Christodoulos A. Floudas Memorial Symposium (May 6, 2017)

���� Dept. of Chem. Engineering, Princeton Univ. 1991

The Princeton years…

���� Chris taught me the audacity of “can do” in research

Systems analysis and engineering(…for living things)

MicrobesChemical Process Plants

Retrofit/grass roots design Strain redesign/genome eng.

Process flow diagram Metabolic model reconstruction

Fault detection Model curation/reconciliation

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Overview

� Reconstruct: Organism-specific genome-scale models

� Redesign: Computational strain design

� Standardize: MetRxn: standardized knowledgebaseof metabolites and reactions

Mathematical core

v1

v2

v3

Optimal solution

� ��� ⋅ ���

�∈= 0, ∀� ∈ �

LP Problem

FBA

�������� ��������subject to:

��� ≤ �� ≤ ���, ∀� ∈ �� ∈ ℝ, ∀� ∈

MILP Problem

minReaction

��"����� � = � #��

�∈

� ��� ⋅ ���

�∈= 0, ∀� ∈ �

subject to:

#� ⋅ ��� ≤ �� ≤ #� ⋅ ��� , ∀� ∈

#� = $ 1, �& ��� ≤ �� ≤ ���0, �& �� = 0

�� ∈ ℝ

Binary variables #� defined as

�������� ≥ 0.1 ����������)

#� ∈ {0,1}

Bilevel Problem

optKnock

�������� �,-�./01

�������� ��������subject to:

subject to:

� ��� ⋅ ���

�∈= 0, ∀� ∈ �

#� ⋅ ��� ≤ �� ≤ #� ⋅ ��� , ∀� ∈ �������� ≥ ��������1�-231

#� ∈ {0,1}�(1 − #�)

�

�∈≤ 7

OptKnock for microbial strain design

CellularObjective

(ex: biomass yield)

BioengineeringObjective

(ex: product yield)

(Burgard et al., Biotech. Bioeng., 2003)

CellularObjective

(ex: biomass yield)

Anthony Burgard Priti Pharkya

Research General Engineer,

National Energy Technology LabSr. Research Scientist,

Genomatica

OptKnock bilevel optimization framework

7

Maximize

s.t.

Biomass Production

� Fixed substrate uptake rate

� Network connectivity

(over fluxes)

s.t.

Maximize Product Flux

� Blocked reactions identified

by outer problem

� Minimum biomass yield

� # Knockouts ≤ limit

(over gene knockouts)

Inner Problem:

adjust reaction fluxes

� optimize cellular objective

Outer Problem:

adjust knockouts

� optimize strain design objective

LP duality theory

8

PRIMAL (Inner problem)

subject to

PRIMAL BiomassZ v=Maximize

0,ij j

j

S v i I= ∀ ∈∑

(1 ),j j j

v LB y j J− ≤ − − ∀ ∈

ZDUAL

ZPRIMAL

Optimal solution

if and only if:

ZDUAL = ZPRIMAL

vj

8�multipliers

(1 ),j j j

v UB y j J≤ − ∀ ∈

9�:;9�<;

DUAL

(1 ) (1 )UB LB

DUAL j j j j j j

j J j J

Z UB y LB yµ µ∈ ∈

= − − −∑ ∑Minimize

subject to

8� , 9�:; , 9�<;(1 ) (1 )

UB LB

DUAL j j j j j j

j J j J

Z UB y LB yµ µ∈ ∈

= − − −∑ ∑

1, { }UB LB

i ij j j

i

S j biomassλ µ µ+ − = ∀ ∈∑

0, \{ }UB LB

i ij j j

i

S j J biomassλ µ µ+ − = ∀ ∈∑

, 0,UB LB

j jj Jµ µ ≥ ∀∈

LP duality theory

9

Maximize Productv

#�, 8� , 9�:;, 9�<;subject to

j

j

y =∑

MILP problem

# of knockouts

� By imposing strong duality condition Optknock can be recast as single-level MILP

Primal0,

ij j

j

S v i I= ∀ ∈∑

(1 ) (1 ),j j j j jLB y v UB y j J− ≤ ≤ − ∀ ∈

Strong duality

Dual

1, { }UB LB

i ij j j

i

S j biomassλ µ µ+ − = ∀ ∈∑

0, \{ }UB LB

i ij j j

i

S j J biomassλ µ µ+ − = ∀ ∈∑

,max0 { | }

LB LB

j j j jy j j LB Mµ µ≤ ≤ ∀ ∈ = −

,max0 { | }

UB UB

j j j jy j j UB Mµ µ≤ ≤ ∀ ∈ =

{ }0,1 , , 0, ,UB LB

j j j jy v j Jµ µ∈ ≥ ∈ ∀ ∈R

,i

i Iλ ∈ ∈R

irrev exch,limitin

( )g

UB LB LB LB

biomass ATPM ATPM biomass biomass ATPM ATPM j j

j J J

v UB LB LB LBµ µ µ µ∈ ∪

= − + + ∑

Graphical representation

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Growth Rate (hr-1)

Pro

du

ct Y

ield

(m

ol/m

ol g

luco

se)

Trade-off plot between biomass and product formation

Wild-typeStrain

OptKnockDesign

0 20 40 60 80 100Biomass Yield (%)

100

80

60

40

20

0

Pro

duct

Yie

ld (

%)

Constrain phenotypic space so as max biomass yield leads to high

product yield

Key Idea:

0

2

4

6

8

10

12

14

0 0.2 0.4 0.6 0.8 1 1.2

1,3

PD

Pro

ducti

on L

imit

s(m

mol/

hr)

Growth Rate (1/hr)

Mutants characterization

Basis: 10 mmol/hr glucose, 1 gDW cells

Maximum Growth:

E. coli (wild type)

Mutant A

Mutant B

Mutant C

Mutant D

Mutant E

Mutant A

Mutant B

Complete E. coli network

Adaptive evolution: Lactate mutant

PEP

G6P

F16P

F6P

13P2DG

3PG

2PG

PEP

PYR

MAL

SUCCOACIT

AKG

GAP

ICIT

DHAP

GLC

PYRD6PGL RL5P

X5P

S7P

E4P F6P

GAP

R5P

D6PGC

FUM

ACCOA

SUCC

ACTP

AC

LAC ETH

FOR

OA

“Anaerobic Conditions”

Knockouts:(2) Phosphotransacetylase (pta)

(1) Acetaldehyde dehydrogenase (adhE)

Blattner Lab: Strain ConstructionPalsson Lab: Adaptive Evolution

MUST sets

Maximize

(over MUST sets)

s.t. Minimize

(over fluxes)

s.t. Stoichiometry

Environmental conditions

MUST set constraints

vproduct

vproduct

∑ # of direct manipulations < k

vproduct

Number of interventions (k)4 6 7

Target yield

2

Alternate interventions

Identify the minimal set of metabolic interventions that guarantee the imposed yield of target chemical

Computational strain design: OptForce

� Prioritization of genetic interventions

� Mostly additive contribution of interventions

� Alternate minimal FORCE sets

Sridhar Ranganathan

Key Idea:

Staff Scientist, Life Technologies

(Ranganathan et al., PLoS Comput. Biol., 2010)

Naringenin production (with Koffas lab, RPI)

BL21*

Naringenin

yield

(mg / g

glucose)

accABD gapA pgk ΔfumB ΔfumC ΔsucC

57

112113

157153

199

55

Δmdh

BL21*

↑ gapA

BL21*

↑ pgk

↑pgk

• Up-regulation of pgk and/or gapAincreases yield by about 98%

• Knock-outs of mdh or acnA decreases yield

• Knock-outs of fumB or fumC and sucCfurther increases yield by about 76%

• Overexpression of pdh boosts yield by 8%resulting in a final yield of 504 mg/L

fumB

Δ sucC

acnA

accABDmdh

gapA

pgk

pdh

Δ scpC

andand and and

or

ororor

fumCor

or

Δ sucD

53

ΔacnA

52

BL21*

Δ mdh

52

155150

↑gapA ↑pgk

BL21*

Δ acnA

↑gapA ↑pgk

BL21*

Δ fumB

↑gapA ↑pgk

BL21*

Δ fumC

↑gapA ↑pgk

BL21*

Δ sucC

↑gapA

196

203

198

↑pgk ↑gapA

Δ fumB Δ fumC

BL21*

Δ sucC

↑pdh

↑pgk ↑gapA

Δ fumC

219213

Δ fumB

pdh

(Xu et al., Metab. Eng., 2011)

Production of platform biochemicals

� Explored muconic acid and shikimic acid overproduction strategies in S. cerevisiae

Collaborator: Zengyi Shao Lab,

Iowa State Univ.

(Suastegui et al, submitted, 2017)(Ranganathan et al, Metab Eng,

2012; Tee et al, Biotech Bioeng,

2013)

� OptForce was used to identify intervention strategies for fatty acid overproduction in E. coli

Collaborator: Jacqueline V. Shanks

Lab, Iowa State Univ.

� OptKnock/OptForce/k-OptForce suggested intervention strategies for TAL overproduction in S. cerevisiae

(Chowdhury et al, PLoS Comput Biol, 2014;

Cardenas and da Silva, Metab Eng, 2016)

Collaborator: Nancy Da Silva Lab,

UC Irvine

3pg

pep

pyr

accoa

acald

etoh

ac

malcoaTAL

ACCOAC

fatty acid biosynthesis

etoh[out]

Glucose

oaa

nadph

nadp

nadh

nad

ENO

PYK

PC

PYRDC

ALDD

nadp nadph

ALCD

193

193

89

46

0.5

21.5

89

0

2pg

32

PDH70

0ACS

2PS

nadp nadph

atp

amp

ser7

k-OptForce

Key Idea: Use available kinetic information to better define base strain and more tightly constrain overproducing phenotype

Anupam

Chowdhury

Scientist,

Zymergen

(Tran et al, Biophys J, 2008; Tan et al, Metab Eng, 2011; Tan & Liao, Biotechnol J, 2012)

Key idea: Successive reduction of the feasible parameter space

using experimentally measured flux data

Rxn

rate

(m

mol/

h)

Time

Ensemble modeling of metabolic networks

James C.Liao Linh M.Tran

A EB

Decomposition

A +

+

A

A

E E

E E

E E B

B

B

Step 1

Step 2

Step 3

Reaction reversibility:

Enzyme balance:

(e: Enzyme fractions)

(for all steps)

Repeat until converge to a single model

Create an ensemble by sampling

R and e within [0,1]

ScreeningScreening

Retained modelsRetained models

Rxn

rate

(m

mol/

h)

Time

Genetic perturbationGenetic perturbation×↓↑

Perturbed modelsPerturbed models

Rxn

rate

(m

mol/

h)

Time

Initialize chromosome in GA using the kinetic values in

the previous iteration

Rxn

rate

(m

mol/

h)

Time

Mutant flux datasetsΔgnd

Parameter identification procedure(Khodayari et al, Metab Eng, 2014)

Initial ensemble: ~ 105Initial ensemble: ~ 105

Add one set of mutant flux data

x

Minimize Deviation from experimental dataover kinetic

parameters

- Conservation of mass for metabolites,

free enzymes and enzyme complexes

- Mass action kinetics for rxn rates

- Thermodynamic feasibility

Subject to:

model#1

model#2

model#3

model#P

rxn #1

rxn #2

rxn #n

GA recombination of models

ΔpykF Δpgi ΔpykA Δrpe ΔppsA Δzwf

Ali Khodayari

Scientist

Genomatica

k-ecoli457: Towards genome-scale kinetic model of E. coli

# knock-out mutants: 7 25

# of reactions: 138 457 # of metabolites: 93 337# of substrate-level regulatory interactions: 60 295

core model

expandedmodel

(Bennet et al., Nat Chem Biol, 2009; Ishii et al., Science, 2007; Kabir et al., Bio Che eng, 2005; Zhao et al., ApplMic Biotech, 2004; Zhao et al., J Biotechnol, 2003)

(4x)

(3x)

(3x)

(5x)

Flux data for Model parameterization

� Glucose substrate: # of mutantsaerobic 19anaerobic 2(wild-type+Δldh)

� Other carbon substrates: pyruvate 3acetate 1

Ali Khodayari

Scientist

Genomatica

Concluding thoughts

���� Dept. of Chem. Engineering, Princeton Univ. 1994