Motion control of musculoskeletal systems with redundancy

Motion control of musculoskeletal systems for functional electrical stimulation (FES) is a challenging problem due to the inherent complexity of the systems. These include being highly nonlinear, strongly coupled, time-varying, time-delayed, and redundant. The redundancy in particular makes it difficult to find an inverse model of the system for control purposes. We have developed a control system for multiple input multiple output (MIMO) redundant musculoskeletal systems with little prior information. The proposed method separates the steady-state properties from the dynamic properties. The dynamic control uses a steady-state inverse model and is implemented with both a PID controller for disturbance rejection and an artificial neural network (ANN) feedforward controller for fast trajectory tracking. A mechanism to control the sum of the muscle excitation levels is also included. To test the performance of the proposed control system, a two degree of freedom ankle–subtalar joint model with eight muscles was used. The simulation results show that separation of steady-state and dynamic control allow small output tracking errors for different reference trajectories such as pseudo-step, sinusoidal and filtered random signals. The proposed control method also demonstrated robustness against system parameter and controller parameter variations. A possible application of this control algorithm is FES control using multiple contact cuff electrodes where mathematical modeling is not feasible and the redundancy makes the control of dynamic movement difficult.     

Widespread conservation of genetic redundancy during a billion years of eukaryotic evolution

Genetic redundancy means that two genes can perform the same function. Using a comprehensive phylogenetic analysis, we show here in both Saccharomyces cerevisiae and Caenorhabditis elegans that genetic redundancy is not just a transient consequence of gene duplication, but is often an evolutionary stable state. In multiple examples, genes have retained redundant functions since the divergence of the animal, plant and fungi kingdoms over a billion years ago. The stable conservation of genetic redundancy contrasts with the more rapid evolution of genetic interactions between unrelated genes and can be explained by theoretical models including a 'piggyback' mechanism in which overlapping redundant functions are co-selected with nonredundant ones.     

Evolutionary dynamics of transposable elements in a small RNA world

Transposable elements (TEs) are selfish elements that cause harmful mutations, contribute to the structure of regulatory networks and shape the architecture of genomes. Natural selection against their harmful effects has long been considered the dominant force limiting their spread. It is now clear that a genome defense system of RNA-mediated silencing also plays a crucial role in limiting TE proliferation. A full understanding of TE evolutionary dynamics must consider how these forces jointly determine their proliferation within genomes. Here I consider these forces from two perspectives - dynamics within populations and evolutionary games within the germline. The analysis of TE dynamics from these two perspectives promises to provide new insight into their role in evolution.     

The conservation of redundancy in genetic systems: effects of sexual and asexual reproduction

The relationship between probability of survival and the number of deleterious mutations in the genome is investigated using three different models of highly redundant systems that interact with a threatening environment. Model one is a system that counters a potentially lethal infection; it has multiple identical components that act in sequence and in parallel. Model two has many different overlapping components that provide three-fold coverage of a large number of vital functions. The third model is based on statistical decision theory: an ideal detector, following an optimum decision strategy, makes crucial decisions in an uncertain world. The probability of a fatal error is reduced by a redundant sampling system, but the chance of error rises as the system is impaired by deleterious mutations. In all three cases the survival profile shows a synergistic pattern in that the probability of survival falls slowly and then more rapidly. This is different than the multiplicative or independent survival profile that is often used in mathematical models. It is suggested that a synergistic profile is a property of redundant systems. Model one is then used to study the conservation of redundancy during sexual and asexual reproduction. A unicellular haploid organism reproducing asexually retains redundancy when the mutation rate is very low (0001 per cell division), but tends to lose high levels of redundancy if the mutation rate is increased (001 to 01 per cell division). If a similar unicellular haploid organism has a sexual phase then redundancy is retained for mutation rates between 0001 and 01 per cell division. The sexual organism outgrows the asexual organism when the above mutation rates apply. If they compete for finite resources the asexual organism will be extinguished. Variants of the sexual organism with increased redundancy will outgrow those with lower levels of redundancy and the sexual process facilitates the evolution of more complex forms. There is a limit to the extent that complexity can be increased by increasing the size of the genome and in asexual organisms this leads to progressive accumulation of mutations with loss of redundancy and eventual extinction. If complexity is increased by using genes in new combinations, the asexual form can reach a stable equilibrium, although it is associated with some loss of redundancy. The sexual form, by comparison, can survive, with retention of redundancy, even if the mutation rate is above one per generation. The conservation and evolution of redundancy, which is essential for complexity, depends on the sexual process of reproduction.     

Evolutionary preservation of redundant duplicated genes

Gene duplication events produce both perfect and imperfect copies of genes. Perfect copies are said to be functionally redundant when knockout of one gene produces no 'scoreable', phenotypic effects. Preserving identical, duplicate copies of genes is problematic as all copies are prone to accumulate neutral mutations as pseudogenes, or more rarely, evolve into new genes with novel functions. We summarise theoretical treatments for the invasion and subsequent evolutionary modification of functionally redundant genes. We then consider the preservation of functionally identical copies of a gene over evolutionary time. We present several models for conserving redundancy: asymmetric mutation, asymmetric efficacy, pleiotropy, developmental buffering, allelic competition and regulatory asymmetries. In all cases, some form of symmetry breaking is required to maintain functional redundancy indefinitely.     

The mutation buffering concept of biomolecular structure

Redundant elements in proteins and nucleic acids serve to buffer the effect of point mutations on features of conformation critical for function. Mutation buffering associated with mechanistically redundant amino acids facilitates the evolution of proteins. Such redundant amino acids accumulate by hitch-hiking along with the evolutionary advances which they facilitate. Redundancies in DNA (such as introns and repetitive DNA) prevent extraneous sequence dependent conformational effects from interfering with readout. They also facilitate regulatory evolution. According to the mutation buffering concept biological organizations are selected to facilitate evolution. As a consequence biological information processing is very different from information processing in man-made computers. The link between molecular conformation, evolutionary processes, and information processing is formulated in terms of a tradeoff principle. By utilizing mutation buffering biological systems sacrifice programmability; by achieving programmability digital computers make mutation buffering computationally expensive and hence sacrifice evolutionary adaptability.     

Enhancing evolvability with mutation buffering mediated through multiple weak interactions

The evolutionary adaptability of a system is dependent on three organizational properties, self-organizing dynamics that are hierarchically organized, component redundancy, and multiple weak interactions [Towards high evolvability dynamics, in: G. van de Vijver, S. Salthe, M. Delpos (Eds.), Evolutionary Systems, Kluwer Academic Publishers, Dordrecht, 1998, pp. 147-169]. This study reports on the use of the dual dynamics network model as an aid in understanding the role multiple weak interactions play in enhancing evolutionary adaptability. Dual dynamics networks are self-organizing systems that consist of simple components that change local state due to the coupled influences from connected components exerting strong discrete decision-making influences and from groups of components exerting multiple weak influences [J. Theor. Biol. 193 (1998) 287]. The dual dynamics model has been enhanced to support investigations of properties relevant to a system's capacity for evolvability, such as structure-function relationships, neutrality, adaptive tolerance, and evolutionary search performance.Three network types are investigated, each utilizing a different method of coupling strong and weak influences. The results demonstrate that the manner of coupling multiple weak interactions into the systems dynamics significantly affects the structure-function maps and the consequent evolvability characteristics. Specifically it is found that a form of coupling, denoted as linear modulation, enhances evolutionary adaptability. Linear modulation coupling requires that the weak interactions be integrated with strong interactions in a manner that implies a linear ordered relation between the possible state values of the components of the systems. When coupling functions that do not imply such an ordering of local state values are used, evolutionary adaptability is decreased.     

Mutation-absorption model of the enzyme

Gradual changes in function of proteins in response to single changes in primary structure are often observed to occur and are a necessary condition for evolution by variation and natural selection at the protein level. A probabilistic (entropy theory_ analysis of the effect of changes in primary structure on three-dimensional shape and function shows that such gradualism is based on the presence of a control system in the molecule involving a definite general form of structure-function degeneracy. The assumptions of the analysis are that primary structure determines tertiary structure (or a thermal distribution of tertiary configurations and allosteric forms), tertiary structure determines function (characterized by rate and other parameters), and that certain features of tertiary structure may be specialized for particular functions. The main conclusion is that embodied in the molecule is a subsystem which serves as a buffer, absorbing mutation or other forms of genetic variation and expressing these as graceful variations in features of the shape critical for function. This buffer system may be realized by numerical redundancy of amino acids or other mechanisms which increase the redundancy of weak interactions responsible for folding, utilization of amino acids having a greater number of analogs with redundant features, or local and global structural formats which allow for more effective utilization of redundancy. The mutation-absorption model has implications for the interpretation of structure-function relations in biology, the topology of the adaptive landscape, the interpretation of isoenzymes and allozymes, the relationship between selection and neutralism in evolution, and the relation between the complexity of and energy required by biological systems and the effectiveness of evolutionary optimization.     

Criticality Is an Emergent Property of Genetic Networks that Exhibit Evolvability

Accumulating experimental evidence suggests that the gene regulatory networks of living organisms operate in the critical phase, namely, at the transition between ordered and chaotic dynamics. Such critical dynamics of the network permits the coexistence of robustness and flexibility which are necessary to ensure homeostatic stability (of a given phenotype) while allowing for switching between multiple phenotypes (network states) as occurs in development and in response to environmental change. However, the mechanisms through which genetic networks evolve such critical behavior have remained elusive. Here we present an evolutionary model in which criticality naturally emerges from the need to balance between the two essential components of evolvability: phenotype conservation and phenotype innovation under mutations. We simulated the Darwinian evolution of random Boolean networks that mutate gene regulatory interactions and grow by gene duplication. The mutating networks were subjected to selection for networks that both (i) preserve all the already acquired phenotypes (dynamical attractor states) and (ii) generate new ones. Our results show that this interplay between extending the phenotypic landscape (innovation) while conserving the existing phenotypes (conservation) suffices to cause the evolution of all the networks in a population towards criticality. Furthermore, the networks produced by this evolutionary process exhibit structures with hubs (global regulators) similar to the observed topology of real gene regulatory networks. Thus, dynamical criticality and certain elementary topological properties of gene regulatory networks can emerge as a byproduct of the evolvability of the phenotypic landscape.     

Quasispecies made simple

Quasispecies are clouds of genotypes that appear in a population at mutation–selection balance. This concept has recently attracted the attention of virologists, because many RNA viruses appear to generate high levels of genetic variation that may enhance the evolution of drug resistance and immune escape. The literature on these important evolutionary processes is, however, quite challenging. Here we use simple models to link mutation–selection balance theory to the most novel property of quasispecies: the error threshold—a mutation rate below which populations equilibrate in a traditional mutation–selection balance and above which the population experiences an error catastrophe, that is, the loss of the favored genotype through frequent deleterious mutations. These models show that a single fitness landscape may contain multiple, hierarchically organized error thresholds and that an error threshold is affected by the extent of back mutation and redundancy in the genotype-to-phenotype map. Importantly, an error threshold is distinct from an extinction threshold, which is the complete loss of the population through lethal mutations. Based on this framework, we argue that the lethal mutagenesis of a viral infection by mutation-inducing drugs is not a true error catastophe, but is an extinction catastrophe.     

MAINTENANCE OF POLYGENIC VARIATION IN SPATIALLY STRUCTURED POPULATIONS: ROLES FOR LOCAL MATING AND GENETIC REDUNDANCY

Although heritable genetic variation is critical to the evolutionary process, we know little about how it is maintained. Obviously, mutation-selection balance must play a role, but there is considerable doubt over whether it can account for heritabilities as high as 0.5, which are commonly found in natural populations. Most models of mutation-selection balance assume panmictic populations. In this paper we use Monte Carlo simulations to examine the effect of isolation by distance on the variation maintained by mutation in a polygenic trait subject to optimizing selection. We show that isolation by distance can substantially increase the total variation maintained in continuous populations over a wide range of dispersal patterns, but only if more than one genotype produces the optimal phenotype (genetic redundancy). Isolation by distance alone has only a slight effect on the variation maintained in the total population for neutral alleles. The combined effect of isolation by distance and genetic redundancy, however, allows the maintenance of substantial variation despite strong stabilizing selection. The mechanism is straightforward. Isolation by distance allows mutation and drift to operate independently in different parts of the population. Because of their independent evolutionary histories, different parts of the population independently draw from the available set of redundant genotypes. Because the genotypes are redundant, selection does not discriminate among them, and they will persist until eliminated by drift. The population as a whole maintains many distinct genotypes. We show that this process allows mutation to maintain high levels of variation, even under strong stabilizing selection, and that over a moderate range of dispersal patterns the amount of variation maintained in the entire population is independent of both the strength of selection and the variance of the dispersal distance. Furthermore, we show that individual heterozygosity is increased in locally mating populations when selection is strong. Finally, our simulations provide a rough picture of how selection and the dispersal pattern influence the spatial distribution of genetic and phenotypic variation.     

Synonymous Constraint Elements Show a Tendency to Encode Intrinsically Disordered Protein Segments

Synonymous constraint elements (SCEs) are protein-coding genomic regions with very low synonymous mutation rates believed to carry additional, overlapping functions. Thousands of such potentially multi-functional elements were recently discovered by analyzing the levels and patterns of evolutionary conservation in human coding exons. These elements provide a good opportunity to improve our understanding of how the redundant nature of the genetic code is exploited in the cell. Our premise is that the protein segments encoded by such elements might better comply with the increased functional demands if they are structurally less constrained (i.e. intrinsically disordered). To test this idea, we investigated the protein segments encoded by SCEs with computational tools to describe the underlying structural properties. In addition to SCEs, we examined the level of disorder, secondary structure, and sequence complexity of protein regions overlapping with experimentally validated splice regulatory sites. We show that multi-functional gene regions translate into protein segments that are significantly enriched in structural disorder and compositional bias, while they are depleted in secondary structure and domain annotations compared to reference segments of similar lengths. This tendency suggests that relaxed protein structural constraints provide an advantage when accommodating multiple overlapping functions in coding regions.     

Kin selection-mutation balance: a model for the origin, maintenance, and consequences of social cheating

Social conflict, in the form of intraspecific selfish "cheating," has been observed in a number of natural systems. However, a formal, evolutionary genetic theory of social cheating that provides an explanatory, predictive framework for these observations is lacking. Here we derive the kin selection-mutation balance, which provides an evolutionary null hypothesis for the statics and dynamics of cheating. When social interactions have linear fitness effects and Hamilton's rule is satisfied, selection is never strong enough to eliminate recurrent cheater mutants from a population, but cheater lineages are transient and do not invade. Instead, cheating lineages are eliminated by kin selection but are constantly reintroduced by mutation, maintaining a stable equilibrium frequency of cheaters. The presence of cheaters at equilibrium creates a "cheater load" that selects for mechanisms of cheater control, such as policing. We find that increasing relatedness reduces the cheater load more efficiently than does policing the costs and benefits of cooperation. Our results provide new insight into the effects of genetic systems, mating systems, ecology, and patterns of sex-limited expression on social evolution. We offer an explanation for the widespread cheater/altruist polymorphism found in nature and suggest that the common fear of conflict-induced social collapse is unwarranted.     

Germline Selection: Population Genetic Aspects of the Sexual/Asexual Life Cycle

Population geneticists make a distinction between sexual and asexual organisms depending on whether individuals inherit genes from one or two parents. When individual genes are considered, this distinction becomes less satisfactory for multicellular sexual organisms. Individual genes pass through numerous asexual mitotic cell divisions in the germline prior to meiosis and sexual recombination. The processes of mitotic mutation, mitotic crossing over, and mitotic gene conversion create genotypic diversity between diploid cells in the germline. Genes expressed in the germline whose products affect cell viability (such as many "housekeeping" enzymes) may be subjected to natural selection acting on this variability resulting in a non-Mendelian output of gametes. Such genes will be governed by the population genetics of the sexual/asexual life cycle rather than the conventional sexual/Mendelian life cycle. A model is developed to investigate some properties of the sexual/asexual life cycle. When appropriate parameter values were included in the model, it was found that mutation rates per locus per gamete may vary by a factor of up to 100 if selection acts in the germline. Sexual/asexual populations appear able to evolve to a genotype of higher fitness despite intervening genotypes of lower fitness, reducing the problems of underdominance and Wright's adaptive landscape encountered by purely sexual populations. As might be expected this ability is chiefly determined by the number of asexual mitotic cell divisions within the germline. The evolutionary consequences of "housekeeping" loci being governed by the dynamics of the sexual/asexual life cycle are considered.     

Connecting the sun to flowering in sunflower adaptation

Species living in seasonal environments often adaptively time their reproduction in response to photoperiod cues. We characterized the expression of genes in the flowering-time regulatory network across wild populations of the common sunflower, Helianthus annuus, that we found to be adaptively differentiated for photoperiod response. The observed clinal variation was associated with changes at multiple hierarchical levels in multiple pathways. Paralogue-specific changes in FT homologue expression and tissue-specific changes in SOC1 homologue expression were associated with loss and reversal of plasticity, respectively, suggesting that redundancy and modularity are gene network characteristics easily exploited by natural selection to produce evolutionary innovation. Distinct genetic mechanisms contribute to convergent evolution of photoperiod responses within sunflower, suggesting regulatory network architecture does not impose strong constraints on the evolution of phenotypic plasticity.     

Duplicate gene expression in allopolyploid <Emphasis Type="Italic">Gossypium</Emphasis>reveals two temporally distinct phases of expression evolution

Background  

Polyploidy has played a prominent role in shaping the genomic architecture of the angiosperms. Through allopolyploidization, several modern Gossypium (cotton) species contain two divergent, although largely redundant genomes. Owing to this redundancy, these genomes can play host to an array of evolutionary processes that act on duplicate genes.     

Rapid Transition towards the Division of Labor via Evolution of Developmental Plasticity

A crucial step in several major evolutionary transitions is the division of labor between components of the emerging higher-level evolutionary unit. Examples include the separation of germ and soma in simple multicellular organisms, appearance of multiple cell types and organs in more complex organisms, and emergence of casts in eusocial insects. How the division of labor was achieved in the face of selfishness of lower-level units is controversial. I present a simple mathematical model describing the evolutionary emergence of the division of labor via developmental plasticity starting with a colony of undifferentiated cells and ending with completely differentiated multicellular organisms. I explore how the plausibility and the dynamics of the division of labor depend on its fitness advantage, mutation rate, costs of developmental plasticity, and the colony size. The model shows that the transition to differentiated multicellularity, which has happened many times in the history of life, can be achieved relatively easily. My approach is expandable in a number of directions including the emergence of multiple cell types, complex organs, or casts of eusocial insects.     

Sperm competition can drive a male-biased mutation rate

A pattern of male-biased mutation has been found in a wide range of species. The standard explanation for this bias is that there are greater numbers of mitotic cell divisions in the history of the average sperm, compared to the average egg, and that mutations typically result from errors made during replication. However, this fails to provide an ultimate evolutionary explanation for why the male germline would tolerate more mutations that are typically deleterious. One possibility is that if there is a tradeoff between producing large numbers of sperm and expending energetic resources in maintaining a lower mutation rate, sperm competition would select for males that produce larger numbers of sperm despite a higher resulting mutation rate. Here I describe a model that jointly considers the fitness consequences of deleterious mutation and mating success in the face of sperm competition. I show that a moderate level of sperm competition can account for the observation that the male germline tolerates a higher mutation rate than the female germline.