Solomon F Brown’s research while affiliated with The University of Sheffield and other places

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Publications (4)


Figure 1. Frequency of closed and first order Sobol' matrix element values across 9 outputs and 5 inputs.
Figure 4. The absolute error [A m ] l×l ′ of the closed Sobol' matrix element [S m ] l×l ′ calculated from MQU moments. Ground truth is the MNU closed Sobol' matrix reported in Section 7. Each plot point is the median (top row) or 90% quantile (bottom row) A over 2 folds, L 2 = 81 matrix elements and M ∈ {5, 7} closed matrices.The top row indicates accuracy, the bottom row reliability.
Figure 5. The absolute error [A T M−m ] l×l ′ of the total Sobol' matrix element [S T M−m ] l×l ′ calculated from MQU moments. Ground truth is S M − S m calculated from the MNU closed Sobol' matrices reported in Section 7. Each plot point is the median A T over 2 folds, L 2 = 81 matrix elements and one or two total matrices. Only MQUs with M = 7 have been used.
Figure 6. The standardized score [A m ] l×l ′ /[T m ] l×l ′ of the closed Sobol' matrix element [S m ] l×l ′ with standard error [T m ] l×l ′ calculated from MQU moments. Ground truth is the MNU Sobol' matrix reported in Section 7. Each plot point is the median (top row) or 90% quantile (bottom row) A/T over 2 folds, L 2 = 81 matrix elements and M ∈ {5, 7} closed matrices. The top row indicates accuracy, the bottom row reliabilty.
Sobol' Matrices For Multi-Output Models With Quantified Uncertainty
  • Preprint
  • File available

January 2025

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13 Reads

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Solomon F. Brown

Variance based global sensitivity analysis measures the relevance of inputs to a single output using Sobol' indices. This paper extends the definition in a natural way to multiple outputs, directly measuring the relevance of inputs to the linkages between outputs in a correlation-like matrix of indices. The usual Sobol' indices constitute the diagonal of this matrix. Existence, uniqueness and uncertainty quantification are established by developing the indices from a putative multi-output model with quantified uncertainty. Sobol' matrices and their standard errors are related to the moments of the multi-output model, to enable calculation. These are benchmarked numerically against test functions (with added noise) whose Sobol' matrices are calculated analytically.

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FIGURE 3 Separation of NTPs from mRNA over time at different permeate fluxes. (A) Circle points correspond to experimental data (AEX HPLC measurements of NTPs), and the line corresponds to the model predictions. (B) The variation of rejection factor calculated from the mass balance after fitting the model with the experimental data at various permeate fluxes. Results were obtained using the 300 kDa mPES HF membrane. AEX, anion exchange chromatography; HF, hollow fiber; HPLC, high-performance liquid chromatography; NTPs, nucleoside triphosphates.
FIGURE 4 TFF membrane fouling based on the Hermia model. Schematic representation of Hermia's fouling mechanisms caused by mRNA, and the variation of TMP over time based on the proposed model. TFF, tangential flow filtration; TMP, transmembrane pressure.
An Experimental and Modeling Approach to Study Tangential Flow Filtration Performance for mRNA Drug Substance Purification

November 2024

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86 Reads

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1 Citation

Biotechnology Journal

Ehsan Nourafkan

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Charlotte Kenyon

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Following the recent COVID-19 pandemic, mRNA manufacturing processes are being actively developed and optimized to produce the next generation of mRNA vaccines and therapeutics. Herein, the performance of the tangential flow filtration (TFF) was evaluated for high-recovery, and high-purity separation of mRNA from unreacted nucleoside triphosphates (NTPs) from the in vitro transcription (IVT) reaction mixture. For the first time, the fouling model was successfully validated with TFF experimental data to describe the adsorption of mRNA on filtration membrane. The fouling model enables monitoring of the mRNA purification processes, designing an appropriate strategy for filter clean-up, replacing the column at the right time and reducing the process cost. Recovery greater than 70% mRNA without degradation was obtained by implementing a capacity load of ∼19 g/m 2 , <2.5 psi transmembrane pressure (TMP) and feed flux of 300 LMH. This approach also enables the purification of multiple mRNA drug substance sequences for the treatment of a wide range of different diseases.


Figure 1: In vitro transcription mechanism.
Ranges of design parameters for IVT reaction
Detailed information for GP model evaluations
Comparison between the predictive (Single-GP model based optimizations) and practical experiment yields under the generated operation conditions
Multiple Gaussian process models based global sensitivity analysis and efficient optimization of in vitro mRNA transcription process

October 2024

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93 Reads

The in vitro transcription (IVT) process is a critical step in RNA production. To ensure the efficiency of RNA manufacturing, it is essential to optimize and identify its key influencing factors. In this study, multiple Gaussian Process (GP) models are used to perform efficient optimization and global sensitivity analysis (GSA). Firstly, multiple GP models were constructed using the data from multiple experimental replicates, accurately capturing the complexities of the IVT process. Then GSA was conducted to determine the dominant reaction factors, specifically the concentrations of reactants NTP and Mg across all data-driven models. Concurrently, a multi-start optimization algorithm was applied to these GP models to identify optimal operational conditions that maximize RNA yields across all surrogate models. These optimized conditions are subsequently validated through additional experimental data.