# Team:SUSTC-Shenzhen-B/algorithm

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<h3>Introduction to scoring system 2</h3> | <h3>Introduction to scoring system 2</h3> | ||

- | <p>Scoring System 2 is based on the model created by d'Aubenton Carafa.[1] The score of terminator consists of two parts, the free energy of stemloop and the score of 15 nt poly T tail. The free energy of stemloop is calculated using Loop Dependent Energy Rules[2]. The minimization of the free energy also determined the secondary structure of the stemloop. T tail score is calculated by the formula given by d’ Aubenton Carafa. | + | <p>Scoring System 2 is based on the model created by d'Aubenton Carafa.[1] The score of terminator consists of two parts, the free energy of stemloop and the score of 15 nt poly T tail. The free energy of stemloop is calculated using Loop Dependent Energy Rules[2]. The minimization of the free energy also determined the secondary structure of the stemloop. T tail score is calculated by the formula given by d’ Aubenton Carafa. </p> |

- | Detailed Calculation of Score | + | <p>Detailed Calculation of Score</p> |

- | 1. Some definitions[2] | + | <p>1. Some definitions[2]</p> |

- | i. Closing Base Pair | + | <p>i. Closing Base Pair</p> |

- | For an RNA sequence, we number it from 5’ to 3’ . If i < j and nucleotides ri and rj form a base pair,we denote it by i.j. We call base ri’ or base pair i’.j’ is accessible from i.j if i < i’ ( < j’ ) < j and if there is no other base pair k.l so that i < k < i’ ( < j’ ) < l < j. We denote the collection of base and base pair accessible from i.j by L(i,j). Then i.j is the closing base pair. Here “L” means loop. | + | <p>For an RNA sequence, we number it from 5’ to 3’ . If i < j and nucleotides ri and rj form a base pair,we denote it by i.j. We call base ri’ or base pair i’.j’ is accessible from i.j if i < i’ ( < j’ ) < j and if there is no other base pair k.l so that i < k < i’ ( < j’ ) < l < j. We denote the collection of base and base pair accessible from i.j by L(i,j). Then i.j is the closing base pair. Here “L” means loop.</p> |

- | ii. n-loop | + | <p>ii. n-loop</p> |

- | If the loop contain n – 1 base pairs, we denote it by n-loop. (Because there is a closing base pair, so we denote it by n-loop even though the closing base pair is not included in the loop.) | + | <p>If the loop contain n – 1 base pairs, we denote it by n-loop. (Because there is a closing base pair, so we denote it by n-loop even though the closing base pair is not included in the loop.)</p> |

- | Here we can divide loops which may be formed in the terminator secondary structure into two kinds. | + | <p>Here we can divide loops which may be formed in the terminator secondary structure into two kinds.</p> |

- | 1-loop : Hairpin loop(size of loop shouldn’t be smaller than 3) | + | <p>1-loop : Hairpin loop(size of loop shouldn’t be smaller than 3) </p> |

- | 2-loop : Interior Loop(right strand size and left strand size are both bigger than 0.) | + | <p>2-loop : Interior Loop(right strand size and left strand size are both bigger than 0.)</p> |

- | Buldge(Size of one strand is bigger than 0 and that of another strand is 0.) | + | <p>Buldge(Size of one strand is bigger than 0 and that of another strand is 0.)</p> |

- | Stack(size of the loop is 0.) | + | <p>Stack(size of the loop is 0.)</p> |

- | 2. Calculation of the Minimum Free Energy Change of Stemloop Formation[3] | + | <p>2. Calculation of the Minimum Free Energy Change of Stemloop Formation[3]</p> |

- | Assume i.j is the closing base pair of the loop | + | <p>Assume i.j is the closing base pair of the loop </p> |

- | G（i,j）= min { GH ( i , j ) , GS( i , j ) + G ( i + 1 , j – 1 ) , GBI( i , j ) } ; | + | <p>G（i,j）= min { GH ( i , j ) , GS( i , j ) + G ( i + 1 , j – 1 ) , GBI( i , j ) } ;</p> |

- | GBI ( i , j ) = min{ gbi( i , j , k , l ) + G( k , l ) } for all 0 < k – i + l – j - 2 < max_size | + | <p>GBI ( i , j ) = min{ gbi( i , j , k , l ) + G( k , l ) } for all 0 < k – i + l – j - 2 < max_size</p> |

- | G(i,j) is the minimum free energy change of stemloop formation. GH is the free energy change to form a hairpin loop. GS is the free energy change to form a stack. GBI is to calculate the minimum free energy change of structure containing 2-loop. gbi(i,j,k,l) is the free energy change to form 2-loop. | + | <p>G(i,j) is the minimum free energy change of stemloop formation. GH is the free energy change to form a hairpin loop. GS is the free energy change to form a stack. GBI is to calculate the minimum free energy change of structure containing 2-loop. gbi(i,j,k,l) is the free energy change to form 2-loop.</p> |

- | 3.Calculation of T Tail Score | + | <p>3.Calculation of T Tail Score</p> |

- | Here we consider 15 nucleotide in the downstream of stemloop. T tail score nT is calculated as follows : | + | <p>Here we consider 15 nucleotide in the downstream of stemloop. T tail score nT is calculated as follows :</p> |

- | In our program, if the length of the T tail( n ) is less than 15, we will only consider n nucleotides. If TL is more than 15, we will only consider 15 nucleotides. | + | <p>In our program, if the length of the T tail( n ) is less than 15, we will only consider n nucleotides. If TL is more than 15, we will only consider 15 nucleotides.</p> |

- | 4.Calculation of Score | + | <p>4.Calculation of Score</p> |

- | Score = nT * 18.16 + deltaG / LH * 96.59 – 116.87 | + | <p>Score = nT * 18.16 + deltaG / LH * 96.59 – 116.87</p> |

- | Here nT is T tail score. deltaG is the minimum free energy change of stemloop formation. LH is the length of stemloop. | + | <p>Here nT is T tail score. deltaG is the minimum free energy change of stemloop formation. LH is the length of stemloop. |

</p> | </p> | ||

## Revision as of 14:53, 7 September 2012

## Introduction to Scoring Systems

### Introduction to scoring system 2

Scoring System 2 is based on the model created by d'Aubenton Carafa.[1] The score of terminator consists of two parts, the free energy of stemloop and the score of 15 nt poly T tail. The free energy of stemloop is calculated using Loop Dependent Energy Rules[2]. The minimization of the free energy also determined the secondary structure of the stemloop. T tail score is calculated by the formula given by d’ Aubenton Carafa.

Detailed Calculation of Score

1. Some definitions[2]

i. Closing Base Pair

For an RNA sequence, we number it from 5’ to 3’ . If i < j and nucleotides ri and rj form a base pair,we denote it by i.j. We call base ri’ or base pair i’.j’ is accessible from i.j if i < i’ ( < j’ ) < j and if there is no other base pair k.l so that i < k < i’ ( < j’ ) < l < j. We denote the collection of base and base pair accessible from i.j by L(i,j). Then i.j is the closing base pair. Here “L” means loop.

ii. n-loop

If the loop contain n – 1 base pairs, we denote it by n-loop. (Because there is a closing base pair, so we denote it by n-loop even though the closing base pair is not included in the loop.)

Here we can divide loops which may be formed in the terminator secondary structure into two kinds.

1-loop : Hairpin loop(size of loop shouldn’t be smaller than 3)

2-loop : Interior Loop(right strand size and left strand size are both bigger than 0.)

Buldge(Size of one strand is bigger than 0 and that of another strand is 0.)

Stack(size of the loop is 0.)

2. Calculation of the Minimum Free Energy Change of Stemloop Formation[3]

Assume i.j is the closing base pair of the loop

G（i,j）= min { GH ( i , j ) , GS( i , j ) + G ( i + 1 , j – 1 ) , GBI( i , j ) } ;

GBI ( i , j ) = min{ gbi( i , j , k , l ) + G( k , l ) } for all 0 < k – i + l – j - 2 < max_size

G(i,j) is the minimum free energy change of stemloop formation. GH is the free energy change to form a hairpin loop. GS is the free energy change to form a stack. GBI is to calculate the minimum free energy change of structure containing 2-loop. gbi(i,j,k,l) is the free energy change to form 2-loop.

3.Calculation of T Tail Score

Here we consider 15 nucleotide in the downstream of stemloop. T tail score nT is calculated as follows :

In our program, if the length of the T tail( n ) is less than 15, we will only consider n nucleotides. If TL is more than 15, we will only consider 15 nucleotides.

4.Calculation of Score

Score = nT * 18.16 + deltaG / LH * 96.59 – 116.87

Here nT is T tail score. deltaG is the minimum free energy change of stemloop formation. LH is the length of stemloop.