Sloppiness, robustness, and evolvability in systems biology

The origins of cancer robustness and evolvability

Unless diagnosed early, many adult cancers remain incurable diseases. This is despite an intense global research effort to develop effective anticancer therapies, calling into question the use of rational drug design strategies in targeting complex disease states such as cancer. A fundamental challenge facing researchers and clinicians is that cancers are inherently robust biological systems, able to survive, adapt and proliferate despite the perturbations resulting from anticancer drugs. It is essential that the mechanisms underlying tumor robustness be formally studied and characterized, as without a thorough understanding of the principles of tumor robustness, strategies to overcome therapy resistance are unlikely to be found. Degeneracy describes the ability of structurally distinct system components (e.g. proteins, pathways, cells, organisms) to be conditionally interchangeable in their contribution to system traits and it has been broadly implicated in the robustness and evolvability of complex biological systems. Here we focus on one of the most important mechanisms underpinning tumor robustness and degeneracy, the cellular heterogeneity that is the hallmark of most solid tumors. Based on a combination of computational, experimental and clinical studies we argue that stochastic noise is an underlying cause of tumor heterogeneity and particularly degeneracy. Drawing from a number of recent data sets, we propose an integrative model for the evolution of therapy resistance, and discuss recent computational studies that propose new therapeutic strategies aimed at defeating the adaptable cancer phenotype.

The effect of scale-free topology on the robustness and evolvability of genetic regulatory networks

We investigate how scale-free (SF) and Erdos-Rényi (ER) topologies affect the interplay between evolvability and robustness of model gene regulatory networks with Boolean threshold dynamics. In agreement with Oikonomou and Cluzel (2006) we find that networks with SF(in) topologies, that is SF topology for incoming nodes and ER topology for outgoing nodes, are significantly more evolvable towards specific oscillatory targets than networks with ER topology for both incoming and outgoing nodes. Similar results are found for networks with SF(both) and SF(out) topologies. The functionality of the SF(out) topology, which most closely resembles the structure of biological gene networks (Babu et al., 2004), is compared to the ER topology in further detail through an extension to multiple target outputs, with either an oscillatory or a non-oscillatory nature. For multiple oscillatory targets of the same length, the differences between SF(out) and ER networks are enhanced, but for non-oscillatory targets both types of networks show fairly similar evolvability. We find that SF networks generate oscillations much more easily than ER networks do, and this may explain why SF networks are more evolvable than ER networks are for oscillatory phenotypes. In spite of their greater evolvability, we find that networks with SF(out) topologies are also more robust to mutations (mutational robustness) than ER networks. Furthermore, the SF(out) topologies are more robust to changes in initial conditions (environmental robustness). For both topologies, we find that once a population of networks has reached the target state, further neutral evolution can lead to an increase in both the mutational robustness and the environmental robustness to changes in initial conditions.

Evolvability and Speed of Evolutionary Algorithms in Light of Recent Developments in Biology

Biological and artificial evolutionary systems exhibit varying degrees of evolvability and different rates of evolution. Such quantities can be affected by various factors. Here, we review some evolutionary mechanisms and discuss new developments in biology that can potentially improve evolvability or accelerate evolution in artificial systems. Biological notions are discussed to the degree they correspond to notions in Evolutionary Computation. We hope that the findings put forward here can be used to design computational models of evolution that produce significant gains in evolvability and evolutionary speed.

Propagation of kinetic uncertainties through a canonical topology of the TLR4 signaling network in different regions of biochemical reaction space

Background

Signal transduction networks represent the information processing systems that dictate which dynamical regimes of biochemical activity can be accessible to a cell under certain circumstances. One of the major concerns in molecular systems biology is centered on the elucidation of the robustness properties and information processing capabilities of signal transduction networks. Achieving this goal requires the establishment of causal relations between the design principle of biochemical reaction systems and their emergent dynamical behaviors.

Methods

In this study, efforts were focused in the construction of a relatively well informed, deterministic, non-linear dynamic model, accounting for reaction mechanisms grounded on standard mass action and Hill saturation kinetics, of the canonical reaction topology underlying Toll-like receptor 4 (TLR4)-mediated signaling events. This signaling mechanism has been shown to be deployed in macrophages during a relatively short time window in response to lypopolysaccharyde (LPS) stimulation, which leads to a rapidly mounted innate immune response. An extensive computational exploration of the biochemical reaction space inhabited by this signal transduction network was performed via local and global perturbation strategies. Importantly, a broad spectrum of biologically plausible dynamical regimes accessible to the network in widely scattered regions of parameter space was reconstructed computationally. Additionally, experimentally reported transcriptional readouts of target pro-inflammatory genes, which are actively modulated by the network in response to LPS stimulation, were also simulated. This was done with the main goal of carrying out an unbiased statistical assessment of the intrinsic robustness properties of this canonical reaction topology.

Results

Our simulation results provide convincing numerical evidence supporting the idea that a canonical reaction mechanism of the TLR4 signaling network is capable of performing information processing in a robust manner, a functional property that is independent of the signaling task required to be executed. Nevertheless, it was found that the robust performance of the network is not solely determined by its design principle (topology), but this may be heavily dependent on the network's current position in biochemical reaction space. Ultimately, our results enabled us the identification of key rate limiting steps which most effectively control the performance of the system under diverse dynamical regimes.

Conclusions

Overall, our in silico study suggests that biologically relevant and non-intuitive aspects on the general behavior of a complex biomolecular network can be elucidated only when taking into account a wide spectrum of dynamical regimes attainable by the system. Most importantly, this strategy provides the means for a suitable assessment of the inherent variational constraints imposed by the structure of the system when systematically probing its parameter space.

Mutational robustness can facilitate adaptation

Robustness seems to be the opposite of evolvability. If phenotypes are robust against mutation, we might expect that a population will have difficulty adapting to an environmental change, as several studies have suggested. However, other studies contend that robust organisms are more adaptable. A quantitative understanding of the relationship between robustness and evolvability will help resolve these conflicting reports and will clarify outstanding problems in molecular and experimental evolution, evolutionary developmental biology and protein engineering. Here we demonstrate, using a general population genetics model, that mutational robustness can either impede or facilitate adaptation, depending on the population size, the mutation rate and the structure of the fitness landscape. In particular, neutral diversity in a robust population can accelerate adaptation as long as the number of phenotypes accessible to an individual by mutation is smaller than the total number of phenotypes in the fitness landscape. These results provide a quantitative resolution to a significant ambiguity in evolutionary theory.

Studying plant-pathogen interactions in the genomics era: beyond molecular Koch's postulates to systems biology

Molecular factors enabling microbial pathogens to cause plant diseases have been sought with increasing efficacy over three research eras that successively introduced the tools of disease physiology, single-gene molecular genetics, and genomics. From this work emerged a unified model of the interactions of biotrophic and hemibiotrophic pathogens, which posits that successful pathogens typically defeat two levels of plant defense by translocating cytoplasmic effectors that suppress the first defense (surface arrayed against microbial signatures) while evading the second defense (internally arrayed against effectors). As is predicted from this model and confirmed by sequence pattern-driven discovery of large repertoires of cytoplasmic effectors in the genomes of many pathogens, the coevolution of (hemi)biotrophic pathogens and their hosts has generated pathosystems featuring extreme complexity and apparent robustness. These findings highlight the need for a fourth research era of systems biology in which virulence factors are studied as pathosystem components, and pathosystems are studied for their emergent properties.

'Glocal' robustness analysis and model discrimination for circadian oscillators

To characterize the behavior and robustness of cellular circuits with many unknown parameters is a major challenge for systems biology. Its difficulty rises exponentially with the number of circuit components. We here propose a novel analysis method to meet this challenge. Our method identifies the region of a high-dimensional parameter space where a circuit displays an experimentally observed behavior. It does so via a Monte Carlo approach guided by principal component analysis, in order to allow efficient sampling of this space. This 'global' analysis is then supplemented by a 'local' analysis, in which circuit robustness is determined for each of the thousands of parameter sets sampled in the global analysis. We apply this method to two prominent, recent models of the cyanobacterial circadian oscillator, an autocatalytic model, and a model centered on consecutive phosphorylation at two sites of the KaiC protein, a key circadian regulator. For these models, we find that the two-sites architecture is much more robust than the autocatalytic one, both globally and locally, based on five different quantifiers of robustness, including robustness to parameter perturbations and to molecular noise. Our 'glocal' combination of global and local analyses can also identify key causes of high or low robustness. In doing so, our approach helps to unravel the architectural origin of robust circuit behavior. Complementarily, identifying fragile aspects of system behavior can aid in designing perturbation experiments that may discriminate between competing mechanisms and different parameter sets.

The ABC of reverse engineering biological signalling systems

Modelling biological systems would be straightforward if we knew the structure of the model and the parameters governing their dynamics. For the overwhelming majority of biological processes, however, such parameter values are unknown and often impossible to measure directly. This means that we have to estimate or infer these parameters from observed data. Here we argue that it is also important to appreciate the uncertainty inherent in these estimates. We discuss a statistical approach--approximate Bayesian computation (ABC)--which allows us to approximate the posterior distribution over parameters and show how this can add insights into our understanding of the system dynamics. We illustrate the application of this approach and how the resulting posterior distribution can be analyzed in the context of the mitogen-activated protein kinase phosphorylation cascade. Our analysis also highlights the added benefit of using the distribution of parameters rather than point estimates of parameter values when considering the notion of sloppy models in systems biology.

Molecular networks and system-level properties

Molecular systems biology aims to describe the functions of complex biological processes through recursive integration of molecular analysis, modeling, simulation and theory. It focuses on networks that originate from interconnection of genes, proteins and metabolites whose dynamic interactions generate, as an emergent property of the system, the corresponding function. Although evolutionary optimized, intracellular biochemical parameters, such as the expression level of gene products or the affinity between two or more proteins, must have a permissible range that gives robustness against perturbations to the system. Using the yeast G(1)-to-S transition network as an example we show that sophisticated relations exist among network structure, emergent property and robustness. Different emergent properties are generated from the same network by changing the strength of its interactions, not only by altering expression level, but also through mono and multi-site phosphorylation/dephosphorylation. Besides, multi-site protein phosphorylation modules, widespread in cell cycle, may ensure robust and coherent timing of cell cycle transitions as it happens for the onset of DNA replication. In conclusion, the modulation of biological function/emergent property by modifying interaction strength provides an efficient, highly tunable device to regulate biological processes. Furthermore, the principles outlined herein may provide new insight to network analysis in drug discovery.

Estimating parameters for generalized mass action models with connectivity information

BACKGROUND

Determining the parameters of a mathematical model from quantitative measurements is the main bottleneck of modelling biological systems. Parameter values can be estimated from steady-state data or from dynamic data. The nature of suitable data for these two types of estimation is rather different. For instance, estimations of parameter values in pathway models, such as kinetic orders, rate constants, flux control coefficients or elasticities, from steady-state data are generally based on experiments that measure how a biochemical system responds to small perturbations around the steady state. In contrast, parameter estimation from dynamic data requires time series measurements for all dependent variables. Almost no literature has so far discussed the combined use of both steady-state and transient data for estimating parameter values of biochemical systems.

RESULTS

In this study we introduce a constrained optimization method for estimating parameter values of biochemical pathway models using steady-state information and transient measurements. The constraints are derived from the flux connectivity relationships of the system at the steady state. Two case studies demonstrate the estimation results with and without flux connectivity constraints. The unconstrained optimal estimates from dynamic data may fit the experiments well, but they do not necessarily maintain the connectivity relationships. As a consequence, individual fluxes may be misrepresented, which may cause problems in later extrapolations. By contrast, the constrained estimation accounting for flux connectivity information reduces this misrepresentation and thereby yields improved model parameters.

CONCLUSION

The method combines transient metabolic profiles and steady-state information and leads to the formulation of an inverse parameter estimation task as a constrained optimization problem. Parameter estimation and model selection are simultaneously carried out on the constrained optimization problem and yield realistic model parameters that are more likely to hold up in extrapolations with the model.

Identification of neutral biochemical network models from time series data

BACKGROUND

The major difficulty in modeling biological systems from multivariate time series is the identification of parameter sets that endow a model with dynamical behaviors sufficiently similar to the experimental data. Directly related to this parameter estimation issue is the task of identifying the structure and regulation of ill-characterized systems. Both tasks are simplified if the mathematical model is canonical, i.e., if it is constructed according to strict guidelines.

RESULTS

In this report, we propose a method for the identification of admissible parameter sets of canonical S-systems from biological time series. The method is based on a Monte Carlo process that is combined with an improved version of our previous parameter optimization algorithm. The method maps the parameter space into the network space, which characterizes the connectivity among components, by creating an ensemble of decoupled S-system models that imitate the dynamical behavior of the time series with sufficient accuracy. The concept of sloppiness is revisited in the context of these S-system models with an exploration not only of different parameter sets that produce similar dynamical behaviors but also different network topologies that yield dynamical similarity.

CONCLUSION

The proposed parameter estimation methodology was applied to actual time series data from the glycolytic pathway of the bacterium Lactococcus lactis and led to ensembles of models with different network topologies. In parallel, the parameter optimization algorithm was applied to the same dynamical data upon imposing a pre-specified network topology derived from prior biological knowledge, and the results from both strategies were compared. The results suggest that the proposed method may serve as a powerful exploration tool for testing hypotheses and the design of new experiments.

Identification of neutral biochemical network models from time series data

Background

The major difficulty in modeling biological systems from multivariate time series is the identification of parameter sets that endow a model with dynamical behaviors sufficiently similar to the experimental data. Directly related to this parameter estimation issue is the task of identifying the structure and regulation of ill-characterized systems. Both tasks are simplified if the mathematical model is canonical, i.e., if it is constructed according to strict guidelines.

Results

In this report, we propose a method for the identification of admissible parameter sets of canonical S-systems from biological time series. The method is based on a Monte Carlo process that is combined with an improved version of our previous parameter optimization algorithm. The method maps the parameter space into the network space, which characterizes the connectivity among components, by creating an ensemble of decoupled S-system models that imitate the dynamical behavior of the time series with sufficient accuracy. The concept of sloppiness is revisited in the context of these S-system models with an exploration not only of different parameter sets that produce similar dynamical behaviors but also different network topologies that yield dynamical similarity.

Conclusion

The proposed parameter estimation methodology was applied to actual time series data from the glycolytic pathway of the bacterium Lactococcus lactis and led to ensembles of models with different network topologies. In parallel, the parameter optimization algorithm was applied to the same dynamical data upon imposing a pre-specified network topology derived from prior biological knowledge, and the results from both strategies were compared. The results suggest that the proposed method may serve as a powerful exploration tool for testing hypotheses and the design of new experiments.

Iron behaving badly: inappropriate iron chelation as a major contributor to the aetiology of vascular and other progressive inflammatory and degenerative diseases

BACKGROUND

The production of peroxide and superoxide is an inevitable consequence of aerobic metabolism, and while these particular 'reactive oxygen species' (ROSs) can exhibit a number of biological effects, they are not of themselves excessively reactive and thus they are not especially damaging at physiological concentrations. However, their reactions with poorly liganded iron species can lead to the catalytic production of the very reactive and dangerous hydroxyl radical, which is exceptionally damaging, and a major cause of chronic inflammation.

REVIEW

We review the considerable and wide-ranging evidence for the involvement of this combination of (su)peroxide and poorly liganded iron in a large number of physiological and indeed pathological processes and inflammatory disorders, especially those involving the progressive degradation of cellular and organismal performance. These diseases share a great many similarities and thus might be considered to have a common cause (i.e. iron-catalysed free radical and especially hydroxyl radical generation).The studies reviewed include those focused on a series of cardiovascular, metabolic and neurological diseases, where iron can be found at the sites of plaques and lesions, as well as studies showing the significance of iron to aging and longevity. The effective chelation of iron by natural or synthetic ligands is thus of major physiological (and potentially therapeutic) importance. As systems properties, we need to recognise that physiological observables have multiple molecular causes, and studying them in isolation leads to inconsistent patterns of apparent causality when it is the simultaneous combination of multiple factors that is responsible.This explains, for instance, the decidedly mixed effects of antioxidants that have been observed, since in some circumstances (especially the presence of poorly liganded iron) molecules that are nominally antioxidants can actually act as pro-oxidants. The reduction of redox stress thus requires suitable levels of both antioxidants and effective iron chelators. Some polyphenolic antioxidants may serve both roles.Understanding the exact speciation and liganding of iron in all its states is thus crucial to separating its various pro- and anti-inflammatory activities. Redox stress, innate immunity and pro- (and some anti-)inflammatory cytokines are linked in particular via signalling pathways involving NF-kappaB and p38, with the oxidative roles of iron here seemingly involved upstream of the IkappaB kinase (IKK) reaction. In a number of cases it is possible to identify mechanisms by which ROSs and poorly liganded iron act synergistically and autocatalytically, leading to 'runaway' reactions that are hard to control unless one tackles multiple sites of action simultaneously. Some molecules such as statins and erythropoietin, not traditionally associated with anti-inflammatory activity, do indeed have 'pleiotropic' anti-inflammatory effects that may be of benefit here.

CONCLUSION

Overall we argue, by synthesising a widely dispersed literature, that the role of poorly liganded iron has been rather underappreciated in the past, and that in combination with peroxide and superoxide its activity underpins the behaviour of a great many physiological processes that degrade over time. Understanding these requires an integrative, systems-level approach that may lead to novel therapeutic targets.