1. Xuhua Xia xxia@uottawa.ca http://dambe.bio.uottawa.ca
Motif characterization: Position weight matrix (PWM), Perceptron and their applications
Xuhua Xia

2. Motif characterization
Input: site-specific sequences
Approaches:
Consensus sequence (the chance of having NNN… increases with increasing number of sequences)
Frequency Profile (the problem of mutation bias)
PWM, Sequence logo, Perceptron and Gibbs sampler (cannot detect column association)
Multiple correspondence analysis
A4GALT ATACCATGTCCAA
ACO2 ACAAAATGGCGCC
ACR GGAGTATGGTTGA
ADM2 CCGCCATGGCCCG

3. Consensus sequence
Sequences flanking the initiation codon of 508 CDSs:
A4GALT AUACCAUGUCCAA
ACO ACAAAAUGGCGCC
ACR GGAGUAUGGUUGA
ADM CCGCCAUGGCCCG
Site A C G U
Cons 1 75
173
171 89 N 2
105
216
144 43 3
199 70
212 27 4
124
236 83 65 5 60
276
143 29 6
502 7
508 8 9 98 71
274 10
141
227 51 11 49
154
221 84 12
196 79 13
121
151
134
102
Sum
1563
1724
2175
1142
Two hypotheses:
H0: site-specific pattern absent in flanking sequences
HA: site-specific pattern present in flanking sequences
Our objective is to find if sites flanking AUG contribute to the start codon recognition. The consensus sequence does not give us the answer

4. Frequencies and the background F.
Sequences flanking the initiation codon of 508 CDSs:
A4GALT AUACCAUGUCCAA
ACO ACAAAAUGGCGCC
ACR GGAGUAUGGUUGA
ADM CCGCCAUGGCCCG
Site A C G U 1 75
173
171 89
0.1476
0.3406
0.3366
0.1752 2
105
216
144 43
0.2067
0.4252
0.2835
0.0846 3
199 70
212 27
0.3917
0.1378
0.4173
0.0531 4
124
236 83 65
0.2441
0.4646
0.1634
0.1280 5 60
276
143 29
0.1181
0.5433
0.2815
0.0571 6
502
0.9882
0.0118
0.0000 7
508
1.0000 8 9 98 71
274
0.1929
0.1398
0.5394 10
141
227 51
0.2776
0.4469
0.1004 11 49
154
221 84
0.0965
0.3031
0.4350
0.1654 12
196 79
0.3858
0.1555 13
121
151
134
102
0.2382
0.2972
0.2638
0.2008
Sum
1563
1724
2175
1142
0.2367
0.2611
0.3293
0.1729
In the table, the red numbers could be just red herrings. G is the most frequent (0.3293) and we expect the G column to have more red, U is the least frequent, and we expect the U column to have to least red. This is exactly the case.
RCCaugGCGG
-3R G?
What background frequencies to use as control?

5. Two hypotheses in numbers
Site A C G U 1 75
173
171 89
0.1476
0.3406
0.3366
0.1752 2
105
216
144 43
0.2067
0.4252
0.2835
0.0846 3
199 70
212 27
0.3917
0.1378
0.4173
0.0531 4
124
236 83 65
0.2441
0.4646
0.1634
0.1280 5 60
276
143 29
0.1181
0.5433
0.2815
0.0571 6
502
0.9882
0.0118
0.0000 7
508
1.0000 8 9 98 71
274
0.1929
0.1398
0.5394 10
141
227 51
0.2776
0.4469
0.1004 11 49
154
221 84
0.0965
0.3031
0.4350
0.1654 12
196 79
0.3858
0.1555 13
121
151
134
102
0.2382
0.2972
0.2638
0.2008
Sum
1563
1724
2175
1142
0.2367
0.2611
0.3293
0.1729
Sequences flanking the initiation codon of 508 CDSs:
A4GALT AUACCAUGUCCAA
ACO ACAAAAUGGCGCC
ACR GGAGUAUGGUUGA
ADM CCGCCAUGGCCCG
S = ACGGTACCACGTT
Likelihood, odds ratio, log-odds, PWMS

6. Position weight matrix (PWM)
Two major purposes of PWM
To characterize the sequence pattern (the motif)
to facilitate the computation of log-odds (or PWM score), e.g., computing the PWMS for S1=ATACCATGTCCAA
Two benefits:
Multiplication to addition
Reduction of rounding errors
Site A C G U
Std 1
0.3844
0.0329
0.0198
0.4453 2
0.7044
0.7076 3
0.7275
0.3426
1.1214 4
0.0457
0.8320
0.7786 5
1.0578
1.1452 6
2.0617
5.5288 7
2.5313
6.0595 8
1.6025
5.5952 9
0.7124
0.6782 10
0.2309
0.7760
0.8112 11
0.2167
0.4025
0.7626 12
0.1200
0.2295
0.2961 13
0.0105
0.1884
0.2163
0.2459
RCCAUGG
PWMSS1 = …
Xuhua Xia

7. PWMS over sites
GGACUGGCUGGGCGAGACUCUCCACCUGCUCCCUGGGACCAUCGCCCACCAUGGCUGUGGCCCAGCAGCUGCGGGCCGAG
Figure 5-1. Illustration of scanning the 5’-end of the NCF4 gene (30 bases upstream of the initiation codon ATG and 27 bases downstream of ATG. The highest peak, with PWMS = , corresponds to the 13-mer with 5 bases flanking the ATG. PWMS computed with  = 0.01.

8. PWM: position weight matrix
Also called position-specific scoring matrix (PSSM)
Used in
Characterizing sequence motifs
Eukaryotic translation initiation consensus
Splicing sites
Branchpoint sites
Shine-Dalgarno sequences
Database searches
PHI-BLAST
PSI-BLAST
RPS-BLAST)
What you can do in research

9. Yeast 5’ ss PWM
Table 3: Site-specific frequencies and position weight matrix (PWM) for 275 5′ ss. The consensus sequence (UAAAG ∣GUAUGUU UAAUU) can be obtained from those large site-specific PWM entries, with the most important sites in bold italics . The χ 2 test is performed for each site against the background frequencies (A = 0.3279, C = 0.1915, G = 0.2043, and U = 0.2763). The nucleotide sites are labeled with the five exon nucleotides as −5 to −1 and the 12 intron nucleotides as 1 to 12. The PWM is nearly identical when the introns in 5′ UTR were excluded.
Site A C G U
χ 2 p −5 94 32 57 92
11.798
0.0641
−0.7117
0.0245
0.2792 −4
119 47 48 61
14.117
0.4032
−0.1599
−0.2225
−0.3115 −3
139 38 43 55
39.672
0.6268
−0.4651
−0.3805
−0.4601 −2
138 40 36
38.899
0.6164
−0.3915
−0.6355 −1 91 45 88 51
27.270
0.0174
−0.2223
0.6492
−0.5685 1
274
−8.1042
−5.4675
2.2855
−8.1044 2 9
266
−2.5200
−8.1048
1.8081 3
268 4
1.5723
−4.6732
−4.1523 17 29
228
−2.3805
−0.8528
−5.5454
1.5859 5
272
−5.2765
−8.1049
2.2750
−5.8967 6 10 8
255
−3.1271
−2.6862
1.7472 7 97 18 39
121
55.570
0.1092
−1.5351
−0.5206
0.6734 95 54 35
11.363
0.0793
0.0397
−0.6759
0.2635
123 34 73
22.172
0.4508
−0.7175
−0.0534
118 41 78
17.334
0.3911
−0.3560
−0.5579
0.0418 11
105 33
17.367
0.2232
−0.6676
0.3101 12 90 44 42 99
12.109
0.0015
−0.2546
−0.4142
0.3847
Ma and Xia 2011

10. Yeast 3’ss PWM
Table 4. Site-specific frequencies and position weight matrix (PWM) for 278 3’ ss. The consensus sequence (UUUUUUUUAYAG|GCUUC) can be obtained from those large site-specific PWM entries, with the most important sites in bold italics. The 2 test is performed for each site against the expected background frequencies. The sites are labeled with first exon site as 1.
Site A C G U 2 p
-12 61 53 34
130
56.0
0.0033
0.7648
-11 70 47 20
141
83.2
0.8813
-10 79 42 12
145
99.9
0.9214 -9 38 30 23
187
219.4
1.2867 -8 51 27
158
121.6
1.0447 -7 91 33 28
126
53.8
0.0093
0.7200 -6 95 35
106
22.0
0.0001
0.0707
0.4722 -5 93
129
63.3
0.0403
0.7537 -4
136 25
43.3
0.5842
0.0517 -3
121
272.3
1.1862 -2
277 1
563.7
1.6056 -1
278
1082.7
2.2900 37 73 75
9.7
0.0217
0.3691 2 72 64 54 88
8.0
0.0466
0.2729
0.2059 3 90 48 86
2.5
0.4771
0.0300
0.1730 4 83 43 98
8.7
0.0337
0.3599 5 65
10.6
0.0140
0.2951
Ma and Xia 2011

12. PWMS as a proxy of splicing strength
Table 6. Position weight matrix scores (PWMS, as a proxy for splicing strength) is significantly smaller for splice sites from intron-containing genes (ICGs) whose transcripts failed to recruit U1 snRNPs (NRG for non-recruiting group) than for those from ICGs whose transcripts binds well to U1 snRNPs (RG for recruiting group). The pattern is consistent for both 5' ss and 3' ss, based on two-sample t-tests assuming equal variances. Mann-Whitney tests yield the same conclusion.
5' ss
3' ss
NRG RG
PWMS Mean
8.8138
5.3129
7.1762
PWMS Var.
4.8646
8.2077 N 44
202 49
229 t p
0.0000
0.0001
Ma and Xia 2011

13. Highly expressed genes should have high splicing efficiency.
Predictions: (1) Highly transcribed genes should, on average, have introns with greater splicing efficiency (2) Lowly transcribed genes should have greater variance in splicing efficiency than highly transcribed genes.
Lowly expressed genes could have their splicing sites drifting to low efficiency

14. PWMS and Gene Expression

15. PWMS and Splicing Mechanisms
Expected PWMS is 0 when there is no site-specific difference in nucleotide frequency distribution
What does a strongly negative PWMS mean?
5’ ss:
HAC1:
HFM1:
HOP2:
3’ ss:
HAC1:
REC102:

16. 5'SS6 (a) I5 I6 I7 I8 E1 E5 E6 E7 E8 E9 E22 5'SS6 3'SS6 5'SS7 3'SS7
BPS6
BPS7
5'SS6
3'SS6
5'SS7
3'SS7
Long flanking introns could lead to E7 exclusion E5 E6 E7 E8 E9
(b) I5 I6 I7 I8
Fig. 1. Exon-intron structure of USP4 (a), with exons represented as Ei and introns as Ii, together with branchpoint sites (BPSi) and 5’ and 3’ splice sites (5'SSi and 3'SSi). E7 could be excluded if it is flanked by two long introns (b) or if 5'SS6 is stronger than 5'SS7 and/or BPS7 is stronger than BPS6 (c). The font size of splicing sites and branchpoint sites indicates the strength of splicing signals. Not drawn to scale. E5 E6 E7 E8 E9
(c)
BPS7
BPS6
5'SS6
3'SS6
5'SS7
3'SS7
Strong 5'SS6 and BPS7 coupled with weak BPS6 and 5'SS7 could lead to E7 exclusion
Caitlyn Vlasschaert et al., Scientific Reports (in press)

17. Perceptron
The perceptron is one of the simplest artificial neural networks invented in 1957 at the Cornell Aeronautical Laboratory by Frank Rosenblatt (Rosenblatt, 1958).
Perceptron has been used in bioinformatics research since 1980s:
The identification of translational initiation sites in E. coli (Stormo et al., 1982a).
Characterizing the ATP/GTP-binding motif (Hirst and Sternberg, 1991).
More recent publications use multi-layer perceptrons which is more complicated than what we cover here.

18. What perceptron does Positive sequences POS1 ACGT POS2 GCGC
Negative sequences NEG1 AGCT NEG2 GGCC
Objective: Find a scoring matrix that can distinguish between the two groups (positive and negative) of sequences

19. Definitions POS1 ACGT POS2 GCGC NEG1 AGCT NEG2 GGCC
The weighting matrix (W) for the fictitious example with two sequences of length 4 in each group, initialized with values of 0. The first row designates sites 1-4.
Base 1 2 3 4 A C G T
For amino acid sequences, the matrix would be 20 by 4.

20. Iterations and convergence
First round of the training process in the perceptron algorithm.
NEG1: AGCT, PS = 0, update
Base 1 2 3 4 A -1
(a) C G T
NEG2: GGCC, PS = -2, no update
(b)
POS1: ACGT, PS = -2, update
(c)
POS2: GCGC, PS = 2, no update
(d)
Let us start with the NEG sequences in the fictitious example. Note that you would waste computational time by starting with sequences in the POS group because the resulting PS will all be 0 and consequently, according to the rules for updating W in Eq. , no updating is made with PS = 0.
PS for NEG1, i.e., PS for S = AGCT, is 0. According to the rules for updating W in Eq., we should update W by reducing the relevant Wij values by 1. The updated W is shown in Table 3-5a, with WA,1, WG,2, WC,3 and WT,4 in the original W (Table 3-4) reduced by 1, with updated values highlighted in bold.
The next input sequence is NEG2 (=GGCC) which has PS = -2 based on the updated W in Table 3-5a. According to the rules of updating W in Eq., no update is made, so the W matrix in Table 3-5b is the same as that in Table 3-5a.
We can proceed with POS1 and POS2 sequences. POS1 (=ACGT) has PS = -2. According to the rules of updating W in Eq. , we should add 1 to the cells corresponding to ACGT. The updated matrix W is shown in Table 3-5c. However, POS2 (= GCGC) has PS = 2. According to the rules in Eq. , there should be no updating, so W in Table 3-5d is the same as that in Table 3-5c. This ends the first round of iteration.
Now we restart with NEG1, NEG2, POS1, and POS2. We found that NEG1 and NEG2 both have negative PS and POS1 and POS2 both have positive PS. So we declare convergence, with the two groups clearly classified correctly.

21. Doublet perceptron 1 2 3 4 5 6 7 8 9 AC CG GU UA AU UC CU UG UU AA CAGA AG CC GC GG
P1 ACGUAUACGU
P2 ACGUCUACGU
P3 ACGUGUACGU
P4 ACGUUAACGU
P5 ACGUUCACGU
P6 ACGUUGACGU
N1 ACGUAAACGU
N1 ACGUACACGU
N1 ACGUAGACGU
N1 ACGUCAACGU
N1 ACGUCCACGU
N1 ACGUCGACGU
N1 ACGUGAACGU
N1 ACGUGCACGU
N1 ACGUGGACGU
N1 ACGUUUACGU

22. Doublet Perceptron
Doublet 1 2 3 4 5 6 7 8 9 AA -6
-4.3 AC -4 AG -2 AU
8.33 CA -1 CC CG CU GA
-0.7 GC GG GU
3.33 UA
-3.7
6.67
5.67 UC UG
0.33 UU
-11
Large amount of data are needed to avoid the problem of overfitting

23. Gene/Motif Prediction
Objective: given molecular sequence, find its biological function (preferably in terms of gene ontology).
Cellular localization
Biological processes the gene (its product) participates in
The biological reaction
Related terms:
Motif: e.g., RccAUGG
Fingerprint: a set of aligned sequences from which a position weight matrix or the like can be constructed to predict the motif effectively
Gene/Motif prediction methods
Position weight matrix
Perceptrons
Supervised learning
Hidden Markov Models (HMMs)
Neural networks (e.g., self-organizing map or SOM)