PuiChing Macau iGEM 2026

Modeling

Can EcN deliver butyrate all day?

We compare one powder dose with continuous bacterial production, then stop the calculation where measurements are missing.

Try the model See how it works
3.2 h above target after giving the full daily amount at once
Primary scenario: 2.20 g/day, a 2.6 mM target increment, a 400 mL effective lumen, and 1.0 h-1 removal. This is a model comparison, not a dose recommendation.

A daily total can still leave long gaps

In our primary scenario, 2.20 g replaces 24-hour turnover. Taken at once, it falls below the 2.6 mM target after 3.2 hours.

Try one powder dose

Green begins at the 24-hour total, 2.20 g. It does not mean one dose lasts 24 hours.

24-hour total27% supplied
Time above target1.9 of 24 h
Not enough total butyrate

This supplies 27% of the 24-hour requirement. The modeled pulse stays above target for 1.9 hours.

Test sensitivity assumptions
0.60 g/day supplies 27% of the 24-hour total.

Modeled butyrate increment over 24 hours

Taken once, 0.60 g starts at 17.0 mM and falls below the 2.6 mM target after about 1.9 hours. Spread evenly over 24 hours, the same daily amount approaches 27% of the target.
Time above target
1.9 h
Time below target
22.1 h/day

A larger dose starts higher, then fades

First-order removal pulls every single pulse down between doses. More powder delays the drop, but does not create continuous production.

EcN changes the shape of delivery

Retained bacteria can produce across the day. The next question is whether that continuous source is strong enough.

EcN must produce 1,527 µg/min

Equation 14 converts the luminal concentration rate into the butyrate production rate used by the transport model.

Published productivity is still too low

The Bai EcN and Wang E. coli W estimates are 691× and 25.8× below the requirement. Continuous delivery solves the timing problem, but current data do not show enough output.

Narrative summary: a once-daily powder pulse declines rapidly, whereas retained EcN could distribute production across the day. The primary scenario requires 1,527 micrograms per minute. The two literature proxies provide 2.21 and 59.1 micrograms per minute, leaving shortfalls of 691-fold and 25.8-fold.

Compare with published production estimates

Choose a literature estimate used as a proxy. The required production rate uses the same target, volume, and removal assumptions as the slider.

Literature estimate
2.21 µg/min
Required production
1,527 µg/min
Production shortfall
691×
The selected literature estimate is 691× below the required production rate.

Continuous production solves the timing problem, but the model does not yet show that EcN can produce enough butyrate. The final construct must be measured.

Check the calculation and study context

Pulse equation: after one swallowed powder dose, Equation 5 becomes B(t) = B0e-kBt. Coverage ends when the curve crosses the selected target.

24-hour total: mday = BtargetkBV MB × 24, where MB = 88.11 mg/mmol and production is spread evenly across the day.

Why one pulse fails: forcing the same first-order equation to stay above target for 24 hours gives 2.43 × 10⁶ kg in the primary scenario. This non-physiological result shows that the delivery pattern is wrong.

Published-study comparison: the selected amount is 0.76× the 0.786 g butyric-acid amount in the cited oral sodium-butyrate study. That study does not set a safety limit or recommended dose.

What still needs measurement: target increment, effective volume, and removal rate are sensitivity inputs. Changing them can change the conclusion.

Follow the calculation from dose to serum

Each step changes the quantity and its unit. The calculation stops when a required parameter has not been measured.

How many EcN cells remain?

After arrival and loss, a daily dose of 1.00 × 10¹⁰ CFU gives a cycle mean of 3.57 × 10¹⁰ retained CFU.

How much butyrate can retained EcN make?

Using the Bai EcN literature estimate, the retained cells produce 0.00377 mM each hour in the modeled lumen.

Convert concentration into an amount

Equation 14 uses lumen volume and molar mass to convert 0.00377 mM/h into 2.21 µg/min.

What reaches the serum?

The fitted gut-to-blood model gives a serum increment of 0.0125 µg/mL for this continuous source.

The calculation stops before the brain

Brain transfer, removal, and distribution volume have not been measured. Equation 12 shows what the next experiment must provide.

Narrative summary: repeated oral EcN doses determine retained cells and luminal production. Equation 14 converts concentration rate into amount rate, and the transport model estimates a serum increment. The calculation stops before the brain because transfer, removal, and distribution volume have not been measured.

Assumptions and model limits

Assumptions used

  • One well-mixed effective lumen
  • Daily dose pulses with first-order viable-cell loss
  • Production proportional to retained-cell density
  • First-order luminal butyrate removal

Not claimed

  • Spatial gradients or microbial competition
  • Therapeutic efficacy or a safe human dose
  • A brain concentration without paired data

Test the assumptions yourself

Change formulation, productivity, dose, volume, or removal. Every result and chart updates from the same equations.

Cycle-mean butyrate in the lumen0.00377 mM

With the Bai EcN literature estimate and 50% enteric arrival, the model gives 0.00377 mM. Change an input to see which assumptions matter most.

Cycle-mean retained EcN
3.57 × 10¹⁰ CFU
Retained-cell density
8.93 × 10⁷ CFU/mL
Butyrate rate for transport model
2.21 µg/min
Modeled serum increment
0.0125 µg/mL

Retained EcN density over 20 daily doses

Retained-cell density (CFU/mL)

Each dose adds surviving cells. First-order loss removes cells before the next dose arrives.

Estimated serum butyrate increment

Serum butyrate increment (µg/mL)

Continuous production. The selected bacterial production rate is supplied continuously to the fitted gut-to-blood model.

How the model works

Each step shows the equations, parameters, units, and evidence needed to reproduce the calculation.

Estimate retained EcN

Each daily dose enters as a separate pulse. Formulation-specific arrival adds viable cells, and first-order loss removes them between doses. Equation 2 gives the cycle-mean retained population.

Model equations

N(t) = Σi FGID e-kN(t-ti) H(t-ti)(1)

Nss = FGID / kN(2)

Parameters and units

D
EcN per daily dose, CFU/dose
FGI
Fraction reaching the modeled gut compartment
kN
First-order viable-cell loss, day-1
H
Switch that activates each dose at ti

Methods narrative: Equations 1 and 2 estimate retained cells. Equations 3 to 6 estimate the luminal concentration rate. Equation 14 converts that rate into butyrate production in micrograms per minute. Equations 10 and 11 model gut-to-blood transport against serum data, while Equation 12 defines the unmeasured brain compartment.

Reproduce the calculations

We solved deterministic trajectories with Python and SciPy solve_ivp. The oral-data fit used bounded L-BFGS-B optimization.

We summed daily pulses over 20 days, swept gut density from 106-1010 CFU/mL, and compared algebraic steady states with numerical trajectories.

Show what is known, assumed, and missing

We label every input as published, derived, assumed, or unmeasured. This shows which results come from data and which need testing.

Start with published measurements

Four studies provide human EcN kinetics, six serum group means, and two productivity values used as proxies.

Show every calculated input

Converted rates and fitted constants keep their source and unit, so matched measurements can replace them without changing the model.

Let readers change the assumptions

Effective volume, luminal removal, and formulation-specific arrival stay visible because matched measurements are not yet available.

Leave unknown values empty

Without brain transfer, removal, and distribution-volume data, the model cannot calculate a brain concentration.

Turn each gap into an experiment

The next cycle must measure construct productivity, validate delivery and retention, test sustained production, and measure brain transport.

Final construct productivity

What we have: two literature proxies that differ by 27-fold.

What to measure: time-resolved production at a matched cell density.

Delivery and retention

What we have: capsule CFU, but not viable arrival or persistence.

What to measure: recovery after simulated digestion and retention under matched conditions.

Delivery profile

What the model shows: the 24-hour total does not guarantee continuous coverage.

What to test: whether retained EcN can persist and produce enough butyrate.

Brain compartment

What is missing: transfer, removal, and effective distribution volume.

What to measure: paired serum and brain data defined by Equation 12.

Narrative summary: published data and traceable proxies enter the model, assumptions remain visible, and unmeasured brain parameters stay empty. Each gap leads to a measurement or design action.

Evidence used in the current model

Bai and Mansell, 2020EcN endpoint productivity proxyView source
Wang et al., 2019Growth-phase upper productivity proxyView source
Kurtz et al., 2018Human EcN recovery and clearance contextView source
La Monica et al., 2025Six serum means used for the oral fitView source

Measurements required for validation

  • Time-resolved productivity of the final engineered construct
  • Formulation-specific viable arrival and retained-cell density
  • Effective lumen volume and luminal removal under matching conditions
  • Brain transfer, removal, and distribution parameters
Oral fitR² 91.45%
ErrorRMSE 0.2251 µg/mL

We fit gut-to-blood rates to six published serum group means, then kept those rates for the continuous-production simulations.

References
  1. Bai, Y., & Mansell, T. J. (2020). Production and sensing of butyrate in a probiotic E. coli strain. International Journal of Molecular Sciences, 21(10), 3615. https://doi.org/10.3390/ijms21103615
  2. Cummings, J. H., Pomare, E. W., Branch, W. J., Naylor, C. P. E., & Macfarlane, G. T. (1987). Short chain fatty acids in human large intestine, portal, hepatic and venous blood. Gut, 28(10), 1221-1227. https://doi.org/10.1136/gut.28.10.1221
  3. Gao, C., Li, B., He, Y., Huang, P., Du, J., He, G., Zhang, P., Tang, H., & Chen, S. (2023). Early changes of fecal short-chain fatty acid levels in patients with mild cognitive impairments. CNS Neuroscience & Therapeutics, 29(11), 3657-3666. https://doi.org/10.1111/cns.14252
  4. International Commission on Radiological Protection. (2002). Basic anatomical and physiological data for use in radiological protection reference values (ICRP Publication 89). Annals of the ICRP, 32(3-4).
  5. Kurtz, C., Denney, W. S., Blankstein, L., Guilmain, S. E., Machinani, S., Kotula, J., Saha, S., Miller, P., & Brennan, A. M. (2018). Translational development of microbiome-based therapeutics: Kinetics of E. coli Nissle and engineered strains in humans and nonhuman primates. Clinical and Translational Science, 11(2), 200-207. https://doi.org/10.1111/cts.12528
  6. La Monica, M. B., Kirby, T., Hartshorn, S. L., Gustat, A., Grdic, J., & Sandrock, J. (2025). A pharmacokinetic comparison of three butyrate products. Journal of Exercise and Nutrition, 8(1), Article 4. Article record
  7. Rowland, M., & Tozer, T. N. (2011). Clinical pharmacokinetics and pharmacodynamics: Concepts and applications (4th ed.). Lippincott Williams & Wilkins.
  8. Virtanen, P., Gommers, R., Oliphant, M., et al. (2020). SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods, 17, 261-272. https://doi.org/10.1038/s41592-019-0686-2
  9. Wang, L., Chauliac, D., Moritz, B. E., Zhang, G., Ingram, L. O., & Shanmugam, K. T. (2019). Metabolic engineering of Escherichia coli for the production of butyric acid at high titer and productivity. Biotechnology for Biofuels, 12, 62. https://doi.org/10.1186/s13068-019-1408-9

Turn model limits into experiments

The model does not provide a therapeutic dose. It shows which delivery design to keep and which measurements must come next.

Measure the final construct

The literature proxies differ by 27-fold, so neither should be treated as the final design input.

Measure butyrate production and cell density over time.

Validate delivery and retention

Capsule CFU does not tell us how many productive cells survive digestion or remain in the lumen.

Measure viable recovery and persistence under matched conditions.

Keep continuous delivery

The primary scenario separates the amount delivered from how long that amount remains available.

Improve EcN output, then measure its delivery profile.

Plan the brain experiment

Serum can be estimated, but brain transfer, removal, and distribution are still unknown.

Use Equation 12 to plan paired serum and brain measurements.

Where this leaves the project

In the primary scenario, 2.20 g/day balances 24-hour turnover, but one pulse stays above target for only 3.2 hours. Continuous EcN production has the delivery pattern required by the model. Current productivity proxies are still 25.8× to 691× too low, so the next step is to measure and improve the final construct before testing whole-system feasibility.

Revisit the slider