Week 3 HW Cell-free reaction design

HTBAA Homework #3

Cell-Free Reaction Design

Part A — Compare cell-free reaction compositions

A1. Why does the concentration of potassium glutamate and magnesium glutamate differ between compositions? Which is more sensitive?

My response.

Because each concentration responds differently to disulfide bonds. For example, in in sfGFP which does not have disulfide bonds, potassium glutamate is more effective at successful folding. Magnesium glutamate is more suited for disulfide bonds as required for Petase and even more so for reteplase

So I am choosing Magnesium for A1 as it provides the reaction energy needed for NTPs

Ok, so adding magnesium is a low cost way to provide a catalyst for the NTP energy source .

I initially attributed the difference between the two salts to disulfide requirement, then to magnesium supplying the reaction energy, before settling on magnesium as a low-cost catalyst.

Feedback. Both salts share the glutamate anion, so the contrast is K⁺ versus Mg²⁺, not the salts. Magnesium is the more sensitive of the two it occupies discrete saturable sites and is chelated roughly 11 by nucleotides and phosphate, so free Mg²⁺ — not added Mg²⁺ — is what the machinery sees, and it operates near 5 mM against potassium’s 270 mM. The first two framings above were tested and discarded neither cation is redox-active, and magnesium is a non-consumed catalyst, not an energy source.

→ Worked analysis, calculations and caveats Appendix E.1.

A2. Explain how a PEP+NTP reaction formulation is different from a Ribose+NMP reaction formulation.

My response.

give me some socratic reasoning around A2 since PEP+NTP different from Ribose+NMP in that one is the energy for transcription and one is the energy for translation. that’s my starting point.

what makes the most sense for me is the pre-made vs in situ process. I believe premade will save energy for other in situ processing.

I proposed a starting frame for the comparison, then replaced it when the first frame did not survive scrutiny.

Feedback. The two formulations differ in whether phosphate-bond energy and nucleotides are bought pre-made or generated in situ — not in which process they feed. Both routes supply both transcription and translation, and translation dominates demand at four phosphate equivalents per peptide bond, so PEP at 30 mM covers only ~39% of one run’s requirement and the remainder comes from metabolism either way. The pre-made route buys a fast start, not a larger total.

→ Worked analysis, calculations and caveats Appendix E.2.

A3. Choose two cell-free reaction compositions from the literature; compare and contrast the choice of reagents and the concentration of reagents.

My response.

for A3, now that we know Mg is important, and is low cost but only provides catalyst, and that kinetic Km sets the floor, we need to look at more impactful tuning levers, that have more kinetic impact AND less cost. GMP seems to be the best focus area to pursue. Let’s test the theory with calculations.

I named a lever and asked for it to be tested numerically rather than asserted.

Feedback. Pair compared PANOx-SP against the cost-optimised RFopt of Olsen et al. The GMP hypothesis was right in direction and wrong in ranking — nucleotide form is the largest coherent lever class, but GTP is third at 15.1% of variable cost, behind PEP at 29.0% and coenzyme A at 22.8%; substituting G, U and C as a class recovers 39.4%. The unexpected result was that a cost substitution silently moves an unrelated optimum the substitution pushes free Mg²⁺ further off target, so nucleotide and magnesium changes are not independent.

→ Worked analysis, calculations and caveats Appendix E.3.

Part B — Design one reaction composition for each of the three proteins

Shared design constraints (Section 2F of the assignment)

Cost anchors (assignment, sourced to Olsen et al. 2026)

Scoring objective cost per gram of functional protein.

Reducing vs oxidizing regime (Section 2C)

Folding difficulty ranking sfGFP (0 disulfides, 2 free thiols) < TfCut2 PETase (1 disulfide) < Reteplase (9 disulfides, all requiring correct pairing).

B1a. sfGFP composition

My response.

for the submittals to the coopetition, it is looking like both PEP and RIBOSE reagents are being made for each of 3

I built the sfGFP composition on the assigned RFopt reference plate, changing five reagents and leaving the rest at reference. The per-reagent rationale is in the table below.

What changed from the source well (full per-reagent table in the appendix)

All other reagents held at the reference value. Designable volume 8,675 nL of 11,000 nL; $0.0263007 per 20 µL reaction; 0 errors, 0 guardrail failures.

Feedback. Five reagents changed, twelve held at reference. The magnesium cut is the mechanistically strongest move, and the AMP trim pays twice — it makes the four nucleotides equimolar and, by removing chelation load, carries free Mg²⁺ onto its optimum at no cost. The cost result is negligible all-in falls 0.49%, because 92% of a reaction is lysate, DNA template and base buffer, none of which is designable.

→ Worked analysis, calculations and caveats Appendix E.4.

B1b. PETase (TfCut2) composition

My response.

I gave PETase the same vector as sfGFP after testing whether any reducing-regime reagent could improve its folding outcome. None could.

What changed from the source well (full per-reagent table in the appendix)

All other reagents held at the reference value. Designable volume 8,675 nL of 11,000 nL; $0.0265907 per 20 µL reaction; 0 errors, 0 guardrail failures.

Feedback. Identical vector to sfGFP. The decision not to diverge is supported rather than assumed all 51 reducing-compatible reagents on the menu were tested at two volumes each and none changed the active fraction. The 57% loss is an unmeasured folding prior, not a formulation fault, and the crystal structure agrees that redox chemistry is not the lever — the single disulfide sits 26 Å from the catalytic serine.

→ Worked analysis, calculations and caveats Appendix E.5.

B1c. Reteplase composition

My response.

let’s compare a more aggressive move on reteplace. make some multiple variable moves to see if we can get cost down in comparison to energy and kinetics

what is the minimum amount of folding we can expect before the choice is not a good candidate

I took a multi-variable approach on reteplase rather than testing one reagent at a time, and set an acceptance threshold from the assay before accepting any design.

What changed from the source well (full per-reagent table in the appendix)

All other reagents held at the reference value. Designable volume 9,350 nL of 11,000 nL; $0.0273835 per 20 µL reaction; 0 errors, 0 guardrail failures. GSSG 4.04 mM and GSH 1.0 mM retained at reference.

Feedback. Order mattered. Removing DsbC alone looks like a bad move until cysteine is fixed first, so one-at-a-time testing would have rejected the correct answer. At the plate’s assigned 5 mM, cysteine acts as a reductant in the DSB regime and modelled pairing falls below the assay’s replicate-safe threshold; with it removed, pairing improves without DsbC at all. Cost falls 206.7× on a single reagent.

→ Worked analysis, calculations and caveats Appendix E.6.

B2. Community reagent contribution

My response.

what can we do to increase the protein output of PetAse without so much misfolding? wIthout raising cost.

we will come back to chaperone, for a future round. Let’s stop here with our first finalized hypothesis and get ready for submittal

I identified the chaperone gap while asking how to raise PETase output, chose to defer it rather than fold it into this submission, and then selected GroEL/GroES as the reagent to propose.

Feedback. GroEL/GroES is proposed for the reducing regime because it is the only identified mechanism that addresses a quantity the present menu cannot move — every reagent that helps PETase helps by raising total titer, leaving the misfolded fraction unchanged. It is also unproven for this substrate and ATP-dependent, and the proposal states both limits rather than claiming a guaranteed gain.

→ Worked analysis, calculations and caveats Appendix E.7.

B3. Forum participation

My response.

make a brief draft of a forum post that summarizes my tool development approach with an example. The initial tool was built in Claude Science without code management. (Week 3). Week 4 introduces a code framework to be introduced.

What I did. Specified the subject and framing of the post, and joined the forum page.

Forum post (draft).

Building a reaction configurator before writing a codebase

For Week 3 I built an interactive CFPS configurator instead of working from a spreadsheet — reagent menu, volume and increment constraints, exact cost arithmetic, magnesium speciation, guardrails, and a folding and kinetics simulator. Every composition I submitted came out of it.

One example of why that mattered. The assigned oxidising plate for Reteplase carries 5 mM cysteine. Running it as a baseline tripped a free-thiol guardrail — in a DSB regime cysteine acts as a reductant. Removing it fixed disulfide pairing and made the DsbC we were paying for unnecessary $5.66 → $0.027 per reaction. The transferable part is the order. Removing DsbC alone looks wrong until cysteine is fixed first, so one-variable-at-a-time testing would have rejected the right answer.

This version was built conversationally in Claude Science, with no repository and no tests. Week 4 moves it onto a proper code framework with version control.

Feedback. The post leads with the cysteine result because the transferable lesson is about the order of a multi-variable move, not about reteplase specifically. The Week 3 / Week 4 framing is accurate and worth stating publicly two of the errors corrected during this work — a g/L unit conversion and a folding prior wrongly multiplying a synthesis rate — are exactly the class a test suite catches and a conversation does not.

→ Numbers behind the worked example, and the full tooling note Appendix E.8.

Part C — Asimov Kernel (optional)

I did not attempt Part C. The supplied sequences were extracted and checked during Part B work, so the starting material exists.

C1. T7-compatible plasmids for cell-free expression

(status not attempted)

Sequences supplied by the assignment for sfGFP, PETase, and Reteplase. Note that the PETase and Reteplase sequences as given carry an N-terminal Strep-tag II (WSHPQFEK) followed by a TEV protease site (ENLYFQS), and both end in a C-terminal GGSGVSGWRLFKKIS extension; sfGFP instead carries the Strep-tag at its C-terminus. These features need to be preserved or deliberately removed in the plasmid design.

C2. Bonus — T7 helper plasmid to improve functional Reteplase yield

(status not attempted)

Candidate cargo categories general chaperones, disulfide-bond formation and isomerization machinery, peptidyl-prolyl isomerases.

Feedback. Not attempted. The three supplied sequences were extracted and verified during Part B (sfGFP 240 aa, PETase 309 aa, Reteplase 399 aa), and the tag architecture is noted above, so C1 has its starting material if revisited.

Use of AI

Model Claude Opus 5 (claude-opus-5), via Claude Science. One continuous session, 86 human-authored prompts and 319 code executions.

Summary. AI was used in three ways to build a provenance rubric separating exact arithmetic (cost, concentrations, free magnesium, pH, volumes, guardrails) from fitted heuristics (titer, folding priors) from illustrative constants (simulation timing); to run the homework questions Socratically — question asked plain, answered first, critiqued after; and to build the CFPS configurator used to design and test every composition submitted here. The rubric is why titer is never used to rank a design. The tool is where the results came from.

Actual prompts, verbatim

“just ask me the question so I can research and answer verbatim, then we will analyze and mentor”

“I would like to create a visual simulator of the kinetic response to a selected formula. using the calculator or now we will call it the CFPS configurator, add a new tab for training and modeling an interactive simulation of the molecular compounds. It can be very abstract and illustrative at first, but based on actual metrics and values, as well as assumptions made in this activity.”

“for A3, now that we know Mg is important, and is low cost but only provides catalyst, and that kinetic Km sets the floor, we need to look at more impactful tuning levers, that have more kinetic impact AND less cost. GMP seems to be the best focus area to pursue. Let’s test the theory with calculations.”

“let’s compare a more aggressive move on reteplace. make some multiple variable moves to see if we can get cost down in comparison to energy and kinetics”

“what is the minimum amount of folding we can expect before the choice is not a good candidate”

Where the prompts led. The Socratic prompt produced A1–A3. The simulator prompt produced the configurator and, through it, the kinetics and folding modules. The GMP prompt was tested and came back partly supported — right that nucleotide form is the largest lever class, wrong that GMP ranks first. The multi-variable prompt produced the cysteine-as-reductant result. The folding-floor prompt set the assay threshold used to accept the reteplase design.

Appendix — worked analysis, by question

The main-body answers above are deliberately short. This appendix carries the worked reasoning, calculations, figures and caveats behind them.

E.1 — A1 potassium vs magnesium glutamate

The contrast is between the cations, not the salts. Potassium glutamate and magnesium glutamate share the same anion, so nothing that distinguishes them can be attributed to glutamate. Glutamate is the counter-ion of choice for both because it mimics the E. coli cytoplasm, and it is not inert — it is also an energy source via oxidative deamination into the TCA cycle, which is why a formulation of potassium glutamate, nucleotide monophosphates and amino acids can make protein with no sugar and no PEP at all. But that contribution is common to both reagents. The real question is K⁺ versus Mg²⁺.

What magnesium does. Mg²⁺ is a catalytic and structural cofactor occupying discrete, saturable sites. It supplies the two metal ions in the T7 RNA polymerase active site — one positioning and activating the attacking 3′-OH, the other coordinating the β,γ-phosphates and stabilizing the departing pyrophosphate. It bridges the 30S and 50S ribosomal subunits, holds the tertiary core of every tRNA together, and is required by the aminoacyl-tRNA synthetases and the translational GTPases. It is also half of the substrate Mg·ATP is the physiological species, so without magnesium the nucleotides are present but chemically inert.

Magnesium is explicitly not an energy source. The energy comes from phosphoanhydride bonds — those in the NTPs themselves and in whatever secondary donor regenerates them (PEP, maltose, maltodextrin, glucose, or glutamate). Magnesium is a catalyst it lowers activation barriers, is not consumed, and contributes no thermodynamic driving force. If anything it reduces the free energy released per nucleotide hydrolysed, since ΔG°′ for ATP hydrolysis becomes less negative as free Mg²⁺ rises.

What potassium does. K⁺ sets bulk ionic strength and reproduces the cytoplasmic potassium environment. It tunes translation-initiation fidelity and the strength of nonspecific protein–nucleic-acid electrostatics. This is a bulk solution property acting through Debye screening — a smooth, monotonic function of ionic strength — rather than occupancy of a defined site.

Why the concentrations differ between compositions chelation. Chelation is the binding and sequestration of a metal ion. Nucleotides chelate magnesium roughly 11, which means what the machinery experiences is free Mg²⁺, not the magnesium written on the recipe. The size of that sink depends on the energy system in my simulator’s engine, NTPs carry a magnesium-chelation weight of 1.0 against 0.3 for NMPs and 0.05 for inorganic phosphate, over a lysate-supplied baseline of ~3.45 mM. (A fourth coefficient for polyphosphate, mg_chelate_poly = 1.5, is defined in the coefficient file but is not applied by the engine’s freeMagnesium() function, which adds the polyphosphate term raw — so its effective weight is 1.0. I checked the source rather than the coefficient table; none of the formulations compared here contain a polyphosphate chelator, so no number in this answer depends on it either way.) A high-phosphate PEP+NTP formulation therefore has to add substantially more total magnesium than a low-phosphate NMP formulation to put the same free Mg²⁺ in front of the ribosome.

A speciation calculation makes the size of the effect concrete at 8 mM total magnesium glutamate, a high-phosphate PEP+NTP load leaves ~1.0 mM free Mg²⁺ while a low-phosphate NMP load leaves ~6.8 mM — roughly a 7-fold difference from identical added magnesium.

Two further sources of between-composition variance each lysate prep carries its own endogenous magnesium — Olsen et al. report an S30 buffer of 14 mM magnesium acetate and 60 mM potassium acetate — and the chelation landscape shifts during the reaction as NTPs are consumed and phosphate accumulates. Olsen et al. accordingly had to determine new optimum magnesium concentrations for each lysate concentration they tested.

Potassium has no comparable sequestration sink, so added potassium is essentially free potassium, and published potassium concentrations cluster far more tightly than magnesium ones.

Which is more sensitive magnesium, for four reasons that stack.

1. Site occupancy versus a bulk property. Function is steeply nonlinear in the occupancy of a saturable site near its binding constant; it is gradual in ionic strength.
2. Opposing failure modes make a peak rather than a plateau. Too little magnesium and ribosomal subunits dissociate, tRNA misfolds and the polymerase loses catalysis; too much and translational fidelity drops, mRNA secondary structure blocks initiation, and Mg-phosphate precipitates. Two distinct mechanisms closing in from either side give a sharp optimum. Potassium’s failure modes arrive gradually, and glutamate as counter-ion buffers the high end.
3. Chelation amplifies error. Free Mg²⁺ is the difference between two comparable large numbers, so a small fractional change in what is added produces a larger fractional change in what is available — I calculate amplification factors of ~1.6–1.9 under phosphate load against ~1.1 without, and that conclusion is robust across a 16-fold range of assumed binding constants. Potassium’s amplification is ~1.0 by construction.
4. Concentration scale. Magnesium operates near 10 mM and potassium near 130 mM, so equal absolute pipetting error is a ~13-fold larger fractional perturbation for magnesium. Under this project’s 25 nL dispensing granularity, one increment of a 100 mM stock into 20 µL is 1.25% of a magnesium setpoint but 0.10% of a potassium setpoint.

One apparent counter-example, resolved. Olsen et al. screened 1,231 formulations and arrived at a minimal active system comprised only of potassium glutamate, nucleotide monophosphates and amino acids — supplemental magnesium glutamate was among the components that did not improve yield on individual add-back. That is not evidence that magnesium is insensitive. Sensitivity is the steepness of yield against concentration near the optimum; it is not the same as needing supplementation. Magnesium is essential but already supplied by the lysate, and the same authors still had to re-determine its optimum for every lysate concentration. Notably, all of that work was on sfGFP, which has no disulfide bonds — so none of this magnesium behaviour has anything to do with disulfide chemistry.

Design consequences I am carrying into Part B. Magnesium glutamate costs fractions of a cent, which makes it a free tuning variable I can titrate it densely across compositions in a way I cannot afford with CTP, GTP, UTP, NAD or coenzyme A. But cheapness is not a licence to add more — the dose is set by the optimum, not by the price. And because NMPs chelate magnesium far less than NTPs, retuning magnesium is the obligatory second step of any NTP→NMP cost substitution GTP at $39.34/mL against GMP at $0.533/mL is a 74-fold saving that silently moves the magnesium optimum the moment it is taken.

Caveat on the numbers the speciation model above uses literature-typical order-of-magnitude binding constants rather than values measured in this session. The ~7-fold free-Mg²⁺ gap is robust to that uncertainty; the absolute millimolar values should not be quoted as measured.

E.2 — A2 PEP+NTP vs Ribose+NMP

Each name contains two slots, not one. Phosphoenolpyruvate is a phosphoryl donor; NTP is a nucleotide. Ribose is a pentose and carbon source; NMP is a nucleotide at a lower level of phosphorylation. So each formulation names one energy term and one nucleotide term PEP+NTP is “high-energy donor plus fully phosphorylated nucleotides,” and Ribose+NMP is “carbon/pentose source plus partially phosphorylated nucleotides.” Framing the contrast as transcription-energy versus translation-energy does not survive the accounting below.

Why the transcription/translation split fails. Translation consumes NTPs too, and it consumes far more of them than transcription does. Charging a tRNA costs 2 high-energy phosphate equivalents (ATP → AMP + PPi), EF-Tu delivery costs 1 GTP and EF-G translocation costs 1 GTP — 4 equivalents per peptide bond. For sfGFP (240 residues) at the 2.4 g/L titer Olsen et al. report, that is 85.3 mM of phosphate equivalents for translation alone. By contrast, each transcript is read many times, so the nucleotides polymerised into mRNA are a small fraction of the budget at 100 copies translated per transcript, pre-purchasing NTPs instead of phosphorylating NMPs saves roughly 1.6% of the translation demand (and between 0.3% and 31% across a 500-to-5 range of ribosome loading). Pre-made nucleotides are therefore a cost and kinetics decision, not an energy-budget decision.

Neither formulation escapes in-situ metabolism. PEP at the 30 mM of a PANOx-SP-type recipe supplies only about 39% of that 85.3 mM translation demand, so even the “pre-made” formulation depends on downstream metabolism of the pyruvate PEP leaves behind for roughly 2.6× more energy than PEP itself carries. The honest contrast is how much in-situ work is required, not whether any is.

Pool versus flux — the asymmetry that matters. The NTP line items in a recipe are pool sizes, not total consumption. A ~3.75 mM total NTP pool has to turn over about 23× to meet an 85 mM demand, recharged continuously by the energy system. This splits the four nucleotides into two classes

At 100 copies per transcript, a 0.85 mM supply of CTP or UTP exceeds stoichiometric demand (~0.17 mM) by about 5×. Those two are the first place to cut.

But the floor is kinetic, not stoichiometric. T7 RNA polymerase follows saturation kinetics, so the limit is the concentration the active site sees, not the total mass available. Because nucleotides are consumed, concentration falls during the run, and supplying exactly the stoichiometric demand drives the rate to zero before the demand is met. Starting at 1× Km retains only 28% of the initial transcription rate by the end of the run; starting at 5× Km retains 97%. Roughly 3–5× Km is the operating choice, and that headroom is what the apparent “excess” actually is. Two further complications a dual-use nucleotide’s floor is set by whichever of its several consumers has the highest Km, and the true substrate is Mg·NTP, so free magnesium and nucleotide supply are not independent knobs.

Byproducts and pH — where the two routes diverge most. PEP donating its phosphate yields pyruvate and releases inorganic phosphate stoichiometrically. That phosphate chelates magnesium, inhibits the reaction, and drops the pH — the three problems that motivated the Cytomim system’s move away from high-energy phosphate donors in the first place. It also raises the apparent Km through product inhibition, so the kinetic floor rises while nucleotide concentration falls two effects converging, which is why batch PEP+NTP reactions have a finite lifetime. Ribose and sugar routes instead accumulate organic acids through glycolysis, which also lowers pH but without the stoichiometric phosphate burst — so buffering capacity (HEPES-KOH, formate) becomes the governing design choice rather than phosphate management.

Cost — the reason any of this matters here. GTP costs $39.34/mL against GMP at $0.533/mL, a 74-fold difference, and CTP, GTP and UTP all sit in the $28–39/mL band. Since the scoring metric is cost per gram of functional protein, nucleotide provisioning is the largest lever available after lysate. What the 74-fold premium buys is real, though faster onset, higher flux, and independence from the lysate’s kinase and salvage capacity — which is a batch-to-batch variable, since those enzymes have to survive lysis and clarification in sufficient activity.

The dichotomy is not even exhaustive. Olsen et al. screened 1,231 formulations and arrived at a minimal active system of potassium glutamate, nucleotide monophosphates and amino acids — no sugar and no PEP at all. The energy in that system comes from glutamate itself, via oxidative deamination into the TCA cycle, and they further showed nucleoside triphosphates could be produced from nitrogenous bases and ribose. So the real design space is not “PEP+NTP or Ribose+NMP” but a continuum of how much nucleotide and phosphate provisioning you delegate to the lysate.

Design consequences I am carrying into Part B. Cut the pure-transcription nucleotides (CTP, UTP) hardest; protect the flux carriers (ATP, GTP); substitute NMPs where the lysate can phosphorylate them; respect a 3–5× Km headroom rather than cutting to stoichiometric demand; buffer for the acid load of whichever energy route is chosen; and retune magnesium after every nucleotide change, because NMPs chelate magnesium at roughly a third the weight of NTPs.

Caveats. Copies translated per transcript and the polymerase Km under these conditions are both unmeasured, and they are the two parameters the argument pivots on — the percentages above are an order-of-magnitude ledger, not measurements. The 0.85 mM per-NTP supply figure is a PANOx-SP-type value that could not be verified against its primary source (see decision log entry 2). Energy stoichiometry (4 equivalents per peptide bond, 1 per nucleotide polymerised, 2 per NMP→NTP conversion) is standard biochemistry; the 2.4 g/L titer is Olsen et al.’s reported value.

E.3 — A3 PANOx-SP vs Olsen RFopt, and the lever test

Reagent-class comparison.

The classes of reagent removed matter more than any concentration change RFopt deletes the secondary energy substrate, all four triphosphates, and four separate cofactors, and pays for it with higher potassium glutamate, higher amino acids, more buffer, and a reliance on lysate kinase and salvage activity.

Variable-cost decomposition (exact). PANOx-SP PEP 29.0%, coenzyme A 22.8%, GTP 15.1%, UTP 14.5%, CTP 10.7%, NAD 5.5%, ATP 0.8%. RFopt CMP 22.6%, AMP 17.6%, UMP 15.0%, ribose 11.3%, potassium glutamate 10.9%, GMP 9.5%. Note the inversion — in the cheap formulation the nucleotides are still the largest line, but the whole variable budget is 19× smaller, so the fixed lysate cost ($0.02/reaction) becomes 75% of the all-in total.

Substitution ladder on PANOx-SP (exact cost, exact free Mg²⁺).

Caveats. Reagent cost, final concentrations, free magnesium, volumes and the 25 nL increment are exact outputs of the engine. The magnesium factor and the 4.6 mM optimum come from the engine’s titer heuristic, which the tool itself documents as having negative leave-one-out R² against eleven published formulations and which must not be used to rank untested designs — so the factor is directional evidence that the substitution moves magnesium off-optimum, not a yield prediction. The substitutions hold nucleotide concentration constant in mM; the engine applies a 0.86 supply weight to NMPs, so matched mM is a ~14% reduction in nucleotide-supply equivalents that a real screen would need to check. Nucleosides and nucleobases are cheaper still per mM but arrive on 0.025 M stocks — 800 nL per mM against 200 nL for NMPs — so they consume the 11,000 nL variable budget four times faster and are gated on ribose.

E.4 — B1a sfGFP composition, full specification

The composition. Source well RFopt (2026) · reducing regime · 8,675 nL of 11,000 designable · $0.0263007 per 20 µL reaction. Removed from the source well added cysteine (5 → 1 mM, base buffer only).

Feedback. Five reagents moved; twelve stayed at reference. The magnesium cut is the mechanistically strongest of them — free Mg²⁺ falls 8.11 → 4.63 mM onto the modelled optimum and the magnesium factor goes 0.587 → 0.9999 for fractions of a cent. The AMP trim is the one that earns twice it makes the four nucleotides equimolar (balance 0.951 → 1.0000) and, by removing chelation load, is what carries free Mg²⁺ onto that optimum at no cost. The cost result here is negligible — variable cost falls 6.7% but all-in only 0.49%, because 92% of a reaction is lysate, DNA template and base buffer, which are not designable. Validity 0 errors, 0 guardrail failures, one inherited warning (nmp_precipitate, total NMP 8.50 mM against a 5 mM threshold). MODEL output, not used for ranking total titer 3.2845 g/L, active fraction 1.0000, active titer 3.2845 g/L.

E.5 — B1b PETase composition, full specification

The composition. Source well RFopt (2026) · reducing regime · 8,675 nL of 11,000 designable · $0.0265907 per 20 µL reaction. Removed from the source well added cysteine (5 → 1 mM, base buffer only).

Feedback. The decision not to diverge from sfGFP is the substantive one here, and it is supported rather than assumed all 51 reducing-compatible reagents on the menu were tested at two volumes each and none changed the active fraction off 0.4295. Decomposing fold_prior × (0.85 + 0.15·p_pair) shows why — the disulfide term spans only 1.14× across its entire reachable range while the unanchored prior’s ±1 sd spans 3.0×. The crystal structure agrees that redox chemistry is not the lever the single disulfide sits 26 Å from the catalytic serine, so it is a stability feature. The 57% loss is an unmeasured parameter, not a formulation fault, and the cheapest way to close it is one 30-minute p-nitrophenyl read, not a reagent. Validity 0 errors, 0 guardrail failures, nmp_precipitate inherited. MODEL output total titer 3.2845 g/L, active fraction 0.4295, active titer 1.4107 g/L.

E.6 — B1c Reteplase composition, full specification

The composition. Source well RFopt (ox.) (2026) · oxidizing / DSB regime · 9,350 nL of 11,000 designable · $0.0273835 per 20 µL reaction. Removed from the source well added cysteine (5 → 1 mM, base buffer only); DsbC (5 µM → absent).

Feedback. The multi-variable approach was the right call and the evidence says so removing DsbC alone looks like a bad move until cysteine is fixed first, so one-at-a-time testing would have rejected the correct answer. At the plate’s assigned 5 mM, cysteine acts as a reductant in the DSB regime — modelled pairing is p_pair 0.3674, which back-solves to 0.56× the replicate-safe assay threshold, i.e. the plate as specified cannot produce a scoreable well. With added cysteine removed, pairing reaches p_pair 0.5132 with no DsbC at all, above the 0.4452 an earlier design bought with 3.5 µM. The cut is stoichiometrically safe 18 cysteines at 0.5–2 g/L protein need 0.23–0.92 mM against the base buffer’s 1.0 mM. Cost falls 206.7×, and it is one reagent — DsbC was 99.97% of that plate’s variable cost. Caveat that belongs with the number the engine treats the 9 disulfides as pairing independently (active = p_pair⁹), while the AlphaFold model of tPA shows three coupled modules of three, so the true active fraction is 7–55× higher than reported and 0.0025 is a floor. Validity 0 errors, 0 guardrail failures, nmp_precipitate inherited. MODEL output total titer 2.0364 g/L, active fraction 0.0025, active titer 0.005029 g/L.

E.7 — B2 GroEL/GroES community reagent proposal

Feedback. The proposal below is GroEL/GroES for the reducing regime. It is the one mechanism identified that addresses the quantity shown to be immovable with the present menu.

double-ring GroEL plus the GroES lid), for the reducing regime.

Rationale. It is the only mechanism I could identify that would move the quantity my own analysis showed is currently immovable. PETase loses 57% of synthesised protein to misfolding, and that loss is a folding-outcome term, not a concentration term. I tested all 51 reducing-compatible reagents on the present menu at two volumes each none of them changed the active fraction off 0.4295. Every reagent that helps at all helps by raising total titer, so active and misfolded protein rise together and the ratio is untouched. The menu has no chaperone at all — DsbC exists but is gated to the oxidising regime, where it addresses disulfide pairing rather than conformational folding.

Why GroEL/ES specifically. Its documented effect is on the soluble/active fraction rather than on expression level, which is exactly the term that is missing. Over-expressing GroEL/GroES increased the fluorescence of GFP-expressing cells without changing the amount of GFP protein made, by raising the fraction that was soluble rather than aggregated — a yield effect, not a titer effect. In a cell-free system specifically, adding GroEL–GroES to nascent CCR5 chains increased both the rate and the yield of functional folding where spontaneous folding was slow and inefficient. On a defined substrate (DapA) the chaperonin accelerated folding ~30-fold and carried the yield to ~100%, and co-expression of both subunits raised soluble aconitase yield to ~39% where GroEL alone did nothing — so both components are needed; GroEL alone is not enough.

How the decision was reached. Not by assumption. The sequence was (1) decompose PETase’s active fraction into fold_prior × (0.85 + 0.15·p_pair) and sweep each part — the disulfide term spans only 1.14× across its entire reachable range while the prior’s ±1 sd spans 3.0×; (2) confirm from the crystal structure (4CG1, 1.4 Å) that the single disulfide sits 26 Å from the catalytic serine, so it is a stability feature and redox chemistry cannot be the answer; (3) sweep every reducing-compatible reagent and find none that moves the fraction. Only then did “the menu is missing a reagent class” become the conclusion rather than the premise.

Honest caveats, which belong in the proposal. GroEL/ES assists roughly 10% of newly synthesised E. coli proteins, so PETase may simply not be a client — this is a hypothesis to test, not a guaranteed gain. The chaperonin is ATP-dependent, and our composition deliberately carries no ATP (only AMP, recharged in situ), so a dosing study would need to confirm the adenylate pool supports the cycle. It can also slow folding of proteins that fold well without it, and in at least one membrane-protein study GroES actively reduced folding yield. Finally, it is a large, costly protein reagent — any menu addition needs a cost per mL before it can be scored against a cost-per-gram objective.

Supporting research (links)

• Chi et al., Folding of newly translated membrane protein CCR5 is assisted by the chaperonin GroEL-GroES — cell-free system, rate and yield of functional folding. https//www.ncbi.nlm.nih.gov/pmc/articles/PMC4653635/
• Georgescauld et al., GroEL/ES chaperonin modulates the mechanism and accelerates the rate of TIM-barrel domain folding — ~30-fold acceleration, ~100% yield on DapA. https//pmc.ncbi.nlm.nih.gov/articles/PMC4071350/
• Tang et al., Essential role of the chaperonin folding compartment in vivo — GroEL alone does not improve yield; GroEL + GroES raises soluble aconitase to ~39%. https//pmc.ncbi.nlm.nih.gov/articles/PMC2396394/
• Horwich & Fenton, Chaperonin-assisted protein folding a chronologue, Quarterly Reviews of Biophysics — the soluble-fraction effect on GFP, and the view that preventing aggregation matters more than accelerating folding. https//www.cambridge.org/core/journals/quarterly-reviews-of-biophysics/article/chaperoninassisted-protein-folding-a-chronologue/99CCB61641B4C118EAA879F177E2AC4B

A note that connects to my own design. The CCR5 cell-free work used Brij-35 to keep nascent chains soluble. Brij-35 is already on the menu, and in my own scan it was the single best gain-per-dollar reagent available (+5.4% active protein for $0.0000108 — 7,105 g/L per dollar). The model books that benefit as a titer multiplier; the literature suggests at least part of it is an anti-aggregation effect, i.e. a fraction effect the model cannot represent. That is a second argument for adding a folding-outcome term to the scoring, not just a folding reagent to the menu.

E.8 — B3 numbers behind the forum example, and the tooling note

The cysteine result, in full. The assigned RFopt (ox.) plate carries 5 mM cysteine. Sweeping cysteine with DsbC held fixed gives modelled pairing of p_pair 0.3674. Back-solving the app’s own assay calibration — 540 RFU per µM AMC, 260 RFU blank, 0.42 µM AMC/min per µM enzyme, a 480-minute window and a lowest calibrated standard of 0.39 µM AMC — puts that at 0.56× the replicate-safe threshold, meaning the plate as specified cannot produce a scoreable well. Sweeping DsbC with cysteine at base level instead gives p_pair 0.5132 with no DsbC at all, above the 0.4452 an earlier design had bought with 3.5 µM of it.

Why the order matters. DsbC was compensating for a problem cysteine was creating. Evaluated alone, removing DsbC lowers modelled pairing and looks like a bad move; evaluated after cysteine is corrected, it is free. A strict one-factor-at-a-time protocol would therefore have rejected the correct design. This is the general case against single-lever screening when two reagents interact through the same term — here, the thiol penalty.

Cost decomposition. DsbC at 5 µM costs 1,000 nL on a 0.1 mM stock and accounts for 99.97% of that plate’s variable cost ($5.632 of $5.634). Removing it takes the reaction from $5.6595134 to $0.0273835 all-in, a 206.7× reduction. It also resolves a budget problem the plate as specified needs 11,750 nL against an 11,000 nL allowance, so it is not loadable as written.

Stoichiometric check before the cut. Reteplase carries 18 cysteine residues. At 0.5–2 g/L total protein that is 0.23–0.92 mM of demand, against 1.0 mM supplied by the base buffer — so removing added cysteine leaves the requirement covered. The engine does not model cysteine as a limiting amino acid, only as a thiol, so it would have permitted the cut regardless; the check is what makes it defensible.

Tooling note. The Week 3 configurator was built conversationally with no repository, version control or test suite. That was a reasonable trade for a first pass — the tool grew as the questions did, and the folding simulator answered questions that were not anticipated when it was started. The cost of that trade is visible in the error record a g/L-to-mM unit conversion on the ribose and glucose stocks (a 3.3× overdose that was reported as correct), and a folding prior multiplying a synthesis rate, which silently produced zero protein for reteplase and half for PETase. Both were found by re-deriving results, not by any automated check. A parity test now runs on every build of the folding module and reproduces the engine’s active fraction to within 2×10⁻¹⁵ — that test is what caught the second error, and it is the pattern Week 4’s code framework is intended to generalise.

E.9 — What is exact, what is modelled, and what is not used for ranking

Stated explicitly so the reader need not infer it.

The titer model’s leave-one-out R² on log titer is −0.26 with median fold error 1.456 across 11 reference formulations — worse than predicting the mean. That is the reason for the second row.

Open items carried forward, not resolved

1. nmp_precipitate warns on all three designs (total NMP 8.50 mM against a 5 mM threshold). Inherited from the reference plates. Clearing it costs ~24% of modelled titer to save 1.4% of variable cost, so the trade was refused.
2. Reteplase’s active fraction is a floor, not an estimate. The engine treats its 9 disulfides as pairing independently; the AlphaFold model of tPA shows three coupled modules of three, so the defensible exponent is between 3 and 9 and the true value is 7–55× higher. The exponent was left at 9 so all reference formulations stay comparable.
3. PETase’s fold_prior is unanchored at 0.50 ± 0.25. One 30-minute p-nitrophenyl read would replace it with a measurement.
4. Submission JSON field names are unverified against ginkgobioworks/autonomous-cfps; the repository was unreachable when the exporter was built.
5. The assignment cites DOI 10.1002/bit.20026 as PANOx-SP; that DOI resolves to the Cytomim paper. The PANOx-SP table used here came from the tool’s own reference record.
6. The tool lists reteplase at 355 aa; the supplied sequence is 399 aa (Strep-tag II / TEV construct). Flagged, not silently resolved.
7. A Brij-35 plus spermidine/putrescine combination raises active titer 18.2% for +$0.000211 per reaction. Deliberately held for a future round so the three levers under test keep clean attribution.

Citations

(status in progress)

• Olsen, M. L., Copeland, C. E., Sundberg, C. A., Aw, R., Shaver, Z. M., Rao, G., Swartz, J. R., Karim, A. S., & Jewett, M. C. (2026). Design-driven optimization of low-cost reagent formulations for reproducible and high-yielding cell-free gene expression. Nature Communications. DOI 10.1038/s41467-026-69605-8. Full text retrieved, open access.
• Smith, A. A., et al. (2026). Using a GPT-5-driven autonomous lab to optimize the cost and titer of cell-free protein synthesis (Ginkgo Bioworks × OpenAI). bioRxiv. DOI 10.64898/2026.02.05.703998. Not yet retrieved.
• Jewett, M. C., & Swartz, J. R. (2004). Mimicking the Escherichia coli cytoplasmic environment activates long-lived and efficient cell-free protein synthesis. Biotechnology and Bioengineering, 86(1), 19–26. DOI 10.1002/bit.20026. Paywalled; abstract only. See decision log entry 2 — this is the Cytomim paper, not the PANOx-SP paper.
• Silverman, A. D., Karim, A. S., & Jewett, M. C. (2020). Cell-free gene expression an expanded repertoire of applications. Nature Reviews Genetics, 21, 151–170. DOI 10.1038/s41576-019-0186-3.
• Rasor, B. J., Vögeli, B., Landwehr, G. M., Bogart, J. W., Karim, A. S., & Jewett, M. C. (2021). Toward sustainable, cell-free biomanufacturing. Current Opinion in Biotechnology, 69, 136–144. DOI 10.1016/j.copbio.2020.12.012.

Decision log

1. A1 mechanism rejected. An initial framing that attributed differing potassium- and magnesium-glutamate concentrations to differing disulfide-bond requirements was discarded. K⁺ and Mg²⁺ are closed-shell, non-redox-active cations and do not participate in thiol oxidation; disulfide outcomes in this system are controlled by the DTT / IAM / GSSG-GSH / DsbC / Δgor variables enumerated in Section 2C. The retained explanation is free-Mg²⁺ buffering by phosphate and nucleotide load.

2. Assignment citation discrepancy, carried into A3. The assignment recommends “PANOx-SP (Jewett & Swartz 2004)” and gives DOI 10.1002/bit.20026, but that DOI resolves to the Cytomim paper — the pyruvate-driven, phosphate-free system assayed with chloramphenicol acetyltransferase at 700 µg/mL. PANOx-SP is a distinct formulation. A primary PANOx-SP source with an actual concentration table is still needed before A3 can be written. Do not describe PANOx-SP while citing this DOI.

3. Part A3 pair not yet selected. Choice is open between the yield-vs-cost contrast (PANOx-SP vs Olsen 2026) and the human-vs-AI contrast (Olsen 2026 vs Smith 2026), the latter being closer to the coopetition’s own question.

4. A1 second correction — magnesium is not an energy source. An intermediate framing held that magnesium “provides the reaction energy needed for NTPs.” Rejected the energy resides in phosphoanhydride bonds (NTPs and the secondary donor regenerating them), while Mg²⁺ is a non-consumed catalyst contributing no driving force — and rising free Mg²⁺ makes ΔG°′ of ATP hydrolysis less negative, so the claim fails in direction as well as kind. Retained instead Mg·NTP is the physiological substrate, so magnesium is what makes the nucleotides usable.

5. A1 — necessity distinguished from sensitivity. Being essential does not make a reagent sensitive (the 20 amino acids are essential with broad optima). The sensitivity argument rests on saturable-site occupancy, opposing high- and low-side failure modes, chelation amplification, and the ~13-fold fractional-precision disadvantage of operating at 10 mM rather than 130 mM.

6. A1 — cheapness is not a dosing argument. Magnesium glutamate costs fractions of a cent, which licenses dense titration across compositions, not a higher setpoint. Overshoot carries real penalties (fidelity loss, mRNA structure, Mg-phosphate precipitation). The cost lever is NTP→NMP substitution; magnesium is the variable that must be retuned to realise it.

7. Engine coefficient claim corrected. An earlier draft of A1 stated the engine applies a polyphosphate magnesium-chelation weight of 1.5. Reading freeMagnesium() in the engine source shows the polyphosphate term is added raw, so its effective weight is 1.0 and mg_chelate_poly is an unused coefficient. The claim is corrected in Appendix E.1. No number in Part A depended on it — none of the compared formulations contain a polyphosphate chelator — and the same error was fixed in the kinetics model so that its free-Mg²⁺ calculation now reproduces the engine to within 1e-9 on all four reference formulations.

8. PANOx-SP source resolved, and a concentration corrected. The configurator’s own reference-formulation record carries PANOx-SP in full (Mg-glutamate 8 mM, K-glutamate 130 mM, ATP 1.2 mM, CTP/GTP/UTP 0.85 mM each, PEP 30 mM, HEPES 57 mM, with cost $4,083/g). This supplies the concentration table A3 needs without relying on the mis-cited DOI in decision log entry 2. It also corrects an earlier draft figure PEP is 30 mM, not ~33 mM.

9. Answer format changed on author instruction. Main-body answers now lead with the author’s own claim in italic, followed by a brief rationale and the key learnings that shaped it. The full worked analysis moved to Appendix E so the submitted answers stay short and the supporting work remains auditable.