Nonlinear delay differential equations and their application to modeling biological network motifs
Bibliographic record
Abstract
Abstract Biological regulatory systems, such as transcription factor or kinase networks, nervous systems and ecological webs, consist of complex dynamical interactions among many components. “Network motif” models focus on small sub-networks to provide quantitative insight into overall behavior. However, conventional network motif models often ignore time delays either inherent to biological processes or associated with multi-step interactions. Here we systematically examine explicit-delay versions of the most common network motifs via delay differential equations (DDEs), both analytically and numerically. We find many broadly applicable results, such as the reduction in number of parameters compared to canonical descriptions via ordinary differential equations (ODE), criteria for when delays may be ignored, a complete phase space for autoregulation, explicit dependence of feedforward loops on a difference of delays, a unified framework for Hill-function logic, and conditions for oscillations and chaos. We emphasize relevance to biological function throughout our analysis, summarize key points in non-mathematical form, and conclude that explicit-delay modeling simplifies the phenomenological understanding of many biological networks and may aid in discovering new functional motifs.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
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".