Dynamics of a state-dependent delay model of repressible and inducible operons
Bibliographic record
Abstract
An operon is a functioning segment of DNA which controls the synthesis of a certain kind of protein.We are interested in the dynamics of both inducible and repressible gene regulation which can be modeled by a system of delay differential equations.The delays arise due to the time taken for DNA transcription and mRNA translation.In the absence of delays, the repressible system is known to have a unique steady state which may undergo a Hopf bifurcation leading to a stable periodic orbit as parameters are varied in the system, and the inducible system is known to possess at most three coexisting steady states which may undergo bifurcations as parameters are varied.In this study, we consider a constant transcriptional delay, but consider the translation velocity to be a variable that depends on the concentration of intermediate protein.This results in a variable state-dependent translational delay which is implicitly defined by an integral threshold condition.We examine the steady states of such a state-dependent delay model analytically and study the stability and bifurcations of and from these steady states as parameters are varied.We primarily use two MATLAB packages, DDE-BIFTOOL and DDESD.We find fold bifurcations, coexisting steady states and Hopf bifurcations.We also show how to study stable periodic orbits arising from the Hopf bifurcations in the presence of implicit delays.We thus demonstrate that state-dependent time delays have an effect on the dynamics of gene regulation.Introduction of state-dependent delays not only improves the physiological meaning of the model, but also makes a difference to the stability of the system.With the state-dependent delay, we find that it is possible for the repressible system to possess up to three coexisting steady states and bistability between a stable periodic orbit and either a stable steady state or another stable periodic orbit.ii ABRG Un opron est un segment d'ADN fonctionnel qui contrle la synthse de certaines protines.Nous nous intressons la rgulation des gnes inductibles et rpressibles ayant une dynamique qui peut tre modlise par un systme d'quations diffrentielles retard.Ces retards sont dus la dure de la transcription de l'ADN et la traduction de l'ARNm.En absence de retards, le systme rpressible possde un unique tat stationnaire qui peut subir une bifurcation de Hopf conduisant une orbite priodique stable.En revanche, le systme inductible possde au plus trois tats staionnaire co-existants qui peuvent subir des bifurcations en fonction des paramtres du systme.Dans cette tude, nous considrons que le retard est constant, mais que la vitesse de traduction dpend de la concentration de la protine intermdiaire.Il en rsulte un retard translationnel dpendant de l'tat qui est implicitement dfini par une condition de seuil intgrale.Nous analysons les tats stationnaires d'un tel modle de retard dpendant de l'tat en tudiant la stabilit et les bifurcations partir de ces tats stationnaires en fonction des paramtres du systme.Nous utilisons principalement deux progiciels MATLAB, DDE-BIFTOOL et DDESD.Nous trouvons des tats stationnaires coexistants et des bifurcations de pli et de Hopf.Nous montrons galement comment tudier des orbites priodiques stables qui rsultent de bifurcations de Hopf en prsence de dlais implicites.Ainsi, nous dmontrons que les retards temporels dpendant de l'tat ont un effet sur la dynamique de la rgulation des gnes.L'introduction de retards dpendant de l'tat amliore non seulement la signification physiologique du modle, mais a galement un impact sur la stabilit du systme.En effet, avec le retard dpendant de l'tat, nous constatons qu'il est possible que le systme rpressible possde jusqu' trois tats stationnaires et une bistabilit entre une orbite priodique stable et soit un point stationnaire stable soit une orbite priodique stable.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".