Biological Robustness

REVIEWS

BIOLOGICAL ROBUSTNESS

Hiroaki Kitano Abstract | Robustness is a ubiquitously observed property of biological systems. It is considered to be a fundamental feature of complex evolvable systems. It is attained by several underlying principles that are universal to both biological organisms and sophisticated engineering systems. Robustness facilitates evolvability and robust traits are often selected by evolution. Such a mutually beneficial process is made possible by specific architectural features observed in robust systems. But there are trade-offs between robustness, fragility, performance and resource demands, which explain system behaviour, including the patterns of failure. Insights into inherent properties of robust systems will provide us with a better understanding of complex diseases and a guiding principle for therapy design.

LYSIS The discovery of fundamental, systems-level principles property has been widely observed across many species, Part of a bacteriophage life that underlie complex biological systems is a prime sci- from the level of gene transcription to the level of sys- cycle in which its genome is entific goal in systems biology1,2.Robustness is a prop- temic homeostasis. For example, fate decision of λ phage expressed to cause dissolution erty that allows a system to maintain its functions despite — the result of which is the activation of either LYSIS or of the bacterial host cell, leading to manufacture of external and internal perturbations. It is one of the fun- LYSOGENY pathways — was once considered the result of more bacteriophage particles damental and ubiquitously observed systems-level phe- fine tuning of the binding affinity of promoters to corre- and subsequent infection of nomena that cannot be understood by looking at the sponding regulatory factors. However, it has been shown other cells. individual components. A system must be robust to that it is the structure of the network, which involves both function in unpredictable environments using unreliable positive and negative feedback, that is responsible for LYSOGENY Part of a bacteriophage life cycle, components. Understanding the origin and principles of making sustainable commitment, not the specific bind- during which its genetic material robustness in biological systems will help us to put vari- ing affinity — the fate-decision behaviour was shown to is integrated into the genome of ous biological phenomena into perspective; it will also be robust against point mutations in the promoter its bacterial host, where it catalyse the formation of principles at the systems level. region3.In addition, cooperative binding of repressors remains in a latent state. In this article, I argue that robustness is a fundamen- that forms implicit local positive feedback also con- 4–6 SEGMENTAL POLARITY tal feature of evolvable complex systems. Complex bio- tributes to the stability of the switch .Many examples of A pathway that regulates the logical systems must be robust against environmental robust properties can be observed in different biological anteroposterior identity of and genetic perturbations to be evolvable. Evolution systems. segments during insect often selects traits that might enhance robustness of the Escherichia coli is capable of chemotaxis over a development. organism. Robustness is, therefore, ubiquitous in living wide range of chemo-attractant concentrations organisms that have evolved. However, systems that are owing to integral intracellular feedback that ensures Sony Computer Science robust face fragility and performance setback as an perfect adaptation and that is independent of ligand Laboratories, Inc., 3-14-13 inherent trade-off. Identification of the basic architecture concentration7–9. Higashi-Gotanda, Shinagawa, Tokyo 141-0022, for a robust system and the associated trade-offs is essen- A biochemical network that is involved in the estab- Japan, and The Systems tial for understanding their faults and countermeasures lishment of SEGMENTAL POLARITY in Drosophila melanogaster Biology Institute, Suite 6A, — diseases and therapies, respectively. has been shown to be robust against changes in initial M31, 6-31-15 Jingumae, values and rate constants of molecular interactions, Shibuya, Tokyo 150-0001, Robustness as an organizational principle 10,11 Japan. enabling stable pattern formation .Similar obser- e-mail: [email protected] Robustness enables the system to maintain its functional- vations have also been made for MORPHOGEN-pattern doi:10.1038/nrg1471 ities against external and internal perturbations. This formations10,12,13.

Robustness is often misunderstood to mean stay- Robust adaptation (return to a periodic attractor) ing unchanged regardless of stimuli or mutations, so that the structure and components of the system, and therefore the mode of operation, is unaffected. In fact, robustness is the maintenance of specific functionali- Transition to a ties of the system against perturbations, and it often new attractor requires the system to change its mode of operation in a flexible way. In other words, robustness allows changes in the structure and components of the system owing to perturbations, but specific functions are Stochastic process maintained. influences the In the following sections, I outline the mechanisms trajectory that ensure the robustness of a system: system control, alternative (or fail-safe) mechanisms, modularity and decoupling.

System control. System control consists of negative and positive feedback to attain a robust dynamic response observed in a wide range of regulatory networks, including the cell cycle, the circadian clock and chemotaxis7,17,18.Negative feedback is the princi- Robust adaptation pal mode of control that enables robust response (return to a point attractor) (or robust adaptation) to perturbations. Bacterial chemotaxis is one of the most studied examples Unstable of robust adaptation that uses negative feedback — Figure 1 | Robust reactions of the system: to stay or to change. The state of a system INTEGRAL FEEDBACK in particular — to attain the perfect can be shown as a point in the state space. In this case, the state space is simplified into two adaptation that allows chemotaxis to occur in response dimensions. Perturbations forcefully move the point representing the system’s state. The state of to a wide range of stimuli7–9.Integral feedback, a par- the system might return to its original attractor by adapting to perturbations, often using a negative feedback loop. Bacterial chemotaxis is an example. There are basins of attractions in the state ticular control strategy, is essential to maintain robust space within which the state of the system moves back to that attractor. If the boundary is adaptation in both E. coli and Bacillus subtilis,despite exceeded, the system might move into an unstable region or move to other attractors. Positive the fact that the network topologies are not the feedback can either move the system’s state away from the current attractor, or push the system same19. towards a new state. The cell cycle involves a combination of positive and negative feedbacks that Positive feedback contributes to robustness by facilitate transition between two attractors (G1 and S/G2/M) creating a bistable system. Often, amplifying the stimuli, often producing bistability, stochastic processes affect transition between attractors, as seen in λ-phage fate decision, but maintenance of a new state has to be robust against minor perturbations. so that the activation level of a downstream pathway can be clearly distinguished from non-stimulated states, and so that these states can be maintained. In D. melanogaster segment-polarity formation — Diseases such as cancer and diabetes are manifesta- repetitive stripes of differential gene expression — is tions of co-opted robustness, in which mechanisms that observed along the antero-posterior axis of the devel- normally protect our bodies are effectively taken-over to oping embryo. The first stripe has to express wingless sustain and promote the epidemic states14–16.As more (wg), the second stripe has to express engrained (en), studies are done, it is becoming important to provide an but the third stripe expresses neither. von Dassow and integrated perspective on the robustness of biological colleagues10 created a computational model of this systems. system, initially without positive autoregulatory feed- MORPHOGEN A diffusible signal that acts at a The robustness of a system can manifest itself in one back on wg and en,but the model failed to reproduce distance to regulate pattern of two ways: the system returns to its current ATTRACTOR experimentally observed patterns. However, with two formation in a dose-dependent or moves to a new attractor that maintains the system’s positive feedbacks on wg and en activations, robust manner. functions (FIG. 1).A return to the current attractor is pattern formation was reproduced10.Recently, Ingolia11 often called ‘robust adaptation’.The attractor can be analysed this model and showed that the bistability ATTRACTOR A point or an orbit in the phase either static (a point attractor; a fixed point in the PHASE caused by positive feedback loops is responsible for space where different states of SPACE that the trajectory of the system state approaches robust pattern formation11. the system asymptotically asymptotically) or oscillatory (a periodic attractor; a Positive feedback is also used in signal transduction converge. cyclic orbit in the phase space that the trajectory of the and the cell cycle to form switch-like behaviour of the

PHASE SPACE system state approaches asymptotically). system by amplification of stimuli, and for fate deci- A multi-dimentional space that A transition to a new attractor has to be made sion (as seen in the λ phage), so that it initiates a tran- represents the dynamics of a robustly in response to stimuli so that the system sition and a new state of the system is made that is system. For a system with behaves consistently against perturbations. As seen in λ- more robust against noise and fluctuations of stim- N-variables, a phase space is a phage fate decision, the stochastic process often influ- uli3,20–27.Many biological subsystems use the combina- 2N dimensional space composed of N-variables and ences the trajectory of transition and the attractor on tion of these system controls to perform their functions their time derivatives. which the system eventually converges. and to maintain robustness27,28.

An alternative, or fail-safe, mechanism (redundancy It is interesting to note that although redundancy and diversity). Robustness can be enhanced if there are through duplicated genes is frequently observed, there is multiple means to achieve a specific function, because no reported case of duplicated circuits, despite the fact failure of one of them can be rescued by others. Here, that there are many circuits with similar topologies. I call this mechanism ‘alternative’,or ‘fail-safe’.This Investigation of networks that share similar topology, as concept encompasses redundancy, overlapping func- far as the degree of homologous genes involved in each tion and diversity, as the differing degrees of similar- network is concerned, revealed that although genes ity between the various alternative means that are might be duplicated, the network as a whole is not available. duplicated43.This indicates that similar network topolo- Redundancy generally refers to a situation in which gies represented in different contexts within and several identical, or similar, components (or modules) between species are the result of convergent evolution, can replace each other when another component fails. rather than duplications43,44.This is consistent with the Diversity, or heterogeneity, represents the other extreme, fact that circuit-level alternative mechanisms are whereby a specific function can be attained by different attained by the differing implementation of overlapping means available in a population of heterogeneous com- functions. ponents. Some of these phenomena are well known as It is important to understand that alternative mecha- phenotypic plasticity29–31. nisms are coupled with system control to ensure robust- In some tissues, cells are surrounded by similar ness. First, the existence of alternative mechanisms at neighbours, so that damaged cells are quickly replaced the system-component level allows regulatory feedback by other cells. However, having multiple identical to remain intact despite mutations. Second, switching components as alternatives is rare. An alternative, or between alternative mechanisms has to be orchestrated fail-safe, mechanism is usually attained by having by specific controls so that the system behaviour is multiple heterogeneous components and modules properly maintained. with overlapping functions. For example, Clb5 and Clb6 of budding yeast are two relatively homologous Modularity. Modularity is an effective mechanism for genes encoding B-type cyclins. They share 49.7% containing perturbations and damage locally to mini- identical residues and both gene products are involved mize the effects on the whole system. Modules are in the entry into the cell cycle32.Deletion ofClb6 has widely observed in various organisms, functioning as little or no effect on the progression of the cell cycle, possible biological design principles30,45,46 and as essen- and deletion of Clb5 caused a prolonged S-phase. tial elements in engineering and industry47,48.Despite Deletion of both genes impedes timely initiation of intuitive consensus, the concept is still ambiguous and DNA replication. Recent findings strongly demon- therefore can be difficult to define46. strate that gene duplication, particularly whole- A cell is an obvious example of a module that consti- genome duplication followed by extensive gene loss tutes multi-cellular systems; it interacts with the environ- and specialization, is one of the crucial mechanisms of ment and other cells. Modules are often hierarchically evolutionary innovation33,34,providing support for the organized; a cell itself is composed of organelles, and, at long-standing hypothesis proposed by Susumu Ohno35. the same time, it is also a part of larger modules such as If the function of duplicated gene pairs overlaps to tissues and organs. some extent, the duplication acts as an evolutionary Aside from physical modules such as a cell, there are capacitor36,37.There is at least one indication from com- functional, spatial and temporal modules that can be putational studies that under certain conditions these recognized as subsystems of metabolic networks, signal pairs could be evolutionary stable38. transduction and developmental regulatory networks. A There are also numerous examples of alternative bacterial flagellum and its control module, for example, mechanisms at the network level. Text-book examples represents both a physical and logical module that is include glycolysis and oxidative phosphorylation39. robust and versatile49.Logical modules, as seen in seg- Although both processes produce ATP, oxidative mental polarity networks10,11 and elsewhere50,are often phosphorylation requires a constant supply of oxy- less obvious than physically partitioned and engineering gen, whereas glycolysis can be either aerobic or anaer- modules. INTEGRAL FEEDBACK obic (although the latter is less efficient). DIAUXIC SHIFT A method of feedback control in in yeast causes a drastic change in metabolic path- Decoupling. Decoupling isolates low-level variation from which control is proportional to the integral of the systems’ ways, depending on whether glucose or ethanol is high-level functionalities. For example, Hsp90 not only output. available for energy metabolism40.The flux balance of fixes proteins that are mis-folded as a result of environ- metabolic pathways is readjusted according to the mental stresses, but also decouples genetic variations DIAUXIC SHIFT available resources in the environment, but either from the phenotype using the same mechanism, there- The process of switching from 51–53 anaerobic to aerobic respiration. pathway can, ultimately, produce essential materials fore providing a genetic buffer against mutations . for survival and growth41,42.These are examples of These genetic buffers decouple the genotype from the CANALIZATION phenotypic plasticity that are often considered to be phenotype, and they provide robustness to cope with The buffering or stabilization of the opposite of robustness. However, I argue that it is mutation while maintaining a degree of genetic diversity. developmental pathways against more consistent to view phenotypic plasticity as a part These buffers have been shown to underpin the robust- mutational or environmental perturbations, by several genetic of robustness, because this plasticity enables organisms ness of developmental processes (as in the case of factors. to robustly adapt to a changing environment. Waddington’s CANALIZATION54). Importantly, the mutations

often decouple genetic and environmental perturba- tions57.There is even a hypothesis, albeit computational, that claims that this buffering is an intrinsic property of complex networks58–60. Another example of decoupling might take place between information encoding and conversion of stim- Perturbations ulus dosage into pulses of protein activations. When the DNA is damaged, p53–MDM2-feedback loops generate oscillatory behaviour; this behaviour was recently found to be a potential converter of graded stimuli (degree of Flight control surfaces and DNA damage) to digital pulses (with a peak of p53 acti- Instructions AFCS propulsion Flight path vation), so that it is only the number of pulses that mat- system ter after the conversion61,62, not the subtle changes in concentration levels. Feedback The mechanisms that underlie robustness can be understood using an example of a sophisticated engineering object, such as an aeroplane (FIG. 2).There are similar mechanisms in various other sophisticated engineering systems: they can be built on less than perfect Flight Flight Flight components, but have to cope with unpredictable envi- control control control ronmental pressures, thereby indicating the universal computer computer computer number 1 number 2 number 3 nature of robustness. It is interesting to consider whether there is a fundamental system architecture for successful robust systems, and what limitations and risks are associated with these systems. Figure 2 | Explaining robustness — the aeroplane example. The concept of robustness is best described using the example of modern aeroplanes. Many commercial passenger The origin of robustness aeroplanes have an automatic flight control system (AFCS) that maintains a flight path (direction, altitude and velocity of flight) against perturbations in atmospheric conditions. This It is now increasingly recognized that robustness is can be accomplished by a feedback control in which deviations from the defined flight path ubiquitous. So, what are the principles and mecha- are automatically corrected. AFCS is the crucial component that allows the robust nisms that lead to the emergence of robustness in bio- maintenance of the flight path by controlling the aeroplane’s flight-control surfaces (rudder, logical systems? My theory is that robustness is an elevator, flaps, aileron, etc) and the propulsion system (engines). AFCS is generally inherent property of evolving, complex dynamic sys- composed of three modules with the same functions, thereby creating redundancy, although each is designed differently (heterogeneity) to avoid a common mode failure. Three tems — various mechanisms incurring robustness of computers are made that are modular, so that failure in one module does not affect the organisms actually facilitate evolution, and evolution functions of other parts of the system. This type of mechanism is implemented using digital favours robust traits. Therefore, requirements for technologies that decouple low-level voltages from digital signal (ON/OFF of pulses), thereby robustness and evolvability are similar. This implies preventing noise from influencing its functions. Although this is a simplified explanation of the that there are architectural requirements for complex actual system, the concept applies to details of the basic system as much as it does to the systems to be evolvable, which essentially requires the more complex systems. Although there are differences between man-made systems and system to be robust against environmental and genetic biological systems , the similarities are overwhelming. Fundamentally, robustness is the basic organizational principle of evolving dynamic systems, be it through evolution, competition, a perturbations. market niche or society. Evolvability requires flexibility in generating diverse phenotypes by means of producing non-lethal muta- tions45,63,64.Kirschner and Gerhart define evolvability, that are masked by genetic buffering are selectively neu- or evolutionary adaptability, as a capacity to generate tral (one of the premises of Kimura’s NEUTRAL THEORY OF heritable and selectable phenotypic variations that EVOLUTION55,56 … NEUTRAL THEORY OF ), providing a source of material for the evo- consists of features that “ reduce the potential lethal- EVOLUTION lution of the system during extreme perturbations. ity of mutations and the number of mutations needed A theory proposed by Motoo Feedback controls sometimes compensate for to produce phenotypically novel traits”63.They argue Kimura which states that most changes in rate constants of interactions within the net- that flexible versatile proteins, WEAK LINKAGE, EXPLORATORY variations at the molecular level work and changes in the initial state of the network, as is SYSTEMS and compartmentalization are central features are neutral to selection. the case for bacterial chemotaxis7–9 and D. melanogaster that foster evolvability63.They also argue that the 10 WEAK LINKAGE segmentation ,or they might even mitigate the impact emerging architecture is composed of highly con- A property of a process that of loss-of-function mutation. A computational study of served core processes that are co-selected with various refers to the coupling of the cell cycle demonstrated that removing some genes other processes, some of which bring about phenotyp- processes; in this case, a process depends minimally on other does not necessarily block the cell cycle, it might only ically novel traits, which is consistent with the BOW-TIE 17 components or processes; make it more fragile against perturbations . architecture. example include neural relays or Bistability created through positive feedback some- These features can be translated into architectural signal transduction pathways, in times results in the decoupling of fluctuations at a mole- requirements of the system that are consistent with which individual components cular level; for example, the decoupling of a number of robustness. First, mechanisms that preserve the com- often have a switch-like capacity to exist in active or inactive molecules that are involved in reactions from the components and interactions against mutation must be states. mitted state of the system. Therefore, dynamic networks capable of generating genetic variation. Second, there

must be modules that robustly maintain their func- robustness against perturbations of various internal tions against external perturbations and mutations. parameters. The genetic buffering mechanism — also Third, there must be highly conserved core processes, referred to as the evolutionary capacitor — attained which are also modular, that have fundamental func- either by chaperons or networks, is one of the fundamen- tions, such as metabolism, the cell cycle and transcrip- tal mechanisms that provides robustness and evolvability. tional machinery, where various modules can be It has been increasingly noted that robustness against interfaced to create diverse phenotypes. The overall mutation might evolve as a side effect of robustness architecture that meets these requirements is probably against environmental perturbations and EMERGENT a modularized nested bow-tie, or hour-glass, structure PROPERTIES of complex networks67. where various input and output modules are connected to a conserved core (FIG. 3); incidentally, the Robust modules same architecture underlies the World Wide Web65. In principle, a modular system allows the generation of This bow-tie structure occurs in various aspects of bio- diverse phenotypes by the rearrangement of its inter- logical systems, from global structure to specific mech- module connections and relatively independent evolu- anisms such as transcription and translation tion of each module through mutations. If the system processes66.The architectural features of a modular- is well integrated without modular structure, change ized bow-tie structure are optimal for enhancing the in any part of the system might have a significant robustness of the various aspects of a system. impact on other parts of the system, and slight changes in stimuli or noise might result in an unexpected and Buffering undesirable outcome. The system will be intractable, The first step towards robustness is to protect compo- and it is difficult for these systems to generate new nents and interactions from perturbations. As well as phenotypes without lethal effects. Notably, modular- correcting misfolded proteins, chaperones also impose a ization mitigates this problem by allowing each mod- particular conformation on some proteins that are genet- ule to function autonomously. However, simply having ically varied; masked genetic variation is exposed when modules is not enough to ensure evolvability. It must these mechanisms are impeded53.Networks also con- also be robust against various perturbations. This fea- tribute to this type of buffering57.This is particularly the ture is essential because modules need to be able to case when a network is robust against external perturba- cope with changes in stimuli from adjacent modules tions, because regulatory feedbacks can also provide that might evolve independently or that function in a

System control Input process Output process (signalling and (responses and nutrients) products)

Input process Output process (signalling and (responses and nutrients) products)

Highly conserved core processes Input process Output process

(signalling and (responses and Diverse reactions nutrients) products) Diverse stimuli and conditions environmental

EXPLORATORY SYSTEMS Systems that are based on Input process Conserved versatile Output process epigenetic variations and (signalling and interfaces (weak linkage) (responses and selection; such as angiogenesis nutrients) products) and nerve outgrowth. Figure 3 | The architectural framework of robust evolvable systems. The bow-tie (or hour-glass) structure has many inputs BOW-TIE and outputs that are connected through a conserved core and versatile weak linkage with the extensive system control governing A structure that has various the system’s dynamics. Core processes and versatile interfaces overlap or merge in some cases. This bow-tie structure appears inputs (fan-in) and outputs at various levels in the system, such as metabolism, signal transduction, transcription and translation66. In signal transduction, (fan-out) that are connected by a diverse stimuli are initially received by receptors, different isoforms of G-proteins are activated, but converge mainly to second knot, resembling a bow-tie. messengers that have a limited variety and cause weak linkage. Then, modulations in second messengers influence core processes to trigger expression of different genes and, ultimately, different reactions. However, this process is not a simple flow of EMERGENT PROPERTY information, as extensive local and global feedback regulations are imposed at every step. During metabolism, diverse nutrients A feature that is characteristic of system-level dynamics that are processed into precursors that core metabolic pathways then covert into basic cellular ‘currencies’ such as ATP and NADH, as cannot be attributed to any of its well as activating biosynthesic pathways to produce amino acids, nucleotides, sugar, and so on. Transcription and translation also components. The existence of an represent structures where common machineries are used to decode a wide range of genetic information and produce diverse emergent property indicates that proteins, but versatile mechanisms themselves make up the conserved core. Various processes are interfaced with core the whole is more than just the processes through versatile interfaces, so that novel processes can be added and removed easily without seriously affecting other sum of the parts. parts of the system.

different context. This robustness is attained through Second, if a modularized phenotype has selective system control and alternative mechanisms that are advantage owing to robustness against environmental inherent to each module. perturbations, modular developmental processes The contribution of system control to module could be co-selected because they are better at generat- robustness is particularly important in development, ing modular phenotypes. This hypothesis assumes that whereby new morphologies can be explored during the modular phenotype has a selective advantage and the evolution. A similar type of robustness to that of the modular developmental processes are better at generat- segment-polarity network in D. melanogaster was also ing the modular phenotype; both assumptions have still identified through the establishment of the BMP (bone to be tested. If these two reasons hold, modularity might morphogenetic protein) morphogen gradient68.The have originated to ensure robustness against environ- organizing centre is a good example of a robust buffer mental perturbations, but congruent with flexibility of against variation in development69,70.There is a subset of development. developmental processes that is tolerant against variations in initial values and that robustly forms patterns The architectural framework that serve as a basis for further elaborations in develop- There are two architectural features that facilitate evolv- mental patterning and that are amenable to reuse in a ability and robustness63,64:highly conserved core different context71,72. Hox genes exemplify the power of processes that are interfaced with diverse inputs (sig- modularity where changes in the Hox cluster alone nalling and nutrients) and outputs (reactions and affects basic body plan — a network of genes down- products); and versatile mechanisms that underlie stream of the Hox gene direct development of a given essential processes of the system, so that any new part of the body autonomously from other parts of the processes that properly interface with these mecha- body73–78. nisms can use them — this is also known as ‘weak link- Signal-transduction pathways have an important age’63.These features represent the bow-tie architecture role in generating phenotypic diversity during evolu- at different levels, ranging from global topology to spe- tion. Hedgehog (Hh), wingless-related (Wnt), TGF-β, cific processes. Below, I argue that the bow-tie structure receptor tyrosine kinase (RTK), Notch, JAK-STAT that is actually observed in biological systems facilitates (signal tranducers and activators of transcription) robustness and evolvability. and nuclear hormone pathways are signal-transduction pathways that are widely used in various aspects Bow-tie structure in biological systems. Genome-wide of development. Co-option of existing signal-trans- analysis has revealed intriguing characteristics of the duction pathways to new processes is considered one biological networks that support bow-tie structure. of the crucial features in evolution. For example, the It has been proposed that metabolic networks and Hh-signalling pathway that is used in wing-pattern protein-interaction networks form a scale-free network formation is co-opted in butterfly-eyespot pattern for- (a property of scale-free networks that predicts that pro- mation71.Several signal-transduction cascades com- teins prefer to form links with other proteins that bine negative and positive feedback loops and are already have the highest number of links)82,83. Scale-free robust against perturbations so that normal cellular networks tolerate random removal of nodes, but not physiology and developmental processes can be main- systematic removal of nodes with high connectivity84. tained25,26,28,79,80.This intrinsic robustness of the path- Ma and Zeng85 considered the directionality of reactions way enables co-option, so that new morphologies can in the analysis of metabolic networks of 65 fully be generated. sequenced genomes. They found that the these networks do not exhibit scale-free structure, but rather a The origin of modularity. The origin of modularity is ‘bow-tie’ structure, in which a large, highly connected still controversial. It is certainly an evolved property, not core cluster is interfaced with less connected in- and necessarily a selectable trait by itself, and it enhances out-clusters. The core of the network is a GIANT STRONG flexible generation of various phenotypes during devel- COMPONENT (GSC) SUB-NETWORK, the components of which opment81.At the same time, modular structures and are tightly connected85.Further comparisons of the modular regulatory networks within a single cell metabolic networks between Streptococcus pneumoniae (including bacteria) that demonstrate enormous diver- and Pyrococcus furiosus showed conservation of essential sity and evolution indicate that flexibility of develop- metabolic pathways, such as the TCA (tricarboxylic ment is not the only reason for modularity. There are acid) cycle, pentosephosphate pathway and glycolysis two possible reasons for why modularity might have pathway, within a GSC sub-network; the conserved core emerged. pathway is robust against perturbations85. First, emergence of modularity of gene regulation Another indication that there is such a division might be required to handle diverse and complex stim- into conserved core processes and those that provide uli and responses49.It is essential that signalling net- novel functions comes from comparative studies that GIANT STRONG COMPONENT works and reaction-related networks are modularized to use functional annotation of 150 fully sequenced SUB-NETWORK some extent, to cope with various external perturba- genomes86,87.The Gene Ontology’s biological process A sub-network in which there tions without losing specificity to stimuli versus hierarchy88 was used to assign functional categories to are a large number of components that have extensive responses, and to prevent the effects of environmental each gene, and the proportion of genes in each func- internal connections. perturbations from spreading system-wide. tional category, for all 150 species, was counted. The

results were presented in terms of a scaling exponent — architecture and have to be maintained robustly. For 1.0 is when the total number of genes in a category is example, cAMP is produced from adenylyl cyclases by doubled, and less than 1.0 is when the number of genes ATP. Various adenylyl cyclase isoforms are involved in in a category that have been increased is less than the multiple pathways, possibly creating alternative pathways. increase in the total number of genes. A cross-species ATP is supplied by a robust metabolic core mechanism study carried out by van Nimwegen on 65 bacterial that is also a bow-tie structure. Here, the bow-tie struc- genomes indicates that basic biological processes have ture at the metabolic level supports the bow-tie structure a scaling exponent of less than 1.0 (these include the at the level of signal transduction. cell cycle, DNA repair and replication, and protein In addition to the robustness of the conserved core, biosynthesis), but processes that might generate evo- the bow-tie architecture might provide an advantage in lutionary novelty tend to have a scaling exponent over generating coordinated response to various stimuli. So, 1.0 (these processes include transcriptional regula- a bow-tie architecture improves robustness against tion, signal transduction, ion transport, two-compo- external perturbation by having many inputs connect- nent systems and cell communication)86.This tendency ing to the robust core where numerous reactions are can also be seen in an extended study of 15 archaeal, mediated. Direct association between stimuli and reac- 116 bacterial and 10 eukaryotic genomes by van tions, without the use of the robust core, requires Nimwegen87.These results show that there are highly extensive individual controls to achieve a coordinated conserved core processes, such as biosynthesis and DNA response, and disruption of any such regulation could replication, and processes that have been added with seriously undermine system behaviour. Unless each increase in genome size, which might be responsible for stimulus reaction can be regarded as independent, the generation of various cell-types and morphological making coordination unnecessary, control through the features, such as signal transduction, transcriptional common robust core might provide better system regulation and intercellular communications. This robustness. implies that new pathways might be constantly added to However, do these mechanisms allow for the accom- the wings of the bow-tie structure as the genome size modation of phenotypic diversity? In fact, versatile increases. mechanisms are essential to accommodate various pos- ‘Weak linkage’64 enables the addition of new pro- sible input stimuli and reactions in a consistent manner. cesses to the existing core process using common ver- For example, the addition of new signal transductions satile mechanisms that operate on diverse inputs and only needs to be interfaced with existing machinery outputs, such as ion channels, G-proteins and transcrip- without inventing an entire cascade. Also, recent find- tion machinery. If transcription machinery is different ings of differential tissue and cell-type specific expres- for each gene, addition of new genes and new transcrip- sion of GPCRs in the human and mouse93 provide tional regulations requires the invention of customized explanations on how various cells might use the con- transcription machinery that makes evolution almost served-core and weak-linage mechanisms. Expression- impossible. GTP-binding proteins and the downstream pattern analyses using real time PCR on 100 randomly cyclic AMP and calcium dynamics, as well as ion chan- selected endoGPCRs (GPCRs for ligands of endogenous nels also represent systems with common underlying origins) revealed that each endoGPCR is expressed in mechanisms that allow new repertoires to be added64,89. numbers of different tissues, with each tissue having a Inputs from various receptor channels, such as RTK and unique combination of endoGPCRs93.This indicates GPCR (G-protein-coupled receptor), converge mainly on the possibility that a relatively small set of second mes- second messengers, such as cAMP and calcium ions, sengers are used in different contexts to allow differenti- which mediates various cellular responses, such as cell ation into various cell types and a range of cellular movement, cell growth, metabolism and so on89.Cdc42, a responses. The same argument applies to a limited set of member of the Rho-family of GTPases, is another com- versatile genetic networks, also referred to as a toolkit72, mon regulator on which various RTK and GPCR path- because they can be used in different contexts. ways converge and mediate different cellular responses90. Most signal-transduction cascades converge to modulate Robustness trade-offs limited numbers of second messengers, but signalling I have argued that robustness is a fundamental fea- pathways are often diverse and include cross-talk91,92. ture that enables complex systems to evolve, and that evolution enhances robustness of organisms. One Bow-tie is robust. Whether bow-tie structure provides possibility following on from this, is to increase the robustness against external perturbations depends on complexity of organisms through successive addition the robustness of the conserved core and the global reg- of regulatory systems, such as diverse regulation, sig- ulations imposed. Ma and Zeng argue that the GSC, a nal-transduction pathways, RNA regulation94–96 and conserved core of the metabolic network, is robust histone modifications97,to enhance robustness against against mutations because there are multiple routes specific environmental perturbations and to allow between any pair of nodes within the GSC85. exploration into unoccupied niches98.However,the Various stimuli activate signal-transduction path- introduction of various control feedback loops gener- ways that converge to modulate second messengers, ates trade-offs by causing instability when unexpected which in turn activate various cellular responses. Here, perturbations are encountered, leading to catastrophic second messengers are the conserved core of the bow-tie failure. Carlson and Doyle tried to generalize these

issues in their HIGHLYOPTIMIZED TOLERANCE (HOT) THEORY by Modularity also causes trade-off between robustness, arguing that systems that have evolved to be robust flexibility and resource demands. Merging modules to against general perturbations are extremely fragile share common circuits and components reduces against certain types of rare perturbations99,100.In resource needs. However, preventing the spread of per- dynamic systems, these evolutionary optimizations are turbation and flexibility of rearrangement in a robust achieved by successively adding feedback controls to way is seriously compromised. the system. It is important to recognize that although Although there are several trade-offs in robust com- the HOT theory describes behaviour of complex sys- plex systems, trade-offs involving system controls are tems designed or evolved towards optimality against the most important ones. System controls define perturbations, other self-organization models such as a dynamic properties of the biological systems that illus- scale-free network83,101 by preferential attachment and trate how complex biological systems behave when per- SELF-ORGANIZED CRITICALITY102 describe systems with sto- turbed and coordinate how alternative components and chastic additions of complexity without design or evo- modules are re-routed to ensure robustness of the lution involved. The nature of robustness and fragility whole system. Owing to the intrinsic trade-offs that that is predicted by the HOT model is generally consis- have been discussed, it is not possible to simply increase tent with observed properties of designed complex sys- general robustness of the system without a sacrifice in tems and is notably different from other models99,100. performance and increased resource demands. Csete and Doyle further argued that trade-offs between robustness and fragility indicate that robust- A system-level view of disease and therapy ness is a conserved quantity, a concept that also applies Properties of robust evolvable systems have direct con- to biological systems103. sequences on our understanding of diseases and ther- Trade-offs between robustness and fragility can be apy design. First, robust systems, whether biological or intuitively understood by using the aeroplane example engineered, are most vulnerable when the system’s again. The Wright brothers’ aeroplane is not robust fragility is exposed. For example, Diabetes mellitus can against atmospheric perturbations, unlike modern be thought of as an exposed fragility of the system that commercial aeroplanes. However, modern aeroplanes has acquired robustness against near-starvation, a high are extremely fragile against unusual perturbations, energy-demand lifestyle and high risk of infection, but such as total power failure — because their flight-control it is unusually perturbed by over-nutrition and a low system is totally dependent on electricity. The Wright energy-demand lifestyle16.Second, the system is rela- brothers’ aeroplane, on the other hand, is not affected by tively tolerant of the removal of some components or this type of failure as it does not use electrical controls in cells, because of available alternative mechanisms and the first place. Although they might seem simple, it is the robustness of the bow-tie architecture. However, important to appreciate these trade-offs because diseases the system is vulnerable when components behave are often manifestations of fragility. inappropriately but are not being removed. Third, the Fragility is not the only cost of improved robustness. epidemic state might exhibit robustness against nat- In electronic-circuit design, the use of negative-feedback ural and therapeutic countermeasures if intrinsic control achieves an improved fidelity or amplification mechanisms for robustness in our bodies are co-opted. for a certain range of inputs by reducing overall gain of The worst-case scenario is when components of the the amplifier. So, the use of negative-feedback control system behave inappropriately without being removed, achieves robustness within a certain range of inputs at and malfunctioning components and their behaviour the cost of some aspects of performance and with the are robustly maintained against countermeasures: the creation of fragility elsewhere. The trade-offs between mechanisms that support robustness of the host are robustness, fragility and performance can be observed also used to protect the failed components. This is in biological systems at different levels. Bacteria, for important because the intrinsic dynamics of diseases example, should be able to swim faster without negative and appropriate countermeasures are different depend- feedback, but this would sacrifice their precision in fol- ing on which scenario the system failure follows. For

HIGHLY OPTIMIZED TOLERANCE lowing a chemical gradient: the use of negative feed- example, cholera toxin interacts with the Gsα subunit to THEORY back improves the bacteria’s ability to follow a chemical trigger the symptoms of the disease105,106.It can be easily A theory about the dynamic gradient, at the cost of reduced swim speed. removed by antibiotics, because the intrinsic robustness properties of systems that are Alternative mechanisms and modularity also of the host has not been hijacked by the pathogen and is designed, or evolved, to be optimal (either towards a global enhance robustness, but at the cost of increased resource not involved in the infection. optimum or sub-optimum). The demands. For example, the probability that a function By contrast, cancer and HIV infection represent a theory predicts whether systems with a single component will fail is p.The probability of worse scenario — they are maintained and even pro- that are robust against certain the function with two components that fail to back up moted through the intrinsic robustness mechanisms of perturbations are fragile against 2 unexpected perturbations. each other will be reduced to (1 – p) .This reduction is host system. Counter measures for these diseases could accompanied by doubling of the resource requirement. include: actively perturbing specific interactions or SELF-ORGANIZED CRITICALITY This type of trade-off is effectively mitigated in biologi- components to maintain or reduce robustness, finding a A phenomenon whereby certain cal systems because components are not identical point of fragility (an ‘Achilles’ heel’) that is inherent in systems reach a crucial state copies, but tend to have overlapping functions. Having robust systems and re-establishing control of the epi- through their intrinsic dynamics, independently of the identical copies as alternatives is only efficient when fail- demic state by introducing a counter-acting decoy (a value of any control parameters. ure rate or turn-over rate, is expected to be high. ‘Trojan horse’) or a new regulatory feedback.

Cancer is a highly robust disease in which the must be associated with a mechanism that gives rise to tumour proliferates and metastasizes, in some cases enhanced robustness. For example, the robustness of a despite much therapeutic effort. Although anti-cancer tumour is sustained by chromosome instability, intra- drugs might temporarily reduce tumour mass, it cellular feedback loops and host-tumour interactions. relapses in many cases and cure is still rare. The diffi- Possible countermeasures include control of the cell culty of treating tumours is attributed to acquired cycle through the combined use of several drugs, possi- robustness, partly owing to the co-option of intrinsic bly using RNAi, selectively destabilizing or stabilizing mechanisms for robustness14,15.The high level of genetic unstable chromosomes, selectively delivering engi- heterogeneity in the tumour forms a fail-safe through neered genes108 to re-establish control of host-tumour genetic diversity and multiple feedback loops in both the interactions or introducing artificial genetic circuits109 to cellular and the tumour-host environment and accounts conditionally express tumour-suppressor genes, should for the robustness of cancer. The genetic heterogeneity be considered. Importantly, these countermeasures have within a tumour cluster, caused by chromosome instabil- to be carefully designed to specifically explore fragility ity, generates a high level of genetic heterogeneity in sur- or to control robustness. vival and proliferation. This genetic heterogeneity allows HIV predominantly infects CD4-positive T cells and some malignant cells to tolerate therapy and re-form a replicates when the cell activates its anti-virus res- tumour. ponses110–113.Infected cells are not removed because Mechanisms that maintain normal functions of infection is hardly detectable. This is a typical case of the body also function to enhance tumour robustness what happens when malfunctioning components (the against therapy. For example, drug resistance is infected cell, in this case) are not removed from the sys- caused by upregulation of MDR1 and other genes, tem. In addition, HIV creates diverse genetic alternation. the products of which pump out toxic chemicals HIV’s strategy is to hijack the robust immune-response from the cell; so a function that protects us under mechanism, which makes AIDS difficult to cure. Robust normal conditions, is exploited by the tumour to pro- persistence of the epidemic state through generation of tect the malignant cells. Low oxygen supply (hypoxia) genetic diversity and various feedback loops is similar to during the tumour-cluster development is countered the strategy found in cancer. Possible therapeutic by metabolic shift from oxygen-dependent TCA cycle approaches already discussed might apply to the effec- to glycolysis, as well as activating a feedback loop by tive treatment of AIDS. Interestingly, one strategy pro- upregulating HIF1,which upregulates VEGF (vascu- posed to combat HIV involves forcing HIV into a latent lar endothelial growth factor)to promote angiogene- state, instead of trying to remove it, by introducing a sis, and MMP (matrix metalloproteases), uPAR decoy — a conditionally replicating HIV-1 vector (urokinase-type plasminogen activator) and CRCX4 (crHIV-1)114–116. crHIV-1 contains cis,but not trans,ele- (a chemokine receptor) to promote tumour-cell ments that are necessary for virus packaging, and carries metastasis107;a series of responses that protects the antiviral genes that inhibit wild-type HIV-1 functions116. body against the effects of hypoxia. If successful, crHIV-1 might re-establish control of the From the robustness perspective, possible clinical system and put HIV-1 virus in a state of prolonged strategies that could be used against cancer are the con- latency. trol of the robustness of the tumour and finding out the point of fragility that is inherent in the robust system. To Towards a theory of biological robustness control robustness, therapy should be directed to induce Given the importance of robustness for the understand- tumour dormancy by selectively inducing cell-cycle ing of the principles of life and its medical implications, arrest, rather than aiming at tumour eradication, it is an intriguing challenge to formulate a mathemati- because one source of robustness is genetic heterogene- cally solid, and possibly unified theory of biological ity created through somatic recombination. Apart from robustness that might serve as a basic organizational specific cases where tumour cells are relatively homoge- principle of biological systems (early attempts date back neous, tumour-mass reduction might not be an appro- to the middle of the last century117,118). Such a unified priate therapeutic goal, because of the high risk of theory could be a bridge between the fundamental prin- relapse if the reduced tumour gained a greater level of ciples of life, medical practice, engineering, physics and heterogeneity, including those cells that are highly resis- chemistry. This is a difficult challenge in which a num- CONTROL THEORY tant to therapeutic efforts. Controlling tumour robust- ber of issues have to be solved, particularly to establish The theory about the design of optimal control methods for ness would be a genuine measure of therapeutic efficacy, mathematically well-founded theories. However, the engineered objects. It is one of so that the risk of relapse could be well controlled. The impact would be enormous. the most successful fields in other approach is to find the fragility of tumours. First, the solid quantitative index of robustness has to which mathematical principles Tumours acquire robustness against a range of thera- be established. This index has to be able to equate with are directly applied to practical products, such as aeroplanes, pies, which must be accompanied by the development experimentally measurable quantities, so that hypotheses hard disks, automobiles, robotics of extreme fragility. on the degree of robustness can be tested experimentally. and chemical plants, and enables The question remains how to find fragility that is There are several concepts on the stability of the system them to function properly. 119 therapeutically effective and practical. It is important to in CONTROL THEORY , and some attempt has been made to Usually, the theory is concerned investigate what the system has been optimized for and apply these ideas to biological robustness120.The practi- with how feedback control can be used in various cases to attain to identify sources of robustness. As fragility is a by- cal application of these concepts to biological systems optimal design behaviour. product of robustness, the fragile point of the system has been limited, mainly owing to the enormous degree

of dimensionality and non-linearity that is intrinsic to unstructured medium, as seen in BZ reactions. Cells biological systems. Measuring perturbations for all are highly structured and have explicit interactions these dimensions is impractical. A practical, theoreti- and physical structures that are controlled by gene cally solid index needs to be developed to provide expression, cytoskeleton and other regulatory systems guidelines for selecting smaller numbers of parame- that are optimized to be robust and evolvable. The ters to be perturbed so that the system’s response can greatest challenge will be to formulate theories that be measured. Haken pointed out that only a few para- account for thermodynamics in heterogeneous and meters are important to describe system behaviour structured systems. Some efforts are being made to near the bifurcation point121,but this approach is too find a theoretical framework by assuming network limited to analyse various types of behaviour of bio- structure as a basis of mathematical description131. logical systems. A number of mathematical methods However, the results are still too abstract to be practi- are being developed that might be of benefit for the cally applied to biological systems. Progress in this field mathematical analysis of the robustness of biological will help to connect biology, chemistry, physics and systems122,123. On the experimental front, comprehen- mathematics in a coherent manner. sive mutant creation and dosage-controlled perturbations are already feasible for some organisms. As there Conclusion are often practical aims to investigate robustness of Robustness is a fundamental property of biological the system — for example, to induce cell-cycle arrest systems. It facilitates evolvability, and evolution selects — experiments can be carefully designed to perturb robust traits. I have argued that there are specific archi- relevant genes and parameters, and published data tectural features required to make organisms robust can be systematically collected to obtain practical, suf- and that they might be universal to any robust and ficient indeces of robustness for specific aspects of the evolvable complex system. System controls, modular- system124. ity, alternative mechanisms and decoupling serve as Second, a theory that embraces the various aspects of basic mechanisms to provide robustness to the system, robustness has not yet been formulated. Control theory but these mechanisms need to be organized into is often used to explain robustness that involves feed- coherent architecture to be effective at the level of the back regulation, but this only covers one aspect of organism. Enhancement of robustness against pertur- robustness. Furthermore, the control theory assumes bations can be made through the combination of these that there is a certain set point, determined by the mechanisms, but system control is the prime mecha- SHANNON’S CHANNEL-CODING designer, that the system’s state will approach, even nism for coping with environmental perturbations THEOREM when perturbed. Of course, there is no such designer in that require proper dynamics. Therefore, evolution of A theorem by Claude Shannon biological systems, and set point is implicit in the equi- organisms can be viewed, at least in one aspect, as evo- which indicates that for a given channel there exists a code that librium state of the system, which often changes dynam- lution of control systems. Modularity, alternative will permit the error-free ically. A new theory is required to reflect these features mechanisms and decoupling, in part, support the transmission across the channel of biological systems. robust maintenance of control loops, but are also con- ≤ at a rate R, provided R C, where Recent efforts to integrate control theory and trolled by control loops either explicitly or implicitly. C is the channel capacity. This means that the probability of SHANNON’S CHANNEL-CODING THEOREM might provide an There is an intriguing possibility that genetic buffering 125,126 error will not equal zero when interesting framework for feedbacks .This theo- and modularity originated from robustness against R>C, that is, transmission is rem tries to formalize cases where information capacity environmental perturbations, and subsequently larger than channel capacity. in the feedback loop is limited, so that the feedback sig- evolved to have wider applicability. It is important to nal is potentially impeded by fidelity, noise and delay. realize that systems that are evolved to be robust LE CHATELIER–BRAUN’S PRINCIPLE This better reflects the reality of biological systems, in against certain perturbations are extremely fragile to A thermodynamics principle which signals are transmitted with noise, delay and unexpected perturbations. This robust yet fragile which states that if a dynamic compromised fidelity. trade-off is fundamental to complex dynamic systems. equilibrium is disturbed by Third, attempts to relate the dynamics of life to ther- It is important to understand architectural features of changing the conditions, then the system tends to adjust to a modynamics have been of limited success. The behav- robust and evolvable systems and the intrinsic nature new equilibrium counteracting iour of physical and chemical systems near equilibrium of robustness and fragility because they dictate a mode the change. have been investigated in the past. LE CHATELIER–BRAUN’S of system failures and effective countermeasures, PRINCIPLE provides the basis for response against pertur- which, as previously discussed, has direct implications BELOUSOV-ZHABOTINSKI bations for systems in equilibrium127.This principle for understanding disease and devising effective thera- REACTIONS This is a chemical reaction that is indicates the emergence of a compensatory feedback pies. Failures and viable countermeasures of these sys- widely used to demonstrate to cope with perturbations. Efforts have been made to tems are often counter-intuitive, which implies that a transition from the near- extend thermodynamics from equilibrium to explain theoretically motivated robustness perspective might equilibrium state to the far- biological phenomena128–130,but apply only to relatively provide new therapeutic approaches. The emerging from-equilibrium state. When a low level of heat is applied, it is simple chemical reactions under a medium, such as in field of systems biology has been trying to identify sys- dissipated without affecting the BELOUSOV-ZHABOTINSKI (BZ) REACTIONS.Signal transduction, tem-level properties, but simple use of large data sets qualitative characteristics of the for example, brings about dramatic changes in the state and computation would not effectively provide insights medium, but when additional of the cell depending on the intensity and types of stim- into biological systems. The perspective on biological heat is applied, the system uli, resembling transition from the near-equilibrium robustness would provide effective guiding principles undergoes a drastic change, and a circulating flow of chemicals state to a state that is far from equilibrium. However, this for understanding many biological phenomena, and emerges. is not the result of simple chemical reactions under an for therapy design.

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