PSSM

Functions related with PSSMs

Setup

from katlas.pssm import *

PSSM

source

get_prob

 get_prob (df:pandas.core.frame.DataFrame, col:str, aa_order=['P', 'G',
           'A', 'C', 'S', 'T', 'V', 'I', 'L', 'M', 'F', 'Y', 'W', 'H',
           'K', 'R', 'Q', 'N', 'D', 'E', 's', 't', 'y'])

Get the probability matrix of PSSM from phosphorylation site sequences.

This function computes a position-specific probability matrix (PSSM) from a list of aligned phosphorylation site sequences.

For each position \(i\) (e.g., from \(-7\) to \(+7\)), the probability of observing amino acid \(x\) is:

\[ P_i(x) = \frac{\text{count of amino acid } x \text{ at position } i}{\text{total counts at position } i} \]

The following 23 amino acids are included:

  • Standard amino acids:
    A, C, D, E, F, G, H, I, K, L, M, N, P, Q, R, S, T, V, W, Y
  • Modified amino acids:
    s, t, y (often used to denote phosphorylated S, T, Y)

In the output, the modified residues are renamed as: - s → pS
- t → pT
- y → pY

The resulting matrix has: - Rows: Amino acids (including pS, pT, pY), - Columns: Sequence positions (centered on the phosphosite), - Values: Probabilities of each amino acid at each position.

ks = Data.get_ks_dataset()
ks_k = ks[ks.kinase_uniprot=='P00519'] # ABL1
pssm_df = get_prob(ks_k,'site_seq')
pssm_df.head()
Position -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
aa
P 0.050061 0.048691 0.062349 0.055489 0.046988 0.054753 0.064787 0.055090 0.056683 0.048272 0.052257 0.054599 0.053974 0.043170 0.060839 0.067138 0.049971 0.055817 0.076968 0.049354 0.0 0.020024 0.049645 0.125370 0.054997 0.056872 0.057382 0.057588 0.062048 0.053463 0.058104 0.052728 0.051140 0.069436 0.063164 0.057716 0.056639 0.051072 0.050697 0.052163 0.060703
G 0.080586 0.080341 0.069007 0.067551 0.082530 0.070397 0.093581 0.073054 0.077566 0.072706 0.067102 0.077745 0.052788 0.078060 0.070880 0.065371 0.087008 0.073443 0.084019 0.065217 0.0 0.091284 0.069740 0.062685 0.070373 0.075237 0.060371 0.072585 0.080120 0.077157 0.072783 0.099939 0.070856 0.071916 0.075672 0.071518 0.064821 0.080076 0.088720 0.062341 0.090735
A 0.080586 0.080341 0.062954 0.054282 0.075301 0.071600 0.070186 0.070060 0.065632 0.070322 0.077791 0.073591 0.053381 0.065050 0.069108 0.071849 0.062316 0.081669 0.063455 0.060517 0.0 0.102473 0.084515 0.075103 0.063276 0.075237 0.083084 0.049190 0.053614 0.073512 0.073394 0.064378 0.077634 0.069436 0.072545 0.063363 0.079924 0.088272 0.087452 0.057888 0.070927
C 0.017094 0.012781 0.013317 0.019903 0.012048 0.017449 0.007798 0.014371 0.013126 0.012515 0.023159 0.015430 0.012456 0.014784 0.010632 0.012956 0.014697 0.009988 0.010576 0.008226 0.0 0.017079 0.017730 0.023655 0.018924 0.010664 0.016736 0.010798 0.008434 0.010328 0.012232 0.007357 0.017868 0.014879 0.012508 0.011920 0.018880 0.019546 0.014575 0.019084 0.014058
S 0.047619 0.035910 0.046610 0.030157 0.037349 0.042720 0.041992 0.041916 0.034010 0.039333 0.037411 0.031454 0.043891 0.035482 0.024808 0.029446 0.026455 0.016451 0.021739 0.009401 0.0 0.019435 0.017730 0.019515 0.031934 0.029028 0.028691 0.034793 0.024699 0.032199 0.029969 0.024525 0.036352 0.047117 0.040025 0.042033 0.040277 0.039092 0.051965 0.041349 0.039617

Transform PSSM

source

pSTY2sty

 pSTY2sty (string)

Convert pS/pT/pY to s/t/y in a string.

pspa_scale = Data.get_pspa_all_scale()
pspa_scale.head()
-5P -5G -5A -5C -5S -5T -5V -5I -5L -5M -5F -5Y -5W -5H -5K -5R -5Q -5N -5D -5E -5pS -5pT -5pY -4P -4G -4A -4C -4S -4T -4V -4I -4L -4M -4F -4Y -4W -4H -4K -4R -4Q -4N -4D -4E -4pS -4pT -4pY -3P -3G -3A -3C ... 2E 2pS 2pT 2pY 3P 3G 3A 3C 3S 3T 3V 3I 3L 3M 3F 3Y 3W 3H 3K 3R 3Q 3N 3D 3E 3pS 3pT 3pY 4P 4G 4A 4C 4S 4T 4V 4I 4L 4M 4F 4Y 4W 4H 4K 4R 4Q 4N 4D 4E 4pS 4pT 4pY
kinase
AAK1 0.05845 0.01989 0.02305 0.03702 0.03450 0.03450 0.07720 0.12615 0.08061 0.07014 0.03450 0.07728 0.02557 0.02687 0.02127 0.07760 0.04546 0.02232 0.01299 0.01242 0.01632 0.01632 0.04960 0.04172 0.05015 0.05515 0.04375 0.04836 0.04836 0.04836 0.04851 0.05796 0.05414 0.04062 0.04172 0.03148 0.04015 0.06320 0.05586 0.04898 0.03351 0.02594 0.04375 0.02594 0.02594 0.02648 0.08610 0.04067 0.08888 0.05203 ... 0.04025 0.03142 0.03142 0.03149 0.05264 0.07135 0.04499 0.05735 0.04499 0.04499 0.04715 0.02999 0.03780 0.03378 0.03324 0.04120 0.03718 0.05210 0.05712 0.06965 0.04816 0.05681 0.03131 0.02868 0.02589 0.02589 0.02775 0.05026 0.05618 0.05170 0.04826 0.04482 0.04482 0.03377 0.03321 0.03689 0.03713 0.04186 0.04170 0.06611 0.04482 0.06651 0.07427 0.05082 0.04738 0.03113 0.03657 0.02009 0.02009 0.02161
ACVR2A 0.02971 0.03443 0.04180 0.03500 0.04137 0.04137 0.04281 0.04474 0.04266 0.03729 0.04295 0.04137 0.05748 0.04080 0.03651 0.03400 0.03078 0.03837 0.06356 0.05648 0.05605 0.05605 0.05440 0.03341 0.03936 0.03979 0.03950 0.03936 0.03936 0.03893 0.03771 0.03728 0.04130 0.04438 0.04201 0.05406 0.03950 0.02911 0.03276 0.03456 0.03592 0.07456 0.06230 0.05800 0.05800 0.04882 0.03345 0.04351 0.03578 0.03918 ... 0.04447 0.04786 0.04786 0.03799 0.04958 0.04381 0.03914 0.03559 0.04366 0.04366 0.04196 0.04099 0.04529 0.04358 0.04765 0.04839 0.04699 0.04366 0.03419 0.02864 0.03692 0.03877 0.04603 0.06438 0.03840 0.03840 0.06031 0.05559 0.03989 0.03652 0.03791 0.04129 0.04129 0.03784 0.04129 0.03755 0.04855 0.03835 0.04246 0.05867 0.04202 0.03865 0.03601 0.04517 0.04077 0.04693 0.04693 0.05155 0.05155 0.04319
ACVR2B 0.03779 0.03665 0.04013 0.05473 0.03779 0.03779 0.03850 0.03134 0.03339 0.03658 0.04282 0.04303 0.05112 0.03672 0.03063 0.03346 0.03531 0.04218 0.07551 0.06381 0.05402 0.05402 0.05268 0.03774 0.04406 0.04048 0.04645 0.04013 0.04013 0.03647 0.03226 0.03640 0.03521 0.04392 0.04273 0.04954 0.04287 0.02663 0.02586 0.03465 0.04013 0.07224 0.06149 0.05538 0.05538 0.05987 0.03044 0.03658 0.03579 0.03882 ... 0.04579 0.06240 0.06240 0.04636 0.05072 0.04699 0.04188 0.03976 0.04268 0.04268 0.04210 0.04297 0.05006 0.04443 0.04122 0.05123 0.04845 0.03727 0.02653 0.03311 0.03888 0.03815 0.04268 0.05423 0.04633 0.04633 0.05130 0.05205 0.04200 0.04735 0.03984 0.04056 0.04056 0.03998 0.03926 0.03832 0.03774 0.03485 0.04244 0.05675 0.04056 0.03261 0.03514 0.04229 0.03846 0.05278 0.05039 0.05502 0.05502 0.04605
AKT1 0.04669 0.04599 0.04274 0.04684 0.03995 0.03995 0.03306 0.03368 0.03592 0.03910 0.04235 0.03995 0.04065 0.05056 0.07355 0.11753 0.03801 0.03616 0.02911 0.02911 0.03298 0.03298 0.03314 0.04161 0.04729 0.04091 0.03858 0.04091 0.04091 0.03461 0.03018 0.03430 0.04114 0.03360 0.03593 0.04449 0.04667 0.08455 0.12592 0.04161 0.03679 0.02598 0.03220 0.03508 0.03508 0.03166 0.02642 0.02358 0.02837 0.02748 ... 0.01816 0.02271 0.02271 0.02975 0.03828 0.05555 0.03828 0.05109 0.04422 0.04422 0.03594 0.03852 0.03797 0.03852 0.04750 0.04500 0.04422 0.06000 0.07180 0.08906 0.04430 0.04875 0.02289 0.02469 0.02633 0.02633 0.02656 0.07361 0.04755 0.03900 0.03884 0.03900 0.03900 0.03301 0.03037 0.03692 0.03637 0.03109 0.02789 0.04156 0.05299 0.09151 0.08648 0.05874 0.05187 0.03541 0.02494 0.03141 0.03141 0.02102
AKT2 0.04617 0.04732 0.04931 0.04464 0.04095 0.04095 0.03321 0.03206 0.03781 0.03934 0.04203 0.04180 0.04095 0.04671 0.07516 0.11320 0.03796 0.03643 0.02339 0.02416 0.03497 0.03497 0.03651 0.04437 0.05416 0.05245 0.04390 0.04056 0.04056 0.03201 0.03023 0.03644 0.04056 0.03194 0.03668 0.03085 0.04701 0.09053 0.10723 0.04507 0.04181 0.02611 0.02953 0.03435 0.03435 0.02930 0.01778 0.01831 0.02729 0.02649 ... 0.02437 0.04664 0.04664 0.04794 0.04509 0.05588 0.04689 0.05708 0.03918 0.03918 0.03273 0.02719 0.03783 0.03236 0.03790 0.03910 0.03918 0.06127 0.07865 0.08030 0.04247 0.04052 0.02592 0.02577 0.03558 0.03558 0.04434 0.07404 0.05528 0.04158 0.04502 0.03668 0.03668 0.02887 0.03093 0.03315 0.03668 0.03063 0.03446 0.03178 0.05199 0.08844 0.07580 0.04992 0.04770 0.02772 0.02680 0.04196 0.04196 0.03193

5 rows × 230 columns

pspa_scale.columns.map(pSTY2sty)
Index(['-5P', '-5G', '-5A', '-5C', '-5S', '-5T', '-5V', '-5I', '-5L', '-5M',
       ...
       '4H', '4K', '4R', '4Q', '4N', '4D', '4E', '4s', '4t', '4y'],
      dtype='object', length=230)

source

flatten_pssm

 flatten_pssm (pssm_df, use_sty=False)

Flatten PSSM dataframe to dictionary

Type Default Details
pssm_df
use_sty bool False if True, use s,t,y instead of pS,pT,pY 
series = pd.Series(flatten_pssm(pssm_df))
series
-20P    0.05006
-20G    0.08059
         ...   
20pT    0.01534
20pY    0.01597
Length: 943, dtype: float64

source

recover_pssm

 recover_pssm (flat_pssm:pandas.core.series.Series, aa_order=['P', 'G',
               'A', 'C', 'S', 'T', 'V', 'I', 'L', 'M', 'F', 'Y', 'W', 'H',
               'K', 'R', 'Q', 'N', 'D', 'E', 's', 't', 'y'])

Recover 2D PSSM from flattened PSSM Series.

recover_pssm(series)
Position -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
aa
A 0.08059 0.08034 0.06295 0.05428 0.07530 0.07160 0.07019 0.07006 0.06563 0.07032 0.07779 0.07359 0.05338 0.06505 0.06911 0.07185 0.06232 0.08167 0.06345 0.06052 0.00000 0.10247 0.08452 0.07510 0.06328 0.07524 0.08308 0.04919 0.05361 0.07351 0.07339 0.06438 0.07763 0.06944 0.07255 0.06336 0.07992 0.08827 0.08745 0.05789 0.07093
C 0.01709 0.01278 0.01332 0.01990 0.01205 0.01745 0.00780 0.01437 0.01313 0.01251 0.02316 0.01543 0.01246 0.01478 0.01063 0.01296 0.01470 0.00999 0.01058 0.00823 0.00000 0.01708 0.01773 0.02365 0.01892 0.01066 0.01674 0.01080 0.00843 0.01033 0.01223 0.00736 0.01787 0.01488 0.01251 0.01192 0.01888 0.01955 0.01458 0.01908 0.01406
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
pT 0.01832 0.01278 0.01574 0.01508 0.01446 0.01504 0.01140 0.00719 0.00955 0.02145 0.00950 0.02077 0.02135 0.01892 0.02363 0.02120 0.02528 0.02585 0.02703 0.03467 0.04818 0.02415 0.03605 0.02720 0.03666 0.02844 0.01973 0.01860 0.01747 0.02187 0.01835 0.01962 0.01109 0.02170 0.01501 0.01443 0.01951 0.01450 0.01458 0.01209 0.01534
pY 0.01648 0.01156 0.00726 0.00905 0.01386 0.01384 0.01320 0.01078 0.01313 0.01967 0.01425 0.01306 0.01483 0.01715 0.01477 0.03121 0.02352 0.04407 0.04465 0.03760 0.89013 0.03828 0.04433 0.04080 0.02543 0.02488 0.01554 0.01800 0.01506 0.01276 0.01284 0.01962 0.01972 0.01116 0.01188 0.01004 0.00944 0.01261 0.00824 0.01908 0.01597

23 rows × 41 columns

Or recover from PSPA data, where s, t, y will be converted to pS, pT, and pY:

pspa = Data.get_pspa_all_norm()
flat_pssm = pspa.loc['AAK1'].dropna()
recovered = recover_pssm(flat_pssm)
recovered
Position -5 -4 -3 -2 -1 0 1 2 3 4
aa
P 0.0720 0.0534 0.1084 0.0226 0.1136 0.0 0.0463 0.0527 0.0681 0.0628
G 0.0245 0.0642 0.0512 0.0283 0.0706 0.0 0.7216 0.0749 0.0923 0.0702
... ... ... ... ... ... ... ... ... ... ...
pT 0.0201 0.0332 0.0303 0.0209 0.0121 1.0 0.0123 0.0409 0.0335 0.0251
pY 0.0611 0.0339 0.0274 0.0486 0.0178 0.0 0.0100 0.0410 0.0359 0.0270

23 rows × 10 columns

PSPA is not scaled per position, and the recovered pssm_df also contained copies of pS,pT,pY in zero position (S,T,Y).

So we need to remove the redundant copy in zero position (leave pS/pT/pY only) and scaled to 1 per position.

source

clean_zero_normalize

 clean_zero_normalize (pssm_df)

Zero out non-last three values in position 0 (keep only s,t,y values at center), and normalize per position

This function applies phosphosite-specific cleaning and normalization to a PSSM.

At the center position (\(i = 0\)), only the last three rows of the matrix — corresponding to phosphorylatable residues s, t, and y — are retained. All other amino acid values at position 0 are set to 0.

After masking, the matrix is column-normalized to ensure the probabilities at each position sum to 1:

\[ P_i(x) = \frac{P_i(x)}{\sum_{x'} P_i(x')} \]

norm_pssm = clean_zero_normalize(recovered)
norm_pssm.head()
Position -5 -4 -3 -2 -1 0 1 2 3 4
aa
P 0.058446 0.041715 0.086100 0.017935 0.096068 0.0 0.042649 0.040482 0.052640 0.050260
G 0.019888 0.050152 0.040667 0.022459 0.059704 0.0 0.664702 0.057536 0.071346 0.056182
A 0.023054 0.055152 0.088880 0.042695 0.032558 0.0 0.028740 0.057613 0.044987 0.051701
C 0.037016 0.043747 0.052025 0.046663 0.026469 0.0 0.020542 0.052543 0.057355 0.048259
S 0.034500 0.048356 0.041859 0.044044 0.046089 0.0 0.013172 0.042403 0.044987 0.044818

PSSM of Log odds

source

get_pssm_LO

 get_pssm_LO (pssm_df, site_type)

Get log odds PSSM: log2 (freq pssm/background pssm).

Details
pssm_df
site_type S, T, Y, ST, or STY

Let \(P_i(x)\) be the frequency of amino acid \(x\) at position \(i\) in the input PSSM, and let \(B_i(x)\) be the background frequency of amino acid \(x\) at the same position, derived from a background model corresponding to the specified site type (S, T, Y, or STY).

The log-odds score at each position \(i\) for amino acid \(x\) is computed as:

\[ \mathrm{LO}_i(x) = \log_2 \left( \frac{P_i(x) + \varepsilon}{B_i(x) + \varepsilon} \right) \]

where \(\varepsilon = 10^{-8}\) is a small constant added for numerical stability and to avoid division by zero.

This results in a matrix where:

  • Positive values indicate enrichment over background,
  • Negative values indicate depletion relative to background,
  • Zero indicates no difference from the expected background.
ks_y = ks_k[ks_k.site.str[0]=='Y']
pssm_y = get_prob(ks_y,'site_seq')
pssm_LO = get_pssm_LO(pssm_y,'Y')
pssm_LO.head()
Position -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
aa
P -0.206189 -0.173852 0.075945 0.048238 -0.332429 -0.080529 0.276989 -0.080693 0.026617 -0.274797 -0.204659 -0.086080 -0.319235 -0.241293 0.099099 0.123279 -0.291828 0.051970 0.168818 -0.040146 0.0 -2.395029 -0.280748 0.670247 -0.160627 -0.023172 -0.103456 -0.079543 -0.118430 -0.369967 -0.067107 -0.348902 -0.015825 0.255922 -0.115999 -0.259846 -0.137766 -0.144998 -0.222180 -0.133928 -0.190894
G 0.097859 0.271252 0.011007 -0.113312 0.335485 0.061852 0.218183 0.002454 0.250731 -0.081028 -0.032525 0.098842 -0.261324 0.224285 -0.008761 -0.027760 0.170070 -0.075929 0.103874 0.094742 0.0 0.293429 0.310956 0.226578 0.011085 0.033597 -0.061252 0.279903 0.193058 0.086542 0.080584 0.422964 0.204529 0.047536 0.282739 0.057069 -0.077271 0.148160 0.305952 -0.002806 0.283357
A 0.120322 0.239305 -0.034339 -0.046638 0.177100 0.036379 0.001452 0.051452 0.004961 -0.055318 0.079303 -0.001929 -0.211467 0.042708 0.032052 0.032729 0.012878 0.335463 -0.093954 0.103941 0.0 0.636043 0.340320 0.211844 0.119820 0.203209 0.163758 -0.364698 -0.267428 -0.002023 0.138489 0.037818 0.130627 -0.054711 0.012698 -0.078897 0.138491 0.113970 0.335229 -0.048975 0.161479
C -0.015903 -0.368177 -0.099183 0.393931 -0.754052 0.128316 -0.936405 0.001518 0.093670 -0.116052 0.206361 0.038752 0.140063 0.040949 -0.046152 -0.302009 0.044481 -0.100333 -0.063927 -0.380166 0.0 0.097430 0.399721 0.484979 0.441042 -0.655705 -0.046665 -0.409536 -0.689994 -0.216082 -0.314273 -0.756429 0.051668 -0.150990 -0.144370 -0.302754 0.023962 0.196713 -0.304713 0.199967 -0.160036
S 0.089429 -0.534911 0.001906 -0.553952 -0.411714 -0.320368 -0.114390 -0.246280 -0.412888 -0.086541 -0.156847 -0.336588 0.086873 -0.321517 -0.432052 -0.263282 -0.591312 -0.916405 -0.440907 -1.495383 0.0 -0.486242 -0.641287 -0.594873 -0.321606 -0.438704 -0.382641 -0.104947 -0.627112 -0.376017 -0.324308 -0.898365 -0.137941 -0.048681 -0.239158 -0.089838 -0.178475 -0.333529 -0.215992 -0.248241 -0.495879 
pssm_y[0][pssm_y[0]==1].index
Index(['pY'], dtype='object', name='aa')
pssm_LO[0].sort_values()
aa
P     0.0
pS    0.0
     ... 
F     0.0
pY    0.0
Name: 0, Length: 23, dtype: float64

PSSMs of clusters

source

get_cluster_pssms

 get_cluster_pssms (df, cluster_col, seq_col='site_seq',
                    id_col='sub_site', count_thr=10, valid_thr=None,
                    plot=False)

Extract motifs from clusters in a dataframe

Type Default Details
df
cluster_col
seq_col str site_seq
id_col str sub_site
count_thr int 10 if less than the count threshold, not include in the return
valid_thr NoneType None percentage of not-nan values in pssm
plot bool False

Entropy & Information Content

source

entropy

 entropy (pssm_df, return_min=False, exclude_zero=False, clean_zero=True)

Calculate entropy per position of a PSSM surrounding 0. The less entropy the more information it contains.

Type Default Details
pssm_df a dataframe of pssm with index as aa and column as position
return_min bool False return min entropy as a single value or return all entropy as a series
exclude_zero bool False exclude the column of 0 (center position) in the entropy calculation
clean_zero bool True if true, zero out non-last three values in position 0 (keep only s,t,y values at center)

Let \(P_i(x)\) be the probability of amino acid \(x\) at position \(i\) in the PSSM, with \(i \in \{-k, \dots, -1, 0, +1, \dots, +k\}\). The entropy at each position \(i\) is defined as:

\[ H_i = - \sum_{x} P_i(x) \log_2 \left( P_i(x) + \varepsilon \right) \]

where \(\varepsilon = 10^{-8}\) is a small constant added for numerical stability.

If exclude_zero=True, the central position \(i = 0\) is omitted from the entropy calculation.

If clean_zero=True, all values at position \(i = 0\) are zeroed out except for amino acids Serine (S), Threonine (T), and Tyrosine (Y), typically the only possible phospho-acceptors in kinase motif analysis.

If return_min=True, the function returns the minimum entropy across all positions:

\[ H_{\min} = \min_i H_i \]

Otherwise, the function returns the full vector \(\{H_i\}\) for each position \(i\), reflecting how much information (or uncertainty) is contained at each position in the motif.

# get entropy per position
entropy(pssm_df).sort_values()
Position
 0     0.608195
-1     4.148746
         ...   
-20    4.324109
-11    4.324761
Length: 41, dtype: float64
# calculate minimum entropy per pssm
entropy(pssm_df,True,True,True)
4.148746038698782

source

entropy_flat

 entropy_flat (flat_pssm:pandas.core.series.Series, return_min=False,
               exclude_zero=False, clean_zero=True)

Calculate entropy per position of a flat PSSM surrounding 0

Type Default Details
flat_pssm Series
return_min bool False return min entropy as a single value or return all entropy as a series
exclude_zero bool False exclude the column of 0 (center position) in the entropy calculation
clean_zero bool True if true, zero out non-last three values in position 0 (keep only s,t,y values at center) 
entropy_flat(series).sort_values() # slight differences due to rounding
Position
 0     0.608192
-1     4.148763
         ...   
-20    4.324115
-11    4.324737
Length: 41, dtype: float64

source

get_pssm_IC_standard

 get_pssm_IC_standard (pssm_df)

Calculate the standard information content (bits) from frequency matrix, using the same number of residues log2(len(pssm_df)) for all positions

Let \(P_i(x)\) be the frequency (probability) of amino acid \(x\) at position \(i\) in the PSSM. The standard information content (IC) at position \(i\) is defined as:

\[ \mathrm{IC}_i = \log_2(N) - H_i \]

where \(N\) is the number of possible amino acids (i.e., \(N = \text{len}(P_i)\)).

This standard definition assumes a uniform maximum entropy baseline of \(\log_2(N)\) for all positions, regardless of which residues are present.

To visualize the motif using Logomaker, the scaled PSSM is computed by weighting each amino acid’s frequency at position \(i\) by the position’s information content:

\[ \text{PSSM\_scaled}_i(x) = P_i(x) \cdot \mathrm{IC}_i \]

This results in a matrix where the total stack height at each position equals the information content, and each letter’s height is proportional to its contribution. This is the standard format used by Logomaker to generate sequence logos.

get_pssm_IC_standard(pssm_df)
Position -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
aa
P 0.009985 0.012965 0.014891 0.014198 0.011902 0.012694 0.015974 0.013986 0.017089 0.009596 0.012575 0.014295 0.012250 0.011231 0.017495 0.018691 0.014269 0.020898 0.026184 0.018499 0.000000 0.007416 0.011363 0.040525 0.011582 0.015780 0.015198 0.012693 0.019187 0.013863 0.015197 0.013824 0.012853 0.014583 0.015643 0.012925 0.011664 0.012481 0.012162 0.011987 0.014786
G 0.016073 0.021392 0.016481 0.017284 0.020904 0.016321 0.023074 0.018547 0.023384 0.014454 0.016147 0.020355 0.011981 0.020308 0.020382 0.018199 0.024845 0.027498 0.028582 0.024445 0.000000 0.033810 0.015962 0.020262 0.014820 0.020876 0.015989 0.015999 0.024776 0.020007 0.019037 0.026202 0.017809 0.015103 0.018741 0.016016 0.013349 0.019569 0.021284 0.014326 0.022101
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
pT 0.003653 0.003403 0.003759 0.003858 0.003662 0.003487 0.002810 0.001824 0.002878 0.004265 0.002286 0.005438 0.004846 0.004923 0.006794 0.005903 0.007218 0.009679 0.009194 0.012993 0.188637 0.008943 0.008252 0.008793 0.007721 0.007890 0.005224 0.004099 0.005402 0.005671 0.004799 0.005144 0.002787 0.004557 0.003717 0.003231 0.004018 0.003544 0.003497 0.002778 0.003735
pY 0.003288 0.003079 0.001735 0.002315 0.003509 0.003208 0.003254 0.002736 0.003957 0.003910 0.003430 0.003418 0.003365 0.004462 0.004246 0.008690 0.006715 0.016499 0.015191 0.014094 3.485183 0.014178 0.010146 0.013190 0.005355 0.006904 0.004116 0.003967 0.004657 0.003308 0.003359 0.005144 0.004955 0.002344 0.002943 0.002248 0.001944 0.003082 0.001976 0.004386 0.003891

23 rows × 41 columns

source

get_IC_per_position

 get_IC_per_position (pssm_df, return_min=False, exclude_zero=False,
                      clean_zero=True)

Calculate the information content (bits) from a frequency matrix, using log2(3) for the middle position and log2(len(pssm_df)) for others. The higher the more information it contains.

Type Default Details
pssm_df a dataframe of pssm with index as aa and column as position
return_min bool False return min entropy as a single value or return all entropy as a series
exclude_zero bool False exclude the column of 0 (center position) in the entropy calculation
clean_zero bool True if true, zero out non-last three values in position 0 (keep only s,t,y values at center)

Let \(P_i(x)\) be the frequency of amino acid \(x\) at position \(i\) in the PSSM. This modified version of information content accounts for the fact that only three amino acids (S, T, Y) are relevant at the central position (\(i = 0\)) in phosphorylation motifs.

The maximum entropy at each position is defined as:

\[ \max H_i = \begin{cases} \log_2(3) & \text{if } i = 0 \\ \log_2(N) & \text{otherwise} \end{cases} \]

where \(N = \text{len}(P_i)\) is the number of amino acid types in the matrix.

Then, the information content at each position is:

\[ \mathrm{IC}_i = \max H_i - H_i \]

get_IC_per_position(pssm_df).sort_values()
Position
-11    0.198801
-20    0.199453
         ...   
-1     0.374816
 0     0.976768
Length: 41, dtype: float64

source

get_IC_per_position_flat

 get_IC_per_position_flat (flat_pssm:pandas.core.series.Series,
                           return_min=False, exclude_zero=False,
                           clean_zero=True)

Calculate the information content (bits) from a flattened pssm pd.Series, using log2(3) for the middle position and log2(len(pssm_df)) for others.

Type Default Details
flat_pssm Series
return_min bool False return min entropy as a single value or return all entropy as a series
exclude_zero bool False exclude the column of 0 (center position) in the entropy calculation
clean_zero bool True if true, zero out non-last three values in position 0 (keep only s,t,y values at center) 
get_IC_per_position_flat(series)
Position
-20    0.199447
-19    0.266280
         ...   
 19    0.229810
 20    0.243570
Length: 41, dtype: float64

source

get_pssm_IC

 get_pssm_IC (pssm_df)

For plotting purpose, calculate the scaled information content (bits) from a frequency matrix, using log2(3) for the middle position and log2(len(pssm_df)) for others.

get_pssm_IC(pssm_df)
Position -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
aa
P 0.009985 0.012965 0.014891 0.014198 0.011902 0.012694 0.015974 0.013986 0.017089 0.009596 0.012575 0.014295 0.012250 0.011231 0.017495 0.018691 0.014269 0.020898 0.026184 0.018499 0.000000 0.007416 0.011363 0.040525 0.011582 0.015780 0.015198 0.012693 0.019187 0.013863 0.015197 0.013824 0.012853 0.014583 0.015643 0.012925 0.011664 0.012481 0.012162 0.011987 0.014786
G 0.016073 0.021392 0.016481 0.017284 0.020904 0.016321 0.023074 0.018547 0.023384 0.014454 0.016147 0.020355 0.011981 0.020308 0.020382 0.018199 0.024845 0.027498 0.028582 0.024445 0.000000 0.033810 0.015962 0.020262 0.014820 0.020876 0.015989 0.015999 0.024776 0.020007 0.019037 0.026202 0.017809 0.015103 0.018741 0.016016 0.013349 0.019569 0.021284 0.014326 0.022101
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
pT 0.003653 0.003403 0.003759 0.003858 0.003662 0.003487 0.002810 0.001824 0.002878 0.004265 0.002286 0.005438 0.004846 0.004923 0.006794 0.005903 0.007218 0.009679 0.009194 0.012993 0.047059 0.008943 0.008252 0.008793 0.007721 0.007890 0.005224 0.004099 0.005402 0.005671 0.004799 0.005144 0.002787 0.004557 0.003717 0.003231 0.004018 0.003544 0.003497 0.002778 0.003735
pY 0.003288 0.003079 0.001735 0.002315 0.003509 0.003208 0.003254 0.002736 0.003957 0.003910 0.003430 0.003418 0.003365 0.004462 0.004246 0.008690 0.006715 0.016499 0.015191 0.014094 0.869450 0.014178 0.010146 0.013190 0.005355 0.006904 0.004116 0.003967 0.004657 0.003308 0.003359 0.005144 0.004955 0.002344 0.002943 0.002248 0.001944 0.003082 0.001976 0.004386 0.003891

23 rows × 41 columns

Plot

Heatmap

/opt/hostedtoolcache/Python/3.10.18/x64/lib/python3.10/site-packages/fastcore/docscrape.py:230: UserWarning: Unknown section See Also
  else: warn(msg)

source

plot_heatmap_simple

 plot_heatmap_simple (matrix, title:str='heatmap', figsize:tuple=(6, 7),
                      cmap:str='binary', vmin=None, vmax=None,
                      center=None, robust=False, annot=None, fmt='.2g',
                      annot_kws=None, linewidths=0, linecolor='white',
                      cbar=True, cbar_kws=None, cbar_ax=None,
                      square=False, xticklabels='auto',
                      yticklabels='auto', mask=None, ax=None)

Plot heatmap based on a matrix of values

Type Default Details
matrix a matrix of values
title str heatmap title of the heatmap
figsize tuple (6, 7) (width, height)
cmap str binary color map, default is dark&white
vmin NoneType None
vmax NoneType None
center NoneType None The value at which to center the colormap when plotting divergent data.
Using this parameter will change the default cmap if none is
specified.
robust bool False If True and vmin or vmax are absent, the colormap range is
computed with robust quantiles instead of the extreme values.
annot NoneType None If True, write the data value in each cell. If an array-like with the
same shape as data, then use this to annotate the heatmap instead
of the data. Note that DataFrames will match on position, not index.
fmt str .2g String formatting code to use when adding annotations.
annot_kws NoneType None Keyword arguments for :meth:matplotlib.axes.Axes.text when annot
is True.
linewidths int 0 Width of the lines that will divide each cell.
linecolor str white Color of the lines that will divide each cell.
cbar bool True Whether to draw a colorbar.
cbar_kws NoneType None Keyword arguments for :meth:matplotlib.figure.Figure.colorbar.
cbar_ax NoneType None Axes in which to draw the colorbar, otherwise take space from the
main Axes.
square bool False If True, set the Axes aspect to “equal” so each cell will be
square-shaped.
xticklabels str auto
yticklabels str auto
mask NoneType None If passed, data will not be shown in cells where mask is True.
Cells with missing values are automatically masked.
ax NoneType None Axes in which to draw the plot, otherwise use the currently-active
Axes.
Returns matplotlib Axes Axes object with the heatmap. 
plot_heatmap_simple(pssm_df,'kinase',figsize=(10,7))

source

plot_heatmap

 plot_heatmap (heatmap_df, ax=None, position_label=True, figsize=(5, 6),
               include_zero=True, scale_pos_neg=False,
               colorbar_title='Prob.')

Plots a heatmap with specific formatting.

This function visualizes a PSSM or log-odds matrix as a heatmap with diverging color scales centered at 0.

Color scale behavior:

  • By default (scale_pos_neg=False), the colormap is centered at 0, but the full data range determines the color intensity:

    \[ \text{color range} = [\min(\text{data}), \max(\text{data})], \quad \text{with center at } 0 \]

    This is useful when you want to emphasize whether values are above or below zero, but without enforcing symmetry.

  • If scale_pos_neg=True, the function uses a balanced diverging scale via TwoSlopeNorm, such that:

    \[ \text{min color} = \min(\text{data}), \quad \text{center} = 0, \quad \text{max color} = \max(\text{data}) \]

    The positive and negative ranges are scaled separately, ensuring that both ends of the heatmap have equal visual weight — especially helpful for symmetric data like log-odds matrices.

Additional visual features: - The center position (\(i = 0\)) can be masked out using include_zero=False.

plot_heatmap(pssm_df-0.3,scale_pos_neg=False,figsize=(20, 6));
# plt.savefig('plot.svg',bbox_inches='tight')

plot_heatmap(pssm_df-0.3,scale_pos_neg=True,figsize=(20, 6));

Logo motif

source

change_center_name

 change_center_name (df)

Transfer the middle pS,pT,pY to S,T,Y for plot.

Now instead of pS, pT, and pY, the center name becomes S, T and Y:

change_center_name(pssm_df)[0].sort_values(ascending=False).head()
aa
Y     0.890129
S     0.061692
T     0.048179
H     0.000000
pT    0.000000
Name: 0, dtype: float64

source

get_pos_min_max

 get_pos_min_max (pssm_df)

Get min and max value of sum of positive and negative values across each position.

source

scale_zero_position

 scale_zero_position (pssm_df)

Scale position 0 so that: - Positive values match the max positive column sum of other positions - Negative values match the min (most negative) column sum of other positions

This function rescales position 0 in a log-odds PSSM so that its total positive and negative stack heights match those of the most extreme positions on either side.

This ensures the central position visually matches the dynamic range of surrounding positions in log-odds logo plots.

source

scale_pos_neg_values

 scale_pos_neg_values (pssm_df)

Globally scale all positive values by max positive column sum, and negative values by min negative column sum (preserving sign).

source

convert_logo_df

 convert_logo_df (pssm_df, scale_zero=True, scale_pos_neg=False)

Change center name from pS,pT,pY to S, T, Y in a pssm and scaled zero position to the max of neigbors.

source

plot_logo_raw

 plot_logo_raw (pssm_df, ax=None, title='Motif', ytitle='Bits',
                figsize=(10, 2))

Plot logo motif using Logomaker.

source

Logo motif of log-odds

source

plot_logo_LO

 plot_logo_LO (pssm_LO, title='Motif', acceptor=None, scale_zero=True,
               scale_pos_neg=True, ax=None, figsize=(10, 1))

Plot logo of log-odds given a frequency PSSM.

To ensure the phosphorylated residue is visible at the center of a log-odds motif (position 0), two mechanisms are used:

  1. Acceptor override: If the center column is entirely zero (e.g., masked), the user can specify an acceptor ('S', 'T', 'Y', or 'STY'). The function then assigns a small nonzero value (e.g., 0.1) to the corresponding phospho-residue row (pS, pT, pY) at position 0. This ensures the central letter appears in the logo plot, even when real log-odds values are absent.

  2. Stack height rescaling: To maintain visual consistency with surrounding columns, position 0 is rescaled so that its total positive and negative stack heights match the most extreme values observed elsewhere.

Together, these adjustments ensure that: - The phospho-acceptor appears explicitly at the center, - The visual scale remains consistent with neighboring positions, - The resulting logo can faithfully reflect both biological relevance and statistical signal.

pssm_LO = get_pssm_LO(pssm_df,'STY')
plot_logo_LO(pssm_LO,scale_zero=False,scale_pos_neg=False)

# with zero position scaled to the max
plot_logo_LO(pssm_LO,scale_zero=True,scale_pos_neg=False)

# scaled positive and negative values for better visualization
plot_logo_LO(pssm_LO,scale_zero=True,scale_pos_neg=True)

# for those specific site type (S,T or Y), show acceptor in the middle instead of empty
pssm_LO = get_pssm_LO(pssm_y,'Y')
plot_logo_LO(pssm_LO,acceptor='Y')

Multiple logos

source

plot_logos_idx

 plot_logos_idx (pssms_df, *idxs)

Plot logos of a dataframe with flattened PSSMs with index ad IDs.

source

plot_logos

 plot_logos (pssms_df, count_dict=None, path=None, prefix='Motif')

Plot all logos from a dataframe of flattened PSSMs as subplots in a single figure.

Type Default Details
pssms_df
count_dict NoneType None used to display n in motif title
path NoneType None
prefix str Motif 
# plot_logos(pssms_df)
# plt.show()
# plt.close()

Logo motif + Heatmap

source

plot_logo_heatmap

 plot_logo_heatmap (pssm_df, title='Motif', figsize=(17, 10),
                    include_zero=False)

Plot logo and heatmap vertically

Type Default Details
pssm_df column is position, index is aa
title str Motif
figsize tuple (17, 10)
include_zero bool False 
plot_logo_heatmap(pssm_df,'Kinase',(17,10))

source

plot_logo_heatmap_LO

 plot_logo_heatmap_LO (pssm_LO, title='Motif', acceptor=None, figsize=(17,
                       10), include_zero=False, scale_pos_neg=True)

Plot logo and heatmap of enrichment bits vertically

Type Default Details
pssm_LO pssm of log-odds
title str Motif
acceptor NoneType None
figsize tuple (17, 10)
include_zero bool False
scale_pos_neg bool True 
plot_logo_heatmap_LO(pssm_LO,acceptor='Y')

pssm_LO = get_pssm_LO(pssm_df,'STY')
plot_logo_heatmap_LO(pssm_LO,scale_pos_neg=False) # normal color scale

PSPA

Normalization

source

raw2norm

 raw2norm (df:pandas.core.frame.DataFrame, PDHK:bool=False)

Normalize single ST kinase data

Type Default Details
df DataFrame single kinase’s df has position as index, and single amino acid as columns
PDHK bool False whether this kinase belongs to PDHK family

This function implement the normalization method from Johnson et al. Nature: An atlas of substrate specificities for the human serine/threonine kinome

Specifically, > - matrices were column-normalized at all positions by the sum of the 17 randomized amino acids (excluding serine, threonine and cysteine), to yield PSSMs. >- PDHK1 and PDHK4 were normalized to the 16 randomized amino acids (excluding serine, threonine, cysteine and additionally tyrosine) >- The cysteine row was scaled by its median to be 1/17 (1/16 for PDHK1 and PDHK4). >- The serine and threonine values in each position were set to be the median of that position. >- The S0/T0 ratio was determined by summing the values of S and T rows in the matrix (SS and ST, respectively), accounting for the different S vs. T composition of the central (1:1) and peripheral (only S or only T) positions (Sctrl and Tctrl, respectively), and then normalizing to the higher value among the two (S0 and T0, respectively, Supplementary Note 1)

This function is usually implemented with the below function, with normalize being a bool argument.

source

get_one_kinase

 get_one_kinase (df:pandas.core.frame.DataFrame, kinase:str,
                 normalize:bool=False, drop_s:bool=True)

Obtain a specific kinase data from stacked dataframe

Type Default Details
df DataFrame stacked dataframe (paper’s raw data)
kinase str a specific kinase
normalize bool False normalize according to the paper; special for PDHK1/4
drop_s bool True drop s as s is a duplicates of t in PSPA

Retreive a single kinase data from PSPA data that has an format of kinase as index and position+amino acid as column.

data = Data.get_pspa_st_norm()
get_one_kinase(data,'PDHK1')
aa A C D E F G H I K L M N P Q R S T V W Y t y
position
-5 0.0594 0.0625 0.0589 0.0550 0.0775 0.0697 0.0687 0.0590 0.0515 0.0657 0.0687 0.0613 0.0451 0.0424 0.0594 0.0594 0.0594 0.0573 0.1001 0.0775 0.0583 0.0658
-4 0.0618 0.0621 0.0550 0.0511 0.0739 0.0715 0.0598 0.0601 0.0520 0.0614 0.0744 0.0549 0.0637 0.0552 0.0617 0.0608 0.0608 0.0519 0.0916 0.0739 0.0528 0.0752
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
3 0.0486 0.0609 0.0938 0.0684 0.1024 0.0676 0.0544 0.0583 0.0388 0.0552 0.0637 0.0505 0.0686 0.0502 0.0561 0.0588 0.0588 0.0593 0.0641 0.1024 0.0539 0.0431
4 0.0565 0.0749 0.0631 0.0535 0.0732 0.0655 0.0664 0.0625 0.0496 0.0552 0.0627 0.0640 0.0677 0.0553 0.0604 0.0626 0.0626 0.0579 0.0864 0.0732 0.0548 0.0575

10 rows × 22 columns

Plot PSPA logo motif

source

End