This page contains an online tool for calculating the parameters of a Fixman-Freire loop approximation for arbitrary DNA sequence length and loop exponent given as user input.

The exact loop entropy factor is(1) |

where

*x*is the loop size (one plus the number of melted basepairs), σ is the cooperativity (or nucleation or initiation) constant,

*d*is the stiffness constant, and α is the exponent (usually 1.5~2.2). The Fixman-Freire approximation of the loop entropy factor is

(2) |

where the power function is replaced by some multi-exponential function

*f:*

(3) |

The parameters

*I*,

*A*and

_{n}*B*(for

_{n}*n*=1,…,

*I*) are determined by fitting

*f(x)*to

*x*

^{-α}for

*x*in the range [2:2

*N*] where

*N*is sequence length. Two alternative solutions, here called the Recursive approximation and the Algebraic approximation, are both calculated below and their precisions are compared. The Recursive approximation is applied in all melting calculations on this server (stitchprofiles.uio.no), and the Algebraic approximation was applied in calculating the human genomic melting map. The parameters can also be applied in other melting algorithms, to allow for calculations on any sequence with length

*≤ N*. The required number of exponentials

*I*is determined as a logarithmic function of the maximum sequence length

*N*

(4) |

The

*B*for

_{n}*n=1,…,I*depend only on

*I*

(5) |

while the

*A*for

_{n}*n=*1,…,

*I*depend on

*I*and α: In the Recursive approximation they are calculated recursively from

*n=*1 to

*I*

(6) |

In the Algebraic approximation they are given algebraically by

(7) |

Finally, the const. in Eq.(2) is determined after calculating the

*I*,

*A*and

_{n}*B*by

_{n}(8) |

Note that in the tables below, this const. is absorbed into the

*A*.

_{n}Loop entropy:

Exponent α :