KinSwingR aims to predict kinase activity from phoshoproteomics data. It implements the alogorithm described in: Engholm-Keller et al. (2019) (in greater detail below). KinSwingR predicts kinase activity by integrating kinase-substrate predictions and the fold change and signficance of change for peptide sequences obtained from phospho-proteomics studies. The score is based on the network connectivity of kinase-substrate networks and is weighted for the number of substrates as well as the size of the local network. P-values are provided to assess the significance of the KinSwing scores, which are determined through random permuations of the overall kinase-substrate network.

KinSwingR is implemented as 3 core functions:

builds position weight matrices (PWMs) from known kinase-substrate sequences`buildPWM()`

score PWMs build using`scoreSequences()`

`buildPWM()`

against input phosphoproteome dataintegrates PWM scores, direction of phosphopeptide change and significance of phosphopeptide change into a “swing” score.`swing()`

The KinSwing score is a metric of kinase activity, ranging from positive to negative, and p-values are provided to determine significance.

Additional functions are also provided:

function to tidy annotations and extract peptide sequences.`cleanAnnotation()`

function to view PWM models`viewPWM()`

Detailed information for each of these functions can be accessed using the `?`

command before the function of interest. E.g. `?buildPWM`

We will now consider an example dataset to predict kinase activity. Kinase-substrate sequences and phosphoproteomics data are provided as example data in the KinSwingR package.

Begin by loading the KinSwingR library and the two data libraries included in the package.

```
library(KinSwingR)
data(example_phosphoproteome)
data(phosphositeplus_human)
# View the datasets:
head(example_phosphoproteome)
```

```
## annotation peptide fc pval
## 1 A0A096MJ61|NA|89|PRRVRNLSAVLAART NA -0.08377538 0.218815889
## 2 A0A096MJB0|Adcy9|1296|LDKASLGSDDGAQTK NA 0.03707147 0.751069301
## 3 A0A096MJB0|Adcy9|610|PRGQGTASPGSVSDL NA -0.06885408 0.594494965
## 4 A0A096MJB0|Adcy9|613|QGTASPGSVSDLAQT NA -0.29418446 0.002806832
## 5 A0A096MJN4|Sept4|49|ILEPRPQSPDLCDDD NA 0.09097982 0.078667811
## 6 A0A096MJN4|Sept4|81|FCPPAPLSPSSRPRS NA -0.12246661 0.078619010
```

```
## kinase substrate
## [1,] "EIF2AK1" "MILLSELSRRRIRSI"
## [2,] "EIF2AK1" "RILLSELSR______"
## [3,] "EIF2AK1" "IEGMILLSELSRRRI"
## [4,] "PRKCD" "MKKKDEGSYDLGKKP"
## [5,] "PRKCD" "FPLRKTASEPNLKVR"
## [6,] "PRKCD" "PLLARSPSTNRKYPP"
```

```
## sample 100 data points for demonstration
sample_data <- head(example_phosphoproteome, 1000)
# Random sample for demosntration purposes
set.seed(1234)
sample_pwm <- phosphositeplus_human[sample(nrow(phosphositeplus_human), 1000),]
# for visualising a motif, sample only CAMK2A
CAMK2A_example <- phosphositeplus_human[phosphositeplus_human[,1]== "CAMK2A",]
```

Where the centered peptide sequences (on the phosphosite of interest) are not provided in the format required for `scoreSequences()`

(see the argument “input_data”, in ?scoreSequences), these can be required to be extracted from another column of annotated data. NB. “input_data” table format must contain columns for “annotation”, “peptide”, “fold-change” and “p-values”.

In the example dataset provided, `example_phosphoproteome`

, peptides have not been extracted into a stand-a-lone peptide column. `cleanAnnotation()`

is provided as a function to extract peptides from annotation columns and place into the peptide column.

In the example dataset, `example_phosphoproteome`

, the peptide sequence is the 4th component of the annotation, which corresponds to using the argument `seq_number = 4`

below, and is seperated by `|`

, which corresponds to the argument `annotation_delimiter = "|"`

. In this case, the annotated data also contains multi-mapped and multi-site information. For example the following annotation `A1L1I3|Numbl|263;270|PAQPGHVSPTPATTS;SPTPATTSPGEKGEA`

contains two peptides `PAQPGHVSPTPATTS`

and `SPTPATTSPGEKGEA`

that map to different sites from the same reference gene `Numbl`

, where the peptides are seperated by `;`

. The annotated data also includes multi-protein mapped (where a peptide could map to more than one protein - not shown) and contains `X`

instead of `_`

to indicate sequences that were outside of the length of the coding sequences. KinSwingR requires that these sequences outside of the coding region are marked with `_`

as deafult and therefore `replace_search = "X"`

and `replace_with = "_"`

can be used as arguments in `cleanAnnotation()`

to replace these. This allows for full flexibility of the input data here, depending of the software used to generate determine the peptide sequences. NB: characters other than `_`

can be used, but these need to be declared when calling buildPWM and scoreSequences functions later (see their help files).

Calling `cleanAnnotation()`

will produce a new table with the unique combinations of peptide sequences extracted from the annotation column into the peptide column:

```
annotated_data <- cleanAnnotation(input_data = sample_data,
annotation_delimiter = "|",
multi_protein_delimiter = ":",
multi_site_delimiter = ";",
seq_number = 4,
replace = TRUE,
replace_search = "X",
replace_with = "_")
head(annotated_data)
```

```
## annotation peptide fc pval
## 1 A0A096MJ61|NA|89|PRRVRNLSAVLAART PRRVRNLSAVLAART -0.08377538 0.218815889
## 2 A0A096MJB0|Adcy9|1296|LDKASLGSDDGAQTK LDKASLGSDDGAQTK 0.03707147 0.751069301
## 3 A0A096MJB0|Adcy9|610|PRGQGTASPGSVSDL PRGQGTASPGSVSDL -0.06885408 0.594494965
## 4 A0A096MJB0|Adcy9|613|QGTASPGSVSDLAQT QGTASPGSVSDLAQT -0.29418446 0.002806832
## 5 A0A096MJN4|Sept4|49|ILEPRPQSPDLCDDD ILEPRPQSPDLCDDD 0.09097982 0.078667811
## 6 A0A096MJN4|Sept4|81|FCPPAPLSPSSRPRS FCPPAPLSPSSRPRS -0.12246661 0.078619010
```

The first step to inferring kinase activity, is to build Position Weight Matrices (PWMs) for kinases. This can be done using `buildPWM()`

for any table containing centered substrate peptide sequences for a list of kinases. The example data `data(phosphositeplus_human)`

indicates the required format for building PWM models. Below, for demosntration, we use a subset that was sampled above `sample_pwm`

To generate the PWMs:

This will build the PWM models, accessible as `PWM$pwm`

and list the number of substrate sequences used to build each PWM, accesible as `PWM$kinase`

.

To view the list of kinases and the number of sequences used:

```
## kinase n
## 1 PLK1 23
## 7 CSNK2A1 60
## 8 MAPK8 21
## 9 AURKA 12
## 10 MAPK3 27
## 11 PRKACA 62
```

Motif amino acids are coloured according to their properties. `color_scheme`

parameter allows options are “lesk” or “shapely” (default). Y-axis is the information content, measured as bits.

Next, we will use the PWM models generated, `pwms`

, to identify matches in the `annotated_data`

table that was cleaned using `cleanAnnotation()`

above. ``scoreSequences`supports multi-core processing - see the example below for setting the number of workers to 4.`

scoreSequences`draws a random background by default of size`

n = 1000`. It is recommended to use`

set.seed()`prior to calling`

scoreSequences`if you wish to reproduce your results. To access the help file, which explains all the arguments, type`

?scoreSequences``` into the console.

```
# As an example of control over multi-core processing
# load BiocParallel library
library(BiocParallel)
# finally set/register the number of cores to use
register(SnowParam(workers = 4))
# set seed for reproducible results
set.seed(1234)
scores <- scoreSequences(input_data = annotated_data,
pwm_in = pwms,
n = 100)
```

The outputs of `scores`

are transparent and accessible. These are however primarily intermediate tables for obtaining swing scores. `scores`

is a simple list object that contains peptide scores `(scores$peptide_scores)`

, p-values for the peptide scores `(scores$peptide_p)`

and the background peptides used to score significance `(scores$background)`

for reproducibility (i.e. the background can saved and reused for reproducibility).

In summary, `scoreSequences()`

scores each input sequence for a match against all PWMs provided using ``buildPWM()`

and generates p-values for scores. This is effectively one large network of kinase-substrate edges of dimensions kinase, ** k**, by substrate,

Having built a kinase-substrate network, `swing()`

then integrates the kinase-substrate predictions, directionality and significance of phosphopeptide fold change to assess local connectivity (or swing) of kinase-substrate networks. The final score is a normalised score of predicted kinase activity that is weighted for the number of substrates used in the PWM model and number of peptides in the local kinase-substrate network. By default, this will permute the network 1000 times (here we use 10 for example purposes). It is recommended to use `set.seed()`

prior to calling `swing`

if you wish to reproduce your results. ``swing``` supports multi-core processing - see the example below for setting the number of workers to 4.

```
# after loading BiocParallel library, set/register the number of cores to use
register(SnowParam(workers = 4))
# set seed for reproducible results
set.seed(1234)
swing_out <- swing(input_data = annotated_data,
pwm_in = pwms,
pwm_scores = scores,
permutations = 10)
# This will produce two tables, one is a network for use with e.g. Cytoscape and the other is the scores. To access the scores:
head(swing_out$scores)
```

```
## kinase pos neg all pk nk swing_raw n swing p_greater
## 2 AKT1 4 1 5 0.8000000 0.2000000 19.726764 19 1.6151652 0.09090909
## 5 AURKB 4 1 5 0.8000000 0.2000000 15.426556 10 1.2855635 0.09090909
## 10 CHEK1 3 1 4 0.7500000 0.2500000 11.364062 12 0.9741821 0.18181818
## 12 CSNK2A1 4 4 8 0.5000000 0.5000000 0.000000 60 0.1031511 0.18181818
## 4 AURKA 4 2 6 0.6666667 0.3333333 9.266994 12 0.8134463 0.27272727
## 6 CAMK2A 4 3 7 0.5714286 0.4285714 4.660630 16 0.4603784 0.27272727
## p_less
## 2 1.0000000
## 5 0.9090909
## 10 0.9090909
## 12 0.6363636
## 4 0.8181818
## 6 0.8181818
```

The outputs of this table indicate the following:

`kinase`

: The kinase`pos`

: Number ofregulated kinase substrates*positively*`neg`

: Number ofregulated kinase substrates*negatively*`all`

: Total number of regulated kinase substrates`pk`

: Proportion ofregulated kinase substrates*positively*`nk`

: Proportion ofregulated kinase substrates*negatively*`swing_raw`

: Raw - weighted score`n`

: Number of subtrate sequence in`kinase`

PWM`swing`

: Normalised (Z-score transformed) - weighted score`p_greater`

: probability of observing a swing score greater than`p_less`

: probability of observing a swing score less than

Note that the `pos`

, `neg`

and `all`

include a pseudo-count, that is set in `?swing`

, note `pseudo_count`

.

*** See Engholm-Keller et al. (2019) for methods description ***

*** For a full description of the KinSwing algorithm, see Engholm-Keller et al. (2019) ***

**In brief:**

`buildPWM()`

generates Position Weight Matrices (PWMs) for kinases based on known substrate sequence (Equation 1), where each kinase, \(K\), is considered as the log-likelihood ratio of the average frequency of amino acid, \(a\), at each position, \(p\), divided by background frequencies, \(B\) (\(C\) is a pseudo count to avoid log zero):

** Equation 1:** \(PWM_{(a,p)}=log((1/n∑^n_{i=1}K_i)+C)/B_a+C)\)

`scoreSequences()`

scores each kinase, \(K\), match to a substrate \(S\), given as \(S_{score}=∑^n_{(i=1)}f(a,p)\) , which corresponds to the sum of the corresponding amino acid, \(a\), of peptide sequence length, \(i\), from position, \(p\), of \(PWM_{(a,p)}\) and \(f(a,p)=PWM_{ap}∈PWM_{(a,p)}\). The probability of observing \(S_score\) for kinase, \(K\), is determined as conditional on a randomly sampled reference distribution of size \(N\) sequences \(P(S_{score}|R,N)\), where \(R\) sequences are determined to have a test statistic less than or equal to \(S_{score}\):

** Equation 2:** \(R= ∑^N_{n=1}I((S_{score})n* ≥ (S_{score})i)\)

`swing()`

integrates phosphosite data and kinase-substrate scores from `scoreSequences()`

into a network for scoring kinase activity based on local connectivity, \(swing_k\), (Equation 3). \(swing_k\) is the weighted product of the proportion of positive, \(Pos_k\), and negative, \(Neg_k\), network edges, determined as the product of a logic function (described here: Engholm-Keller et al. (2019)) given a local network of size, \(C_k\), with \(n\) substrates for kinase, \(K\):

** Equation 3:** \(swing_k=log_2((Pos_k+c)/(Neg_k+c))*log_2(C_k)*log_2(S_n)\)

\(swing_k\), is transformed into a z-score, \(Z(swing_k)\), where, \(μ\), is the mean and, \(σ\), the standard deviation of swing scores, thus allowing for comparison of predicted kinase activity across multiple timepoints and/or conditions.

KinSwingR addresses the question of “how likely is it is observe the predicted activity of kinase, \(K\), by random chance?” by computing \(swing_k\) given \(N\) permutations of kinase node labels, \(K\), to substrates, \(S\), of the total network, \(M_{ks}\). Thus, the probability of observing \(swing_k\) is conditional on this permuted reference distribution, of size, \(N\) (Equation 2). This is computed for each tail of the distribution, that is, positive and negative \(swing_k\) scores.

Engholm-Keller, K*, AJ* Waardenberg, JA Müller, JR Wark, RN Fernando, JA Arthur, PJ Robinson, D Dietrich, S Schoch, and ME Graham. 2019. “The Temporal Profile of Activity-Dependent Presynaptic Phospho-Signalling Reveals Long Lasting Patterns of Post-Stimulus Regulation,” March. PloS Biology. https://doi.org/10.1371/journal.pbio.3000170.