# Effects of Time Point Measurement on the Reconstruction of Gene Regulatory Networks

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental

#### 2.1. Data and software

#### 2.2. Method

#### 2.2.1. Dynamic Bayesian network method

_{i}

^{j }is the jth variable at time i and x

_{i}

^{j}is the value of jth variable at time i, is the vector composed by variables at time i and is the vector composed by jth variable at all times.

^{j}

_{0}= Ф, denotes the random variables that correspond to the parents of node i.

#### 2.2.2. Network structure analysis

Statistics | Definition | Descriptions |

Average degree K [29] | de(v): the degree of node v | |

N: the number of nodes in network S | ||

Average path length l[30,32] | d_{ij}: the shortest path between v_{i} and v_{j} | |

Betweenness B_{v}[33] | g_{ivj}: the number of shortest paths from i to j that pass through a node v | |

g_{ij} : the number of shortest geodesic paths from i to j. | ||

Clustering coefficient CC [34] | _{Nt}_{: number of closed triplets} | |

_{Ntn}_{: number of connected triples of nodes} | ||

Centralization Ce( S ) [35] | C(v): the degree centrality for node v and | |

Global efficiency of the network E[36] | d_{ij }: shortest path length | |

Maximum vulnerability of the networks Vu [37] | E: the efficiency of the network | |

E_{i }: the efficiency of the network without the node i and all edges connecting it with other vertices |

#### 2.2.3. Arabidopsis gene regulatory networks reconstruction based on different time point deletion

_{k}is a statistics of network G

_{k}and ave is the average of Q

_{k}. It is obvious that a low diversity score denotes a low undulatory property and here indicating the insensitivity to the time point measurement.

## 3. Results and Discussion

#### 3.1. The analysis of constructed Arabidopsis gene regulatory networks

**Figure 1.**The directed network of Arabidopsis gene regulation. Red nodes represent genes and arcs represent the regulation between genes.

K | Dia | l | N0 | Rn | E | Vu | CC | Ce |
---|---|---|---|---|---|---|---|---|

1.1175 | 12 | 3.0467 | 306 | 447 | 0.0013 | 0.0302 | 0.0019 | 0.0093 |

**Figure 2.**The degree of nodes in the Arabidopsis gene regulatory network. The three pie charts A, B and C denote outdegree, indegree, and total degree separately.

#### 3.2. Identification of network statistics insensitive to time points measurement

Network | K | Dia | l | Ce | Rn | E | Vu |

G0 | 1.1175 | 12 | 3.0467 | 0.0093 | 447 | 0.001258 | 0.0302 |

G1 | 0.9750 | 10 | 2.4462 | 0.0101 | 390 | 0.000944 | 0.0397 |

G2 | 0.8725 | 6 | 1.6998 | 0.0095 | 349 | 0.000726 | 0.0499 |

G3 | 0.9175 | 6 | 1.9530 | 0.0076 | 367 | 0.000849 | 0.0366 |

G4 | 0.9525 | 11 | 2.3965 | 0.0101 | 381 | 0.000859 | 0.0602 |

G5 | 0.9625 | 5 | 1.8720 | 0.0289 | 385 | 0.000919 | 0.0809 |

fG6 | 0.9425 | 7 | 2.0107 | 0.0076 | 377 | 0.000811 | 0.0344 |

G7 | 0.8475 | 10 | 2.5515 | 0.0083 | 339 | 0.000804 | 0.0396 |

G8 | 0.9250 | 7 | 2.4457 | 0.0082 | 370 | 0.000892 | 0.0472 |

G9 | 0.8625 | 7 | 2.2134 | 0.0139 | 345 | 0.000784 | 0.0590 |

G10 | 0.9200 | 7 | 2.0985 | 0.0239 | 368 | 0.000863 | 0.0728 |

G11 | 0.9500 | 5 | 1.7365 | 0.0126 | 380 | 0.000806 | 0.0466 |

ave | 0.9371 | 7.7500 | 2.2059 | 0.0125 | 374.8300 | 0.000876 | 0.0497 |

d_score | 0.5785 | 2.7400 | 1.4780 | 4.6882 | 0.5800 | 1.07808 | 2.5885 |

#### 3.3. Comparison of the influence of different time points on the networks reconstruction

**Figure 3.**The degree logarithmic distribution for 12 networks (G0-G11). Most of them fit power-law distribution well.

Measurement | Definition | Descriptions | |
---|---|---|---|

sensitivity | N_{tp}: number of true positivesN _{fn}: number of false negatives N _{fp}: number of false positives | ||

precision | |||

F-measure |

**Figure 4.**A is sensitivity of 11 time point removing networks with G0 as the standard network. B is precision of 11 networks and C shows F-measure.

**Figure 6.**A is sensitivity of G2, G3, G9, G10, G2_3 and G9_10 with G0 as the standard network. B is precision of these 6 networks and C shows F-measure.

#### 3.4. Detection of key regulatory modules

Predictor | Target | Networks with the regulation | Network without the regulation |
---|---|---|---|

At1g77510 | At1g17430 | G0, G1, G2, G3, G5, G6, G7, G8, G9, G10, G11 | G4 |

At3g02720 | At2g30010 | G0, G1, G2, G3, G4, G5, G6, G7, G8, G9, G10 | G11 |

At5g06280 | At1g77510 | G0, G1, G2, G3, G4, G5, G6, G7, G9, G10, G11 | G8 |

At5g58870 | At5g38510 | G0, G1, G2, G3, G4, G5, G6, G7, G8, G10, G11 | G9 |

Predictor | Target | Networks with the regulation | Network without the regulation |
---|---|---|---|

At1g01250 | At4g16780 | G0, G2, G3, G4, G5, G7, G8, G9, G10, G11 | G1, G6 |

At1g36390 | At4g09570 | G0, G1, G4, G5, G6, G7, G8, G9, G10, G11 | G2, G3 |

At1g07180 | At3g01060 | G0, G1, G2, G3, G5, G6, G7, G8, G9, G11 | G4, G10 |

At1g07180 | At5g35970 | G0, G1, G2, G3, G5, G6, G7, G8, G9, G11 | G4, G10 |

At3g5490 | At3g10720 | G0, G1, G2, G4, G5, G7, G8, G9, G10, G11 | G3, G6 |

At5g40890" | At3g11710 | G0, G1, G2, G3, G4, G6, G7, G8, G10, G11 | G5, G9 |

At5g56900 | At4g02380 | G0, G2, G3, G4, G5, G6, G7, G8, G9, G10 | G1, G11 |

At5g56900 | At5g66920 | G0, G1, G2, G3, G4, G6, G7, G8, G10, G11 | G5, G9 |

At1g51110 | At3g12760 | G0, G1, G2, G3, G4, G5, G6, G7, G8, G10 | G9, G11 |

At2g40890 | At4g35090 | G0, G1, G2, G3, G5, G6, G7, G8, G10, G11 | G4, G9 |

## 4. Discussion and Conclusions

## Acknowledgements

## References

- Kato, M.; Tsunoda, T.; Takagi, T. Inferring genetic networks from DNA microarray data by multiple regression analysis. Genome Inform. Ser. Workshop Genome Inform.
**2000**, 11, 118–128. [Google Scholar] - Chen, T.; He, H.L.; Church, G.M. Modeling gene expression with differential equations. Pac. Symp. Biocomput.
**1999**, 29–40. [Google Scholar] - de Hoon, M.J.; Imoto, S.; Kobayashi, K.; Ogasawara, N.; Miyano, S. Inferring gene regulatory networks from time-ordered gene expression data of Bacillus subtilis using differential equations. Pac. Symp. Biocomput.
**2003**, 17–28. [Google Scholar] - Basso, K.; Margolin, A.A.; Stolovitzky, G.; Klein, U.; Dalla-Favera, R.; Califano, A. Reverse engineering of regulatory networks in human B cells. Nat. Genet.
**2005**, 37, 382–390. [Google Scholar] - Liang, S.; Fuhrman, S.; Somogyi, R. Reveal, a general reverse engineering algorithm for inference of genetic network architectures. Pac. Symp. Biocomput.
**1998**, 18–29. [Google Scholar] - Friedman, N.; Linial, M.; Nachman, I.; Pe'er, D. Using Bayesian networks to analyze expression data. J. Comput. Biol.
**2000**, 7, 601–620. [Google Scholar] [CrossRef] - Ong, I.M.; Glasner, J.D.; Page, D. Modelling regulatory pathways in E. coli from time series expression profiles. Bioinformatics
**2002**, 18 Suppl. 1, S241–S248. [Google Scholar] - Zou, M.; Conzen, S.D. A new dynamic Bayesian network (DBN) approach for identifying gene regulatory networks from time course microarray data. Bioinformatics
**2005**, 21, 71–79. [Google Scholar] - Opgen-Rhein, R.; Strimmer, K. Learning causal networks from systems biology time course data: an effective model selection procedure for the vector autoregressive process. BMC Bioinformatics
**2007**, 8 Suppl 2, S3. [Google Scholar] [CrossRef] - Beal, M.J.; Falciani, F.; Ghahramani, Z.; Rangel, C.; Wild, D.L. A Bayesian approach to reconstructing genetic regulatory networks with hidden factors. Bioinformatics
**2005**, 21, 349–356. [Google Scholar] [CrossRef] - Perrin, B.E.; Ralaivola, L.; Mazurie, A.; Bottani, S.; Mallet, J.; d'Alche-Buc, F. Gene networks inference using dynamic Bayesian networks. Bioinformatics
**2003**, 19 Suppl. 2, ii138–ii148. [Google Scholar] [CrossRef] - Rangel, C.; Angus, J.; Ghahramani, Z.; Lioumi, M.; Sotheran, E.; Gaiba, A.; Wild, D.L.; Falciani, F. Modeling T-cell activation using gene expression profiling and state-space models. Bioinformatics
**2004**, 20, 1361–1372. [Google Scholar] [CrossRef] - Wu, F.X.; Zhang, W.J.; Kusalik, A.J. Modeling gene expression from microarray expression data with state-space equations. Pac. Symp. Biocomput.
**2004**, 581–592. [Google Scholar] - Smith, S.M.; Fulton, D.C.; Chia, T.; Thorneycroft, D.; Chapple, A.; Dunstan, H.; Hylton, C.; Zeeman, S.C.; Smith, A.M. Diurnal changes in the transcriptome encoding enzymes of starch metabolism provide evidence for both transcriptional and posttranscriptional regulation of starch metabolism in Arabidopsis leaves. Plant Physiol.
**2004**, 136, 2687–2699. [Google Scholar] [CrossRef] - Boyes, D.C.; Zayed, A.M.; Ascenzi, R.; McCaskill, A.J.; Hoffman, N.E.; Davis, K.R.; Gorlach, J. Growth stage-based phenotypic analysis of Arabidopsis: A model for high throughput functional genomics in plants. Plant Cell
**2001**, 13, 1499–1510. [Google Scholar] - May, S. NASC's International Affymetrix Service. Available online: http://affymetrix.arabidopsis.info/ (accessed on 13 October 2009).
- The Comprehensive R Archive Network. Available online: http://mirrors.geoexpat.com/cran/ (accessed on 10 May 2010).
- LÃ¨bre, S. Inferring Dynamic Genetic Networks with Low Order Independencies. Stat. Appl. Genet. Mol. Biol.
**2009**, 8, 9. [Google Scholar] - Murphy, K.; Mian, S. Modelling Gene Expression Data using Dynamic Bayesian Networks; University of California, Computer Science Division: Berkeley, CA, USA, 1999. [Google Scholar]
- Carlson, J.M.; Chakravarty, A.; Khetani, R.S.; Gross, R.H. Bounded search for de novo identification of degenerate cis-regulatory elements. BMC Bioinformatics
**2006**, 7, 254. [Google Scholar] [CrossRef] - Todeschini, R.; Consonni, V.; Mannhold, R.; Kubinyi, H.; Timmerman, H. Handbook of Molecular Descriptors; Wiley-VCH: Weinheim, Germany, 2000. [Google Scholar]
- Gonzalez-Diaz, H.; Gonzalez-Diaz, Y.; Santana, L.; Ubeira, F.M.; Uriarte, E. Proteomics, networks and connectivity indices. Proteomics
**2008**, 8, 750–778. [Google Scholar] [CrossRef] - González-Díaz, H.; Munteanu, C.R. Topological Indices for Medicinal Chemistry, Biology, Parasitology, Neurological and Social Networks; Transworld Research Network: Kerala, India, 2010; p. 212. [Google Scholar]
- Stefan, B.; Heinz Georg, S. Handbook of Graphs and Networks: From the Genome to the Internet; John Wiley & Sons, Inc.: New York, NY, USA, 2003; p. 401. [Google Scholar]
- Mrabet, Y.; Semmar, N. Mathematical methods to analysis of topology, functional variability and evolution of metabolic systems based on different decomposition concepts. Curr. Drug Metab.
**2010**, 11, 315–341. [Google Scholar] [CrossRef] - Chou, K.C. Graphic rule for drug metabolism systems. Curr. Drug Metab.
**2010**, 11, 369–378. [Google Scholar] - Gonzalez-Diaz, H. Network topological indices, drug metabolism, and distribution. Curr. Drug Metab.
**2010**, 11, 283–284. [Google Scholar] [CrossRef] - Gonzalez-Diaz, H.; Duardo-Sanchez, A.; Ubeira, F.M.; Prado-Prado, F.; Perez-Montoto, L.G.; Concu, R.; Podda, G.; Shen, B. Review of MARCH-INSIDE & complex networks prediction of drugs: ADMET, anti-parasite activity, metabolizing enzymes and cardiotoxicity proteome biomarkers. Curr. Drug Metab.
**2010**, 11, 379–406. [Google Scholar] [CrossRef] - Diestel, R. Graph theory. In Graduate Texts in Mathematics; 1997; Volume 173, p. 410. [Google Scholar]
- West, D. Introduction to Graph Theory, 2nd ed; Prentice Hall: Englewood Cliffs, NJ, 1996. [Google Scholar]
- Chia, T.; Thorneycroft, D.; Chapple, A.; Messerli, G.; Chen, J.; Zeeman, S.C.; Smith, S.M.; Smith, A.M. A cytosolic glucosyltransferase is required for conversion of starch to sucrose in Arabidopsis leaves at night. Plant J.
**2004**, 37, 853–863. [Google Scholar] [CrossRef] - Albert, R.; Barabasi, A.-L. Statistical mechanics of complex networks. Rev. Mod. Phys.
**2002**, 74, 47–97. [Google Scholar] - Freeman, L.C. A set of measures of centrality based on betweenness. Sociometry
**1977**, 40, 35–41. [Google Scholar] [CrossRef] - Wasserman, S.; Faust, K. Social Network Analysis: Methods and Applications (Structural Analysis in the Social Sciences), 1st ed; Cambridge University Press: New York, NY, USA, 1994; p. 857. [Google Scholar]
- Freeman, L. Centrality in social networks: Conceptual clarification. Soc. Networks
**1979**, 1, 215–239. [Google Scholar] [CrossRef] - Latora, V.; Marchiori, M. Efficient behavior of small-world networks. Phys. Rev. Lett.
**2001**, 87, 198701. [Google Scholar] [CrossRef] - Gol'dshtein, V.; Koganov, G.A.; Surdutovich, G.I. Vulnerability and Hierarchy of Complex Networks. arXiv: preprint cond-mat/0409298
**2004**. [Google Scholar] - Riechmann, J.L.; Meyerowitz, E.M. The AP2/EREBP family of plant transcription factors. Biol. Chem.
**1998**, 379, 633–646. [Google Scholar] - Barabasi, A.L.; Bonabeau, E. Scale-free networks. Sci. Am.
**2003**, 288, 60–69. [Google Scholar] [CrossRef] - Altman, D.G.; Bland, J.M. Diagnostic tests. 1: Sensitivity and specificity. BMJ
**1994**, 308, 1552. [Google Scholar] [CrossRef] - Dzeroski, S.; Todorovski, L. Equation discovery for systems biology: finding the structure and dynamics of biological networks from time course data. Curr. Opin. Biotechnol.
**2008**, 19, 360–368. [Google Scholar] [CrossRef] - Wang, Y.; Joshi, T.; Zhang, X.S.; Xu, D.; Chen, L. Inferring gene regulatory networks from multiple microarray datasets. Bioinformatics
**2006**, 22, 2413–2420. [Google Scholar] [CrossRef]

- Sample Availability: Samples of the compounds are available from the authors.

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**MDPI and ACS Style**

Yan, W.; Zhu, H.; Yang, Y.; Chen, J.; Zhang, Y.; Shen, B.
Effects of Time Point Measurement on the Reconstruction of Gene Regulatory Networks. *Molecules* **2010**, *15*, 5354-5368.
https://doi.org/10.3390/molecules15085354

**AMA Style**

Yan W, Zhu H, Yang Y, Chen J, Zhang Y, Shen B.
Effects of Time Point Measurement on the Reconstruction of Gene Regulatory Networks. *Molecules*. 2010; 15(8):5354-5368.
https://doi.org/10.3390/molecules15085354

**Chicago/Turabian Style**

Yan, Wenying, Huangqiong Zhu, Yang Yang, Jiajia Chen, Yuanyuan Zhang, and Bairong Shen.
2010. "Effects of Time Point Measurement on the Reconstruction of Gene Regulatory Networks" *Molecules* 15, no. 8: 5354-5368.
https://doi.org/10.3390/molecules15085354