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SW1PerS: Sliding windows and 1-persistence scoring; discovering periodicity in gene expression time series data.

Perea JA, Deckard A, Haase SB, Harer J - BMC Bioinformatics (2015)

Bottom Line: Results on biological data are also analyzed and compared.In data from the Yeast cell cycle SW1PerS identifies genes not preferred by other algorithms, hence not previously reported as periodic, but found in other experiments such as the universal growth rate response of Slavov.Indeed, by having an initial set of periodic genes with a rich variety of signal types, pattern/shape information can be included in the study of systems and the generation of hypotheses regarding the structure of gene regulatory networks.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics, Duke University, Science Dr, Durham, 27708, NC, USA. joperea@math.duke.edu.

ABSTRACT

Background: Identifying periodically expressed genes across different processes (e.g. the cell and metabolic cycles, circadian rhythms, etc) is a central problem in computational biology. Biological time series may contain (multiple) unknown signal shapes of systemic relevance, imperfections like noise, damping, and trending, or limited sampling density. While there exist methods for detecting periodicity, their design biases (e.g. toward a specific signal shape) can limit their applicability in one or more of these situations.

Methods: We present in this paper a novel method, SW1PerS, for quantifying periodicity in time series in a shape-agnostic manner and with resistance to damping. The measurement is performed directly, without presupposing a particular pattern, by evaluating the circularity of a high-dimensional representation of the signal. SW1PerS is compared to other algorithms using synthetic data and performance is quantified under varying noise models, noise levels, sampling densities, and signal shapes. Results on biological data are also analyzed and compared.

Results: On the task of periodic/not-periodic classification, using synthetic data, SW1PerS outperforms all other algorithms in the low-noise regime. SW1PerS is shown to be the most shape-agnostic of the evaluated methods, and the only one to consistently classify damped signals as highly periodic. On biological data, and for several experiments, the lists of top 10% genes ranked with SW1PerS recover up to 67% of those generated with other popular algorithms. Moreover, the list of genes from data on the Yeast metabolic cycle which are highly-ranked only by SW1PerS, contains evidently non-cosine patterns (e.g. ECM33, CDC9, SAM1,2 and MSH6) with highly periodic expression profiles. In data from the Yeast cell cycle SW1PerS identifies genes not preferred by other algorithms, hence not previously reported as periodic, but found in other experiments such as the universal growth rate response of Slavov. These genes are BOP3, CDC10, YIL108W, YER034W, MLP1, PAC2 and RTT101.

Conclusions: In biological systems with low noise, i.e. where periodic signals with interesting shapes are more likely to occur, SW1PerS can be used as a powerful tool in exploratory analyses. Indeed, by having an initial set of periodic genes with a rich variety of signal types, pattern/shape information can be included in the study of systems and the generation of hypotheses regarding the structure of gene regulatory networks.

No MeSH data available.


g along with a window of length w starting at t∈[0,2π−w]
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Fig8: g along with a window of length w starting at t∈[0,2π−w]

Mentions: More specifically, given a time series g0,g1,…,gS (e.g. of gene expression data) measured at times t0,t1,…,tS, we map the interval [t0,tS] linearly onto [0,2π] and apply cubic splining to obtain a continuous function so that g(0)=g0 and g(2π)=gS. For a fixed 0<w<2π, referred to as the window size, and each time t∈[0,2π−w] we consider the graph of g restricted to the interval [t,t+w]. Let us use Fig. 8, where we depict a prototypical function g with a window of length w, as a running example.Fig. 8


SW1PerS: Sliding windows and 1-persistence scoring; discovering periodicity in gene expression time series data.

Perea JA, Deckard A, Haase SB, Harer J - BMC Bioinformatics (2015)

g along with a window of length w starting at t∈[0,2π−w]
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

License 1 - License 2
Show All Figures
getmorefigures.php?uid=PMC4537550&req=5

Fig8: g along with a window of length w starting at t∈[0,2π−w]
Mentions: More specifically, given a time series g0,g1,…,gS (e.g. of gene expression data) measured at times t0,t1,…,tS, we map the interval [t0,tS] linearly onto [0,2π] and apply cubic splining to obtain a continuous function so that g(0)=g0 and g(2π)=gS. For a fixed 0<w<2π, referred to as the window size, and each time t∈[0,2π−w] we consider the graph of g restricted to the interval [t,t+w]. Let us use Fig. 8, where we depict a prototypical function g with a window of length w, as a running example.Fig. 8

Bottom Line: Results on biological data are also analyzed and compared.In data from the Yeast cell cycle SW1PerS identifies genes not preferred by other algorithms, hence not previously reported as periodic, but found in other experiments such as the universal growth rate response of Slavov.Indeed, by having an initial set of periodic genes with a rich variety of signal types, pattern/shape information can be included in the study of systems and the generation of hypotheses regarding the structure of gene regulatory networks.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics, Duke University, Science Dr, Durham, 27708, NC, USA. joperea@math.duke.edu.

ABSTRACT

Background: Identifying periodically expressed genes across different processes (e.g. the cell and metabolic cycles, circadian rhythms, etc) is a central problem in computational biology. Biological time series may contain (multiple) unknown signal shapes of systemic relevance, imperfections like noise, damping, and trending, or limited sampling density. While there exist methods for detecting periodicity, their design biases (e.g. toward a specific signal shape) can limit their applicability in one or more of these situations.

Methods: We present in this paper a novel method, SW1PerS, for quantifying periodicity in time series in a shape-agnostic manner and with resistance to damping. The measurement is performed directly, without presupposing a particular pattern, by evaluating the circularity of a high-dimensional representation of the signal. SW1PerS is compared to other algorithms using synthetic data and performance is quantified under varying noise models, noise levels, sampling densities, and signal shapes. Results on biological data are also analyzed and compared.

Results: On the task of periodic/not-periodic classification, using synthetic data, SW1PerS outperforms all other algorithms in the low-noise regime. SW1PerS is shown to be the most shape-agnostic of the evaluated methods, and the only one to consistently classify damped signals as highly periodic. On biological data, and for several experiments, the lists of top 10% genes ranked with SW1PerS recover up to 67% of those generated with other popular algorithms. Moreover, the list of genes from data on the Yeast metabolic cycle which are highly-ranked only by SW1PerS, contains evidently non-cosine patterns (e.g. ECM33, CDC9, SAM1,2 and MSH6) with highly periodic expression profiles. In data from the Yeast cell cycle SW1PerS identifies genes not preferred by other algorithms, hence not previously reported as periodic, but found in other experiments such as the universal growth rate response of Slavov. These genes are BOP3, CDC10, YIL108W, YER034W, MLP1, PAC2 and RTT101.

Conclusions: In biological systems with low noise, i.e. where periodic signals with interesting shapes are more likely to occur, SW1PerS can be used as a powerful tool in exploratory analyses. Indeed, by having an initial set of periodic genes with a rich variety of signal types, pattern/shape information can be included in the study of systems and the generation of hypotheses regarding the structure of gene regulatory networks.

No MeSH data available.