## Abstract

A common model for the time σ_{L} (sec) taken by a DNA strand of length L (cm) to unravel is to assume that new points of unraveling occur along the strand as a Poisson process of rate λ 1/(cm x sec) in space-time and that the unraveling propagates at speed v/2 (cm/sec) in each direction until time σ_{L}. We solve the open problem to determine the distribution of σ_{L} by finding its Laplace transform and using it to show that as x = L^{2}λ/v → ∞, σ_{L} is nearly a constant:σ_{L}= 1 λvlog L^{2}λ v^{ 1 2}We also derive (modulo some small gaps) the more precise limiting asymptotic formula: for - ∞ < θ < ∞,Pσ_{L}< 1 λvψ 1 2[log(L^{2} λ v)]+ θ ψ^{ 1 2}[log(L^{2} λ v)]→e^{-e-θ}where ψ is defined by the equation: ψ(x) = log ψ(x)+x, x≥1. These results are obtained by interchanging the role of space and time to uncover an underlying Markov process which can be studied in detail.

Original language | English (US) |
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Pages (from-to) | 1177 |

Number of pages | 1 |

Journal | Mathematical and Computer Modelling |

Volume | 12 |

Issue number | 9 |

DOIs | |

State | Published - 1989 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Modeling and Simulation
- Computer Science Applications