Mathematical Model for Chemical Reactions in Electrolytes Applied to Cytochrome c Oxidase: An Electro-Osmotic Approach
Bibliographic record
Abstract
This study introduces a mathematical model for electrolytic chemical reactions, employing an energy variation approach grounded in classical thermodynamics. Our model combines electrostatics and chemical reactions within well-defined energetic and dissipative functionals. Extending the energy variation method to open systems consisting of charge, mass, and energy inputs, this model explores energy transformation from one form to another. Electronic devices and biological channels and transporters are open systems. By applying this generalized approach, we investigate the conversion of an electrical current to a proton flow by cytochrome c oxidase, a vital mitochondrial enzyme contributing to ATP production, the ‘energetic currency of life’. This model shows how the enzyme’s structure directs currents and mass flows governed by energetic and dissipative functionals. The interplay between electron and proton flows, guided by Kirchhoff’s current law within the mitochondrial membrane and the mitochondria itself, determines the function of the systems, where electron flows are converted into proton flows and gradients. This important biological system serves as a practical example of the use of energy variation methods to deal with electrochemical reactions in open systems. We combine chemical reactions and Kirchhoff’s law in a model that is much simpler to implement than a full accounting of all the charges in a chemical system.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".