growth . the first three knockouts were relatively straightforward as they involved removal of competing acetate , lactate , and ethanol production mechanisms . in addition , the entner - doudoroff pathway ( either phosphogluconate dehydratase or 2 - keto - 3 - deoxy - 6 - phosphogluconate aldolase ), four respiration reactions ( i . e ., nadh dehydrogenase i , nadh dehydrogenase ii , glycerol - 3 - phosphate dehydrogenase , and the succinate dehydrogenase complex ), and an initial glycolyis step ( i . e ., phosphoglucose isomerase ) are disrupted . this strategy resulted in a 3 - hpa yield that , assuming the maximum biomass yield , is 69 % higher than the previously identified mutants utilizing the glycerol conversion route . all results described previously were obtained by invoking the maximization of biomass yield as the cellular objective that drives flux allocation . this hypothesis essentially assumes that the metabolic network could arbitrarily change and / or even rewire regulatory loops to maintain biomass yield maximality under changing environmental conditions ( maximal response ). recent evidence suggests that this is sometimes achieved by the k - 12 strain of e . coli after multiple cycles of growth selection ( ibarra et al ., 2002 ). in this section , a contrasting hypothesis was examined ( i . e ., minimization of metabolic adjustment ( moma ) ( segre et al ., 2002 )) that assumed a myopic ( minimal ) response by the metabolic network upon gene deletions . specifically , the moma hypothesis suggests that the metabolic network will attempt to remain as close as possible to the original steady state of the system rendered unreachable by the gene deletion ( s ). this hypothesis has been shown to provide a more accurate description of flux allocation immediately after a gene deletion event ( segre et al ., 2002 ). fig6 pictorially shows the two differing new steady states predicted by the two hypotheses , respectively . for this study , the moma objective was utilized to predict the flux distributions in the mutant strains identified by optknock . the base case for the lactate and succinate simulations was assumed to be maximum biomass formation under anaerobic conditions , while the base case for the pdo simulations was maximum biomass formation under aerobic conditions . the results are shown in the last column of table 1 . in all cases , the suggested multiple gene knock - 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