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PubMedDate not supplied

Evolution and analysis of model CPGs for walking: II. General principles and individual variability.

Are there general principles for pattern generation? We examined this question by analyzing the operation of large populations of evolved model central pattern generators (CPGs) for walking. Three populations of model CPGs were evolved, containing three, four, or five neurons. We identified six general principles. First, locomotion performance increased with the number of interneurons. Second, the top 10 three-, four-, and five-neuron CPGs could be decomposed into dynamical modules, an abstract description developed in a companion article. Third, these dynamical modules were multistable: they could be switched between multiple stable output configurations. Fourth, the rhythmic pattern generated by a CPG could be understood as a closed chain of successive destabilizations of one dynamical module by another. A combinatorial analysis enumerated the possible dynamical modular structures. Fifth, one-dimensional modules were frequently observed and, in some cases, could be assigned specific functional roles. Finally, dynamic dynamical modules, in which the modular structure itself changed over one cycle, were frequently observed. The existence of these general principles despite significant variability in both patterns of connectivity and neural parameters was explained by degeneracy in the maps from neural parameters to neural dynamics to behavior to fitness. An analysis of the biomechanical properties of the model body was essential for relating neural activity to behavior. Our studies of evolved model circuits suggest that, in the absence of other constraints, there is no compelling reason to expect neural circuits to be functionally decomposable as the number of interneurons increase. Analyzing idealized model pattern generators may be an effective methodology for gaining insights into the operation of biological pattern generators.

Algorithms↗
PubMedDate not supplied

Evolution and analysis of model CPGs for walking: I. Dynamical modules.

Can one develop an abstract description of the dynamics of pattern generators that provides quantitative insight into their operation? We explored this question by examining the dynamics of a model central pattern generator that was created using an evolutionary algorithm. We propose an abstract description based on the concept of a dynamical module, a set of neurons that simultaneously make their transitions from one quasistable state to another while the synaptic inputs that they receive from other neurons remain essentially constant, thus temporarily reducing the dimensionality of the circuit dynamics. Using the mathematical tools of dynamical systems theory, we describe a method for identifying dynamical modules and demonstrate that this concept can be used to quantitatively characterize constraints on neural architecture, account for phase durations, and predict the effects of parameter changes. Moreover, this abstract description reveals coordinated parameter changes that leave the overall circuit dynamics essentially unchanged. In a companion article we employ this abstract description to examine the relationship between general principles and individual variability in large populations of evolved model pattern generators.

Gait↗
PubMed2003

Tertiary trisomics in the garden pea as a model of B chromosome evolution in plants.

It is hypothesized that, in plants, genetically empty B chromosomes may originate from the extra chromosome (E) of tertiary trisomics if (i) the region of basic chromosomes homologous to the E (H-region) harbors a sporophytic lethal covered by the wild-type allele in E, and (ii) crossing-over between E and the H-region is suppressed. Under these conditions, most loss-of-function mutations occurring in the H-region are deleterious for haploid gametophytes, whereas those occurring in E are neutral or advantageous for hyperploid (n+1) gametophytes. As a result, natural selection at the gametophyte level can lead to the degeneration of E, leaving the H-region intact. Using Hammarlund translocation T(3-6)a, we synthesized two trisomic lines of the garden pea (Pisum sativum L.), where E was composed of the short arms of chromosomes 3 and 6 and the H-region carried recessive markers. In the trisomic line TRIS, we found few crossovers between E and the H-region. In the trisomic line TRUST, obtained after a change of basic chromosome constitution, recombination in this region was completely suppressed. After induction in the H-region of TRUST of a recessive sporophytic mutation rmv, two 15-chromosome lines of stable trisomics were established. One of them passed 11 generations, having produced more than 6000 individuals, all of them trisomic, and E remained present as a single element with no pairing partners. No tetrasomics were detected in these lines. If such trisomics occurred in nature, their extra chromosomes are likely to become a B chromosome.

Chromosomes, Plant↗
PubMed2002

Evolutionary and statistical properties of three genetic distances.

Many genetic distances have been developed to summarize allele frequency differences between populations. I review the evolutionary and statistical properties of three popular genetic distances: DS, DA, and theta;, using computer simulation of two simple evolutionary histories: an isolation model of population divergence and an equilibrium migration model. The effect of effective population size, mutation rate, and mutation mechanism upon the parametric value between pairs of populations in these models explored, and the unique properties of each distance are described. The effect of these evolutionary parameters on study design is also investigated and similar results are found for each genetic distance in each model of evolution: large sample sizes are warranted when populations are relatively genetically similar; and loci with more alleles produce better estimates of genetic distance.

Computer Simulation↗
PubMed2004

Bayesian Markov chain Monte Carlo sequence analysis reveals varying neutral substitution patterns in mammalian evolution.

We describe a model of neutral DNA evolution that allows substitution rates at a site to depend on the two flanking nucleotides ("context"), the branch of the phylogenetic tree, and position within the sequence and implement it by using a flexible and computationally efficient Bayesian Markov chain Monte Carlo approach. We then apply this approach to characterize phylogenetic variation in context-dependent substitution patterns in a 1.7-megabase genomic region in 19 mammalian species. In contrast to other substitution types, CpG transition substitutions have accumulated in a relatively clock-like fashion. More broadly, our results support the notion that context-dependent DNA replication errors, cytosine deamination, and biased gene conversion are major sources of naturally occurring mutations whose relative contributions have varied in mammalian evolution as a result of changes in generation times, effective population sizes, and recombination rates.

Animals↗
PubMed1994

A discrete Fourier analysis for evolutionary trees.

Discrete Fourier transformations have recently been developed to model the evolution of two-state characters (the Cavender/Farris model). We report here the extension of these transformations to provide invertible relationships between a phylogenetic tree T (with three probability parameters of nucleotide substitution on each edge corresponding to Kimura's 3ST model) and the expected frequencies of the nucleotide patterns in the sequences. We refer to these relationships as spectral analysis. In either model with independent and identically distributed site substitutions, spectral analysis allows a global correction for all multiple substitutions (second- and higher-order interactions), independent of any particular tree. From these corrected data we use a least-squares selection procedure, the closest tree algorithm, to infer an evolutionary tree. Other selection criteria such as parsimony or compatibility analysis could also be used; each of these criteria will be statistically consistent for these models. The closest tree algorithm selects a unique best-fit phylogenetic tree together with independent edge length parameters for each edge. The method is illustrated with an analysis of some primate hemoglobin sequences.

Animals↗
PubMedDate not supplied

Scaling laws and similarity detection in sequence alignment with gaps.

We study the problem of similarity detection by sequence alignment with gaps, using a recently established theoretical framework based on the morphology of alignment paths. Alignments of sequences without mutual correlations are found to have scale-invariant statistics. This is the basis for a scaling theory of alignments of correlated sequences. Using a simple Markov model of evolution, we generate sequences with well-defined mutual correlations and quantify the fidelity of an alignment in an unambiguous way. The scaling theory predicts the dependence of the fidelity on the alignment parameters and on the statistical evolution parameters characterizing the sequence correlations. Specific criteria for the optimal choice of alignment parameters emerge from this theory. The results are verified by extensive numerical simulations.

Algorithms↗
PubMed2002

Fast recovery of evolutionary trees with thousands of nodes.

We present a novel distance-based algorithm for evolutionary tree reconstruction. Our algorithm reconstructs the topology of a tree with n leaves in O(n(2)) time using O(n) working space. In the general Markov model of evolution, the algorithm recovers the topology successfully with (1 - o(1)) probability from sequences with polynomial length in n. Moreover, for almost all trees, our algorithm achieves the same success probability on polylogarithmic sample sizes. The theoretical results are supported by simulation experiments involving trees with 500, 1,895, and 3,135 leaves. The topologies of the trees are recovered with high success from 2,000 bp DNA sequences.

Algorithms↗
PubMed1996

Beta-blockade in the management of chronic heart failure. Another step in the conceptual evolution of a neurohormonal model of the disease.

Although heart failure has been viewed primarily as a haemodynamic disorder, the development of pharmacologic agents that address the haemodynamic derangements has not proved to be a successful approach to its management. Consequently, attention in recent years has shifted to the development of neurohormonal antagonists in the hope that prolonged interference with the renin-angiotensin system and the sympathetic nervous system would have favourable effects on the natural history of heart failure. Both converting-enzyme inhibitors and beta-adrenergic blockers have been shown to produce long-term haemodynamic and clinical benefits in patients with left ventricular systolic dysfunction in controlled clinical trials. For both classes of drugs, the improvement evolves gradually over several months, although initiation of therapy may be accompanied by undesirable (but usually transient) haemodynamic effects. This pattern of response contrasts sharply with the response pattern seen with direct-acting vasodilators that stimulate neurohormonal systems (e.g. flosequinan). Initiation of treatment with flosequinan produces immediate clinical benefits due to the haemodynamic actions of the drug, but this improvement may disappear within weeks as a result of neurohormonal activation, which also may contribute to the increased risk of death seen during long-term administration of the drug. Recognition of the prognostic importance of neurohormonal activation has led to the hope that long-term treatment with beta-blockers might reduce mortality in heart failure in a manner similar to that seen with converting-enzyme inhibitors. Large-scale, long-term studies are being planned to evaluate this possibility.

Adrenergic beta-Antagonists↗