Predicting Combinatorial Protein-Protein Interactions from Protein Expression DataBased on Correlation Coefficient

Sho Murakami, Takuya Yoshihiro, Etsuko Inoue and Masaru Nakagawa

Faculty of Systems Engineering, Wakayama UniversityJCKBSE2010 KaunasJCKBSE2010KaunasWakayama University22AgendaBackgroundCombinatorial Protein-Protein InteractionsThe Proposed Data Mining MethodEvaluationConclusion

JCKBSE2010KaunasWakayama University2BackgroundFinding Interactions among genes/proteins are importantMany data-mining algorithms to discover gene-gene (or protein-protein) interactions are proposed so far. One of the main source is gene or protein expression data

3

2D Electorophoresisfor protein expressionMicroarrayfor gene expression)

Color strength is expression levelSize of spot is expression levelJCKBSE2010KaunasWakayama UniversityWe start with the background of this study. First of all, you know that finding interactions among genes or proteins are regarded as important to clarify the system of creatures. Many data-mining algorithms to discover gene-gene or protein-protein interactions are proposed so far. Here, one of the main source data is gene or protein expression data shown below. The left figure is called microarray which is the experiment to measure the expression level or each gene. The color strength of each spot is the expression level. The right figure is called 2d-electrophoresis which is an experiment to measure the expression level of proteins. Each black point represent one protein and the area of each black point represent the expression level of each protein.

3Related Work for Interaction DiscoveryBayesian NetworksDiscovering interactions from expression data based on conditional probability among events

4ACBAB

CEx. to discover protein-protein interactions among proteins A, B and C, 1. Define events A, B and C2. Compute conditional probability related with A, B and CsamplesEvent C is expressedIf high, Interaction ispredictedJCKBSE2010KaunasWakayama UniversityAs a related work for interaction discovery, a typical method would be a bayesian networks, Which dicovers interactions from expression data based on conditional probability among events. For example, to discover protein-protein interactions among proteins A, B and C, We first define events A, B and C, then, compute conditional probability related with A, B and C. See this figure. Those three circles represent the events that protein A, B and C is expressed. Then, regard those black points as samples which is placed somewhere in this venn-diagram. Then, we compute the conditional probability of the event C is expressed under the condition that Both A and B are expressed like this. If this value is high enough, then the interaction that A and B effect on the expression of C is predicted.

4Problems of Bayesian NetworksBayesian Networks Require large Number of SamplesFor gene: microarray supplies cheap and high-speed experimentFor protein: 2D-electrophoresis takes time and expensive5

ACBsufficient samplesin the area ?Many Samples are Necessary to obtain statistically reliable resultsABCex. to discover protein-protein interactions among proteins A, B and C, 1. Define events A, B and C2. Compute conditional probability related with A, B and CJCKBSE2010KaunasWakayama UniversityHowever, bayesian network has a problem that it requires large number of samples. Fortunately for gene, the microarray supplies cheap and high-speed experiment so that it is easy to prepare large number of samples. However, unfortunately for proteins, 2D-electrophoresis experiment takes time and expensive so that it is difficult to prepare large number of samples. The point is here, whether sufficient number of samples exist or not. You know so many samples are necessary to obtain statistically reliable results.

56The Objective of our studyFinding combinatorial protein-protein interactionsfrom small-size protein expression dataJCKBSE2010KaunasWakayama UniversityThen, here is the objective of our study. 677Expression Data2D-electrophoresis processed for each sample which includes expression levels of each protein. Expression levels: obtained by measuring size of areasAs pre-processing, normalization is applied

Each black area indicates a protein: size of areas represent expression levels

sample3

sample2

sample1ProteinsJCKBSE2010KaunasWakayama University7In this slide I talk about the expression data as a source data of our data mining method. This data is obtained by processing 2D-electrophoresis for each samples. It includes the expression level of every protein included in the sample. Look at the figure. As mentioned before, each black area indicates a protein which area is measured to obtain expression levels. Then, the data like this table is obtained. This is our source data from which we try to find combinatorial effects. 88Model of Protein-Protein Interaction ConsideredModel: two proteins A and B effect on other protein Cs expression level only when both A and B are expressedWe want to estimate the combinatorial Effect!ABCCABCEffect on expression levelsComplex of A and BABABABSole effect from A,B on C is usually consideredOnly If both A and B exist, Combinatorial effect works on C!JCKBSE2010KaunasWakayama UniversityWe first consider a model of protein-protein interactions to design the method. Look at this figure. Here there are two sole effect from A to C, and from B to C. This is normal effect among two proteins. Instead, we consider the effect of complex form of A and B on C. The blue arrow represents the effect of total effect from A and B on C. This effect includes two sole effects like this. And the difference is the effect which appears only if both A and B exist, and is called the combinatorial effect. In this work we want to estimate this combinatorial effect.

899Predicting Interactions by Correlation CoefficientComputing correlation coefficient of (A,B) and CCorrelation coefficient requires less number of samplesThe amount of complex (A,B) is estimated by min(A,B)Total effect on C will be high if correlation is highExpression levelABExpression level of A and Bof a sampleEstimated amount of complex of A and BCompute correlation of min(A,B) and CThis amount wouldEffect on Cmin(A,B)CJCKBSE2010KaunasWakayama UniversityIn this slide I talk about how to measure protein-protein interactions. The central idea to measure protein-protein interaction is to use correlation coefficient among A, B and C.Here, we assume that the amount of complex form (A, B) is estimated by minimum of the expression levels of A and B. Namely, the amount depends on the less protein of A and B. Then, we consider that the amount would effect on C, So, compute correlation coefficient of min(A,B) and C, and if this value is high, The combinatorial effect is predicted.

91010The problem of scale differenceAmount of expression level for 1 molecular is different among proteins, so the same amount of A and B not always combined.Therefore, taking min cannot express correct amount of complexExp.levelABProteins A and BEstimated number of complexABProteins A and BThe amount of complex is not correctTaking minleads correctamount of complexSolutioncorrect the scale of AScaling problem and solutionis the expression level required for a complexExp.levelJCKBSE2010KaunasWakayama University10But there are several problems in this idea. One of them is the problem of scale difference. See the figure. There are the expression levels of A and B, in which scale is not correct. Consider that the molecular size is this size and one molecular combines one other molecular. Then, the number of complex is estimated as one, it is not correct. The solution is to correct the scale of A. if we do so, taking minumum leads to correct amount of complex. How to correct the scale of A is the problem.

1111How to determine correct scale?Expression levelABk1Ak2Ak3AWe compute Score S: the total effect of (A, B) on CComputeCorrelationSelect the scale which leads the maximum correlation coefficient of min(A,B) and CIf interaction of our model exists, high correlation value must appear. min(A,B)min(A,B)min(A,B)min(A,B)Score SCorrelation0.1Correlation0.2Correlation0.3Correlation0.7JCKBSE2010KaunasWakayama UniversityThen I talk now how to determine the proper scale. The idea is a simple. It is to select the scale which leads the maximum correlation coefficient of min(A,B) and C. See the figure. We try various possible scale of A and for each trial we compute correlation coefficient of min(A,B) and C. If interaction of our model exists in this combination A, B and C, high and correct correlation value must appear somewhere. So, we select the scale of the maximum correlation coefficient as a correct scale, and define the maximum correlation coefficient as Score S. The score S is, as mentioned before, the total effect of A and B on C, From which we compute the combinatorial effect of A and B on C.

Estimating Combinatorial Effect from Score SScore S consists of Sole Effect and Combinatorial EffectCompute Score S: Score S assuming no combinatorial effectDifference between S and S is the level of Combinatorial Effect12Level of combinatorial effectBCAThe difference between score S and S is the combinatorial effectABCBCACAssuming no combinatorial EffectABCCScore SBCAScore SComputing Statistic Distribution JCKBSE2010KaunasWakayama UniversityThis slide describes how to estimate combinatorial effect from score S. As mentioned before, Score S consists of both sole effect and combinatorial effect.To estimate the combinatorial effect, we compute the statistic distribution of Score S, Which is the distribution of score S assuming that no combinatorial effect exist. Then, the difference between score S and score S is the level of combinatorial effect.

12Assume that expression levels of proteins A, B and C follow normal distributionComputer simulation leads the distribution of Score SHow to compute distribution of score S?13

CorrelationCorrelationDistribution of ADistribution of BDistribution of C

Score S of =0.5, =0.3Obtain distribution of score SRandomly create a distribution of A, B and C where correlation coefficient of A-B is , that of B-C is Create the table of average and stddev for each and Repeat computation of score S

Score S of =0.5, =0.4We can obtain the distribution for each and .Upper: averageLower: stddevJCKBSE2010KaunasWakayama UniversityThen, how to compute distribution of score S?To compute it, we first assume that expression levels of proteins A, B and C follow normal distribution. And, compute simulation leads to the distribution of score S. Specifically, first, we randomly create a distribution of A, B and C, where correlation coefficient of A-B is alpha, and that of B-C is beta. By computing score S from this data, we obtain one value of score S. So, by accumulating the value, we obtain the distribution of score S. Note that if alpha and beta is fixed the ditribution of score S is fixed. As a result of repeating this process, we obtain the table of average and standard deviation of for each alpha and beta. This table represents the distribution of score S for each alpha and beta.

13Place the score S in distribution of SZ-score: Measure difference between score S and average of S as the count of standard deviation

Score SComputing Combinatorial Effect as Z-score 14The higher z-score is, the stronger the combinatorial effect is !

Distribution of score SCompute score ScorrespondingThe amount of combinatorial effect level Z-score(score S-avg(S)) / stddev(S)Measurement as count of standard deviationaverageScore SZ-scoreScore SJCKBSE2010KaunasWakayama UniversityFinally we compute the combinatorial effect as z-score. This is done by placing the score S in the distribution of score S. Then, the difference between the average of the distribution and score S corresponds to the combinatorial effect. Here, z-score is the measurement of the difference as the count of standard deviation. Here, the higher z-score is, the stronger the combinatorial effect is.

14Trying all combination of A, B and C Compute the maximum correlation coefficient among all scale of A and B to compute Score SCompute z-score and create ranking by them15Compute z-scoresfrom distribution of SSummary of the proposed algorithmABCDsample1sample2sample3ExpressionData(A,B)C(A,B)D(A,B)E(A,B)F (A,C)B(A,C)D(A,C)E(A,C)F (B,C)A(B,C)D(B,C)E(B,C)FTrying all combinations1Compute max correlationamong every scale2ABABABTry every scalescorrelation0.3correlation0.8correlation: 0.5

SZ-score = 5.5list of all combinations3Ranking by z-scorerankCombinationsZ-score(A,C)B5.5(B,C)E4.9(A,B)F4.7Score S = 0.8SJCKBSE2010KaunasWakayama UniversityHere we show the summary of the proposed method. First, we try all the combinations proteins A, B and C from expression data. For each combinations A, B and C, we compute the maximum correlation coefficient among every possible scales. Then score S is obtained. After that, we compute the z-score from distribution table of score S. Finally we create the ranking of combinations by z-score.

16EvaluationApplying our method into real expression dataProtein expression data of black cattle # of samples is 195, # of proteins is 879finding combinatorial protein-protein interactionsusing our methodJCKBSE2010KaunasWakayama UniversityThen we go to evaluation of this method. Evaluation is done by applying our method into real expression data. The data is protein expression data of black cattle obtained from our co-operate researchers.In the data, the number of samples is 195, and the number of proteins is 879. From the data, we tried to find combinatorial protein-protein interactions using our method.

The Expression Data Follows Normal DistributionBy way of Jarque-Bera test with confidential level of 95%, we test if expression data follows normal distribution.

Result: 454 proteins out of 879 proteins follow normal distribution

Thus, we use 454 proteins for evaluation

17JCKBSE2010KaunasWakayama UniversityBefore we show the result, we present the property of the data that the data follows the normal distribution. To confirm the property, by way of Jarque-Bera test with confidential level of 95%, we test if expression data follows normal distribution. The result is that 454 proteins out of 879 proteins follow normal distribution. Since our method assumes normal distribution, we use 454 proteins for evaluation.

17ResultsWe found so many combinations of proteinswhich would have combinatorial effectThe maximum value of z-score is 11.0The combinations where z-value is more than about 5.5(p-value is less than 0.000000019(=0.05/454C3))) would have combinatorial effect with confidential level of 95%.

18

The histogram of z-score # of combinations Z-score JCKBSE2010KaunasWakayama UniversityThe results are shown here. This figure shows the histogram of high z-score combinations. Note that z-score of over 7.0 is very high. Many combinations are found in which combinatorial effect is predicted. Here, statistically, the combinations where z-value is more than about 5.5 Would have combinatorial effect with confidential level of 95%. They have p-values of less than this very small value.

18Comparing z-scores with normal distribution19We compare the histogram with that of without combinatorial effectCreated by augmenting normal distribution with the number of trials (454C3)It is inferred that this data includes considerable amount of combinatorial effect

Distribution of z-score underassumption no combinatorial effect

Estimated distribution of z-score obtained from real data

# of combinations Z-score Histogram of real data

# of combinations Z-score Histogram without combinatorial effect JCKBSE2010KaunasWakayama UniversityIn this slide we compare z-scores of the result with normal distribution. Note that the normal distribution means the case in which no combinatorial effect is assumed. This red curve is the estimated curve of the obtained result and the blue one is the normal distribution curve. The normal distribution curve is obtained by augmenting normal distribution with the number of trials. Then, the result shown in the previous slides corresponds to this position. In contrast, in the normal distribution the counts are only about 6 or so. This implies that this data includes considerable amount of combinatorial effect.

19The Ranking based on Z-score20The ranking table shows that Combinations with low score S are retrieved.Same protein tends to appear many times.

The ranking of Z-score obtained from real data

BC

ACCorrelationof B-CScore SBCAZ-scoreRankAProtein NumBProtein NumCProtein NumCorrelationof A-CJCKBSE2010KaunasWakayama UniversityThis is the top 10 ranking table based on z-score. The ranking table shows that, first, not only the combinations of high value of score S, but also low S is retrieved. This is possible because we separate combinatorial effect from total effect. Also, we found that the same protein tends to appear many times. There are some property of this method.

20Conclusion21Summary We propose a method to estimate combinatorial effect of three proteins from protein expression dataApplying the method into real data, we found many combinations which would have combinatorial effect

Future workTo confirm the reliability, we are planning to study whether the found combinations include well-known protein-protein interactions or not.JCKBSE2010KaunasWakayama UniversityFinally we conclude the work.

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