Cell Division Commitment via P = C·S²/E
Rob Merivale
5 December 2024 • ~12 min read
Commitment via P = C·S²/E
A Theoretical Framework for Biological Persistence
Correspondence
Academic or technical correspondence regarding this paper may be directed via:
science@robmerivale
Preprint Disclaimer
This paper is a preprint and has not yet undergone peer review. It is published to invite critique, clarification, and interdisciplinary discussion.
Abstract
This paper proposes an empirically testable framework for cell division commitment based on a persistence equation, P = C·S²/E, where C denotes molecular coherence, S denotes genetic stability, and E denotes entropy load. The framework treats cell division as an information-preserving commitment made under thermodynamic constraints. Cells are hypothesised to commit to division only when persistence exceeds a cell-type-specific threshold. The paper provides a complete biological mapping, measurable molecular proxies, and falsifiable hypotheses suitable for empirical interrogation.
1. Executive Summary
This research programme implements empirical validation of the persistence framework:
P = C·S²/E
for cell division commitment. The framework proposes that cells evaluate their capacity to successfully complete division based on three integrated factors:
- C (Coherence): Molecular organisation and system integration
- S (Stability): DNA repair capacity and checkpoint robustness
- E (Entropy Load): Energy cost and accumulated damage burden
The persistence value P represents the viability of completing division. Cells are predicted to commit to division when P exceeds a cell-type-specific threshold.
2. Theoretical Foundation
Cell division is fundamentally an information-transmission problem operating under thermodynamic constraints. Accurate duplication of genetic and epigenetic information requires coordinated molecular organisation, robust error-correction, and sufficient energetic headroom.
The persistence equation captures this by:
- Requiring coherent molecular organisation (C) to coordinate complex, multistep processes
- Demanding robust error-correction (S²), where the squared term reflects redundant and non-linear checking mechanisms
- Balancing against entropy load (E), representing metabolic cost, energetic stress, and accumulated damage
Division is therefore not a binary trigger but an emergent commitment governed by system-level viability.
3. Biological Mapping
3.1 Coherence (C)
Operational definition: The degree of organised, coordinated molecular state within a cell.
Measurable proxies:
- Transcriptional orderliness: Low coefficient of variation in housekeeping gene expression
- Pathway coordination: High correlation within glycolytic pathway gene expression
- Proteostasis quality: Low stress-response marker expression (inverse relationship)
Gene sets:
Housekeeping genes
ACTB, GAPDH, PGK1, RPL19, RPS18, TBP
Glycolysis pathway
HK2, PFKM, ALDOA, GAPDH, PGK1, ENO1, PKM
Stress markers (inverse)
HSPA1A, HSPA1B, DDIT3, ATF4, XBP1
3.2 Stability (S)
Operational definition: The cell’s capacity to maintain and accurately replicate genetic information.
Measurable proxies:
- DNA repair capacity: Expression of DNA repair pathway genes
- Checkpoint robustness: Activity of p53 and ATM/ATR-mediated checkpoints
Gene sets:
DNA repair
BRCA1, BRCA2, RAD51, MSH2, MSH6, MLH1, APEX1, OGG1, XRCC1
Cell-cycle checkpoints
TP53, CDKN1A, ATM, ATR, CHEK1, CHEK2, BUB1, MAD2L1
Rationale for S²:
Error-checking mechanisms in biological systems scale non-linearly. Redundancy, cross-validation, and checkpoint cascades justify a squared contribution rather than a linear one.
3.3 Entropy Load (E)
Operational definition: The energetic cost of maintaining function plus the burden of accumulated damage.
Measurable proxies:
- Energy stress: AMPK pathway activation
- Energy surplus: mTOR pathway activity (inverse relationship)
- Damage burden: DNA damage response activation and oxidative stress markers
Gene sets:
AMPK pathway
PRKAA1, PRKAA2, PPARGC1A
mTOR pathway
MTOR, RPS6KB1, EIF4EBP1, RPS6
Damage response
H2AFX, RNF8, RNF168, TP53BP1
4. Hypotheses
4.1 H1: Persistence increases across the cell cycle
Prediction:
P(G1) < P(S) < P(G2/M)
Test:
Mann–Whitney U tests between cell-cycle phases
Success criterion:
p < 0.001 for each phase transition
4.2 H2: Persistence predicts division commitment
Prediction:
Persistence exceeds a threshold prior to S-phase entry
Test:
Receiver operating characteristic (ROC) analysis
Success criterion:
AUC > 0.75
5. Implications
5.1 Cancer Biology
Oncogenic transformation is interpreted as artificial elevation of P, typically via inflation of C or suppression of effective E, while true S is compromised.
5.2 Regenerative Medicine
Stem-cell quiescence and activation may be regulated by modulating persistence rather than forcing proliferative signals.
5.3 Aging Research
Replicative senescence is modelled as a collapse of S, driven by telomere erosion and accumulated repair deficits.
6. Scope and Limitations
This paper defines a theoretical and operational framework but does not present original wet-lab data. The persistence equation is intended to be falsifiable and is contingent on the quality of proxy selection, normalisation, and cell-type specificity. Threshold values are expected to vary across lineages and contexts. The framework does not claim exclusivity and is compatible with existing regulatory models of the cell cycle.
7. Conclusion
This paper provides a complete roadmap for empirical validation of P = C·S²/E as a unifying principle governing cell division commitment. It reframes proliferation as a thermodynamically constrained persistence decision rather than a simple regulatory switch, offering testable predictions across cancer biology, regeneration, and aging.
References
References are intentionally limited in this preprint to preserve conceptual clarity. Canonical literature on cell-cycle checkpoints, DNA repair, AMPK/mTOR signalling, and systems biology provides the empirical substrate against which this framework may be tested.