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A robustness-based approach to systems-oriented drug design Hiroaki Kitano

Abstract | Many potential drugs that specifically target a particular protein considered to underlie a given disease have been found to be less effective than hoped, or to cause significant side effects. The intrinsic robustness of living systems against various perturbations is a key factor that prevents such compounds from being successful. By studying complex network systems and reformulating control and communication theories that are well established in engineering, a theoretical foundation for a systems-oriented approach to more effectively control the robustness of living systems, particularly at the cellular level, could be developed. Here, I use examples that are based on existing drugs to illustrate the concept of robustness, and then discuss how a greater consideration of the importance of robustness could influence the design of new drugs that will be intended to control complex systems. Advances in genomic research in the past two decades fuelled the expectation that agents that specifically target a single disease-causing molecule — ‘magic bullets’ — could cure cancer, diabetes and other complex diseases. However, although some such agents have proven to be successful drugs, many others have been found to be ineffective or to cause significant side effects. This disappointing outcome highlights the limitations of the single-target–drug paradigm1–3, and is considered by some to be the underlying cause of stagnation in productivity in the pharmaceutical industry. Given these limitations, the production of effective combinatorial drugs, drugs with multiple targets and advances in systems biology3–6 have led to an increased interest in systems-oriented approaches to drug discovery. These include multicomponent approaches7, synthetic lethality8, high-throughput screening and data integration5,6,9, cell-based systems biology assays3,4 and metabolome-based approaches10–12. As such approaches continue to emerge, the establishment of a theoretical and conceptual framework that can cope with the large volume of biological data generated by today’s technology could have a key role in realizing their promise. An analysis of both successful and failed drugs reveals that one fundamental factor that determines the success of a drug is how the robustness and fragility of the biological systems in terms of disease onset and progression are exploited. Living systems are

generally robust against various perturbations, such as mutation, toxins and environmental changes, but can be extremely fragile when faced with perturbations for which the system has not been optimized. Drugs can be ineffective when the inherent robustness of the systems in patients (or pathogens in some cases) that are being targeted compensates for any changes caused by drugs. By contrast, drug side effects can be the result of interference with an unexpected point of fragility of these systems. Understanding the relationships between robustness, disease, and drug efficacy and side effects is the first step towards the design of drugs that can target robust systems to achieve the desired therapeutic goals. With this in mind, using a conceptual framework that is based on the complexities of biological systems, as well as control and communication theories from engineering, this article considers the success and failure of drugs from the perspective of biological robustness, and suggests a basis for strategies for systems-oriented drug design. Basics of biological robustness Robustness is an intrinsic property of biological systems that enables them to maintain their functions in the face of various perturbations, and has been reviewed extensively elsewhere13–16. Biological systems have to be robust yet evolvable, which requires trade-offs between robustness, fragility, resource demands and performance17,18. This imposes constraints on the

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type of architecture and mechanisms that constitute such systems. Recent research has identified that robustness is enabled by four basic mechanisms13: systems control; fail-safe by means of redundancy and diversity; modularity; and decoupling in which physical-level perturbation is isolated from functional-level activities of the system. Systems control introduces negativefeedback, positive-feedback, feed-forward regulation and other regulatory loops to maintain the homeostasis of the system, as well as bistable behaviours19,20, which enable the system to move between two stable states. For example, the effects of a drug can be neutralized if a negative-feedback loop compensates for changes in the level of the molecule that the drug targets. Fail-safe mechanisms enable a system to continue to function even if one of its molecules or pathways is disabled, because there are other molecules or pathways that have partly overlapping functions that can compensate. This implies that drugs that target molecules in such pathways are likely to have limited efficacy. Modularity blocks perturbations that are applied to a specific module from spreading throughout the system. Although this is useful to prevent local damage from causing system-wide pertubations, it can also localize drug effects. Decoupling isolates a functional level from a physical level. An example is digital systems in which the functional level that is a bit-stream of on and off is isolated from the actual voltage fluctuation of electric circuits. So, the functional layer is robust against a minor change in the physical layer. A biological example of decoupling is the correction of protein folding by heat-shock proteins (HSP) such as HSP90 (REF. 21). In addition to these mechanisms, there is a specific network architecture often recognized as ‘bow-tie’ networks16 that can be observed in molecular-interaction networks for various functional subsystems, including metabolic networks22, signalling networks23 and the immune system24. The bow-tie architecture is composed of a highly conserved and often robust core part of the network connected by diverse and redundant input and output subnetworks with various feedback control loops (FIG. 1a). This network architecture provides robust and flexible responses to various stimuli and inhibition of molecules involved owing to the redundancy of pathways in input and output modules. However, the network architecture can also be fragile in response to the perturbation of molecules that constitute

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PERSPECTIVES a Bow-tie architecture in a cellular system

Nutrients

Metabolic bow-tie

Environmental stimuli

Metabolites

Signalling bow-tie

Regulation Physiological responses

b Genetic diversity of tumour cells and pathogens

Perturbation

Proliferation

c Diversity of signalling pathways

Figure 1 | Basic mechanisms for robustness. Some of the basic mechanisms that contribute to the robustness of biological systems are illustrated. a | A ‘bow-tie’ structure of networks might exist for metabolic networks and signalling networks. A similar figure is also depicted by Csete and Doyle16. Bow-tie networks often have an asymmetrical structure with a large ‘fan-in’ wing with diverse and redundant pathways that converge into the core of the bow-tie, and a ‘fan-out’ wing with moderate diversity as the number of possible responses are limited. The metabolic bow-tie and the signalling bow-tie are interlocked to form a global cellular system. b | Pathogens and tumour cells have a high level of genetic diversity. Therapeutic perturbations might be able to eliminate a subset of pathogens or tumour cells that respond to drugs. However, there are survivors that do not respond to drugs. These drug-resistant survivors proliferate to form a more resistant group of pathogens and tumour cells. Diversity and redundancy are a main source of robustness for many biological systems. c | Diversity of signalling pathways, by means of overlapping functions and cross-talk between different signalling pathways, contributes to the robustness of cells against inhibition of one or more of their signalling pathways. Some anticancer drugs that target molecules in a single pathway can be made ineffective owing to other pathways that cross-talk with that pathway, and so proliferation of tumour cells is not prevented. Diversity of signalling pathways in cellular networks is one of the main obstacles for anticancer drugs.

the core network when it is not built to be robust to such perturbations, perhaps by not being redundant or by missing regulatory feedback. For example, the core of the bow-tie network found in the Toll-like receptor signalling cascade is fragile as it has a non-redundant core with MYD88 (myeloid differentiation primary response gene 88)25. Complex systems that have evolved (or have been designed) to be optimal (or suboptimal) have a ‘robust yet fragile’ feature17,18.

It has been asserted that the robust-yet-fragile feature is an inherent systems property, in which robustness in response to certain perturbations is inevitably associated with fragility in response to other perturbations15. Furthermore, evolved systems may be constrained by trade-offs between robustness, fragility, performance and resource demands13. Evolved complex networks tend to demonstrate robustness in response to removal of nodes, but are vulnerable to

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sustained malfunction of nodes. An example of such a network is the internet, which is robust against the removal of some of its nodes, such as routers (as such a perturbation would only affect local users), but fragile against the malfunctions of nodes, such as the persistent sending of spam and viruses, which often have global consequences and continue to pose threats to the system26. This type of failure, in which nodes of the network continue to function but in an undesirable way, is often called ‘fail-on’ failure, in contrast with ‘fail-off ’ failure in which failed nodes are removed. Fail-on failure (also known as Byzantine failure) has been a major problem for communication networks, and is considered to be a crucial problem in complex network systems in general27. Biological networks are expected to share similar characteristics — namely that the most serious threats to the system are unwanted interactions by mutant or invading components, overexpression or amplification of genes and uncontrollable hyperactivation of their regulatory loops. Robustness and disease Disease can be viewed as a breakdown of the robustness of normal physiological systems and the re-establishment of robust, and potentially progressive, disease states. From the aspect of robustness trade-offs, diseases can be classified into one or more of the following: a simple disease, with a breach in the robustness that protects the host system from various perturbations; a parasitic disease, in which the mechanisms for robustness are hijacked for the triggering and progression of the disease state in the face of various perturbations, including therapeutic interventions; and a systemic disease, in which the mechanisms that provide robustness in a certain environment work unfavourably under a current environment that is significantly different from the conditions that the system has adapted to24,28–30. Cancer and infectious diseases can be considered as parasitic diseases, because tumour cells and pathogens form a parasitic symbiosis with the host by hijacking the host’s mechanisms of robustness to protect and proliferate themselves, as well as to establish robustness mechanisms of their own. For example, in cancer, tumours establish robustness against various therapeutic perturbations through various mechanisms, such as multiple-drug resistance, micro-environment remodelling, hypoxia-inducible factor 1 (HIF1) upregulation and intra-tumoural genetic heterogeneity — mechanisms that are consistent with the general framework of

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PERSPECTIVES robust systems29,30. The counteraction of the therapeutic intervention by enhanced genetic diversity is commonly observed, so that drugs are only effective for a subpopulation of tumour cells or pathogens. Both tumour cells and HIV, for example, are known to possess a high level of genetic variation, and the emergence of drug-resistant pathogen variants and the transfer of drug-resistance genes through horizontal gene transfer provide similar mechanisms at a population level. With these mechanisms in mind, strategies for drug design include finding the point of fragility of the target cells, circumventing robustness mechanisms that the target cells might exploit and pre-empting possible enhancement of the robustness of the target cells against specific drug interventions, with the aim being to remove the target cells or induce dormancy. Diseases such as type 2 diabetes and autoimmune disorders can be considered systemic diseases, as malfunctions of systemic control cause the symptoms of the disorders. The typical indication of type 2 diabetes is a persistently high plasma-glucose level due to insulin resistance. However, in the ancient environment during evolution, insulin resistance might have been a mechanism for providing robustness against nearstarvation levels of food supply in a highly pathogenic and hostile environment by maintaining a higher blood-sugar level (on which neuronal cells and innate-immunerelated cells are dependent). So, the system might have adapted on an evolutionary timescale28 to provide robustness against these historical environmental threats, but it is now working undesirably in the situation of a totally different lifestyle. In this type of disease, there is no target cell to be removed, or induced to be dormant. There are issues such as β-cell dysfunction that merit celltype-specific intervention, but such strategies tend to provide only a temporary solution if disorders of the systemic level network are left untouched, as most dysfunctions at the level of specific cell types are manifestations of cascading failures that stem from systemic disorders. Mechanisms for robustness are distributed throughout the organism, and drugs have to be designed to control disease status in a systemic manner. Robustness and drug efficacy The concept of robustness in biological systems can be valuable for interpreting the efficacy and side effects of drugs. This concept is valid from the systemic physiology level to the cellular level, but owing to space limitations, this article will focus only on

Box 1 | Robustness and drug resistance Case study: gefitinib. Gefitinib (Iressa; AstraZeneca) is a dose-dependent inhibitor of epidermalgrowth-factor receptor (EGFR) autophosphorylation that competitively binds at the ATP site on EGFR66. The rationale behind this drug is that because EGFR is expressed, or overexpressed, in various solid tumours, such as non-small-cell lung cancer (NSCLC), breast, colorectal, gastric, ovarian, prostate and bladder cancer, and because it correlates with poor prognosis67,68, inhibition of EGFR activity should provide therapeutic benefits. However, clinical benefits were demonstrated for only a specific subpopulation of patients with advanced NSCLC with overexpression of amphiregulin69 and a specific mutation (L858R and exon 19 deletion) in EGFR70,71. Incidents of interstitial lung disease as a side effect of gefitinib have been reported, and although gefitinib has been considered to be selective for EGFR, it can also inhibit downstream-signalling proteins or ATP-dependent kinases other than EGFR, which could cause toxicity72. A study on gefitinib-resistant tumour cells indicates that gefitinib’s antiproliferative effect is due to the activation of glycogen synthase kinase-3β (GSK3β) that degrades cyclin D1, and activation of platelet-derived-growth factor receptor (PDGFR) signalling overrides gefitinib’s effect by activating mitogen-activated protein kinase (MAPK) and by inhibiting GSK3β activity73. Furthermore, gefitinib-resistant tumour cells have a specific mutation in the tyrosine kinase domain of EGFR that replaces threonine with methionine at position 790 (T790M), which prevents the access of gefitinib to its binding site74. This case highlights the diversity of mutations and pathways already prevalent in patient populations that give rise to the robustness of tumour cells against gefitinib intervention, which prevents the drug from being effective. Case study: trastuzumab. Trastuzumab (Herceptin; Genentech) is a humanized monoclonal antibody that binds to the extracellular domain of ERBB2 (also called HER2/neu), thereby downregulating ERBB2 signalling75. Its development was inspired by the fact that about 30% of breast and ovarian cancer cases have higher levels of ERBB2 expression and gene amplification, and overexpression of this gene is associated with poor prognosis76. Although efficacy of trastuzumab monotherapy has been reported for ERBB2-overexpressing breast cancer patients77, only a limited response rate at around 35% has been attained78. Furthermore, resistance arises possibly owing to the activation of insulin-like growth factor 1 receptor signalling79 and the loss of phosphatase and tensin homologue80, which enables tumour-cell proliferation regardless of ERB family signalling. This is another example in which robustness of tumour cells against specific intervention through genetic diversity can compromise the effectiveness of a drug.

the cellular level. Drugs are often ineffective owing to the robustness of cellular systems against the intended interventions, and can cause side effects when they interact with fragile points of off-target cells. Several cases are analysed below to illustrate these points. Drugs that target a single specific molecule are most effective when the target molecule is only observed in cells and pathogens that trigger disease symptoms and is the single causative factor that maintains the disease state. Inhibition of the target molecule alone can mitigate, if not eliminate, the symptoms without harming other cells. The target molecule, therefore, is the point of fragility of the system that maintains the disease state. Some anti-infectives are examples of this type of drug, as most of the target molecules only exist in pathogens, but not in the host cells, and inhibition of the target molecule can significantly reduce disease symptoms. For example, Vibrio cholerae is a pathogen that causes epidemics in many developing countries. It produces a toxin that interacts with a G-protein and causes diarrhoea. Cholera toxin is encoded in a pathogenicity island (PAI), and is considered to be acquired through horizontal

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gene transfer31. A small-molecule inhibitor, 4-N-(1,8-naphthalimide)-n-butyric acid (virstatin), suppresses the expression of the V. cholerae virulence factors, cholera toxin and toxin-coregulated pilus, by inhibiting the transcriptional regulator ToxT32. This agent is successful because ToxT only exists in pathogens, and it is the single transcription factor that controls virulence factors, which therefore implies that the pathogen system is not robust against the inhibition of ToxT. The situation could have been different if the virulence factors were controlled by multiple transcription factors with no common binding site for potential drugs — a system that resembles a fail-safe mechanism through its diversity of transcription factors. However, drug-resistant infections involve the emergence of one or more bacteria that acquire drug-resistance, followed by horizontal transfer of genes that are responsible for the drug-resistant phenotype33. This phenomenon represents a robustness of bacteria against drugs on the basis of genetic diversity and modular structure of a PAI that makes horizontal gene transfer efficient. At the same time, drug resistance could be

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PERSPECTIVES mitigated by interrupting horizontal gene transfer that depends on a modular PAI region. This example illustrates how the concept of robustness helps to interpret efficacy and resistance to drugs. A further illustrative case is that of imatinib (Gleevec; Novartis), which is considered as a successful example of a drug that targets the protein product of a disease-causative gene34. Using mice, a characteristic genetic anomaly — a translocation between the long arms of chromosomes 9 and 22 that produces the BCR–ABL fused gene observed in most patients with chronic myeloid leukaemia (CML) — has been identified as a cause of the disease35–39. Imatinib binds to a specific conformation of the mutant BCR–ABL kinase to hold it in the inactive state. The high efficacy of imatinib for a subset of the patients with CML can be attributed to the fact that the rare incidence of BCR–ABL indicates that the fusion protein is a single cause of CML at the initial stage and only exists in target cells. So, similar to the anti-infectives example above, imatinib hits the point of fragility for CML. However, imatinib efficacy is compromised by the emergence of various mutations of BCR–ABL, as well as drug resistance that is not dependent on BCR–ABL mutations40. This indicates that the CML disease state regains its robustness against the drug through the diversity of mutations and pathways that maintain the activity of tumour cells. The lesson that can be learned from these examples is that a drug can be effective if it hits the point of fragility, but can become less effective if robustness of pathogens or tumour cells against interventions emerges through diversity, which is a type of fail-safe mechanism (FIG. 1b,c). That biological systems have evolved to form complex systems that are robust against a broad range of external and internal perturbations implies that they can also be robust against therapeutic drug interventions. Examples of such cases are analysed in BOX 1. The side effects of a drug can be most serious when the drug hits a point of fragility of the patient’s system (BOX 2). Although obvious side effects can be identified and addressed at the early stages of drug development, difficulties occur when side effects develop only in a specific subpopulation that has particular genetic polymorphisms and/or lifestyle that make the patients susceptible to such interventions. It is therefore important that extensive data are collected to better prevent unwanted effects. This requires the sampling of numerous cells in different

Box 2 | Fragility and drug side effects Case study: rofecoxib. Drug side effects can be caused by unwanted interactions with molecules that expose the fragility of cellular or organ-level functions to specific interventions in both target cells and off-target cells. For example, the coxibs, such as rofecoxib (Vioxx; Merck) and celecoxib (Celebrex; Pfizer), were developed to selectively inhibit cyclooxygenase 2 (COX2) for mitigating inflammation81, although rofecoxib has higher selectivity for COX2 over COX1 than celecoxib. Selectivity for COX2 over COX1 has been considered to be important because COX2 is selectively expressed in tissues with inflammation. Moreover, the adverse gastrointestinal effects of some anti-inflammatory drugs have been attributed to the inhibition of COX1, which is constitutively expressed in gastrointestinal tissues82, as well as in cultured endothelial and vascular smooth-muscle cells83. Therefore, the more selective inhibition of COX2 by rofecoxib compared with other anti-inflammatory drugs was considered to be a desirable property of the compound84. However, rofecoxib was shown to be associated with an increased risk of adverse cardiovascular events at high doses85, which might be due to a reduced production of antithrombotic products that have cardio-protective functions86. This highlights the fact that selectivity for a molecule in the target cells does not eliminate the risk of side effects, as the target molecule might have an important role in off-target cells.

human tissues for the identification of a functional role of potential unintended drug targets, and the screening of unusual genotypes to identify possible points of fragility in rare subpopulations. Multicomponent therapies Each compound of a multicomponent therapy simultaneously targets and interacts with a different molecule so that the combined effect can change the cellular state. This is useful for when such change cannot be made, or would be less effective, by using individual drugs7. Multicomponent therapies are increasingly gaining attention, with several marketing successes reported — salmeterol/fluticasone (Advair; GlaxoSmithKline)41, nicotinic acid/lovastatin (Advicor; Kos Pharmaceuticals)42,43 and AZT–3TC (Combivir; GlaxoSmithKline)44. A combined effect of atorvastatin and fenofibrate in lowering cholesterol levels has also been reported6, and a combination high-throughput screening strategy has been proposed and implemented in stages in the drug discovery pipeline45. Moreover, the application of a system-response profile that captures differences in gene transcripts, proteins and metabolites between drugperturbed and unperturbed cells has been proposed6. Although the exact mechanisms that underlie the combinatorial effects of successful multicomponent therapies have yet to be elucidated, three explanations have been put forward (examples are highlighted in BOX 3). First, the effect of each component converging at a certain part of the pathway could trigger a more-than-additive effect. Second, if different components of the targeted pathway compensate for the inhibitory effects of one drug, the administration of a combination of drugs could overcome

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this neutralization effect, thereby effectively eliminating robustness caused by a fail-safe mechanism through diversity. Third, each component could target a different molecule or specific mutation site, in such a way that the result is non-cross-resistance, as highlighted by the AZT–3TC combination therapy for HIV described in BOX 3. Recent studies related to the effects of multiple weak perturbations on biological networks might provide theoretical accounts for the effects of multicomponent drugs46,47. Properly designed multicomponent therapies are the first step in controlling robustness to achieve clinical efficacy, and can be widely useful. However, the selectivity of a drug combination depends on the relative response of target cells over non-target cells. This is particularly problematic for cancer chemotherapy. Unless the molecules targeted are uniquely expressed in the target cells, and not in off-target cells, such an approach might not attain a sufficient level of selectivity. Use of synthetic lethality for multicomponent anticancer drug discovery might improve selectivity 8, but it has yet to be shown whether practical targets can be found. An extreme extension of the multicomponent therapy approach involves using large numbers of components that target a broad range of molecules, instead of targeting just one or two ‘major’ genes or proteins. Traditional Chinese medicine emphasizes minor interventions over a broad range of factors48,49, although most components in traditional Chinese medicine are unidentified. It is interesting to note that the US National Cancer Institute has screened 35,000 samples of roots and fruits from 12,000 plant species only to find 3 new drugs48, which implies that the central issue is patterns of intervention rather than a single component. Traditional

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PERSPECTIVES Chinese medicine can be an inspiration to create a drug discovery strategy that uses large numbers of components to systematically control a complex network system. Such therapies could be considered as ‘long-tail’ drugs because most targets are on the long tail of a statistical distribution. Long-tail distribution in this context does not need to be scale free or follow an exact power law; it is only necessary that there are very long tails of statistical distribution that might be an overlay of scale-rich distributions. Recent discoveries related to the scale-richness of molecular interaction networks, as seen in metabolic networks50, might imply that perturbations of molecules in different parts of long-tail distributions could have qualitatively different impacts on the system. There are practical implications of a long-tail distribution. For example, cancer subtype classification indicates that the expression profile of large numbers of genes has to be considered for accurate prediction, rather than focusing on a small number of major genes51, and a theoretical study using microarray data for cancer classification concluded that expression of genes at the middle range of expression levels, rather than top-ranking expression levels, has more importance in improving classification accuracy52. Although highly speculative, it might be interesting to investigate whether the systematic control of complex molecular networks can be achieved using perturbations of long-tail components. Multistage targeting of cellular dynamics A more sophisticated approach to controlling robustness is multistage therapy. The general concept is to use a sequence of drugs administered at specific doses and time intervals so that the dynamic state of target cells can be selectively perturbed into the system state that is desired for therapeutic purposes. This requires a more sophisticated understanding of the dynamic cell states and methods to control them. An effective multidrug therapy could be composed of one or more series of preemptive interventions and target interventions. Pre-emptive interventions target molecules that are involved in controlling cellular states, such as cell-cycle and regulatory feedback loops, so that the cell can be induced into specific states for which the target intervention will be most effective or so that compensatory mechanisms that could nullify the target interventions can be disabled. Target interventions ultimately

Box 3 | Multicomponent therapies Case study: combinations with HSP90 inhibitors. The use of imatinib, an inhibitor of the BCR–ABL kinase, and heat-shock protein 90 (HSP90) inhibitors represents an interesting potential combination anticancer strategy87. 17-allylamino-demethoxygeldanamycin (17-AAG) is an inhibitor of HSP90, which is a molecular chaperone that stabilizes proteins by correcting misfolding88. 17-AAG reduces BCR–ABL levels and induces apoptosis in in vitro experiments89, and BCR–ABL-point-mutation cells that are imatinib-resistant are still sensitive to 17-AAG90. 17-AAG was also reported to reduce ERBB2 levels and to inhibit the proliferation of a trastuzumab-resistant tumour cell line in an in vitro experiment91. Furthermore, a comparison of responses against HSP90 inhibition using geldanamycins indicated higher apoptosis rates in tumour cells with epidermal-growth-factor receptor (EGFR) mutations (NCI-H3255, NCI-H1650, NCI-H1975) than tumour cells without EGFR mutations (A549)92. An interesting point in this report is that even a gefitinib-resistant cell line (NCI-H1975) that harbours the secondary mutation (T790M) demonstrated a higher apoptosis rate than non-EGFR mutation cells, which implies that HSP90 inhibition is effective even for gefitinib-resistant tumours. Overall, these findings imply that the viability of tumour cells is partly dependent on HSP90 function, and at least certain types of BCR–ABL, ERBB2 and EGFR-mutant proteins require HSP90 to be functional. So, HSP90 is an example of a protein that provides decoupling to enhance robustness of component functions against mutations and environmental perturbations by means of fixing protein-structure folding. Case study: AZT–3TC. A combination of drugs for non-cross-resistant targets can be particularly effective when one of the components is designed to target the point of fragility that is induced by the other components in the combination. A successful example of this approach is seen in HIV therapy with AZT–3TC combination therapy. HIV-1 can acquire resistance to 3′-azidothymidine (AZT, zidovudine) through stepwise accumulation of 4 out of 5 mutations in reverse transcriptase at codons 41, 67, 70, 215 or 219 (REF. 93). For HIV-1 to be resistant to L-2′-deoxy-3′-thiacytidine (3TC, lamivudine), it must develop an allele substitution of valine for methionine at codon 184 in reverse transcriptase94. It was found that AZT-resistant virus is 3TC-sensitive, and 3TC-resistant virus is AZT-sensitive owing to interactions on these mutations on viral reverse transcriptase44. This is an impressive example in which the trade-off of being robust against AZT is fragility against 3TC, and vice versa. Case study: multikinase inhibition. The combination of gefitinib and trastuzumab was reported to inhibit tumour-cell proliferation of non-small-cell lung cancer (NSCLC) cells more effectively than either drug alone95. Multikinase inhibitors can attain an effect in a single drug that is analogous to that of multicomponent therapies that are based on drugs that target a single kinase. For example, sunitinib malate (Sutent; Pfizer) is a compound that interacts with several receptor tyrosine kinases (RTKs) such as platelet-derived growth-factor receptor-α (PDGFRα), PDGFRβ, vascular endothelial growth-factor receptor 2 (VEGFR2), KIT and fms-related tyrosine kinase 3 (FLT3)96. The efficacy of such drugs could be related to the inhibition of multiple pathways, which lead to effects through interactions with key molecules in each pathway — that is, they attain therapeutic effects by mitigating the robustness of cellular functions against inhibitory perturbations that is gained through a diversity of pathways.

induce desired changes in cellular states, such as apoptosis and dormancy for tumour cells, and various functional remedies for other diseases. The timing of interventions is crucial, because the target interventions can often trigger compensatory robustness mechanisms that offset the effects of the interventions, and such effects cannot be easily countered once invoked, although they can be easily pre-empted. By disabling the mechanism that provides robustness against the target intervention first by pre-emptive intervention, the robustness of the cell against the target intervention is significantly reduced, which increases the chance of success. In such cases, it is important that the correct order and individual dose of the drugs to be administered, as well as the interval between the administration

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of each drug, are examined. The general concept of the multistage drug is described in Supplementary information S1 (figure). The importance of the order of administration of drugs in a multidrug therapy has been documented in recent years, particularly in relation to the cell cycle of tumour cells53. For example, in a study using colorectal cancer cell lines (DLD1 and SW480), effects on the order of administration for paclitaxel (Taxol; Bristol–Myers Squibb) and oxaliplatin (Eloxatin, Sanofi–Aventis) have been investigated; a taxol–oxaliplatin sequence had greater growth-inhibitory effects than an oxaliplatin–taxol sequence and than single-reagent treatment54. An experiment using the human colon cancer cell line HCT-116 demonstrated that a sequence of SN-38 (the active metabolite of irinotecan)

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PERSPECTIVES followed by flavopiridol induced apoptosis at a high rate (about 44%), but a reverse sequence attained only a modest level of apoptosis (about 15%) and SN-38 as a single reagent induced only 1% of apoptosis55,56. The use of SN-38 induces p21 expression and a concomitant G2 arrest, which makes the tumour cells resistant to SN-38 (and therefore irinotecan) because SN-38 is most effective in the S phase owing to its mechanism of action as a topoisomerase-I inhibitor. Flavopiridol induces G1 and G2 arrest, and inhibits CDK1, CDK2, CDK4, CDK6 and a series of anti-apoptotic molecules such as BCL2, p21 and phospho-survivin56. Therefore, the use of SN-38 followed by flavopiridol is synergistic, as cells arrested in G2 by SN-38 might be induced to undergo apoptosis owing to the inhibitory effect of flavopiridol on anti-apoptotic molecules, or released from arrest through p21 inhibition by flavopiridol to progress into the G1–S phase, when SN-38 is most effective. However, the use of flavopiridol followed by SN-38 offsets some of the effects of flavopiridol, such as p21 inhibition, by antagonistic effects of SN-38, which upregulate p21. Also, the cell cycle is arrested at G1 and G2 by flavopiridol, and lower numbers of cells enter S phase when SN-38 is most effective. The combination of irinotecan followed by flavopiridol is currently in clinical trials57. Sequential use of cancer drugs can be extended to involve scheduling to reflect circadian rhythms, as these might affect cell cycle and metabolism — cancer chronotherapy58,59 (BOX 4). Cancer chronotherapy is based on the idea that tumour and normal cells have different circadian rhythms that affect drug response and side effects. For example, if a taxol–oxaliplatin sequence is effective and the use of oxaliplatin at a certain time of the day is most effective and minimizes the side effects, this time of day shall determine the overall optimal schedule for sequential multiple drug use that maximizes the difference of drug response between tumour and normal cells. The observation that circadian rhythms might be deregulated in tumour cells, but not in normal cells, provides one such clue that might enhance the selectivity of therapeutic effects60, and research into the relationship between circadian rhythms, the cell cycle and tumours is making rapid progress61. The next important step for this type of therapeutic strategy is to firmly establish the scientific basis of temporal dynamics of cells in disease and normal conditions, and of differential temporal responses of cells to various drugs and their combinations.

Box 4 | Cancer chronotherapy Case study: 5-fluorouracil, leucovorin and oxaliplatin. Cancer chronotherapy is an example of when the timing of drug use is synchronized with circadian rhythms, which might be interacting with the cell cycle and systemic metabolic conditions58,59,97,98. Although cancer chronotherapy does not actively induce certain cellular states, it exploits natural circadian rhythms to attain a context-dependent efficacy of the drug use. Furthermore, circadian rhythms have been argued to be deregulated in advanced tumours99. Clinical studies are scarce, but have shown promising results. In a study for patients with colorectal cancer, 5-fluorouracil (5-FU), leucovorin (LV) and oxaliplatin were administered in a phased manner; oxaliplatin infusion peaked at 16:00 hours, and 5-FU and LV peaked at 04:00 hours. Patients with chronomodulatory treatment showed significantly higher objective responsiveness and a threefold reduction in the incidence of World Health Organization (WHO) Grade 4 toxicity compared with patients that received the drugs in a standard manner100 . A significant difference in the 5-year survival rates in patients with acute lymphoblastic leukaemia has also been reported between those who had drugs (6-mercaptopurine and methotrexate) administered during the evening (80%) and those who had drugs administered in the morning (40%)101. However, how robustness and fragility are affected by different phases of circadian rhythms has yet to be fully elucidated, although correlation with cell-cycle and metabolic changes are reasonable causes for such effects. While circadian rhythms are not properly maintained in tumour cells, cell-cycle and metabolic states might also be affected. If this is the case, tolerable doses of normal cells against cell-cycle-dependent drugs can be increased by optimizing the time of use, so that overall therapeutic efficacy can be improved.

Systems-oriented drug design The question now is how to design systemsoriented drugs that take into account the aspects of system robustness discussed above. How can targets, timing and dosage be optimized to attain the desired effects? This requires an in-depth understanding of cellular- and organism-level dynamics, combined with advanced high-throughput screening and computational analysis tools. The approaches discussed here also call for the use of multiple drugs in sophisticated combinations. This adds a considerable level of combinatorial complexity in the drug discovery and therapy design process, because multiple components (often in large numbers) have to be identified and validated, and their proper combination, dosage and timing of use have to be identified, which might raise the cost of drug development. Nevertheless, the corresponding growth in potential strategies to treat presently intractable diseases could represent an excellent opportunity. So, establishment of effective and efficient methods to systematically identify appropriate strategies is the key. A range of possible options to tackle this challenge for different degrees of complexity and use of dynamics discussed here are summarized in FIG. 2. Theoretically, the main challenge, in both a biological and a mathematical sense, is to find out how to control complex network systems. Although the dynamics of simple feedback systems have been well understood from classical and modern control theory, the control of highly distributed nonlinear network systems has yet to be established.

NATURE REVIEWS | DRUG DISCOVERY

Mathematics that describe biological systems, particularly from a control aspect, have yet to be developed. Questions such as how can we control a complex network using components on a long-tail distribution have yet to be answered. Advanced communication theories can be a source of inspiration. For example, spread-spectrum communication62 is used for mobile phones to achieve highly selective and noiseless communication between users. Perhaps the strategy used to attain peer-to-peer communication without interference could be applied for highly sophisticated drug design for particular cases, such as a spreadspectrum drug that is at the extreme end of complex drug systems (Supplementary information S2 (box)). Many intriguing theories and methods exist, although most are for engineering and physics, and cannot be simply translated into the biological domain. Reformulation and invention of new theories can be a fruitful challenge for researchers in both mathematics and biology. These studies might also shed light on the science behind traditional Chinese medicine, and such a series of theories could lead to an integration of Western and Oriental medicine on a scientific basis. From a technological and experimental viewpoint, effective screening methods and analysis software tools must be developed, as well as a more in-depth understanding of cellular systems. As mentioned above, a systematic screening study for multicomponent drugs has been reported45, and a number of successful combination drugs are already on the market. These developments have

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PERSPECTIVES Complexity of perturbations

Spread-spectrum drugs

Use of dynamics

Multistage drugs

Chronotherapy

Long-tail drugs

Singlemoleculartarget drugs

Conventional drugs

Multicomponent drugs

Traditional Chinese medicine

between target and off-target cells65. Although the accuracy of computational simulation today is not at a satisfactory level, owing to problems of quantitative data acquisition and modelling techniques, the situation will improve rapidly. It should be remembered that computational fluid dynamics, one of the most successful computational approaches, took decades of efforts to become practically applicable. In addition, high-precision comprehensive mapping of molecular interactions need to be created and properly maintained because such maps uncover robustness and fragility of networks, as seen in examples of epidermal-growth-factor receptor23 and Toll-like receptor25 networks. Furthermore, to best identify characteristic dynamics that are unique to target cells and to avoid side effects, differential systems biology needs to be developed for which differences in the interactions and dynamics of different cell types together with different genetic backgrounds have to be compared in an efficient manner.

Numbers of components and/or targets Simplicity of perturbations

Figure 2 | A range of options for drug design. Different types of therapeutic strategies can be classified by the numbers of component drugs, the number of their targets and the use of dynamics. Current conventional drugs often target a small number of molecules, whereas ‘long-tail’ drugs and Chinese herbal medicines use a large number of components. Drugs that target single molecules and spread-spectrum drugs (still a speculative concept at present) that would extensively use dynamics to attain selectivity are two extremes in the diagram. Both strategies could be highly effective in special cases, but might not be generic enough to be broadly applicable. Multistage drugs, long-tail drugs and multicomponent drugs, perhaps in combination with chronotherapy, could have broad applicability and are expected to represent mainstream therapeutic strategies in the future.

not explicitly taken robustness issues into account, but they explore a set of factors that can counteract the robustness of the cellular systems against drug interventions. The issues for the next step are to systematically identify targets in the context of robustness and fragility, rather than just combinatorial effects. Recently, my group has developed a new experimental method called gene tug-of-war (gTOW) to comprehensively and quantitatively measure robustness of cellular functions against quantitative perturbations of gene dosage63. Such an approach could be scaled up and improved for genome-wide robustness-based screening and provides a new approach for drug screening and target identification. Techniques that can efficiently identify new drugs and their targets are essential for providing options for multicomponent therapies, multistage therapies and, most notably, the long-tail therapies. Cell-based screening

of both natural compounds and chemical genomics might provide us with a broad base of effective drugs3,4, and microfluidics technologies could provide us with opportunities for high-throughput cell-based screening64. A set of computational and mathematical tools also has to be developed to support the robustness-based approach. The robustnessbased approach has a specific goal: to find a set of targets that has a specific robustness property for which combinatorial perturbation generates both efficacy and selectivity. So, in the future, the process can be made more sophisticated by applying a range of mathematical and experimental tools geared to this specific goal. Highly sophisticated bifurcation and other systems-dynamics analysis packages that can handle comparative high-dimension analyses for large-scale models are essential. Such software enables the application of computational models to identify differences in dynamical behaviours

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Conclusion This article has put forward the proposal that drug and therapy design should be based on an in-depth understanding of robustness and its trade-offs in the organism, from the cellular level to the systemic level. With the explosion of knowledge in genomics, proteomics and systems biology, the immediate concern should be to attain an understanding of robustness and fragility against drug interventions at the cellular level. This eventually translates to robustness analysis at the systemic level. It is clear that many successful drugs in the past have affected a point of fragility of the target system so that a single intervention modulating specific molecules or biological processes can trigger dramatic effects. However, cancer, diabetes, autoimmune disorders and other diseases that are proving challenging to treat with this simple strategy stem from the robustness of the human body, from the cellular level to the systemic level. Given that robustness is a fundamental property of biological systems, systems-based approaches to future drug design should consider robustness as the central framework. A new way of controlling complex and robust biological systems through higher-complexity drugs will need to be established, as complexity has to be controlled by complexity, but addressing these challenges and making robustnessbased approaches to drug design a reality could cause a fundamental transformation in the drug industry and in medical practice.

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PERSPECTIVES Hiroaki Kitano is at Sony Computer Science Laboratories Inc., 3-14-13 Higashi-Gotanda, Shinagawa, Tokyo 141-0022, Japan; The Systems Biology Institute, Suite 6A M31 6-31-15 Jingumae, Shuibuya, Tokyo 150-0001, Japan; and the Department of Cancer Systems Biology, The Cancer Institute, 3-10-6 Ariake, Koutou-ku, Tokyo 135-8550, Japan. e-mail: [email protected] doi:10.1038/nrd2195 Published online 23 February 2007 1. 2.

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FURTHER INFORMATION Hiroaki Kitano: Sony Computer Science Laboratories, Inc.: http://www.csl.sony.co.jp The Systems Biology Institute: http://www.sbi.jp

SUPPLEMENTARY INFORMATION See online article: S1 (figure) | S2 (box) Access to this links box is available online.

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Figure S1 | Using multistage drugs to achieve efficacy and selectivity. The multistage approach involves successively administering a set of drugs to differentiate between target and off-target cells. The assumption behind this approach is that there might be differences between target and off-target cells regarding their response to drugs, and that successive intervention, rather than a single intervention, could better exploit such differences to attain a greater level of selectivity. The states of target and off-target cells are initially assumed to be at the steady state. a | Target and off-target cells respond differently to drug 1, but at the level of the cellular state, there is no difference observed (A1 and A2). Cellular states might stay the same in both cells, but, in this example, target cells might only be stable in a sense that is termed mathematically ‘Lyapnov stable’ (the system’s state can fluctuate but remain within the basin of attraction, which is a mathematically defined area in which the state of the system tends to stay within its boundary), whereas the off-target cell can be asymptotically stable (meaning that the state of the system returns to its original state, a block dot in the centre in the example of A2). b | Target and off-target cells (B1 and B2) respond identically to drug 2. In this example, both cells maintain asymptotical stability against drug 2 when the perturbation is applied at the certain dose and the state of the cell is at its original state. c | Simultaneous use of two drugs offsets their effects and causes no main effect on both target and off-target cells (C1 and C2). d | The successful multistage drug will use two drugs in appropriate order, timing and dosage. In this case, drug 1 is used first at a dosage that can perturb the cell state to some extent, but not enough to induce the cell into a different stable state (red trajectory in D1 and D2). Drug 2 might perturb the cell further so that the cell moves into the new steady state in target cells (blue trajectory in D1), but not in off-target cells (D2). In order to attain such effects, differences of dynamics against drugs between target and offtarget cells have to be investigated. If there are differences in robustness against drug interventions, which might, for example, be due to genetic mutations that are unique in tumour cells, such differences can be explored. e | Such effects might be dosage- and order-dependent, so that reverse-order administration might not generate the same effect (E1 and E2).

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Off-target cells

Target cells A2

A1

b

Drug 1

Drug 1 B2

B1

Drug 2

Drug 2

c

C2

C1

d

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Drug 1 and 2 simultaneously

Drug 1 and 2 simultaneously D2

D1

Drug 1 then Drug 2

e

Drug 1 then Drug 2 E2

E1

Drug 2 then Drug 1

Drug 2 then Drug 1

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Box S2 | The spread spectrum control problem and the long-tail control problem

Frequency

Despreading

Frequency

Intensity

Spreading

Intensity

Intensity

The spread spectrum control problem and the long-tail control problem are mathematical problems motivated by the need to discover a highly selective system of drugs for cancer chemotherapy and other diseases for which systemic interventions are warranted. The problem that cancer researchers and pharmaceutical companies are facing is to find a set of drugs, their dosage and timing of administration that can effectively intervene in tumour cells, but not normal cells. Ineffective interventions would not eradicate the tumour, and unwanted intervention in normal cells would cause serious side-effects. Given that cellular systems can be viewed as network of genes, RNAs, proteins, and other molecules, the problem can be abstracted and reformulated into a more general mathematical problem. The solution to the problem would be a step towards more effective cancer chemotherapy, but could also be used widely for other problems in both the medical and engineering fields. The spread spectrum method (the original idea was invented by Hedy Lamarr (a Hollywood actress) and George Antheil (a composer) in the 1940s), is a communication technique that is now used for mobile phone and satellite-based global positioning systems. Owing to its unusual origin, there is no paper by the inventor, but there are numerous textbooks that highlight the importance of the method62. It modulates signal in the way it spread over broad spectrum each of which is at the noise level for unintended recipients, and the target recipients with a proper decoding key can reassemble signals spread over broad frequencies, and restore high fidelity signal (Figure). The beauty of spread spectrum approach is that it can attain high level of selectivity and tolerance against noise; signals will not be heard by non-target and it cannot even detect signal exits and noise will be dispersed under the noise level.

Frequency

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Figure | A simple conceptual scheme for spread spectrum communication The challenge is whether such an approach can be used for controlling a network system, rather than communication of signals. The spread spectrum control problem can be stated as: “Given the two or more networks that are not identical, find a set of sequential minor perturbations on nodes in networks similarly applied to every network that can induce desired changes in specified unperturbed nodes in one of the networks, but not in the other networks.” The minor perturbation means that the perturbation in which a node can return to its original state once the perturbation is removed. When the node changes into another steady state, it is no longer a minor perturbation as it has incurred a phase transition onto the network. Such perturbations are called a “major perturbation”. As a result of perturbations imposed on nodes in the network, states of unperturbed nodes are affected. When a state of a node has changed, but returned to the original state, then the change is called a minor change. When the state of a node has been so affected that it caused transition to a new steady state, such a change is called a “major change”. Networks are classed as being identical only when their connection topology, interconnection parameters, and node functions are the same. The “target node” is the node that undergoes the desired change, and other nodes are called “offtarget nodes”. A network where desired change of target nodes is expected is called a “target network”, and other networks are called “off-target networks.” The term “desired change” means either a major change which transit to a specific new steady state, a major change without a new steady state specified, or a minor change above a specific threshold defined. When the desired change of one or more nodes in the target network requires a major change, the condition is called “strong”; the condition is called “weak” otherwise. An additional condition, a “super-weak” condition, can be defined that sets an upper bound on the level of minor perturbations and minor changes in off-target nodes of the target network and all nodes in off-target networks. Also, a stochastic version of the problem can be defined and could be very important for realistic use of solutions to biological problems. Challenges are to find a set of perturbations with specific nodes to be perturbed, the level of perturbations, and timing of perturbations that leads to the desired change only on the target nodes of the target network. It is most likely that such perturbation is possible only in the

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specific set of networks and in specific desired changes. Thus, a whole set of theorems has to be created to solve this problem. The problem is called the spread spectrum control problem because the aim of perturbation is to control the state of the network, by means of changing states of nodes in the network, without directly perturbing these nodes. The perturbations are expected to spread over numbers of nodes, rather than one small number of nodes, to attain the expected outcome. The possible solution is also analogous to the spread spectrum technique for wireless digital communications. The long-tail control problem can be stated as: “Given the two or more networks that are not identical but interconnected, find a set of sequential (minor) perturbations on nodes in networks that are on the long-tail of a defined distribution index, whereas such perturbations are similarly applied to every network to induce desired global changes networks.” Here, nodes on the long-tail distribution means nodes that are classified below the defined rank based on a certain index such as connectivity, expression level, the degree of change in expression, etc. Such an index can be problem-dependent, and may require further elaboration of the problem statement. “Desired global change” is another ambiguous term, but it means that the state of connected network to be induced to a certain attractor in the certain phase space. Again, the choice of dimensions for the phase space is arbitrary and problem-dependent requiring further elaboration. It is unclear if “minor” perturbation is required in the problem statement, but the problem can be subdivided if the solution can be founded only by using minor perturbations or not. These two mathematical problems are not only challenging to mathematics, complex systems, and engineering studies, they are directly relevant to drug discovery.

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