BACKGROUND
study of interactome, the entire set of molecular interactions within cells, has provided many insights into the etiology and regulation of cancer  <cit> .
tumorigenesis is a multi-step process caused by genetic alterations that drive the progressive transformation of normal cells into malignant cells.
at the molecular level, genetic mutations, translocations, amplifications, deletions, and viral gene insertions can alter translated proteins and thereby disrupt signal transduction pathways and protein-protein interactions that are essential for apoptosis and other important cellular processes  <cit> .
inactivation of pro-apoptotic proteins or up-regulation of anti-apoptotic proteins results in unchecked growth of cells and ultimately to cancer  <cit> .
from a systems biology perspective, cancer is mainly caused by malfunctions of perturbed protein interaction networks in the cell  <cit> .
apoptosis is necessary for normal human development and survival, in that cells must die in order to prevent uncontrolled growth  <cit> .
apoptosis requires activation of multiple pathways via regulated protein-protein interactions  <cit> .
apoptosis is mediated by an intrinsic pathway, which is triggered by "death stimuli"  within a cell, or by an extrinsic pathway, which is initiated by binding of an extracellular "death ligand".
the extrinsic pathway can link to the intrinsic pathway, which then triggers the release of mitochondria proteins via protein-protein interactions  <cit> .
during apoptosis, several proteins are released from the intermembrane space of the mitochondria into the cytoplasm and these proteins activate initiator caspases and trigger a series of protein-protein interactions in the caspase cascade.
evading apoptosis is one of the six acquired capabilities of cancer cells  <cit> , and anticancer treatment using cytotoxic drugs is considered to mediate cell death by activating key elements of the apoptosis program and the cellular stress response  <cit> .
comprehensive knowledge of protein-protein interactions provides a framework for understanding the biology of cancer as an integrated system  <cit> .
most gene products mediate their functions within complex networks of interconnected macromolecules, forming a dynamic topological interactome  <cit> .
high throughput two-hybrid experiments  <cit>  and several online interactome databases, such as bind  <cit> , hprd  <cit> , intact  <cit> , and himap  <cit> , allow analysis of the global topologies of human protein-protein interactions.
bind  <cit>  is a database designed to store full descriptions of interactions, molecular complexes and pathways.
hprd  <cit>  provides detailed data including protein sequences, localization, domains, and motifs, and thousands of protein-protein interactions, with other data.
intact  <cit>  contains an enrichment of protein-protein interactions, related literature, and experimental detail.
himap  <cit>  combines two datasets of yeast-two-hybrid experiments  <cit>  to form a human protein reference database  <cit> , with references to functions and predictions.
however, experimental and database approaches often yield "false-positives"  <cit> .
for example, yeast two-hybrid experiments based on transactivation of reporter genes require the presence of auto-activators, where the bait activates gene expression in the absence of any prey  <cit> .
the yeast two-hybrid technique can yield false-positives , and false-negatives   <cit> .
computational methods can refine protein-protein interaction networks and result in fewer false-positives  <cit> .
because of the complex nature of interactomes, such as that observed in the apoptosome complex during caspase formation  <cit> , a nonlinear mathematical model provides better characterization than a linear model  <cit> .
in addition, a stochastic model allows consideration of intrinsic and extrinsic molecular "noise" that causes stochastic variations in transcription and translation  <cit> .
in this paper, we describe a nonlinear stochastic model that characterizes dynamic protein-protein interaction networks of apoptosis in cancerous and normal cells.
in this study, we built an initial protein-protein interaction network based on two human yeast two-hybrid data sets  <cit>  and four online interactome databases such as bind  <cit> , hprd  <cit> , intact  <cit> , and himap  <cit> .
next, we constructed a nonlinear stochastic model of dynamic protein-protein interactions to eliminate false-positives from the network by applying a statistical method  to the high-throughput protein interaction data.
we regard all proteins in an organism as a large dynamic interaction system.
protein-protein interactions are considered as nonlinear stochastic processes with several expression profiles of interactive protein partners as input, and the expression profile of a target protein as output.
because of random noise and uncertainties during experiments, we describe protein-protein interactions with stochastic discrete nonlinear dynamic equations.
we considered linear individual  protein interactions and nonlinear cooperative protein complex interactions, but not dna-protein or metabolite interactions.
first, we constructed protein-protein interaction networks of apoptosis in hela  cells and normal primary human lung fibroblasts based on microarray data  <cit> .
next, we obtained the cancer-perturbed protein-protein interaction network by comparison of apoptosis in normal cells via gain-of-function and loss-of-function networks.
because current drugs designed to induce apoptosis kill cancer cells as well as normal cells, these cancer-perturbed protein-protein interaction networks allow identification of potential selective targets of apoptosis-promoting drugs  <cit> .
RESULTS
construction of the cancer-perturbed protein-protein interaction network of apoptosis
initially, we selected proteins that are known to have roles in apoptosis and considered them as the "core nodes" of our network.
these included bax , bcl <dig> , bid , casp <dig> , birc <dig> , casp <dig> , cycs , and diablo .
networks, such as ours, that are developed from initially selected genes or proteins as the core nodes are referred to as "brac-centered networks"  <cit> .
our initial apoptosis network contained  <dig> protein nodes and  <dig> protein-protein interaction edges.
from equations  to  , we calculated each protein interaction twice, with each partner considered as the target protein.
the final results are shown in figure  <dig> and supplementary table  <dig> .
figure  <dig> illustrates the individual and cooperative protein-protein interaction networks of apoptosis in cancerous cells  and normal cells .
these networks are easily modeled by undirected graphs, where the nodes are proteins and two nodes are connected by an undirected edge if the corresponding proteins bind one another  <cit> .
supplementary table  <dig> compares the networks of apoptosis in hela cells and normal primary human lung fibroblasts.
these data show, for example, that bax and peg <dig> interact in both cell types, that bax and ccnd <dig> interact in neither cell type, that bax and rarg interact in normal cells but not in cancerous cells, and that bax and bcl2l <dig> interact in cancerous cells but not in normal cells.
in order to identify drug targets for anti-cancer drugs, it is important to identify cancer-perturbed protein-protein interaction networks to identify drug targets to kill cancer cells  <cit> .
if an interaction is absent in normal cells, but present in cancer cells, we call it "gain-of-function"; if an interaction is present in normal cells but not in cancerous cells, we term it "loss-of-function".
for the  <dig> interactions that we identified, we classified  <dig>  as "gain-of-function" and  <dig>  as "loss-of-function" .
this network analysis identified 38%  of all protein-protein interactions during apoptosis as potential drug targets.
in order to confirm the topology of our networks , we calculated the false-positive and false-negative rates for the  <dig> bcl2-interacting proteins in normal cells by use of the hprd   <cit>  and literature review .
after refinement by our algorithms, we reduced the false-positive rate to  <dig> %.
however, the false-negative rate remained at  <dig> %, indicating incomplete construction of the network from current experiments and databases.
therefore, compensation by k  in "methods") is important for estimation of model parameters.
cancer-perturbed apoptosis mechanism at the systems level
in many cancers, pro-apoptotic proteins are inactivated or anti-apoptotic proteins are upregulated, leading to unchecked growth and an inability to respond to cellular stresses  <cit> .
these gain- and loss-of-function mutations lead to aberrations in protein-protein interaction networks.
an integration of interactome data and genomic data can provide a clearer understanding of the functional relationships that underlie apoptosis and other biological processes  <cit> .
the results of our investigation of the apoptosis mechanism at the systems level and the elucidation of cancer-perturbed protein-protein interaction network topology are depicted in figs.
2a and 2b.
extrinsic pathway, intrinsic pathway and crosstalk
members of the death receptor superfamily trigger the extrinsic apoptosis pathway upon recruit of caspase- <dig> through the adaptor protein fas -associated death domain   <cit> .
binding of a "death ligand" to a receptor triggers formation of a signaling complex that activates caspase- <dig> or caspase- <dig>  which then activates caspase- <dig>  and finally promotes cell death  <cit> .
extracellular and intracellular stress triggers the intrinsic apoptosis pathway , which involves activation of pro-apoptotic members of the bcl- <dig> family  <cit> .
bid, a pro-apoptotic member of the bcl- <dig> family, allows crosstalk between the extrinsic and intrinsic pathways.
the three subfamilies of bcl-2-related proteins are the anti-apoptotic proteins , the pro-apoptotic multi-domain proteins , and pro-apoptotic bh3-only proteins   <cit> .
of the  <dig> bcl- <dig> proteins or regulators ,  <dig> are present in figs.
2a and 2b ,  <dig> are present in fig.
2a alone  and  <dig> are present in fig.
2b alone .
this indicates that there is not a simple dichotomy between gain-of-function and loss-of-function proteins in the cancer interactome.
for example, bax has  <dig> gain-of-function interactions with bcl2l <dig>  tp <dig>  mfn <dig>  and bcl2l <dig> but it also has  <dig> loss-of-function interactions with rarg, mcl <dig>  bcl2a <dig>  cdkn1a, mapk <dig>  app, apc, casp <dig>  prkce, rnf <dig>  adprt, tgfbr <dig>  and tnfrsf <dig> .
caspases family and caspases regulators
the apoptosis death signal is activated via a series of protease caspases  which require activation by proteolysis  <cit> .
with the exception of casp <dig>  which is present only in the gain-of-function network, the caspases  occur in the gain-of-function and loss-of-function networks.
seven caspase activators, inhibitors, and regulators  are present in both networks .
this reveals the different roles of caspase regulators in cancerous and normal cells.
regulation of apoptosis at the systems level
besides bcl- <dig> and caspases, proteins involved in apoptosis regulation include birc <dig>  pten, card <dig>  map3k <dig>  dedd <dig>  mitf, malt <dig>  bcl <dig>  nalp <dig>  cradd, rtn <dig>  psen <dig>  igfbp <dig>  bnip3l, rarg, cflar, traf <dig>  traf <dig>  mcl <dig>  card <dig>  traf <dig>  vegf, birc <dig>  fgfr <dig>  pea <dig>  dedd, mmp <dig>  hrk, and tp <dig> .
thus, we have identified  <dig> proteins, in addition to members of the bcl- <dig> and caspase families, that regulate apoptosis at the systems level.
apoptosis and cell cycle regulation
proteins generally function as components of complexes that contain other macromolecules, to carry out specific biological processes.
networks of interactions connect different cellular processes  <cit> .
we have identified  <dig> proteins in the protein-protein interaction network of apoptosis that also participate in cell-cycle regulation.
these are pten, cdc <dig>  mfn <dig>  pkmyt <dig>  dcc, and e2f <dig> in fig.
2a, and birc <dig>  nras, mki <dig>  e1f <dig>  ppp3ca, bcl <dig>  tp <dig>  mapk <dig>  ccnd <dig>  pcna, egfr, mapk <dig>  vegf, bax, cdkn1a, tgfb <dig>  apc, msh <dig>  app, kras <dig>  hras, cdkn1b, cdkn2a, and pml in fig.
2b.
although figs.
2a and 2b describe the perturbation of apoptosis at the systems level, most proteins with high degree of perturbation  are also included in fig.
2b.
in other words, it is not possible to uniquely describe protein hubs as "gain-of-function" or "loss-of-function" hubs.
therefore, we summarized the degree of perturbation  to identify the perturbed protein hubs in the network of cancer cells.
after identifying targeted proteins as inhibitors or activators, it is necessary to study how a drug target is wired into the control circuitry of a complex cellular network  <cit> .
next, we show a flow chart for identification and prediction of apoptosis drug targets in cancer drug discovery.
prediction of apoptosis drug targets using cancer-perturbed networks of apoptosis
systems-based drug design is a major application of systems biology  <cit> .
this method constructs disease-perturbed protein-protein interaction networks and identifies potential drug targets by comparison of the networks of normal and abnormal cells.
this contrasts with the traditional approach, which reduces cellular processes to their individual components or signal transduction pathways and targets a specific molecule or signaling pathway.
a limitation of this traditional approach is that a single molecule or pathway does not adequately describe most biological systems, including those affected in cancer  <cit> .
by comparisons of the protein-protein interaction networks of normal and cancerous cells derived from microarray data, we can identify potential drug targets through a systems-based approach .
thus, we built initial protein-protein interaction networks from large-scale experiments and databases, and then employed each microarray data set of hela cells and primary lung fibroblasts to modify these networks.
for network modification, we used a nonlinear stochastic model and the akaike information criterion .
we next compared the networks of cancerous and normal cells, derived gain-of-function and loss-of-function networks, and identified protein hubs with high degree of perturbation as potential drug targets.
scale-free networks are extremely sensitive to removal of targeted hubs , so we summed the degree of perturbation  of each node in the cancer-perturbed network  to obtain these perturbed hubs.
proteins with sum of degree of perturbation ≥  <dig>  differentiate the cancerous and normal interactomes and are potential drug targets  <cit> .
we classified the  <dig> potential drug targets  into six categories:  intrinsic pathway: bcl <dig>  bax, bcl2l <dig>  bid, and cycs;  extrinsic pathway: tnf and tnfrsf6;  common pathway: casp <dig> and casp9;  apoptosis regulators: tp <dig>  myc, cflar, and egfr;  stress-induced signaling: mapk <dig> and mapk3; and  others: cdkn1a and ccnd <dig>  our results indicate that most proteins interact with few partners, whereas hubs interact with many partners, consistent with current views on interactome networks with a scale-free or power law degree distribution  <cit> .
intrinsic pathway: bcl <dig>  bax, bcl2l <dig>  and cycs
defective apoptosis in human cancers often results from over-expression or inhibition of bcl <dig> proteins.
these proteins regulate mitochondrial permeability by inhibiting  or promoting  release of cytochrome c   <cit> .
bcl <dig> and several anti-apoptotic relatives, such as bcl2l <dig>  associate with the mitochondrial outer membrane and the endoplasmic reticulum nuclear membrane and maintain the integrity of these membranes.
initiation of apoptosis requires pro-apoptotic family members that closely resemble bcl <dig> and distantly related proteins that are related only by the small bh <dig> protein-interaction domain  <cit> .
in our results, proteins with gain-of-function interactions with bcl <dig> include ccnd <dig>  bad, mcl <dig>  mapk <dig>  adm, kitlg, egfr, bag <dig>  pkmyt <dig>  tp <dig>  pcna, mitf, abcb <dig>  bcl <dig>  znf <dig>  hrk, ppp2r5a, and vegf .
proteins with loss-of-function interactions with bcl <dig> include cdkn1a, tnf, wt <dig>  bag <dig>  bcl2l <dig>  dek, grn, raf <dig>  blk, bag <dig>  capn <dig>  ghr, cdkn1b, rtn <dig>  bnip3l, map3k <dig>  and clc .
we predict bcl <dig> to be the best potential drug target because this protein best differentiates protein-protein interaction networks of hela and normal cells  <cit> .
our analysis agrees with the conclusions of previous studies which showed that bcl <dig> protein family members are good targets for cancer therapy.
drugs that target bcl <dig> include genasense  <cit>  and abt- <dig>  <cit> .
the activation of bax can be induced by gene therapy through delivery of bax vectors, and this approach has been successful in inducing apoptosis in cancer cell lines  <cit> .
antisense bcl2l <dig>  downregulates the expression of bcl <dig> and bcl2l <dig>  induces apoptosis, and inhibits growth of several tumor types in vitro and in vivo  <cit> .
unfortunately, targeting of bcl- <dig> also causes adverse effects, presumably because many normal cells depend on proteins in the bcl- <dig> family to maintain normal mitochondrial function.
difficulty in using bcl- <dig> antisense dna or rna as a delivery system is a problem with genasense  <cit> .
cytochrome c, once released into the cytosol, interacts with apaf- <dig> and this leads to activation of caspase- <dig> proenzymes  <cit> .
the chief function of bcl- <dig> proteins is to regulate the release of cytochrome c from mitochondria.
thus, targeting cycs or apaf- <dig> would also be expected to cause severe adverse effects  <cit> .
extrinsic pathway and crosstalk: tnf, tnfrsf <dig>  and bid
the extrinsic pathway activated by death receptors, such as fas  and other tnf receptor family members, allows apoptosis to maintain normal tissue homeostasis  <cit> .
although death receptors of the tnf superfamily members are potential targets for anti-cancer drugs, toxic side effects have been observed that place limits on their therapeutic use  <cit> .
tnf and fas  were also found to activate nonspecific tnf receptors resulting in extensive ischemic and hemorrhagic lesions in several tissues leading to septic shock and fulminating hepatic failure in animal models  <cit> .
a more promising approach involves targeting the trail  receptors  <cit> .
activation of the trail death receptor can kill cancerous cells but not normal cells, whereas monoclonal antibodies against trail and recombinant trail ligand can cause trail resistance  <cit> .
thus, administration of such a drug might cause tumors to develop resistance, or cause the death of normal cells.
bid, a pro-apoptotic bcl- <dig> family member, provides crosstalk and integration between the death-receptor and mitochondrial pathways  <cit> .
targeting bid, however, is rarely discussed, although such work has potential for use in combined therapy  <cit> .
common pathway: casp <dig> and casp9
caspases are the central components of the apoptotic response network.
an effector caspase  is activated by an initiator caspase  and the initiator caspase is activated via other protein-protein interactions  <cit> .
targeting inhibitors of caspases could potentially cause apoptosis of cancerous cells.
synthetic activators of caspases include apoptin and iap  <cit> .
caspase- <dig> and - <dig> are subject to inhibition by iaps such as livin  <cit> .
like bcl- <dig> inhibitors, xiap inhibitors must block protein-protein interactions.
when released from mitochondria, smac binds xiap and inactivates it, triggering apoptosis  <cit> .
apoptosis regulators: tp <dig>  myc, cflar, and egfr
one of the most dramatic responses to p <dig> is induction of apoptosis and regulation via the intrinsic pathway  <cit> .
drug trials that target p <dig> include gene therapy involving onyx- <dig> and ingn <dig> and antisense therapy that targets a protein controlling p <dig> activity by nutlins which blocks p53/mdm <dig> interaction  <cit> .
the proto-oncogene c-myc encodes a transcription factor that is implicated in various cellular processes, including cell growth, proliferation, loss of differentiation, and apoptosis.
the induction of cell-cycle entry sensitizes the cell to apoptosis, so that cell-proliferation and apoptotic pathways are coupled  <cit> .
cflar  regulates caspase- <dig> and fadd-like apoptosis.
whereas cflar blocks the activation of the initiator caspase- <dig>  xiap can block the initiation phase  and the execution phase   <cit> .
some agents, for example, agent zd <dig> as an egfr  inhibitor, do not primarily target apoptosis, but indirectly modulate apoptosis  <cit> .
stress-induced signaling and others: mapk <dig>  mapk <dig>  cdkn1a, and ccnd1
proteins of the mapk  family are crucial in many signaling pathways  <cit> .
three mek  inhibitors, ci- <dig>  pd <dig>  and arry- <dig>  are currently in clinical trials for treatment of various cancers  <cit> .
although some drugs target mapks, mapk <dig> , and mapk <dig>  are not the main drug targets in the apoptotic pathway  <cit> .
cdkn1a   plays a role in cell cycle arrest and induction of apoptosis.
the activities of cyclin d- and cyclin e-dependent kinases are linked through the cip/kip family of cdk inhibitors, including p <dig> and p <dig>  <cit> .
ccnd <dig> is cyclin d <dig> in the g1/s transition of the cell cycle, and is controlled by the tumor suppressor gene rb through cdk-cyclin d complexes  <cit> .
prediction of additional drug targets by decreasing the degree of perturbation
in addition to identifying several apoptosis drug targets that have already been identified by other studies, we applied our method to predict additional drug targets by decreasing the perturbation threshold.
thus, if we reduce the sum of degree of perturbation to  <dig>  we predict the following additional targets: bak <dig>  casp <dig>  bcl2a <dig>  igf <dig>  prkcd, nfkb <dig>  and pcna.
nfkb <dig> has both anti- and pro-apoptotic functions that are determined by the nature of the death stimulus.
the drug ps <dig> targets the nfkb <dig> inhibitor ikkβ  <cit>  but the other proteins have not previously been considered as drug targets.
prediction of new go annotations of the four proteins: cdkn1a, ccnd, pcna, and prkcd
if we consider all  <dig> proteins with sum of degree of perturbation ≥  <dig>  four proteins  are also considered to have a role in apoptosis.
if the function of any one protein in a network is known, identification of its interacting partners allows prediction of their functions  <cit> .
however, two of these proteins  are known to have a role in dna damage-induced apoptosis.
pcna  is ubiquitinated and involved in rad6-dependent dna repair in response to dna damage.
prkcd  is also associated with dna damage-induced apoptosis  <cit> , whereas gene ontology annotations of prkcd do not include apoptosis .
although other methods  allow prediction of protein-protein interactions in different organisms  <cit> , these methods do not allow identification of potential drug targets.
our method provides efficient and precise prediction of anti-cancer drug targets and also specifies these target proteins with detailed gene ontology annotations.
this will help researchers identify additional drug targets by examination of other cellular mechanisms involved in cancer.
network modeling has been used to identify genes potentially associated with breast cancer in a brac-centered network  <cit> .
however, there are very few time-series microarray databases for cancerous and normal cells, so it is difficult to use our method to compare protein hubs for different types of cancer.
moreover, our method does not address the potential adverse effects of targeting a specific protein and the problem of drug delivery.
we expect that more genomic time-series microarray experiments and clinical research will address these limitations in the future.
caspase activation through static and dynamic hubs
static network topology is not sufficient to define function, and incorporating time-dependent expression data is important for understanding pathway function  <cit> .
a number of computational approaches have been proposed for prediction of protein-protein interactions, such as domain-domain interactions  <cit> , the confidence score resulting from sequence similarity and number of edges  <cit> , and integration of genomic data sets  <cit> .
a nonlinear stochastic model can depict protein-protein interaction networks at different times by using linear binary interactions and nonlinear protein complex relationships.
previous studies have used linear stochastic models to describe the multiple feedback loops of p <dig>  <cit> , but nonlinear effects cannot be depicted by this method.
our method also illustrates the dynamic behavior of protein-protein interaction networks, which cannot be examined by probabilistic methods of data integration  <cit> .
networks consist of party hubs  and date hubs .
party hubs are found in static complexes with most of their partners present at the same time, whereas date hubs bind their interaction partners at different times or locations  <cit> .
to further investigate dynamic apoptotic properties in human cells, we considered caspases as protein hubs in our dynamic nonlinear stochastic protein-protein models .
in order to identify party hubs and date hubs, we first summed the degree of perturbation of each protein as 'plus degree of perturbation' and then subtracted the degree of perturbation of each protein as 'minus degree of perturbation' at two time periods in cancerous and normal cells.
if the plus degree of perturbation of one protein was ≥  <dig>  we defined this protein as a 'hub'.
if the minus degree of perturbation of the hub was ≤  <dig>  we defined the hub as a party hub .
if the minus degree of perturbation of the hub was > <dig>  we defined the hub as a date hub.
figures 4a–d illustrate the time-dependence of the networks, where bold lines represent distinct interactions at different times.
caspase signaling results in time-variant protein-protein interactions, and dynamic modeling allows specification of the time-dependent interactome.
in cancerous cells, the date hubs include birc <dig>  casp <dig>  and casp <dig>  and the party hubs include tp <dig>  tnf, birc <dig>  bax, casp <dig>  and casp <dig>  in normal cells, date hubs include casp <dig> and casp <dig> and party hubs include tnfrsf <dig>  tp <dig>  birc <dig>  birc <dig>  bcl <dig>  bax, and casp <dig>  effector caspase- <dig> is a date hub in both cell types because intrinsic and extrinsic pathways converge on caspase- <dig>  because date hubs appear to be more important than party hubs  <cit> , caspase- <dig> and - <dig> are important date hubs that differentiate network topologies of cancerous and normal cells.
tp <dig>  birc <dig>  bax, and casp <dig> are party hubs in both cell types.
party hubs are found in static complexes where they interact with most of their partners simultaneously  <cit> .
in other words, we believe these four proteins play central roles in functional complexes in both cancerous and normal cells.
CONCLUSIONS
the cancer-perturbed protein-protein interaction networks of apoptosis that we developed here shed light on the mechanism of cancer at the systems level and allow identification of potential drug targets.
in this study, we applied nonlinear stochastic modeling to describe individual and cooperative protein interactions.
our method is more precise than the linear models used in previous research.
we successfully integrated microarray and proteome databases to identify cancer-perturbed protein-protein interaction networks.
our predictions of potential drug targets agreed with potential targets identified by other studies and also identified additional targets which may guide the development of new anti-cancer drugs in future.
we also identified static and dynamic hubs in human protein-protein interaction networks, which have heretofore been identified only in yeast.

 study of interactome, the entire set of molecular interactions within cells, has provided many insights into the etiology and regulation of cancer. tumorigenesis is a multi-step process caused by genetic alterations that drive the progressive transformation of normal cells into malignant cells. at the molecular level, genetic mutations, translocations, amplifications, deletions, and viral gene insertions can alter translated proteins and thereby disrupt signal transduction pathways and protein-protein interactions that are essential for apoptosis and other important cellular processes. inactivation of pro-apoptotic proteins or up-regulation of anti-apoptotic proteins results in unchecked growth of cells and ultimately to cancer. from a systems biology perspective, cancer is mainly caused by malfunctions of perturbed protein interaction networks in the cell. apoptosis is necessary for normal human development and survival, in that cells must die in order to prevent uncontrolled growth. apoptosis requires activation of multiple pathways via regulated protein-protein interactions. apoptosis is mediated by an intrinsic pathway, which is triggered by "death stimuli" within a cell, or by an extrinsic pathway, which is initiated by binding of an extracellular "death ligand". the extrinsic pathway can link to the intrinsic pathway, which then triggers the release of mitochondria proteins via protein-protein interactions. during apoptosis, several proteins are released from the intermembrane space of the mitochondria into the cytoplasm and these proteins activate initiator caspases and trigger a series of protein-protein interactions in the caspase cascade. evading apoptosis is one of the six acquired capabilities of cancer cells, and anticancer treatment using cytotoxic drugs is considered to mediate cell death by activating key elements of the apoptosis program and the cellular stress response. comprehensive knowledge of protein-protein interactions provides a framework for understanding the biology of cancer as an integrated system. most gene products mediate their functions within complex networks of interconnected macromolecules, forming a dynamic topological interactome. high throughput two-hybrid experiments and several online interactome databases, such as bind, hprd, intact, and himap, allow analysis of the global topologies of human protein-protein interactions. bind is a database designed to store full descriptions of interactions, molecular complexes and pathways. hprd provides detailed data including protein sequences, localization, domains, and motifs, and thousands of protein-protein interactions, with other data. intact contains an enrichment of protein-protein interactions, related literature, and experimental detail. himap combines two datasets of yeast-two-hybrid experiments to form a human protein reference database, with references to functions and predictions. however, experimental and database approaches often yield "false-positives". for example, yeast two-hybrid experiments based on transactivation of reporter genes require the presence of auto-activators, where the bait activates gene expression in the absence of any prey. the yeast two-hybrid technique can yield false-positives, and false-negatives. computational methods can refine protein-protein interaction networks and result in fewer false-positives. because of the complex nature of interactomes, such as that observed in the apoptosome complex during caspase formation, a nonlinear mathematical model provides better characterization than a linear model. in addition, a stochastic model allows consideration of intrinsic and extrinsic molecular "noise" that causes stochastic variations in transcription and translation. in this paper, we describe a nonlinear stochastic model that characterizes dynamic protein-protein interaction networks of apoptosis in cancerous and normal cells. in this study, we built an initial protein-protein interaction network based on two human yeast two-hybrid data sets and four online interactome databases such as bind, hprd, intact, and himap. next, we constructed a nonlinear stochastic model of dynamic protein-protein interactions to eliminate false-positives from the network by applying a statistical method to the high-throughput protein interaction data. we regard all proteins in an organism as a large dynamic interaction system. protein-protein interactions are considered as nonlinear stochastic processes with several expression profiles of interactive protein partners as input, and the expression profile of a target protein as output. because of random noise and uncertainties during experiments, we describe protein-protein interactions with stochastic discrete nonlinear dynamic equations. we considered linear individual protein interactions and nonlinear cooperative protein complex interactions, but not dna-protein or metabolite interactions. first, we constructed protein-protein interaction networks of apoptosis in hela cells and normal primary human lung fibroblasts based on microarray data. next, we obtained the cancer-perturbed protein-protein interaction network by comparison of apoptosis in normal cells via gain-of-function and loss-of-function networks. because current drugs designed to induce apoptosis kill cancer cells as well as normal cells, these cancer-perturbed protein-protein interaction networks allow identification of potential selective targets of apoptosis-promoting drugs.  construction of the cancer-perturbed protein-protein interaction network of apoptosis initially, we selected proteins that are known to have roles in apoptosis and considered them as the "core nodes" of our network. these included bax, bcl, bid, casp, birc, casp, cycs, and diablo. networks, such as ours, that are developed from initially selected genes or proteins as the core nodes are referred to as "brac-centered networks". our initial apoptosis network contained protein nodes and protein-protein interaction edges. from equations to, we calculated each protein interaction twice, with each partner considered as the target protein. the final results are shown in figure and supplementary table. figure illustrates the individual and cooperative protein-protein interaction networks of apoptosis in cancerous cells and normal cells. these networks are easily modeled by undirected graphs, where the nodes are proteins and two nodes are connected by an undirected edge if the corresponding proteins bind one another. supplementary table compares the networks of apoptosis in hela cells and normal primary human lung fibroblasts. these data show, for example, that bax and peg interact in both cell types, that bax and ccnd interact in neither cell type, that bax and rarg interact in normal cells but not in cancerous cells, and that bax and bcl2l interact in cancerous cells but not in normal cells. in order to identify drug targets for anti-cancer drugs, it is important to identify cancer-perturbed protein-protein interaction networks to identify drug targets to kill cancer cells. if an interaction is absent in normal cells, but present in cancer cells, we call it "gain-of-function"; if an interaction is present in normal cells but not in cancerous cells, we term it "loss-of-function". for the interactions that we identified, we classified as "gain-of-function" and as "loss-of-function". this network analysis identified 38% of all protein-protein interactions during apoptosis as potential drug targets. in order to confirm the topology of our networks, we calculated the false-positive and false-negative rates for the bcl2-interacting proteins in normal cells by use of the hprd and literature review. after refinement by our algorithms, we reduced the false-positive rate to %. however, the false-negative rate remained at %, indicating incomplete construction of the network from current experiments and databases. therefore, compensation by k in "methods") is important for estimation of model parameters. cancer-perturbed apoptosis mechanism at the systems level in many cancers, pro-apoptotic proteins are inactivated or anti-apoptotic proteins are upregulated, leading to unchecked growth and an inability to respond to cellular stresses. these gain- and loss-of-function mutations lead to aberrations in protein-protein interaction networks. an integration of interactome data and genomic data can provide a clearer understanding of the functional relationships that underlie apoptosis and other biological processes. the results of our investigation of the apoptosis mechanism at the systems level and the elucidation of cancer-perturbed protein-protein interaction network topology are depicted in figs. 2a and 2b. extrinsic pathway, intrinsic pathway and crosstalk members of the death receptor superfamily trigger the extrinsic apoptosis pathway upon recruit of caspase- through the adaptor protein fas -associated death domain. binding of a "death ligand" to a receptor triggers formation of a signaling complex that activates caspase- or caspase- which then activates caspase- and finally promotes cell death. extracellular and intracellular stress triggers the intrinsic apoptosis pathway, which involves activation of pro-apoptotic members of the bcl- family. bid, a pro-apoptotic member of the bcl- family, allows crosstalk between the extrinsic and intrinsic pathways. the three subfamilies of bcl-2-related proteins are the anti-apoptotic proteins, the pro-apoptotic multi-domain proteins, and pro-apoptotic bh3-only proteins. of the bcl- proteins or regulators, are present in figs. 2a and 2b, are present in fig. 2a alone and are present in fig. 2b alone. this indicates that there is not a simple dichotomy between gain-of-function and loss-of-function proteins in the cancer interactome. for example, bax has gain-of-function interactions with bcl2l tp mfn and bcl2l but it also has loss-of-function interactions with rarg, mcl bcl2a cdkn1a, mapk app, apc, casp prkce, rnf adprt, tgfbr and tnfrsf. caspases family and caspases regulators the apoptosis death signal is activated via a series of protease caspases which require activation by proteolysis. with the exception of casp which is present only in the gain-of-function network, the caspases occur in the gain-of-function and loss-of-function networks. seven caspase activators, inhibitors, and regulators are present in both networks. this reveals the different roles of caspase regulators in cancerous and normal cells. regulation of apoptosis at the systems level besides bcl- and caspases, proteins involved in apoptosis regulation include birc pten, card map3k dedd mitf, malt bcl nalp cradd, rtn psen igfbp bnip3l, rarg, cflar, traf traf mcl card traf vegf, birc fgfr pea dedd, mmp hrk, and tp. thus, we have identified proteins, in addition to members of the bcl- and caspase families, that regulate apoptosis at the systems level. apoptosis and cell cycle regulation proteins generally function as components of complexes that contain other macromolecules, to carry out specific biological processes. networks of interactions connect different cellular processes. we have identified proteins in the protein-protein interaction network of apoptosis that also participate in cell-cycle regulation. these are pten, cdc mfn pkmyt dcc, and e2f in fig. 2a, and birc nras, mki e1f ppp3ca, bcl tp mapk ccnd pcna, egfr, mapk vegf, bax, cdkn1a, tgfb apc, msh app, kras hras, cdkn1b, cdkn2a, and pml in fig. 2b. although figs. 2a and 2b describe the perturbation of apoptosis at the systems level, most proteins with high degree of perturbation are also included in fig. 2b. in other words, it is not possible to uniquely describe protein hubs as "gain-of-function" or "loss-of-function" hubs. therefore, we summarized the degree of perturbation to identify the perturbed protein hubs in the network of cancer cells. after identifying targeted proteins as inhibitors or activators, it is necessary to study how a drug target is wired into the control circuitry of a complex cellular network. next, we show a flow chart for identification and prediction of apoptosis drug targets in cancer drug discovery. prediction of apoptosis drug targets using cancer-perturbed networks of apoptosis systems-based drug design is a major application of systems biology. this method constructs disease-perturbed protein-protein interaction networks and identifies potential drug targets by comparison of the networks of normal and abnormal cells. this contrasts with the traditional approach, which reduces cellular processes to their individual components or signal transduction pathways and targets a specific molecule or signaling pathway. a limitation of this traditional approach is that a single molecule or pathway does not adequately describe most biological systems, including those affected in cancer. by comparisons of the protein-protein interaction networks of normal and cancerous cells derived from microarray data, we can identify potential drug targets through a systems-based approach. thus, we built initial protein-protein interaction networks from large-scale experiments and databases, and then employed each microarray data set of hela cells and primary lung fibroblasts to modify these networks. for network modification, we used a nonlinear stochastic model and the akaike information criterion. we next compared the networks of cancerous and normal cells, derived gain-of-function and loss-of-function networks, and identified protein hubs with high degree of perturbation as potential drug targets. scale-free networks are extremely sensitive to removal of targeted hubs, so we summed the degree of perturbation of each node in the cancer-perturbed network to obtain these perturbed hubs. proteins with sum of degree of perturbation ≥ differentiate the cancerous and normal interactomes and are potential drug targets. we classified the potential drug targets into six categories: intrinsic pathway: bcl bax, bcl2l bid, and cycs; extrinsic pathway: tnf and tnfrsf6; common pathway: casp and casp9; apoptosis regulators: tp myc, cflar, and egfr; stress-induced signaling: mapk and mapk3; and others: cdkn1a and ccnd our results indicate that most proteins interact with few partners, whereas hubs interact with many partners, consistent with current views on interactome networks with a scale-free or power law degree distribution. intrinsic pathway: bcl bax, bcl2l and cycs defective apoptosis in human cancers often results from over-expression or inhibition of bcl proteins. these proteins regulate mitochondrial permeability by inhibiting or promoting release of cytochrome c. bcl and several anti-apoptotic relatives, such as bcl2l associate with the mitochondrial outer membrane and the endoplasmic reticulum nuclear membrane and maintain the integrity of these membranes. initiation of apoptosis requires pro-apoptotic family members that closely resemble bcl and distantly related proteins that are related only by the small bh protein-interaction domain. in our results, proteins with gain-of-function interactions with bcl include ccnd bad, mcl mapk adm, kitlg, egfr, bag pkmyt tp pcna, mitf, abcb bcl znf hrk, ppp2r5a, and vegf. proteins with loss-of-function interactions with bcl include cdkn1a, tnf, wt bag bcl2l dek, grn, raf blk, bag capn ghr, cdkn1b, rtn bnip3l, map3k and clc. we predict bcl to be the best potential drug target because this protein best differentiates protein-protein interaction networks of hela and normal cells. our analysis agrees with the conclusions of previous studies which showed that bcl protein family members are good targets for cancer therapy. drugs that target bcl include genasense and abt-. the activation of bax can be induced by gene therapy through delivery of bax vectors, and this approach has been successful in inducing apoptosis in cancer cell lines. antisense bcl2l downregulates the expression of bcl and bcl2l induces apoptosis, and inhibits growth of several tumor types in vitro and in vivo. unfortunately, targeting of bcl- also causes adverse effects, presumably because many normal cells depend on proteins in the bcl- family to maintain normal mitochondrial function. difficulty in using bcl- antisense dna or rna as a delivery system is a problem with genasense. cytochrome c, once released into the cytosol, interacts with apaf- and this leads to activation of caspase- proenzymes. the chief function of bcl- proteins is to regulate the release of cytochrome c from mitochondria. thus, targeting cycs or apaf- would also be expected to cause severe adverse effects. extrinsic pathway and crosstalk: tnf, tnfrsf and bid the extrinsic pathway activated by death receptors, such as fas and other tnf receptor family members, allows apoptosis to maintain normal tissue homeostasis. although death receptors of the tnf superfamily members are potential targets for anti-cancer drugs, toxic side effects have been observed that place limits on their therapeutic use. tnf and fas were also found to activate nonspecific tnf receptors resulting in extensive ischemic and hemorrhagic lesions in several tissues leading to septic shock and fulminating hepatic failure in animal models. a more promising approach involves targeting the trail receptors. activation of the trail death receptor can kill cancerous cells but not normal cells, whereas monoclonal antibodies against trail and recombinant trail ligand can cause trail resistance. thus, administration of such a drug might cause tumors to develop resistance, or cause the death of normal cells. bid, a pro-apoptotic bcl- family member, provides crosstalk and integration between the death-receptor and mitochondrial pathways. targeting bid, however, is rarely discussed, although such work has potential for use in combined therapy. common pathway: casp and casp9 caspases are the central components of the apoptotic response network. an effector caspase is activated by an initiator caspase and the initiator caspase is activated via other protein-protein interactions. targeting inhibitors of caspases could potentially cause apoptosis of cancerous cells. synthetic activators of caspases include apoptin and iap. caspase- and - are subject to inhibition by iaps such as livin. like bcl- inhibitors, xiap inhibitors must block protein-protein interactions. when released from mitochondria, smac binds xiap and inactivates it, triggering apoptosis. apoptosis regulators: tp myc, cflar, and egfr one of the most dramatic responses to p is induction of apoptosis and regulation via the intrinsic pathway. drug trials that target p include gene therapy involving onyx- and ingn and antisense therapy that targets a protein controlling p activity by nutlins which blocks p53/mdm interaction. the proto-oncogene c-myc encodes a transcription factor that is implicated in various cellular processes, including cell growth, proliferation, loss of differentiation, and apoptosis. the induction of cell-cycle entry sensitizes the cell to apoptosis, so that cell-proliferation and apoptotic pathways are coupled. cflar regulates caspase- and fadd-like apoptosis. whereas cflar blocks the activation of the initiator caspase- xiap can block the initiation phase and the execution phase. some agents, for example, agent zd as an egfr inhibitor, do not primarily target apoptosis, but indirectly modulate apoptosis. stress-induced signaling and others: mapk mapk cdkn1a, and ccnd1 proteins of the mapk family are crucial in many signaling pathways. three mek inhibitors, ci- pd and arry- are currently in clinical trials for treatment of various cancers. although some drugs target mapks, mapk, and mapk are not the main drug targets in the apoptotic pathway. cdkn1a plays a role in cell cycle arrest and induction of apoptosis. the activities of cyclin d- and cyclin e-dependent kinases are linked through the cip/kip family of cdk inhibitors, including p and p. ccnd is cyclin d in the g1/s transition of the cell cycle, and is controlled by the tumor suppressor gene rb through cdk-cyclin d complexes. prediction of additional drug targets by decreasing the degree of perturbation in addition to identifying several apoptosis drug targets that have already been identified by other studies, we applied our method to predict additional drug targets by decreasing the perturbation threshold. thus, if we reduce the sum of degree of perturbation to we predict the following additional targets: bak casp bcl2a igf prkcd, nfkb and pcna. nfkb has both anti- and pro-apoptotic functions that are determined by the nature of the death stimulus. the drug ps targets the nfkb inhibitor ikkβ but the other proteins have not previously been considered as drug targets. prediction of new go annotations of the four proteins: cdkn1a, ccnd, pcna, and prkcd if we consider all proteins with sum of degree of perturbation ≥ four proteins are also considered to have a role in apoptosis. if the function of any one protein in a network is known, identification of its interacting partners allows prediction of their functions. however, two of these proteins are known to have a role in dna damage-induced apoptosis. pcna is ubiquitinated and involved in rad6-dependent dna repair in response to dna damage. prkcd is also associated with dna damage-induced apoptosis, whereas gene ontology annotations of prkcd do not include apoptosis. although other methods allow prediction of protein-protein interactions in different organisms, these methods do not allow identification of potential drug targets. our method provides efficient and precise prediction of anti-cancer drug targets and also specifies these target proteins with detailed gene ontology annotations. this will help researchers identify additional drug targets by examination of other cellular mechanisms involved in cancer. network modeling has been used to identify genes potentially associated with breast cancer in a brac-centered network. however, there are very few time-series microarray databases for cancerous and normal cells, so it is difficult to use our method to compare protein hubs for different types of cancer. moreover, our method does not address the potential adverse effects of targeting a specific protein and the problem of drug delivery. we expect that more genomic time-series microarray experiments and clinical research will address these limitations in the future. caspase activation through static and dynamic hubs static network topology is not sufficient to define function, and incorporating time-dependent expression data is important for understanding pathway function. a number of computational approaches have been proposed for prediction of protein-protein interactions, such as domain-domain interactions, the confidence score resulting from sequence similarity and number of edges, and integration of genomic data sets. a nonlinear stochastic model can depict protein-protein interaction networks at different times by using linear binary interactions and nonlinear protein complex relationships. previous studies have used linear stochastic models to describe the multiple feedback loops of p, but nonlinear effects cannot be depicted by this method. our method also illustrates the dynamic behavior of protein-protein interaction networks, which cannot be examined by probabilistic methods of data integration. networks consist of party hubs and date hubs. party hubs are found in static complexes with most of their partners present at the same time, whereas date hubs bind their interaction partners at different times or locations. to further investigate dynamic apoptotic properties in human cells, we considered caspases as protein hubs in our dynamic nonlinear stochastic protein-protein models. in order to identify party hubs and date hubs, we first summed the degree of perturbation of each protein as'plus degree of perturbation' and then subtracted the degree of perturbation of each protein as'minus degree of perturbation' at two time periods in cancerous and normal cells. if the plus degree of perturbation of one protein was ≥ we defined this protein as a'hub'. if the minus degree of perturbation of the hub was ≤ we defined the hub as a party hub. if the minus degree of perturbation of the hub was > we defined the hub as a date hub. figures 4a–d illustrate the time-dependence of the networks, where bold lines represent distinct interactions at different times. caspase signaling results in time-variant protein-protein interactions, and dynamic modeling allows specification of the time-dependent interactome. in cancerous cells, the date hubs include birc casp and casp and the party hubs include tp tnf, birc bax, casp and casp in normal cells, date hubs include casp and casp and party hubs include tnfrsf tp birc birc bcl bax, and casp effector caspase- is a date hub in both cell types because intrinsic and extrinsic pathways converge on caspase- because date hubs appear to be more important than party hubs, caspase- and - are important date hubs that differentiate network topologies of cancerous and normal cells. tp birc bax, and casp are party hubs in both cell types. party hubs are found in static complexes where they interact with most of their partners simultaneously. in other words, we believe these four proteins play central roles in functional complexes in both cancerous and normal cells.  the cancer-perturbed protein-protein interaction networks of apoptosis that we developed here shed light on the mechanism of cancer at the systems level and allow identification of potential drug targets. in this study, we applied nonlinear stochastic modeling to describe individual and cooperative protein interactions. our method is more precise than the linear models used in previous research. we successfully integrated microarray and proteome databases to identify cancer-perturbed protein-protein interaction networks. our predictions of potential drug targets agreed with potential targets identified by other studies and also identified additional targets which may guide the development of new anti-cancer drugs in future. we also identified static and dynamic hubs in human protein-protein interaction networks, which have heretofore been identified only in yeast. 
we constructed initial networks of protein-protein interactions involved in the apoptosis of cancerous and normal cells by use of two human yeast two-hybrid data sets and four online databases. our method allows identification of cancer-perturbed protein-protein interactions involved in apoptosis and identification of potential molecular targets for development of anti-cancer drugs. next, we applied a nonlinear stochastic model, maximum likelihood parameter estimation, and akaike information criteria to eliminate false-positive protein-protein interactions in our initial protein interaction networks by use of microarray data. the potential targets include bcl caspase- and tp our comparison of cancerous and normal cells also allowed derivation of several party hubs and date hubs in the human protein-protein interaction networks involved in caspase activation. cancer is caused by genetic abnormalities, such as mutations of oncogenes or tumor suppressor genes, which alter downstream signal transduction pathways and protein-protein interactions. comparisons of the interactions of proteins in cancerous and normal cells can shed light on the mechanisms of carcinogenesis. comparisons of the networks of apoptosis in hela cells and in normal primary lung fibroblasts provided insight into the mechanism of apoptosis and allowed identification of potential drug targets.
 cancer is caused by genetic abnormalities, such as mutations of oncogenes or tumor suppressor genes, which alter downstream signal transduction pathways and protein-protein interactions. comparisons of the interactions of proteins in cancerous and normal cells can shed light on the mechanisms of carcinogenesis.  we constructed initial networks of protein-protein interactions involved in the apoptosis of cancerous and normal cells by use of two human yeast two-hybrid data sets and four online databases. next, we applied a nonlinear stochastic model, maximum likelihood parameter estimation, and akaike information criteria to eliminate false-positive protein-protein interactions in our initial protein interaction networks by use of microarray data. comparisons of the networks of apoptosis in hela cells and in normal primary lung fibroblasts provided insight into the mechanism of apoptosis and allowed identification of potential drug targets. the potential targets include bcl caspase- and tp our comparison of cancerous and normal cells also allowed derivation of several party hubs and date hubs in the human protein-protein interaction networks involved in caspase activation.  our method allows identification of cancer-perturbed protein-protein interactions involved in apoptosis and identification of potential molecular targets for development of anti-cancer drugs. 