lecture 4
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Lecture 4. Reaction system as ordinary differential equations Reaction system as stochastic process Metabolic network and stoichiometric matrix Graph spectral analysis/Graph spectral clustering and its application to metabolic networks - PowerPoint PPT PresentationTRANSCRIPT
Lecture 4•Reaction system as ordinary differential equations•Reaction system as stochastic process•Metabolic network and stoichiometric matrix•Graph spectral analysis/Graph spectral clustering and its application to metabolic networks•Metabolomics approach for determining growth-specific metabolites in based on FT-ICR-MS
Introduction
Metabolism is the process through which living cells acquire energy and building material for cell components and replenishing enzymes.
Metabolism is the general term for two kinds of reactions: (1) catabolic reactions –break down of complex compounds to get energy and building blocks, (2) anabolic reactions—construction of complex compounds used in cellular functioning
How can we model metabolic reactions?
What is a Model?Formal representation of a system using--Mathematics--Computer program
Describes mechanisms underlying outputs
Dynamical models show rate of changes with time or other variable
Provides explanations and predictions
Typical network of metabolic pathways
Reactions are catalyzed by enzymes. One enzyme molecule usually catalyzes thousands reactions per second (~102-107)
The pathway map may be considered as a static model of metabolism
Dynamic modeling of metabolic reactions is the process of understanding the reaction rates i.e. how the concentrations of metabolites change with respect to time
An Anatomy of Dynamical Models
DiscreteTime
DiscreteVariables
ContinuousVariables
Deterministic--No Space -- -- Space --
Stochastic
--No Space -- -- Space --
Finite StateMachines
Boolean Networks;Cellular Automata
Discrete Time Markov Chains
Stochastic Boolean Networks;Stochastic Cellular Automata
Iterated Functions;Difference Equations
Iterated Functions;Difference Equations
Discrete Time Markov Chains
Coupled Discrete Time Markov Chains
Continuous Time
DiscreteVariables
ContinuousVariables
Boolean Differential Equations
Ordinary Differential Equations
Coupled Boolean Differential Equations
Partial Differential Equations
Continuous Time Markov Chain
Stochastic Ordinary Differential Equations
Coupled Continuous Time Markov Chains
Stochastic Partial Differential Equations
Differential equations
Differential equations are based on the rate of change of one or more variables with respect to one or more other variables
An example of a differential equation
Source: Systems biology in practice by E. klipp et al
An example of a differential equation
Source: Systems biology in practice by E. klipp et al
Source: Systems biology in practice by E. klipp et al
An example of a differential equation
Schematic representation of the upper part of the Glycolysis
Source: Systems biology in practice by E. klipp et al.
The ODEs representing this reaction system
Realize that the concentration of metabolites and reaction rates v1, v2, …… are functions of time
ODEs representing a reaction system
The rate equations can be solved as follows using a number of constant parameters
The temporal evaluation of the concentrations using the following parameter values and initial concentrations
Notice that because of bidirectional reactions Gluc-6-P and Fruc-6-P reaches peak earlier and then decrease slowly and because of unidirectional reaction Fruc1,6-P2 continues to grow for longer time.
The use of differential equations assumes that the concentration of metabolites can attain continuous value.But the underlying biological objects , the molecules are discrete in nature.When the number of molecules is too high the above assumption is valid.But if the number of molecules are of the order of a few dozens or hundreds then discreteness should be considered.Again random fluctuations are not part of differential equations but it may happen for a system of few molecules.The solution to both these limitations is to use a stochastic simulation approach.
Stochastic Simulation
Stochastic modeling for systems biologyDarren J. Wilkinson2006
Molecular systems in cell
Molecular systems in cell[ ]: concentration of ith object
[m1(in)] [m2] [m3]
[m4]
[m5]
[m1(out)]
[r1] [r2] [r3] [r 4 ]
[p1][p2]
[p3]
[p4]
Molecular systems in cellcj: cj’: efficiency of jth process
[m1(in)] [m2] [m3]
[m4]
[m5]
[m1(out)]
[r1] [r2] [r3] [r 4 ]
[p1][p2]
[p3]
[p4]
c1
c2
c3 c4
c5c6
c7
c8
c9
c10
c11
c12
c13
Molecular systems for small molecules in cell
[m1(in)] [m2] [m3]
[m4]
[m5]
[m1(out)]
c1
c2
c3 c4
c5h1=c1 [m1(out)] h2=c2 [m1(in)]
h4=c5 [m2]
h3=c3 [m2] h5=c4 [m3]
c2 p1 ,r1
c5 p3 ,r3
c3 p2 ,r2 c4 p4 ,r4
Stochastic selection of reaction based on(h1, h2, h3, h4, h5)
Molecular systems for small molecules in cell
[m1(in)] [m2] [m3]
[m4]
[m5]
[m1(out)]=100
c1
c2
c3 c4
c5h1=c1 [m1(out)] = 100 c1
h2=c2 [m1(in)]
h4=c5 [m2]
h3=c3 [m2] h5=c4 [m3]
c2 p1 ,r1
c5 p3 ,r3
c5 p2 ,r2 c4 p4 ,r4
Stochastic selection of reaction based on(100 c1, h2, h3, h4, h5)Reaction 1
Molecular systems for small molecules in cell
[m1(in)]=1[m2]=0
[m3]=0
[m4]=0
[m5]=0
[m1(out)]=99
c1
c2
c3 c4
c5h1=c1 [m1(out)]= 99 c1
h2=c2 [m1(in)]= 1 c2
h4=c5 [m2]=0
h3=c3 [m2]=0
h5=c4 [m3]=0
Stochastic selection of Reaction based on (99 c1, 1 c2, 0, 0, 0) Reaction 1
Molecular systems for small molecules in cell
[m1(in)]=2[m2]=0
[m3]=0
[m4]=0
[m5]=0
[m1(out)]=98
c1
c2
c3 c4
c5h1=c1 [m1(out)]= 98 c1
h2=c2 [m1(in)]= 2 c2
h4=c5 [m2]=0
h3=c3 [m2]=0
h5=c4 [m3]=0
Stochastic selection of Reaction based on (98 c1, 2 c2, 0, 0, 0) Reaction 1
Molecular systems for small molecules in cell
[m1(in)]=3[m2]=0
[m3]=0
[m4]=0
[m5]=0
[m1(out)]=97
c1
c2
c3 c4
c5h1=c1 [m1(out)]= 97 c1
h2=c2 [m1(in)]= 3 c2
h4=c5 [m2]=0
h3=c3 [m2]=0
h5=c4 [m3]=0
Stochastic selection of Reaction based on (97 c1, 3 c2, 0, 0, 0) Reaction 2
Molecular systems for small molecules in cell
[m1(in)]=2[m2]=1
[m3]=0
[m4]=0
[m5]=0
[m1(out)]=97
c1
c2
c3 c4
c5h2=c2 [m1(in)]= 2 c2
h4=c5 [m2]=1 c5
h3=c3 [m2]=1 c3
h5=c4 [m3]=0
h1=c1 [m1(out)]= 97 c1
Stochastic selection of Reaction based on (97 c1, c2, 1 c3, 0, 1 c5) Reaction 1
Molecular systems for small molecules in cell
[m1(in)]=3 [m2]=1[m3]=0
[m4]=0
[m5]=0
[m1(out)]=96
c1
c2
c3 c4
c5h1=c1 [m1(out)]= 97 c1
h2=c2 [m1(in)]= 3 c2
h4=c5 [m2]=1 c5
h3=c3 [m2]=1 c3
h5=c4 [m3]=0
Stochastic selection of Reaction(96 c1, 3 c2, 1 c3, 0, 1 c5)Reaction 3
Molecular systems for small molecules in cell
[m1(in)]=3 [m2]=0[m3]=1
[m4]=0
[m5]=0
[m1(out)]=96
c1
c2
c3 c4
c5h1=c1 [m1(out)]= 97 c1
h2=c2 [m1(in)]= 3 c2
h4=c5 [m2]=0
h3=c3 [m2]=0
h5=c4 [m3]=1 c4
Stochastic selection of Reaction based on (96 c1, 3 c2, 0, 1 c4 , 0)…
Input data
[m1(in)] [m2] [m3]
[m4]
[m5]
[m1(out)]
c1
c2
c3 c4
c5
c1m1(out) m1(in)
c2m1(in) m2
c3m2 m3 m3 m5
c4
m2 m5
c5
[m1(out)] [m1(in)] [m2] [m3] [m4] [m5]Initial concentrations
Reaction parameters and Reactions
Gillespie AlgorithmStep 0: System Definitionobjects (i = 1, 2,…, n) and their initial quantities: Xi(init) reaction equations (j=1,2,…,m)
Rj: m(Pre)j1 X1 + ...+ m(Pre)
jn Xn = m (Post) j1 X1 +...+ m (Post)
jnXn
reaction intensities: ci for Rj
Step 4: Quantities for individual objects are revised base on selected reaction equation[Xi] ← [Xi] – m (Pre)
s + m(Post)s
Step 1: [Xi]Xi(init)
Step 2: hj: :probability of occurrence of reactions based on cj (j=1,2,..,m) and [Xi] (i=1,2,..,n)
Step 3: Random selection of reaction Here a selected reaction is represented by index s.
Gillespie Algorithm (minor revision)
Step 0: System Definitionobjects (i = 1, 2,…, n) and their initial quantities Xi(init) reaction equations (j=1,2,…,m)Rj: m(Pre)
j1 X1 + ...+ m(Pre)jn Xn = m (Post)
j1 X1 +...+ m (Post) jnXn
reaction intensities: ci for Rj
Step 4: Quantities for individual objects are revised base on selected reaction equation X’i = [Xi] – m (Pre)
s + m(Post)s
Step 1: [Xi]Xi(init)
Step 2: hj: :probability of occurrence of reactions based on cj (j=1,2,..,m) and [Xi] (i=1,2,..,n)
Step 3: Random selection of reaction Here a selected reaction is represented by index s.
X’i 0 No
Step 5: [Xj] X’i
YesX’i Xi
max No
Yes
Software: Simple Stochastic Simulator1.Create stoichiometric data file and initial condition file
Reaction Definition: REQ**.txtR1 [X1] = [X2]R2 [X2] = [X1]
Reaction Parameter ci [X1] [X1] [X2] [X2]R1 1 1 0 0 1R2 1 0 1 1 0
Stoichiometetric data and ci: REACTION**.txt
ci is set by user
[X1] 100 0[X2] 100 0
Initial condition: INIT**.txt
max number (for ith object, max number is set by 0 for ith , [Xi]0 Initial quantitiy
Objects used are assigned by [ ] .
http://kanaya.naist.jp/Lecture/systemsbiology_2010
Software: Simple Stochastic Simulator2. Stochastic simulation
Stoichiometetric data and ci: REACTION**.txt
Initial condition: INIT**.txt
Reaction Parameterc: 1.0 1.0//time [X1] [X2]0.00 100.0 100.00.0015706073545097992 101.0 99.00.015704610011372147 100.0 100.00.01670413203960951 101.0 99.0….….
Simulation results: SIM**.txt
0
50
100
150
0 10 20 30 40 50
[X1][X2]
Example of simulation results# of type of chemicals =2
0100200300400500600700800900
1000
0 2 4 6 8
[X1][X2]
[X1][X2] c=1, [X1]=1000, [X2]=0
[X1][X2] [X2][X1]c1=c2=1[X1]=1000
0100200300400500600700800900
1000
0 1 2 3 4 5 6 7 8 9 10
[X1][X2]
# of type of chemicals =3
[X1][X2][X3], [X1]=1000, c=1
0100200300400500600700800900
1000
0 2 4 6 8 10
[X1][X2][X3]
[X1] [X2][X3], [X1]=1000, c=1
0100200300400500600700800900
1000
0 5 10 15 20
[X1][X2][X3]
[X1][X2][X3], [X1]=1000, c=1
0100200300400500600700800900
1000
0 2 4 6 8 10
[X1][X2][X3]
[X1][X2][X3],[X1]=1000, c=1
0100200300400500600700800900
1000
0 2 4 6 8
[X1][X2][X3]
loop reaction [X1][X2][X3][X1], [X1]=1000, c=1
0100200300400500600700800900
1000
0 2 4 6 8 10
[X1][X2][X3]
Representation of ReactionData Set
[X1] 2[X1]c1
[X1] + [X2] 2[X2]c2
[X2] Φc3
Reaction Data Initial Condition
[X1]= X1(init)
[X2]= X2(init)
Example 2 EMP
glcK ATP + [D-glucose] -> ADP + [D-glucose-6-phosphate]glcK ATP + [alpha-D-glucose] -> ADP + [D-glucose-6-phosphate]pgi [D-glucose-6-phosphate] <-> [D-fructose-6-phosphate]pgi [D-fructose-6-phosphate] <-> [D-glucose-6-phosphate]pgi [alpha-D-glucose-6-phosphate] <-> [D-fructose-6-phosphate]pgi [D-fructose-6-phosphate] <-> [alpha-D-glucose-6-phosphate] pfk ATP + [D-fructose-6-phosphate] -> ADP + [D-fructose-1,6-bisphosphate]fbp [D-fructose-1,6-bisphosphate] + H(2)O -> [D-fructose-6-phosphate] + phosphatefbaA [D-fructose-1,6-bisphosphate] <-> [glycerone-phosphate] + [D-glyceraldehyde-3-phosphate]fbaA [glycerone-phosphate] + [D-glyceraldehyde-3-phosphate] <-> [D-fructose-1,6-bisphosphate]tpiA [glycerone-phosphate] <-> [D-glyceraldehyde-3-phosphate]tpiA [D-glyceraldehyde-3-phosphate] <-> [glycerone-phosphate]gapA [D-glyceraldehyde-3-phosphate] + phosphate + NAD(+) -> [1,3-biphosphoglycerate] + NADH + H(+)gapB [1,3-biphosphoglycerate] + NADPH + H(+) -> [D-glyceraldehyde-3-phosphate] + NADP(+) + phosphatepgk ADP + [1,3-biphosphoglycerate] <-> ATP + [3-phospho-D-glycerate]pgk ATP + [3-phospho-D-glycerate] <-> ADP + [1,3-biphosphoglycerate]pgm [3-phospho-D-glycerate] <-> [2-phospho-D-glycerate]pgm [2-phospho-D-glycerate] <-> [3-phospho-D-glycerate]eno [2-phospho-D-glycerate] <-> [phosphoenolpyruvate] + H(2)Oeno [phosphoenolpyruvate] + H(2)O <-> [2-phospho-D-glycerate]
Example 2 EMP
D-glucose alpha-D-glucose
D-fructose-6-phosphatealpha-D-glucose-6-phosphate
[D-fructose-1,6-bisphosphate]
[D-glyceraldehyde-3-phosphate]
D-glucose-6-phosphate
[glycerone-phosphate]
[1,3-biphosphoglycerate]
[3-phospho-D-glycerate]
[2-phospho-D-glycerate]
[phosphoenolpyruvate]
Metabolic network and stoichiometric matrix
Typical network of metabolic pathways
Reactions are catalyzed by enzymes. One enzyme molecule usually catalyzes thousands reactions per second (~102-107)
The pathway map may be considered as a static model of metabolism
For a metabolic network consisting of m substances and r reactions the system dynamics is described by systems equations.
The stoichiometric coefficients nij assigned to the substance Si and the reaction vj can be combined into the so called stoichiometric matrix.
What is a stoichiometric matrix?
Example reaction system and corresponding stoichiometric matrix
There are 6 metabolites and 8 reactions in this example system
stoichiometric matrix
Binary form of N
To determine the elementary topological properties, Stiochiometric matrix is also represented as a binary form using the following transformation
nij’=0 if nij =0nij’=1 if nij ≠0
Stiochiometric matrix is a sparse matrix
Source: Systems biology by Bernhard O. Palsson
Information contained in the stiochiometric matrix
Stiochiometric matrix contains many information e.g. about the structure of metabolic network , possible set of steady state fluxes, unbranched reaction pathways etc. 2 simple information:•The number of non-zero entries in column i gives the number of compounds that participate in reaction i.
•The number of non-zero entries in row j gives the number of reactions in which metabolite j participates.
So from the stoicheometric matrix, connectivities of all the metabolites can be computed
Information contained in the stiochiometric matrix
There are relatively few metabolites (24 or so) that are highly connected while most of the metabolites participates in only a few reactions
Source: Systems biology by Bernhard O. Palsson
Information contained in the stiochiometric matrix
In steady state we know that
The right equality sign denotes a linear equation system for determining the rates v
This equation has non trivial solution only for Rank N < r(the number of reactions)
K is called kernel matrix if it satisfies NK=0
The kernel matrix K is not unique
The kernel matrix K of the stoichiometric matrix N that satisfies NK=0, contains (r- Rank N) basis vectors as columns
Every possible set of steady state fluxes can be expressed as a linear combination of the columns of K
Information contained in the stiochiometric matrix
-
With α1= 1 and α2 = 1, , i.e. at steady state v1 =2, v2 =-1 and v3 =-1
Information contained in the stiochiometric matrix
And for steady state flux it holds that J = α1 .k1 + α2.k2
That is v2 and v3 must be in opposite direction of v1 for the steady state corresponding to this kernel matrix which can be easily realized.
Information contained in the stiochiometric matrix
Reaction SystemStoicheometric Matrix
The stoicheomatric matrix comprises r=8 reactions and Rank =5 and thus the kernel matrix has 3 linearly independent columns. A possible solution is as follows:
Information contained in the stiochiometric matrix
Reaction System
The entries in the last row of the kernel matrix is always zero. Hence in steady state the rate of reaction v8 must vanish.
Reaction System
The entries for v3 , v4 and v5 are equal for each column of the kernel matrix, therefore reaction v3 , v4 and v5 constitute an unbranched pathway . In steady state they must have equal rates
Information contained in the stiochiometric matrix
If all basis vectors contain the same entries for a set of rows, this indicate an unbranched reaction path
Elementary flux modes and extreme pathwaysThe definition of the term pathway in a metabolic network is not straightforward.
A descriptive definition of a pathway is a set of subsequent reactions that are in each case linked by common metabolites
Fluxmodes are possible direct routes from one external metabolite to another external metabolite.
A flux mode is an elementary flux mode if it uses a minimal set of reactions and cannot be further decomposed.
Elementary flux modes and extreme pathways
Elementary flux modes and extreme pathways
Extreme pathway is a concept similar to elementary flux modeThe extreme pathways are a subset of elementary flux modes
The difference between the two definitions is the representation of exchange fluxes. If the exchange fluxes are all irreversible the extreme pathways and elementary modes are equivalent
If the exchange fluxes are all reversible there are more elementary flux modes than extreme pathways
One study reported that in human blood cell there are 55 extreme pathways but 6180 elementary flux modes
Elementary flux modes and extreme pathways
Source: Systems biology by Bernhard O Palsson
Elementary flux modes and extreme pathways
Elementary flux modes and extreme pathways can be used to understand the range of metabolic pathways in a network, to test a set of enzymes for production of a desired product and to detect non redundant pathways, to reconstruct metabolism from annotated genome sequences and analyze the effect of enzyme deficiency, to reduce drug effects and to identify drug targets etc.
Lecture7Topic1: Graph spectral analysis/Graph spectral clustering and its application to metabolic networksTopic 2: Concept of Line GraphsTopic 3: Introduction to Cytoscape
Graph spectral analysis/
Graph spectral clustering
PROTEIN STRUCTURE: INSIGHTS FROM GRAPH THEORY
bySARASWATHI VISHVESHWARA, K. V. BRINDA and N. KANNANy
Molecular Biophysics Unit, Indian Institute of ScienceBangalore 560012, India
Laplacian matrix L=D-A
Adjacency Matrix Degree Matrix
Eigenvalues of a matrix A are the roots of the following equation
|A-λI|=0, where I is an identity matrix
Let λ is an eigenvalue of A and x is a vector such that
then x is an eigenvector of A corresponding to λ .
-----(1)N×N N×1 N×1
Eigenvalues and eigenvectors
Node 1 has 3 edges, nodes 2, 3 and 4 have 2 edges each and node 5 has only one edge. The magnitude of the vector components of the largest eigenvalue of the Adjacency matrix reflects this observation.
Node 1 has 3 edges, nodes 2, 3 and 4 have 2 edges each and node 5 has only one edge. Also the magnitude of the vector components of the largest eigenvalue of the Laplacian matrix reflects this observation.
The largest eigenvalue (lev) depends upon the highest degree in the graph. For any k regular graph G (a graph with k degree on all the vertices), the eigenvalue with the largest absolute value is k. A corollary to this theorem is that the lev of a clique of n verticesis n − 1. In a general connected graph, the lev is always less than or equal to (≤ ) to the largest degree in the graph. In a graph with n vertices, the absolute value of lev decreasesas the degree of vertices decreases. The lev of a clique with 11 vertices is 10 and that of a linearchain with 11 vertices is 1.932
a linear chain with 11 vertices
In graphs 5(a)-5(e), the highest degree is 6. In graphs 5(f)-5(i), the highest degree is 5, 4, 3 and 2 respectively.
It can be noticed that the lev is generally higher if the graph contains vertices of high degree. The lev decreases gradually from the graph with highest degree 6 to the one with highest degree 2. In case of graphs 5(a)-5(e), where there is one common vertex with degree 6 (highest degree) and the degrees of the other vertices are different (less than 6 in all cases), the lev differs i.e. the lev also depends on the degree of the vertices adjoining the highest degree vertex.
This paper combines graph 4(a) and graph 4(b) and constructs a Laplacian matrix with edge weights (1/dij ), where dij is the distance between vertices i and j. The distances between the vertices of graph 4(a) and graph 4(b) are considered to be very large (say 100) and thus the matrix elements corresponding to a vertex from graph 4(a) and the other from graph 4(b) is considered to have a very small value of 0.01. The Laplacian matrix of 8 vertices thus considered is diagonalized and their eigenvalues and corresponding vector components are given in Table 3.
The vector components corresponding to the second smallest eigenvalue contains the desired information about clustering, where the cluster forming residues have identical values. In Fig. 4, nodes 1-5 form a cluster (cluster 1) and 6-8 form another cluster (cluster 2).
Metabolome Based Reaction Graphs of M. tuberculosis and M. leprae: A Comparative Network AnalysisbyKetki D. Verkhedkar1, Karthik Raman2, Nagasuma R. Chandra2, Saraswathi Vishveshwara1*1 Molecular Biophysics Unit, Indian Institute of Science, Bangalore, India, 2 Bioinformatics Centre, Supercomputer Education and Research Centre, Indian Institute of Science, Bangalore, IndiaPLoS ONE | www.plosone.org September 2007 | Issue 9 | e881
Construction of network
R1 R2
R3 R4
Stoichrometric matrix
Following this method the networks of metabolic reactions corresponding to 3 organisms were constructed
Analysis of network parameters
Giant component of the reaction network of e.coli
Giant components of the reaction networks of M. tuberculosis and M. leprae
Analyses of sub-clusters in the giant componentGraph spectral analysis was performed to detect sub-clusters of reactions in the giant component.To obtain the eigenvalue spectra of the graph, the adjacency matrix of the graph is converted to a Laplacian matrix (L), by the equation:L=D-Awhere D, the degree matrix of the graph, is a diagonal matrix in which the ith element on the diagonal is equal to the number of connections that the ith node makes in the graph.
It is observed that reactions belonging to fatty acid biosynthesis and the FAS-II cycle of the mycolic acid pathway in M. tuberculosis form distinct, tightly connected sub-clusters.
Identification of hubs in the reaction networksIn biological networks, the hubs are thought to be functionally important and phylogenetically oldest.
The largest vector component of the highest eigenvalue of the Laplacian matrix of the graph corresponds to the node with high degree as well as low eccentricity. Two parameters, degree and eccentricity, are involved in the identification of graph spectral (GS) hubs.
Identification of hubs in the reaction networks
Alternatively, hubs can be ranked based on their connectivity alone (degree hubs).
It was observed that the top 50 degree hubs in the reaction networks of the three organisms comprised reactions involving the metabolite L-glutamate as well as reactions involving pyruvate. However, the top 50 GS hubs of M. tuberculosis and M. leprae exclusively comprised reactions involving L-glutamate while the top GS hubs in E. coli only consisted of reactions involving pyruvate.
The difference in the degree and GS hubs suggests that the most highly connected reactions are not necessarily the most central reactions in the metabolome of the organism
91
Metabolomics approach for determining growth-specific metabolites based on FT-ICR-MS
92
[1] Metabolomics
Metabolite 1 Metabolite 2 Metabolite 3
Metabolite 4
Metabolite 5
Metabolite 6
B C
D EF
I L
H K
Interpretation of Metabolome
Species
Molecular weight and formula
Fragmentation Pattern
Metabolite information
Species Metabolites
Tissue Samples
Species-Metabolite relation DB
Experimental Information
MS
Data Processing from FT-MS data acquisition of a time series experiment to assessment of cellular conditions
0.1
1
10
0 200 400 600 800Time (min)
OD
600
T1T2
T3T4
T5T6 T7 T8(a) Metabolite quantities
for time series experiments
Metabolites
MM+1M/2(e) Assessment of cellular condition by metabolite composition
sM
Mk
Mk
ss
j
j
x
xxxx
xx
xxxxx
...............................
........
..........
..........
...................................
22
11
21
221
11211
m/zTi
me
poin
t
(b) Data preprocessing and constructing data matrix
(d) Annotation of ions as metabolites
(c) Classification of ions into metabolite-derivative group
Detectedm/z
Theoreticalm/z
Molecular formula Exact mass Error Candidate Species
72.9878 73.9951 C2H2O3 74.0004 0.0053 Glyoxylic acid Escherichia coli
143.1080 144.1153 C8H16O2 144.1150 0.0003 Octanoic acid Escherichia coli
662.1037 663.1109 C21H27N7O14P2 663.1091 0.0018 NAD Escherichia coli
664.1095 665.1168 C21H29N7O14P2 665.1248 0.0080 NADH Escherichia coli
.....
..........
..........
.....
..... ..........
.......... .....
.....
.....
.....
.....
..........
.....
.....
.....
E. coli
94
time
719.4869
722.505
747.5112
NMNk
tMtjtt
sM
Mk
Mk
ss
j
j
xx
x
xxx
xxx
x
xxxx
xx
xxxxx
NjNN ..........................
...............................
.........................
.........................
...............................
........
..........
..........
...................................
21
21
22
11
21
221
11211time 1
time 8
time 2
metab.1 metab.200(b) Data matrix
Software are provided by T. Nishioka (Kyoto Univ./Keio Univ.)
95
1-1
1-2
1-3
1-4,5
1-6
2-1
2-2
2-3
3
45
6
78
9
10
11
PG5
PG7
PG9 PG3
PG1PG6
PG2
PG4
PG10
PG8
M-1
M-2 M-3
M-4
M-5
M-6M-7
M-8
M-9M-10
M-11M-12
M-13
M-14
M-15
M-16
M-17
(c) Classification of ions into metabolite-derivative group (DPClus)
Correlation network for individual ions.
Intensity ratio between Monoisotope (M) and Isotope (M+1) # of Carbons in molecular formula:
96
(d) Annotation of ions as metabolites using KNApSAcK DBDetected
m/zaTheoretical
m/zMolecular
formula Exact mass Error Candidate Species
72.9878 73.9951 C2H2O3 74.0004 0.0053 Glyoxylic acid Escherichia coli143.1080 144.1153 C8H16O2 144.1150 0.0003 Octanoic acid Escherichia coli253.2137 254.2210 C16H30O2 254.2246 0.0036 omega-Cycloheptanenonanoic acid Alicyclobacillus acidocaldarius253.2185 254.2258 C16H30O2 254.2246 0.0012 omega-Cycloheptanenonanoic acid Alicyclobacillus acidocaldarius281.2444 282.2516 C18H34O2 282.2559 0.0042 Oleic acid Escherichia coli
C18H34O2 282.2559 0.0042 cis-11-Octadecanoic acid Lactobacillus plantarumC18H34O2 282.2559 0.0042 omega-Cycloheptylundecanoic acid Alicyclobacillus acidocaldarius
297.2410 298.2482 C18H34O3 298.2508 0.0026 alpha-Cycloheptaneundecanoic acid Alicyclobacillus acidocaldarius297.2467 298.2540 C18H34O3 298.2508 0.0032 alpha-Cycloheptaneundecanoic acid Alicyclobacillus acidocaldarius297.2516 298.2589 C18H34O3 298.2508 0.0081 alpha-Cycloheptaneundecanoic acid Alicyclobacillus acidocaldarius321.0506 322.0579 C10H15N2O8P 322.0566 0.0013 dTMP Escherichia coli K12346.0570 347.0643 C10H14N5O7P 347.0631 0.0012 AMP Escherichia coli
C10H14N5O7P 347.0631 0.0012 3'-AMP Escherichia coliC10H14N5O7P 347.0631 0.0012 dGMP Escherichia coli
401.0168 402.0241 C10H16N2O11P2 402.0229 0.0012 dTDP Escherichia coli402.9962 404.0035 C9H14N2O12P2 404.0022 0.0013 UDP Escherichia coli426.0237 427.0310 C10H15N5O10P2 427.0294 0.0016 Adenosine 3',5'-bisphosphate Escherichia coli
C10H15N5O10P2 427.0294 0.0016 ADP Escherichia coliC10H15N5O10P2 427.0294 0.0016 dGDP Escherichia coli
454.0391 455.0464 C20H19Cl2NO7 455.0539 0.0075 Antibiotic MI 178-34F18A2 Actinomadura spiralis MI178-34F18C20H19Cl2NO7 455.0539 0.0075 Antibiotic MI 178-34F18C2 Actinomadura spiralis MI178-34F18
458.1112 459.1185 C15H22N7O8P 459.1267 0.0083 Phosmidosine B Streptomyces sp. strain RK-16495.1039 496.1112 C24H20N2O10 496.1118 0.0006 Kinamycin A Streptomyces murayamaensis sp. nov.
C24H20N2O10 496.1118 0.0006 Kinamycin C Streptomyces murayamaensis sp. nov.505.9908 506.9981 C10H16N5O13P3 506.9957 0.0023 ATP,dGTP Escherichia coli547.0756 548.0829 C16H26N2O15P2 548.0808 0.0020 dTDP-L-rhamnose Escherichia coli565.0503 566.0576 C15H24N2O17P2 566.0550 0.0025 UDP-D-glucose Escherichia coli
C15H24N2O17P2 566.0550 0.0025 UDP-D-galactose Escherichia coli606.0775 607.0848 C17H27N3O17P2 607.0816 0.0032 UDP-N-acetyl-D-mannosamine Escherichia coli
C17H27N3O17P2 607.0816 0.0032 UDP-N-acetyl-D-glucosamine Escherichia coli
618.0897 619.0970 C17H27N5O16P2 619.0928 0.0042 ADP-L-glycero-beta-D-manno-heptopyranose Escherichia coli
662.1037 663.1109 C21H27N7O14P2 663.1091 0.0018 NAD Escherichia coli664.1095 665.1168 C21H29N7O14P2 665.1248 0.0080 NADH Escherichia coli741.4729 742.4801 C32H62N12O8 742.4814 0.0012 Argimicin A Sphingomonas sp.786.4712 787.4785 C41H65N5O10 787.4731 0.0054 BE 32030B Nocardia sp. A32030853.3166 854.3239 C41H46N10O9S 854.3170 0.0069 Argyrin G Archangium gephyra Ar 8082
C45H56Cl2N2O10 854.3312 0.0073 Decatromicin B Actinomadura sp. MK73-NF4C39H50N8O12S 854.3269 0.0030 Napsamycin C Streptomyces sp. HIL Y-82,11372
97
PLSY
Responses
X
N=8
M=220K=1
N=8
PLS (Partial Least Square regression model) -- extract important combinations of metabolites. N (biol.condition) << M (metabolites)
(e) Estimation of cell condition based on a function of the composition of metabolites.
Y(Cell density)= a1 x1 +…+ aj xj +….+ aM xM
xj, the quantity for jth metabolites
cell condition cell condition
mea
sure
men
t poi
nts
Metabolites0.1
1
10
0 200 400 600 800Time (min)
OD
600
T1T2T3
T4T5
T6 T7 T8
0.1
0.0
ajUDP-glucose, UDP-galactose
NAD
Parasperone A
UDP-N-acetyl-D-glucosamineUDP-N-acetyl-D-mannosamine
ADP, Adenosine 3',5'-bisphosphate, dGDP
UDP
omega-Cycloheptyl-alpha-hydroxyundecanoate
Octanoic aciddTMP, dGMP, 3'-AMP
NADH
Argyrin G
dTDP
ATP, dGTP
Lenthionine
omega-CycloheptylnonanoatedTDP-6-deoxy-L-mannoseomega-Cycloheptylundecanoate, cis-11-Octadecanoic acid
ADP-(D,L)-glycero-D-manno-heptose
Glyoxylate
omega-Cycloheptyl-alpha-hydroxyundecanoate
-0.15
Stationary-phase dominantExponential-phase dominant
y(OD600 Cell Density)= a1 x1 +…+ aj xj +….+ aM xM
aj > 0, stationary phase-dominant metabolites
xj , the quantity for jth
aj < 0, exponential phase-dominant metabolites
(e) Assessment of cellular condition by metabolite compositionDetection of stage-specific metabolites
(PLS model of OD600 to metabolite intensities)
Red: E.coli metabolites;Black: Other bacterial metabolites
PG1,3,5,7,9MS/MS analyses
120 metabolites
80 metabolites
MS/MS analysesPG2,4,6,8,10
10 Phosphatidylglycerols detected by MS/MS spectra
(b) Relation of mass differences among PG1 to 10marker molecules
PG530:1(14:0,16:1)
PG132:1(16:0,16:1)
PG334:1(16:0,18:1)
PG631:0(14:0,c17:0)
PG233:0(16:0,c17:0)
PG434:5(16:0,c19:0)
PG734:2(16:1,18:1)
PG936:2(18:1,18:1)
PG835:1(16:1,c19:1)
PG1037:1(18:1,c19:0)
(Cluster 1)28.0281
14.0170
(Cluster 2)
14.0187 14.0110
14.0181
28.0315
28.0298 28.0237
2.0138
2.0051
28.0330
28.0314
14.0197
CFA CFA CFA
CFA CFA∆(CH2)2
US
US
∆(CH2)2
∆(CH2)2
∆(CH2)2
∆(CH2)2
∆(CH2)2
O
O C15H31
O
O
OX3
O
O C15H31
O
O
OX3
Cyclopropane Formation of PGs occurs in the transition from exponential to stationary phase.
Exponential phase
Stationary phase
Cyclopropane Formaiton of PGs
unsaturated PGs
cyclopropanated PGs