# Stability of Signaling Pathways during Aging—A Boolean Network Approach

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## Abstract

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## 1. Introduction

## 2. Results

#### 2.1. Experimental Settings

#### 2.1.1. Data Processing

#### 2.1.2. Inferring Boolean Networks from Binarized Time-Series Data

#### 2.2. Stability Measure of Boolean Networks

#### Analysis of Reconstructed Boolean Networks

#### 2.3. Boolean Functions

#### 2.4. Network Stability

## 3. Discussion

## 4. Conclusions

## 5. Materials and Methods

#### 5.1. Data

#### 5.2. Boolean Networks

#### 5.3. Inferring Boolean Networks

#### 5.3.1. Binarization of Time-Series Data

#### 5.3.2. Inferring Boolean Functions

## Supplementary Materials

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Sauer, U.; Heinemann, M.; Zamboni, N. Genetics. Getting closer to the whole picture. Science
**2007**, 316, 550–551. [Google Scholar] [CrossRef] [PubMed] - Kauffman, S.A. Metabolic stability and epigenesis in randomly constructed genetic nets. J. Theor. Biol.
**1969**, 22, 437–467. [Google Scholar] [CrossRef] - Naldi, A.; Monteiro, P.T.; Müssel, C.; Consortium for Logical Models and Tools; Kestler, H.A.; Thieffry, D.; Xenarios, I.; Saez-Rodriguez, J.; Helikar, T.; Chaouiya, C. Cooperative development of logical modelling standards and tools with CoLoMoTo. Bioinformatics
**2015**, 31, 1154–1159. [Google Scholar] [CrossRef] [PubMed] - Tilstra, J.S.; Clauson, C.L.; Niedernhofer, L.J.; Robbins, P.D. NF-κB in Aging and Disease. Aging Dis.
**2011**, 2, 449–465. [Google Scholar] [PubMed] - Manolagas, S.C.; Almeida, M. Gone with the Wnts: β-Catenin, T-Cell Factor, Forkhead Box O, and Oxidative Stress in Age-Dependent Diseases of Bone, Lipid, and Glucose Metabolism. Mol. Endocrinol.
**2007**, 21, 2605–2614. [Google Scholar] [CrossRef] [PubMed] - Liu, H.; Fergusson, M.M.; Castilho, R.M.; Liu, J.; Cao, L.; Chen, J.; Malide, D.; Rovira, I.I.; Schimel, D.; Kuo, C.J.; et al. Augmented Wnt signaling in a mammalian model of accelerated aging. Science
**2007**, 317, 803–806. [Google Scholar] [CrossRef] [PubMed] - Kenyon, C. The first long-lived mutants: Discovery of the insulin/IGF-1 pathway for ageing. Philos. Trans. R. Soc. B Biol. Sci.
**2010**, 366, 9–16. [Google Scholar] [CrossRef] [PubMed] - Richardson, A.; Liu, F.; Adamo, M.L.; Remmen, H.V.; Nelson, J.F. The role of insulin and insulin-like growth factor-I in mammalian ageing. Best Pract. Res. Clin. Endocrinol. Metab.
**2004**, 18, 393–406. [Google Scholar] [CrossRef] [PubMed] - Zs-Nagy, I.; Cutler, R.G.; Semsei, I. Dysdifferentiation hypothesis of aging and cancer: A comparison with the membrane hypothesis of aging. Ann. N. Y. Acad. Sci.
**1988**, 521, 215–225. [Google Scholar] [CrossRef] [PubMed] - Gruber, J.; Yee, Z.; Tolwinski, N. Developmental Drift and the Role of Wnt Signaling in Aging. Cancers
**2016**, 8, 73. [Google Scholar] [CrossRef] [PubMed] - Peterson, J.M.; Bakkar, N.; Guttridge, D.C. NF-κB Signaling in Skeletal Muscle Health and Disease. In Myogenesis; Elsevier: Amsterdam, The Netherlands, 2011; pp. 85–119. [Google Scholar]
- Salminen, A.; Kaarniranta, K. NF-kappaB signaling in the aging process. J. Clin. Immunol.
**2009**, 29, 397–405. [Google Scholar] [CrossRef] [PubMed] - Adler, A.S.; Kawahara, T.L.A.; Segal, E.; Chang, H.Y. Reversal of aging by NFkappaB blockade. Cell Cycle
**2008**, 7, 556–559. [Google Scholar] [CrossRef] [PubMed] - Osorio, F.G.; Soria-Valles, C.; Santiago-Fernández, O.; Freije, J.M.P.; López-Otín, C. NF-κB signaling as a driver of ageing. Int. Rev. Cell Mol. Biol.
**2016**, 326, 133–174. [Google Scholar] [PubMed] - Welle, S.; Brooks, A.I.; Delehanty, J.M.; Needler, N.; Thornton, C.A. Gene expression profile of aging in human muscle. Physiol. Genom.
**2003**, 14, 149–159. [Google Scholar] [CrossRef] [PubMed] - Harper, J.M.; Salmon, A.B.; Chang, Y.; Bonkowski, M.; Bartke, A.; Miller, R.A. Stress resistance and aging: Influence of genes and nutrition. Mech. Ageing Dev.
**2006**, 127, 687–694. [Google Scholar] [CrossRef] [PubMed] - Durinck, S.; Spellman, P.T.; Birney, E.; Huber, W. Mapping identifiers for the integration of genomic datasets with the R/Bioconductor package biomaRt. Nat. Protoc.
**2009**, 4, 1184–1191. [Google Scholar] [CrossRef] [PubMed] - Kanehisa, M. KEGG: Kyoto Encyclopedia of Genes and Genomes. Nucleic Acids Res.
**2000**, 28, 27–30. [Google Scholar] [CrossRef] [PubMed] - Hopfensitz, M.; Müssel, C.; Wawra, C.; Maucher, M.; Kühl, M.; Neumann, H.; Kestler, H.A. Multiscale Binarization of Gene Expression Data for Reconstructing Boolean Networks. IEEE/ACM Trans. Comput. Biol. Bioinform.
**2012**, 9, 487–498. [Google Scholar] [CrossRef] [PubMed] - Müssel, C.; Schmid, F.; Blätte, T.J.; Hopfensitz, M.; Lausser, L.; Kestler, H.A. BiTrinA—Multiscale binarization and trinarization with quality analysis. Bioinformatics
**2015**, 32, 465–468. [Google Scholar] [CrossRef] [PubMed] - Müssel, C.; Hopfensitz, M.; Kestler, H.A. BoolNet—An R package for generation, reconstruction and analysis of Boolean networks. Bioinformatics
**2010**, 26, 1378–1380. [Google Scholar] [CrossRef] [PubMed] - Lähdesmäki, H.; Shmulevich, I.; Yli-Harja, O. On Learning Gene Regulatory Networks Under the Boolean Network Model. Mach. Learn.
**2003**, 52, 147–167. [Google Scholar] [CrossRef] - Szklarczyk, D.; Franceschini, A.; Kuhn, M.; Simonovic, M.; Roth, A.; Minguez, P.; Doerks, T.; Stark, M.; Muller, J.; Bork, P.; et al. The STRING database in 2011: Functional interaction networks of proteins, globally integrated and scored. Nucleic Acids Res.
**2010**, 39, D561–D568. [Google Scholar] [CrossRef] [PubMed] - Kitano, H. Biological robustness. Nat. Rev. Genet.
**2004**, 5, 826–837. [Google Scholar] [CrossRef] [PubMed] - Peixoto, T.P.; Drossel, B. Noise in random Boolean networks. Phys. Rev. E
**2009**, 79, 036108. [Google Scholar] [CrossRef] [PubMed] - Au, P.Y.B.; Yeh, W.C. Physiological Roles and Mechanisms of Signaling by TRAF2 and TRAF5. In TNF Receptor Associated Factors (TRAFs); Springer: New York, NY, USA, 2007; pp. 32–47. [Google Scholar]
- Schütze, S.; Potthoff, K.; Machleidt, T.; Berkovic, D.; Wiegmann, K.; Krönke, M. TNF activates NF-κB by phosphatidylcholine-specific phospholipase C-induced “Acidic” sphingomyelin breakdown. Cell
**1992**, 71, 765–776. [Google Scholar] [CrossRef] - Liu, G.; Park, Y.J.; Abraham, E. Interleukin-1 receptor-associated kinase (IRAK)-1-mediated NF-kappaB activation requires cytosolic and nuclear activity. FASEB J.
**2008**, 22, 2285–2296. [Google Scholar] [CrossRef] [PubMed] - Blonska, M.; Lin, X. NF-κB signaling pathways regulated by CARMA family of scaffold proteins. Cell Res.
**2010**, 21, 55–70. [Google Scholar] [CrossRef] [PubMed] - Kitano, H. A robustness-based approach to systems-oriented drug design. Nat. Rev. Drug Discov.
**2007**, 5, 202–210. [Google Scholar] [CrossRef] [PubMed] - Kitano, H. Towards a theory of biological robustness. Mol. Syst. Biol.
**2007**, 3, 137. [Google Scholar] [CrossRef] [PubMed] - Kriete, A. Robustness and aging—A systems-level perspective. Biosystems
**2013**, 112, 37–48. [Google Scholar] [CrossRef] [PubMed] - Albert, R.; Othmer, H.G. The topology of the regulatory interactions predicts the expression pattern of the segment polarity genes in Drosophila melanogaster. J. Theor. Biol.
**2003**, 223, 1–18. [Google Scholar] [CrossRef] - Herrmann, F.; Groß, A.; Zhou, D.; Kestler, H.A.; Kühl, M. A Boolean Model of the Cardiac Gene Regulatory Network Determining First and Second Heart Field Identity. PLoS ONE
**2012**, 7, e46798. [Google Scholar] [CrossRef] [PubMed] - Karlebach, G.; Shamir, R. Modelling and analysis of gene regulatory networks. Nat. Rev. Mol. Cell Biol.
**2008**, 9, 770–780. [Google Scholar] [CrossRef] [PubMed] - Kauffman, S.A. The origins of order. Self-organization and selection in evolution. J. Evolut. Biol.
**1994**, 7, 518–519. [Google Scholar] - Harvey, I.; Bossomaier, T. Time Out of Joint: Attractors in Asynchronous Random Boolean Networks. In Fourth European Conference on Artificial Life; Langton, C.G., Ed.; MIT Press: Cambridge, MA, USA, 1997; pp. 67–75. [Google Scholar]
- Shmulevich, I.; Dougherty, E.R.; Kim, S.; Zhang, W. Probabilistic Boolean networks: A rule-based uncertainty model for gene regulatory networks. Bioinformatics
**2002**, 18, 261–274. [Google Scholar] [CrossRef] [PubMed] - Fauré, A.; Naldi, A.; Chaouiya, C.; Thieffry, D. Dynamical analysis of a generic Boolean model for the control of the mammalian cell cycle. Bioinformatics
**2006**, 22, e124–e131. [Google Scholar] [CrossRef] [PubMed] - Dahlhaus, M.; Burkovski, A.; Hertwig, F.; Müssel, C.; Volland, R.; Fischer, M.; Debatin, K.M.; Kestler, H.A.; Beltinger, C. Boolean modeling identifies Greatwall/MASTL as an important regulator in the AURKA network of neuroblastoma. Cancer Lett.
**2016**, 371, 79–89. [Google Scholar] [CrossRef] [PubMed] - García-Gómez, M.; Azpeitia, E.; Álvarez Buylla, E.R. A dynamic genetic-hormonal regulatory network model explains multiple cellular behaviors of the root apical meristem of Arabidopsis thaliana. PLoS Comput. Biol.
**2017**, 13, e1005488. [Google Scholar] [CrossRef] [PubMed] - Meyer, P.; Maity, P.; Burkovski, A.; Schwab, J.; Müssel, C.; Singh, K.; Ferreira, F.F.; Krug, L.; Maier, H.J.; Wlaschek, M.; et al. A model of the onset of the senescence associated secretory phenotype after DNA damage induced senescence. PLoS Comput. Biol.
**2017**, 13, e1005741. [Google Scholar] [CrossRef] [PubMed] - Thomas, R.; Kaufman, M. Multistationarity, the basis of cell differentiation and memory. II. Logical analysis of regulatory networks in terms of feedback circuits. Chaos Interdiscip. J. Nonlinear Sci.
**2001**, 11, 180. [Google Scholar] [CrossRef] [PubMed] - Saadatpour, A.; Albert, R.; Reluga, T.C. A Reduction Method for Boolean Network Models Proven to Conserve Attractors. SIAM J. Appl. Dyn. Syst.
**2013**, 12, 1997–2011. [Google Scholar] [CrossRef] - Schwab, J.; Burkovski, A.; Siegle, L.; Müssel, C.; Kestler, H.A. ViSiBooL-visualization and simulation of Boolean networks with temporal constraints. Bioinformatics
**2017**, 33, 601–604. [Google Scholar] [CrossRef] [PubMed] - Dubrova, E.; Teslenko, M. A SAT-Based Algorithm for Finding Attractors in Synchronous Boolean Networks. IEEE/ACM Trans. Comput. Biol. Bioinform.
**2011**, 8, 1393–1399. [Google Scholar] [CrossRef] [PubMed] - Klarner, H.; Bockmayr, A.; Siebert, H. Computing Symbolic Steady States of Boolean Networks. In Cellular Automata; Springer International Publishing: Cham, Switzerland, 2014; pp. 561–570. [Google Scholar]
- Zañudo, J.G.T.; Albert, R. An effective network reduction approach to find the dynamical repertoire of discrete dynamic networks. Chaos Interdiscip. J. Nonlinear Sci.
**2013**, 23, 025111. [Google Scholar] [CrossRef] [PubMed] - Steinway, S.N.; Biggs, M.B.; Loughran, T.P., Jr.; Papin, J.A.; Albert, R. Inference of Network Dynamics and Metabolic Interactions in the Gut Microbiome. PLoS Comput. Biol.
**2015**, 11. [Google Scholar] [CrossRef] [PubMed] - Lavrova, A.I.; Postnikov, E.B.; Zyubin, A.Y.; Babak, S.V. Ordinary differential equations and Boolean networks in application to modelling of 6-mercaptopurine metabolism. R. Soc. Open Sci.
**2017**, 4, 160872. [Google Scholar] [CrossRef] [PubMed] - Natalie Berestovsky, L.N. An Evaluation of Methods for Inferring Boolean Networks from Time-Series Data. PLoS ONE
**2013**, 8, e66031. [Google Scholar] [CrossRef] [PubMed] - Maucher, M.; Kracher, B.; Kuhl, M.; Kestler, H.A. Inferring Boolean network structure via correlation. Bioinformatics
**2011**, 27, 1529–1536. [Google Scholar] [CrossRef] [PubMed] - Maucher, M.; Kracht, D.V.; Schober, S.; Bossert, M.; Kestler, H.A. Inferring Boolean functions via higher-order correlations. Comput. Stat.
**2012**, 29, 97–115. [Google Scholar] [CrossRef] - Akutsu, T.; Miyano, S.; Kuhara, S. Identification of genetic networks from a small number of gene expression patterns under the Boolean network model. Pac. Symp. Biocomput.
**1999**, 4, 17–28. [Google Scholar]

**Figure 1.**Schematic representation of a Boolean network approach to investigate stability changes in aging signaling networks. First, the time-series data is binarized and reduced using the BASC A algorithm of the R-package BiTrinA [20]. The resulting time-series data is split into two age groups (young (n = 7) and aged (n = 8)) and used to infer Boolean networks using the R-package BoolNet [21]. In the next step, the stability of the resulting Boolean networks is investigated by perturbation experiments. The best-fit algorithm can return a number of different Boolean functions for each gene in the network. From these possible functions 1000 synchronous Boolean networks are created for each age group by randomly drawing one of the inferred Boolean functions for each gene. Next, randomly generated states ($x\left(t\right)$) are perturbed using bitflips (${x}^{\prime}\left(t\right)$). The normalized Hamming distance ($H(x,{x}^{\prime})$) of the successor states $x(t+1)$ and ${x}^{\prime}(t+1)$ and $x(t+5)$ and ${x}^{\prime}(t+5)$ of $x\left(t\right)$ and ${x}^{\prime}\left(t\right)$ is computed. This is repeated for 1000 random states, the successor states of 1000 random states and random attractor state following 1000 random states with random bitflips. Finally, the mean normalized Hamming distance of these 3000 tests for each of the 1000 networks of each phenotype is compared.

**Figure 2.**Network wiring of reconstructed Boolean networks, showing one of the possible combinations of the reconstructed functions which were drawn. (

**A**) shows a network representing the young phenotype and (

**B**) the aged phenotype.

**Figure 3.**(

**A**) shows the mean of the number of inputs of all Boolean functions of the young and aged phenotype Boolean networks as a bar plot. The standard deviations are included as error bars. (

**B**) The boxplot shows the average, normalized Hamming distance between the successor states $t+1$ and $t+5$ of 1000 random states, the successor states of 1000 random states, attractor states following on 1000 random states and their perturbed versions for 1000 random combinations of inferred Boolean functions of the young and aged phenotype (Wilcoxon rank sum test $p<2.2\times {10}^{-16}$ for all robustness comparisons).

**Figure 4.**Schematic representation of one gene in the gene expression data (NCBI GEO ID GSE362). In the experiments muscle samples from 15 healthy humans of different age (21–75) were taken. The samples were arranged in ascending order by age to form a time-series. Samples of all humans between 21–27 years represent the young phenotype. The samples of all humans between 67–75 years represent the aged phenotype.

**Table 1.**Overview over the measured normalized Hamming distances of the young and aged phenotypes starting from random initial states, random successor states and random attractor states compared to perturbed networks after one and after five state transitions.

After One State Transition | After Five State Transitions | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Young Phenotype | Aged Phenotype | Young Phenotype | Aged Phenotype | |||||||||

Min | Max | Mean | Min | Max | Mean | Min | Max | Mean | Min | Max | Mean | |

random initial state | 0.041 | 0.056 | 0.048 | 0.044 | 0.065 | 0.053 | 0.028 | 0.151 | 0.063 | 0.040 | 0.201 | 0.085 |

random successor state | 0.041 | 0.057 | 0.048 | 0.045 | 0.067 | 0.055 | 0.027 | 0.143 | 0.064 | 0.034 | 0.209 | 0.087 |

random attractor state | 0.036 | 0.057 | 0.047 | 0.037 | 0.064 | 0.054 | 0.004 | 0.144 | 0.060 | 0.007 | 0.211 | 0.083 |

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**MDPI and ACS Style**

Schwab, J.D.; Siegle, L.; Kühlwein, S.D.; Kühl, M.; Kestler, H.A. Stability of Signaling Pathways during Aging—A Boolean Network Approach. *Biology* **2017**, *6*, 46.
https://doi.org/10.3390/biology6040046

**AMA Style**

Schwab JD, Siegle L, Kühlwein SD, Kühl M, Kestler HA. Stability of Signaling Pathways during Aging—A Boolean Network Approach. *Biology*. 2017; 6(4):46.
https://doi.org/10.3390/biology6040046

**Chicago/Turabian Style**

Schwab, Julian Daniel, Lea Siegle, Silke Daniela Kühlwein, Michael Kühl, and Hans Armin Kestler. 2017. "Stability of Signaling Pathways during Aging—A Boolean Network Approach" *Biology* 6, no. 4: 46.
https://doi.org/10.3390/biology6040046