3. Kinase Analysis
Introduction to Upstream Kinase Analysis
Kinase prediction (Upstream Kinase Analysis, UKA) is the main output of PamGene analysis.
UKA predicts upstream kinases explaining coordinated changes across kinase-associated phosphosite sets (it is a functional class scoring method*). The UKA relies on public databases of kinase–to–phosphosite relationships to score kinases, indicating how strongly a kinase is associated with the observed changes in peptide signal.
The UKA is run on all peptides after QC — not only significant peptides.
Output: kinases changed between two conditions (T vs C): LFC & Significance
Visualizations:
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Dotplot (see below)
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Volcano
* Another functional class scoring method is GSEA, Gene Set Enrichment Analysis. For GSEA, a pathway is considered a functional class of members - in UKA, a kinase is considered as a functional class of phosphosites.
The UKA Algorithm in a Nutshell
- Calculate Kinase FC from the FCs of its phosphosites.
- Significance score: permute samples 500 times and recalculate kinase FC. This gives the probability that the observed kinase FC could not have been obtained from random samples. This tells: “Is this kinase signal reliably different?”
- Specificity score: permute phosphosites and recalculate kinase FC. This gives the probability that the observed FC could not have been obtained from a random peptide set. This tells: _“Is this kinase specifically responsible for these phosphorylation changes?”
- Final score = Significance Score + Specificity Score
| Score | Permutation | High score means | Comments |
|---|---|---|---|
| Significance | Samples | High probability that the kinase FC is not due to sample noise. | Can be biased toward promiscuous kinases or abundant activity. With a limited number of replicates (such as n=3), the statistical power is relatively low, which can make the significance score less robust and more prone to variability. In addition, it tends to favour kinases that act on many substrates. These “hub” kinases (like MAPKs or CDKs) often rank high simply because they affect a large number of peptides.. |
| Specificity | Phosphosites | High probability that the kinase FC is not due to a random peptide set. Accounts for overlap of substrates between kinases | This is the most important score. It helps identify kinases whose activity is more likely to specifically explain the data, rather than those that are broadly active. |
Permutation Test Results
The UKA dotplot
The Kinase dotplots show the specificity and Fold Change of the significant kinases in different comparisons. Larger dots indicate higher specificity. The kinases are clustered by families.
The UKA Table
Most important columns:
| Sgroup_contrast | Kinase Name | (Median) Kinase Statistic | (Mean) Significance Score | (Mean) Specificity Score | (Median) Final Score |
|---|---|---|---|---|---|
| Sgroup1_T vs C | ROR1 | 1.06 | 0.97 | 1.34 | 2.31 |
| Sgroup1_T vs C | MAP2K3 | 0.77 | 0.52 | 1.01 | 1.53 |
| Sgroup1_T vs C | MAP2K6 | 0.77 | 0.52 | 1.01 | 1.53 |
Usage:
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Use the Kinase Statistic as a proxy for LFC between T vs C.
- < 0 means inhibition, > 0 means activation.
- The Kinase statistic is signal-to-noise ratio: the LFC scaled by noise. This is more relevant than simple LFC for predicted data. (Median Kinase Change is the actual LFC.)
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To find significant results, set a cutoff on Specificity Score. We suggest > 1 (p<0.1) or 1.3 (p<0.05)
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If you are using the UKA algorithm, scores are Mean or Median because the algorithm considers multiple peptide sets per kinase (of varying size based on interaction strength). The confidence scoring UKA algorithm works differently and outputs scores without mean or median.
Additional columns:
- Peptide set size: Kinases with small peptide sets are usually more specific.
UKA vs csUKA: what are the differences?
- UKA algorithm (legacy, deprecated but supported)
- Confidence scoring UKA algorithm (csUKA): Confidence scoring is a newer algorithm compared to the UKA algorithm. The outputs of UKA and csUKA are equivalent with the same set of UKA databases, but csUKA has practical benefits.
Main differences between UKA and csUKA
- csUKA integrates evidence from multiple kinase–substrate databases more systematically. UKA scores (determines the strength of) kinase-substrate relationships based on rank-thresholds. csUKA offers more flexibility to score relationships: not only based on kinase ranks but also on different databases or kinase scores.
- csUKA accounts for peptide specificity. csUKA adjusts the contribution of a peptide depending on how specifically it points toward a particular kinase. This helps reduce the influence of peptides that can be associated with many kinases.
- csUKA algorithm is faster. Legacy UKA repeatedly evaluates different kinase–peptide sets using increasingly permissive rank cutoffs and then summarizes the resulting scores and the Kinase Statistic. (Summarizing via mean or median leads to the "Mean" part of the Specificity Score.) csUKA instead incorporates the information across ranks into one confidence-weighted kinase–substrate matrix.
csUKA and legacy UKA outputs are equivalent. Based on our evaluation across a large and diverse set of datasets, the results generated by csUKA are equivalent to those produced by the legacy UKA app. While individual scores may differ slightly due to methodological improvements, these differences are substantially smaller than the typical variability observed between experimental replicates.
Detailed steps of the UKA and csUKA algorithm
Step 1. Calculation of the Peptide Difference Statistic
This step is done in the same way between csUKA and UKA.
The Peptide Difference Statistic (Peptide Statistic) is calculated for each peptide comparing two conditions, using the \(\log_{2}\) kinase activity profiles measured on the chips.
The Peptide Statistic is the Signal to Noise Ratio (SNR) of the difference between the \(\log_{2}\) kinase activity profiles.
where \(p\) = Peptide Statistic, \(\overline{x}\) = mean \(\log_{2}\) kinase activity of \(T\) (Test) or \(C\) (Control) conditions, \(\sqrt{\sigma^{2}}\) = standard deviation of kinase activity of the two conditions.
A similar value that describes the peptide difference is the Peptide Change:
This is used to calculate the Kinase Change (see later).
Step 2. Construction of the UKAdb from public kinase-to-substrate databases
The main differences between csUKA and legacy UKA lie in how the UKAdb is constructed.
- Kinase-to-substrate data from public databases such as PhosphoNet and Kinase Library (KL) contain Kinase Ranks. For each substrate (peptide), the rank of the phosphorylating kinase is based on the likelihood of phosphorylation. Lower ranks mean that the kinase is more likely to phosphorylate the peptide. The first 12 kinases (ranks 0-12) per peptide are used.
- From the data, Kinase-to-Substrate matrices are constructed in different ways.
- The legacy UKA constructs multiple matrices based on Kinase Rank thresholds. Thus for each kinase, multiple peptide sets are considered – by decreasing the stringency of the cutoff, the size of the peptide set increases. The basic set includes the peptides of ranks 0 to 4 and subsequent peptide sets are formed by including the lower ranks from 5 to 12, one-by-one.
- The confidence scoring UKA constructs only 1 matrix. It synthetizes information using all Kinase Ranks in a transparent way. Additional to the legacy UKA, it does a correction for peptide specificity.
- The UKA algorithm combines the Kinase-to-Substrate matrix and the observed peptide signal to calculate the Kinase fold change and its significance (specificity and significance scores). The legacy UKA does this for each data matrix, and takes the mean / median of these scores (e.g. Mean Specificity Score).
csUKA has the following advantages:
- Central part under the hood is a Kinase-to-Substrate matrix with confidence values. The assignment of these confidence values is straightforward, transparent, and may be discussed based on a researchers' assessment of phosphorylation databases.
- It is straightforward to extend the approach to additional databases.
- Faster computation than legacy UKA, as no rank scanning is done.
Step2 / csUKA db construction
- Assigning confidence values for Kinase-Substrate Relations
First step is to assign probability-like confidence values \(p\) to kinase to substrate relations (KSR) based on entries found in various PTM databases. I.e. these values are assigned based on our belief about what a database entry means for the probability of a kinase phosphorylating a certain peptide on our chip.
The following confidence values are used:
| Database | Rank | p |
|---|---|---|
| in vitro, in vivo | 0 | 0.90 |
| PhosphoNET | 1–4 | 0.90 |
| PhosphoNET | 4–8 | 0.75 |
| PhosphoNET | 9–12 | 0.50 |
| Kinase Library | 1–12 | 0 or 0.30 |
KSR's that are not found in any of the databases: \(p_0\) = 0.
Note that this is open to discussion based on biological arguments, and easy to extent to additional databases and types of databases.
- Confidence values are combined, since a single KSR may appear in multiple databases.
For each KSR we may therefore obtain 1 to N confidence values: \(p1, p2, ..., pN\).
These are combined into a single confidence value \(p_c\) using:
\(1-p_c = min[1-p_0, \prod_{n=1}^{N}(1-p_n)]\)
Equivalently:
\(p_c = 1 - min[ 1 - p_0, (1 - p_1)(1 - p_2)...(1 - p_N) ]\)
This formulation treats different database entries as independent evidence and caps the combined confidence by the prior uncertainty defined by \(p_0\).
E.g. if a KSR appears in a in vivo/ in vitro database and with rank 6 in the PhosphoNET database, the combined confidence value is:
\(p_c = 1 - min[1-0, (1-0.9)(1-0.75)] = 0.975\)
- Normalization for Peptide Specificity.
Assume an experiment with P peptides mapping to K kinases.
We construct a P x K matrix M, where rows correspond to peptides, columns correspond to kinases and entries contain the combined confidence values \(p_c\).
We take the specificity of a peptide into account by normalizing each KSR using the probability that a given peptide is phosphorylated by any of the included kinases.
Hence, for the elements of M we have (dropping the subscript \(c\) of \(p_c\) for clarity):
\(m_{ij} = \displaystyle \frac{p_{ij}}{\sum_{h=1}^K p_{ih}}\)
, each element of M normalized using the corresponding row sum of M.
Relation to Bayesian stats
This formulation is motivated by Bayes’ rule. Let:
\(p(k | s)\) be the probability that kinase k has changed activity, given that substrate s has changed phosphorylation.
Bayes’ rule gives:
\(p(k|s) = \displaystyle \frac{p(s|k)}{\sum p(s|k)}.p(s)\)
Hence, matrix M elements \(m_{ij}\) correspond to the normalized prior of the KSR between peptide i and kinase j. The matrix represents the prior belief in KSRs.
Summary
The peptide–kinase confidence matrix provides a biologically interpretable way to relate peptides to upstream kinases. It combines evidence from multiple databases, accounts for peptide specificity, and has a clear Bayesian interpretation, making it a generic and extensible tool for kinase activity analysis.
Step 2 / legacy UKAdb construction
The kinase-to-peptide matrix, \(M\), is binarized where zeroes represent no connection between peptides and Upstream Kinases and ones represent a connection.
There is a connection (a peptide is enriched with an UK) if:
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the peptide has a match to a phosphosite for which the UK is found in an in vivo / in vitro database (Kinase rank designated as 0).
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the peptide has a match to a phosphosite for which the UK has a PhosphoNET (in silico database) 'Kinase Predictor V2 Score' > 300 and a rank less than or equal to a cut-off (see in the next section).
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For each kinase, different size of peptide sets are considered
In each analysis, multiple \(M\) matrices are calculated based on varying the Kinase rank cutoff. Thus for each kinase, multiple peptide sets are considered -- by decreasing the stringency of the cutoff, the size of the peptide set increases. The basic set includes the peptides of ranks 0 to 4 and subsequent peptide sets are formed by including the lower ranks from 5 to 12, one-by-one.
Step 3: Calculation of The Kinase Statistic and the Kinase Change
The Kinase Statistic represents the direction of effect: the change in kinase activity in a Test condition (T) compared to a Control condition (C). \< 0 means inhibition, > 0 means activation in T versus C.
The Kinase Statistic is the median of the Peptide Statistics of the set of peptides that a kinase can phosphorylate. Thus, the Kinase Statistic represents the log fold change scaled by the noise.
For each \(M\) matrix (for each peptide set per kinase), the normalized Kinase Statistic is calculated:
\(\mathbf{s = b\ *}\left( \mathbf{M}^{\mathbf{T}}\mathbf{p} \right)\)
\(\mathbf{b}_{\mathbf{i}}\mathbf{= 1/}\mathbf{a}_{\mathbf{i}}\), where
\(\mathbf{s}\): the Kinase Statistic is the weighted average of \(\mathbf{p}\), the peptide difference statistic. \(\mathbf{b}\) is a normalization vector, \(\mathbf{a}_{\mathbf{i}}\) is the number of nonzero elements in column \(i\) of \(M\) (the number of peptides that a kinase phosphorylates).
An example calculation:
Formulated in a different way: for kinase i,
For each peptide set considered for a kinase, the Kinase Statistic is calculated, and in the results, the Median Kinase Statistic across different peptide sets is given.
The Kinase Change is calculated similarly as the Kinase Statistic, but using the \(p_{change}\) values:
The Kinase Statistic, in contrast to Kinase Change, is a value that also describes the significance of the change, i.e. whether the change is higher than the noise.
Step 4. Calculation of Significance and Specificity scores
Significance score: permute samples 500 times and recalculate kinase FC. This gives the probability that the observed kinase FC could not have been obtained from random samples. This tells: “Is this kinase signal reliably different?”
Specificity score: permute phosphosites and recalculate kinase FC. This gives the probability that the observed FC could not have been obtained from a random peptide set. This tells: _“Is this kinase specifically responsible for these phosphorylation changes?”
Final score = Significance Score + Specificity Score
For legacy UKA, mean and median scores are calculated across the different peptide sets (different M matrices) considered for a kinase.