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.     

Review: Towards the agroecological management of ruminants,pigs and poultry through the development of sustainable breeding programmes: I-selection goals and criteria

Agroecology uses natural processes and local resources rather than chemical inputs to ensure production while limiting the environmental footprint of livestock and crop production systems. Selecting to achieve a maximization of target production criteria has long proved detrimental to fitness traits. However, since the 1990s, developments in animal breeding have also focussed on animal robustness by balancing production and functional traits within overall breeding goals. We discuss here how an agroecological perspective should further shift breeding goals towards functional traits rather than production traits. Breeding for robustness aims to promote individual adaptive capacities by considering diverse selection criteria which include reproduction, animal health and welfare, and adaptation to rough feed resources, a warm climate or fluctuating environmental conditions. It requires the consideration of genotype×environment interactions in the prediction of breeding values. Animal performance must be evaluated in low-input systems in order to select those animals that are adapted to limiting conditions, including feed and water availability, climate variations and diseases. Finally, we argue that there is no single agroecological animal type, but animals with a variety of profiles that can meet the expectations of agroecology. The standardization of both animals and breeding conditions indeed appears contradictory to the agroecological paradigm that calls for an adaptation of animals to local opportunities and constraints in weakly artificialized systems tied to their physical environment.     

Robustness of Oscillatory Behavior in Correlated Networks

Understanding network robustness against failures of network units is useful for preventing large-scale breakdowns and damages in real-world networked systems. The tolerance of networked systems whose functions are maintained by collective dynamical behavior of the network units has recently been analyzed in the framework called dynamical robustness of complex networks. The effect of network structure on the dynamical robustness has been examined with various types of network topology, but the role of network assortativity, or degree–degree correlations, is still unclear. Here we study the dynamical robustness of correlated (assortative and disassortative) networks consisting of diffusively coupled oscillators. Numerical analyses for the correlated networks with Poisson and power-law degree distributions show that network assortativity enhances the dynamical robustness of the oscillator networks but the impact of network disassortativity depends on the detailed network connectivity. Furthermore, we theoretically analyze the dynamical robustness of correlated bimodal networks with two-peak degree distributions and show the positive impact of the network assortativity.     

Distributed robustness versus redundancy as causes of mutational robustness

A biological system is robust to mutations if it continues to function after genetic changes in its parts. Such robustness is pervasive on different levels of biological organization, from macromolecules to genetic networks and whole organisms. I here ask which of two possible causes of such robustness are more important on a genome-wide scale, for systems whose parts are genes, such as metabolic and genetic networks. The first of the two causes is redundancy of a system's parts: A gene may be dispensable if the genome contains redundant, back-up copies of the gene. The second cause, distributed robustness, is more poorly understood. It emerges from the distributed nature of many biological systems, where many (and different) parts contribute to system functions. I will here discuss evidence suggesting that distributed robustness is equally or more important for mutational robustness than gene redundancy. This evidence comes from the functional divergence of redundant genes, as well as from large-scale gene deletion studies. I also ask whether one can quantify the extent to which redundancy or distributed robustness contribute to mutational robustness.     

Emergent buffering balances evolvability and robustness in the evolution of phenotypic flexibility

Evolution of adaptive phenotypic flexibility requires a system that can dynamically restore and update a functional phenotype in response to environmental change. The architecture of such a system evolves under the conflicting demands of versatility and robustness, and resolution of these demands should be particularly evident in organisms that require external inputs for reiterative trait production within a generation, such as in metabolic networks that underlie yearly acquisition of diet‐dependent coloration in birds. Here, we show that a key structural feature of carotenoid networks–redundancy of biochemical pathways–enables these networks to translate variable environmental inputs into consistent phenotypic outcomes. We closely followed life‐long changes in structure and utilization of metabolic networks in a large cohort of free‐living birds and found that greater individual experience with dietary change between molts leads to wider occupancy of the metabolic network and progressive accumulation of redundant pathways in a functionally active network. This generated a regime of emergent buffering whereby greater dietary experience was mechanistically linked to greater robustness of resulting traits and an increasing ability to retain and implement previous adaptive solutions. Thus, experience‐related buffering links evolvability and robustness in carotenoid‐metabolizing networks and we argue that this mechanistic principle facilitates the evolution of phenotypic flexibility.     

Attack Robustness and Centrality of Complex Networks

Many complex systems can be described by networks, in which the constituent components are represented by vertices and the connections between the components are represented by edges between the corresponding vertices. A fundamental issue concerning complex networked systems is the robustness of the overall system to the failure of its constituent parts. Since the degree to which a networked system continues to function, as its component parts are degraded, typically depends on the integrity of the underlying network, the question of system robustness can be addressed by analyzing how the network structure changes as vertices are removed. Previous work has considered how the structure of complex networks change as vertices are removed uniformly at random, in decreasing order of their degree, or in decreasing order of their betweenness centrality. Here we extend these studies by investigating the effect on network structure of targeting vertices for removal based on a wider range of non-local measures of potential importance than simply degree or betweenness. We consider the effect of such targeted vertex removal on model networks with different degree distributions, clustering coefficients and assortativity coefficients, and for a variety of empirical networks.     

Development of the cypriniform protrusible jaw complex in Danio rerio: Constructional insights for evolution

Studies on the evolution of complex biological systems are difficult because the construction of these traits cannot be observed during the course of evolution. Complex traits are defined as consisting of multiple elements, often of differing embryological origins, with multiple linkages integrated to form a single functional unit. An example of a complex system is the cypriniform oral jaw apparatus. Cypriniform fishes possess an upper jaw characterized by premaxillary protrusion during feeding. Cypriniforms effect protrusion via the kinethmoid, a synapomorphy for the order. The kinethmoid is a sesamoid ossification suspended by ligaments attaching to the premaxillae, maxillae, palatines, and neurocranium. Upon mouth opening, the kinethmoid rotates as the premaxillae move anteriorly. Along with bony and ligamentous elements, there are three divisions of the adductor mandibulae that render this system functional. It is unclear how cypriniform jaws evolved because although the evolution of sesamoid elements is common, the incorporation of the kinethmoid into the protrusible jaw results in a function that is atypical for sesamoids. Developmental studies can show how biological systems are assembled within individuals and offer clues about how traits might have been constructed during evolution. We investigated the development of the protrusible upper jaw in zebrafish to generate hypotheses regarding the evolution of this character. Early in development, the adductor mandibulae arises as a single unit. The muscle divides after ossification of the maxillae, on which the A1 division will ultimately insert. A cartilaginous kinethmoid first develops within the intermaxillary ligament; it later ossifies at points of ligamentous attachment. We combine our structural developmental data with published kinematic data at key developmental stages and discuss potential functional advantages in possessing even the earliest stages of a system for protrusion. J. Morphol. 2010. © 2010 Wiley‐Liss, Inc.     

Selfish cellular networks and the evolution of complex organisms

Human gametogenesis takes years and involves many cellular divisions, particularly in males. Consequently, gametogenesis provides the opportunity to acquire multiple de novo mutations. A significant portion of these is likely to impact the cellular networks linking genes, proteins, RNA and metabolites, which constitute the functional units of cells. A wealth of literature shows that these individual cellular networks are complex, robust and evolvable. To some extent, they are able to monitor their own performance, and display sufficient autonomy to be termed "selfish". Their robustness is linked to quality control mechanisms which are embedded in and act upon the individual networks, thereby providing a basis for selection during gametogenesis. These selective processes are equally likely to affect cellular functions that are not gamete-specific, and the evolution of the most complex organisms, including man, is therefore likely to occur via two pathways: essential housekeeping functions would be regulated and evolve during gametogenesis within the parents before being transmitted to their progeny, while classical selection would operate on other traits of the organisms that shape their fitness with respect to the environment.     

The Quantitative Genetics of Phenotypic Robustness

Phenotypic robustness, or canalization, has been extensively investigated both experimentally and theoretically. However, it remains unknown to what extent robustness varies between individuals, and whether factors buffering environmental variation also buffer genetic variation. Here we introduce a quantitative genetic approach to these issues, and apply this approach to data from three species. In mice, we find suggestive evidence that for hundreds of gene expression traits, robustness is polymorphic and can be genetically mapped to discrete genomic loci. Moreover, we find that the polymorphisms buffering genetic variation are distinct from those buffering environmental variation. In fact, these two classes have quite distinct mechanistic bases: environmental buffers of gene expression are predominantly sex-specific and trans-acting, whereas genetic buffers are not sex-specific and often cis-acting. Data from studies of morphological and life-history traits in plants and yeast support the distinction between polymorphisms buffering genetic and environmental variation, and further suggest that loci buffering different types of environmental variation do overlap with one another. These preliminary results suggest that naturally occurring polymorphisms affecting phenotypic robustness could be abundant, and that these polymorphisms may generally buffer either genetic or environmental variation, but not both.     

Robustness elasticity in complex networks

Network robustness refers to a network's resilience to stress or damage. Given that most networks are inherently dynamic, with changing topology, loads, and operational states, their robustness is also likely subject to change. However, in most analyses of network structure, it is assumed that interaction among nodes has no effect on robustness. To investigate the hypothesis that network robustness is not sensitive or elastic to the level of interaction (or flow) among network nodes, this paper explores the impacts of network disruption, namely arc deletion, over a temporal sequence of observed nodal interactions for a large Internet backbone system. In particular, a mathematical programming approach is used to identify exact bounds on robustness to arc deletion for each epoch of nodal interaction. Elasticity of the identified bounds relative to the magnitude of arc deletion is assessed. Results indicate that system robustness can be highly elastic to spatial and temporal variations in nodal interactions within complex systems. Further, the presence of this elasticity provides evidence that a failure to account for nodal interaction can confound characterizations of complex networked systems.     

Animal models and conserved processes

Background

The concept of conserved processes presents unique opportunities for using nonhuman animal models in biomedical research. However, the concept must be examined in the context that humans and nonhuman animals are evolved, complex, adaptive systems. Given that nonhuman animals are examples of living systems that are differently complex from humans, what does the existence of a conserved gene or process imply for inter-species extrapolation?

Methods

We surveyed the literature including philosophy of science, biological complexity, conserved processes, evolutionary biology, comparative medicine, anti-neoplastic agents, inhalational anesthetics, and drug development journals in order to determine the value of nonhuman animal models when studying conserved processes.

Results

Evolution through natural selection has employed components and processes both to produce the same outcomes among species but also to generate different functions and traits. Many genes and processes are conserved, but new combinations of these processes or different regulation of the genes involved in these processes have resulted in unique organisms. Further, there is a hierarchy of organization in complex living systems. At some levels, the components are simple systems that can be analyzed by mathematics or the physical sciences, while at other levels the system cannot be fully analyzed by reducing it to a physical system. The study of complex living systems must alternate between focusing on the parts and examining the intact whole organism while taking into account the connections between the two. Systems biology aims for this holism. We examined the actions of inhalational anesthetic agents and anti-neoplastic agents in order to address what the characteristics of complex living systems imply for inter-species extrapolation of traits and responses related to conserved processes.

Conclusion

We conclude that even the presence of conserved processes is insufficient for inter-species extrapolation when the trait or response being studied is located at higher levels of organization, is in a different module, or is influenced by other modules. However, when the examination of the conserved process occurs at the same level of organization or in the same module, and hence is subject to study solely by reductionism, then extrapolation is possible.     

Wild Mice As Bountiful Resources of Novel Genetic Variants for Quantitative Traits

Most traits of biological importance, including traits for human complex diseases (e.g., obesity and diabetes), are continuously distributed. These complex or quantitative traits are controlled by multiple genetic loci called QTLs (quantitative trait loci), environments and their interactions. The laboratory mouse has long been used as a pilot animal model for understanding the genetic architecture of quantitative traits. Next-generation sequencing analyses and genome-wide SNP (single nucleotide polymorphism) analyses of mouse genomes have revealed that classical inbred strains commonly used throughout the world are derived from a few fancy mice with limited and non-randomly distributed genetic diversity that occurs in nature and also indicated that their genomes are predominantly Mus musculus domesticus in origin. Many QTLs for a huge variety of traits have so far been discovered from a very limited gene pool of classical inbred strains. However, wild M. musculus mice consisting of five subspecies widely inhabit areas all over the world, and hence a number of novel QTLs may still lie undiscovered in gene pools of the wild mice. Some of the QTLs are expected to improve our understanding of human complex diseases. Using wild M. musculus subspecies in Asia as examples, this review illustrates that wild mice are untapped natural resources for valuable QTL discovery.     

A High-throughput Platform for the Production and Analysis of Transgenic Cassava (Manihot esculenta) Plants

A platform for high-throughput production and analysis of transgenic cassava (Manihot esculenta) has been developed for the variety 60444 and implemented to generate plants expressing traits for nutritional enhancement, modified metabolism, promoter analysis and disease resistance. Over a three and a half year period this system has been utilized to produce more than 3500 independent transgenic plant lines from 50 different genetic constructs within a single laboratory. Plants recovered through this system have proven robust and efficacious for engineered traits under greenhouse conditions and within the first confined field trials of transgenic cassava carried out in Uganda, Kenya, Nigeria and Puerto Rico. Detailed procedures are described for the operation of this platform, including all steps in tissue culture, genetic transformation, copy number estimation, greenhouse establishment for shoot and storage root formation and systems for centralized quality control, transgenic plant tracking and regulatory compliance. In addition to providing reliable transgenic plant production for proof of concept studies in the variety 60444, the systems implemented and described here form the structure for high throughput production of transgenic farmer-preferred cultivars of cassava.     

Multimodal signalling in the North American barn swallow: a phenotype network approach

Complex signals, involving multiple components within and across modalities, are common in animal communication. However, decomposing complex signals into traits and their interactions remains a fundamental challenge for studies of phenotype evolution. We apply a novel phenotype network approach for studying complex signal evolution in the North American barn swallow (Hirundo rustica erythrogaster). We integrate model testing with correlation-based phenotype networks to infer the contributions of female mate choice and male–male competition to the evolution of barn swallow communication. Overall, the best predictors of mate choice were distinct from those for competition, while moderate functional overlap suggests males and females use some of the same traits to assess potential mates and rivals. We interpret model results in the context of a network of traits, and suggest this approach allows researchers a more nuanced view of trait clustering patterns that informs new hypotheses about the evolution of communication systems.     

Functions of Multivector Variables

As is well known, the common elementary functions defined over the real numbers can be generalized to act not only over the complex number field but also over the skew (non-commuting) field of the quaternions. In this paper, we detail a number of elementary functions extended to act over the skew field of Clifford multivectors, in both two and three dimensions. Complex numbers, quaternions and Cartesian vectors can be described by the various components within a Clifford multivector and from our results we are able to demonstrate new inter-relationships between these algebraic systems. One key relationship that we discover is that a complex number raised to a vector power produces a quaternion thus combining these systems within a single equation. We also find a single formula that produces the square root, amplitude and inverse of a multivector over one, two and three dimensions. Finally, comparing the functions over different dimension we observe that C?(?³) provides a particularly versatile algebraic framework.     

Spatio-temporal dependence of the signaling response in immune-receptor trafficking networks regulated by cell density: a theoretical model

Cell signaling processes involve receptor trafficking through highly connected networks of interacting components. The binding of surface receptors to their specific ligands is a key factor for the control and triggering of signaling pathways. In most experimental systems, ligand concentration and cell density vary within a wide range of values. Dependence of the signal response on cell density is related with the extracellular volume available per cell. This dependence has previously been studied using non-spatial models which assume that signaling components are well mixed and uniformly distributed in a single compartment. In this paper, a mathematical model that shows the influence exerted by cell density on the spatio-temporal evolution of ligands, cell surface receptors, and intracellular signaling molecules is developed. To this end, partial differential equations were used to model ligand and receptor trafficking dynamics through the different domains of the whole system. This enabled us to analyze several interesting features involved with these systems, namely: a) how the perturbation caused by the signaling response propagates through the system; b) receptor internalization dynamics and how cell density affects the robustness of dose-response curves upon variation of the binding affinity; and c) that enhanced correlations between ligand input and system response are obtained under conditions that result in larger perturbations of the equilibrium ligand + surface receptor [Please see text] ligand - receptor complex. Finally, the results are compared with those obtained by considering that the above components are well mixed in a single compartment.     

A Multi-Trait,Meta-analysis for Detecting Pleiotropic Polymorphisms for Stature,Fatness and Reproduction in Beef Cattle

Polymorphisms that affect complex traits or quantitative trait loci (QTL) often affect multiple traits. We describe two novel methods (1) for finding single nucleotide polymorphisms (SNPs) significantly associated with one or more traits using a multi-trait, meta-analysis, and (2) for distinguishing between a single pleiotropic QTL and multiple linked QTL. The meta-analysis uses the effect of each SNP on each of n traits, estimated in single trait genome wide association studies (GWAS). These effects are expressed as a vector of signed t-values (t) and the error covariance matrix of these t values is approximated by the correlation matrix of t-values among the traits calculated across the SNP (V). Consequently, t''V⁻¹t is approximately distributed as a chi-squared with n degrees of freedom. An attractive feature of the meta-analysis is that it uses estimated effects of SNPs from single trait GWAS, so it can be applied to published data where individual records are not available. We demonstrate that the multi-trait method can be used to increase the power (numbers of SNPs validated in an independent population) of GWAS in a beef cattle data set including 10,191 animals genotyped for 729,068 SNPs with 32 traits recorded, including growth and reproduction traits. We can distinguish between a single pleiotropic QTL and multiple linked QTL because multiple SNPs tagging the same QTL show the same pattern of effects across traits. We confirm this finding by demonstrating that when one SNP is included in the statistical model the other SNPs have a non-significant effect. In the beef cattle data set, cluster analysis yielded four groups of QTL with similar patterns of effects across traits within a group. A linear index was used to validate SNPs having effects on multiple traits and to identify additional SNPs belonging to these four groups.     

Differential effects of flower feeding in an insect host–parasitoid system

In many insect host–parasitoid systems, both the host and its parasitoids forage on shared floral resources. As a result of insect behaviour, morphology and physiology, flower species may act selectively at different levels of such systems, e.g., between the trophic levels of hosts and parasitoids, between species within a guild, between sexes or individuals within a species or between life history traits within an individual. We asked if effects of selectivity are consistent across levels in the horse chestnut leafminer, Cameraria ohridella, and its parasitoid complex. Insects were exposed singly in no-choice feeding trials to twelve common flower species and their survival and reproduction were recorded. Only one of twelve flower species (Ranunculus acris) tended to selectively favour the longevity of leafminers, but not of parasitoids. No flower species were found to favour parasitoids only. Both trophic levels profited from feeding on Anthriscus sylvestris, however, parasitoids benefited up to eight times more than their hosts. No differences were found among the species of the parasitoid guild, but females lived significantly longer than males, and single individuals within species were able to exploit generally unfavourable flower species. Out of the seven flower species that increased the longevity of leafminer females, only Chaerophyllum hirsutum significantly enhanced the number of eggs laid. Fecundity was generally positively correlated with longevity of leafminer females, but two flower species (C. hirsutum, Taraxacum officinale) had an additional positive effect on fecundity. In conclusion, we demonstrated that flowers act differently on life history traits in a host–parasitoid system at a multitude of biological levels and that these effects are not always consistent across levels. Selective plant-derived resources can therefore modify herbivore–natural enemy interactions in ways that are more complex than currently appreciated.     

Mechanisms of developmental robustness

We present a review of noise buffering mechanisms responsible for developmental robustness. We focus on functions of chaperone Hsp90, miRNA, and cross-regulation of gap genes in Drosophila. The noise buffering mechanisms associated with these functions represent specific examples of the developmental canalization, reducing the phenotypical variability in presence of either genetic or environmental perturbations. We demonstrate that robustness often appears as a function of a network of interacting elements and that the system level approach is needed to understand the mechanisms of noise filtering.