Enzyme-Kinetic Identifiability Laboratory
A completed enzyme-kinetics study of inhibition mechanism, concentration placement, observation error, parameter uncertainty, and experimental identifiability.
Project definition
Problem statement
Different enzyme-inhibition mechanisms can produce similar rate curves over a limited concentration range, making a visually good fit insufficient for identifying the correct mechanism or its parameters.
The biotechnology problem is to compare candidate mechanisms, quantify parameter uncertainty and correlation, and choose concentration combinations that improve identifiability within a fixed observation budget.
Project objectives
- Implement Michaelis-Menten and five inhibited enzyme rate laws under one consistent parameter convention.
- Generate a declared mixed-inhibition synthetic truth on a rich substrate and inhibitor grid.
- Fit all six candidate models using weighted multistart nonlinear optimisation.
- Compare models using AICc, BIC, residual evidence, and Akaike weights.
- Measure Fisher information, conditioning, parameter covariance, and profile likelihood.
- Compare conventional and D-optimal 48-observation designs.
- Test model-selection reliability across four observation-error levels.
Project structure
Project components
Rate-law library
Implements the uninhibited, competitive, uncompetitive, noncompetitive, mixed, and substrate-inhibition equations.
Synthetic experiment
Creates reproducible rich-grid observations from declared mixed-inhibition parameters and combined absolute and relative error.
Model inference
Fits each mechanism, calculates information criteria, and retains full parameter and residual evidence.
Identifiability analysis
Calculates information matrices, standard errors, correlations, profiles, and bootstrap intervals.
Experimental design
Constructs equal-budget conventional and D-optimal designs and compares their information content.
Verification pipeline
Checks equations, limiting behaviour, design constraints, reproducibility, results, documents, dependencies, and the container workflow.
Methodology
Project workflow
- 01Define the experiment
Load the kinetic truth, observation-error model, candidate mechanisms, concentration grid, and random seeds.
- 02Generate observations
Create the rich synthetic dataset while retaining the exact clean rates, uncertainties, and noisy observations.
- 03Compare mechanisms
Fit all rate laws and compare parameter estimates, residuals, AICc, BIC, and model weights.
- 04Measure identifiability
Calculate local information, parameter correlations, likelihood profiles, and bootstrap intervals.
- 05Improve the design
Compare conventional concentration placement with a D-optimal design under the same 48-observation budget.
Demonstration scenario
The rich-grid study selects mixed inhibition with an Akaike weight of 0.999983. Under the 48-observation budget, the D-optimal design raises the log information determinant from 20.0939 to 21.9932 and lowers the condition number from 244.58 to 116.96. At relative CV 0.12, correct model selection rises from 76.67 percent to 95.00 percent.
Engineering
Tools and method
- Tools
- The project uses Python 3.12, NumPy, SciPy, pandas, Matplotlib for subject analysis, simulation, and results.
- Kinetic models
- Python and NumPy implement six vectorised steady-state enzyme rate laws with explicit positive parameter bounds.
- Numerical inference
- SciPy performs weighted multistart least-squares fitting, likelihood profiling, and seeded bootstrap estimation.
- Experimental design
- A sequential D-optimal procedure selects substrate and inhibitor combinations using local parameter sensitivities.
- Evidence
- CSV, JSON, PNG, PDF, and Word files retain the observations, fits, trials, figures, references, and interpretation.
- Verification
- Automated tests, static analysis, dependency auditing, repository validation, and a digest-pinned non-root Docker run support the release.
Testing
Evaluation
Evaluation measures
- AICc, BIC, Akaike weight, and weighted residual behaviour
- Estimated Vmax, Km, Kic, and Kiu with standard errors and bootstrap intervals
- Information-matrix log determinant and condition number
- Parameter-correlation and profile-likelihood evidence
- Correct mechanism-selection rate under increasing observation error
- Equal-budget conventional and D-optimal design comparison
Project boundaries
- All observations are synthetic and do not represent measurements from a named enzyme or assay.
- The study assumes steady-state initial-rate equations and independent Gaussian observation error.
- Local D-optimality depends on the declared nominal parameters and candidate concentration grid.
- Confidence intervals and model-selection rates describe this simulated experiment only.
- A real adaptation requires assay validation, raw wet-lab observations, independent batches, and biochemical review.
Included
- 01Complete enzyme-kinetics source code
- 02Six implemented enzyme rate laws
- 03Rich-grid, conventional, and D-optimal experimental designs
- 04Weighted multistart fitting, model comparison, profile likelihood, and bootstrap analysis
- 05Thirteen generated figures and two attributed literature figures
- 06Seventy-six-page project report in PDF and editable Word formats
- 07Twelve-page setup and usage guide in PDF and editable Word formats
- 08Fifty-seven annotated references
- 09Fifty-four automated tests with 98.12 percent branch-aware coverage
Project record
No information is collected on this page.
- Permanent project ID
- GP-BT-0N9N463
- Catalogued
- 21 Aug 2026
- Completed
- 28 Aug 2026
- Verified
- 28 Aug 2026
- Demonstration
- Included in repository
Handover
After purchase
- 01Payment is confirmed
The project is marked unavailable and cannot be purchased again.
- 02Repository access is granted
The buyer's submitted GitHub account receives access to the private repository.
- 03The purchase record is delivered
The certification sheet is prepared from the reviewed buyer details and sent privately by email.