Diffusion-Constrained Continuum Models of Engineered Membranes
Bibliographic record
Abstract
Introduction In this chapter (and the following three chapters) we study mesoscopic mathematical models for the dynamics of engineered membranes. This chapter constructs mesoscopic models for the following two synthetic biological devices built out of artificial membranes: (i) the ion-channel switch (ICS) biosensor and (ii) the pore formation measurement platform (PFMP). Mesoscopic models deal with physical phenomena at the micrometer length scale and millisecond time scale – their level of abstraction lies between the macroscopic reactionrate models and the microscopic atomistic models. To put this chapter into perspective, recall that Chapter 4 dealt with the construction of engineered membrane devices. Also, Chapters 8 and 9 constructed macroscopic reaction-rate models of these devices which comprised ordinary and fractional-order differential equations. At the end of this chapter we illustrate how approximations of the continuum models can be used to construct the parameters of the macroscopic models in Chapters 8 and 9. As discussed in Chapter 9 the ICS biosensor operates in either the mass-transportinfluenced kinetics or the reaction-rate-limited kinetics regime. A schematic of the ICS biosensor and PFMP in the flow chamber is provided in Figure 10.1. If the analyte concentration and/or fluid flow velocity is sufficiently large, the advection-diffusion dynamics of the analyte can be neglected and only the macroscopic surface reaction dynamics govern the impedance response of the ICS and PFMP. These reaction-rate-limited kinetics models were the focus of Chapter 9. In this chapter we consider the masstransport- influenced kinetics regime, where the advection-diffusion dynamics cannot be neglected in the fluid flow chamber. Therefore, the dynamic mesoscopic models involve diffusion-type partial differential equations (PDEs) with boundary conditions determined by reaction-rate-type ordinary differential equations (ODEs). Figure 10.1 illustrates the mesoscopic model which couples the electrolyte dynamics with the surface reactions. The electrolyte dynamics involve the advection-diffusion of molecules and ions, and may also include electrodiffusion effects if the molecules and ions are charged. The study of the electrodiffusion of charged particles such as molecules and ions in the presence of an applied external electric field is of great importance in a number of disciplines. For example, in semiconductors these mesoscopic models describe the dynamics of electrons and holes and are used for the design of modern electronic components such as transistors, diodes, and infrared lasers [80].
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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 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 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".