a partition function algorithm for rna rna interaction
play

A partition function algorithm for RNA-RNA interaction Hamidreza - PowerPoint PPT Presentation

Jun 24, 2023 •99 likes •1.18k views

A partition function algorithm for RNA-RNA interaction Hamidreza Chitsaz Raheleh Salari, Cenk Sahinalp, Rolf Backofen Wayne State University chitsaz@wayne.edu Benasque RNA Meeting July 27 th , 2012 1/76, Mini biography Robotics RNA

  1. Partition function for two strands straight vertical line: intermolecular bond solid: a base pair dotted: not a base pair dashed: either of those two k 1 k 1 i R j R = Ia I Ib j S i S k 2 k 2 ∑ Q I Q i R , k 1 − 1 Q k 2 + 1 , j S Q Ib i R , j R , i S , j S = Q i R , j R Q i S , j S + k 1 , j R , i S , k 2 + iR ≤ k 1 < jR iS < k 2 ≤ jS ∑ Q i R , k 1 − 1 Q k 2 + 1 , j S Q Ia k 1 , j R , i S , k 2 . iR ≤ k 1 < jR iS < k 2 ≤ jS 18/76,

  2. Partition function for two strands straight vertical line: intermolecular bond solid: a base pair dotted: not a base pair dashed: either of those two k 1 k 1 i R j R = Ia I Ib j S i S k 2 k 2 ∑ Q I Q i R , k 1 − 1 Q k 2 + 1 , j S Q Ib i R , j R , i S , j S = Q i R , j R Q i S , j S + k 1 , j R , i S , k 2 + iR ≤ k 1 < jR iS < k 2 ≤ jS ∑ Q i R , k 1 − 1 Q k 2 + 1 , j S Q Ia k 1 , j R , i S , k 2 . iR ≤ k 1 < jR iS < k 2 ≤ jS 18/76,

  3. Q Ib = Ihh k 1 k ′ k 1 j R i R 1 = Ih Ih Ia Ib k 2 k 2 k ′ j S i S 2 k ′ k 1 k ′ k 1 1 bz 1 Ih Ib Ih Ib bz k 2 k 2 k ′ k ′ 2 2 = Ihb b : stands for bond 19/76,

  4. Q Ia a : stands for arc s : stands for subsume e : stands for equivalent k 1 k 1 k 1 i R j R = Ia Is ′ I I Is I Ie i S j S k 2 k 2 k 2 20/76,

  5. Q Is and Q Ie j R i R = Is Ism Isk j S i S s : stands for subsume k : stands for kissing-loop m : stands for multi-loop i R j R = Ie Ism Isk k 2 k 1 k 2 k 1 j S i S gm gk e : stands for equivalent 21/76,

  6. All tables bz = b j i i j k 1 k 2 22/76,

  7. All tables g g = d e i d i i j e j d e j k 1 k 2 bz bz bz bz i e i i d e j d j d e j g g g bz bz i d i bz bz i d e j e j d e j k 1 k 2 k 1 k 2 k 1 k 2 23/76,

  8. All tables g gm = d e i j i d e j i d e j k 1 k 2 24/76,

  9. All tables i R j R = I nd I dd I ∗ d j S i S 25/76,

  10. All tables k 1 k 1 k 1 i R j R = Is ′ Ia I I Is I Ie j S i S k 2 k 2 k 2 26/76,

  11. All tables i R j R = I ∗ n I nn I dn j S i S 27/76,

  12. All tables k 1 k 1 k 1 i R j R = Is ′ Ia r I r I r Is I r Ie j S i S k 2 k 2 k 2 28/76,

  13. All tables = Ihh k ′ k 1 j R k 1 i R 1 = Ih Ih Ia Ib k ′ k 2 k 2 j S i S 2 k ′ k ′ k 1 k 1 bz 1 1 Ih Ih Ib Ib bz k ′ k 2 k ′ k 2 2 2 29/76,

  14. All tables i R j R = I d ∗ I dn I dd j S i S 30/76,

  15. All tables k 1 i R j R = I dn Ia dn j S i S k 2 31/76,

  16. All tables k 1 k 1 i R j R = Ia I Ib i S j S k 2 k 2 32/76,

  17. All tables i R j R k 1 = Ih Ih j S i S k 2 33/76,

  18. All tables i R j R = Ikk Ib r Ib Is Ib Is ′ Ib Ie Ia r j S i S Ia dd Is ′ Isk ′ Is Ia dd Ia dd Ie Ia dn Isk Ia nd 34/76,

  19. All tables i R j R = Ism ′ Imk Ia nd Is Ia nd Ia nd Ie Ia nn Isk j S i S 35/76,

  20. All tables i R j R = I n ∗ I nn I nd j S i S 36/76,

  21. All tables k 1 i R j R = I nn Ia nn j S i S k 2 37/76,

  22. All tables i R j R = Is Ism Isk j S i S 38/76,

  23. All tables gm gk i R j R = Ism Imm Ikm i S j S 39/76,

  24. All tables b = bz i j i j i b j i b j k 1 k 2 k 1 k 2 40/76,

  25. All tables = b i j i j j i k 2 k 1 41/76,

  26. All tables g gk = d e i j i d e j i d e j k 1 k 2 42/76,

  27. All tables k 1 k 1 k 1 k 1 k 1 i R j R = Isk ′ Ia dd Isk I d ∗ I ∗ d Ism ′ I dd Ism I dd Ie I dd j S i S k 2 k 2 k 2 k 2 k 2 43/76,

  28. All tables k 1 k 1 k 1 k 1 i R j R = Isk ′ I ∗ n Ism ′ Ia dn I dn I dn Ism I dn Ie j S i S k 2 k 2 k 2 k 2 44/76,

  29. All tables k 1 k 1 k 1 k 1 i R j R = Isk I n ∗ Ism ′ Ia nd I nd I nd Ism I nd Ie j S i S k 2 k 2 k 2 k 2 45/76,

  30. All tables gm gk i R j R = Isk Imk Ikk j S i S 46/76,

  31. All tables k 1 k 1 k 1 i R j R = Ism ′ I nn Ia nn I nn Ism I nn Ie j S i S k 2 k 2 k 2 47/76,

  32. All tables k 1 k 1 i R j R = Ihh Ihm Ihh Ib Ia Ib k 2 k 2 j S i S 48/76,

  33. All tables k 1 k 1 i R j R = Ihb Ihh Ih Ib r Ia r Ib r k 2 k 2 j S i S 49/76,

  34. All tables i R j R = Ie Ism Isk k 2 k 1 k 2 k 1 j S i S gm gk 50/76,

  35. All tables k 1 k 1 i R j R = Ia dd I dd Ib j S i S k 2 k 2 51/76,

  36. All tables i R j R k 1 k 1 bz = Ih Ihb Ih bz k 2 j S i S k 2 52/76,

  37. All tables i R j R k 1 = Ihh Ih j S i S k 2 53/76,

  38. All tables i R j R = Isk ′ Is ′ Ia nn Ikm Ia dn Ism Ia dn Ia dn Ie j S i S 54/76,

  39. All tables i R j R = Ism ′ Imm Ia nn Ism Ia nn Ia nn Ie j S i S 55/76,

  40. All tables k 1 i R j R = I nd Ia nd j S i S k 2 56/76,

  41. All tables k 1 k 1 i R j R = I r Ia r Ib r j S i S k 2 k 2 57/76,

  42. Equilibrium concentrations For two RNAs R and S Assume five types of chemical compounds: R , S , RR , SS , RS . Solve K R = Q I R = N RR RR R , Q 2 N 2 Q I S = N SS K S = SS S , Q 2 N 2 Q I N RS K RS = RS Q R Q S = N R N S , N RS = N 0 R − 2 N RR − N R = N 0 S − 2 N SS − N S , to obtain the equilibrium concentrations N . N 0 are the initial concentrations of single strands. 58/76,

  43. Equilibrium concentration of OxyS with wild type fhlA 100 OxyS in complex [%] 80 60 wild type fhlA 40 20 Our Algorithm Experiment 0 0 200 400 600 800 1000 fhlA Concentration [nM] Init. [OxyS] = 2nM, [fhlA] = 0 to 1000nM 59/76,

  44. Equilibrium concentration of OxyS with fhlA mutants 100 100 OxyS in complex [%] OxyS in complex [%] 80 80 60 60 fhlA A8G fhlA C13G 40 40 20 20 Our Algorithm Our Algorithm Experiment Experiment 0 0 0 100 200 300 400 0 100 200 300 400 500 600 700 fhlA A8G Concentration [nM] fhlA C13G Concentration [nM] 100 100 OxyS in complex [%] OxyS in complex [%] 80 80 60 60 fhlA G37C;G38C fhlA G38C;G39C 40 40 20 20 Our Algorithm Our Algorithm Experiment Experiment 0 0 0 200 400 600 800 1000 0 150 300 450 600 750 900 fhlA G37C;G38C Concentration [nM] fhlA G38C;G39C Concentration [nM] 60/76,

  45. Melting temperature prediction Comparison of piRNA results over three data sets Set Size Length Avg error piRNA RNAcofold UNAFold 1 . 48 ◦ C 9 . 35 ◦ C 8 . 55 ◦ C I 9 short pairs 5-7nt 4 . 86 ◦ C 22 . 97 ◦ C 9 . 12 ◦ C ∼ 20nt II 12 pairs 1 . 91 ◦ C 14 . 34 ◦ C 26 . 53 ◦ C III 62 pairs 22 − 40nt Set Size Length Spearman rank correlation piRNA RNAcofold UNAFold 0 . 97 0 . 97 0 . 57 I 9 short pairs 5-7nt 0 . 41 ∼ 20nt − 0 . 03 0 . 1 II 12 pairs 0 . 3 22 − 40nt − 0 . 04 0 . 24 III 62 pairs 61/76,

  46. Promised base pairing probabilities P I and P Ia examples ( Q Is k 1 , i R , j S , k 2 + Q Is ′ k 1 , i R , j S , k 2 + Q Ie k 1 , i R , j S , k 2 ) Q I i R , j R , i S , j S = ∑ i R , j R , i S , j S P I P Ia , k 1 , j R , i S , k 2 Q Ia k 1 , j R , i S , k 2 1 ≤ k 1 < iR jS < k 2 ≤ LS Q k 1 , i R − 1 Q j S + 1 , k 2 Q Ia i R , j R , i S , j S = ∑ i R , j R , i S , j S P Ia P I + k 1 , j R , i S , k 2 Q I k 1 , j R , i S , k 2 1 ≤ k 1 ≤ iR jS ≤ k 2 ≤ LS Q Ihh k 1 , i R , j S , k 2 Q Ia ∑ i R , j R , i S , j S P Ib . k 1 , j R , i S , k 2 Q Ib k 1 , j R , i S , k 2 1 ≤ k 1 < iR jS ≤ k 2 ≤ LS More on this part will be presented by Peter Stadler. 62/76,

  47. Sampling from the Boltzmann ensemble ◮ Push I ( 1 , n , 1 , m ) onto the stack. ◮ Iterate until the stack is empty, i.e. reaching a leaf (structure) in the recursions. ◮ In each iteration, sample 0 ≤ α ≤ 1 uniformly at random. ◮ Pop from the stack top ( i R , j R , i S , j S ) . ◮ Pick a case of top according to α . For simplicity, we assume there is only one case here, i.e. ∑ i R , k 1 , k 2 , j S Q right Q top = Q left k 1 + 1 , j R , i S , k 2 + 1 iR ≤ k 1 < jR iS < k 2 ≤ jS ◮ Find k ∗ 1 , k ∗ 2 such that ··· ≃ α ∑ ∑ ··· . iR ≤ k 1 < k ∗ iR ≤ k 1 < jR 1 iS < k 2 ≤ jS iS < k 2 ≤ k ∗ 2 ◮ Push left ( i R , k ∗ 1 , k ∗ 2 , j S ) and right ( k 1 + 1 , j R , i S , k 2 + 1 ) onto the stack. 63/76,

  48. Sampling from the Boltzmann ensemble ◮ Push I ( 1 , n , 1 , m ) onto the stack. ◮ Iterate until the stack is empty, i.e. reaching a leaf (structure) in the recursions. ◮ In each iteration, sample 0 ≤ α ≤ 1 uniformly at random. ◮ Pop from the stack top ( i R , j R , i S , j S ) . ◮ Pick a case of top according to α . For simplicity, we assume there is only one case here, i.e. ∑ i R , k 1 , k 2 , j S Q right Q top = Q left k 1 + 1 , j R , i S , k 2 + 1 iR ≤ k 1 < jR iS < k 2 ≤ jS ◮ Find k ∗ 1 , k ∗ 2 such that ··· ≃ α ∑ ∑ ··· . iR ≤ k 1 < k ∗ iR ≤ k 1 < jR 1 iS < k 2 ≤ jS iS < k 2 ≤ k ∗ 2 ◮ Push left ( i R , k ∗ 1 , k ∗ 2 , j S ) and right ( k 1 + 1 , j R , i S , k 2 + 1 ) onto the stack. 63/76,

  49. Sampling from the Boltzmann ensemble ◮ Push I ( 1 , n , 1 , m ) onto the stack. ◮ Iterate until the stack is empty, i.e. reaching a leaf (structure) in the recursions. ◮ In each iteration, sample 0 ≤ α ≤ 1 uniformly at random. ◮ Pop from the stack top ( i R , j R , i S , j S ) . ◮ Pick a case of top according to α . For simplicity, we assume there is only one case here, i.e. ∑ i R , k 1 , k 2 , j S Q right Q top = Q left k 1 + 1 , j R , i S , k 2 + 1 iR ≤ k 1 < jR iS < k 2 ≤ jS ◮ Find k ∗ 1 , k ∗ 2 such that ··· ≃ α ∑ ∑ ··· . iR ≤ k 1 < k ∗ iR ≤ k 1 < jR 1 iS < k 2 ≤ jS iS < k 2 ≤ k ∗ 2 ◮ Push left ( i R , k ∗ 1 , k ∗ 2 , j S ) and right ( k 1 + 1 , j R , i S , k 2 + 1 ) onto the stack. 63/76,

  50. Sampling from the Boltzmann ensemble ◮ Push I ( 1 , n , 1 , m ) onto the stack. ◮ Iterate until the stack is empty, i.e. reaching a leaf (structure) in the recursions. ◮ In each iteration, sample 0 ≤ α ≤ 1 uniformly at random. ◮ Pop from the stack top ( i R , j R , i S , j S ) . ◮ Pick a case of top according to α . For simplicity, we assume there is only one case here, i.e. ∑ i R , k 1 , k 2 , j S Q right Q top = Q left k 1 + 1 , j R , i S , k 2 + 1 iR ≤ k 1 < jR iS < k 2 ≤ jS ◮ Find k ∗ 1 , k ∗ 2 such that ··· ≃ α ∑ ∑ ··· . iR ≤ k 1 < k ∗ iR ≤ k 1 < jR 1 iS < k 2 ≤ jS iS < k 2 ≤ k ∗ 2 ◮ Push left ( i R , k ∗ 1 , k ∗ 2 , j S ) and right ( k 1 + 1 , j R , i S , k 2 + 1 ) onto the stack. 63/76,

  51. Sampling from the Boltzmann ensemble ◮ Push I ( 1 , n , 1 , m ) onto the stack. ◮ Iterate until the stack is empty, i.e. reaching a leaf (structure) in the recursions. ◮ In each iteration, sample 0 ≤ α ≤ 1 uniformly at random. ◮ Pop from the stack top ( i R , j R , i S , j S ) . ◮ Pick a case of top according to α . For simplicity, we assume there is only one case here, i.e. ∑ i R , k 1 , k 2 , j S Q right Q top = Q left k 1 + 1 , j R , i S , k 2 + 1 iR ≤ k 1 < jR iS < k 2 ≤ jS ◮ Find k ∗ 1 , k ∗ 2 such that ··· ≃ α ∑ ∑ ··· . iR ≤ k 1 < k ∗ iR ≤ k 1 < jR 1 iS < k 2 ≤ jS iS < k 2 ≤ k ∗ 2 ◮ Push left ( i R , k ∗ 1 , k ∗ 2 , j S ) and right ( k 1 + 1 , j R , i S , k 2 + 1 ) onto the stack. 63/76,

  52. Sampling from the Boltzmann ensemble ◮ Push I ( 1 , n , 1 , m ) onto the stack. ◮ Iterate until the stack is empty, i.e. reaching a leaf (structure) in the recursions. ◮ In each iteration, sample 0 ≤ α ≤ 1 uniformly at random. ◮ Pop from the stack top ( i R , j R , i S , j S ) . ◮ Pick a case of top according to α . For simplicity, we assume there is only one case here, i.e. ∑ i R , k 1 , k 2 , j S Q right Q top = Q left k 1 + 1 , j R , i S , k 2 + 1 iR ≤ k 1 < jR iS < k 2 ≤ jS ◮ Find k ∗ 1 , k ∗ 2 such that ··· ≃ α ∑ ∑ ··· . iR ≤ k 1 < k ∗ iR ≤ k 1 < jR 1 iS < k 2 ≤ jS iS < k 2 ≤ k ∗ 2 ◮ Push left ( i R , k ∗ 1 , k ∗ 2 , j S ) and right ( k 1 + 1 , j R , i S , k 2 + 1 ) onto the stack. 63/76,

  53. Sampling from the Boltzmann ensemble ◮ Push I ( 1 , n , 1 , m ) onto the stack. ◮ Iterate until the stack is empty, i.e. reaching a leaf (structure) in the recursions. ◮ In each iteration, sample 0 ≤ α ≤ 1 uniformly at random. ◮ Pop from the stack top ( i R , j R , i S , j S ) . ◮ Pick a case of top according to α . For simplicity, we assume there is only one case here, i.e. ∑ i R , k 1 , k 2 , j S Q right Q top = Q left k 1 + 1 , j R , i S , k 2 + 1 iR ≤ k 1 < jR iS < k 2 ≤ jS ◮ Find k ∗ 1 , k ∗ 2 such that ··· ≃ α ∑ ∑ ··· . iR ≤ k 1 < k ∗ iR ≤ k 1 < jR 1 iS < k 2 ≤ jS iS < k 2 ≤ k ∗ 2 ◮ Push left ( i R , k ∗ 1 , k ∗ 2 , j S ) and right ( k 1 + 1 , j R , i S , k 2 + 1 ) onto the stack. 63/76,

  54. Fast Ponty-style sampling of the Boltzmann ensemble k 2 k 2 j S � i S + j S � 2 · · · · · · j S − 1 i S + 2 i S + 1 j S i S + 1 k 1 k 1 i S i S i R j R · · · � i R + j R � j R − 1 i R j R i R + 1 i R + 1 i R + 2 · · · 2 Naïve traversal of indices Balanced traversal of indices O ( n 2 log n ) O ( n 4 ) 64/76,

  55. Time and space complexity of piRNA ◮ O ( n 4 m 2 + n 2 m 4 ) time. ◮ O ( n 2 m 2 ) space. ◮ about 100 tables in the dynamic programming. ◮ takes about 1 day on 64 CPUs with 150GB RAM for two 110nt RNAs (OxyS-fhlA). Therefore, a fast heuristic is on demand for high-throughput applications, possibly as a filtering step. 65/76,

  56. Time and space complexity of piRNA ◮ O ( n 4 m 2 + n 2 m 4 ) time. ◮ O ( n 2 m 2 ) space. ◮ about 100 tables in the dynamic programming. ◮ takes about 1 day on 64 CPUs with 150GB RAM for two 110nt RNAs (OxyS-fhlA). Therefore, a fast heuristic is on demand for high-throughput applications, possibly as a filtering step. 65/76,

  57. Binding sites prediction biRNA : a fast algorithm to predict simultaneous binding sites of two nucleic acids Pros ◮ Predicts multiple simultaneous binding sites. ◮ Computes a more accurate local energy of binding. ◮ Considers zigzags and crossing interactions. ◮ Maintains tractability for existing cases in the literature. Cons ◮ Approximates the intramolecular site accessibility energy. ◮ Its running time grows exponentially with the maximum number of simultaneous binding sites. 66/76,

  58. Binding sites prediction biRNA : a fast algorithm to predict simultaneous binding sites of two nucleic acids Pros ◮ Predicts multiple simultaneous binding sites. ◮ Computes a more accurate local energy of binding. ◮ Considers zigzags and crossing interactions. ◮ Maintains tractability for existing cases in the literature. Cons ◮ Approximates the intramolecular site accessibility energy. ◮ Its running time grows exponentially with the maximum number of simultaneous binding sites. 66/76,

  59. biRNA Steps of the algorithm for R and S 1. For all short subsequences W , compute P u ( W ) , the prob. of being unpaired (Mückstein et al. 2008). 2. Obtain V , a short list of candidate sites. 3. For all pairs W 1 , W 2 , compute P u ( W 1 , W 2 ) , the joint pairwise prob. of being simultaneously unpaired. 4. Build tree-structured Markov Random Fields (MRF) T = ( V , E ) to approximate the distribution of being simultaneously unpaired (Chow and Liu 1968). 5. Compute Q I W R W S , the interaction partition functions restricted to subsequences W R and W S using piRNA . 6. Compute a matching between T R and T S that minimizes the binding energy or equivalently maximizes the binding probability. 67/76,

  60. biRNA Steps of the algorithm for R and S 1. For all short subsequences W , compute P u ( W ) , the prob. of being unpaired (Mückstein et al. 2008). 2. Obtain V , a short list of candidate sites. 3. For all pairs W 1 , W 2 , compute P u ( W 1 , W 2 ) , the joint pairwise prob. of being simultaneously unpaired. 4. Build tree-structured Markov Random Fields (MRF) T = ( V , E ) to approximate the distribution of being simultaneously unpaired (Chow and Liu 1968). 5. Compute Q I W R W S , the interaction partition functions restricted to subsequences W R and W S using piRNA . 6. Compute a matching between T R and T S that minimizes the binding energy or equivalently maximizes the binding probability. 67/76,

  61. biRNA Steps of the algorithm for R and S 1. For all short subsequences W , compute P u ( W ) , the prob. of being unpaired (Mückstein et al. 2008). 2. Obtain V , a short list of candidate sites. 3. For all pairs W 1 , W 2 , compute P u ( W 1 , W 2 ) , the joint pairwise prob. of being simultaneously unpaired. 4. Build tree-structured Markov Random Fields (MRF) T = ( V , E ) to approximate the distribution of being simultaneously unpaired (Chow and Liu 1968). 5. Compute Q I W R W S , the interaction partition functions restricted to subsequences W R and W S using piRNA . 6. Compute a matching between T R and T S that minimizes the binding energy or equivalently maximizes the binding probability. 67/76,

  62. biRNA Steps of the algorithm for R and S 1. For all short subsequences W , compute P u ( W ) , the prob. of being unpaired (Mückstein et al. 2008). 2. Obtain V , a short list of candidate sites. 3. For all pairs W 1 , W 2 , compute P u ( W 1 , W 2 ) , the joint pairwise prob. of being simultaneously unpaired. 4. Build tree-structured Markov Random Fields (MRF) T = ( V , E ) to approximate the distribution of being simultaneously unpaired (Chow and Liu 1968). 5. Compute Q I W R W S , the interaction partition functions restricted to subsequences W R and W S using piRNA . 6. Compute a matching between T R and T S that minimizes the binding energy or equivalently maximizes the binding probability. 67/76,

  63. biRNA Steps of the algorithm for R and S 1. For all short subsequences W , compute P u ( W ) , the prob. of being unpaired (Mückstein et al. 2008). 2. Obtain V , a short list of candidate sites. 3. For all pairs W 1 , W 2 , compute P u ( W 1 , W 2 ) , the joint pairwise prob. of being simultaneously unpaired. 4. Build tree-structured Markov Random Fields (MRF) T = ( V , E ) to approximate the distribution of being simultaneously unpaired (Chow and Liu 1968). 5. Compute Q I W R W S , the interaction partition functions restricted to subsequences W R and W S using piRNA . 6. Compute a matching between T R and T S that minimizes the binding energy or equivalently maximizes the binding probability. 67/76,

  64. biRNA Steps of the algorithm for R and S 1. For all short subsequences W , compute P u ( W ) , the prob. of being unpaired (Mückstein et al. 2008). 2. Obtain V , a short list of candidate sites. 3. For all pairs W 1 , W 2 , compute P u ( W 1 , W 2 ) , the joint pairwise prob. of being simultaneously unpaired. 4. Build tree-structured Markov Random Fields (MRF) T = ( V , E ) to approximate the distribution of being simultaneously unpaired (Chow and Liu 1968). 5. Compute Q I W R W S , the interaction partition functions restricted to subsequences W R and W S using piRNA . 6. Compute a matching between T R and T S that minimizes the binding energy or equivalently maximizes the binding probability. 67/76,

  65. biRNA Binding energy minimization Exhaustive search to find matching M = { ( W R 1 , W S 1 ) , ( W R 2 , W S 2 ) ,..., ( W R k , W S k ) } that minimizes ∆ G ( M ) = ED R u ( M )+ ED S u ( M )+∆ G RS b ( M ) , in which ED R u ( M ) = − RT log P R ∗ u ( W R 1 , W R 2 ,..., W R k ) ED S u ( M ) = − RT log P S ∗ u ( W S 1 , W S 2 ,..., W S k ) b ( M ) = − RT ∑ ∆ G RS log ( Q I i − Q W R i Q W S i ) . W R i W S 1 ≤ i ≤ k R is the universal gas constant and T is temperature. 68/76,

  66. Experimental results Multi-sites biRNA RNAup Pair Binding Site(s) Literature Site(s) Site OxyS-fhlA [22,30] [95,87] (23,30) (94,87) - - [98,104] [45,39] (96,104) (48,39) (96,104) (48,39) CopA-CopT [22,33] [70,59] (22,31) (70,61) - - [48,56] [44,36] (49,57) (43,35) (49,67) (43,24) [62,67] [29,24] (58,67) (33,24) - - 69/76,

  67. Experimental results Uni-sites Pair GcvB gltI GcvB argT GcvB dppA GcvB livJ GcvB livK GcvB oppA GcvB STM4351 MicA lamB MicA ompA DsrA rpoS RprA rpoS IstR tisA MicC ompC MicF ompF RyhB sdhD RyhB sodB SgrS ptsG IncRNA 54 repZ Lengths: 71-253 nt Running time: 10 min - 1 hour on 8 dual core CPUs and 20GB of RAM 70/76,

  68. Summary ◮ We presented piRNA an O ( n 4 m 2 + n 2 m 4 ) -time O ( n 2 m 2 ) -space complexity algorithm for interaction partition function, base-pair probabilities, minimum free energy secondary structure, equilibrium concentrations, melting temperature, and some other derivatives of the partition function. ◮ piRNA outperforms all other alternatives and is available at http://compbio.cs.wayne.edu/chitsaz/ . ◮ We presented biRNA , a fast RNA-RNA binding sites prediction algorithm. ◮ biRNA ’s tree-structured MRF approximation is accurate enough for predicting binding sites and may be used in other applications. 71/76,

  69. Summary ◮ We presented piRNA an O ( n 4 m 2 + n 2 m 4 ) -time O ( n 2 m 2 ) -space complexity algorithm for interaction partition function, base-pair probabilities, minimum free energy secondary structure, equilibrium concentrations, melting temperature, and some other derivatives of the partition function. ◮ piRNA outperforms all other alternatives and is available at http://compbio.cs.wayne.edu/chitsaz/ . ◮ We presented biRNA , a fast RNA-RNA binding sites prediction algorithm. ◮ biRNA ’s tree-structured MRF approximation is accurate enough for predicting binding sites and may be used in other applications. 71/76,

  70. Summary ◮ We presented piRNA an O ( n 4 m 2 + n 2 m 4 ) -time O ( n 2 m 2 ) -space complexity algorithm for interaction partition function, base-pair probabilities, minimum free energy secondary structure, equilibrium concentrations, melting temperature, and some other derivatives of the partition function. ◮ piRNA outperforms all other alternatives and is available at http://compbio.cs.wayne.edu/chitsaz/ . ◮ We presented biRNA , a fast RNA-RNA binding sites prediction algorithm. ◮ biRNA ’s tree-structured MRF approximation is accurate enough for predicting binding sites and may be used in other applications. 71/76,

  71. Summary ◮ We presented piRNA an O ( n 4 m 2 + n 2 m 4 ) -time O ( n 2 m 2 ) -space complexity algorithm for interaction partition function, base-pair probabilities, minimum free energy secondary structure, equilibrium concentrations, melting temperature, and some other derivatives of the partition function. ◮ piRNA outperforms all other alternatives and is available at http://compbio.cs.wayne.edu/chitsaz/ . ◮ We presented biRNA , a fast RNA-RNA binding sites prediction algorithm. ◮ biRNA ’s tree-structured MRF approximation is accurate enough for predicting binding sites and may be used in other applications. 71/76,

Download Presentation
Download Policy: The content available on the website is offered to you 'AS IS' for your personal information and use only. It cannot be commercialized, licensed, or distributed on other websites without prior consent from the author. To download a presentation, simply click this link. If you encounter any difficulties during the download process, it's possible that the publisher has removed the file from their server.

Recommend

I. FAQ S Q. What is partition? Partition is a proceeding in equity to determine the way in

I. FAQ S Q. What is partition? Partition is a proceeding in equity to determine the way in

Partition Actions: Everything You Never Realized You Ought to Know About Them William J. Maffucci, J.D. Partition is a hoary proceeding. I say that mischievously, hoping that the phonetics will fool a few readers into thinking that the topic

306 views • 14 slides
Interaction Model Distributed algorithm vs. simple algorithm Difficulties Complex

Interaction Model Distributed algorithm vs. simple algorithm Difficulties Complex

Interaction Model Distributed algorithm vs. simple algorithm Difficulties Complex Hard to predict: executing rate, transmission rate No general state Performance of communication channels Latency; Bandwidth; Jitter

534 views • 14 slides
CS 225 Data Structures April 23 Dijkstras Algorithm Wad ade Fag agen-Ulm lmschneid

CS 225 Data Structures April 23 Dijkstras Algorithm Wad ade Fag agen-Ulm lmschneid

CS 225 Data Structures April 23 Dijkstras Algorithm Wad ade Fag agen-Ulm lmschneid ider Partition Property Consider an arbitrary partition of the vertices on G into two subsets U and V . V U A 4 Let e be an edge of 8 2 B D

296 views • 18 slides
Superfluid Hydrodynamics, Thermal Partition Function and Lifshitz Scaling Oxford - Theoretical

Superfluid Hydrodynamics, Thermal Partition Function and Lifshitz Scaling Oxford - Theoretical

Superfluid Hydrodynamics, Thermal Partition Function and Lifshitz Scaling Oxford - Theoretical Physics Shira Chapman, Carlos Hoyos, Yaron Oz arXiv: 1310.2247, 1402.2981 Tel Aviv University March 04, 2014 Outline Superfluids and

619 views • 30 slides
Superfluid Hydrodynamics, Thermal Partition Function and Lifshitz Scaling Crete Center for

Superfluid Hydrodynamics, Thermal Partition Function and Lifshitz Scaling Crete Center for

Superfluid Hydrodynamics, Thermal Partition Function and Lifshitz Scaling Crete Center for Theoretical Physics Shira Chapman, Carlos Hoyos, Yaron Oz arXiv: 1310.2247, 1402.2981 Tel Aviv University February 20, 2014 Outline Superfluids and

347 views • 30 slides
Confronting the Partition Function Lecture slides for Chapter 18 of Deep Learning

Confronting the Partition Function Lecture slides for Chapter 18 of Deep Learning

Confronting the Partition Function Lecture slides for Chapter 18 of Deep Learning www.deeplearningbook.org Ian Goodfellow Last updated 2017-12-29 Unnormalized models 1 p ( x ; ) = Z ( ) p ( x ; ) . (18.1) where Z is Z p ( x ) d x

425 views • 9 slides
Statistical mechanics, the partition function, and fj rst- order phase transitions Magnus

Statistical mechanics, the partition function, and fj rst- order phase transitions Magnus

Protein Physics 2016 Lecture 5, February 2 Statistical mechanics, the partition function, and fj rst- order phase transitions Magnus Andersson magnus.andersson@scilifelab.se Theoretical &amp; Computational Biophysics Recap Secondary

527 views • 36 slides
Combinatorics of the PASEP partition function Matthieu Josuat-Verg` es Universit e Paris-sud

Combinatorics of the PASEP partition function Matthieu Josuat-Verg` es Universit e Paris-sud

Combinatorics of the PASEP partition function Matthieu Josuat-Verg` es Universit e Paris-sud 11 FPSAC 2010 August 2nd 1 / 35 Introduction The Partially Asymmetric Self-Exclusion Process (PASEP) is a probabilistic model describing the

479 views • 35 slides
Radial basis function partition of unity methods for PDEs RBF-PUM Elisabeth Larsson, Scientific

Radial basis function partition of unity methods for PDEs RBF-PUM Elisabeth Larsson, Scientific

Radial basis function partition of unity methods for PDEs RBF-PUM Elisabeth Larsson, Scientific Computing, Uppsala Outline University Introduction RBFPUM Theoretical results Credit goes to a number of RBF-PUM collaborators Numerical

742 views • 28 slides
Graph Partition Refinement Algorithm Angen Zheng , Alexandros Labrinidis, Patrick Pisciuneri,

Graph Partition Refinement Algorithm Angen Zheng , Alexandros Labrinidis, Patrick Pisciuneri,

Paragon: Parallel Architecture-Aware Graph Partition Refinement Algorithm Angen Zheng , Alexandros Labrinidis, Patrick Pisciuneri, Panos K. Chrysanthis, and Peyman Givi University of Pittsburgh 1 Importance of Graph Partitioning

687 views • 52 slides
The CalderoChapoton formula as a dimer partition function joint work with lke anak and

The CalderoChapoton formula as a dimer partition function joint work with lke anak and

The CalderoChapoton formula as a dimer partition function joint work with lke anak and Alastair King Matthew Pressland Universitt Stuttgart Tropical Geometry Meets Representation Theory, Universitt zu Kln Matthew Pressland

343 views • 10 slides
Order Statistics Algorithm Quicksort(A, first, last) if first &lt; last then // // Partition

Order Statistics Algorithm Quicksort(A, first, last) if first &lt; last then // // Partition

Order Statistics Algorithm Quicksort(A, first, last) if first &lt; last then // // Partition reorders A[first . . . last] so // All elements of A[first . . . mid - 1] are A[mid] // All elements of A[mid + 1 . . . last] are &gt; A[mid] //

52 views • 3 slides
HOTRG study on partition function zeros in the p-state clock model Dong-Hee Kim Dept. Physics

HOTRG study on partition function zeros in the p-state clock model Dong-Hee Kim Dept. Physics

Tensor Network States: Algorithms and Applications @ NCCU, 4-6 Dec. 2019 HOTRG study on partition function zeros in the p-state clock model Dong-Hee Kim Dept. Physics and Photon Science Gwangju Institute of Science and Technology, Korea

611 views • 32 slides
1 Space-Partition Constraints Solving the Space-Partition Constraints Accesses sharing a

1 Space-Partition Constraints Solving the Space-Partition Constraints Accesses sharing a

Cetus Compiler Synchronization-Free Parallelism Status Today Written in Java SPMD and OpenMP programming models Parses C Synchronization-free affine partitioning algorithm Announced new release late last night

193 views • 4 slides
Vector-partition functions Matthias Beck San Francisco State University math.sfsu.edu/beck

Vector-partition functions Matthias Beck San Francisco State University math.sfsu.edu/beck

Vector-partition functions Matthias Beck San Francisco State University math.sfsu.edu/beck Vector partition functions A an ( m d ) -integral matrix b Z m x Z d Goal: Compute vector partition function A ( b ) := #

838 views • 41 slides
Fermion pair correlation function exchange hole ( s = s' ) (Pauli exclusion principle) radius ~ k F

Fermion pair correlation function exchange hole ( s = s' ) (Pauli exclusion principle) radius ~ k F

Jellium model - Hartree-Fock approximation Jellium model with interactions charge neutrality kinetic electron-electron ion-ion electron-ion interaction interaction energy interaction Coulomb interaction field operator ''free electrons''

287 views • 4 slides
Programming Molecules Anne Condon U. British Columbia 100 nm Paul Rothemund, 2006 Programming

Programming Molecules Anne Condon U. British Columbia 100 nm Paul Rothemund, 2006 Programming

Programming Molecules Anne Condon U. British Columbia 100 nm Paul Rothemund, 2006 Programming Molecules Anne Condon, U. British Columbia Programming Molecules | outline motivation principles experimental successes C G theory A T open

910 views • 60 slides
1-10: Learning Goals Lets use different base-height pairs to find the area of a triangle.

1-10: Learning Goals Lets use different base-height pairs to find the area of a triangle.

Download for free at openupresources.org. 1-10: Learning Goals Lets use different base-height pairs to find the area of a triangle. Download for free at openupresources.org. 1-10-1: An Area of 12 Download for free at openupresources.org.

291 views • 8 slides
Stanford-UBC at TAC-KBP Eneko Agirre , Angel Chang, Dan Jurafsky, Christopher Manning, Valentin

Stanford-UBC at TAC-KBP Eneko Agirre , Angel Chang, Dan Jurafsky, Christopher Manning, Valentin

Stanford-UBC at TAC-KBP Eneko Agirre , Angel Chang, Dan Jurafsky, Christopher Manning, Valentin Spitkovsky, Eric Yeh Ixa NLP group, University of the Basque Country NLP group, Stanford University Outline Entity linking Slot filling

218 views • 21 slides
Using Big Data to Assess Rare Sequence Variants Kirk

Using Big Data to Assess Rare Sequence Variants Kirk

Using Big Data to Assess Rare Sequence Variants Kirk Wilhelmsen, MD-PhD Professor UNC Department of GeneDcs and Neurology Chief Domain ScienDst for

104 views • 7 slides
Information Theory and Coding i f s f f Image, Video and Audio Compression Markus

Information Theory and Coding i f s f f Image, Video and Audio Compression Markus

Sampling, aliasing and Nyquist limit Information Theory and Coding i f s f f Image, Video and Audio Compression Markus Kuhn 0 Lent 2003 Part II Computer Laboratory 0 3fs 2fs fs 0 fs 2fs 3fs A wave cos(2 tf )

783 views • 8 slides
Sleep Modes Pacemaker Training Program The heart benefits from a decreased heart rate

Sleep Modes Pacemaker Training Program The heart benefits from a decreased heart rate

Sleep Modes Pacemaker Training Program The heart benefits from a decreased heart rate at night Special Functions: Without this nightly rest diastolic function Sleep Modes and systolic function decline Affects

555 views • 7 slides
BLAST: Basic Local Alignment Search Tool Altschul et al. J. Mol Bio. 1990. One of the

BLAST: Basic Local Alignment Search Tool Altschul et al. J. Mol Bio. 1990. One of the

BLAST: Basic Local Alignment Search Tool Altschul et al. J. Mol Bio. 1990. One of the highest cited papers in history B asic L ocal A lignment S earch T ool Why is database search difficult? Consider a simpler problem p t Goal: Find

315 views • 20 slides
Global and local alignments Global vs. local alignments Global: align all nucleotides

Global and local alignments Global vs. local alignments Global: align all nucleotides

Global and local alignments Global vs. local alignments Global: align all nucleotides Local: align subsequences with best score Align these sequences: GCAT, GCT (match = 1, mismatch = -1, gap = -1) global alignment: local alignment: ?

506 views • 19 slides

More recommend