若手研究者インターナショナル・トレーニング・プログラム(ITP)
バイオインフォマティクスとシステムズバイオロジーの国際連携教育研究プログラム 報告書
Name: Yang Zhao
Title: Modelling the Robustness of Metabolic Pathways
Institute: Bioinformatics Center (Akutsu Laboratory), Institute for Chemical Research, Kyoto
University, Uji, Gokasho, Kyoto 6110011 Japan
Partner institute: Centre for Computational Biology, Mines ParisTech – Curie Institute – INSERM
U900 joint laboratory, Institut Curie, 11-13 rue Pierre et Marie Curie, 75005 Paris
Duration: September 9, 2011 – November 26, 2011
Report:Introduction of laboratory
The partner laboratory is Centre for ComputationalBiology belonging to Mines ParisTech. The group leaderis Prof. Jean-Philippe Vert who works at both
MineParisTech and Curie Institute. For thisinternational training program, I was staying in one ofProf. Jean-Philippe’s office at Curie institute. Curie
institute has a very nice building located in the southbank of Seine River, closed to the Luxembourg garden
and the Pantheon. Jean-Philippe laboratory shares anopen space with several other groups in this nicebuilding. Members in Curie Institute are free to chooseseats since each of them has a personal account for anaccess to all of the computers (with Linux OS) in thebuilding. These public computers are administrated bytheir media center so that they always ensure acontinuously upgraded and safe computational
environment for the researchers. Jean-Philippe lab havegroup meeting once a week, machine learning class

Figure 1: Curie Institute and the lobby where I

twice a week and also some other sporadic seminars.

had discussion with Prof. Jean-Philippe every

During my stay, I went to the institute by rental bikeweek.

(called velib’) every workday, shared different room with different people in the institute, and worked
directly together with Prof. Jean-Philippe on the project. All of the members in this lab were very
nice and they helped me to quickly get a hang of the study and life in Paris.

Research objective
As we know that metabolic pathways are complex systems of chemical reactions taking place inevery living cell to degrade substrates and synthesize molecules needed for life. Reactions can beperturbed by, e.g., drugs or mutations in DNA. When one or a few reactions are perturbed, the若手研究者インターナショナル・トレーニング・プログラム(ITP)
バイオインフォマティクスとシステムズバイオロジーの国際連携教育研究プログラム 報告書
impact of this perturbation on the cell can vary widely, depending on how many other reactions areimpacted in cascade. The group was recently interested in the project of modeling the robustness of
metabolic pathways in cancer research. Related approaches also proposed some measures such asFBA, MOMA, EMA and Synthetic Accessibility [3] for robustness evaluation, while our motivation
was to propose and implement new computational models to quantify the impact of inhibiting one ora few reactions on the global metabolic network, and to evaluate the robustness of metabolic
networks based on this model. During this international collaboration, my work is to propose such anew computational model and apply it to E-coli data [2].

Graph spectrum method
Through continually discussion with Prof. Jean-Philippe and Prof. Akutsu, I proposed a new method― Graph spectrum to study the robustness of metabolic networks.
1. Preliminaries
During this study, a metabolic network wasrepresented by its Laplacian graph spectrum

Given networkand topological change (on reaction removal)

Network by knockout R6i○

was represented by spectral distance. This
work was focused on computing spectrum
distance between metabolic network andsome new network, where such a newii Adjacent matrix
○

⋯ 0 1
⋱ 0 …
1 ⬚

network was constructed by removing all
inhibited reactions caused by knockout of a0 ⋯
1 ⋱1

⋯ 0 1
⋱ 0 …
1 ⬚0 ⋯
1 ⋱1single reaction from the original one (see alsoi ). I used a narrow Cauchy-Lorentz
Fig. 2: ○iii

𝜔1 ≤ 𝜔2 … ≤ 𝜔14

distribution showing as follows to computeiv )the spectral density of a network: (Fig. 2: ○𝑁𝑟2
𝜌(ω) = K ∑(𝜔 − 𝜔𝑖 )2 + 𝑟 2

Eigenvalues
𝜆1 ≤ 𝜆2 … ≤ 𝜆10iv
Graph spectral density
○(1)

𝑖=1

where 𝑟 is a scale parameter, K is anormalization factor and ω𝑖 (𝑖 = 1, … , 𝑁) is
eigenvalues of the adjacent matrix of a graphin ascending order.

v○Spectrum distance (red color hatched pattern)

The distance between two networks withspectrum densities 𝜌1 (𝜔), 𝜌2 (𝜔) was definedv )as: (Fig. 2: ○+∝ε = √∫ [𝜌1 (𝜔) − 𝜌2 (𝜔)]2 𝑑𝜔
02. Program design(2)
Figure 2: An outline of graph spectrum method.

若手研究者インターナショナル・トレーニング・プログラム(ITP)
バイオインフォマティクスとシステムズバイオロジーの国際連携教育研究プログラム 報告書
In this section, I would like to introduce the major steps of this Graph spectrum method. There werefive steps involved in this research: (Fig. 2 gives a simple instance of the outline.)(i).Construct all possible networks by removing inhibited reactions and compounds caused by theknockout of some reaction in metabolic network;(ii).Construct the adjacent matrices of the given network and each new network;(iii).Compute the eigenvalues of these matrices;(iv).Use formula (1) to compute the density of a spectrum between the given data and each new data;(v).Finally, the distance between original network and each new network can be computed byfollowing formula (2).

Experimental results & Discussion
1. Spectrum distance results
I applied this method to E-coli data from KEGG
database and finished computing the spectrum
distance between the E-coli network and some newnetwork. Here a new network was constructed bysome reaction knockout. As an illustration, Fig. 3
shows a plot of the spectrum density of E-coli
network and new network constructed by reaction

Figure 3: Plot of the spectrum density ofR00416 knockout.

E-coli network and R00416 knockout. Red

2. Comparison to impact degree

and green dots represent E-coli data and new

I also investigated the correlation between spectrum

date with R00416 knockout, respectively.

distance and impact degree proposed by
Tamura-san’s recent paper [1]. The results areshown in Fig. 4. From the results, we can see that it
seems to have correlation between impact degreeand spectrum distance. However, there still existed
some cases that large (small) impact degreecorresponds to small (large) spectrum distance.
3. Discussion
Prof. Jean-Philippe and I discussed the reason why
the above cases were obtained. We got a conclusionthat in some cases, removing a large number ofinhibited reactions and compounds caused by a single
reaction did not change the structure of the metabolic
network too much because this reaction may not play anFigure 4: Result of comparison to impact
degree, where x axis and y axis denote
impact degree and spectrum distanceimportant role in the network and vice-versa. Through this collaboration, I successfully proposed a
new method to evaluate the robustness of metabolic network. Further comparison to some otherexisting approaches is supposed to be done to evaluate the efficiency of this method in the next step.

若手研究者インターナショナル・トレーニング・プログラム(ITP)
バイオインフォマティクスとシステムズバイオロジーの国際連携教育研究プログラム 報告書

Some activities
There were some parties during my stay in Curie
institute, some of which are organized by the schooland some others are hold by the office of my living
place. I joint several of them (Fig. 5: left), enjoyed thefood and also had very good time with those kindly
people (institute members or just people lived in thesame apartment). In the weekend, I also visited somefamous places in Paris, such as the Eiffel Tower (Fig.
5: top right) and the Sacre Coeru (Fig. 5: bottomright), etc.

Acknowledgements
First and foremost, I would like to express my sincere

Figure 5: Parties and travels.

thanks to Prof. Akutsu for his permission of my participation to this program and valuable advice
during my stay. My heartfelt thanks also go to Prof. Mamitsuka and Prof. Kanehisa for giving me
this international collaboration chance. I shall extend my thanks to Prof. Jean-Philippe for hisvaluable comments and helpful suggestions on the project < Modelling the Robustness of Metabolic
Pathways >. I would like to particularly thank the members in Jean-Philippe lab and the secretaryJennifer for their kindness, encouragement and help in my studies and life in Paris.

Figure 6: Jean-Philippe group (left), the secretary Jennifer (center) and PhD. Student Toby (right).

References[1]

K. Takemoto, T. Tamura, Y. Cong, W. K. Ching, J.P. Vert and Tatsuya Akutsu, Analysis of the Impact Degree
Distribution in Metabolic Networks Using Branching Process Approximation, Physica A: Statistical Mechanics
and its Applications, 391(1): 379-387, 2011

[2]

J. S. Edwards and B. O. Palsson, The Escherichia coli MG1655 in Silico Metabolic Genotype: its Definition,
Characteristices and Capabilities, PNAS, 97(10):5528-5533, 2000.

[3]

Z. Wunderlich and L. A. Mirny, Using the Topology of Metabolic Networks to Predict Viability of Mutant Strains,

Biophysical Journal, 91(6): 2304-2311, 2006.