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Boolean Modeling and Simulation of Tumor Necrosis Factor- α Signaling Network Satyajit Rao 27 th June 2013
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  • Boolean Modeling and Simulation of Tumor

    Necrosis Factor- Signaling Network

    Satyajit Rao

    27th June 2013

  • Abstract

    Tumor necrosis factor- is known for its anti tumor effects. Molecu-

    lar details of TNF- signaling pathway have been elucidated well. However,

    mechanism of regulation between two opposing decisions, survival and death,

    remains unclear. Understanding of this mechanism could lead to identifica-

    tion of target molecules in order to favour apoptosis, and eventually to an

    improvement in treatment. Using Boolean modeling, we try to compute dy-

    namic steady states as a tool to predict a cells response to TNF- ligation.

    We analyse the steady states in a systematic manner, with the ultimate aim

    of determining an optimal set of target nodes in the above stated interest.

  • Contents

    List of Tables iv

    List of Figures v

    1 Introduction 1

    2 Basins of Attraction for Random Networks 4

    2.1 Response to stimuli . . . . . . . . . . . . . . . . . . . . . . . . 4

    2.2 Dynamic Network Model . . . . . . . . . . . . . . . . . . . . . 5

    2.3 Dynamic Equations . . . . . . . . . . . . . . . . . . . . . . . . 5

    2.4 Attractors and basin of attraction . . . . . . . . . . . . . . . . 6

    2.5 Numerical simulations . . . . . . . . . . . . . . . . . . . . . . 7

    2.6 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . 9

    3 Boolean Modeling and Simulation 11

    3.1 Boolean formalism for qualitative modeling . . . . . . . . . . . 12

    3.2 Structural Analysis . . . . . . . . . . . . . . . . . . . . . . . . 13

    3.3 Dynamic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 14

    3.4 Network Reduction . . . . . . . . . . . . . . . . . . . . . . . . 15

    i

  • 3.5 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

    3.6 Initialization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

    3.6.1 Housekeeping Constraint . . . . . . . . . . . . . . . . . 16

    3.7 Simulations in MATLAB . . . . . . . . . . . . . . . . . . . . . 16

    4 Methods of Quantitative Analysis of Attractors 18

    4.1 Analysis of Distance . . . . . . . . . . . . . . . . . . . . . . . 18

    4.2 Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

    4.3 Stability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 20

    4.3.1 Steady State Stability . . . . . . . . . . . . . . . . . . 20

    4.3.2 Asynchronous Markovian perturbation . . . . . . . . . 21

    5 Case Study Results 23

    5.1 Modeling TNF- Network . . . . . . . . . . . . . . . . . . . . 23

    5.2 Distance Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 25

    5.2.1 min-Hamming Distance . . . . . . . . . . . . . . . . . 25

    5.3 Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

    5.4 Stability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 26

    5.4.1 Perturbation analysis for steady states . . . . . . . . . 26

    5.4.2 Asychronous Markovian perturbation for cyclic attrac-

    tors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

    5.5 Phenotype switch . . . . . . . . . . . . . . . . . . . . . . . . . 29

    5.6 Toll-Like Receptor (TLR) Network . . . . . . . . . . . . . . . 30

    6 Conclusions and future work 32

    Bibliography 33

    ii

  • Bibliography 34

    Appendices 37

    A A simulation example: TOYNET 38

    B Identifying unsteady part of network 40

    C TNF pathway 43

    D List of Interactions 44

    iii

  • List of Tables

    5.1 Sets of nodes randomized or constrained while initializing . . . 24

    5.2 Truth table for phenotype based classification of steady states 26

    D.1 Table of Interactions in TNF- signaling . . . . . . . . . . . . 44

    D.2 Index of Species Alias used in Table D.1 . . . . . . . . . . . . 53

    iv

  • List of Figures

    2.1 Random network: distribution of size of basin of attraction . . 9

    2.2 Basin of attraction distribution for Storkey & Valabregue rule 10

    5.1 Flowchart for constructing Signaling Networks . . . . . . . . . 24

    5.2 Distribution of Hamming distances for a set of attractors . . . 25

    5.3 Histograms for transition fractions in TNF steady state sta-

    bility analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

    5.4 distribution of transition fractions returning to the same state

    for asynchronous perturbations . . . . . . . . . . . . . . . . . 29

    5.5 Transition fractions for TLR network . . . . . . . . . . . . . . 31

    A.1 Interaction hypergraph of a sample network TOYNET . . . . 39

    B.1 frequency with which a particular node is changing states in

    a set of cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

    B.2 Part of TNF network responsible for unsteady behaviour . . . 42

    C.1 Figure shows a part of TNF- signaling network in CellDesigner 43

    v

  • Chapter 1

    Introduction

    Interactions among biomolecules are being studied and elucidated at a very

    fast pace. Complex networks of interactions involving both intracellular and

    extracellular biomolecules (signaling networks) emerging out of these stud-

    ies, give us clues as to how a cell reacts to environmental stimuli. Tools for

    studying biological functions and reaction mechanisms of these biomolecules

    are very well established. It is the integrated behaviour of these networks as

    a whole, however, that has not been studied to a large extent.

    Leaving the study of individual biological entities, a paradigm of study

    of biological systems as a whole, has emerged as the field of Systems Biol-

    ogy. This field uses Mathematical and Computational modeling techniques to

    attempt to extract biological understanding from an integrated systems per-

    spective. The modeling formalism used is usually correlated with the amount

    of data one has about the system. Various formalisms exist, one extreme be-

    ing Ordinary Differential Equation paradigm, which is a true representation

    1

  • of interactions in a chemical reaction format. This is one extreme since it re-

    quires a huge amount of kinetic data to completely model one network. The

    other extreme is to compute graphical representations for networks, which

    is a data-driven regression approach as opposed to the specificity of ODEs.[11]

    Modeling of networks in a logic-based way is an approach lying between

    the two extremes, in that it requires minimal data about the reaction ki-

    netics, yet it can be used to study dynamics and make predictions on the

    networks behaviour. First used by Kauffman [8] to model gene regulation

    process, this modeling technique has garnered a lot of interest, since it came

    to light that certain dynamic steady states from logic-based model might

    correspond to specific cell phenotypes.[7]

    TNF- is a multifunctional cytokine playing a key role in apoptosis as

    well as cell survival in addition to inflammation and immunity. Antitumor

    activity of TNF- was shown in 1975 when William Coley found Coleys

    toxin, whose active component was isolated as TNF-, caused haemorrhagic

    necrosis of mice tumors [13]. It is known to exert cytotoxicity towards some

    cell lines in vitro while causing hemorrhagic tumor necrosis in vivo without

    affecting normal cells [14]. Though the complete underlying mechanism is

    unknown, the potential selective antitumoral activity has created interest

    in the cytokine. Currently TNF- is used synergistically with chemother-

    apy drugs in regional treatment of locally advanced soft tissue sarcomas and

    metastatic melanomas to avoid limb amputation [19].

    2

  • In this project, we curate, model and simulate a Boolean network of Tu-

    mor Necrosis Factor - signaling. The aim of the project is to find a set of

    most likely targets which can switch a cells fate from survival to apoptosis

    upon ligation by TNF-. From the simulations, we find steady states and

    limit cycles and conduct quantitative analysis of their stability. We also qual-

    itatively classify the steady states based on the two end responses of TNF-

    signaling: apoptosis and survival, using biological markers. We conduct a

    similar modeling and simulation exercise on another signaling network (Toll-

    like receptor, TLR) and perform the same stability analysis.

    Chapter 2 contains a graph theoretical exercise which deals with model-

    ing and simulating undirected random networks. We create attractors using

    some learning rules, and then study their stability to random stimuli (pertur-

    bations) using dynamic network models. Chapter 3 discusses the formalism

    of Boolean modeling and provides details of the simulation procedure.

    Chapter 4 describes methods of quantitative analysis of attractors found

    using synchronous simulation procedure. Chapter 5 presents the results ob-

    tained by simulating real networks, TNF- and TLR.

    3

  • Chapter 2

    Basins of Attraction for

    Random Networks

    2.1 Response to stimuli

    It is important for a network to respond with high sensitivity for small but

    important stimuli as well as with robustness to large stimuli. Scale free

    topologies that are often found in nature, are seen to enable high sensitivity

    to directed stimuli yet protecting the network from failure to random stimuli.

    Lot of recent studies have gone into studying topology of network formed by

    links (connections) between nodes. The distribution of these links, the degree

    distribution, carries important information about the networks capacity. [2]

    4

  • 2.2 Dynamic Network Model

    We use the Little-Hopfield model [10],[6]. This assumes that each node is

    influenced by the states of other nodes to which it is linked. Such models are

    useful to study the properties of multiple network states as attractors of the

    dynamics [2]. An undirected graph with N labelled nodes n edges distributed

    such that degree distribution is exponential or scale free, is the system. Each

    node has two internal Ising spin states of i = 1 [4] The topology of thenetwork is stored in a network adjacency matrix I with element Iij = 1 if i and

    j are nearest neighbours else zero [20]. The influence of nearest neighbours

    depends on the patterns stored. In general we can store any number of

    patterns using Hebbian learning rule of neural networks

    Jij = Iij1p

    p=1

    i j (2.1)

    2.3 Dynamic Equations

    Local field is defined at each vertex i by

    hi(t) =j

    Jijj(t) (2.2)

    Where j(t) is the spin state at time t at vertex j. So the field is a weighted

    sum of all spins states of nearest neighbouring nodes, the weights (Jij) being

    determined by the p stored patterns. Parallel dynamics are used in which,

    5

  • at time t, all spins are updated synchronously using Glauber dynamics as[5],

    i(t+ t) =

    +1 with probability

    (1 + exp

    (2hi(t)T0

    ))11 with probability

    (1 + exp

    (2hi(t)T0

    ))1 (2.3)We use the local majority rules for time evolution of spin patterns, which is

    actually Glauber dynamics at zero temperature. Thus,

    i(t+ 1) =

    +1 if hi(t) > 0

    1 if hi(t) < 0(2.4)

    If however, hi(t) = 0 we select the spin of that state to be +1 or -1 with

    equal probability. [20]

    2.4 Attractors and basin of attraction

    A subset of state space to which orbits originating from typical initial condi-

    tions tend as time increases is called an attractor. For an attractor, the set

    of initial conditions with long time behaviour approaching the attractor is

    called its basin of attraction. An attractor can be identified with a functional

    state of the system.[2]

    Impact of external stimuli can be understood through response of a sys-

    tem to perturbation as a measure of robustness for the process of switching

    between attractors. Since this is an undirected network, an edge between i

    and j is not different from an edge between j and i. hence it can be deduced

    6

  • that the influence matrix J is symmetric.

    A particular state of a network is a collection of spins of all the N nodes.

    A pattern is a state which is a functional state (and so an attractor of the

    dynamics) to be learnt by a network. For the current simulation, two random

    states are chosen from the state space and are learnt as patterns. This learn-

    ing sets the pairwise influence between nodes Jij such that they are stable

    states of the network.

    For sufficiently large number of links and for a broad range of network

    topologies, this form of non-zero pairwise influence will make the randomly

    selected patterns into attractors [2]. Now that the attractors are set, we

    can confirm that these are attractors by measuring size of their basin of

    attraction. A stimulus is modelled by flipping certain number of nodes of

    the pre-selected patterns and the resulting state is used as initial state for

    the dynamical equations. Size of basin of attraction for a given attractor

    is that number of nodes that need to be flipped before the dynamics of the

    network fails to bring it back to the attractor state.

    2.5 Numerical simulations

    A 200 node random network with connection probability of 0.04 was created.

    The expected number of nodes n is 796. 1000 simulations were carried out

    for random stimuli (flipping random nodes). The number of nodes flipped

    was increased until the dynamics failed to bring it back to original state.

    7

  • Simulation procedure:

    1. Generate a random network adjacency matrix was generated with pa-

    rameters N=200, p=0.04

    2. Generate two random state vectors out of the state space to store as

    patterns in the adjacency matrix

    3. Proceed to make them attractors by the Hebbian imprinting rule

    4. Flip n nodes to get an initial state for dynamical equations, update

    spins using dynamical equations.

    5. If the state doesnt come back to the attractor, that n is the size of basin

    of attraction. If it does come back, increase n and repeat procedure

    8

  • 2.6 Simulation results

    Figure 2.1: histogram obtained for a 1000 simulations of a 200 node network

    with connection probability 0.04. B is the size of basin of attraction (in

    number of nodes)

    A histogram for size of basin of attraction in 1000 simulations was obtained.

    The histogram is approximately centred around 100, this shows that basin of

    attraction for a random network to a random stimulus is 50% of the nodes.

    The same algorithm was employed, but with a different learning rule-

    9

  • Storkey and Valabregue [17] given by:

    J0ij = 0i, j and Jij = J1ij +1

    ni

    j

    1

    ni h

    ji

    1

    nhij

    j (2.5)

    where

    hij =n

    k=1,k 6=i,jJ1ik

    k (2.6)

    The distribution of sizes of basin of attraction for this rule is shown in 2.2

    Figure 2.2: Basin of attraction distribution for Storkey & Valabregue rule

    10

  • Chapter 3

    Boolean Modeling and

    Simulation

    With the increase in data available about biological interactions due to ad-

    vances in technology, disciplines like Systems Biology have emerged. Such

    disciplines try to model and analyze the immense amount of data using math-

    ematical modeling techniques. Gene regulation, metabolism, signal trans-

    duction are being studied at a high rate giving rise to the need for coherent

    representation of whole systems.[15] Modeling complex interactions of a large

    number of proteins is intuitively represented by a network. Interactions in a

    network are represented by directed edges, pointing in the direction of mass

    (flux) transfer or signal propagation. Species in the network are represented

    by nodes. Further, an edge can have a sign along with a direction, with

    positive sign modeling activation and negative, inhibition.[15]

    11

  • 3.1 Boolean formalism for qualitative model-

    ing

    A set of biological interactions is represented by a network. For further anal-

    ysis however, the graph must be converted into a set of equations, i.e. a

    model. A signal transduction network can be modeled either in a discrete

    or a continuous space. Continuous models include ODEs for the different

    reactions while discrete models include Boolean models and Petri Nets [16].

    A qualitative modeling formalism represents each entity by a variable which

    can only take up a finite set of values. However, the set of values may not

    be linearly correlated with the actual concentrations of the entity.

    The continuous ODE model requires a large amount of kinetic data which

    is rarely available. Hence Boolean models introduced by S. Kauffman [8] and

    R. Thomas [18] are preferred since they require no parameters. Each node

    can have two distinct states: ON (1) and OFF (0) when their concentration

    levels are above and below respective thresholds.

    Boolean equations are constructed with the following rules:

    The AND condition models the situation where two or more species aresimultaneously required to be at high concentrations for the reaction

    to occur.

    St+1(1) = St(5) AND St(6)

    12

  • The OR conditions model situations where any one species at high con-centration is enough for the reaction to occur.

    St+1(2) = St(3) OR St(4)

    NOT condition models the inhibition of one species by another.

    St+1(3) = NOT St(7)

    Thus, modeling signal transduction interactions as a network provides

    a unified template to coherently represent the whole system. Next, it is

    important to develop effective approaches to analyze the assembled network.

    A network model can be subject to two types of analyses- structural and

    dynamic.

    3.2 Structural Analysis

    A network model of biological interactions is as such a graph. Graph-

    theoretical measures can thus be used to shed light on the topological or-

    ganization of the network. Local topological measures provide information

    on individual nodes (e.g. node degree) while global topological measures

    provide information on the whole network. A degree distribution is a use-

    ful property to measure. In particular the node(s) with the highest degree,

    which upon removal can break the network down into multiple clusters.

    13

  • 3.3 Dynamic Analysis

    Time can be easily incorporated into a Boolean network model. Each node

    has its Boolean function. That function is evaluated to get the updated value

    (state) of the node.

    St+1(i) = fi(S(t)) (3.1)

    where St+1(i) is the state of the ith node at time (t+1) and fi is the Boolean

    function for that node. S(t) is the vector of states of all N nodes.

    The update paradigm can be of two types:

    1. Synchronous: In synchronous update paradigm, it is assumed that

    all species update simultaneously. In other words, the time scales of

    all reactions in the signaling network are assumed to be equal. This

    is of course, not accurate. Time scales of reactions can vary from

    a few seconds to a few hours. In that sense, synchronous update is

    deterministic. The synchronous paradigm is computationally efficient,

    but it gives rise to spurious cycles. [9]

    2. Asynchronous: To overcome the time scale drawback of synchronous

    paradigm, asynchronous algorithms are used. Knowing time scale data

    of some reactions, a metric can be assigned for each reaction, so that it

    updates at time steps which are multiples of its metric. This is called

    a deterministic asynchronous algorithm. Other algorithms include ran-

    dom order asynchronous, general asynchronous, etc. Asynchronous

    simulations are computationally exhaustive, especially for larger bio-

    14

  • logical systems, however they are able to replicate a wider range of

    biological behaviours.

    3.4 Network Reduction

    In a Boolean framework, the number of possible states of a network (the state

    space) is 2N where N is the number of nodes. Hence, it becomes impossible

    to map entire state transition graph for networks of large size. In such cases

    it is beneficial to reduce the number of nodes while keeping the essential

    biological features intact. For example, nodes which have both in-degree and

    out-degree equal to 1 can be clubbed with their respective preceding nodes.

    This reduces the actual number of nodes (and hence the state space) in the

    model but does not alter the models essence. some nodes attain the same

    state irrespective of update method or initial condition. Such nodes can be

    determined and removed.

    3.5 Simulations

    Simulation of Boolean network aims at generating a state transition graph.

    An example simulation of a dummy network is included in Appendix. In the

    following simulations we have implemented a synchronous update protocol

    for the Boolean network model since the focus was on finding steady states

    and limit cycles. Various kinds of asynchronous protocols can however be

    implemented easily. Synchronous update protocols are prone to generating

    spurious cycles [9], however steady states found using both protocols are the

    15

  • same.

    3.6 Initialization

    Synchronous update algorithm evaluates states of all species at time step

    t+1 using old values for all updates, that is, values at time step t. Hence it

    requires initialization of all nodes at t = 0. We randomly assign a value of 0

    to each node with half probability.

    3.6.1 Housekeeping Constraint

    From literature we have knowledge of the initial state of some species. Some

    constitutive proteins are known to be present in high concentrations, also

    called Housekeeping species. We found 114 such species and added the con-

    straint of keeping these nodes equal to 1 during initialization.

    3.7 Simulations in MATLAB

    There are many softwares for the purpose of Boolean simulations like Boolean-

    Net(Python) , SimboolNet(Cytoscape plugin) , GINsim, etc. However, for

    a large network, these softwares provided less flexibility. Hence, a set of

    MATLAB codes was written for the dynamic simulations with algorithms

    to detect steady states and cyclic attractors with filters for repeated steady

    states/ limit cycles.

    16

  • Finding all attractors of the dynamics of large size networks (e.g.TNF-

    -330 nodes) is a herculean task. But simulating this way we can get as

    many attractors as required, forming a fairly random sample. The results

    obtained here are then subject to various analysis methods. The algorithm

    of synchronous simulations is given below.

    1. State of the network is stored as a vector, S of dimension N 1.

    2. To generate an initial state of the network, we first fix the values of all

    Housekeeping nodes to 1.

    3. The complete state of the network at S(t = 0) , S0 is generated using

    a random number generator for the rest of the nodes.

    4. Update equations are written in the form of a function file. The input

    to that file is S(t) and the output is S(t+1)

    5. State vectors after each time step are stored in a matrix, STG (State

    transition graph) with the first column being S0, second S1 and so on.

    6. At each update step, we check if S(t+1) is equal to any column of the

    matrix STG. If S(t+1)=S(t), it is a steady state. Else if S(t+1) is

    equal to any other column, it is a cycle.

    7. If S(t+1) is not equal to any column in STG, we store S(t+1) in STG

    and move to the next iteration, till an attractor is reached.

    17

  • Chapter 4

    Methods of Quantitative

    Analysis of Attractors

    4.1 Analysis of Distance

    We can hypothesize that each attractor represents a functional state of the

    cell. It is useful to have a metric to measure the distance between two

    attractors. We have used two types of distances:

    1. min-Hamming distance:

    Min-Hamming distance between two attractors is the minimum number

    of nodes that must be flipped so as to change the state of the network

    directly from one attractor to another. In other words, it is the number

    of nodes which do not have the same state in both attractors.

    2. Euclidean distance:

    Considering a state of the network as an n 1 vector, the Euclidean

    18

  • distance between two attractors is

    d(Ai Aj) = n

    k=1

    (vik vjk)2 (4.1)

    where vi is the attractor state Ai represented as a vector.

    4.2 Classification

    The main aim of this project is to be able to identify ways to increase net-

    works disposition to one of the end results (apoptosis) over the other (pro-

    liferation). To enable this, we must first identify markers which differentiate

    a apoptosis-bound cell phenotype from that which is proliferation-bound.

    Caspase 8 is known for its role in initiation of apoptosis, but it is also

    required in non-apoptotic roles. The role of caspase 8 along with Fas-

    associated death domain (FADD), FLICE like inhibitory protein (FLIP),

    receptor-interacting protein kinase 1 and 3 (RIPK1, RIPK3) was reconciled

    with some previous findings by [12].

    Following ligation of TNF Receptor, RIPK1 is recruited to form a re-

    ceptor complex. This complex-I activates NF-B transcription. FLIP is a

    transcriptional target of NF-B whose upregulation is responsible for the

    non-apoptotic phenotype witnessed upon TNF ligation in most cell types.

    [12] FLIP forms a heterodimer with caspase-8 and inhibits the downstream

    activation of RIPK3 by RIPK1. If FLIP is blocked, TNF signalling follows

    19

  • the caspase 8 induced pro-apoptotic pathway. In the absence of caspase-8

    however, RIPK1-RIPK3 signalling proceeds unchecked resulting in RIPK3

    dependent programmed necrosis.

    To summarize,

    a High levels of FLIP: RIPK1-RIPK3 signalling inhibited by caspase 8-

    FLIP heterodimer, leads to cell survival.

    b Low levels of FLIP: caspase 8 activation proceeds unchecked, leads to

    apoptosis.

    c No caspase 8: RIPK3 induced programmed necrosis.

    4.3 Stability Analysis

    Similar to stability analysis of steady states in other mathematical mod-

    elling paradigms, stability of steady states and limit cycles can be checked

    in Boolean networks.

    4.3.1 Steady State Stability

    The steady states obtained from Boolean simulations are subject to per-

    turbation, and the resulting perturbed state is dynamically simulated till it

    reaches a steady state. Perturbation of an attractor Ai is done as follows.

    Only one node Ai(j),j (1, N) of the state is flipped at a time. Inputnodes, i.e. nodes which only have outgoing edges are not flipped, since

    20

  • they will always transition to a new attractor. Hence, for each attractor,

    we will have N perturbed states Aip

    Aip(j) = NOT(Ai(j)) (4.2)

    The perturbed state Aip is then subjected to dynamic simulation as aninput state.

    The resulting steady state/limit cycle is studied. A transition prob-ability is calculated based on fractions of the N perturbations of Ai

    returning to the same steady state or reaching a different steady state

    or limit cycle.

    Essentially, we study the dynamics of a subset of state space falling in the

    region of unit Hamming distance from an attractor. The transition probabil-

    ities thus help us define the shape of the basin around the attractor. If each

    perturbation returns to the same attractor, we can conclude it is a completely

    rounded basin.

    4.3.2 Asynchronous Markovian perturbation

    Synchronous Boolean framework does not account for the stochasticity that

    is possible in state transitions. Markov processes have been used to analyze

    gene regulatory networks[3]. Kervizic and Corcos (2008) [9] have described a

    methodology that computes the stability of cycles. A set of cycles is chosen

    as the state space for this analysis. Let S be the result of simulations. S is

    a set of cyclic attractors, and C is a cycle having k states {s1, s2, s3, . . . , sk}.

    21

  • Each state in C, si is perturbed by sequentially reevaluating each species by

    its own Boolean function one at a time, hence asynchronous.

    It is possible that in asynchronously triggering Node i, si will not change

    its state. The set of all input nodes will not be a part of this triggering since

    they do not update. This is similar in methodology to steady state stability

    analysis, only differing in the perturbation strategy. Here for each C Shaving k states,

    sip(j) = fj(X(t)),j (1, N)&i (1, k) (4.3)

    Thus each cycle C gives rise to Nk perturbed states. These Nk states are

    simulated synchronously until they reach attractors. Again, as computed in

    stability analysis of steady states, we compute fractions of kN perturbations.

    22

  • Chapter 5

    Case Study Results

    5.1 Modeling TNF- Network

    The signaling network of Tumor Necrosis Factor - was constructed from

    various studies available in literature. The representation was drawn using

    CellDesigner. Figure 3.1 provides a flowchart of the procedure used for con-

    struction of TNF- network. 330 nodes take part in the complex network, of

    which 216 nodes have Boolean equations associated with them. Hence, the

    rest 114 nodes are all input nodes, with only outgoing edges. The Boolean

    update rules for the 216 nodes were constructed by combining a subset of

    330 nodes using logical operators AND, OR or NOT.

    Next we study the set of nodes with housekeeping constraints (section

    3.6.1). Of 114 housekeeping nodes, 84 are input nodes. Hence, these nodes

    are effectively always ON in any simulation at any time step. Hence the

    initialization procedure for TNF- network is described in Table 5.1

    23

  • Figure 5.1: Flowchart for constructing Signaling Networks

    SET Input nodes Non-input nodes Type TOTAL

    SET A 30 84 constrained 114

    SET B 84 132 randomized 216

    TOTAL 114 216 - 330

    Table 5.1: Sets of nodes randomized or constrained while initializing

    24

  • 5.2 Distance Analysis

    5.2.1 min-Hamming Distance

    Figure 5.2: Distribution of Hamming distances for a set of attractors

    Figure 5.2 shows the distribution of Hamming distance between pairs of

    steady states. On an average, the distance between two attractors is approx-

    imately 80 nodes, that is, two attractors have on an average 80 nodes (out

    of 330) differing in states.

    25

  • 5.3 Classification

    The dynamics of a network goes through many states. While non-attractor

    states are visited in a transient fashion, attractors are visited often and from

    multiple paths. Attractors are also independent of the update paradigm

    used, and hence can be identified with phenotypes. Phenotypes of interest

    to us for the TNF- network are: Apoptosis and Survival. The markers

    for phenotypes are described in section 4.2. Accordingly, we classify steady

    states with respect to the states of the marker nodes.

    CASPASE-8 0 1 1 0

    FLIP 0 0 1 1

    Phenotype Necrosis Apoptosis Survival Necrosis

    Table 5.2: Truth table for phenotype based classification of steady states

    Of the 9638 steady states available, 45% (4411) attractors identify with

    the apoptosis phenotype markers while the rest (5227) fall under the survival

    category.

    5.4 Stability Analysis

    5.4.1 Perturbation analysis for steady states

    Following the procedure listed in section 4.3, all steady states were subject

    to unit perturbations per node. The distributions of transition fractions is

    shown in Figure 5.3. The results for about 9600 steady states are obtained

    as follows

    26

  • For 90 % of the steady states (approx. 8500) the results are the same.37% of 216 unit perturbations (79) return to the same steady state and

    the rest 63% take up new steady states.

    The set of 79 (and hence rest 137) nodes is also the same for these 8500attractors.

    The remaining 10% attractors show different results.

    We verified the possibility that the 8500 steady states might have thesame states for this set of 79 nodes, and vary only in the states of the

    rest. It is a possibility since the set of 8500 states can easily fall in the

    2137 state sub-space. However, that is not the case.

    5.4.2 Asychronous Markovian perturbation for cyclic

    attractors

    Following the procedure in section 4.3.2, the set of cyclic attractors obtained

    from synchronous simulations was analysed. It follows that input nodes

    (nodes with outgoing edges only) will not be a triggered since they do not

    have an update function. Thus we trigger each of the 216 updating nodes

    asynchronously. The results obtained are shown in figure 5.4.

    Transition fraction returning to the same cycle is greater than 0.9 for88% of state cycles.

    The same transition fraction is equal to 1 for 23% of state cycles

    27

  • Figure 5.3: Histograms for transition fractions in TNF steady state stabilityanalysis

    28

  • Figure 5.4: distribution of transition fractions returning to the same statefor asynchronous perturbations

    State cycles which have all perturbations transitioning back to the samecycle are termed as absorbing states. Other states are concluded to be

    spurious. [9]

    5.5 Phenotype switch

    Having classified the steady state attractors of TNF- network, we look at

    the possibility of phenotype switching. The procedure is same as the previous

    section, however, the set of attractors classified under the Survival category

    is used in stead of the whole set of attractors. At each perturbation, we check

    29

  • against the classification markers and note if the new steady state matches

    the markers of the switched phenotype, i.e. apoptosis. It is interesting to note

    that for 5227216 independent perturbations, not one incident of phenotypeswitch is observed. The same computation done with the set of attractors

    classified under apoptosis also yielded no instances of phenotype switch. It

    follows that all the unit-perturbed states of both sets fall in the basin of

    attraction of the respective phenotypes.

    5.6 Toll-Like Receptor (TLR) Network

    We have access to many curated signal transduction networks, and our lab

    members have developed codes to generate Boolean equations from graphs.

    One such network is that of Toll-like receptor. TLR networks Boolean model

    was simulated synchronously to get attractors. The stability analysis de-

    scribed in section 4.3 was performed on steady state attractors of TLR net-

    work as well.

    Figure 5.5 shows the transition fractions obtained from stability anal-ysis. Subplots 1 and 2 show histograms of transition fractions to other

    steady states and limit cycles respectively.

    For 92% of the 2460 steady states subject to this analysis, we haveobtained a transition fraction of 95% (of 1229) per attractor.

    Rest of the transitions all occur to limit cycles.

    For all 2460 1229 perturbations, the transition back to same steadystate is 0.

    30

  • Figure 5.5: The two plots show a histogram of transition fractions upon

    producing unit perturbations. TLR network has 1229 nodes. 2460 steady

    states were studied. x-axis is number of nodes as a fraction of 1229. Y- axis

    is the number of times (out of 2460) that a particular fraction was obtained.

    subplot 1 is for transitions to other steady states, subplot 2 is for transitions

    to limit cycles. For the set of steady states studied, fraction of transitions

    coming back to the same steady states is 0.

    31

  • Chapter 6

    Conclusions and future work

    From the examples of TNF- and TLR networks, we can see that we have

    developed a methodology to model and simulate Boolean networks to obtain

    attractors: point as well as cycles, and examine their stability. This method-

    ology can be applied to any known network, and we may observe systemic

    properties of signaling networks in general. Since attractors may be corre-

    lated with phenotypes, this methodology can be extended to finding domain

    of attraction of a particular phenotype.

    Future Work With the study of random networks, we found that it takes

    approximately 50% node flips to leave a particular attractors basin and reach

    another attractor. Though degree distributions of random networks and bio-

    logical networks are significantly different, it is a fair result that a unit node

    flip does not result in a switch from one phenotypes basin of attraction to

    another. Seeing as real networks have a degree distribution that is scale free

    as opposed to a Poissonian for random networks [1], we can fairly predict

    32

  • that the number of node flips, on an average, will not be as high as 50% to

    switch phenotype. It is then an interesting problem to identify, for a first,

    a single instance of phenotype switch, and eventually to identify an optimal

    set of nodes key to switch from survival phenotype to apoptosis.

    Synchronous simulation is computationally efficient, but wrong in its as-

    sumption of equal time scales of all reactions. Incorporating time-scales of

    different reactions, i.e. a deterministic asynchronous algorithm, will generate

    biologically more relevant attractors since it represents dynamics of a signal-

    ing network more accurately than a simple synchronous algorithm.

    As of now, we are scanning a large state space. However, the network

    can be simplified by removing particular nodes and interactions, without

    affecting the biological model. This procedure will require manual curation,

    but a reduced network will increase computational efficiency.

    33

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    36

  • Appendices

    37

  • Appendix A

    A simulation example:

    TOYNET

    Figure A.1 shows a sample interaction hypergraph with signed and directed

    edges. The model equations for TOYNET can be written as follows:

    A(t+1) = NOT D(t)

    B(t+1) = A(t) AND I1(t)

    C(t+1) = B(t) OR E(t)

    D(t+1) = C(t)

    E(t+1) = NOT I1(t) AND I2(t)

    F(t+1) = E(t) OR G(t)

    G(t+1) = F(t)

    We have 9 nodes and 7 Boolean functions. Nodes I1 and I2 are input

    nodes, they will not be updated. The state vector

    S(t)=[I1(t) I2(t) A(t) B(t) C(t) D(t) E(t) F(t) G(t)]

    38

  • Figure A.1: Interaction hypergraph of a sample network TOYNET

    keeps track of the state of the network. The network size is small, so is

    the state space (29 = 512). A state number can be assigned to each vector,

    which is the decimal counterpart of the binary number formed by S(t). For

    example,

    S = [1 0 0 0 0 1 1 0 0] will be termed State-268.

    1. Initialize S randomly.

    2. Calculate state number.

    3. Obtain S(t+1) from S(t) from the Boolean equations

    4. Update till an attractor is reached

    Say S(0) = [1 0 1 1 0 1 0 0 1] or 361 (hereafter referred to by state number).

    The state transitions which occur are: 361 53 89 381 125 125hence state 125 is an attractor.

    39

  • Appendix B

    Identifying unsteady part of

    network

    Initially, synchronous simulations would yield only limit cycles of length 4 for

    all inputs. Hence, we estimated there must be a continuously cycling part of

    the network. To detect that, we ran a simulation for all cycles which would

    detect nodes which were changing their value from one state in a cycle to

    another. The set of cycles C consists of m cycles {c1, c2, . . . , cm}of varyinglengths {l1, l2, . . . , lm,}. For each ci , ci(x) ci(x+ 1) is computed and thosenodes for which this difference is not zero are noted for all x (1, li). Thus wecan compute the frequency with which a particular node is changing states

    in a set of cycles.

    40

  • Figure B.1: This shows a frequency bar graph for a set of 500 cycles, with fre-

    quency of appearance of a node plotted against node number. As is evident,

    4 nodes are changing states in each of the 500 cycles.

    We infer from the above bar chart that these 4 nodes are responsible for

    the unsteady behaviour of the network. They are all connected and form a

    part of the network which cannot attain steady state for any input values.

    This part was later modified to reflect correct biological behavior. As can be

    seen from figure B.2, this part of the network does not have a steady state

    for any combination of inputs.

    41

  • Figure B.2: Part of TNF network responsible for unsteady behaviour

    42

  • Appendix C

    TNF pathway

    Figure C.1: Figure shows a part of TNF- signaling network in CellDesigner

    43

  • Appendix D

    List of Interactions

    Table D.1: Table of Interactions in TNF- signaling

    Target

    Node

    Boolean Equation

    SA39 SA40 |(SA31 & SA42 & SA539 ) |(SA31 & SA45 )SA137 (SA136 & SA135 ) |(SA136 & SA177 ) |(SA136 & SA27 )SA141 SA140 & SA139 & (SA688 |SA700 )SA134 CSA2 |(SA133 & SA132 ) |(SA133 & SA156 ) |(SA133 &

    SA292 )

    SA152 (CSA31 & SA291 ) |(CSA31 & SA151 )SA158 (SA159 & SA291 ) |(SA159 & SA135 ) |(SA159 & SA154 )SA161 (SA162 & SA291 ) |(SA162 & CSA31 )CSA31 (SA145 & SA149 ) |(SA145 & SA150 )SA222 (CSA36 & SA220 ) |(CSA36 & SA445 & SA58 & SA125 )SA223 (CSA36 & SA220 ) |(CSA36 & SA445 & SA58 & SA125 )

    44

  • SA451 (SA450 & SA126 ) |(SA450 & SA127 ) |(SA450 & SA130 )SA129 (SA530 ) |(SA291 ) |(SA128 & SA92 & SA90 ) |(SA128

    & SA21 ) |(SA128 & SA51 )SA58 (SA59 & SA21 ) |(SA59 & SA57 )SA125 (SA92 ) |(SA124 & SA106 ) |(SA124 & SA21 ) |(SA124 &

    SA51 )

    SA73 (SA72 & SA65 ) |(SA72 & SA71 )SA92 (SA88 & SA100 ) |(SA88 & SA102 )SA91 (SA87 & SA77 ) |(SA87 & SA100 & SA102 )CSA19 (CSA20 & SA31 ) |(CSA20 & SA76 ) |(CSA20 & SA84 &

    SA58 )

    SA117 (SA116 & SA115 ) |(SA116 & SA179 )CSA22 SA108 |CSA15SA254 SA243 |SA256SA263 SA256 |SA284SA276 SA243 |SA284SA272 SA256 |SA284SA146 SA141 |SA142SA154 SA152 |SA157SA250 SA247 |SA252 |SA249 |SA268 |SA266 |SA271 |SA246

    |SA251 |SA255 |SA257 |SA260 |SA262 |SA261 |SA264|SA267 |SA265 |SA269 |SA270 |SA143 |SA147

    SA568 SA567 |SA585SA572 SA571 |SA608 |SA609 |SA607SA291 SA146 |SA144

    45

  • SA701 CSA3 |SA135SA208 SA205 |SA202 |SA129SA77 SA539 |SA113 |(SA74 & CSA5 )SA176 SA21 |(SA175 & SA174 )SA31 SA135 |SA113 |(CSA3 & SA667 & SA38 )SA38 SA42 |SA113 |(SA37 & SA97 & SA58 )SA452 (SA451 & SA126 ) |(SA451 & SA130 )SA491 (SA492 & SA500 ) |(SA492 & SA503 )SA49 SA125 |(SA48 & SA47 )SA57 SA533 |(SA55 & SA56 & SA21 )CSA29 SA676 |SA677 |SA594 |(CSA27 & SA119 )SA106 SA125 |(SA105 & CSA11 )CSA18 SA113 |(CSA19 & SA76 & SA102 )SA112 SA113 |(SA111 & CSA5 )SA273 SA284

    SA245 SA243

    SA281 SA284

    SA253 SA284

    SA274 SA284

    SA282 SA284

    SA287 SA284

    SA279 SA284

    SA275 SA243

    SA280 SA284

    46

  • SA244 SA243

    SA248 SA243

    SA542 SA539

    SA294 SA539

    SA135 SA134

    SA144 SA141

    SA145 SA141

    SA143 SA141

    SA147 SA141

    SA138 SA136 & SA129

    SA139 SA137

    SA19 SA18 & CSA1

    SA142 SA138

    SA148 SA151 & SA58

    SA157 SA158

    SA156 SA155 & SA157

    SA21 SA20 & SA23

    SA160 SA161

    SA153 SA154 & SA125

    SA163 SA156

    SA23 SA22 & SA11

    SA173 SA172 & SA17

    SA174 SA173

    SA179 SA180 & SA176

    47

  • SA177 SA178

    CSA33 CSA32

    SA178 CSA33 & SA179

    SA175 CSA33 & CSA1 & SA132 & SA135 & SA160

    SA25 SA24 & SA157

    SA27 SA26

    SA26 SA25 & SA19

    CSA3 CSA1 & CSA2 & SA28 & SA29 & SA32

    SA34 SA33 & CSA1

    SA220 SA221 & SA222

    SA32 SA31 & SA34

    SA284 SA157

    SA243 SA163

    CSA1 SA2 & SA5

    SA249 SA259 & SA284

    SA258 SA259 & SA284

    SA268 SA283 & SA284

    SA36 SA35 & SA174

    SA37 SA36

    SA256 SA160

    SA289 SA288 & SA129

    SA35 CSA3

    SA98 SA208

    SA45 SA44 & CSA1

    48

  • SA292 SA294

    SA293 SA294

    SA444 SA443 & SA446

    SA445 CSA15

    SA446 SA445

    SA448 SA447 & SA130 & SA127

    SA449 SA448 & SA130

    SA453 SA452 & SA126

    SA455 SA454 & SA126

    CSA54 CSA52 & SA471

    CSA55 CSA53 & SA471

    CSA52 SA453 & SA470

    CSA53 SA455 & SA470

    SA486 SA485 & SA127 & SA126

    SA485 SA484

    SA492 SA493 & SA130

    SA42 SA43 & CSA18

    SA490 SA491 & SA500

    SA489 SA490 & SA503

    SA500 SA109

    SA502 SA501 & SA58

    SA503 SA502

    CSA56 SA494 & SA492 & SA449

    SA47 SA46 & CSA1

    49

  • SA2 SA1

    SA539 SA538 & SA129

    SA540 SA542

    SA541 SA540 & SA130

    CSA57 SA486 & SA541

    SA51 SA50 & CSA1

    SA560 SA562

    SA561 SA560 & SA503

    SA56 SA53 & SA49

    CSA59 SA569 & SA568

    SA570 CSA59

    SA571 SA570

    SA565 CSA58 & SA268

    SA567 SA566 & SA565

    SA566 SA559

    SA577 SA550

    SA578 SA558

    CSA58 SA577 & SA578

    SA581 CSA61 & CSA60

    SA582 CSA61 & CSA60

    CSA60 SA560 & SA580

    SA595 SA596 & SA126

    SA594 SA595 & SA503

    SA59 SA58 & SA61

    50

  • SA607 SA603

    SA608 SA604

    SA609 SA605

    SA61 SA60 & SA11

    SA615 SA616

    SA614 SA130 & SA615

    SA128 SA614

    SA63 SA62 & SA57

    SA65 SA64 & SA68

    SA616 SA208

    SA662 SA660 & SA125 & SA38

    SA667 SA665 & SA663

    SA663 SA662

    SA68 SA69 & SA63

    SA8 SA9 & CSA1

    SA29 SA146

    SA676 SA533

    SA677 SA288

    SA71 SA70 & SA38

    SA688 SA288

    SA606 SA563

    CSA17 SA288

    SA700 SA223

    CSA5 CSA6 & SA29 & SA31

    51

  • CSA4 CSA5 & SA123

    SA89 SA85 & SA100

    SA76 SA75 & SA77

    SA84 SA80 & SA77 & SA38

    SA104 SA92 & SA58

    SA7 SA6 & SA8

    SA90 SA86 & SA102

    SA81 SA84 & CSA19

    CSA9 SA93 & SA94

    SA97 SA96 & SA17

    CSA11 CSA8 & SA23

    SA96 SA97 & SA61

    CSA7 CSA9 & SA65 & SA56

    CSA12 CSA10 & SA445

    SA11 SA10 & SA7

    CSA8 CSA7 & SA97

    CSA10 CSA11 & SA125

    SA100 SA99 & SA38

    SA99 SA98

    SA102 SA73 & SA31

    CSA20 CSA14 & SA29 & SA112

    CSA16 CSA17 & CSA18

    CSA15 CSA16 & CSA25

    CSA23 CSA15

    52

  • CSA24 CSA23 & CSA18

    CSA21 CSA24 & SA445

    CSA26 CSA21 & SA109

    SA111 SA110

    SA115 SA114 & SA31

    SA119 SA118

    CSA27 CSA30 & SA120

    CSA30 CSA28 & SA444

    CSA28 CSA26 & SA565

    SA15 SA14 & CSA1

    SA120 SA117

    SA118 SA121 & SA123 & SA125

    SA123 SA122 & SA89 & SA91

    SA127 SA123

    SA126 SA125

    SA130 SA129

    SA132 SA131 & CSA3

    SA17 SA16 & SA15

    Table D.2: Index of Species Alias used in Table D.1

    Species

    Alias

    Species Name

    53

  • CSA1 TNF-R1-STNF ALPHA BR COMPLEX COM ACT

    C1-OUT CRD2 SIM PLAD SIM STNF ALPHA PRO

    ACT MULTI TNF-R1 PRO ACT MULTI CRD3 SIM

    CSA10 RAF COMPLEX COM C1-INS 14-3-3 PRO ACT B-RAF

    PRO PHO PHO CRAF/RAF-1 PRO ACT EMP PHO

    PHO PHO PHO PHO

    CSA11 RAF COMPLEX COM ACT C1-INS CRAF/RAF-1 PRO

    ACT EMP PHO PHO PHO PHO PHO PHO B-RAF PRO

    ACT PHO 14-3-3 PRO ACT

    CSA12 RAF COMPLEX COM C1-INS 14-3-3 PRO ACT B-RAF

    PRO PHO PHO CRAF/RAF-1 PRO PHO PHO PHO

    PHO PHO PHO

    CSA14 IKK COMPLEX COM C1-INS IKK ALPHA BR IKK1

    PRO EMP EMP MULTI IKK BETA BR IKK2 PRO EMP

    EMP MULTI IKK GAMMA BR NEMO PRO EMP

    MULTI ELKS PRO ACT HSP 90 PRO ACT MULTI

    CDC37 PRO ACT

    CSA15 NF- KAPPA B-I KAPPA B-PKA COMPLEX COM

    C1-INS NF- KAPPA B COM I KAPPA B COMPLEX

    COM PKAC PRO

    CSA16 NF- KAPPA B-I KAPPA B-PKA COMPLEX COM

    C1-INS I KAPPA B COMPLEX COM NF- KAPPA B

    COM PKAC PRO

    CSA17 NF- KAPPA B-I KAPPA B-PKA COMPLEX COM

    C1-INS I KAPPA B COMPLEX COM ACT NF- KAPPA

    B COM PKAC PRO P65/RELA PRO

    54

  • CSA18 IKK COMPLEX COM ACT C1-INS ELKS PRO ACT

    HSP 90 PRO ACT MULTI CDC37 PRO ACT IKK

    GAMMA BR NEMO PRO ACT UBI MULTI IKK BETA

    BR IKK2 PRO ACT PHO PHO MULTI IKK ALPHA BR

    IKK1 PRO ACT PHO PHO PHO MULTI

    CSA19 IKK COMPLEX COM C1-INS IKK BETA BR IKK2

    PRO EMP EMP MULTI IKK ALPHA BR IKK1 PRO

    ACT PHO PHO PHO MULTI IKK GAMMA BR NEMO

    PRO ACT UBI MULTI ELKS PRO ACT HSP 90 PRO

    ACT MULTI CDC37 PRO ACT

    CSA2 TRAF1/2 COMPLEX COM C1-INS TRAF 2 PRO TRAF

    1 PRO

    CSA20 IKK COMPLEX COM C1-INS IKK ALPHA BR IKK1

    PRO EMP EMP MULTI IKK BETA BR IKK2 PRO EMP

    EMP MULTI IKK GAMMA BR NEMO PRO ACT UBI

    MULTI ELKS PRO ACT HSP 90 PRO ACT MULTI

    CDC37 PRO ACT

    CSA21 NF- KAPPA B COM C1-INS P50 PRO ACT P65/RELA

    PRO PHO PHO

    CSA22 I KAPPA B COMPLEX COM C1-INS I KAPPA B

    ALPHA PRO PHO PHO UBI UBI I KAPPA B BETA

    PRO PHO PHO UBI

    CSA23 NF- KAPPA B COM C1-INS P65/RELA PRO P50 PRO

    CSA24 NF- KAPPA B COM C1-INS P65/RELA PRO PHO P50

    PRO ACT

    CSA25 (SCF)-TYPE E3 COM ACT C1-INS CUL1 PRO ACT

    SKP1 PRO ACT

    55

  • CSA26 NF- KAPPA B COM C1-INS P50 PRO ACT P65/RELA

    PRO PHO PHO PHO

    CSA27 NF- KAPPA B COM C2-INS P50 PRO ACT P65/RELA

    PRO PHO PHO PHO PHO UBI CREB/P300 PRO ACT

    PHO

    CSA28 NF- KAPPA B COM C2-INS P50 PRO ACT P65/RELA

    PRO PHO PHO PHO

    CSA29 NF- KAPPA B COM ACT C2-INS P50 PRO ACT

    P65/RELA PRO ACT PHO PHO PHO PHO UBI

    CREB/P300 PRO ACT PHO

    CSA3 TRADD COMPLEX COM ACT C1-INS TRAF1/2-CIAP

    COMPLEX COM TRADD PRO RIP PRO CIAP1/2 PRO

    CSA30 NF- KAPPA B COM C2-INS P50 PRO ACT P65/RELA

    PRO PHO PHO PHO UBI CREB/P300 PRO ACT PHO

    CSA31 APOPTOSOME COM ACT C1-INS APAF-1 PRO ACT

    DATP SIM CYTOCHROME C PRO ACT

    CSA32 CTSD COMPLEX COM C3-INS PRO-A-SMASE PRO

    PRE-PRO-CTSD PRO

    CSA33 CTSD COMPLEX COM C4-INN PRE-PRO-CTSD PRO

    PRO-A-SMASE PRO

    CSA36 BCL-BAD BR COMPLEX COM C1-INS BCL-XL PRO

    BAD PRO ACT

    CSA4 TAB COMPLEX COM C1-INS TAB1 PRO PHO PHO

    TAB2 PRO ACT PHO PHO PHO TAB3 PRO PHO PHO

    PHO

    CSA41 TRAF1/2-CIAP COMPLEX COM TRAF 1 PRO TRAF 2

    PRO

    56

  • CSA42 I KAPPA B COMPLEX COM I KAPPA B ALPHA PRO

    PHO PHO UBI UBI I KAPPA B BETA PRO PHO PHO

    UBI

    CSA43 NF- KAPPA B COM P50 PRO P65/RELA PRO

    CSA44 NF- KAPPA B COM P65/RELA PRO P50 PRO

    CSA45 I KAPPA B COMPLEX COM I KAPPA B BETA PRO

    PHO PHO I KAPPA B ALPHA PRO PHO PHO

    CSA46 NF- KAPPA B COM P50 PRO

    CSA47 I KAPPA B COMPLEX COM ACT I KAPPA B ALPHA

    PRO ACT EMP EMP I KAPPA B BETA PRO ACT

    EMP EMP

    CSA5 TAB COMPLEX COM ACT C1-INS TAB1 PRO ACT

    TAB2 PRO ACT PHO PHO TAB3 PRO ACT EMP EMP

    CSA52 TCF-SRECOMPLEX COM C2-INS SRE PRO ACT

    ELK-1 PRO ACT PHO PHO PHO PHO PHO

    CSA53 SAP1A-SRE COMPLEX COM C2-INS SAP-1A PRO

    ACT PHO PHO PHO PHO SRE PRO ACT

    CSA54 TCF-SRE-SRF COMPLEX COM ACT C2-INS SRE PRO

    ACT ELK-1 PRO ACT PHO PHO PHO PHO PHO SRF

    PRO ACT

    CSA55 SAP1A-SRE-SRF COMPLEX COM ACT C2-INS SRE

    PRO ACT SAP-1A PRO ACT PHO PHO PHO PHO SRF

    PRO ACT

    CSA56 TRE COMPLEX COM ACT C2-INS TRE PRO ACT

    ATF-2 PRO ACT PHO PHO PHO C-JUN PRO ACT

    PHO PHO PHO PHO

    57

  • CSA57 AP1 COM ACT C2-INS C-FOS PRO ACT PHO PHO

    PHO PHO C-JUN PRO ACT PHO PHO PHO PHO

    CSA58 P53-MDM-2 COMPLEX COM ACT C2-INS MDM-2

    PRO ACT P53 PRO

    CSA59 CYCLIN E-CDK2 COMPLEX COM C2-INS CDK2 PRO

    ACT CYCLIN E PRO ACT

    CSA6 TAB COMPLEX COM C1-INS TAB1 PRO TAB2 PRO

    TAB3 PRO

    CSA60 CYCLIN D1-CDK4 COMPLEX COM ACT C2-INS

    CYCLIN D1 PRO ACT CDK4 PRO ACT

    CSA61 RB COMPLEX COM ACT C2-INS RB PRO ACT E2F

    PRO DP1 PRO ACT

    CSA7 RAF COMPLEX COM C1-INS B-RAF PRO ACT PHO

    CRAF/RAF-1 PRO EMP PHO PHO PHO 14-3-3 PRO

    ACT

    CSA8 RAF COMPLEX COM C1-INS CRAF/RAF-1 PRO EMP

    PHO PHO PHO PHO PHO B-RAF PRO ACT PHO

    14-3-3 PRO ACT

    CSA9 RAF COMPLEX COM C1-INS CRAF/RAF-1 PRO EMP

    PHO PHO 14-3-3 PRO ACT B-RAF PRO 14-3-3 PRO

    ACT

    SA1 TNF-R1 PRO C1-OUT

    SA10 SPHINGOMYELIN SIM C1-OUT

    SA100 ASK1 PRO ACT PHO PHO C1-INS

    SA102 MEKK1 PRO ACT PHO PHO PHO PHO C1-INS

    SA104 MKK4/JNKK1/SEK1 PRO PHO PHO C1-INS

    SA105 MEK1/2 PRO C1-INS

    58

  • SA106 MEK1/2 PRO ACT PHO PHO C1-INS

    SA107 IKB DEG C1-INS

    SA108 26S PROTEOSOME PRO ACT C1-INS

    SA109 CK II PRO ACT C1-INS

    SA11 CERAMIDE SIM C1-INS

    SA110 TRAF6 PRO C1-INS

    SA111 TRAF6 PRO EMP MULTI C1-INS

    SA112 TRAF6 PRO ACT UBI MULTI C1-INS

    SA113 CYLD PRO ACT C1-INS

    SA114 P62 PRO C1-INS

    SA115 P62 PRO ACT C1-INS

    SA116 PKC ZETA PRO C1-INS

    SA117 PKC ZETA PRO ACT PHO C1-INS

    SA118 MSK1/2 PRO ACT PHO C1-INS

    SA119 MSK1/2 PRO ACT PHO C2-INS

    SA120 PKC ZETA PRO ACT PHO C2-INN

    SA121 MSK1/2 PRO C1-INS

    SA122 P38 PRO EMP C1-INS

    SA123 P38 PRO ACT PHO PHO C1-INS

    SA124 ERK1/2 PRO C1-INS

    SA125 ERK1/2 PRO ACT PHO PHO C1-INS

    SA126 ERK1/2 PRO ACT PHO PHO C2-INS

    SA127 P38 PRO ACT PHO PHO C2-INS

    SA128 JNK 1 PRO EMP C1-INS

    59

  • SA129 JNK 1 PRO ACT PHO PHO C1-INS

    SA130 JNK 1 PRO ACT PHO PHO C2-INS

    SA131 FADD PRO C1-INS

    SA132 FADD PRO ACT C1-INS

    SA133 PROCASPASE 8 PRO C1-INS

    SA134 CASPASE 8 BR (MACH COMMA FLICE COMMA BR

    MCH5 ) PRO DON C1-INS

    SA135 CASPASE 8 BR (MACH COMMA FLICE COMMA BR

    MCH5 ) PRO ACT DON MULTI C1-INS

    SA136 BID PRO C1-INS

    SA137 TBID PRO ACT DON C1-INS

    SA138 JBID PRO ACT C1-INS

    SA139 TBID PRO ACT DON C5-INS

    SA14 PC-PLC PRO C1-OUT

    SA140 BAX/BAK PRO C5-INS

    SA141 BAX/BAK PRO ACT MULTI C5-OUT

    SA142 JBID PRO ACT C5-INN

    SA143 AIF PRO ACT C1-INS

    SA144 OMI/HTRA2 PRO ACT C1-INS

    SA145 CYTOCHROME C PRO ACT C1-INS

    SA146 SMAC/DIABLO PRO ACT C1-INS

    SA147 ENDOG PRO ACT C1-INS

    SA148 PROCASPASE 9 PRO PHO C1-INS

    SA149 APAF-1 PRO ACT C1-INS

    SA15 PC-PLC PRO ACT C1-INN

    60

  • SA150 DATP SIM C1-INS

    SA151 PROCASPASE 9 PRO ACT EMP C1-INS

    SA152 CASPASE 9 BR ( ICE-LAP6 COMMA BR MCH6) PRO

    DON C1-INS

    SA153 CASPASE 9 BR ( ICE-LAP6 COMMA BR MCH6) PRO

    DON DON PHO MULTI C1-INS

    SA154 CASPASE 9 BR ( ICE-LAP6 COMMA BR MCH6) PRO

    ACT DON DON EMP MULTI C1-INS

    SA155 PROCASPASE 6 PRO C1-INS

    SA156 CASPASE 6 BR (MCH2 ALPHA ) PRO DON DON DON

    C1-INS

    SA157 CASPASE 3 BR (CPP32 COMMA YAMA COMMA BR

    APOPAIN) PRO ACT DON MULTI C1-INS

    SA158 CASPASE 3 BR (CPP32 COMMA YAMA COMMA BR

    APOPAIN) PRO DON C1-INS

    SA159 PROCASPASE 3 PRO C1-INS

    SA16 PC SIM C1-OUT

    SA160 CASPASE 7 BR (MCH3 COMMA ICE-LAP3 COMMA

    BR CMH-1) PRO ACT DON MULTI C1-INS

    SA161 CASPASE 7 BR (MCH3 COMMA ICE-LAP3 COMMA

    BR CMH-1) PRO DON C1-INS

    SA162 PROCASPASE 7 PRO C1-INS

    SA163 CASPASE 6(MCH2 ALPHA ) PRO ACT DON DON

    DON MULTI C1-INS

    SA17 DAG PRO ACT C1-INN

    SA172 PKC DELTA PRO C1-INS

    SA173 PKC DELTA PRO EMP PHO C1-INS

    61

  • SA174 PKC DELTA PRO ACT PHO PHO C1-INS

    SA175 A-SMASE PRO DON C4-TRA

    SA176 A-SMASE PRO ACT DON PHO C4-INS

    SA177 CATHEPSIN D PRO ACT C1-INS

    SA178 CATHEPSIN D PRO ACT C4-INN

    SA179 CERAMIDE SIM C4-OUT

    SA18 RAIDD PRO C1-INS

    SA180 SPHINGOMYELIN SIM C4-OUT

    SA19 RAIDD PRO ACT C1-INS

    SA2 TNF-R1 PRO MULTI C1-OUT

    SA20 C1P PRO C1-INS

    SA202 FHC PRO ACT C5-INS

    SA205 MN-SOD PRO ACT C5-INS

    SA208 ROS SIM C5-INS

    SA21 C1P PRO ACT C1-INS

    SA22 CAPK PRO C1-INS

    SA220 BAD14-3-3 PRO C1-INS

    SA221 P14-3-3 PRO ACT C1-INS

    SA222 BAD PRO PHO PHO PHO C1-INS

    SA223 BCL-XL PRO ACT C1-INS

    SA23 CAPK PRO ACT C1-INS

    SA24 PROCASPASE 2 PRO C1-INS

    SA243 CASPASE 6(MCH2 ALPHA ) PRO ACT DON DON

    DON MULTI C2-INS

    SA244 SATB1 PRO ACT C2-INS

    62

  • SA245 LAMIN PRO ACT C2-INS

    SA246 S3734 DEG C2-INS

    SA247 S3733 DEG C2-INS

    SA248 AP2- ALPHA PRO ACT C2-INS

    SA249 CAD PRO ACT C2-INS

    SA25 CASPASE 2 BR (NEDD2 COMMA ICH-1) PRO DON

    C1-INS

    SA250 APOPTOSIS PHE C2-INS

    SA251 S3732 DEG C2-INS

    SA252 S1 DEG C2-INS

    SA253 ACINUS PRO ACT C2-INS

    SA254 VIMENTIN PRO ACT C2-INS

    SA255 S11 DEG C2-INS

    SA256 CASPASE 7 BR (MCH3 COMMA ICE-LAP3 COMMA

    CMH-1) PRO ACT DON MULTI C2-INS

    SA257 S12 DEG C2-INS

    SA258 ICAD PRO C2-INS

    SA259 DFF PRO ACT C2-INS

    SA26 CASPASE 2 BR (NEDD2 COMMA ICH-1) PRO DON

    DON C1-INS

    SA260 S13 DEG C2-INS

    SA261 S15 DEG C2-INS

    SA262 S14 DEG C2-INS

    SA263 GAS2 PRO ACT C2-INS

    SA264 S16 DEG C2-INS

    63

  • SA265 S17 DEG C2-INS

    SA266 S22 DEG C2-INS

    SA267 S18 DEG C2-INS

    SA268 T PARP PRO C2-INS

    SA269 S19 DEG C2-INS

    SA27 CASPASE 2 BR (NEDD2 COMMA ICH-1) PRO ACT

    DON DON MULTI C1-INS

    SA270 S20 DEG C2-INS

    SA271 S21 DEG C2-INS

    SA272 FAK PRO ACT C2-INS

    SA273 GELSOLIN PRO ACT C2-INS

    SA274 D4-GDI PRO ACT C2-INS

    SA275 NUMA PRO ACT C2-INS

    SA276 DNA BR TOPOISOMERASE I PRO ACT C2-INS

    SA279 SREBPS PRO ACT C2-INS

    SA28 TRADD PRO C1-INS

    SA280 LIM-K1 PRO ACT C2-INS

    SA281 ALPHA ACTIN PRO ACT C2-INS

    SA282 SLK PRO ACT C2-INS

    SA283 PARP PRO ACT C2-INS

    SA284 CASPASE 3 BR (CPP32 COMMA YAMA COMMA

    APOPAIN) PRO ACT DON MULTI C2-INS

    SA287 AP24 PRO ACT C2-INS

    SA288 BCL-2 PRO ACT C1-INS

    SA289 BCL-2 PRO PHO C1-INS

    64

  • SA29 CIAP1/2 PRO ACT C1-INS

    SA291 XIAP PRO ACT C1-INS

    SA292 C-FLIP SUB L PRO ACT C1-INS

    SA293 C-FLIP SUB S PRO C1-INS

    SA294 C-FLIP PRO C1-INS

    SA3 CRD3 SIM

    SA31 RIP PRO ACT UBI C1-INS

    SA317 CRD2 SIM

    SA318 PLAD SIM

    SA319 STNF ALPHA PRO ACT MULTI

    SA32 RIP PRO C1-INS

    SA320 TNF-R1 PRO ACT MULTI

    SA321 CRD3 SIM

    SA322 TRAF 2 PRO

    SA323 TRAF 1 PRO

    SA324 TRADD PRO

    SA325 RIP PRO

    SA326 CIAP1/2 PRO

    SA327 TRAF 1 PRO

    SA328 TRAF 2 PRO

    SA329 TAB1 PRO PHO PHO

    SA33 CEZANNE PRO C1-INN

    SA330 TAB2 PRO ACT PHO PHO PHO

    SA331 TAB3 PRO PHO PHO PHO

    65

  • SA332 TAB1 PRO ACT

    SA333 TAB2 PRO ACT PHO PHO

    SA334 TAB3 PRO ACT EMP EMP

    SA335 TAB1 PRO

    SA336 TAB2 PRO

    SA337 TAB3 PRO

    SA338 B-RAF PRO ACT PHO

    SA339 CRAF/RAF-1 PRO EMP PHO PHO PHO

    SA34 CEZANNE PRO ACT C1-INS

    SA340 14-3-3 PRO ACT

    SA341 CRAF/RAF-1 PRO EMP PHO PHO PHO PHO PHO

    SA342 B-RAF PRO ACT PHO

    SA343 14-3-3 PRO ACT

    SA344 CRAF/RAF-1 PRO EMP PHO PHO

    SA345 14-3-3 PRO ACT

    SA346 B-RAF PRO

    SA347 14-3-3 PRO ACT

    SA348 14-3-3 PRO ACT

    SA349 B-RAF PRO PHO PHO

    SA35 TRAF2 PRO EMP EMP C1-INS

    SA350 CRAF/RAF-1 PRO ACT EMP PHO PHO PHO PHO

    PHO

    SA351 CRAF/RAF-1 PRO ACT EMP PHO PHO PHO PHO

    PHO PHO

    SA352 B-RAF PRO ACT PHO

    66

  • SA353 14-3-3 PRO ACT

    SA354 14-3-3 PRO ACT

    SA355 B-RAF PRO PHO PHO

    SA356 CRAF/RAF-1 PRO PHO PHO PHO PHO PHO PHO

    SA359 IKK ALPHA BR IKK1 PRO EMP EMP MULTI

    SA36 TRAF2 PRO PHO EMP C1-INS

    SA360 IKK BETA BR IKK2 PRO EMP EMP MULTI

    SA361 IKK GAMMA BR NEMO PRO EMP MULTI

    SA362 ELKS PRO ACT

    SA363 HSP 90 PRO ACT MULTI

    SA364 CDC37 PRO ACT

    SA365 PKAC PRO

    SA366 I KAPPA B ALPHA PRO PHO PHO UBI UBI

    SA367 I KAPPA B BETA PRO PHO PHO UBI

    SA368 P50 PRO

    SA369 P65/RELA PRO

    SA37 TRAF2 PRO PHO UBI MULTI C1-INS

    SA370 PKAC PRO

    SA371 P65/RELA PRO

    SA372 P50 PRO

    SA373 I KAPPA B BETA PRO PHO PHO

    SA374 I KAPPA B ALPHA PRO PHO PHO

    SA375 PKAC PRO

    SA376 P65/RELA PRO

    67

  • SA377 P50 PRO

    SA378 I KAPPA B ALPHA PRO ACT EMP EMP

    SA379 I KAPPA B BETA PRO ACT EMP EMP

    SA38 TRAF2 PRO ACT PHO UBI PHO MULTI C1-INS

    SA380 ELKS PRO ACT

    SA381 HSP 90 PRO ACT MULTI

    SA382 CDC37 PRO ACT

    SA383 IKK GAMMA BR NEMO PRO ACT UBI MULTI

    SA384 IKK BETA BR IKK2 PRO ACT PHO PHO MULTI

    SA385 IKK ALPHA BR IKK1 PRO ACT PHO PHO PHO

    MULTI

    SA386 IKK BETA BR IKK2 PRO EMP EMP MULTI

    SA387 IKK ALPHA BR IKK1 PRO ACT PHO PHO PHO

    MULTI

    SA388 IKK GAMMA BR NEMO PRO ACT UBI MULTI

    SA389 ELKS PRO ACT

    SA39 RIP PRO EMP UBI C1-INS

    SA390 HSP 90 PRO ACT MULTI

    SA391 CDC37 PRO ACT

    SA392 IKK ALPHA BR IKK1 PRO EMP EMP MULTI

    SA393 IKK BETA BR IKK2 PRO EMP EMP MULTI

    SA394 IKK GAMMA BR NEMO PRO ACT UBI MULTI

    SA395 ELKS PRO ACT

    SA396 HSP 90 PRO ACT MULTI

    SA397 CDC37 PRO ACT

    68

  • SA398 P50 PRO ACT

    SA399 P65/RELA PRO PHO PHO

    SA4 CRD2 SIM

    SA40 26S PROTEOSOME PRO ACT C1-INS

    SA400 I KAPPA B ALPHA PRO PHO PHO UBI UBI

    SA401 I KAPPA B BETA PRO PHO PHO UBI

    SA402 P65/RELA PRO

    SA403 P50 PRO

    SA404 P65/RELA PRO PHO

    SA405 P50 PRO ACT

    SA406 CUL1 PRO ACT

    SA407 SKP1 PRO ACT

    SA408 P50 PRO ACT

    SA409 P65/RELA PRO PHO PHO PHO

    SA41 S3815 DEG C1-INS

    SA410 P50 PRO ACT

    SA411 P65/RELA PRO PHO PHO PHO PHO UBI

    SA413 P50 PRO ACT

    SA414 P65/RELA PRO PHO PHO PHO

    SA415 P50 PRO ACT

    SA416 P65/RELA PRO ACT PHO PHO PHO PHO UBI

    SA418 P50 PRO ACT

    SA419 P65/RELA PRO PHO PHO PHO UBI

    SA42 A20 PRO ACT PHO C1-INS

    69

  • SA421 APAF-1 PRO ACT

    SA422 DATP SIM

    SA423 CYTOCHROME C PRO ACT

    SA424 PRO-A-SMASE PRO

    SA425 PRE-PRO-CTSD PRO

    SA426 PRE-PRO-CTSD PRO

    SA427 PRO-A-SMASE PRO

    SA43 A20 PRO C1-INS

    SA432 BCL-XL PRO

    SA433 BAD PRO ACT

    SA44 CARP2 PRO C1-INS

    SA443 CREB/P300 PRO EMP C2-INS

    SA444 CREB/P300 PRO ACT PHO C2-INS

    SA445 PKAC PRO ACT C1-INS

    SA446 PKAC PRO ACT C2-INS

    SA447 ATF-2 PRO C2-INS

    SA448 ATF-2 PRO PHO PHO C2-INS

    SA449 ATF-2 PRO ACT PHO PHO PHO C2-INS

    SA45 CARP2 PRO ACT C1-INS

    SA450 ELK-1 PRO C2-INS

    SA451 ELK-1 PRO PHO C2-INS

    SA452 ELK-1 PRO PHO PHO C2-INS

    SA453 ELK-1 PRO ACT PHO PHO PHO PHO PHO C2-INS

    SA454 SAP-1A PRO C2-INS

    70

  • SA455 SAP-1A PRO ACT PHO PHO PHO PHO C2-INS

    SA46 GRB-2 PRO C1-INS

    SA47 GRB-2 PRO ACT C1-INS

    SA470 SRE PRO ACT C2-INS

    SA471 SRF PRO ACT C2-INS

    SA472 C-FOS GEN C2-INS

    SA473 C-FOS RNA C2-INS

    SA474 SRE PRO ACT

    SA475 ELK-1 PRO ACT PHO PHO PHO PHO PHO

    SA476 SAP-1A PRO ACT PHO PHO PHO PHO

    SA477 SRE PRO ACT

    SA478 SRE PRO ACT

    SA479 ELK-1 PRO ACT PHO PHO PHO PHO PHO

    SA48 SOS PRO C1-INS

    SA480 SRF PRO ACT

    SA481 SRE PRO ACT

    SA482 SAP-1A PRO ACT PHO PHO PHO PHO

    SA483 SRF PRO ACT

    SA484 C-FOS PRO EMP EMP C1-INS

    SA485 C-FOS PRO EMP EMP C2-INS

    SA486 C-FOS PRO ACT PHO PHO PHO PHO C2-INS

    SA489 C-JUN PRO PHO PHO PHO PHO PHO PHO PHO PHO

    C2-INS

    SA49 SOS PRO ACT C1-INS

    71

  • SA490 C-JUN PRO PHO PHO PHO EMP PHO PHO PHO PHO

    C2-INS

    SA491 C-JUN PRO PHO PHO PHO EMP PHO EMP PHO PHO

    C2-INS

    SA492 C-JUN PRO ACT PHO PHO PHO PHO C2-INS

    SA493 C-JUN PRO EMP EMP EMP EMP EMP EMP EMP

    EMP C2-INS

    SA494 TRE PRO ACT C2-INS

    SA495 C-JUN RNA C2-INS

    SA496 C-JUN GEN C2-INS

    SA497 TRE PRO ACT

    SA498 ATF-2 PRO ACT PHO PHO PHO

    SA499 C-JUN PRO ACT PHO PHO PHO PHO

    SA5 STNF ALPHA PRO ACT MULTI

    SA50 MADD PRO C1-INS

    SA500 CK II PRO ACT C2-INS

    SA501 GSK3 BETA PRO ACT EMP C1-INS

    SA502 GSK3 BETA PRO PHO C1-INS

    SA503 GSK3 BETA PRO ACT EMP C2-INS

    SA506 XIAP GEN C2-INS

    SA507 A20 GEN C2-INS

    SA508 BCL2 GEN C2-INS

    SA509 GADD45 BETA RNA C2-INS

    SA51 MADD PRO ACT C1-INS

    SA510 GADD45 BETA GEN C2-INS

    72

  • SA511 BCL2 RNA C2-INS

    SA512 XIAP RNA C2-INS

    SA513 A20 RNA C2-INS

    SA514 CIAP1/2 GEN C2-INS

    SA515 CIAP1/2 RNA C2-INS

    SA516 I KAPPA B GEN C2-INS

    SA517 I KAPPA B RNA C2-INS

    SA518 CYLD RNA C2-INS

    SA519 CYLD GEN C2-INS

    SA520 TRAF2 GEN C2-INS

    SA521 TRAF2 RNA C2-INS

    SA522 TRAF1 GEN C2-INS

    SA523 TRAF1 RNA C2-INS

    SA524 CFLIP GEN C2-INS

    SA525 CFLIP RNA C2-INS

    SA526 MN-SOD GEN C2-INS

    SA527 MN-SOD RNA C2-INS

    SA528 FHC GEN C2-INS

    SA529 FHC RNA C2-INS

    SA53 RAS PRO C1-INS

    SA530 GADD45 BETA PRO ACT C1-INS

    SA531 PTEN GEN C2-INS

    SA532 PTEN RNA C2-INS

    SA533 PTEN PRO ACT C1-INS

    73

  • SA538 ITCH PRO EMP C1-INS

    SA539 ITCH PRO ACT PHO PHO PHO C1-INS

    SA540 C-JUN PRO EMP EMP EMP EMP EMP EMP EMP

    EMP C2-INS

    SA541 C-JUN PRO ACT PHO PHO PHO PHO C2-INS

    SA542 C-JUN PRO EMP EMP EMP EMP EMP EMP EMP

    EMP C1-INS

    SA543 C-FOS PRO ACT PHO PHO PHO PHO

    SA544 C-JUN PRO ACT PHO PHO PHO PHO

    SA545 P53 GEN C2-INS

    SA546 EGR-1 RNA C2-INS

    SA547 P53 RNA C2-INS

    SA548 P21 SUPER WAF1/CIP1 GEN C2-INS

    SA549 P21 SUPER WAF1/CIP1 RNA C2-INS

    SA55 PI3K (P85) PRO EMP C1-INS

    SA550 MDM-2 PRO C1-INS

    SA551 EGR-1 GEN C2-INS

    SA552 CYCLIN D1 GEN C2-INS

    SA553 CYCLIN D1 RNA C2-INS

    SA554 MDM-2 GEN C2-INS

    SA555 MDM-2 RNA C2-INS

    SA558 P53 PRO C1-INS

    SA559 P21 SUPER WAF1/CIP1 PRO C1-INS

    SA56 RAS PRO ACT C1-INS

    SA560 CYCLIN D1 PRO ACT C2-INS

    74

  • SA561 CYCLIN D1 PRO PHO C2-INS

    SA562 CYCLIN D1 PRO C1-INS

    SA563 EGR-1 PRO C1-INS

    SA565 P53 PRO ACT PHO C2-INS

    SA566 P21 SUPER WAF1/CIP1 PRO C2-INS

    SA567 P21 SUPER WAF1/CIP1 PRO ACT C2-INS

    SA568 CYCLIN E PRO ACT C2-INS

    SA569 CDK2 PRO ACT C2-INS

    SA57 PI3K (P85) PRO ACT PHO C1-INS

    SA570 G1-S PHASE TRANSITION PHE C2-INS

    SA571 CELL CYCLE PHE C2-INS

    SA572 CELL PROLIFERATION PHE C2-INS

    SA573 MDM-2 PRO ACT

    SA574 P53 PRO

    SA575 CDK2 PRO ACT

    SA576 CYCLIN E PRO ACT

    SA577 MDM-2 PRO ACT C2-INS

    SA578 P53 PRO ACT C2-INS

    SA58 AKT/PKB PRO ACT PHO PHO C1-INS

    SA580 CDK4 PRO ACT C2-INS

    SA581 RB PRO PHO C2-INS

    SA582 E2F PRO ACT C2-INS

    SA583 CYCLIN E GEN C2-INS

    SA584 CYCLIN E RNA C2-INS

    75

  • SA585 CYCLIN E PRO C1-INS

    SA587 CYCLIN D1 PRO ACT

    SA588 CDK4 PRO ACT

    SA589 RB PRO ACT

    SA59 AKT/PKB PRO EMP C1-INS

    SA590 E2F PRO

    SA591 DP1 PRO ACT

    SA594 C-MYC PRO ACT PHO PHO C2-INS

    SA595 C-MYC PRO EMP PHO C2-INS

    SA596 C-MYC PRO EMP EMP C2-INS

    SA597 IL-6 GEN C2-INS

    SA598 IL-8 GEN C2-INS

    SA599 CCL-2 GEN C2-INS

    SA6 NSMASE PRO C1-OUT

    SA60 CAPP PRO C1-INS

    SA600 CCL-2 RNA C2-INS

    SA601 IL-8 RNA C2-INS

    SA602 IL-6 RNA C2-INS

    SA603 CCL-2 PRO C1-INS

    SA604 IL-6 PRO ACT C1-INS

    SA605 IL-8 PRO ACT C1-INS

    SA606 EGR-1 PRO ACT C2-INS

    SA607 CCL-2 PRO ACT C2-INS

    SA608 IL-6 PRO ACT C2-INS

    76

  • SA609 IL-8 PRO ACT C2-INS

    SA61 CAPP PRO ACT C1-INS

    SA611 MKPS GEN C2-INS

    SA612 MKPS RNA C2-INS

    SA614 JNK 1 PRO EMP C2-INS

    SA615 MKPS PRO ACT C2-INS

    SA616 MKPS PRO ACT C1-INS

    SA62 VAV PRO C1-INS

    SA63 VAV PRO ACT PHO C1-INS

    SA64 PAK 3 PRO C1-INS

    SA65 PAK 3 PRO ACT PHO C1-INS

    SA660 SPHK1 PRO C1-INS

    SA661 SPHK1 PRO ACT C1-INS

    SA662 SPHK1 PRO ACT PHO C1-INS

    SA663 SPHK1 PRO ACT PHO C1-INS

    SA665 SPHINGOSINE PRO C1-INS

    SA667 SPHINGOSINE PRO ACT PHO C1-INS

    SA672 S4560 DEG C1-INS

    SA673 S4561 DEG C1-INS

    SA676 PTEN PRO ACT C2-INS

    SA677 BCL-2 PRO ACT C2-INS

    SA68 RAC/CDC42 PRO ACT C1-INS

    SA688 BCL-2 PRO ACT C5-INS

    SA69 RAC/CDC42 PRO C1-INS

    77

  • SA7 NSMASE PRO ACT C1-INS

    SA70 GCK PRO C1-INS

    SA700 BCL-XL PRO ACT C5-INS

    SA701 RIPK3 PRO ACT C1-INS

    SA703 CREB/P300 PRO ACT PHO

    SA704 CREB/P300 PRO ACT PHO

    SA705 CREB/P300 PRO ACT PHO

    SA71 GCK PRO ACT C1-INS

    SA72 MEKK1 PRO EMP EMP C1-INS

    SA73 MEKK1 PRO PHO PHO C1-INS

    SA74 TAK1 PRO C1-INS

    SA75 MEKK3 PRO C1-INS

    SA76 MEKK3 PRO ACT PHO C1-INS

    SA77 TAK1 PRO ACT PHO PHO PHO C1-INS

    SA78 S4075 DEG C1-INS

    SA8 FAN PRO ACT C1-INN

    SA80 NIK PRO EMP C1-INS

    SA81 NIK PRO EMP PHO PHO PHO C1-INS

    SA84 NIK PRO ACT PHO C1-INS

    SA85 MKK6 (MAPKK6 COMMA BR MEK6 COMMA

    SAPKK3 ) PRO C1-INS

    SA86 MKK7 BR (JNKK2) PRO C1-INS

    SA87 MKK3 (MEK3 COMMA BR MAPKK3) PRO C1-INS

    SA88 MKK4/JNKK1/SEK1 PRO EMP C1-INS

    78

  • SA89 MKK6 (MAPKK6 COMMA BR MEK6 COMMA

    SAPKK3 ) PRO ACT PHO PHO C1-INS

    SA9 FAN PRO C1-OUT

    SA90 MKK7 BR (JNKK2) PRO ACT PHO PHO C1-INS

    SA91 MKK3 (MEK3 COMMA BR MAPKK3) PRO ACT PHO

    PHO C1-INS

    SA92 MKK4/JNKK1/SEK1 PRO ACT PHO C1-INS

    SA93 CRAF/RAF-1 PRO C1-INS

    SA94 B-RAF PRO C1-INS

    SA96 PKC ALPHA PRO C1-INS

    SA97 PKC ALPHA PRO ACT PHO PHO PHO PHO C1-INS

    SA98 TRX PRO ACT C1-INS

    SA99 ASK1 PRO C1-INS

    79

    List of TablesList of FiguresIntroductionBasins of Attraction for Random NetworksResponse to stimuliDynamic Network ModelDynamic EquationsAttractors and basin of attractionNumerical simulationsSimulation results

    Boolean Modeling and SimulationBoolean formalism for qualitative modelingStructural AnalysisDynamic AnalysisNetwork ReductionSimulationsInitializationHousekeeping Constraint

    Simulations in MATLAB

    Methods of Quantitative Analysis of AttractorsAnalysis of DistanceClassificationStability AnalysisSteady State StabilityAsynchronous Markovian perturbation

    Case Study ResultsModeling TNF- NetworkDistance Analysismin-Hamming Distance

    ClassificationStability AnalysisPerturbation analysis for steady statesAsychronous Markovian perturbation for cyclic attractors

    Phenotype switchToll-Like Receptor (TLR) Network

    Conclusions and future workBibliographyBibliographyAppendicesA simulation example: TOYNETIdentifying unsteady part of networkTNF pathwayList of Interactions