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Kinetic modeling of enzymatic cephalexin synthesis with neural ODEs and surrogate-accelerated Bayesian inference
No full textα-Amino ester hydrolases (AEHs) offer a promising route to the stereoselective synthesis of β-lactams such as cephalexin. However, published kinetic studies have encountered difficulty when extended beyond fitting of the data, indicating practical non-identifiability of the underlying kinetic models. Here, we address this issue using Bayesian inference combined with a reaction-consistent neural ODE surrogate that substantially accelerates parameter estimation. This framework enables efficient development of complex enzyme kinetic models even on limited hardware while providing rigorous uncertainty quantification of all parameters. To account for batch-dependent differences in active enzyme concentration, it was treated as a free parameter in each time series. Using this approach, the number of kinetic parameters was reduced from 12 to 9, and a useful kinetic model was obtained which is identifiable, mechanistically consistent, and predictive even under high substrate conditions.
Available Models
models/model_04.json: The most comprehensive 12-parameter model including all major reaction pathways, competitive inhibition, substrate inhibition, and detailed enzyme regulation mechanisms. This model provides the most biologically detailed description but requires the most parameters to be estimated.
models/model_06.json: A streamlined 9-parameter model that simplifies some regulatory interactions while maintaining core kinetic behavior. This represents a good compromise between detail and parameter identifiability.
models/model_07.json: An intermediate 10-parameter model that includes additional regulatory terms compared to Model 06, capturing more complex enzyme behavior under varying substrate conditions.
models/model_08.json: An optimized 9-parameter model that balances predictive accuracy with parameter parsimony. This model was developed through systematic model reduction to retain essential kinetic features while minimizing parameter uncertainty.
models/model_04_no_e0.json: Identical to Model 04 but with fixed enzyme concentration (E₀) rather than estimating it from data. Use this when enzyme concentration is known or measured separately.
models/model_08_no_e0.json: Identical to Model 08 but with fixed enzyme concentration. This provides a direct comparison of modeling approaches with and without enzyme concentration estimation.
Model File Structure and Components
Each model file (JSON format) contains a complete mathematical description of the kinetic system:
Species definitions: Lists all chemical species with their names and symbolic identifiers used in equations
Constants: Fixed parameters like enzyme concentration (p0) that may be estimated or held constant
ODEs: The system of ordinary differential equations describing how each species concentration changes over time. These equations encode the reaction kinetics and mass balances.
Parameters: Adjustable kinetic parameters (rate constants, binding affinities, inhibition constants) with their prior distributions for Bayesian inference
Algebraic assignments: Complex mathematical expressions that define reaction rates, enzyme-substrate complexes, and regulatory terms as functions of the parameters and species concentrations
The models use symbolic mathematics where enzyme-substrate complexes and reaction rates are expressed algebraically, making them both interpretable and computationally efficient.
System Requirements
Software Dependencies
The analysis pipeline requires several specialized Python packages for scientific computing, probabilistic programming, and machine learning:
<pre
class="sourceCode bash">pip install catalax
Hardware Requirements
The computational analysis is moderately demanding due to Bayesian MCMC sampling and neural network training:
CPU: Multi-core processor (recommended: 12+ cores) - MCMC chains run in parallel across available cores for efficient sampling
RAM: 16GB minimum, 32GB recommended - Memory requirements peak during MCMC sampling when storing large arrays of posterior samples
Operating System and Python Version
Supported OS: Linux or macOS (primary testing on macOS)
Python version: 3.10 or higher required for compatibility with JAX and NumPyro
Shell: Bash-compatible shell for running analysis scripts
How to Reproduce
Quick Start
Install dependencies:
<pre
class="sourceCode bash">pip install catalax
Train the neural ODE surrogate:
<pre
class="sourceCode bash">jupyter notebook TrainNeuralODE.ipynb
# Run all cells to create trained/rateflowode.eqx
Run the complete analysis:
<pre
class="sourceCode bash">export XLA_FLAGS="--xla_force_host_platform_device_count=12" # Adjust number for your CPU cores
chmod +x fit_all.sh
./fit_all.sh
What This Does
The analysis pipeline:
Uses Bayesian inference (MCMC) to estimate kinetic parameters with uncertainty quantification
Compares multiple model complexities (Models 04, 06, 07, 08)
Treats enzyme concentration as a free parameter in each experiment
Generates diagnostic plots and statistical summaries
Saves all results to the results/ directory
Individual Model Analysis
To analyze just one model:
<pre
class="sourceCode bash">python run_inference.py models/model_08.json
For analysis without enzyme concentration estimation:
<pre
class="sourceCode bash">python run_inference.py models/model_08_no_e0.json --no-e0
Outputs
Statistical Results Files
These files contain the quantitative outcomes of the parameter estimation and model evaluation:
{model_name}_summary.csv: Comprehensive MCMC parameter statistics including posterior means, standard deviations, 95% credible intervals, effective sample sizes (ESS), and R-hat convergence diagnostics. This file provides the key numerical results for parameter interpretation.
{model_name}_samples.nc: Complete posterior distribution samples stored in NetCDF format. Contains 10,000 samples × 12 chains for each parameter, enabling detailed uncertainty analysis, prediction intervals, and further statistical computations.
{model_name}_metrics.json: Model performance metrics including various error measures (L1, L2 losses), coefficient of determination (R²), Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC). These metrics allow comparison of model quality and complexity.
{model_name}_mean_e0.npy: Estimated enzyme concentrations for each experimental measurement (when E₀ estimation is enabled). This file contains the posterior mean enzyme concentrations that can be used for subsequent analyses or experimental validation.
Visualization Outputs
(plots/ subdirectory)
Diagnostic and result plots for model assessment and interpretation:
Trace plots: Time series of MCMC samples for each parameter, allowing visual inspection of mixing and convergence
Corner plots: Two-dimensional projections of parameter correlations and marginal distributions
Posterior distributions: Histograms and density plots showing parameter uncertainty
Model fit plots: Comparison of model predictions vs. experimental data over time
MCMC diagnostics: Monte Carlo Standard Error (MCSE) and Effective Sample Size (ESS) plots to assess sampling quality
Fitted Model Files (models/ subdirectory)
Updated model definitions with estimated parameters:
{model_name}_bi.json: Model with parameters set to Bayesian posterior means. This represents the most probable parameter values given the data and priors, suitable for point predictions and further analysis.
{model_name}_fitted.json: Model with parameters optimized using deterministic methods. These parameters minimize prediction errors and are typically used for the best-fit model predictions.
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Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Dispelling the Myths Behind First-author Citation Counts
Get PDFWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
koamabayili/VECTRON-author-checklist: VECTRON author checklist
No full textWe have done our best to complete the author checklist relating to the use of animals in the hut study. Note that the objective for the hut study was to evaluate the IRS treatment applications for residual efficacy against Anopheles mosquitoes, including the local An. coluzzii mosquito population. Cows were only used to attract mosquitoes into the huts and no tests were carried out directly on the cows. The author checklist is intended for use with studies where experiments are carried out on animals, which is why we have had such difficulty in completing this for the hut study, as many of the questions do not relate to how the cows were used
Author-wise bibliometric analysis based on entropy.
No full textAuthor-wise bibliometric analysis based on entropy.</p
Author Under Sail The Imagination of Jack London, 1893-1902
No full textIn Author Under Sail, Jay Williams offers the first complete literary biography of Jack London as a professional writer engaged in the labor of writing. It examines the authorial imagination in London's work, the use of imagination in both his fiction and nonfiction, and the ways he defined imagination in the creative process in his business dealings with his publishers, editors, and agents. In this first volume of a two-volume biography, Williams traverses the years 1893 to 1902, from London's "Story of a Typhoon" to The People of the Abyss. The Jack London who emerges in the pages of Author Under Sail is a writer whose partnership with publishers, most notably his productive alliance with George Brett of Macmillan, was one of the most formative in American literary history. London pioneered many author models during the heyday of realism and naturalism, blurring the boundaries of these popular genres by focusing on absorption and theatricality and the representation of the seen and unseen. London created an impassioned, sincere, and extremely personal realism unlike that of other American writers of the time. Author Under Sail is a literary tour de force that reveals the full range of London as writer, creative citizen, and entrepreneur at the same time it sheds light on the maverick side of machine-age literature.Intro -- Title Page -- Copyright Page -- Dedication -- Contents -- Acknowledgments -- Introduction -- 1. Spirit Truth -- 2. From Absorption to Theatricality and Back Again -- 3. "I Will Build a New Present" -- 4. Sons as Authors -- 5. Fathers as Publishers -- 6. The Daughter as Author -- 7. Lovers as Authors -- 8. At Sea with the Family -- 9. Yellow News, Yellow Stories -- 10. The Return Home -- Notes -- Bibliography -- Index -- About Jay WilliamsIn Author Under Sail, Jay Williams offers the first complete literary biography of Jack London as a professional writer engaged in the labor of writing. It examines the authorial imagination in London's work, the use of imagination in both his fiction and nonfiction, and the ways he defined imagination in the creative process in his business dealings with his publishers, editors, and agents. In this first volume of a two-volume biography, Williams traverses the years 1893 to 1902, from London's "Story of a Typhoon" to The People of the Abyss. The Jack London who emerges in the pages of Author Under Sail is a writer whose partnership with publishers, most notably his productive alliance with George Brett of Macmillan, was one of the most formative in American literary history. London pioneered many author models during the heyday of realism and naturalism, blurring the boundaries of these popular genres by focusing on absorption and theatricality and the representation of the seen and unseen. London created an impassioned, sincere, and extremely personal realism unlike that of other American writers of the time. Author Under Sail is a literary tour de force that reveals the full range of London as writer, creative citizen, and entrepreneur at the same time it sheds light on the maverick side of machine-age literature.Description based on publisher supplied metadata and other sources.Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, YYYY. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
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