Note: Descriptions are shown in the official language in which they were submitted.
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TITLE: METHOD FOR REDESIGN OF MICROBIAL PRODUCTION SYSTEMS
CROSS-REFERENCE TO RELATED APPLICATIONS
This application is a continuation-in-part of U.S. Patent Application Serial
No.
10/616,659, filed July 9, 2003 which is a conversion of U.S. Patent
Application Serial No.
60/395,763, filed July 10, 2002; U.S. Patent Application Serial No.
60/417,511, filed
October, 9, 2002; and U.S. Patent Application Serial No. 60/444,933, filed
February 3,
2003, each of which is herein incorporated by reference in its entirety.
GRANT REFERENCE
This work has been supported by Department of Energy pursuant to Grant No.
58855 and the National Science Foundation Grant No. BES0120277. Accordingly,
the
U.S. government may have certain rights in the invention.
BACKGROUND OF THE INVENTION
The present invention relates to a computational framework that guides pathway
modifications, through reaction additions and deletions.
The generation of bioconversion pathways has attracted significant interest in
recent
years. The first systematic effort towards this end was made by Seressiotis
and Bailey
(Seressiotis & Bailey, 1988), who utilized the concepts of Artificial
Intelligence in
developing their software. This was followed by a case study on the production
of lysine
from glucose and ammonia performed by Mavrovouniotis et al. (Mavrovouniotis et
al.,
1990) utilizing an algorithm based on satisfying the stoichiometric
constraints on reactions
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and metabolites in an iterative fashion. More recently, elegant graph
theoretic concepts
(e.g., P-graphs (Fan et al., 2002) and k-shortest paths algorithm (Eppstein,
1994)) were
pioneered to identify novel biotransformation pathways based on the tracing of
atoms
(Arita, 2000; Arita, 2004), enzyme function rules and thermodynamic
feasibility constraints
(Hatzimanikatis et al., 2003). Most of these approaches have been demonstrated
by
applying them on a relatively small database of reactions. Their performance
on genome-
scale databases of metabolic reactions, such as the KEGG database which
consists of
approximately 5000 reactions (Kanehisa et al., 2002), will dramatically
suffer.
Very recently, a heuristic approach based on determining the minimum pathway
cost (based on any biochemical property) was proposed (McShan et al., 2003).
This
approach is quite successful in delineating the pathways for conversion of one
metabolite
into another. However, like all other approaches discussed earlier, it fails
to predict the
yield of the product obtained by employing a specific pathway. Furthermore,
these
approaches mostly identify linear biotransformation pathways without ensuring
the
balanceability of all metabolites, especially the cofactors.
Therefore it is a primary object, feature, or advantage of the present
invention to
provide an optimization-based procedure which addresses the complexity
associated with
genome-scale networks.
It is a further object, feature, or advantage of the present invention to
provide a
method for constructing stoichiometrically-balanced bioconversion pathways,
both
branched and linear, that are efficient in terms of yield and the number of
non-native
reactions required in a host for product formation.
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Another object, feature, or advantage of the present invention is to provide a
method that enables the evaluation of multiple substrate choices.
Yet another object, feature, or advantage of the present invention is to
provide a
method for computationally suggesting the manner in which to achieve
bioengineering
objectives, including increased production objectives.
A further object, feature or advantage of the present invention is to
determine
candidates for gene deletion or addition through use of a model of a network
of
bioconversion pathways.
Yet another object, feature or advantage of the present invention is to
provide an
] 0 optimized method for computationally achieving a bioengineering objective
that is flexible
and robust.
A still further object, feature, or advantage of the present invention is to
provide a
method for computationally achieving a bioengineering objective that can take
into account
not only central metabolic pathways, but also other pathways such as amino
acid
biosynthetic and degradation pathways.
Yet another object, feature, or advantage of the present invention is to
provide a
method for computationally achieving a bioengineering objective that that can
take into
account transport rates, secretion pathways or other characteristics as
optimization
variables.
One or more of these and/or other objects, features and advantages of the
present
invention will become apparent after review of the following detailed
description of the
disclosed embodiments and the appended claims.
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BRIEF SUMMARY OF THE INVENTION
The present invention provides hierarchical computational framework, which is
referred to as "OptStrain" and is aimed at guiding pathways modifications,
through
reaction additions and deletions, of microbial networks for the overproduction
of targeted
compounds. These compounds may range from electrons or hydrogen in bio-fuel
cell and
environmental applications to complex drug precursor molecules. A
comprehensive
database of biotransformations, referred to as the Universal database (with
over 5,000
reactions), is compiled and regularly updated by downloading and curating
reactions from
multiple biopathway database sources. Combinatorial optimization is then
employed to
elucidate the set(s) of non-native functionalities, extracted from this
Universal database, to
add to the examined production host for enabling the desired product
formation.
Subsequently, competing functionalities that divert flux away from the
targeted product are
identified and removed to ensure higher product yields coupled with growth.
The present
invention represents a significant advancement over earlier efforts by
establishing an
integrated computational framework capable of constructing stoichiometrically
balanced
pathways, imposing maximum product yield requirements, pinpointing the optimal
substrate(s), and evaluating different microbial hosts.
The range and utility of OptStrain is demonstrated by addressing two very
different
product molecules. The hydrogen case study pinpoints reaction elimination
strategies for
improving hydrogen yields using two different substrates for three separate
production
hosts. Tn contrast, the vanillin study primarily showcases which non-native
pathways need
to be added into Escherichia coli. In summary, OptStrain provides a useful
tool to aid
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microbial strain design and, more importantly, it establishes an integrated
frainework to
accommodate future modeling developments.
The OptStrain process incorporates the OptKnock process which has been
previously described in U.S. Patent Application Serial No. 10/616,659, filed
July 9, U.S.
Patent Application Serial No. 60/395,763, filed July 10, 2002, U.S. Patent
Application
Serial No. 60/417,511, filed October, 9, 2002, and U.S. Patent Application
Serial No.
60/444,933, filed February 3, 2003, all of which have been previously
incorporated by
reference in their entirety. The OptKnock process provides for the systematic
development
of engineered microbial strains for optimizing the production of chemical or
biochemicals
which is an overarching challenge in biotechnology. The advent of genome-scale
models
of metabolism has laid the foundation for the development of computational
procedures for
suggesting genetic manipulations that lead to overproduction. This is
accomplished by
ensuring that a drain towards growth resources (i.e., carbon, redox potential,
and energy) is
accompanied, due to stoichiometry, by the production of a desired production.
Specifically, the computation framework identifies multiple gene deletion
combinations
that maximally couple a postulated cellular objective (e.g., biomass
formation) with
externally imposed chemical production targets. This nested structure gives
rise to a
bilevel optimization problem which is solved based on a transformation
inspired by duality
theory. This procedure of this framework, by coupling biomass formation with
chemical
production, suggest a growth selection/adaption system for indirectly evolving
overproducing mutants.
OptKnock can also incorporate strategies that not only include central
metabolic
network genes, but also the amino acid biosynthetic and degradation pathways.
In addition
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to gene deletions, the transport rates of carbon dioxide, ammonia and oxygen
as well as the
secretion pathways for key metabolites can be introduced as optimizaiion
variables in the
framework. Thus, the present invention is both robust and flexible in order to
address the
complexity associated with genome-scale networks.
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BRIEF DESCRIPTION OF THE DRAWINGS
Figure 1 is a pictorial representation of the OptStrain procedure. Step 1
involves
the curation of database(s) of reactions to compile the Universal database
which comprises
of only elementally balanced reactions. Step 2 identifies a path enabling the
desired
biotransformation from a substrate (e.g., glucose, methanol, xylose) to
product (e.g.,
hydrogen, vanillin) without any consideration for the origin of reactions.
Note that the
both, native reactions of the host and non-native reactions, are present. Step
3 minimizes
the reliance on non-native reactions while Step 4 incorporates the non-native
functionalities into the microbial host's stoichiometric model and applies the
OptKnock
procedure to identify and eliminate competing reactions with the targeted
product. The
(X)'s pinpoint the deleted reactions.
Figure 2 is a graph indicating maximum hydrogen yield on a weight basis for
different substrates.
Figure 3 is a graph illustrating hydrogen production envelopes as a function
of the
biomass production rate of the wild-type E. coli network under aerobic and
anaerobic
conditions as well as the two-reaction and three-reaction deletion mutant
networks. The
basis glucose uptake rate is fixed at 10 mmol/gDW/hr. These curves are
constructed by
finding the maximum and minimum hydrogen production rates under different
rates of
biomass fornnation. Point A denotes the required theoretical hydrogen
production rate at
the maximum biomass formation rate of the wild-type network under anaerobic
conditions.
Points B and C identify the theoretical hydrogen production rates at maximum
growth for
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the two mutant networks respectively after fixing the corresponding carbon
dioxide
transport rates at the values suggested by OptKnock.
Figure 4 is a graph illustrating hydrogen formation limits of the wild-type
(solid)
and mutant (dotted) Clostridium acetobutylicum metabolic network for a basis
glucose
uptake rate of 1 mmol/gDW/hr. Line AB denotes different alternate maximum
biomass
yield solutions that are available to the wild-type network. Point C pinpoints
the hydrogen
yield of the mutant network at maximum growth. This can be contrasted with the
reported
experimental hydrogen yield (2 mol/mol glucose) in C. acetobutylicum (45).
Figure 5 is a graph illustrating vanillin production envelope of the augmented
E.
coli metabolic network for a basis 10 rnmol/gDW/hr uptake rate of glucose.
Points A, B
- and C denote the maximum growth points associated with the one, two and four
reaction
deletion mutant networks, respectively. In contrast to the wild-type network
for which
vanillin production is not guaranteed at any rate of biomass production, the
mutant
networks require significant vanillin yields to achieve high levels of biomass
production.
Note that an anaerobic mode of growth is suggested in all cases.
Figure 6 depicts the bilevel optimization structure of Optknock. The inner
problem
performs the flux allocation based on the optimization of a particular
cellular objective
(e.g., maximization of biomass yield, MOMA). The outer problem then maximizes
the
bioengineering objective (e.g., chemical production) by restricting access to
key reactions
available to the optimization of the inner problem.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
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The present invention provides for methods and systems for guiding pathway
modifications, through reaction additions and deletions. Preferably the
methods are
computer implemented or computer assisted or otherwise automated. The term
"computer"
as used herein should be construed broadly to include, but not to be limited
to, any number
of eleotronic devices suitable for practicing the methodology described
herein. It is further
to be understood that because the invention relates to computer-assisted
modeling that the
scope of the invention is broader than the specific embodiments provided
herein and that
one skilled in the art would understand how to apply the present invention in
different
environments and contexts to address different problems in part due to the
predictability
associated with computer implementations.
1. OptStrain
A fundamental goal in systems biology is to elucidate the complete "palette"
of
biotransformations accessible to nature in living systems. This goal parallels
the
continuing quest in biotechnology to construct microbial strains capable. of
accomplishing
an ever-expanding array of desired biotransformations. These
biotransformations are
aimed at products that range from simple precursor chemicals (Nakamura &
Whited,
2003; Causey et al., 2004) or complex molecules such as carotenoids (Misawa et
al.,
1991), to electrons in bio fuel cells (Liu et al., 2004) or batteries (Bond et
al., 2002; Bond
et al., 2003) to even microbes capable of precipitating heavy metal complexes
in
bioremediation applications (Methe et al., 2003; Lovley, 2003; Finneran et
al., 2002).
Recent developments in molecular biology and recombinant DNA technology have
ushered
a new era in the ability to shape the gene content and expression levels for
microbial
production strains in a direct and targeted fashion (Bailey, 1991;
Stephanopoulos &
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Sinskey, 1993). The astounding range and diversity of these newly acquired
capabilities
and the scope of biotechnological applications imply that now more than ever
we need
modeling and computational aids to a priori identify the optimal sets of
genetic
modifications for strain optimization projects.
. ,
The recent availability of genome-scale models of microbial organisms has
provided the pathway reconstructions necessary for developing computational
methods
aimed at identifying strain engineering strategies (Bailey, 2001). These
models, already
available for H. pylori (Schilling et al., 2002), E. coli (Reed et al., 2003;
Edwards &
Palsson, 2000), S. cerevisiae (Forster et al., 2003) and other microorganisms
(David et al.,
2003; Van Dien & Lindstrom, 2002; Valdes et al., 2003) provide successively
refined
abstractions of the microbial metabolic capabilities. An automated process to
expedite the
construction of stoichiometric models from annotated genomes (Segre et al.,
2003)
promises to further accelerate the metabolic reconstructions of several
microbial
organisms. At the same time, individual reactions are deposited in databases
such as
KEGG, EMP, MetaCyc, UM-BBD, and many more (Overbeek et al., 2000; Selkov et
al.,
1998; Kanehisa et al., 2004; Krieger et al., 2004; Ellis et al., 2003; Karp et
al., 2002),
forming encompassing and growing collections of the biotransformations for
which we
have direct or indirect evidence of existence in different species. Already
many thousands
of such reactions have been deposited; however, unlike organism specific
metabolic
reconstructions (Schilling et al., 2002; Reed et al., 2003; Edwards & Palsson,
2000; Forster
et al., 2003), these compilations include reactions from not a single but many
different
species in a largely uncurated fashion. This means that currently there exists
an ever-
expanding collection of microbial models and at the same time ever more
encompassing
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compilations of non-native functionalities. This newly acquired plethora of
data has
brought to the forefront a number of computational and modeling challenges
which form
the scope of this article. Specifically, how can we systematically select from
the thousands
of functionalities catalogued in various biological databases, the appropriate
set of
pathways/genes to recombine into existing production systems such as E. coli
so as to
endow them with the desired new functionalities? Subsequently, how can we
identify
which competing functionalities to eliminate to ensure high product yield as
well as
viability?
Existing strategies and methods for accomplishing this goal include database
queries to explore all feasible bioconversion routes from a substrate to a
target compound
from a given list of biochemical transformations (Seressiotis & Bailey, 1988;
Mavrovouniotis et al., 1990). More recentfy, elegant graph theoretic concepts
(e.g., P-
graphs (Fan et al., 2002) and k-shortest paths algorithm (Eppstein, 1994))
were pioneered
to identify novel biotransformation pathways based on the tracing of atoms
(Arita, 2000;
Arita 2004), enzyme function rules and thermodynamic feasibility constraints _
(Hatzimanikatis et al., 2003). Also an interesting heuristic search approach
that uses the
enzymatic biochemical reactions found in the KEGG database (Kanehisa et al.,
2004) to
construct a connected graph linking the substrate and product metabolites was
recently
proposed (McShan et al., 2003). Most of these approaches, however, generate
linear paths
that link substrates to fmal products without ensuring that the rest of the
metabolic network
is balanced and that metabolic imperatives on cofactor usage/generation and
energy
balances are met.
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The present invention provides a hierarchical optimization-based framework,
OptStrain to identify stoichiometrically-balanced pathways to be generated
upon
recombination of non-native functionalities into a host organism to confer the
desired
phenotype. Candidate metabolic pathways are identified from an ever-expanding
array of
thousands (currently 5,734) of reactions pooled together from different
stoichiometric
models and publicly available databases such as KEGG (Kanehisa et al., 2004).
Note that
the identified pathways satisfy maximum yield considerations while the choice
of
substrates can be treated as optimization variables. Important information
pertaining to the
cofactor/energy requirements associated with each pathway is deduced enabling
the
comparison of candidate pathways with respect to the aforementioned criteria.
Production
host selection is examined by successively minimizing the reliance on
heterologous genes
while satisfying the performance targets identified above. A gene set that
encodes for all
the enzymes needed to catalyze the identified non-native functionalities can
then be
constructed accounting for isozymes and multi-subunit enzymes. Subsequently,
gene
deletions are identified (Burgard et al., 2003; Pharkya et al., 2003) in the
augmented host
networks to improve product yields by removing competing functionalities which
decouple
biochemical production and growth objectives. The breadth and scope of
OptStrain is
demonstrated by addressing in detail two different product molecules (i.e.,
hydrogen and
vanillin) which lie at the two extremes in terms of product- molecule size.
Briefly,
computational results in some cases match existing strain designs and
production practices
whereas in others pinpoint novel engineering strategies.
1.1 Materials and Methods
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The first challenge addressed is to develop a systematic computational
framework
to identify which functionalities to add to the organism-specific metabolic
network (e.g., E.
coli (Reed et al., 2003; ), S. cerevisiae (Forster et al., 2003), , Edwards &
Palsson, 2000 C.
acetobutylicum (Desai et al., 1999; Papoutsakis, 1984), etc.) to enable the
desired
biotransformation. The present inventors have already contributed towards this
objective at
a much smaller scale (Burgard & Maranas, 2001). Due to the extremely large
size of the
compiled database and the presence of multiple and sometimes conflicting
objectives that
need to be simultaneously satisfied, we developed the OptStrain procedure
illustrated in
Figure 1. Each step introduces different computational challenges arising from
the specific
structure and size of the optimization problems that need to be solved.
Step 1. Automated downloading and curation of the reactions in our Universal
database to
ensure stoichiometric balance;
Step 2. Calculation of the maximum theoretical yield of the product given a
substrate
choice without restrictions on the reaction origin (i.e., native or non-
native);
Step 3. Identification of a stoichiometrically-balanced pathway(s) that
minimizes the
number of non-native functionalities in the examined production host given the
maximum
theoretical yield and the optimum substrate(s) found in Step 2. Alternative
pathways that
meet both criteria of maximum yield and minimum number of heterologous genes
are
generated along with comparisons between different host choices. Information
pertaining
to the cofactor/energy usage associated with each pathway is also derived at
this stage.
~
Finally, one or multiple gene sets can be derived at this stage that ensure
the presence of
the targeted biotransformations by encoding for the appropriate enzymes;
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Step 4. Incorporation of the identified non-native biotransformations into the
stoichiometric models, if available, of the examined microbial production
hosts. The
OptKnock framework is next applied (Burgard et al., 2003; Pharkya et aL, 2003)
on these
augmented models to suggest gene deletions that ensure the production of the
desired
product becomes an obligatory byproduct of growth by "shaping" the
connectivity of the
metabolic network. The OptKnock framework is further described herein.
Curation of the database. The first step of the OptStrain procedure begins
with the
downloading and curation of reactions acquired from various sources in our
Universal
database. Specifically, given the fact that new reactions are incorporated in
the KEGG
database on a monthly basis, we have developed customized scripts using Perl
(Brown,
1999) to automatically download all reactions in the database on a regular
basis. A
different script is then used to parse the number of atoms of each element in
every
compound. The number of atoms of each type among the reactants and products of
all
reactions are calculated and reactions which are elementally unbalanced are
excluded from
consideration. In addition, compounds with an unspecified number of repeat
units, (e.g.,
trans-2-Enoyl-CoA represented by C25H39N7017P3S(CHZ)õ) or unspecified alkyl
groups R
in their chemical formulae are remoyed from the downloaded sets. This step
enables the
automated downloading of functionalities present in genomic databases and the
subsequent
verification of their elemental balanceabilities forming large-scale sets of
functionalities to
be used as recombination targets.
The present invention, contemplates that any number of particular methods can
be
used to automate the duration and/or curation of reactions. These automated
functions can
be performed in any number of ways depending upon the resources available, the
type of
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access to the resources, and other factors related to the specific environment
or context in
which the present invention is implemented.
Determination of the maximum yield Once the reaction sets are determined, the
second step is geared towards determining the maximum theoretical yield of the
target
product from a range of substrate choices, without restrictions on the number
or origin of
the reactions used. The maximum theoretical product yield is obtained for a
unit uptake
rate of substrate by maximizing the sum of all reaction fluxes producing minus
those
consuming the target metabolite, weighted by the stoichiometric coefficient of
the target
metabolite in these reactions. .The maximization of this yield subject to
stoichiometric
constraints and transport conditions yields a Linear Programming (LP) problem
(see
Supporting Information for mathematical formulation), often encountered in
Flux Balance
Analysis frameworks (Varma & Palsson, 1994). Given the computational
tractability of LP
problems, even for many thousands for reactions, a large number of different
substrate
choices can thoroughly be explored here.
Although, in this specific embodiment, the bioengineering objective relates to
maximizing production, the present invention contemplates that other
bioengineering
objectives can be used. In such instances, instead of determining or selecting
a maximum
yield, a separate and appropriate objective or constraint can be used.
Identification of the minimum number of heterologous reactions for a host
organism. The next step in OptStrain uses the knowledge of the maximum
theoretical
yield to determine the minimum number of non-native functionalities that need
to be added
into a specific host organism network. Mathematically, this is achieved by
first introducing
a set of binary variables y, that serve as switches to tum the associated
reaction fluxes v, on
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or off.
Note that the binary variable y, assumes a value of one if reactionj is active
and a
value of zero if it is inactive. This constraint will be imposed on only
reactions associated
with genes heterologous to the specified production host. The parameters vj""
and vj"' are
calculated by minimizing and maximizing every reaction flux vj subject to the
stoichiometry of the metabolic network (Burgard & Mamas, 2001). This leads to
a Mixed
Integer Linear Programming (MILP) model for finding the minimum number of
genes to
be added into the host organism network while meeting the yield target for the
desired
product. This formulation, discussed in greater detail later herein, enables
the exploration
of tradeoffs between the required numbers of heterologous genes versus the
maximum
theoretical product yield and also the iterative identification of all
alternate optimal
solutions. The end result of this step is a set of distinct pathways and
corresponding gene
complements that provide a ranked list of all alternatives for the efficient
conversion of the
substrate(s) into the desired product.
Incorporating the non-native reactions into the host organism's stoichiometric
model. Upon identification of the appropriate host organism, the analysis
proceeds with an
organism-specific stoichiometric model augmented by the set of the identified
non-native
reactions. Hqwever, simply adding genes to a microbial production strain will
not
necessarily lead to the desired overproduction due to the fact that microbial
metabolism is
primed to be as responsive as possible to the imposed selection pressures
(e.g., outgrow its
competition). These survival objectives are typically in direct competition
with the
overproduction of targeted biochemicals. To combat this, we use our previously
developed
bilevel computational framework, OptKnock (Burgard et al., 2003; Pharkya et
al., 2003) to
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eliminate all those functionalities which uncouple the cellular fitness
objective, typically
exemplified as the biomass yield, from the maximum yield of the product of
interest.
1.2 Results
Computational results for microbial strain optimization focused on the
production
of hydrogen and vanillin. One skilled in the art having the benefit of this
disclosure would
understand the present invention is in no way limited to these particular
bioengineering
objectives which are merely illustrative of the present invention. The
hydrogen production
case study underscores the importance of investigating multiple substrates and
microbial
hosts to pinpoint the optimal production environment as well as the need to
eliminate
competing functionalities. In contrast, in the vanillin study, identifying the
smallest
number of non-native reactions is found to be the key challenge for strain
design. A
common database of reactions, as outlined in (Step 1), was constructed for
both examples
by pooling together metabolic pathways from the methylotroph Methylobacterium
extorquens AMI (Van Dien & Lindstrom, 2002) and the KEGG database (Kanehisa et
al.,
2004) of reactions.
1.2.1 Hydrogen Production Case Study
An efficient microbial hydrogen production strateg,~ requires the selection of
an
optimal substrate and a microbial strain capable of forming hydrogen at high
rates. First
we solved the maximum yield LP formulation (Step 2) using all catalogued
reactions which
were balanced with respect to hydrogen, oxygen, nitrogen, sulfur, phosphorus
and carbon
(approximately 3,000 reactions) as recombination candidates. Note that
OptStrain allowed
for different substrate choices such as pentose and hexose sugars as well as
acetate, lactate,
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malate, glycerol, pyruvate, succinate and methanol. The highest hydrogen yield
obtained
for a methanol substrate was equal to 0.126 g/g substrate consumed. This is
not surprising
given that the hydrogen to carbon ratio for methanol is the highest at four to
one. A
comparison of the yields for some of the more efficient substrates is shown in
Figure 2.
We decided to explore methanol and glucose further, motivated by the high
yield on
methanol and the favorable costs associated with the use of glucose.
The next step in the OptStrain procedure entailed the determination of the
minimum number of non-native functionalities for achieving the theoretical
maximum
yield in a host organism. We examined three different uptake scenarios: (i)
glucose as the
substrate in Escherichia coli (an established production system), (ii) glucose
in Clostridium,
acetobutylicum (a known hydrogen producer), and (iii) methanol in
Methylobacterium
extorquens (a known methanol consumer).
1.2.1.1 Escherichia coli
The MILP framework (described in Step 3) correctly verified that with glucose
as
the substrate no ndn-native functionalities were required by E. coli for
hydrogen
production. Interestingly, hydrogen production was possible through either the
ferredoxin
hydrogenase reaction (E.C.# 1.12.7.2) which reduces protons to form hydrogen
or via the
hydrogen dehydrogenase reaction (E.C.# 1.12.1.2) which converts NADH into
NAD+while
forming hydrogen through proton association. Subsequently, the upper and lower
limits of
maximum hydrogen formatiori were explored for the E. coli stoichiometric model
(Reed et
al., 2003) as a function of biomass formation rate (i.e., growth rate) for
both aerobic and
anaerobic conditions and a basis glucose uptake rate of 10 mmol/gDW/hr (see
Figure 3).
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Notably, the maximum theoretical hydrogen yield is higher under aerobic
conditions.
However, only under anaerobic conditions hydrogen is formed at maximum growth
(see
point A, in Fig. 3) leading to a growth-coupled production mode. Note that
hydrogen
production takes place through the formate hydrogen lyase reaction which
converts formate
into hydrogen and carbon dioxide under anaerobic conditions, in agreement with
current
experimental observations (Nandi & Sengupta., 1998).
Moving to phenotype restriction to curtail byproduct formation (Step 4), we
explored whether the production of hydrogen in the wild type E. coli network
(Reed et al.,
2003) could be enhanced by removing functionalities from the network that were
in direct
~ or indirect competition with hydrogen production. To this end, we employed
the
OptKnock framework (Burgard et al., 2003; Pharkya et al., 2003), to pinpoint
gene
deletion strategies that couple hydrogen production with growth. Here we
highlight two of
the identified strategies. The first (double deletion) removes both enolase
(E.C.# 4.2.1.11)
and glucose 6-phosphate dehydrogenase (E.C.# 1.1.1.49). The removal of the
enolase
reaction strongly promotes hydrogen formation by directing the glycolytic flux
towards the
3-phosphoglycerate branching point into the serine biosynthesis pathway.
Subsequently,
serine participates in a series of reactions in one-carbon metabolism to form
10-
formyltetrahydrofolate which eventually is converted to formate and
tetrahydrofolate. The
elimination of dehydrogenase reaction prevents the shunting of any glucose 6-
phosphate
flux into the pentose phosphate pathway. The second strategy, a three-reaction
deletion
study, involves the removal of ATP synthase (E.C.# 3.6.3.14), alpha-
ketoglutarate
dehydrogenase, and acetate kinase (E.C.# 2.7.2.1). The removal of the first
reaction
enhances proton availability whereas the other two deletions ensure that
maximum carbon
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flux is directed towards pyruvate which is then converted into formate through
pyruvate
formate lyase. Formate is catabolized into hydrogen and carbon dioxide through
formate
hydrogen lyase.
A comparison of the hydrogen production limits as a function of growth rate
for
both the wild-type and mutant networks is shown in Figure 3. The transport
rates of carbon
dioxide for the mutant networks were fixed at the values suggested by
OptKnock, thus
setting the operational imperatives (Pharkya et al., 2003). Note that while
the two-reaction
deletion mutant has a theoretical hydrogen production rate of 22.7 mmol/gDW/hr
(0.025
g/g glucose) at the maximum growth rate (Point B), the three-reaction deletion
mutant
produces a maximum of 29.5 mmol/gDW/hr (0.033 g/g glucose) (Point C) at the
expense
of a reduced maximum growth rate. Interestingly, in both mutant networks,
maximum
hydrogen production requires the uptake of oxygen. This is in contrast to the
wild-type
case where the lack of oxygen was preferred for hydrogen formation. Notably,
it has been
reported (Nandi & Sengupta, 1996) that although formate hydrogen lyase can
only be
induced in the absence of oxygen, it can function in aerobic environments.
This will have
to be accounted for in any experimental study conducted on the basis of these
results.
1.2.1.2 Clostridium acetobutylicum
Ample literature evidence has identified the organisms of the Clostridium
species
as natural hydrogen production systems (Nandi & Sengupta, 1998; Katakoka et
al., 1997;
Chin et al., 2003; Das & Veziroglu, 2001). The reduction of protons into
hydrogen through
ferredoxin hydrogenase (E.C.# 1.12.7.2) is the key associated reaction. Not
surprisingly,
using OptStrain (Step 3), we verified that no non-native reactions were
required for
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hydrogen production (Papoutsakis & Meyer, 1985) in Clostridium acetobultylicum
with
glucose as a substrate. We next explored, as in the E. coli =case,'whether
hydrogen
production could be enhanced by judiciously removing competing functionalities
using the
OptKnock framework. To this end, we used the stoichiornetric model for
Clostridium
acetobutylicum developed by Papoutsakis and coworkers (Desai et al., 1999;
Papoutsakis,
1984). OptKnock suggested the deletion of the acetate-forming and butyrate-
transport
reactions.
This deletion strategy is reasonable in hindsight upon considering the
energetics of
the entire network. Specifically, in the wild-type case the formation and
secretion of each
butyrate molecule requires the consumption of 2 NADH molecules, thus reducing
the
hydrogen production capacity of the network. However, if butyrate is not
secreted, but is
instead recycled to form acetone and butyryl CoA, then butyryl CoA can again
be
converted to butyrate without any NADH consumption. The double deletion mutant
has a
theoretical hydrogen yield of 3.17 mol/mol glucose (0.036g /g glucose) at the
expense of
slightly lower growth rate (point C in Figure 4). Notably, in this case,
biomass formation
and hydrogen production are tightly coupled, in contrast to the wild-type
network where a
range (1.38-2.96 mmol/gDW/hr) of hydrogen formation rates are possible (Line
AB in
Figure 4) at the maximum growth rate. Experimental results (Nandi & Sengupta,
1998)
indicate that only up to 2 mol of hydrogen can be produced per mol of glucose
anaerobically in Clostridium. In -fact, it has been reported=that inhibitory
effects of butyrate
directly on hydrogen production and indirect, effects of acetate on growth
inhibition (Chin
et al., 2003) are responsible for the observed low hydrogen yields.
Interestingly, the
suggested reaction eliminations directly circumvent these inhibition
bottlenecks.
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1.2.1.3 A<lethylobacterium extorguens AMl
Moving from glucose to methanol as the substrate, we next investigated
hydrogen
production in'Methylobacterium extorquens AMl , a facultative methylotroph
capable of
surviving solely on methanol as a carbon and energy source (Van Dien &
Lidstrom, 2002).
The organism has been well-studied (Anthony, 1982; Chistoserdova et al., 2004;
Chistoserdova et al., 1998; Korotkova et al., 2002; Van Dien et al., 2003) and
recently, a
stoichiometric model of its central metabolism was published (Van Dien &
Lidstrom,
2002). Using Step 3 of OptStrain, we identified that only a single reaction
needs to be
introduced into the metabolic network of M. extorquens to enable hydrogen
production.
Two such candidates are hydrogenase (E.C.# 1.12.7.2) which reduces protons to
hydrogen
or alternatively N5,.N10-methenyltetrahydromethanopterin hydrogenase which
catalyzes the
following transformation:
E.C.# 1.12.98.2: 5,10-Methylenetrahydromethanopterin +-+ 5,10-
Methenyltetrahydromethanopterin + H2.
The need for an additional reaction is expected because the central metabolic
pathways in the methylotroph, as abstracted in (Van Dien & Lidstrom, 2002), do
not
include any reactions that convert protons into hydrogen such as the
hydrogenases found in
E. coli and the anaerobes of the Clostridia species. Therefore, it is not
surprising that, to
the best of our knowledge, no one has achieved hydrogen production using
methylotrophs
such as Pseudomonas AMI and P. methylica (Nandi & Sengupta, 1998). The
identified
reaction additions provide a plausible explanation for this outcome by
pinpointing the lack
of a mechanism to convert the generated protons to hydrogen.
1.2.2 Vanillin Production Case Study
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Vanillin is an important flavor and aroma molecule. The low yields of vanilla
from
cured vanilla pods have motivated efforts for its biotechnological production.
In this case
study, we identify metabolic network redesign strategies for the de novo
production of
vanillin from glucose in E. coli. Using OptStrain, we first determined the
maximum
i
theoretical yield of vanillin from glucose to be 0.63 g/g glucose by solving
the LP
optimization over approximately 4,000 candidate reactions balanced with
respect to all
elements but hydrogen (Step 2). We next identified that the minimum number of
non-
native reactions that must be'recombined into E. coli to endow it with the
pathways
necessary to achieve the maximum yield is three (Step 3). Numerous alternative
pathways,
differing only in their cofactor usage, which satisfy both the optimality
criteria of yield and
minimality of recombined reactions, were identified. For example, one such
pathway uses
the following three non-native reactions:
(i) E.C.# 1.2.1.46: Formate + NADH + H+<-+ Formaldehyde + NAD+ + H20,
(ii) E.C.# 1.2.3.12: 3, 4-dihydroxybenzoate (or protocatechuate) + NAD+ + H20
+
Forrnaldehyde <--> Vanillate + Oa + NADH, and
(iii) E.C.# 1.2.1.67: Vanillate + NADH +'H+ +-+ Vanillin + NAD+ + H20.
Interestingly, these steps are essentially the same as those used in the
experimental study by
Li and Frost (1998) to convert glucose to vanillin in recombinant E. coli
cells
demonstrating that the computational procedure can indeed uncover relevant
engineering
strategies. Note, however, that the reported experimental yield of 0.15 g/g
glucose is far
from the maximum theoretical yield (i.e., 0.63 g/g glucose) of the network
indicating the
potential for considerable improvement.
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This motivates examining whether it is possible to reach higher yields of
vanillin by
systematically pruning the metabolic network using OptKnock (Step 4). Here the
genome-
scale model of E. coli metabolism, augmented with the three functionalities
identified
above, is integrated into the OptKnock framework to determine the set(s) of
reactions
whose deletion would, force a strong coupling between growth and vanillin
production. The
highest vanillin-yielding single, double, and quadruple knockout strategies
are discussed
next for a basis glucose uptake rate of 10 mmol/gDW/hr. In all cases,
anacrobic conditions
are selected by OptKnock as the most favorable for vanillin production. It is
worth
emphasizing that, in general, the deletion strategies identified by OptStrain
are dependent
upon the specific gene addition strategy fed into Step 4 of OptStrain.
Accordingly, we
tested whether altexnative and possibly better, deletion strategies would
accompany some
of the other candidate addition strategies alluded to above. For the vanillin
case study, we
found the deletion suggestioris and anticipated vaniliin yields at maximal
growth to be
quite similar regardless of the gene addition strategy employed.
The first deletion strategy identified by OptStrain suggests removing
acetaldehyde
dehydrogenase (E.C.# 1.2.1.10) to prevent the conversion of acetyl-CoA into
ethanol.
Vanillin production in this network, at the maximum biomass production rate of
0.205 hr-1,
is 3.9 mmoUgDW/hr or 0.33 g/g glucose based on the assumed uptake rate of
glucose. In
this deletion strategy, flux is redirected through the vanillin precursor
metabolites,
phosphoenolpyruvate (PEP) and erythrose-4-phosphate (E4P), by blocking the
loss of
carbon through ethanol secretion. The second (double) deletion strategy
involves the
additional removal of glucose-6-phosphate isomerase (E.C.# 5.3.1.9)
essentially blocking
the upper half of glycolysis. These deletions cause the network to place a
heavy'reliance on
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the Entner-Doudoroff pathway to generate pyntvate and glyceraldehyde-3-
phosphate
(GAP) which undergoes further conversion into PEP in the lower half of
glycolysis.
Fructose-6-phosphate (F6P), produced through the non-oxidative part of the
pentose
phosphate pathway, is subsequently converted to E4P. Vanillin production, at
the expense
of a reduced maximum growth rate of 0.06 hr"t, is increased to 4.78
mmol/gDW/hr or 0.40
g/g glucose. A substantially higher level of vanillin production is predicted
in the four-
reaction deletion mutant network without imposing a high penalty on the growth
rate. This
strategy leads to the production of 6.79 mmol/gDW/hr of vanillin or 0.57 g/g
glucose at the
maximum growth rate of 0.052 hr"1. The OptKnock framework suggests the
deletion of
acetate kinase (E.C.# 2.7.2.1), pyruvate kinase (E.C.# 2.7.1.40), the PTS
transport
mechanism, and fructose 6-phosphate aldolase. The first three deletions
prevent leakage of
flux from PEP and redirect it instead to vanillin synthesis. The elimination
of fructose 6-
phosphate aldolaseprevents the direct conversion of F6P into GAP and
dihydroxyacetone
(DHA). Note that both F6P and GAP are used to form E4P in the non-oxidative
branch of
the pentose phosphate pathway. DHA can be further reacted to form
dihydroxyacetone
phosphate (DHAP) with the consumption of a PEP molecule. Thus, elimination of
fructose
6-phosphate aldolase prevents theutilization of both F6P and PEP which are
required for
vanillin synthesis. Furthermore, a surprising network flux redistribution
involves the
employment of a group of reactions from one-carbon metabolism to form 10-
formyltetrahydrofolate, which is subsequently converted to formaldehyde.
Figure 5 compares the vanillin production envelopes, obtained by maximizing
and
minimizing vanillin formation at different biomass production rates for the
wild-type and
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mutanat networks. These deletions endow the network with high levels of
vanillin
production under any growth conditions.
1.3 I)iscussion
The OptStrain framework of the present invention is aimed at systematically
reshaping whole genome-scale metabolic networks of microbial systems for the
overproduction of not only small but also complex molecules. We have so far
examined a
number of different products (e.g., 1,3 propanediol, inositol, pyruvate,
electron transfer,
etc.) using a variety of hosts (i.e., E. coli, C. acetobut,ylicum, M.
extorquens). The two
case studies, hydrogen and vanillin, discussed earlier show that OptStrain can
address the
range of challenges associated with strain redesign. At the same time, it is
important to
emphasize that the validity and relevance of the results obtained with the
OptStrain
framework are dependent on the level of completeness and accuracy of the
reaction
databases and microbial metabolic models considered. We have identified
numerous
instances of unbalanced reactions, especially with respect to hydrogen atoms,
and
ambiguous reaction directionality in the reaction.databases that we mined.
Careful curation
of the downloaded reactions preceded all of our case studies. Whenever the
balanceability
of a reaction with respect to carbon could not be restored, the reaction was
removed from
consideration. We expect that this step will become less time-consuming as
automated
tools for reaction database testing and verification (Segre et al., 2003) are
becoming
available. The purely stoichiometric representation of metabolic pathways in
microbial
models can lead to unrealistic flux distributions by not accounting for
kinetic barriers and
regulatory interactions (e.g., allosteric regulation). To alleviate this, the
present invention
contemplates incorporating regulatory information in the form of Boolean
constraints
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(Covert & Palsson, 2002) into the stoichiometric model of E. coli and the use
of kinetic
expressions on an as-needed basis (Castellanos et al. 2004; Tomita et al.,
1999; Vamer &
Ramkrishna, 1999). Further, the present invention contemplates using OptKnock
to
account for not only reaction deletions but also up or down regulation of
various key
reaction steps. Despite these simplifications, OptStrain has already provided
in many
cases useful insight into microbial host redesign and, more importantly,
established for the
first time an integrated framework open to future modeling improvements.
It should be understood that a computer is iused in implementing the
methodology
of the present invention. The present invention contemplates that any number
of
computers can be used, and any number of types of software or programming
languages
can be used. It should further be understood that the present invention
provides for storing
a representation of the networks created. The representations of the networks
can be-stored
in a memory, in a signal, or in a bioengineered organism.
1.4 Mathematical Formulation for OntStrain
The redesign of microbial metabolic networks to enable enhanced product yields
by
employing the OptStrain procedure requires the solution of multiple types of
optimization
problems. The first optimization task (Step 2) involves determining the
maximum yield of
the desired product in a metabolic network comprised of a set N= { 1, ..., N}
of
metabolites and a set 9K ={1, ..., M} of reactions. The Linear Programming
(LP) problem
for maximizing the yield on a weight basis of a particular product P (in the
set 9V} from a
set 91 of substrates is formulated as:
u
, i=P
Max MW =IS,,v)
Vj I=1
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subject to ESv, _ 0 , 'd i E N, io 91 (1)
J=J
M
~ (MW, - isJv! -Z (2)
101 f al -
where MYI', is the molecular weight of metabolite i, vj is the molar flux of
reactionj, and S.
is the stoichiometric coefficient of metabolite i in reaction j. In our work,
the metabolite
set Nwas comprised of approximately 4,800 metabolites and the reaction set 94
consisted
of more than 5,700 reactions. The inequality in constraint (1) allows only
for' secretion and
prevents the uptake of all metabolites in the network other than the
substrates in 93.
Constraint (2) scales the results for a total substrate uptake flux of one
gram. The reaction
fluxes vi can either be irreversible (i.e., v, _ 0) or reversible in which
case they can assume
either positive or negative values. Reactions which enable the uptake of
essential-for-
growth compounds such as oxygen, carbon dioxide, ammonia, sulfate and
phosphate are
also present.
In Step 3 of OptStrain, the minimum number of non-native reactions needed to
meet the identified maximum yield from Step 2 is found. First the Universal
database
reactions which are absent in the examined microbial host's metabolic model
are flagged as
non-native. This gives rise to the following Mixed Integer Linear Programming
(MILP)
problem:
Min EyJ
v, I yi JEMrren-nanve
M
subject to ySuvj >_ 0 , b' i E N, io 91 (1)
J=~
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,~f =
MI3; = ~ S#vi (2)
IE92 j=1
M
t er ' 1= P (3)
Syvj Yleld m
MW; =Y >_
.%=J
v j:5 jmx .Y j b J E I"Inon-native (4)
vj ~ v~p vi d.1 E I"lnon-native (5)
y'j {0,1} , b J E Mnon-native (6)
The set W noõ_narõe comprises of the non-native reactions for the examined
host and is a
subset of the set 9f. Constraints (1) and (2) are identical to those in the
product yield
maximization problem. Constrairit (3) ensures that the product yield meets the
maximum
theoretical yield, Yiela~age1, calculated in step 2. The binary variables yl
in constraints (4)
and (5) serve as switches to turn reactions on or off. A value of zero for yJ
forces the
corresponding flux vj to be zero, while a value of one enables it to take on
nonzero values.
The parameters vjm'n and vj" can either assume very low and very high values,
respectively, or they can be calculated by minimizing and maximizing every
reaction flux
vj subject to constraints (1-3).
.15 Alternative pathways that satisfy both optimality criteria of maximum
yield and
minimum non-native reactions are obtained by the iterative solution of the
MILP
formulation upon the accumulation of additional constraints referred to as an
integer cuts.
Integer cut constraints exclude from consideration all sets of reactions
previously
identified. For example, if a previously identified pathway utilizes reactions
1, 2, and 3,
then the following constraint prevents the same reactions from being
simultaneously
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considered in subsequent solutions: yr + y2 + y3 < 2. More details can be
found in
Burgard and Maranas (2001).
Step 4 of OptStrain identifies which reactions to eliminate from the network
augrnented with the non-native functionalities, using the OptKnock framework
developed
previously (Burgard et al., 2003; Pharkya et al., 2003). The objective of this
step is to
constrain the phenotypic behavior of the network so that growth is coupled
with the
formation of the desired biochemical, thus curtailing byproduct formation. The
envelope
of allowable targeted product yields versus biomass yields is constructed by
solving a
series of linear optimization problems which maximize and then, minimize
biochemical
production,for various levels of biomass formation rates available to the
network. More
details on the optimization formulation can be found in (Pharkya et al.,
2003). All the
optimization problems were solved in the order of minutes to hours using CPLEX
7.0
(http://www.ilog.com/products/cplex/) accessed via the GAMS (Brooke et al.,
1998)
modeling environment on an IBM RS6000-270 workstation.
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2. OUtKDOCk
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. colf metabolic network as abstracted
in the in
silico E. coli model of Palsson and coworkers (Edwards & 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 Figure 6 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
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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 (MO,MA) (Segre et al., 2002) as the
cellular
objective. Based on the OptKnock framework, it is possible to 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
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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. Fo'r 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 iargeted 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 mrnol/gDW-hr. Therefore, all reported chemical production and
biomass
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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; Vamer and Ramkrishna, 1999), metabolic control
analysis
(Kacser and Bums, 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.
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2.1 Methods
The maximization of a cellular objective quantified as an aggregate reaction
flux
for a steady state metabolic network comprising a set N= { 1,. .., 9V) of
metabolites and a
set 91= { 1,..., M} of metabolic reactions fueled by a glucose substrate is
expressed
mathematically as follows,
maximize vicellular objective (Primal)
subject to YSvj = 0, 'd i E N
j=1
Vpts. + Vglk = Vgic_uptake mmol/gDWhr
vatp ~ vatp main mmol/gDW-hr
Vbiamass ~ Vbiamass 1 /hr
1' j? O, 'd j E Mirrev
v j< 0, f/ j E Msecr only
vJ E R, t'1 j E Mrev
where Sy is the stoichiometric coefficient of metabolite i in reactionj, vj
represents the flux
of reactionj, Vglc_uptake is the basis glucose uptake scenario, vatp mai>: is
the non-growth
associated ATP maintenance requirement, and vb orMass 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,
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whereas the reverse (i.e., negative) direction corresponds to metabolite
secretion. The
uptake of glucose through the phosphotransferase system and glucokinase are
denoted by
vprs and vgtk, respectively. Transport fluxes for metabolites that can only be
secreted from
the network are members Of Msecr oõly. Note also that the complete set of
reactions M is
subdivided into reversible M, and irreversible M1Reõ 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/gDWhr or 1/hr.
The modefing 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,
1 if reaction flux vj is active
y' 0 if reaction flux, vj is not active VjE M
assume a value of one if reaction j is active and a value of zero if it is
inactive. The
following constraint,
vimm. yf<v,<v,~'*yJ b'jE M
ensures tliat reaction flux vj is set to zero only if variable yj is equal to
zero. Alternatively,
wheny, is equal to one, vj is free to assume any value between a lower vJ ""
and an upper v.,"
bound. In this study, vJ""" and vj'" " 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 (yj = 1)
so as the optimization of the celluldr objective indirectly leads to the
overproduction of the
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chemical or biochemical of interest (see also Figure 6). Using biomass
formation as the
cellular objective, this is expressed mathematically as the following bilevel
mixed-integer
optimization problem.
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maximize vchemrcal (OptKnock)
Yi
subject to maximize vbromass (Primal)
vJ
subject to E.S' vl = 0, V1 E N
vpts + Vglk - vgtc _ uptake
Vaip ~ Vatp matn
t arg et
Vblomass > V
biomass
v ;in =y, 5v, <_V;ax =y,, ej E M
yi ={0,1 }, fI j E M
F, (1-yj )SK
JEM
where K is the number of allowable knockouts. The fmal constraint ensures that
the
resulting network meets a miriimum biomass yield, ' btomass =
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
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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
P
minimize Vatp_mQtn =Patp + Vbromnss Aromass + Vglc_up(ake gic (Dual)
N
subj ect to r a~ ~oEch Si glk +~lgik + gIC - 0
6j-~i
Xitolch Si pts +,ll pts + gl c= 0
' i=t
N
stofch
~i Si,biomass + Pbiomass 1
r'=1
N
Ivi 1o"hS,J +,u j= 0, 'd j E M; j~ glk, pts, biomass
~ min y, ) < Pj < ~,'."a" = (1- yj), b' j E Mrev and1 0- Msecr only
fl~ ~ fl j n(1 -.j1]Vj E Mrev and Msecr only
fl; <_ ~Cl ,niax(1 - yj), d j E Mirrev and J SE Msecr only
j E R, Vj E Mirrev and Msecr only
Ztoich E R, t'/ j E N
glcER
where .its' "h is the dual variable associated with the stoichiometric
constraints, glc is the
dual variable associated with the glucose uptake constraint, and pj is the
dual variable
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associated with any other restrictions on its corresponding flux vJ in the
Primal. Note that,
the dual variable,uj acquires unrestricted sign if its corresponding flux in
the OptKnock
inner problem is set to zero by enforcing yj = 0. The parameters ,-limin and
qj' 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
MII,P.
maximize Vchemical (OptKnock)
subject to
t et
Vbiomass - Vatp main',uatp + Vb,omass ~-omass +Vgic_uptake ' glc
M
Y'S;;vi = 0, 'd i E N
1=J
Vpts + Vglk = 1'gic_uptake mmol/gDW-hr
1'atp ~ Vatp main mmol/gDI Y=hr
N
Y, Ivi toich S*f glk + /uglk + glC = 0
i=1
N =
Z,~itoichsi,p, + tLl pta + gic = 0
i=1
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N
a'stofch
i si,bfomass + Pbiomass - 1
i=1
N
sloich
Su +,u j= 0, Vj E M, j glk, pts, biomass
E(1-yj):5"T';
jEM
vbtomass ~ Vbiomass
,47 n .(1- y J):5'Y, ~~'ax .(1- y j), Vj E Mrev and j0 Msecr oniy
~ j >~ jdn '(1 -y d f E Mrev and Msecr only
Pj:gp~'(1- Y j), d j E Mirrev and j 0 Msecr only
pj ERr V,J E Mirrev and Msecr only
~ftn.yj<_vjSv!'a' yj, VjE M
A,toich E R, b'jE N
glc E R
yj d j E M
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
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phosphate pathway, respiration, and all anaplerotic reactions. This is
accomplished by
limiting the number of reactions included in the summation (i.e., (1- y j)=
K).
jeCentral Metabolism
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 w-ill be, apparent to those skilled in the art and that
the invention is
not limited to these specific illustrative examples.
2.2 EXAMPLE 1
Succinate and Lactate Production
' Wtuch reactions, if any, that could be removed from the E. coli K-12
stoichiometric
model (Edwards.8z 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
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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 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 (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. The succinate production
limits 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
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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,
there was 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). =. 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 & 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. It is also noted 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.
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. . o .
Table I - 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
mmoUhr 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,
glycerol secretion was disabled for both knockout strategies.
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Succinate max yblomasa Rl1n ME(yo - v)2
Biomass Succinate Suceinate
ID Knockouts Enzyme (1/hr) (mmoUhr) (mmol/hr)
Wild "Complele network" 0 38 D.12 0
A I COA+ PYR -r ACCOA'+FOR Pyruvatc fomtatc lyase
2 NADH + PYR *-s LAC + NAD Lactate dehydrogenase 0=3 i 10.70 1,65
B I COA + PYR -). ACCOA + FOR Pytnvate fonnata lyase
2 NADH + PYR E-s LAC + NAD Lactate dehydrogenase 0.31 10.70 4.79
3 ACCOA + 2 NADH COA + ETH + 2 NAD Acetaldehyde dehydrogenase
C I ADP + PEP -+ ATP + PYR Pynrvato kinasc
2 ACTP + ADP ea AC + ATP or Acetate Idnase 0.16 15.15 621
ACCOA + Pi e-+ ACTP + COA Phosphotransacetylase
3 GLC + PEP -- G6P + PYR Phosphatran9ferase system
Lactate max V btomau min ME(v v) 2
Biornass Lactate Lactate
ID Knockouts Enzyme (1/hr) (mmol/hr) (mmoUhr)
Wlld "Complete network" 0 38 D 0
A I ACTP + ADP t+ AC + ATP or Acatate kinase
ACCOA + Pi c-s ACTP + COA Phosphotransacetylasc 0.28 10.46 5 58
2 ACCOA + 2 NADH - COA + ETH + 2 NAD Acetaldehydc dehydrogouasc
B I ACTP + ADP <-s AC + ATP or Acetate kinase
ACCOA + Pi t-r ACTP + COA Phosphotransacetylase 0.13 1900 0 19
2 ATP + F6P --> ADP + F'DP or Phosphofructoldnase
FDP r+ T3P1 + T3P2 Fntctose-1,6-blspbosphatate aldolase
C 1 ACTP + ADP a-s AC + ATP or Acetate kinase
ACCOA + P( E+ ACTP + CDA Phosphotransacctylase
2 ATP + F6P -s ADP + FDP or Phosphofruclokinase
FDPHT3P1+T3P2 Fructose-I.6-bisphosphatataaldolase 0=12 18.13 1053
3 ACCOA + 2 NADH - COA + ETH + 2 NAD Acetaldehyde dehydrogenase
4 GLC + ATP -+ G6P + PEP Glucokinasr
1,3-Propanediot mar y biomau rxin t$ (v a- v)'
Biomass 1,3-PD 1,3-PD
ID Knockouts Enzyme (1/hr) (mmol/hr) (mmol/hr)
Wad "Complcta network" 1.06 0 0
A I FDP -+ F6P + Pi or Fructose-1,6-bispbosphatase
FDP f+ T3P1 + T3P2 Fructosc-1,6-bisphosphatc aldolase
2 13PDG + ADP ++ 3PG + ATP or Phosphoglycemte kinase 0.21 9.66 8.66
NAD + Pi + T3P 1 t-+ I 3PDG + NADH Glyceraldehyde-3-phosphate dehydrogenase
3 GL + NAD <-- GLAL + NADH Aldehyde dehydrogenase
B I T3P1 ta T3P2 Triosphosphate isometase
2 G6P + NADP ea D6PGL+NADPH or Glucase 6-phosphate-l-dehydrogenase
D6PGL -r D6PGC 6-Phosphoglaconolactonase 0.29 9.67 9.54
3 DRSP -s ACAL+T3P1 Deo.yn'bose-phosphate aldolase
4 GL + NAD H GLAL + NADH Aldehyde dchydrogenase
2.2 EXAMPLE 2
1,3-Propanediol (PDO) Production
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In addition to devise 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 & 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
=J
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-
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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).
Review of the flux distributions of the wild-type E. coli, mutant A, and
mutant B
networks that maximize the biomass yield indicates that, 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 inactivatiori of the pentose phosphate and glycolysis
(with the
exception of triose phosphate isomerase) pathways. To compensate, the Entner-
Doudoroff
glycolysis pathway is activated to cliannel 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.
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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, 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 Chlorof lexus 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
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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.
2.3 EXAMPLE 3
Alternative Cellular Objective: Minimization of Metabolic Adjustment
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 miultiple cycles of growth selection
(Ibarra et al., 2002).
In this section, a contrasting hypothesis was examined (i.e., minimization of
metabolic
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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). 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-out strategy suggests
only slightly
lower chemical production yields for the MOMA case compared to the maximum
biomass
hypothesis. This implies that the OptKnock results are fairly robust with
respect to the
choice of cellular objective.
3.0 Alternative Embodiments
The publications and other material used hereiri to illuminate the background
of the
invention or provide additional details respecting the practice, are herein
incorporated by
reference in their entirety. The present invention contemplates numerous
variations,
including variations in organisms, variations in cellular objectives,
variations in
bioengineering objectives, variations in types of optimization problems formed
and
solutions used. These and/or other variations, modifications or alterations
may be made
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therein without departing from the spirit and the scope of the invention as
set forth in the
appended claims. -
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