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SCIENTIA SINICA Informationis, Volume 47, Issue 10: 1334-1348(2017) https://doi.org/10.1360/N112017-00012

Computing exact permutation ${\boldsymbol~p}$-values for phosphorylation motifs

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  • ReceivedJan 12, 2017
  • AcceptedFeb 9, 2017
  • PublishedAug 30, 2017

Abstract

Protein phosphorylation motifs refer to position-specific amino acid patterns near phosphorylation sites. Mining phosphorylation motifs is an important task in the field of bioinformatics and several efficient methods have been proposed to uncover phosphorylation motifs. However, a large percentage of the phosphorylation motifs discovered by these algorithms are false positives. Using such motifs to perform further research will lead to inaccurate conclusions. Generally, statistical significance testing is an effective technique to filter out meaningless phosphorylation motifs. Among statistical significance testing methods, permutation testing is a commonly used method. Its usability and popularity can be attributed to its non-parametric nature. However, in permutation testing, several drawbacks narrow its range of usability. In this paper, we provide an analysis of these disadvantages and propose an algorithm called exact permutation $p$-values for phosphorylation motifs (EPPM) for generating an exact null distribution, from which the exact $p$-values of tested phosphorylation motifs can be calculated. Experiments on several datasets demonstrate that EPPM can successfully alleviate the aforementioned disadvantages and outperform the direct permutation-based method for several performance measures. To the best of our knowledge, there are still no methods in the literature that can compute exact permutation $p$-values for assessing phosphorylation motifs.


Funded by

国家自然科学基金(61572094)


References

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  • Figure 1

    (Color online) (a) The original data set; (b) the permuted data set

  • Figure 3

    (Color online) The number of phosphorylation motifs whose $p$-values are zeros and non-zeros reported by DSP. (a) Non-kinase-specific; (b) CDK-specific; (c) PKA-specific

  • Figure 4

    (Color online) The distribution of the test statistic values

  • Figure 5

    (Color online) (a) The $p$-values of a randomly selected phosphorylation motifs with 100 different runs on CDK-specific data set reported by DSP; (b) the number of significant phosphorylation motifs returned from DSP and EPPM in 100 different runs on CDK-specific data set

  • Figure 6

    (Color online) The running time of DSP with different number of permutations and EPPM on PKA-specific data set

  • Figure 7

    (Color online) The running time of DSP and EPPM under different min$\_$sups on each data set. (a) Non-kinase-specific; (b) CDK-specific; (c) PKA-specific

  •   

    Algorithm 1 EPPM ($P$, $N$, min$\_$sup, $\alpha$)

    Require:前景集合$P$; 背景集合$N$; 最小支持度阈值min$\_$sup; 置信水平$\alpha$.

    Output:统计显著的磷酸化基序集合Result.

    Result $\leftarrow~\emptyset$, $T~\leftarrow~\emptyset$, sum$\_$ts $\leftarrow~0$;

    $M_1~\leftarrow$ FP-Growth ($P$, min$\_$sup);

    $M_2~\leftarrow$ FP-Growth ($D$, min$\_$sup);

    for each $m_1~\in~{M_1}$

    $~{\rm~ms}(m_1)~\leftarrow~0$;

    end for

    for each $m_2~\in~{M_2}$

    for $s~\leftarrow~L(m_2)$ to $U(m_2)$

    ${\rm~ts}~\leftarrow~z(m_2,s)$;

    ${\rm~fc}~\leftarrow~h_2(m_2,s)$;

    $T~=~T~\cup~$$\{$$\langle$${\rm~ts,fc}$$\rangle$$\}$;

    sum$\_$ts $\leftarrow$ sum$\_$ts+${\rm~fc}$;

    end for

    end for

    sort(T);

    accumulate(T);

    for each $~m_1~\in~{M_1}$

    ${\rm~ms}~(m_1)~\leftarrow~{\rm~search}~({\rm~org\_ts}(m_1),~T)$;

    $p(m_1)~\leftarrow~{\rm~ms}~(m_1)~/~$sum$\_$ts;

    end for

    Result$~\leftarrow~{\rm~BH}~(M_1,\alpha)$;

    return Result.

  • Table 1   The distributions of the $p$-values returned from DSP with the different number of permutations and EPPM on non-kinase-specific data set
    $p$-value 250 500 1000 2000 4000 EPPM
    $(0.1,~1]$ 3290 3290 3290 3270 3270 3270
    $(0.01,~0.1]$ 1700 1660 1660 1680 1680 1680
    $(0.001,~0.01]$ 905 900 900 889 889 889
    $(10^{-4},~0.001]$ 571 566 550 559 554 554
    $(10^{-5},~10^{-4}]$ 273 316 318 344 342 340
    $(10^{-6},~10^{-5}]$ 135 197 216 218 225 225
    $(10^{-7},~10^{-6}]$ 33 69 134 121 123 124
    $(0,~10^{-7}]$ 0 0 0 45 87 484
    $0$ 659 568 498 440 396 0

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