Jun 14, 2018 - OO β. // W2 δ. OO γ. // cγ. M M cα. M M c β. M M. (34). The corresponding flux: ΦSerial = kα cat[α] + c β. M min(kα cat[α],k β cat[β]) + c γ. M min(kα.
Supporting Information Derivation of fluxes for three catalyst networks • Serial The serial recycler case reactions: A + α → cα MM + W1 W1 + β → β + cβM M + W2 (33)
W1 → ∅ W2 + γ → γ +
cγM M
W2 → ∅
A
α
∅O
∅O
δ
δ
/ W1
β
(34)
/ W2
γ
/ cγ M M
cβM M
cα MM The corresponding flux:
β β γ α α α ΦSerial = kcat [α] + cβM min(kcat [α], kcat [β]) + cγM min(kcat [α], kcat [β], kcat [γ])
(35)
• Parallel For the parallel recycler case we have the following reactions: A + α → cα M M + α + W1 + W2 W1 + β → β + cβM M (36)
w1 → ∅ W2 + γ → γ +
cγM M
W2 → ∅ ∅O
(37)
δ
= W1
A
β
/ cβ M M
γ
/ cγ M M
∅O
α
δ
cα MM
"
W2
The corresponding flux: β γ α α α ΦP arallel = kcat [α] + cβM min(kcat [α], kcat [β]) + cγM min(kcat [α], kcat [γ])
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(38)
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Derivation of fluxes for the bimolecular motiff For the bimolecular architecture we have the following reactions: A + α → α + cα M M + W1 A + β → β + cβM M + W2 W1 + W2 + γ → cγM M
(39)
W1 → ∅ W2 → ∅ ∅O
(40)
δ
A
α
/ W1
cα MM
∅O
γ
/ cγ M M
δ
β
/ W2
cβM M For this architecture, the velocities of the first two reactions are: α vα = kcat [α]
(41)
β kcat [β]
(42)
vβ =
and the velocity of the third reaction depends upon them: γ β γ α vγ = min (vα , vβ , kcat [γ]) = min kcat [α], kcat [β], kcat [γ]
(43)
Hence the total flux equals: β β γ β γ α α ΦBimolecular = cα M kcat [α] + cM kcat [β] + cM min kcat [α], kcat [β], kcat [γ]
(44)
Derivation of the fluxes for the four catalyst networks We will now derive the metabolite fluxes of the following four catalyst architectures: • Serial For the four catalyst serial recycler the following reactions are considered:
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A + α → α + W 1 + cα MM W1 + β → β + W2 + cβM M W1 → ∅ W2 + γ → γ + W3 + cγM M
(45)
W2 → ∅ W3 + θ → θ + cθM M W3 → ∅
A
α
∅O
∅O
∅O
δ
δ
δ
/ W1
β
/ W2
cβM M
cα MM
γ
/ W3
/ θ
/ cθ M M
cγM M (46)
The corresponding flux: β β γ β γ α α α ΦSerial = cα M kcat [α] + cM min(kcat [α], kcat [β]) + cM min(kcat [α], kcat [β], kcat [γ]) β γ α θ + cθM min(kcat [α], kcat [β], kcat [γ], kcat [θ])
(47)
• Parallel The reactions: A + α → α + W 1 + W 2 + W 3 + cα MM W1 + β → β + cβM M W1 → ∅ W2 + γ → γ + cγM M
(48)
W2 → ∅ W3 + θ → θ + cθM M W3 → ∅
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∅O δ
W E 1
β
/ cβ M M
γ
/ cγ M M
/ θ
/ cθ M M
∅O δ
α
/ W2
cα MM
∅O
A
δ
W3 The corresponding flux:
β β γ γ α α α Φparallel = cα M kcat [α] + cM min(kcat [α], kcat [β]) + cM min(kcat [α], kcat [γ]) α θ + cθM min(kcat [θ], kcat [θ]
(49)
• Parallel-Serial The reactions: A + α → α + W1 + W2 + cα MM W1 + β → β + W3 + cβM M W1 → ∅ W2 + γ → γ + cγM M
(50)
W2 → ∅ W3 + θ → θ + cθM M W3 → ∅ ∅O
∅O
δ
δ
= W1
A
∅O
α
β
/ W3
(51)
/ θ
/ cθ M M
cβM M
δ
cα MM
!
W2
γ
/ cγ M M
The corresponding flux:
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β β γ γ α α α Φparallel-serial = cα M kcat [α] + cM min(kcat [α], kcat [β]) + cM min(kcat [α], kcat [γ]) β α θ + cθM min(kcat [α], kcat [β], kcat [θ])
(52)
• Serial-Parallel The reactions: A + α → α + W 1 + cα MM W1 + β → β + W2 + W3 + cβM M W1 → ∅ W2 + γ → γ + cγM M
(53)
W2 → ∅ W3 + θ → θ + cθM M W3 → ∅ ∅O
)
(54)
δ
∅O
> W2
γ
/ cγ M
θ
/ cθ M
δ
α
A
/ W1
∅O
β
δ
cα M
cβ M
W3
The corresponding flux: β β γ β γ α α α Φserial-parallel = cα M kcat [α] + cM min(kcat [α], kcat [β]) + cM min(kcat [α], kcat [β], kcat [γ]) β α θ + cθM min(kcat [α], kcat [β], kcat [θ])
(55) • Bimolecular The reactions: A + α → α + W1 + W2 + cα MM W1 + β → W3 + cβM M W1 → ∅ W2 + γ → γ + W4 + cγM M W2 → ∅
(56)
W3 + W4 + θ → θ + cθM M W3 → ∅ W4 → ∅
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∅O
∅O
δ
δ
= W1
β
∅O
cβM M
/ W3
A
α
δ
cα MM
!
W2
∅O
?θ
/ cθ M M
δ
γ
/ W4
cγM M The corresponding flux: γ γ β β α α α ΦBimolecular = cα M kcat [α] + cM min(kcat [α], kcat [β]) + cM min(kcat [α], kcat [γ]) β γ α θ + cθM min(kcat [α], kcat [β], kcat [γ], kcat [θ])
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(57)
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