Slide deck on Fast-SL, an efficient algorithm to identify synthetic lethals. Presented at the annual NNMCB meeting at Pune, India on 27 Dec 2015. Original paper reference: http://bioinformatics.oxfordjournals.org/content/31/20/3299

1. Fast-SL: An efficient algorithm to identify synthetic
lethals in metabolic networks
Karthik Raman
Department of Biotechnology
Indian Institute of Technology Madras
https://home.iitm.ac.in/kraman/lab/
2015 NNMCB National Meeting
December 27, 2015

2. Introduction Fast-SL Results Conclusions
Genome-Scale Metabolic Networks (GSMNs)
▶ GSMNs account for the functions of all the known metabolic genes
in an organism
▶ Constructed primarily from the genome sequence with annotations
from enzyme and pathway databases
▶ 100+ GSMNs are presently available
Karthik Raman Fast-SL: An efficient algorithm to identify synthetic lethals in metabolic networks 1 / 24

3. Introduction Fast-SL Results Conclusions
What can GSMNs tell us?
McCloskey D et al (2013) Molecular Systems Biology 9:661–661
∆gene
A = 0
B = 6.7
Prokaryotes
A
E
DC
Loss of
redundant
pathways
Wild type
A = 3.8
B = 2.9
B
t
OD
orf2
CAATCGACAG
TGATAGCCAG
TTAGTCTGAG
Design
E. coli
B. aphidicola
F
Flux
coupling
Coupled
reaction
sets
Mutualistic
growth
E. coli
M. barkeri
No
growth
E
M
ME
orf1 orf3?
No
growth
Growth
Active
pathways
TTTT
Model-drivendiscovery
18studies
7.3%
Studiesofevolutionaryprocesses
19studies
7.7%
Metabolic engineering
68 studies
27.4%
Interspecies Interaction
7 studies2.8%
25.8%64 studies
Prediction of cellular phenotypes
29.0%
72 studies
Analysis of biological network properties
A
B
A
B
E. coli
Reconstruction
248 total studies
E. coli
reconstruction
248 Total studies
Karthik Raman Fast-SL: An efficient algorithm to identify synthetic lethals in metabolic networks 2 / 24

4. Introduction Fast-SL Results Conclusions
What can GSMNs tell us?
▶ Predict potential drug targets, by identifying essential and synthetic
lethal genes
Editor’s Choice Identification of potential drug targets in Salmonella
enterica sv. Typhimurium using metabolic modelling
and experimental validation
Hassan B. Hartman,1
David A. Fell,1
Sergio Rossell,2
3
Peter Ruhdal Jensen,2
Martin J. Woodward,3
Lotte Thorndahl,4
Lotte Jelsbak,4
John Elmerdahl Olsen,4
Anu Raghunathan,5
4
Simon Daefler5
and Mark G. Poolman1
Correspondence
Mark G. Poolman
mgpoolman@brookes.ac.uk
1
Department of Medical and Biological Sciences, Oxford Brookes University, Gipsy Lane,
Headington, Oxford OX3 OBP, UK
2
Department of Systems Biology, Technical University of Denmark, Lyngby, Denmark
3
Department of Food and Nutritional Sciences, University of Reading, Reading, UK
4
Department of Veterinary Disease Biology, University of Copenhagen, Copenhagen, Denmark
5
Department of Infectious Diseases, Mount Sinai School of Medicine, New York, NY, USA
Karthik Raman Fast-SL: An efficient algorithm to identify synthetic lethals in metabolic networks 3 / 24

5. Introduction Fast-SL Results Conclusions
What are Synthetic Lethals?
Synthetic lethal gene (or reaction) sets are sets of genes where only the
simultaneous removal of all genes in the set abolishes growth:
Gene abc
Wild-type
Gene pqr
Δabc
Gene abc
Gene pqr
Gene abc
Δpqr
Gene pqr
Gene abc
ΔabcΔpqr
Gene pqr
The concept of synthetic lethality can be extended to higher orders,
e.g. triplets
Karthik Raman Fast-SL: An efficient algorithm to identify synthetic lethals in metabolic networks 4 / 24

6. Introduction Fast-SL Results Conclusions
Why Identify Synthetic Lethals?
▶ Synthetic lethals find applications in
▶ Understanding gene function and functional associations¹
▶ Combinatorial drug targets against pathogens²
▶ Cancer therapy³
¹Ooi SLL et al (2006) Trends Genet 22:56–63
²Hsu KC et al (2013) PLoS Comput Biol 9:e1003127+
³Kaelin WG (2005) Nat Rev Cancer 5:689–698
Karthik Raman Fast-SL: An efficient algorithm to identify synthetic lethals in metabolic networks 5 / 24

7. Introduction Fast-SL Results Conclusions
How to Identify Synthetic Lethals?
▶ Yeast synthetic lethals have been identified experimentally using
yeast synthetic genetic arrays¹,²
▶ Previous in silico approaches have built on the framework of Flux
Balance Analysis — restricted to metabolic genes
¹Tong AHY et al (2001) Science 294:2364–2368
²Tong AHY et al (2004) Science 303:808–813
Karthik Raman Fast-SL: An efficient algorithm to identify synthetic lethals in metabolic networks 6 / 24

8. Introduction Fast-SL Results Conclusions
What is Flux Balance Analysis?
▶ Effective constraint-based method to study genome-scale metabolic
networks¹
▶ The mass balance constraints in system of reactions can be
represented by a system of linear equations involving reaction fluxes
at steady state
▶ The system is under-determined — so we compute the flux
distribution that maximises biomass: mathematically, this is a linear
programming problem
max vbio (the biomass flux)
s.t.
Σjsijvj = 0 ∀i ∈ M (set of metabolites)
LBj ≤ vj ≤ UBj ∀j ∈ J (set of reactions)
¹Varma A & Palsson BO (1994) Applied and Environmental Microbiology 60:3724–3731
Karthik Raman Fast-SL: An efficient algorithm to identify synthetic lethals in metabolic networks 7 / 24

9. Introduction Fast-SL Results Conclusions
Geometrical interpretation of FBA
Orth JD et al (2010) Nature Biotechnology 28:245–248
×฀
participating
coefficient
v2
v1
v3
Allowable
solution space Optimal solution
v3
Unconstrained
solution space
Constraints
1) Sv = 0
2) ai < vi < bi
v2 v2
v1
v3
Optimization
maximize Z
v1
Karthik Raman Fast-SL: An efficient algorithm to identify synthetic lethals in metabolic networks 8 / 24

10. Introduction Fast-SL Results Conclusions
Flux Balance Analysis
▶ FBA has been proven to accurately predict phenotypes following
various genetic perturbations¹,²
▶ To delete reaction k, set vk = 0 and repeat the simulation:
max vbio
s.t.
Σjsijvj = 0 ∀i ∈ M
LBj ≤ vj ≤ UBj ∀j ∈ J
vd = 0 d ∈ D ∈ J
▶ FBA can also reliably predict synthetic lethal genes in metabolic
networks of organisms such as yeast³
¹Edwards JS & Palsson BO (2000) BMC Bioinformatics 1:1
²Famili I et al (2003) PNAS 100:13134–13139
³Harrison R et al (2007) PNAS 104:2307–2312
Karthik Raman Fast-SL: An efficient algorithm to identify synthetic lethals in metabolic networks 9 / 24

11. Introduction Fast-SL Results Conclusions
Identifying Synthetic Lethals
Brute Force/Exhaustive Enumeration
▶ Single lethals are easier to identify
▶ Solve one optimisation problem for each gene deletion (genotype)
▶ Synthetic lethals are more difficult to identify
▶ Combinatorial Explosion
▶ e.g.
(1000
3
)
≈ 170 million simulations!
▶ Quickly becomes infeasible for larger organisms …
▶ However, simulations are independent and can be easily parallelised
on a computer cluster¹
¹Deutscher D et al (2006) Nature Genetics 38:993–8
Karthik Raman Fast-SL: An efficient algorithm to identify synthetic lethals in metabolic networks 10 / 24

12. Introduction Fast-SL Results Conclusions
Identifying Synthetic Lethals
Bi-Level Mixed Integer Linear Programming Problem
▶ SL-Finder¹ poses the synthetic lethal identification problem elegantly
as a bi-level MILP
▶ Synthetic lethal double and triple reaction deletions have been
reported for E. coli
▶ However, the MILP problems become incrementally difficult to solve
▶ Time taken, on a workstation, was ≈ 6.75 days, for E. coli iAF1260
model
▶ MCSEnumerator is another MILP-based method, which runs even
faster²
¹Suthers PF et al (2009) Molecular Systems Biology 5:301
²von Kamp A & Klamt S (2014) PLoS Computational Biology 10:e1003378
Karthik Raman Fast-SL: An efficient algorithm to identify synthetic lethals in metabolic networks 11 / 24

13. Is there a way to surmount the
complexity of exhaustive
enumeration and bi-level MILP?

14. Introduction Fast-SL Results Conclusions
An Alternate Approach: Fast-SL
Pratapa A et al (2015) Bioinformatics 31:3299–3305
▶ Heavily prunes search space for synthetic lethals, and
▶ Exhaustively iterates through remaining (much fewer) combinations
▶ We successively compute:
▶ Jsl, the set of single lethal reactions,
▶ Jdl ⊂ J × J, the set of synthetic lethal reaction pairs, and
▶ Jtl ⊂ J3
, the set of synthetic lethal reaction triplets
▶ Central idea: We use FBA to compute a flux distribution,
corresponding to maximum growth rate, while minimising the sum of
absolute values of the fluxes, i.e. the ℓ1-norm of the flux vector — the
‘minimal norm’ solution of the FBA LP problem
Karthik Raman Fast-SL: An efficient algorithm to identify synthetic lethals in metabolic networks 12 / 24

15. Introduction Fast-SL Results Conclusions
Fast-SL: Eliminating Non-Lethal Sets
max vbio (1)
s.t. S.v = 0 (2)
LBj ≤ vj ≤ UBj ∀j ∈ J (3)
▶ Identify a flux distribution which
obeys the constraints of FBA(2),(3)
and also sustains maximum growth(1)
(sparse!)
▶ The set of reactions that carry a
non-zero flux in this solution is Jnz
▶ How does this help?
Karthik Raman Fast-SL: An efficient algorithm to identify synthetic lethals in metabolic networks 13 / 24

16. Introduction Fast-SL Results Conclusions
Fast-SL: Eliminating Non-Lethal Sets
max vbio (1)
s.t. S.v = 0 (2)
LBj ≤ vj ≤ UBj ∀j ∈ J (3)
▶ Identify a flux distribution which
obeys the constraints of FBA(2),(3)
and also sustains maximum growth(1)
(sparse!)
▶ The set of reactions that carry a
non-zero flux in this solution is Jnz
▶ How does this help?
�
Karthik Raman Fast-SL: An efficient algorithm to identify synthetic lethals in metabolic networks 13 / 24

17. Introduction Fast-SL Results Conclusions
Fast-SL: Eliminating Non-Lethal Sets
max vbio (1)
s.t. S.v = 0 (2)
LBj ≤ vj ≤ UBj ∀j ∈ J (3)
▶ Identify a flux distribution which
obeys the constraints of FBA(2),(3)
and also sustains maximum growth(1)
(sparse!)
▶ The set of reactions that carry a
non-zero flux in this solution is Jnz
▶ How does this help?
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Karthik Raman Fast-SL: An efficient algorithm to identify synthetic lethals in metabolic networks 13 / 24

18. Introduction Fast-SL Results Conclusions
Fast-SL: Eliminating Non-Lethal Sets
max vbio (1)
s.t. S.v = 0 (2)
LBj ≤ vj ≤ UBj ∀j ∈ J (3)
▶ Identify a flux distribution which
obeys the constraints of FBA(2),(3)
and also sustains maximum growth(1)
(sparse!)
▶ The set of reactions that carry a
non-zero flux in this solution is Jnz
▶ How does this help?
�
���
Karthik Raman Fast-SL: An efficient algorithm to identify synthetic lethals in metabolic networks 13 / 24

19. Introduction Fast-SL Results Conclusions
Fast-SL Massively Prunes Search Space for Synthetic Lethals
▶ If a reaction j carries zero flux in the minimal
norm solution (j /∈ Jnz), which is constrained
to support growth, it cannot be lethal
▶ If a pair of reactions i, j carry zero flux in the
minimal norm solution (i, j /∈ Jnz), they cannot
be a synthetic lethal pair
⇒ There are no synthetic lethal pairs that
comprise reactions that are both not in Jnz
▶ All synthetic lethal pairs lie in the narrow ‘red
region’ of J × J (drawn to scale for E. coli)
�
���
Karthik Raman Fast-SL: An efficient algorithm to identify synthetic lethals in metabolic networks 14 / 24

20. Introduction Fast-SL Results Conclusions
Fast-SL Massively Prunes Search Space for Synthetic Lethals
▶ If a reaction j carries zero flux in the minimal
norm solution (j /∈ Jnz), which is constrained
to support growth, it cannot be lethal
⇒ There is no single lethal reaction outside Jnz
▶ If a pair of reactions i, j carry zero flux in the
minimal norm solution (i, j /∈ Jnz), they cannot
be a synthetic lethal pair
⇒ There are no synthetic lethal pairs that
comprise reactions that are both not in Jnz
▶ All synthetic lethal pairs lie in the narrow ‘red
region’ of J × J (drawn to scale for E. coli)
�
���
���
Karthik Raman Fast-SL: An efficient algorithm to identify synthetic lethals in metabolic networks 14 / 24

21. Introduction Fast-SL Results Conclusions
Fast-SL Massively Prunes Search Space for Synthetic Lethals
▶ If a reaction j carries zero flux in the minimal
norm solution (j /∈ Jnz), which is constrained
to support growth, it cannot be lethal
⇒ The set of all single lethals (Jsl) is contained
entirely in Jnz
▶ If a pair of reactions i, j carry zero flux in the
minimal norm solution (i, j /∈ Jnz), they cannot
be a synthetic lethal pair
⇒ There are no synthetic lethal pairs that
comprise reactions that are both not in Jnz
▶ All synthetic lethal pairs lie in the narrow ‘red
region’ of J × J (drawn to scale for E. coli)
�
���
���
Karthik Raman Fast-SL: An efficient algorithm to identify synthetic lethals in metabolic networks 14 / 24

22. Introduction Fast-SL Results Conclusions
Fast-SL Massively Prunes Search Space for Synthetic Lethals
▶ If a reaction j carries zero flux in the minimal
norm solution (j /∈ Jnz), which is constrained
to support growth, it cannot be lethal
⇒ The set of all single lethals (Jsl) is contained
entirely in Jnz
▶ If a pair of reactions i, j carry zero flux in the
minimal norm solution (i, j /∈ Jnz), they cannot
be a synthetic lethal pair
⇒ There are no synthetic lethal pairs that
comprise reactions that are both not in Jnz
▶ All synthetic lethal pairs lie in the narrow ‘red
region’ of J × J (drawn to scale for E. coli)
�
���
���
J
J-Jnz
Jsl
Jnz
Karthik Raman Fast-SL: An efficient algorithm to identify synthetic lethals in metabolic networks 14 / 24

23. Introduction Fast-SL Results Conclusions
Fast-SL Massively Prunes Search Space for Synthetic Lethals
▶ If a reaction j carries zero flux in the minimal
norm solution (j /∈ Jnz), which is constrained
to support growth, it cannot be lethal
⇒ The set of all single lethals (Jsl) is contained
entirely in Jnz
▶ If a pair of reactions i, j carry zero flux in the
minimal norm solution (i, j /∈ Jnz), they cannot
be a synthetic lethal pair
⇒ There are no synthetic lethal pairs that
comprise reactions that are both not in Jnz
▶ All synthetic lethal pairs lie in the narrow ‘red
region’ of J × J (drawn to scale for E. coli)
�
���
���
J
J-Jnz
Jsl
Jnz
Karthik Raman Fast-SL: An efficient algorithm to identify synthetic lethals in metabolic networks 14 / 24

24. Introduction Fast-SL Results Conclusions
Fast-SL Massively Prunes Search Space for Synthetic Lethals
▶ If a reaction j carries zero flux in the minimal
norm solution (j /∈ Jnz), which is constrained
to support growth, it cannot be lethal
⇒ The set of all single lethals (Jsl) is contained
entirely in Jnz
▶ If a pair of reactions i, j carry zero flux in the
minimal norm solution (i, j /∈ Jnz), they cannot
be a synthetic lethal pair
⇒ There are no synthetic lethal pairs that
comprise reactions that are both not in Jnz
▶ All synthetic lethal pairs lie in the narrow ‘red
region’ of J × J (drawn to scale for E. coli)
�
���
���
J
J-Jnz
Jsl
Jnz
Karthik Raman Fast-SL: An efficient algorithm to identify synthetic lethals in metabolic networks 14 / 24

25. Introduction Fast-SL Results Conclusions
Fast-SL Achieves Massive Speedups
▶ Even in the narrow red region, further gains are
made by re-applying the idea
▶ The gains are even more substantial for higher
order lethals:
J
J-Jnz
Jsl
Jnz
Order Exhaustive LPs LPs solved after
eliminating non-lethal sets
Reduction in
search-space
Single 2.05 × 103
393 ≈ 5 fold
Double 1.57 × 106
7, 779 ≈ 200 fold
Triple 9.27 × 108
432, 487 ≈ 2100 fold
Quadruple 4.10 × 1011
4.53 × 107
≈ 9050 fold
Karthik Raman Fast-SL: An efficient algorithm to identify synthetic lethals in metabolic networks 15 / 24

26. Introduction Fast-SL Results Conclusions
Fast-SL: Minimum Norm Solution
▶ Smaller the set of non-zero reactions, Jnz, lesser the number of LPs to
be solved for identifying lethal sets
▶ Minimised ℓ0-norm solution of the FBA LP problem finds the
sparsest solution
▶ However, it requires solving an MILP problem
▶ We use the ℓ1-norm solution instead
min. Σj|vj|
s.t.
Σjsijvj = 0 ∀i ∈ M
LBj ≤ vj ≤ UBj ∀j ∈ J
vbio = vbio,max
Karthik Raman Fast-SL: An efficient algorithm to identify synthetic lethals in metabolic networks 16 / 24

27. Introduction Fast-SL Results Conclusions
Fast-SL Achieves 4x Speedup over MCSEnumerator
▶ Fast-SL can also be parallelised, leading to further speed-ups
▶ Fast-SL achieves ≈ 4x speed-up over the MCSEnumerator method¹
for the E. coli iAF120 model for higher order reaction deletions
▶ Results obtained using Fast-SL match precisely with exhaustive
enumeration of gene deletions
▶ Similar approach can be used to identify lethal gene sets by
incorporating gene–reaction rules
Order
of SLs
No. of
SLs
CPU time taken for
MCSEnumerator
(using 12 cores)
CPU time taken for
Fast-SL Algorithm
(using 6 cores)
Speed-up
Single 278 11 s 2.8 s ≈ 8x
Double 96 39.1 s 17.2 s ≈ 4x
Triple 247 16.8 min 8.5 min ≈ 4x
Quadruple 402 18.5 h 9.3 h ≈ 4x
¹von Kamp A & Klamt S (2014) PLoS Computational Biology 10:e1003378
Karthik Raman Fast-SL: An efficient algorithm to identify synthetic lethals in metabolic networks 17 / 24

28. Introduction Fast-SL Results Conclusions
Synthetic Lethal Gene Deletions
▶ Most previous algorithms only computed synthetic reaction
deletions
▶ Not easily modified for computing gene deletions
▶ We extended our algorithm to gene deletions by using the
gene–reaction mapping
▶ Fast-SL formulation identified 75 new gene triplets in E. coli that
were not identified previously
▶ We have also identified up to synthetic lethal gene and reaction
quadruplets for other pathogenic organisms such as Salmonella
Typhimurium, Mycobacterium tuberculosis, Staphylococcus aureus
and Neisseria meningitidis
Karthik Raman Fast-SL: An efficient algorithm to identify synthetic lethals in metabolic networks 18 / 24

29. Introduction Fast-SL Results Conclusions
Missing Biomass Precursors in E. coli
▶ Gene/reaction lethality is a result of organism’s inability to produce
any of the biomass precursors
▶ Most triple and quadruple gene deletions affect mechanisms
involved in ATP production
0%
10%
20%
30%
40%
50%
Reiterates critical role played by co-factors and ATP in cellular metabolism!
Karthik Raman Fast-SL: An efficient algorithm to identify synthetic lethals in metabolic networks 19 / 24

30. Introduction Fast-SL Results Conclusions
Synthetic Lethals Illustrate Complex Metabolic Dependencies
▶ atpB, cydA, gap
▶ ATP synthase, cytochrome D ubiquinol oxidase and glyceraldehyde
3-phosphate dehydrogenase
▶ Perhaps bring about their effect by disabling both substrate-level and
oxidative phosphorylation
▶ eno, pps, sdhA/B/C
▶ Enolase, PEP synthase and succinate dehydrogenase subunits
▶ Seem to bring about their effect by affecting production of
phosphoenolpyruvate and consequently disabling OXPHOS
Karthik Raman Fast-SL: An efficient algorithm to identify synthetic lethals in metabolic networks 20 / 24

31. Introduction Fast-SL Results Conclusions
Combinatorial Drug Targets
▶ Only few combinatorial deletions abolish growth in silico
▶ Re-emphasises the robust nature of the metabolic networks in both
M. tuberculosis and S. Typhimurium
▶ 28 triplets and 20 doublets in M. tuberculosis have no homologues in
human
▶ 21 triplets and 39 doublets in S. typhimurium have no homologues
▶ Some of these may be interesting drug targets
Karthik Raman Fast-SL: An efficient algorithm to identify synthetic lethals in metabolic networks 21 / 24

32. Introduction Fast-SL Results Conclusions
Limitations
▶ Metabolic models considered here do not account for regulation or
other functions of proteins
▶ The method can identify synthetic lethals only in metabolism
▶ Any inadequacies/gaps in the metabolic model will affect the results,
e.g. some isozymes may not have been characterised yet
▶ Lethality results can be useful to refine the metabolic model
Karthik Raman Fast-SL: An efficient algorithm to identify synthetic lethals in metabolic networks 22 / 24

33. Introduction Fast-SL Results Conclusions
Summary
▶ Synthetic lethals are difficult to identify computationally —
combinatorial explosion of possibilities
▶ Previous approaches have used FBA to exhaustively search the entire
space, or pose the problem as a bi-level MILP
▶ Our algorithm, Fast-SL, circumvents the complexities of previous
approaches, through a massive reduction of search space, exploiting
the minimal norm solution of FBA
▶ For E. coli, the reduction in search space is ≈ 4000-fold for synthetic
lethal triplets!
▶ Ours is also the first method that systematically evaluates gene
deletions
▶ Our results agree exactly with exhaustive enumeration
▶ Fast-SL finds application in identifying functional associations and
combinatorial drug targets
Karthik Raman Fast-SL: An efficient algorithm to identify synthetic lethals in metabolic networks 23 / 24

34. Introduction Fast-SL Results Conclusions
Acknowledgments
▶ Aditya Pratapa
▶ Dr. Shankar Balachandran
▶ High Performance Computing Facility IIT Madras
▶ Funding: Department of Biotechnology, Government
of India; IIT Madras; nVidia
Karthik Raman Fast-SL: An efficient algorithm to identify synthetic lethals in metabolic networks 24 / 24

35. Introduction Fast-SL Results Conclusions
Thank you!
MATLAB implementation of Fast-SL is available
for download from:
https://github.com/RamanLab/FastSL
Karthik Raman Fast-SL: An efficient algorithm to identify synthetic lethals in metabolic networks 24 / 24