Similarity between average distance maps of structurally homologous proteins

A similarity between average distance maps (Kikuchiet al., 1988a)—that is, predicted contact maps of two tertiary structurally homologous proteins—is examined. Comparisons of shapes of average distance maps (we refer to this as ADM) are made by superpositions of ADMs for two homologous proteins. Also, we compare shapes of actual contact maps for the pair of proteins. We search a optimal superposition mode of each pair of maps showing that two proteins are most similar. It is concluded that two ADMs are also similar when actual tertiary structures between two proteins show similarity. A criterion for similarity of maps is also proposed. The possibility of application of this method to detect weak homology between protein structures is discussed.     

On certain homologies between proteins

Summary Using, in part, comparisons between reconstructed ancestral sequences, homologies are suggested between certain proteins. Genetically related groups seem to be: 1. pancreatic and bacterial nucleases, 2. lysozymes and subtilisins, 3. c type cytochromes, ferredoxins and rubredoxins, 4. b type cytochromes, myoglobins and hemoglobins, catalase, and glutamic dehydrogenase. These homologies suggest that a given ancestral sequence can evolve into quite different tertiary structures.     

Towards optimal distance functions for stochastic substitution models

Distance based reconstruction methods of phylogenetic trees consist of two independent parts: first, inter-species distances are inferred assuming some stochastic model of sequence evolution; then the inferred distances are used to construct a tree. In this paper we concentrate on the task of inter-species distance estimation. Specifically, we characterize the family of valid distance functions for the assumed substitution model and show that deliberate selection of distance function significantly improves the accuracy of distance estimates and, consequently, also improves the accuracy of the reconstructed tree.Our contribution consists of three parts: first, we present a general framework for constructing families of additive distance functions for stochastic evolutionary models. Then, we present a method for selecting (near) optimal distance functions, and we conclude by presenting simulation results which support our theoretical analysis.     

A method for determining overall protein fold from NMR distance restraints

Summary We describe a simple method for determining the overall fold of a polypeptide chain from NOE-derived distance restraints. The method uses a reduced representation consisting of two particles per residue, and a force field containing pseudo-bond and pseudo-angle terms, an electrostatic term, but no van der Waals or hard shell repulsive terms. The method is fast and robust, requiring relatively few distance restraints to approximate the correct fold, and the correct mirror image is readily determined. The method is easily implemented using commercially available molecular modeling software.     

Computer comparison of new and existing criteria for constructing evolutionary trees from sequence data

Summary Three new methods for constructing evolutionary trees from molecular sequence data are presented. These methods are based on a theory for correcting for non-constant evolutionary rates (Klotz et al. 1979; Klotz and Blanken 1981). Extensive computer simulations were run to compare these new methods to the commonly used criteria of Dayhoff (1978) and Fitch and Margoliash (1967). The results of these simulations showed that two of the new methods performed as well as Dayhoff's criterion, significantly better than that of Fitch and Margoliash, and as well as a simple variation of the latter (Prager and Wilson 1978) where any topology containing negative branch mutations is discarded. However, no method yielded the correct topology all of the time, which demonstrated the need to determine confidence estimates in a particular result when evolutionary trees are determined from sequence data.     

On the stock estimation for some fishery systems

In this work we address the stock estimation problem for two fishery models. We show that a tool from nonlinear control theory called “observer” can be helpful to deal with the resource stock estimation in the field of renewable resource management. It is often difficult or expensive to measure all the state variables characterising the evolution of a given population system, therefore the question arises whether from the observation of certain indicators of the considered system, the whole state of the population system can be recovered or at least estimated. The goal of this paper is to show how some techniques of control theory can be applied for the approximate estimation of the unmeasurable state variables using only the observed data together with the dynamical model describing the evolution of the system. More precisely we shall consider two fishery models and we shall show how to built for each model an auxiliary dynamical system (the observer) that uses the available data (the total of caught fish) and which produces a dynamical estimation of the unmeasurable stock state x(t). Moreover the convergence speed of towards x(t) can be chosen.     

The origin of the tRNA molecule: Independent data favor a specific model of its evolution

The properties, historical and empirical observations of a model of the origin of the tRNA molecule are discussed. This model would predict that this molecule originated by means of the assembly of two hairpin-like structures of RNA. The conclusion is that the model possesses a relevant part of the truth on the origin of the tRNA molecule.     

A stochastic model of evolutionary dynamics with deterministic large-population asymptotics

An evolutionary birth-death process is proposed as a model of evolutionary dynamics. Agents residing in a continuous spatial environment X, play a game G, with a continuous strategy set S, against other agents in the environment. The agents’ positions and strategies continuously change in response to other agents and to random effects. Agents spawn asexually at rates that depend on their current fitness, and agents die at rates that depend on their local population density. Agents’ individual evolutionary trajectories in X and S are governed by a system of stochastic ODEs. When the number of agents is large and distributed in a smooth density on (X,S), the collective dynamics of the entire population is governed by a certain (deterministic) PDE, which we call a fitness-diffusion equation.     

A simple quantitative model of the molecular clock

Summary We present the ideas, and their motivation, at the basis of a simple model of nucleic acid evolution: thestationary Markov process, or Markov clock. After a brief review of its relevant mathematical properties, the Markov clock is applied to nucleotide sequences from mitochondrial and nuclear genes of different species. Particular emphasis is given to the necessity of carrying out a correct statistical analysis, which allows us to check quantitatively the applicability of our model. We find evidence that the Markov clock ticks in many different processes, and that its limitations can be understood in terms of a simple idea that we call the base-drift hypothesis. This hypothesis correlates the deviations from the stationarity of the Markov process to the evolutionary distanced _AB ^(P) of two species A and B, relative to the processP. We conclude by discussing the implications of our findings for future work.     

Quaternary structure predictions and estimation of mutational effects on the free energy of dimerization of the OMPLA protein

This study represents an extension to the outer membrane phospholipase A protein (OMPLA) of the docking-based protocols previously developed for quaternary structure predictions of transmembrane oligomeric proteins and for estimating mutational effects on the thermodynamics of protein–protein and protein–DNA association.Predictions of the likely architecture of OMPLA homo-dimers were carried out on 31 different forms of the monomer, 30 of which were variants of the unbound state. In all the test cases but the ones characterized by combined deletions of the 98–110 and 145–153 segments (L2 and L3, respectively), native-like complexes could be predicted, independent of the bound or unbound state of the structural model, of side chain conformation and presence or absence of amino acid deletions at the putative inter-monomer interface.The protocol for estimating mutational effects on the thermodynamics of protein–protein association proved effective as well. In fact, it was possible to estimate correctly the effects of five mutants on the free energy of dimerization of the sulfonylated form of OMPLA.The integrity of L2 and either one of the L1, L3 and L4 loops turned out to be more important than sulfonylation for the achievement of the native dimeric architecture. On the other hand, sulfonylation seems to be essential for a favorable dimerization energetics.     

On the cysteine and cystine content of proteins

Summary Analysis of published data on the cysteine and half-cystine content of proteins indicates that most intracellular proteins may be classified as sulfhydryl proteins (those containing cysteine but little or no half-cystine) and that such sulf-hydryl proteins have a low cysteine content. The mean cysteine content found for 32 intracellular mammalian proteins was 1.6 % and intracellular proteins of many bacteria have similar or lower values. Extracellular mammalian proteins are primarily disulfide proteins (those containing half-cystine but little or no cysteine) and have a high half-cystine content, the mean value found for some 34 extracellular mammalian proteins being 4.1 %. This is contrasted with many of the extracellular proteins from facultative bacteria which are cyst(e)ine-free proteins, being lacking in both cysteine and half-cystine. These and related observations are interpreted in terms of the evolution of life in a reducing atmosphere and the subsequent transition to an oxidizing environment. It is suggested that disulfide proteins evolved primarily after the accumulation of oxygen in the atmosphere.     

Intrinsic nature of the three-dimensional structure of proteins as determined by distance geometry with good sampling properties

Summary A protocol for distance geometry calculation is shown to have excellent sampling properties in the determination of three-dimensional structures of proteins from nuclear magnetic resonance (NMR) data. This protocol uses a simulated annealing optimization employing mass-weighted molecular dynamics in four-dimensional space (Havel, T.F. (1991) Prog. Biophys. Mol. Biol., 56, 43–78). It attains an extremely large radius of convergence, allowing a random coil conformation to be used as the initial estimate for the succeeding optimization process. Computations are performed with four systems of simulated distance data as tests of the protocol, using an unconstrained l-alanine 30mer and three different types of proteins, bovine pancreatic trypsin inhibitor, the -amylase inhibitor Tendamistat, and the N-terminal domain of the 434-repressor. The test of the unconstrained polypeptide confirms that the sampled conformational space is that of the statistical random coil. In the larger and more complicated systems of the three proteins, the protocol gives complete convergence of the optimization without any trace of initial structure dependence. As a result of an exhaustive conformational sampling by the protocol, the intrinsic nature of the structures generated with distance restraints derived from NMR data has been revealed. When the sampled structures are compared with the corresponding X-ray structures, we find that the averages of the sampled structures always show a certain pattern of discrepancy from the X-ray structure. This discrepancy is due to the short distance nature of the distance restraints, and correlates with the characteristic shape of the protein molecule.Abbreviations r.m.s.d. root-mean-square deviation - MD molecular dynamics - NMR nuclear magnetic resonance - NOE nuclear Overhauser enhancement - BPTI bovine pancreatic trypsin inhibitor     

A stochastic model for estimation of mutation rates in multiple-replication proliferation processes

In this paper we propose a stochastic model based on the branching process for estimation and comparison of the mutation rates in proliferation processes of cells or microbes. We assume in this model that cells or microbes (the elements of a population) are reproduced by generations and thus the model is more suitably applicable to situations in which the new elements in a population are produced by older elements from the previous generation rather than by newly created elements from the same current generation. Cells and bacteria proliferate by binary replication, whereas the RNA viruses proliferate by multiple replication. The model is in terms of multiple replications, which includes the special case of binary replication. We propose statistical procedures for estimation and comparison of the mutation rates from data of multiple cultures with divergent culture sizes. The mutation rate is defined as the probability of mutation per replication per genome and thus can be assumed constant in the entire proliferation process. We derive the number of cultures for planning experiments to achieve desired accuracy for estimation or desired statistical power for comparing the mutation rates of two strains of microbes. We establish the efficiency of the proposed method by demonstrating how the estimation of mutation rates would be affected when the culture sizes were assumed similar but actually diverge.      

Overrepresentation of interactions between homologous proteins in interactomes

It is well proved that the probability that a protein interacts with itself is higher than that it interacts with another protein. It has been recently shown that the probability of interaction is also higher for proteins with significant sequence similarity. In this paper we show that proteins sharing identical PFAM domains interact more often than expected by chance in Saccharomyces cerevisiae and Escherichia coli. We also analyze the variety of domain interfaces used by homologous proteins to interact and show that the overrepresentation of interactions between homological proteins is not caused by small number of pairs of identical "sticky domains" shared between interacting proteins.