Critical Sequence Identity: An analytical threshold using the incomplete gamma function
Fuente:
Zenodo
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Recurso digital |
| Lenguaje: | inglés |
| Publicado: |
Zenodo
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866901748266827776 |
|---|---|
| author | miyamoto, ikutoshi |
| author_facet | miyamoto, ikutoshi |
| contents | <div>Let p denote the per-base mutation probability during genome replication, and let n denote the genome length. In a primitive genome model possessing only self-replication capability, we derive the critical sequence identity Q required to maintain replication function as follows. Using the Poisson approximation to the binomial mutation count, we obtain</div> <div><span dir="auto"><span dir="auto">Q = max{q ∈ {0, 1/n , 2/n , ..., 1} | Γ (1 + n − ⌊nq⌋, np) /Γ (1 + n − ⌊nq⌋) = 1/2}</span></span></div> <div>where ⌊ x ⌋ denotes the floor function.</div> <div> <div> <div>Notably, in the regime where the expected number of mutations np is sufficiently large, this analytical threshold simplifies to Q ⋍ 1 - p, which aligns with the intuitive understanding that higher mutation rates necessitate stricter sequence identity.</div> </div> </div> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18284958 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Critical Sequence Identity: An analytical threshold using the incomplete gamma function miyamoto, ikutoshi Minimum sequence identity Error threshold Poisson approximation Genome replication Mathematical biology Self-replication Primitive genome 1.06 Biological sciences 1.01 Mathematics Bioinformatics <div>Let p denote the per-base mutation probability during genome replication, and let n denote the genome length. In a primitive genome model possessing only self-replication capability, we derive the critical sequence identity Q required to maintain replication function as follows. Using the Poisson approximation to the binomial mutation count, we obtain</div> <div><span dir="auto"><span dir="auto">Q = max{q ∈ {0, 1/n , 2/n , ..., 1} | Γ (1 + n − ⌊nq⌋, np) /Γ (1 + n − ⌊nq⌋) = 1/2}</span></span></div> <div>where ⌊ x ⌋ denotes the floor function.</div> <div> <div> <div>Notably, in the regime where the expected number of mutations np is sufficiently large, this analytical threshold simplifies to Q ⋍ 1 - p, which aligns with the intuitive understanding that higher mutation rates necessitate stricter sequence identity.</div> </div> </div> |
| title | Critical Sequence Identity: An analytical threshold using the incomplete gamma function |
| topic | Minimum sequence identity Error threshold Poisson approximation Genome replication Mathematical biology Self-replication Primitive genome 1.06 Biological sciences 1.01 Mathematics Bioinformatics |
| url | https://doi.org/10.5281/zenodo.18284958 |