Confidence from uncertainty - A multi-target drug screening method from robust control theory

Background  

Robustness is a recognized feature of biological systems that evolved as a defence to environmental variability. Complex diseases such as diabetes, cancer, bacterial and viral infections, exploit the same mechanisms that allow for robust behaviour in healthy conditions to ensure their own continuance. Single drug therapies, while generally potent regulators of their specific protein/gene targets, often fail to counter the robustness of the disease in question. Multi-drug therapies offer a powerful means to restore disrupted biological networks, by targeting the subsystem of interest while preventing the diseased network from reconciling through available, redundant mechanisms. Modelling techniques are needed to manage the high number of combinatorial possibilities arising in multi-drug therapeutic design, and identify synergistic targets that are robust to system uncertainty.     

Robustness analysis of biochemical network models

Biological systems that have been experimentally verified to be robust to significant changes in their environments require mathematical models that are themselves robust. In this context, a necessary condition for model robustness is that the model dynamics should not be sensitive to small variations in the model's parameters. Robustness analysis problems of this type have been extensively studied in the field of robust control theory and have been found to be very difficult to solve in general. The authors describe how some tools from robust control theory and nonlinear optimisation can be used to analyse the robustness of a recently proposed model of the molecular network underlying adenosine 3',5'-cyclic monophosphate (cAMP) oscillations observed in fields of chemotactic Dictyostelium cells. The network model, which consists of a system of seven coupled nonlinear differential equations, accurately reproduces the spontaneous oscillations in cAMP observed during the early development of D. discoideum. The analysis by the authors reveals, however, that very small variations in the model parameters can effectively destroy the required oscillatory dynamics. A biological interpretation of the analysis results is that correct functioning of a particular positive feedback loop in the proposed model is crucial to maintaining the required oscillatory dynamics.     

Degeneracy: A design principle for achieving robustness and evolvability

Robustness, the insensitivity of some of a biological system's functionalities to a set of distinct conditions, is intimately linked to fitness. Recent studies suggest that it may also play a vital role in enabling the evolution of species. Increasing robustness, so is proposed, can lead to the emergence of evolvability if evolution proceeds over a neutral network that extends far throughout the fitness landscape. Here, we show that the design principles used to achieve robustness dramatically influence whether robustness leads to evolvability. In simulation experiments, we find that purely redundant systems have remarkably low evolvability while degenerate, i.e. partially redundant, systems tend to be orders of magnitude more evolvable. Surprisingly, the magnitude of observed variation in evolvability can neither be explained by differences in the size nor the topology of the neutral networks. This suggests that degeneracy, a ubiquitous characteristic in biological systems, may be an important enabler of natural evolution. More generally, our study provides valuable new clues about the origin of innovations in complex adaptive systems.     

Quasi-multiparameter sensitivity measure for robustness analysis of complex biochemical networks

Robustness is the ability to resume reliable operation in the face of different types of perturbations. Analysis of how network structure achieves robustness enables one to understand and design cellular systems. It is typically true that all parameters simultaneously differ from their nominal values in vivo, but there have been few intelligible measures to estimate the robustness of a system's function to the uncertainty of all parameters.We propose a numerical and fast measure of a robust property to the uncertainty of all kinetic parameters, named quasi-multiparameter sensitivity (QMPS), which is defined as the sum of the squared magnitudes of single-parameter sensitivities. Despite its plain idea, it has hardly been employed in analysis of biological models. While QMPS is theoretically derived as a linear model, QMPS can be consistent with the expected variance simulated by the widely used Monte Carlo method in nonlinear biological models, when relatively small perturbations are given. To demonstrate the feasibility of QMPS, it is employed for numerical comparison to analyze the mechanism of how specific regulations generate robustness in typical biological models.QMPS characterizes the robustness much faster than the Monte Carlo method, thereby enabling the extensive search of a large parameter space to perform the numerical comparison between alternative or competing models. It provides a theoretical or quantitative insight to an understanding of how specific network structures are related to robustness. In circadian oscillators, a negative feedback loop with multiple phosphorylations is demonstrated to play a critical role in generating robust cycles to the uncertainty of multiple parameters.     

Robustness and complexity co-constructed in multimodal signalling networks

In animal communication, signals are frequently emitted using different channels (e.g. frequencies in a vocalization) and different modalities (e.g. gestures can accompany vocalizations). We explore two explanations that have been provided for multimodality: (i) selection for high information transfer through dedicated channels and (ii) increasing fault tolerance or robustness through multichannel signals. Robustness relates to an accurate decoding of a signal when parts of a signal are occluded. We show analytically in simple feed-forward neural networks that while a multichannel signal can solve the robustness problem, a multimodal signal does so more effectively because it can maximize the contribution made by each channel while minimizing the effects of exclusion. Multimodality refers to sets of channels where within each set information is highly correlated. We show that the robustness property ensures correlations among channels producing complex, associative networks as a by-product. We refer to this as the principle of robust overdesign. We discuss the biological implications of this for the evolution of combinatorial signalling systems; in particular, how robustness promotes enough redundancy to allow for a subsequent specialization of redundant components into novel signals.     

Robustness and evolution: concepts, insights and challenges from a developmental model system

Robustness, the persistence of an organismal trait under perturbations, is a ubiquitous property of complex living systems. We here discuss key concepts related to robustness with examples from vulva development in the nematode Caenorhabditis elegans. We emphasize the need to be clear about the perturbations a trait is (or is not) robust to. We discuss two prominent mechanistic causes of robustness, namely redundancy and distributed robustness. We also discuss possible evolutionary causes of robustness, one of which does not involve natural selection. To better understand robustness is of paramount importance for understanding organismal evolution. Part of the reason is that highly robust systems can accumulate cryptic variation that can serve as a source of new adaptations and evolutionary innovations. We point to some key challenges in improving our understanding of robustness.     

Accounting for robustness in modeling signal transduction responses

Abstract

A classical question in systems biology is to find a Boolean model which is able to predict the observed responses of a signaling network. It has been previously shown that such models can be tailored based on experimental data. While fitting a minimum-size network to the experimentally observed data is a natural assumption, it can potentially result in a network which is not so robust against the noises in the training dataset. Indeed, it is widely accepted now that biological systems are generally evolved to be very robust. Therefore, in the present work, we extended the classical formulation of Boolean network construction in order to put weight on the robustness of the created network. We show that our method results generally in more relevant networks. Consequently, considering robustness as a design principle of biological networks can result in more realistic models.     

EvoRSR: an integrated system for exploring evolution of RNA structural robustness

Background  

Robustness, maintaining a constant phenotype despite perturbations, is a fundamental property of biological systems that is incorporated at various levels of biological complexity. Although robustness has been frequently observed in nature, its evolutionary origin remains unknown. Current hypotheses suggest that robustness originated as a direct consequence of natural selection, as an intrinsic property of adaptations, or as a congruent correlate of environment robustness. To elucidate the evolutionary origins of robustness, a convenient computational package is strongly needed.     

Robustness of cellular functions

Robustness, the ability to maintain performance in the face of perturbations and uncertainty, is a long-recognized key property of living systems. Owing to intimate links to cellular complexity, however, its molecular and cellular basis has only recently begun to be understood. Theoretical approaches to complex engineered systems can provide guidelines for investigating cellular robustness because biology and engineering employ a common set of basic mechanisms in different combinations. Robustness may be a key to understanding cellular complexity, elucidating design principles, and fostering closer interactions between experimentation and theory.     

Evolution of mutational robustness in an RNA virus

Mutational (genetic) robustness is phenotypic constancy in the face of mutational changes to the genome. Robustness is critical to the understanding of evolution because phenotypically expressed genetic variation is the fuel of natural selection. Nonetheless, the evidence for adaptive evolution of mutational robustness in biological populations is controversial. Robustness should be selectively favored when mutation rates are high, a common feature of RNA viruses. However, selection for robustness may be relaxed under virus co-infection because complementation between virus genotypes can buffer mutational effects. We therefore hypothesized that selection for genetic robustness in viruses will be weakened with increasing frequency of co-infection. To test this idea, we used populations of RNA phage φ6 that were experimentally evolved at low and high levels of co-infection and subjected lineages of these viruses to mutation accumulation through population bottlenecking. The data demonstrate that viruses evolved under high co-infection show relatively greater mean magnitude and variance in the fitness changes generated by addition of random mutations, confirming our hypothesis that they experience weakened selection for robustness. Our study further suggests that co-infection of host cells may be advantageous to RNA viruses only in the short term. In addition, we observed higher mutation frequencies in the more robust viruses, indicating that evolution of robustness might foster less-accurate genome replication in RNA viruses.     

Stability and Responsiveness in a Self-Organized Living Architecture

Robustness and adaptability are central to the functioning of biological systems, from gene networks to animal societies. Yet the mechanisms by which living organisms achieve both stability to perturbations and sensitivity to input are poorly understood. Here, we present an integrated study of a living architecture in which army ants interconnect their bodies to span gaps. We demonstrate that these self-assembled bridges are a highly effective means of maintaining traffic flow over unpredictable terrain. The individual-level rules responsible depend only on locally-estimated traffic intensity and the number of neighbours to which ants are attached within the structure. We employ a parameterized computational model to reveal that bridges are tuned to be maximally stable in the face of regular, periodic fluctuations in traffic. However analysis of the model also suggests that interactions among ants give rise to feedback processes that result in bridges being highly responsive to sudden interruptions in traffic. Subsequent field experiments confirm this prediction and thus the dual nature of stability and flexibility in living bridges. Our study demonstrates the importance of robust and adaptive modular architecture to efficient traffic organisation and reveals general principles regarding the regulation of form in biological self-assemblies.     

Evolution of robustness to noise and mutation in gene expression dynamics

Phenotype of biological systems needs to be robust against mutation in order to sustain themselves between generations. On the other hand, phenotype of an individual also needs to be robust against fluctuations of both internal and external origins that are encountered during growth and development. Is there a relationship between these two types of robustness, one during a single generation and the other during evolution? Could stochasticity in gene expression have any relevance to the evolution of these types of robustness? Robustness can be defined by the sharpness of the distribution of phenotype; the variance of phenotype distribution due to genetic variation gives a measure of 'genetic robustness', while that of isogenic individuals gives a measure of 'developmental robustness'. Through simulations of a simple stochastic gene expression network that undergoes mutation and selection, we show that in order for the network to acquire both types of robustness, the phenotypic variance induced by mutations must be smaller than that observed in an isogenic population. As the latter originates from noise in gene expression, this signifies that the genetic robustness evolves only when the noise strength in gene expression is larger than some threshold. In such a case, the two variances decrease throughout the evolutionary time course, indicating increase in robustness. The results reveal how noise that cells encounter during growth and development shapes networks' robustness to stochasticity in gene expression, which in turn shapes networks' robustness to mutation. The necessary condition for evolution of robustness, as well as the relationship between genetic and developmental robustness, is derived quantitatively through the variance of phenotypic fluctuations, which are directly measurable experimentally.     

Robustness and state-space structure of Boolean gene regulatory models

Robustness to perturbation is an important characteristic of genetic regulatory systems, but the relationship between robustness and model dynamics has not been clearly quantified. We propose a method for quantifying both robustness and dynamics in terms of state-space structures, for Boolean models of genetic regulatory systems. By investigating existing models of the Drosophila melanogaster segment polarity network and the Saccharomyces cerevisiae cell-cycle network, we show that the structure of attractor basins can yield insight into the underlying decision making required of the system, and also the way in which the system maximises its robustness. In particular, gene networks implementing decisions based on a few genes have simple state-space structures, and their attractors are robust by virtue of their simplicity. Gene networks with decisions that involve many interacting genes have correspondingly more complicated state-space structures, and robustness cannot be achieved through the structure of the attractor basins, but is achieved by larger attractor basins that dominate the state space. These different types of robustness are demonstrated by the two models: the D. melanogaster segment polarity network is robust due to simple attractor basins that implement decisions based on spatial signals; the S. cerevisiae cell-cycle network has a complicated state-space structure, and is robust only due to a giant attractor basin that dominates the state space.     

Simple networks for spike-timing-based computation,with application to olfactory processing

Spike synchronization across neurons can be selective for the situation where neurons are driven at similar firing rates, a "many are equal" computation. This can be achieved in the absence of synaptic interactions between neurons, through phase locking to a common underlying oscillatory potential. Based on this principle, we instantiate an algorithm for robust odor recognition into a model network of spiking neurons whose main features are taken from known properties of biological olfactory systems. Here, recognition of odors is signaled by spike synchronization of specific subsets of "mitral cells." This synchronization is highly odor selective and invariant to a wide range of odor concentrations. It is also robust to the presence of strong distractor odors, thus allowing odor segmentation within complex olfactory scenes. Information about odors is encoded in both the identity of glomeruli activated above threshold (1 bit of information per glomerulus) and in the analog degree of activation of the glomeruli (approximately 3 bits per glomerulus).     

Development and validation of computational models of cellular interaction

In this paper we take the view that computational models of biological systems should satisfy two conditions – they should be able to predict function at a systems biology level, and robust techniques of validation against biological models must be available. A modelling paradigm for developing a predictive computational model of cellular interaction is described, and methods of providing robust validation against biological models are explored, followed by a consideration of software issues.     

High‐order combination effects and biological robustness

Biological systems are robust, in that they can maintain stable phenotypes under varying conditions or attacks. Biological systems are also complex, being organized into many functional modules that communicate through interlocking pathways and feedback mechanisms. In these systems, robustness and complexity are linked because both qualities arise from the same underlying mechanisms. When perturbed by multiple attacks, such complex systems become fragile in both theoretical and experimental studies, and this fragility depends on the number of agents applied. We explore how this relationship can be used to study the functional robustness of a biological system using systematic high‐order combination experiments. This presents a promising approach toward many biomedical and bioengineering challenges. For example, high‐order experiments could determine the point of fragility for pathogenic bacteria and might help identify optimal treatments against multi‐drug resistance. Such studies would also reinforce the growing appreciation that biological systems are best manipulated not by targeting a single protein, but by modulating the set of many nodes that can selectively control a system's functional state.     

Evolving Robust Gene Regulatory Networks

Design and implementation of robust network modules is essential for construction of complex biological systems through hierarchical assembly of ‘parts’ and ‘devices’. The robustness of gene regulatory networks (GRNs) is ascribed chiefly to the underlying topology. The automatic designing capability of GRN topology that can exhibit robust behavior can dramatically change the current practice in synthetic biology. A recent study shows that Darwinian evolution can gradually develop higher topological robustness. Subsequently, this work presents an evolutionary algorithm that simulates natural evolution in silico, for identifying network topologies that are robust to perturbations. We present a Monte Carlo based method for quantifying topological robustness and designed a fitness approximation approach for efficient calculation of topological robustness which is computationally very intensive. The proposed framework was verified using two classic GRN behaviors: oscillation and bistability, although the framework is generalized for evolving other types of responses. The algorithm identified robust GRN architectures which were verified using different analysis and comparison. Analysis of the results also shed light on the relationship among robustness, cooperativity and complexity. This study also shows that nature has already evolved very robust architectures for its crucial systems; hence simulation of this natural process can be very valuable for designing robust biological systems.     

Sloppiness, robustness, and evolvability in systems biology

The functioning of many biochemical networks is often robust-remarkably stable under changes in external conditions and internal reaction parameters. Much recent work on robustness and evolvability has focused on the structure of neutral spaces, in which system behavior remains invariant to mutations. Recently we have shown that the collective behavior of multiparameter models is most often sloppy: insensitive to changes except along a few 'stiff' combinations of parameters, with an enormous sloppy neutral subspace. Robustness is often assumed to be an emergent evolved property, but the sloppiness natural to biochemical networks offers an alternative nonadaptive explanation. Conversely, ideas developed to study evolvability in robust systems can be usefully extended to characterize sloppy systems.