# Is Subcellular Localization Informative for Modeling Protein-Protein Interaction Signal?

Authors: Junfeng Liu; Hongyu Zhao; Jun Tan; Dajie Luo; Weichuan Yu; E. James Harner; Weichung Joe Shih
Journal: Research Letters in Signal Processing
 (2008)

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## Abstract

Statistical methods have been intensively applied in genomic signal processing
(Dougherty et al. 2005). For budding yeastSaccharomyces
cerevisiae with around 6000 proteins, genome-wide
protein-protein-interaction (PPI) (Fromont-Racine et al. 2000, Ito
et al. 2001, Newman et al. 2000, and Uetz et al. 2000 among
others) and protein subcellular localization (PSL) (Huh et al.
2003) data recently became available and for the latter the
presence of 4152 proteins is experimentally tested in each of the
22 subcellular compartments. Recent work shows that multiple
biological sources are helpful for both PSL and PPI predictions,
and this paper studies statistical feasibility of modeling PPI
from PSL since PSLs may play different marginal or joint roles in
the complex regulatory network. However, our results indicate that
PSL may be controversial for this purpose as an independent
source.


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## Body

## 1. Statistical Methods

### 1.1. Two-Way PPI Count Contingency Table

We extracted 2712 PPIs from MIPS [1]
which were available at http://hto-b.usc.edu/~msms/AssessInteraction/MIPSMatchYPD.txt
as of 2005 and used by Lin and Zhao [2] for PPI network robustness study. We
use 1641 PPIs with complete PSL information in Huh et al. [3], for example,
protein A has a
22-dimensional PSL vector L˜A=(LA,1,LA,2,…,LA,22), where LA,i=1 represents
presence of protein A at PSL i and LA,i=0 represents absence of protein A at PSL i. For proteins A and B, we create 44-dimensional PSL vector L˜AB (L˜A, L˜B) along with an
exchanged counterpart L˜BA (L˜B, L˜A) for naive
balance. Since log-linear model with large number (244) of
cross-classified cells may lack power where the total PPI count is relatively
small (<10 000), we
instead explore an alternative two-way (222) contingency
table whose rows (compartments: i=1,…,22) and columns
(compartments: j=1,…,22) jointly
assign each PPI into cell (i,j) with one
protein in compartment i and the other
one in compartment j (i,j=1,2,…,22) (Figure 1). Note that one PPI may be redundantly counted due to
multiple PSL occupation. Cytoplasm and nucleus likely play crucial roles since
these two compartments hold most PPI entries and other compartment pairs have
much less entries. Negative binomial model avoids overdispersion and shows ER
to Golgi, lipid particle and nucleus may be significant effects for this
two-way contingency table.Pseudoimages for two-way PPI count contingency table by combining pairwise
PSLs (Section1.1). The left panel includes cytoplasm and nucleus and the right
panel excludes cytoplasm and nucleus. From left (bottom) to right (top) on the
x(y)-axis: compartments [1:22].
(a)(b)


### 1.2. PSL Correlation Pattern

For 44-dimensional joined PSL vectors we calculate allC442+C441(=990) pairwise
Pearson correlation coefficients(1)Corr(L˜AB,L˜AB)=[Corr(L˜A,L˜A),Corr(L˜A,L˜B)Corr(L˜B,L˜A),Corr(L˜B,L˜B)]. This
calculation was carried over to the following four disjoint sets of protein pairs:
(1) interacting protein pairs from PPIs (set [1]), (2) non-PPI protein pairs
from those  proteins with PPI (set [2]), (3) non-PPI protein pairs from those
proteins without PPI (set [3]), and (4) non-PPI protein pairs from combining
protein without PPI and protein with PPI (set [4]). As in Section 1.1, by
selecting those PPIs (MIPS) with PSL information (Huh et al. [3]), we obtained
2883 proteins without PPI, 3282 exchanging PSL vectors for (set [1]), 1 591 338
exchanging PSL vectors for (set [2]), 8 308 806 exchanging PSL vectors for (set [3]) and 7 317 054 exchanging PSL vectors for (set [4]). 30% of non-PPI protein
pairs and 69% of PPI protein pairs have colocalization, thus 31% of PPIs may be
transient. The pseudoimages and contour plots for PSL correlations (1) are
given in Figure 2, where the upper-left quadrat in panel 1 shows significant
between-protein colocalization pattern for (set [1]) and no clear colocalization
pattern occurs for between-protein PSLs for (sets [2,3,4]). These observations
motivate us to study if between-protein PSL pattern could potentially
discriminate between protein pairs with PPI and those without PPI.Correlation pseudoimages and contour plots for PPIs (set [1]: panel 1) and
non-PPIs (sets [2,3,4], panels 2, 3, 4). From left (bottom) to right (top) on thex(y)-axis in each panel: compartments [1:22] for protein A(B).
(a)(b)(c)(d)(e)(f)(g)(h)


### 1.3. Retrospective Logistic Regression

We propose a realistic model for quantifying PPI
tendency from fused PSLs of proteinsA and B (with exchanging). The PSL and PPI
information is expressed as(2)(LA,1,LA,2,…,LA,22,LB,1,LB,2,…,LB,22)∼IAB,(LB,1,LB,2,…,LB,22,LA,1,LA,2,…,LA,22)∼IBA, where IAB(=IBA) is the binary
PPI indicator (response) and the logistic regression model is proposed to be
logit
(3)Pr⁡(PPI∣A,B)=β0+∑i=122βi(LA,i+LB,i)+∑i<jβij(LA,iLA,j+LB,iLB,j)+∑i≤jβij'(LA,iLB,j+LB,iLA,j), where β0 and βi imply default
PPI probability and PPI tendency of single protein with PSL i, βij, and βij' represent PPI
tendency of single protein with PSLs i and j and two
proteins with PSLs i and j, respectively, where i=j describes PPI
tendency of two proteins with common PSL i. The number of model parameters is 1+2C221+2C222=507. For
efficiency we consider a reduced model β0+∑i≤jβij'(LA,iLB,j+LB,iLA,j) which incorporates second-order PSL effects between two proteins. The yeast
interactome and proteome are inherent libraries and not subject to arbitrary
experimental design, which indicates a retrospective (case-control) study. On
the other hand, we have ∼18×106 total protein
pairs and only ∼2×103 PPIs in our
data. In order to overcome computer memory limitation and achieve reasonable
sample sizes for both case (PPI) and control (non-PPI) groups, we need to
select out a sample subset under statistical justification. For logistic model
with responses yis and
predictors xis, we let Zi indicate
whether subject i is selected and
assume ρ1=Pr⁡(Zi=1∣yi=1) and ρ0=Pr⁡(Zi=1∣yi=0), both of them
are free of xi. If the logistic model based on all subjects has
logit (Pr⁡(yi=1∣xi))=α+βxi, then the retrospective logistic regression (RLR)
after selection probability adjustment would be logit (Pr⁡(yi=1∣xi,zi=1))=α+log⁡(ρ1/ρ0)+βxi (Chapter 4.3.3,
McCullagh and Nelder [4]). We apply case selection probability 1 and control
selection probability 2×10−3 (3282 PPIs, 38
338 entries and 254 parameters) and identify around 60 significant effects. The
resultant prospective PPI probabilities are to be adjusted based on foregoing
theory.


### 1.4. PPI Prediction from PSL

After fitting the preceding model, we apply certain
thresholdτ to the simple classification rule(4)Pr⁡(PPI∣L˜ABorL˜BA)>τ⇒PPI,Pr⁡(PPI∣L˜ABorL˜BA)≤τ⇒non-PPI. We randomly divide the whole dataset for retrospective study into 10 disjoint portions.
Each portion (includes PPIs and non-PPIs in proportion) acts as one testing set
and the other nine portions are combined into one training set for 10-fold
cross validation. We classify each protein-protein pair in the testing set into
PPI or non-PPI by comparing the calculated probabilities (from trained model
parameters) with some threshold τ. We find that PPI probability median of the non-PPI
subset in the training set is always equal to that of the PPI subset in the
training set and the PPI probability median (1.88×10−4) for PPI
subset also equals that of non-PPI subset for the whole dataset in
retrospective study. For retrospective study with PPI probability median
threshold, we have specificity around 98% and sensitivity around 15%,
RandomForest Breiman [5] in R reaches specificity around 99% and
sensitivity around 20% and support vector machine (SVM) in R reaches
specificity around 50% and sensitivity around 90%. The PPI probabilities from
retrospective study dataset and 10-fold cross-validation are plotted in Figure 3. The logistic model-based classification results are found to be sensitive to
threshold. If we use “Pr⁡(PPI∣L˜ABorL˜BA)≥τ⇒PPI” and “Pr⁡(PPI∣L˜ABorL˜BA)<τ⇒non-PPI”, where τ equals PPI
probability median, then we obtained very different classification results.
After prospective PPI probability adjustment, the threshold-based
classification (4) is applied to the complete PPI and PSL data ([Sets 1,2,3,4], Section 1.2) and the resultant ROC curve is given in Figure 4 with
area under curve (AUC) less than 0.5. Since we may simply invert this classifier
to make AUC greater than 0.5, Figure 4 indicates that the proposed logistic
regression model ((3) in Section 1.3) may not be highly sufficient even if this
model is carefully chosen. We also observe the following facts: selection
procedure in retrospective study may involve some bias, the joined PSL patterns
(from two proteins) are finite with uncertain overlap between PPI set and
non-PPI set, false positives and false negatives may exist in both PPI and PSL
data and others. From statistical point of view, interprotein PSL pattern may
not independently determine PPI tendency, and threshold-based PPI prediction
rule may not discriminate PPI from non-PPI either. The former conclusion is
also a major concern from biologists who consider PPI mechanism far beyond only
PSL information.(Top panel) PPI probabilities from retrospective study. (Lower panel) PPI
probabilities from 10-fold cross-validation (after prospective adjustment),
each pair of consecutive boxplots is for individual testing set where PPI
subset follows non-PPI subset.
(a)(b)Figure 4
ROC (∇ connection)
based on prospective PPI probability (adjusted from retrospective study)
threshold-based classification.


## 1.1. Two-Way PPI Count Contingency Table

We extracted 2712 PPIs from MIPS [1]
which were available at http://hto-b.usc.edu/~msms/AssessInteraction/MIPSMatchYPD.txt
as of 2005 and used by Lin and Zhao [2] for PPI network robustness study. We
use 1641 PPIs with complete PSL information in Huh et al. [3], for example,
protein A has a
22-dimensional PSL vector L˜A=(LA,1,LA,2,…,LA,22), where LA,i=1 represents
presence of protein A at PSL i and LA,i=0 represents absence of protein A at PSL i. For proteins A and B, we create 44-dimensional PSL vector L˜AB (L˜A, L˜B) along with an
exchanged counterpart L˜BA (L˜B, L˜A) for naive
balance. Since log-linear model with large number (244) of
cross-classified cells may lack power where the total PPI count is relatively
small (<10 000), we
instead explore an alternative two-way (222) contingency
table whose rows (compartments: i=1,…,22) and columns
(compartments: j=1,…,22) jointly
assign each PPI into cell (i,j) with one
protein in compartment i and the other
one in compartment j (i,j=1,2,…,22) (Figure 1). Note that one PPI may be redundantly counted due to
multiple PSL occupation. Cytoplasm and nucleus likely play crucial roles since
these two compartments hold most PPI entries and other compartment pairs have
much less entries. Negative binomial model avoids overdispersion and shows ER
to Golgi, lipid particle and nucleus may be significant effects for this
two-way contingency table.Pseudoimages for two-way PPI count contingency table by combining pairwise
PSLs (Section1.1). The left panel includes cytoplasm and nucleus and the right
panel excludes cytoplasm and nucleus. From left (bottom) to right (top) on the
x(y)-axis: compartments [1:22].
(a)(b)


## 1.2. PSL Correlation Pattern

For 44-dimensional joined PSL vectors we calculate allC442+C441(=990) pairwise
Pearson correlation coefficients(1)Corr(L˜AB,L˜AB)=[Corr(L˜A,L˜A),Corr(L˜A,L˜B)Corr(L˜B,L˜A),Corr(L˜B,L˜B)]. This
calculation was carried over to the following four disjoint sets of protein pairs:
(1) interacting protein pairs from PPIs (set [1]), (2) non-PPI protein pairs
from those  proteins with PPI (set [2]), (3) non-PPI protein pairs from those
proteins without PPI (set [3]), and (4) non-PPI protein pairs from combining
protein without PPI and protein with PPI (set [4]). As in Section 1.1, by
selecting those PPIs (MIPS) with PSL information (Huh et al. [3]), we obtained
2883 proteins without PPI, 3282 exchanging PSL vectors for (set [1]), 1 591 338
exchanging PSL vectors for (set [2]), 8 308 806 exchanging PSL vectors for (set [3]) and 7 317 054 exchanging PSL vectors for (set [4]). 30% of non-PPI protein
pairs and 69% of PPI protein pairs have colocalization, thus 31% of PPIs may be
transient. The pseudoimages and contour plots for PSL correlations (1) are
given in Figure 2, where the upper-left quadrat in panel 1 shows significant
between-protein colocalization pattern for (set [1]) and no clear colocalization
pattern occurs for between-protein PSLs for (sets [2,3,4]). These observations
motivate us to study if between-protein PSL pattern could potentially
discriminate between protein pairs with PPI and those without PPI.Correlation pseudoimages and contour plots for PPIs (set [1]: panel 1) and
non-PPIs (sets [2,3,4], panels 2, 3, 4). From left (bottom) to right (top) on thex(y)-axis in each panel: compartments [1:22] for protein A(B).
(a)(b)(c)(d)(e)(f)(g)(h)


## 1.3. Retrospective Logistic Regression

We propose a realistic model for quantifying PPI
tendency from fused PSLs of proteinsA and B (with exchanging). The PSL and PPI
information is expressed as(2)(LA,1,LA,2,…,LA,22,LB,1,LB,2,…,LB,22)∼IAB,(LB,1,LB,2,…,LB,22,LA,1,LA,2,…,LA,22)∼IBA, where IAB(=IBA) is the binary
PPI indicator (response) and the logistic regression model is proposed to be
logit
(3)Pr⁡(PPI∣A,B)=β0+∑i=122βi(LA,i+LB,i)+∑i<jβij(LA,iLA,j+LB,iLB,j)+∑i≤jβij'(LA,iLB,j+LB,iLA,j), where β0 and βi imply default
PPI probability and PPI tendency of single protein with PSL i, βij, and βij' represent PPI
tendency of single protein with PSLs i and j and two
proteins with PSLs i and j, respectively, where i=j describes PPI
tendency of two proteins with common PSL i. The number of model parameters is 1+2C221+2C222=507. For
efficiency we consider a reduced model β0+∑i≤jβij'(LA,iLB,j+LB,iLA,j) which incorporates second-order PSL effects between two proteins. The yeast
interactome and proteome are inherent libraries and not subject to arbitrary
experimental design, which indicates a retrospective (case-control) study. On
the other hand, we have ∼18×106 total protein
pairs and only ∼2×103 PPIs in our
data. In order to overcome computer memory limitation and achieve reasonable
sample sizes for both case (PPI) and control (non-PPI) groups, we need to
select out a sample subset under statistical justification. For logistic model
with responses yis and
predictors xis, we let Zi indicate
whether subject i is selected and
assume ρ1=Pr⁡(Zi=1∣yi=1) and ρ0=Pr⁡(Zi=1∣yi=0), both of them
are free of xi. If the logistic model based on all subjects has
logit (Pr⁡(yi=1∣xi))=α+βxi, then the retrospective logistic regression (RLR)
after selection probability adjustment would be logit (Pr⁡(yi=1∣xi,zi=1))=α+log⁡(ρ1/ρ0)+βxi (Chapter 4.3.3,
McCullagh and Nelder [4]). We apply case selection probability 1 and control
selection probability 2×10−3 (3282 PPIs, 38
338 entries and 254 parameters) and identify around 60 significant effects. The
resultant prospective PPI probabilities are to be adjusted based on foregoing
theory.


## 1.4. PPI Prediction from PSL

After fitting the preceding model, we apply certain
thresholdτ to the simple classification rule(4)Pr⁡(PPI∣L˜ABorL˜BA)>τ⇒PPI,Pr⁡(PPI∣L˜ABorL˜BA)≤τ⇒non-PPI. We randomly divide the whole dataset for retrospective study into 10 disjoint portions.
Each portion (includes PPIs and non-PPIs in proportion) acts as one testing set
and the other nine portions are combined into one training set for 10-fold
cross validation. We classify each protein-protein pair in the testing set into
PPI or non-PPI by comparing the calculated probabilities (from trained model
parameters) with some threshold τ. We find that PPI probability median of the non-PPI
subset in the training set is always equal to that of the PPI subset in the
training set and the PPI probability median (1.88×10−4) for PPI
subset also equals that of non-PPI subset for the whole dataset in
retrospective study. For retrospective study with PPI probability median
threshold, we have specificity around 98% and sensitivity around 15%,
RandomForest Breiman [5] in R reaches specificity around 99% and
sensitivity around 20% and support vector machine (SVM) in R reaches
specificity around 50% and sensitivity around 90%. The PPI probabilities from
retrospective study dataset and 10-fold cross-validation are plotted in Figure 3. The logistic model-based classification results are found to be sensitive to
threshold. If we use “Pr⁡(PPI∣L˜ABorL˜BA)≥τ⇒PPI” and “Pr⁡(PPI∣L˜ABorL˜BA)<τ⇒non-PPI”, where τ equals PPI
probability median, then we obtained very different classification results.
After prospective PPI probability adjustment, the threshold-based
classification (4) is applied to the complete PPI and PSL data ([Sets 1,2,3,4], Section 1.2) and the resultant ROC curve is given in Figure 4 with
area under curve (AUC) less than 0.5. Since we may simply invert this classifier
to make AUC greater than 0.5, Figure 4 indicates that the proposed logistic
regression model ((3) in Section 1.3) may not be highly sufficient even if this
model is carefully chosen. We also observe the following facts: selection
procedure in retrospective study may involve some bias, the joined PSL patterns
(from two proteins) are finite with uncertain overlap between PPI set and
non-PPI set, false positives and false negatives may exist in both PPI and PSL
data and others. From statistical point of view, interprotein PSL pattern may
not independently determine PPI tendency, and threshold-based PPI prediction
rule may not discriminate PPI from non-PPI either. The former conclusion is
also a major concern from biologists who consider PPI mechanism far beyond only
PSL information.(Top panel) PPI probabilities from retrospective study. (Lower panel) PPI
probabilities from 10-fold cross-validation (after prospective adjustment),
each pair of consecutive boxplots is for individual testing set where PPI
subset follows non-PPI subset.
(a)(b)Figure 4
ROC (∇ connection)
based on prospective PPI probability (adjusted from retrospective study)
threshold-based classification.


## 2. Discussion

In this article, we proposed statistical analysis of
the association between PPI and PSL with the possibility of offering clues for
further specific biological experiments. The aforementioned model is only one
possible approach out of many helpful tries. It is likely that a totally
different approach based on PSL information may lead to disparate results. As
an alternative, if we could describe the distribution of 44-dimensional joined
binary PSL vectors given PPI or non-PPI:Pr⁡(L˜AB∣PPI) and Pr⁡(L˜AB∣non-PPI), then armed with some prior PPI probability, say Pr⁡(PPI)=3:(1.8×104), we can
predict PPI probability for joined PSL pattern L˜AB by Bayes rule(5)Pr⁡(PPI∣L˜AB)=Pr⁡(L˜AB∣PPI)Pr(PPI)Q, where Q=Pr(L˜AB∣PPI)Pr(PPI)+Pr(L˜AB∣non-PPI)Pr(non-PPI). Section 1.2 is
essentially an attempt to work on either the PPI or non-PPI set to study PSL
pattern without considering the non-PPI or PPI counterpart, which may be only a
matter of exploring Pr⁡(L˜AB∣PPI) or Pr⁡(L˜AB∣non-PPI) separately.
However, the explicit probability of high-dimensional binary vector is
difficult to be constructed. Empirical approaches (Sections 1.1 and 1.2, Huh et
al. [3]) offer informative results from different perspectives. On the other
hand, Liu et al. [6] modeled PPI based on domain-domain interaction
information and computational PSL prediction from other sources which are also
feasible, the readers are referred to Lu et al. [7], Szafron et al. [8],
Höglund et al. [9], Horton et al. [10], Guda [11], Yu et al. [12], and Zhang
et al. [13, 14] among many others.



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*Source: 365152-2008-02-28.xml*