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Quick Help


(C) Daniel Jacob - INRAE UR BIA, BIBS 2025




Purpose


This application allows you to model and analyze proton-to-carbon transfer kinetics from solid-state NMR experiments. It uses data extracted from NMRProcFlow [1] (a TSV - Tab-Separated Values - file corresponding to a bucket matrix ) resulting from processing by the ERVA (Extraction of Relevant Variables for Analysis) [2] approach to identify relevant buckets (corresponding to C₁–C₆). Each kinetic curve is fitted using nonlinear least-squares modeling.


The app fits kinetic transfer curves (e.g. C₁–C₆ carbons) using nonlinear least-squares modeling and provides a full suite of goodness-of-fit, predictivity, parsimony, sensitivity, and robustness analyses.


In short, it helps you to :


    

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    fit appropriate kinetic models to your experimental curves,
    

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    quantify the quality and reliability of each fit,
    

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    evaluate how robust and identifiable your fitted parameters are.
    

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User Inputs (Interface)


The main controls in the Shiny interface allow you to tailor the modeling procedure:








Parameter
Description / Purpose






Bucket/compound to model
Select the variable (i.e bucket or a compound) you want to analyze




Model
Choose the kinetic model to fit (the corresponding equations are given into the ‘Models’ tab)




Parameter constraints
Fixe the value range [min, max] for each parameter




Maximum contact time
Define the upper limit of the time range used for fitting (depending on the model and/or if the modeling is partial or total)




Number of fits
Specify how many model fits to perform (helps evaluate stability and reproducibility)




Residual threshold
Set a cutoff for excluding outlier points based on residuals before refitting (useful to reduce the influence of experimental noise)




Bootstap samples
Number of bootstrap resamplings to estimate parameter robustness and confidence intervals.








So the steps to follow in order are: :


    

  1. Select the variable to analyze
    2. 

  2. Choose a kinetic model (see Models tab).
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  3. Choose the maximul contact time (depending on the model).
    4. 

  4. Set parameters:

      

    • Number of model estimations
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    • Residual threshold (exclude outliers)
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    • Number of bootstrap samples
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    5. 

  5. Run the model fit and interpret the outputs below.
    6. 





Modeling Method




Model fitting is performed using the Levenberg–Marquardt algorithm (nlsLM function from the R minpack.lm package [3]). This algorithm minimizes the difference between the experimental data and the model prediction to estimate the kinetic parameters.


    

  • This algorithm combines the strengths of the Gauss–Newton and gradient descent methods, making it robust for nonlinear kinetic models.
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  • You can apply constraints (i.e value range [min, max] for each parameter).
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Each fit estimates model parameters by minimizing the Residual Sum of Squares (RSS) between the observed data and the model.


Outlier removal can be performed by applying a threshold to the residuals corresponding to the number of times their standard deviation (value between 2 and 3) after unfiltered modeling.


    

  • This allows for the elimination of the few extreme values ​​that could adversely affect the optimization.
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  • Caution: Some points may be considered extreme if the model is not suitable. Thus, information not taken into account by the model may be found in the residuals. Particular attention should be paid to the first points, especially if the polarization transfer is rapid.
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  • A value of zero indicates no filtering.
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Results and Interpretation


The app provides several categories of results:




1. Fit Quality








Metric
Meaning
How to interpret






RSS
Measures the overall deviation between model and data
Lower = better fit




R² (adjusted)
Fraction of variance explained by the model
Values near 1 indicate a good fit; adjusted R² corrects for overfitting




RMSE (Root Mean Square Error)
Average deviation between model and observations, same unit as data
Lower = more accurate fit.




MAE (Mean Abs. Error)
Mean absolute prediction error, less sensitive to outliers than RMSE
Lower = better predictive accuracy.




AIC / BIC
Information criteria balancing fit quality and model complexity.
Lower = better trade-off between accuracy and simplicity.






➡️ Good fit: high R², low RMSE, low AIC/BIC.




2. Predictive Power (pMSE)




This metric measures how well the model predicts unseen or resampled data


    

  • Based on Predictive Mean Squared Error (pMSE) via cross-validation.
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  • Lower pMSE → higher predictive ability.
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Qualitative rule of thumb:


    

  • If pMSE ≈ RMSE, the model generalizes well.
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  • If pMSE >> RMSE, possible overfitting.
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3. Parsimony / Identifiability




Using the R FME package [4], the collinearity index measures how distinct the model parameters are from each other.


    

  • Collinearity index < 10 → parameters are identifiable and stable.
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  • > 20 → parameters are correlated or redundant.
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Interpretation:


    

  • A model is parsimonious when it fits the data well (low RSS, high R²) with few parameters that are identifiable (low collinearity).
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4. Residual Analysis




Evaluates how well the model captures the data trend.


    

  • Mean and Standard Deviation: Should be centered around zero.
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  • Normality test (Shapiro–Wilk): Checks if residuals follow a Gaussian distribution.

      

    • p-value > 0.05 → residuals consistent with normal noise.
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    • p-value < 0.05 → systematic deviation → model may miss some trend.
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Plot of residuals helps detect heteroscedasticity or autocorrelation (e.g., structure vs. time).




5. Robustness (Bootstrap)




Using residual bootstrapping (See Bootstrapping) to tests how stable parameter estimates are, the model is repeatedly re-estimated on resampled data.


    

  • Narrow confidence intervals → robust, reliable parameters.
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  • Wide intervals → uncertain estimates, possible model instability.
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Qualitative rule of thumb:


    

  • Visually, if the empirical distributions of the parameters are more or less symmetrical then this means that we have good robustness of the parameters.
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  • If the parameter distributions are very wide or multimodal, it is a sign that your data does not contain enough information.
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6. Sensitivity Analysis




Using the R sensitivity package [5], this quantifies how much each parameter influences the model’s predictions.


    

  • High sensitivity → parameter strongly affects output → key for interpretation.
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  • Low sensitivity → parameter has little influence → minor or possibly redundant parameter.
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This helps understand which kinetic constants drive the behavior of the transfer curve.




Summary – What to Look For








Aspect
Good Indicator
Possible Issue






Fit quality
R² ≈ 1, low RMSE
Large residuals




Predictivity
pMSE ≈ RMSE
pMSE much higher




Parsimony
Collinearity < 10
Collinearity > 20




Residuals
Random, normal
Systematic pattern




Sensitivity
Maximum of key parameters
All small / equal




Robustness
Narrow bootstrap CI
Wide CI intervals








Model Comparison Tip




When comparing multiple models:


    

  • Prefer the one with lowest AIC and lowest pMSE.
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  • If ΔAIC < 2 → models are equivalent → choose the simpler one.
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Exporting results




To export the results as a Workbook (XLSX format), you must first save the results for each variable using the Save Results button located on the left panel. The Export tab lists the saved variables.


    

  • You can save one or more models for the same variable
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  • Saving a previously saved variable/model couple overwrites the results with the new ones.
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  • For each variable/model couple, you can view a summary of the previously saved results.
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  • You can delete a variable/model couple from the list.
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  • An Export WorkBook button will export all saved results, with a tab for each variable.
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References




[1] Jacob D., Deborde C., Lefebvre M., Maucourt M. and Moing A. (2017) NMRProcFlow: A graphical and interactive tool dedicated to 1D spectra processing for NMR-based metabolomics, Metabolomics 13:36. https://pubmed.ncbi.nlm.nih.gov/28261014/


[2] Jacob D., Deborde C. and Moing A. (2013). An efficient spectra processing method for metabolite identification from 1H-NMR metabolomics data. Analytical and Bioanalytical Chemistry 405(15), https://pubmed.ncbi.nlm.nih.gov/23525538/


[3] Elzhov T., Mullen K., Spiess A-N.,  Bolker B. (2023) R Interface to the Levenberg-Marquardt Nonlinear Least-Squares Algorithm Found in MINPACK, Plus Support for Bounds, R package version 1.2-4, https://cran.r-project.org/package=minpack.lm


[4] Soetaert K., Petzoldt T. (2010). Inverse Modelling, Sensitivity and Monte Carlo Analysis in R Using Package FME, Journal of Statistical Software, 33(3), 1–28. doi:10.18637/jss.v033.i03


[5] Iooss B. et al, (2025) Global Sensitivity Analysis of Model Outputs and Importance Measures, R package version 1.30.2, https://cran.r-project.org/package=sensitivity