Simple model for treating evolution of multigene families.
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Among-site rate variation (alpha) and transition bias (kappa) have been shown, most often as independent parameters, to be important dynamics in DNA evolution. Accounting for these dynamics should result in better estimates of phylogenetic relationships. To test this idea, we simultaneously estimated overall (averaged over all codon positions) and codon-specific values of alpha and kappa, using maximum likelihood analyses of cytochrome b data from all genera of pipits and wagtails (Aves: Motacillidae), and six outgroup species, using initial trees generated with default values. Estimates of alpha and kappa were robust to initial tree topology and suggested substantial among-site rate variation even within codon classes; alpha was lowest (large among-site rate variation) at second-codon and highest (low among-site rate variation) at third-codon positions. When overall values were applied, there were shifts in tree topology and dramatic and statistically significant improvements in log-likelihood scores of trees compared with the scores from application of default values. Applying codon-specific values resulted in yet another highly significant increase in likelihood. However, although incorporating substitution dynamics into maximum likelihood, maximum parsimony, and neighbor-joining analyses resulted in increases in congruence among trees, there were only minor improvements in phylogenetic signal, and none of the successive approximations tree topologies were statistically distinguishable from one another by the data. We suggest that the bushlike nature of many higher-level phylogenies in birds makes estimating the dynamics of DNA evolution less sensitive to tree topology but also less susceptible to improvement via weighting.
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A simple model for the evolution of the rate of molecular evolution is presented. With a Bayesian approach, this model can serve as the basis for estimating dates of important evolutionary events even in the absence of the assumption of constant rates among evolutionary lineages. The method can be used in conjunction with any of the widely used models for nucleotide substitution or amino acid replacement. It is illustrated by analyzing a data set of rbcL protein sequences.
A conceptual model is proposed for the genetic evolution of many human solid tumors that is based on the observations that cancer cells may spontaneously double their chromosome number; that cells with excessive chromosome numbers may be cytogenetically unstable, both losing chromosomes randomly during subsequent cell divisions, and often developing structural abnormalities in the chromosomes that are retained; and that some structural chromosome abnormalities may activate growth-promoting genes. The sequence of tetraploidization with chromosome loss can occur repeatedly in a given tumor. The available evidence supporting the model is reviewed. A computer simulation system that embodies these concepts is described and the model is used to generate distributions of chromosome number/cell under various simulated conditions and in a variety of simulated biological settings. A simulation of the time course of changes in chromosome number per cell that accompany the spontaneous neoplastic transformation of mouse fibroblasts in vitro is described. The best fit to the data was obtained when provision was made for the activation of at least two growth-promoting genes. The conditions for generating discrete aneuploid peaks in cytogenetic and flow cytometric studies were explored; our modeling studies suggest that the activation of a growth promoting gene is required in order to produce a discrete aneuploid peak. Our modeling studies suggest that the overrepresentation of individual oncogene-bearing chromosomes in aneuploid cell lines may require the activation of gene dose-dependent growth-promoting genes and is not likely to occur in cell lines in which at least two copies of each normal chromosome are required for cell survival. Overall, the results obtained using the model are consistent with a wide variety of flow cytometric and cytogenetic studies in human solid tumors.
Progress in understanding the evolution of infectious diseases has inspired proposals to manage the evolution of pathogen (including parasite) virulence. A common view is that social interventions that lower pathogen transmission will indirectly select lower virulence because of a trade-off between transmission and virulence. Here, we argue that there is little theoretical justification and no empirical evidence for this plan. Although a trade-off model might apply to some pathogens, the mechanism appears too weak for rapid selection of substantial changes in virulence. Direct selection against virulence itself might be a more rewarding approach to managing the evolution of virulence.
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The evolutionary implications of the path-analysis model most often used in human behavior genetics are examined. With directional selection, a model of pure vertical environmental transmission does not respond in a fully adaptive fashion. Unless the coefficients of transmission are exactly 0.50, the population mean will not equilibrate at the selective optimum over time. If there is both genetic and vertical environmental transmission, then the population mean can equilibrate at the selective optimum. In the presence of genetic transmission, vertical environmental transmission increases population fitness and has a strong effect on the rapid movement of the mean toward the selective optimum. This raises the intriguing paradox of why empirical evidence suggests that vertical environmental transmission is usually small when it possesses such important fitness properties.
The human olfactory subgenome represents several hundred olfactory receptor (OR) genes in a dozen or more clusters on several chromosomes. One OR gene cluster on human chromosome 17 has been characterized by us in detail. Based on a large-scale DNA sequence analysis, we have identified events of gene duplication and fusion as well as the generation of pseudogenes. The latter instances of 'gene death' could underlie the widespread phenomenon of human specific anosmias. Sixteen OR coding regions were found on this cluster, and six of them are pseudogenes. One of these pseudogenes, OR17-23, was found to be an intact open reading frame in an old world monkey. This may be a reflection of an OR repertoire diminution in man. A homology model of the OR protein was constructed by utilizing the rich information available on approximately 200 OR sequences. The putative odorant complementarity determining regions (CDR) was found to consist of 20 hypervariable residues facing an interior caving defined by transmembrane helices 3, 4 and 5. Such a model could be useful in analyzing additional OR gene sequences in the human genome in terms of odorant binding.
The chicken c-ets-1 locus encodes two transcription factors, p54c-ets-1 and p68c-ets-1 that differ in their N-termini, encoded respectively by the I54 and alpha beta exons. p68c-ets-1 equivalents are only found in birds and reptiles while p54c-ets-1 is widely conserved in vertebrates, from amphibians to mammals. Thus, the classical view concerning the evolution of the c-ets-1 gene has been to consider that I54 is of ancient origin whereas alpha and beta, which provide an additional activating domain in p68c-ets-1, would have been acquired much more recently. Sequencing the alpha and beta exons in various species pinpointed a highly conserved region of 13 amino acids which is rich in acidic and hydrophobic residues, a feature of some other transactivating domains. Strikingly, this subdomain is also present in the otherwise unrelated N-terminal activating region of p58c-ets-2 and was thus named BEC for Ets-1-beta/Ets-2-Conserved sequence. Moreover, the two N-termini share the BEC sequence at a homologous position in their highly similar genomic organization indicating a common origin. This structural homology underlies a functional similarity since fusion of the heterologous GAL4 DNA-binding domain with either of the two isolated domains demonstrates that BEC is essential in both cases for the transactivating activity. The function of the alpha beta domain in the context of p68c-ets-1 also strictly depends on the presence of the BEC sequence. Finally, the whole N-terminus of p58c-ets-2 can functionally substitute for its counterpart in p68c-ets-1 further demonstrating that p68c-ets-1 and p58c-ets-2 are structurally and functionally more closely related than previously thought. Besides, we also found BEC in the N-terminus of the Drosophila pointed gene which may be considered as closely related to the uncommitted 'ets1/2' common ancestor. These data demonstrate that the alpha and beta exons are not a recent and specific acquisition but stem, like the p58c-ets-2 N-terminus, from the invertebrate unduplicated 'ets 1/2' gene. This work unravels a new model for the ets-1/ets-2 gene's evolution, based for the first time on both structural and functional evidences. Accordingly, p68c-ets-1 and p58c-ets-2 are the direct descendants of the ancestral 'ets1/2' gene whereas I54 may have been acquired as a second promoter in the c-ets-1 gene after the duplication. Indeed, I54 is not found in the Drosophila pointed gene. The high degree of similarity, and hence of functional redundancy, between p68c-ets-1 and p58c-ets-2 may have led to the rapid divergence (and even loss in mammals) of alpha and beta during evolution whereas I54, which provided a novel function unique to c-ets-1, was maintained within the presently widespread p54c-ets-1 version.
We model the non-local mechanisms of genomic evolution and propose methods for studying the evolutionary divergence of species based on these models. Mechanisms include the movement of segments of genomes within a single chromosome (transpositions), the reciprocal translocation of segments between two chromosomes, and the inversion of segments. Each of these is studied in the context of a different type of genomic data. We introduce the theory of phylogenetic invariants for evolutionary inference based on very long macromolecular sequences.
Gliomas are well known for their potential for aggressive proliferation as well as their diffuse invasion of the normal-appearing parenchyma peripheral to the bulk lesion. This review presents a history of the use of mathematical modeling in the study of the proliferative-invasive growth of gliomas, illustrating the progress made in understanding the in vivo dynamics of invasion and proliferation of tumor cells. Mathematical modeling is based on a sequence of observation, speculation, development of hypotheses to be tested, and comparisons between theory and reality. These mathematical investigations, iteratively compared with experimental and clinical work, demonstrate the essential relationship between experimental and theoretical approaches. Together, these efforts have extended our knowledge and insight into in vivo brain tumor growth dynamics that should enhance current diagnoses and treatments.
Mammalian leukotriene A4 (LTA4) hydrolase is a bifunctional zinc metalloenzyme possessing an Arg/Ala aminopeptidase and an epoxide hydrolase activity, which converts LTA4 into the chemoattractant LTB4. We have previously cloned an LTA4 hydrolase from Saccharomyces cerevisiae with a primitive epoxide hydrolase activity and a Leu aminopeptidase activity, which is stimulated by LTA4. Here we used a modeled structure of S. cerevisiae LTA4 hydrolase, mutational analysis, and binding studies to show that Glu-316 and Arg-627 are critical for catalysis, allowing us to a propose a mechanism for the epoxide hydrolase activity. Guided by the structure, we engineered S. cerevisiae LTA4 hydrolase to attain catalytic properties resembling those of human LTA4 hydrolase. Thus, six consecutive point mutations gradually introduced a novel Arg aminopeptidase activity and caused the specific Ala and Pro aminopeptidase activities to increase 24 and 63 times, respectively. In contrast to the wild type enzyme, the hexuple mutant was inhibited by LTA4 for all tested substrates and to the same extent as for the human enzyme. In addition, these mutations improved binding of LTA4 and increased the relative formation of LTB4, whereas the turnover of this substrate was only weakly affected. Our results suggest that during evolution, the active site of an ancestral eukaryotic zinc aminopeptidase has been reshaped to accommodate lipid substrates while using already existing catalytic residues for a novel, gradually evolving, epoxide hydrolase activity. Moreover, the unique ability to catalyze LTB4 synthesis appears to be the result of multiple and subtle structural rearrangements at the catalytic center rather than a limited set of specific amino acid substitutions.
Electrodes are widely used to measure bioelectric events and to stimulate excitable tissues. In one form or another, electrodes have been around for nearly two centuries; yet our ability to predict their properties is extremely limited, despite considerable research, especially during the last century. This paper chronicles the accumulation of knowledge about the electrode-electrolyte interface as a circuit element. Our understanding of this interface starts with the Helmholtz double layer of charge and progresses through the Warburg and Fricke low-current-density models, which demonstrated that the resistive and capacitive components are polarization elements, the values of which depend on frequency. The discovery by Schwan, showing that the components of the Warburg-Fricke model are current-density dependent, is recounted, along with the discovery of the rectifying properties of the electrode-electrolyte interface and how it was put to practical use. The very high current-density operation of the interface is discussed in terms of gas evolution, arching, and shock-wave production. Finally the evolution of recording electrodes is traced. Because electrodes can be operated over a very wide range of current density, it is unlikely that a single model can be created for the electrode-electrolyte interface, although over a restricted current-density range such a model may be possible.
This study develops a theoretical model for accident evolutions and how they can be arrested. The model describes the interaction between technical and human-organizational systems which may lead to an accident. The analytic tool provided by the model gives equal weight to both these types of systems and necessitates simultaneous and interactive accident analysis by engineers and human factors specialists. It can be used in predictive safety analyses as well as in post hoc incident analyses. To illustrate this, the AEB model is applied to an incident reported by the nuclear industry in Sweden. In general, application of the model will indicate where and how safety can be improved, and it also raises questions about issues such as the cost, feasibility, and effectiveness of different ways of increasing safety.
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Although the time-courses of power in the delta and sigma frequency bands over the NREM episode in the human sleep EEG have been studied for several years, and their detailed forms have been well measured, no mathematical model has yet been formulated to account for the relation between them. The model presented here attempts to explain the form and relative timing of these curves by a consideration of the behavior of the thalamocortical neuronal populations that are believed to play a part in their generation. The model applies the mathematics of the cascade radioactive decay process, adapted to a finite population of thalamocortical neurons oscillating initially in the beta mode. At the beginning of the NREM episode, each neuron of this population is assumed to acquire a constant probability of transitionning to the sigma oscillation mode and, at the same time, each neuron of the newly created sigma population is assumed to acquire a constant probability of transitionning to the delta oscillation mode. This simple model is sufficient to explain the main characteristics of the first half of the time-courses of the sigma and delta powers: the initial positive correlation as they increase together, followed by the sigma peak and the subsequent negative correlation. At the end of this first phase, the model initiates an identical, but reverse, process that reproduces the observed delta maximum and sigma plateau, followed by the concomitant fall of both sigma and delta power. The time-course of the beta power and the overall negative correlation between beta and delta are also reproduced as integral consequences of the model.
Homologous sequences are correlated due to their common ancestry. Probabilistic models of sequence evolution are employed routinely to properly account for these phylogenetic correlations. These increasingly realistic models provide a basis for studying evolution and for exploiting it to better understand protein structure and function. Notable recent advances have been made in the treatment of insertion and deletion events, the estimation of amino-acid replacement rates, and the detection of positive selection.