Biomedical subjects

Eric J Deeds

Publications and source records attributed to Eric J Deeds.

4 recordsLinked to original sources

PubMed2004

Semiconservative replication in the quasispecies model.

This paper extends Eigen's quasispecies equations to account for the semiconservative nature of DNA replication. We solve the equations in the limit of infinite sequence length for the simplest case of a static, sharply peaked fitness landscape. We show that the error catastrophe occurs when micro, the product of sequence length and per base pair mismatch probability, exceeds 2 ln [2/ ( 1+1/k ) ], where k>1 is the first-order growth rate constant of the viable "master" sequence (with all other sequences having a first-order growth rate constant of 1 ). This is in contrast to the result of ln k for conservative replication. In particular, as k--> infinity, the error catastrophe is never reached for conservative replication, while for semiconservative replication the critical micro approaches 2 ln 2. Semiconservative replication is therefore considerably less robust than conservative replication to the effect of replication errors. We also show that the mean equilibrium fitness of a semiconservatively replicating system is given by k ( 2 e(-micro/2) -1 ) below the error catastrophe, in contrast to the standard result of k e(-micro) for conservative replication (derived by Kimura and Maruyama in 1966). From this result it is readily shown that semiconservative replication is necessary to account for the observation that, at sufficiently high mutagen concentrations, faster replicating cells will die more quickly than more slowly replicating cells. Thus, in contrast to Eigen's original model, the semiconservative quasispecies equations are able to provide a mathematical basis for explaining the efficacy of mutagens as chemotherapeutic agents.

Base Pair Mismatch↗

PubMed2004

Proteomic traces of speciation.

Recent work has shown that the network of structural similarity between protein domains exhibits a power-law distribution of edges per node. The scale-free nature of this graph, termed the protein domain universe graph or PDUG, may be reproduced via a divergent model of structural evolution. The performance of this model, however, does not preclude the existence of a successful convergent model. To further resolve the issue of protein structural evolution, we explore the predictions of both convergent and divergent models directly. We show that when nodes from the PDUG are partitioned into subgraphs on the basis of their occurrence in the proteomes of particular organisms, these subgraphs exhibit a scale-free nature as well. We explore a simple convergent model of structural evolution and find that the implications of this model are inconsistent with features of these organismal subgraphs. Importantly, we find that biased convergent models are inconsistent with our data. We find that when speciation mechanisms are added to a simple divergent model, subgraphs similar to the organismal subgraphs are produced, demonstrating that dynamic models can easily explain the distributions of structural similarity that exist within proteomes. We show that speciation events must be included in a divergent model of structural evolution to account for the non-random overlap of structural proteomes. These findings have implications for the long-standing debate over convergent and divergent models of protein structural evolution, and for the study of the evolution of organisms as a whole.

Bacterial Proteins↗

PubMed2003

Equilibrium distribution of mutators in the single fitness peak model.

This Letter develops an analytically tractable model for determining the equilibrium distribution of mismatch repair deficient strains in unicellular populations. The approach is based on the single fitness peak model, which has been used in Eigen's quasispecies equations in order to understand various aspects of evolutionary dynamics. As with the quasispecies model, our model for mutator-nonmutator equilibrium undergoes a phase transition in the limit of infinite sequence length. This "repair catas-trophe" occurs at a critical repair error probability of epsilon(r)=L(via)/L, where L(via) denotes the length of the genome controlling viability, while L denotes the overall length of the genome. The repair catastrophe therefore occurs when the repair error probability exceeds the fraction of deleterious mutations. Our model also gives a quantitative estimate for the equilibrium fraction of mutators in Escherichia coli.

Base Pair Mismatch↗

PubMed2003

Protein evolution within a structural space.

Understanding of the evolutionary origins of protein structures represents a key component of the understanding of molecular evolution as a whole. Here we seek to elucidate how the features of an underlying protein structural "space" might impact protein structural evolution. We approach this question using lattice polymers as a completely characterized model of this space. We develop a measure of structural comparison of lattice structures that is analogous to the one used to understand structural similarities between real proteins. We use this measure of structural relatedness to create a graph of lattice structures and compare this graph (in which nodes are lattice structures and edges are defined using structural similarity) to the graph obtained for real protein structures. We find that the graph obtained from all compact lattice structures exhibits a distribution of structural neighbors per node consistent with a random graph. We also find that subgraphs of 3500 nodes chosen either at random or according to physical constraints also represent random graphs. We develop a divergent evolution model based on the lattice space which produces graphs that, within certain parameter regimes, recapitulate the scale-free behavior observed in similar graphs of real protein structures.

Amino Acid Sequence↗