Connectivity of Neutral Networks,Overdispersion, and Structural Conservation in Protein Evolution

Abstract Protein structures are much more conserved than sequences during evolution. Based on this observation, we investigate the consequences of structural conservation on protein evolution. We study seven of the most studied protein folds, determining that an extended neutral network in sequence space is associated with each of them. Within our model, neutral evolution leads to a non-Poissonian substitution process, due to the broad distribution of connectivities in neutral networks. The observation that the substitution process has non-Poissonian statistics has been used to argue against the original Kimura neutral theory, while our model shows that this is a generic property of neutral evolution with structural conservation. Our model also predicts that the substitution rate can strongly fluctuate from one branch to another of the evolutionary tree. The average sequence similarity within a neutral network is close to the threshold of randomness, as observed for families of sequences sharing the same fold. Nevertheless, some positions are more difficult to mutate than others. We compare such structurally conserved positions to positions conserved in protein evolution, suggesting that our model can be a valuable tool to distinguish structural from functional conservation in databases of protein families. These results indicate that a synergy between database analysis and structurally based computational studies can increase our understanding of protein evolution.     

Molecular modeling and mutagenesis of the ligand-binding pocket of the mGlu3 subtype of metabotropic glutamate receptor

A homology model of the extracellular domain of the mGlu3 subtype of metabotropic glutamate (mGlu) receptor was generated and tested using site-directed mutagenesis, a radioligand-binding assay using the Group II selective agonist (2S,2'R,3'R)-2-(2',3'-[3H]dicarboxycyclopropyl) glycine ([3H]DCG-IV), and in a fluorescence-based functional assay in live transiently transfected human embryonic kidney cells. Ten of the 12 mGlu3 mutants (R64A, R68A, Y150A, S151A, T174A, D194A, Y222A, R277A, D301A and K389) showed either no binding or a 90% or greater loss of specific [3H]DCG-IV binding. Several analogous mutations in mGlu2 supported the results obtained with mGlu3. These results demonstrate that the binding of [3H]DCG-IV to mGlu3 is exceptionally sensitive to mutagenesis-induced perturbations. In silico docking of DCG-IV into the agonist binding pocket of mGlu3 facilitated the interpretation the mutagenesis results. Tyrosines 150 and 222, and arginine 277 show close contacts with the third carboxylic acid group in DCG-IV, which is not present in glutamate or (2S,1'S,2'S)-2-(carboxycyclopropyl)glycine (L-CCG-I). Mutation of these three amino acids to alanine resulted in a near complete loss of receptor activation by DCG-IV and retention of near wild-type affinity for L-CCG-I. It is proposed that hydrogen bonding between this carboxylate and tyrosines 150 and 222 and arginine 277 provide a partial explanation for the high affinity and Group II selectivity of DCG-IV. These findings define the essential features of the ligand-binding pocket of mGlu3 and, together with other recent studies on mGlu receptors, provide new opportunities for structure-based drug design.     

A logistic branching process for population genetics

A logistic (regulated population size) branching process population genetic model is presented. It is a modification of both the Wright-Fisher and (unconstrained) branching process models, and shares several properties including the coalescent time and shape, and structure of the coalescent process with those models. An important feature of the model is that population size fluctuation and regulation are intrinsic to the model rather than externally imposed. A consequence of this model is that the fluctuation in population size enhances the prospects for fixation of a beneficial mutation with constant relative viability, which is contrary to a result for the Wright-Fisher model with fluctuating population size. Explanation of this result follows from distinguishing between expected and realized viabilities, in addition to the contrast between absolute and relative viabilities.     

Random Fields Approach to the Study of DNA Chains

We apply the random field theory tothe study of DNA chains which we assume tobe trajectories of a stochastic process. Weconstruct statistical potential betweennucleotides corresponding to theprobabilities of those trajectories thatcan be obtained from the DNA data basecontaining millions of sequences. It turnsout that this potential has aninterpretation in terms of quantitiesnaturally arrived at during the study ofevolution of species i.e. probabilities ofmutations of codons. Making use of recentlyperformed statistical investigations of DNAwe show that this potential has differentqualitative properties in coding andnoncoding parts of genes. We apply ourmodel to data for various organisms andobtain a good agreement with the resultsjust presented in the literature. We alsoargue that the coding/noncoding boundariescan corresponds to jumps of the potential.     

The frequency spectrum of a mutation,and its age,in a general diffusion model

General formulae are derived for the probability density and expected age of a mutation of frequency x in a population, and similarly for a mutation with b copies in a sample of n genes. A general formula is derived for the frequency spectrum of a mutation in a sample. Variable population size models are included. Results are derived in two frameworks: diffusion process models for the frequency of the mutation; and birth and death process models. The coalescent structure within the mutant gene group and the non-mutant group is considered.     

Biochemical evidence for a calcium-dependent protein kinase from Pharbitis nil and its involvement in photoperiodic flower induction

A soluble Ca(2+)-dependent protein kinase (CDPK) was isolated from seedlings of the short-day plant Pharbitis nil and purified to homogeneity. Activity of Pharbitis nil CDPK (PnCDPK) was strictly dependent on the presence of Ca(2+) (K(0,5)=4,9 microM). The enzyme was autophosphorylated on serine and threonine residues and phosphorylated a wide diversity of substrates only on serine residues. Histone III-S and syntide-2 were the best phosphate acceptors (K(m) for histone III-S=0,178 mg ml(-1)). Polyclonal antibodies directed to a regulatory region of the soybean CDPK recognized 54 and 62 kDa polypeptides from Pharbitis nil. However, only 54 kDa protein was able to catalyse autophosphorylation and phosphorylation of substrates in a Ca(2+)-dependent manner. CDPK autophosphorylation was high in 5-day-old Pharbitis nil seedlings grown under non-inductive continuous white light and was reduced to one-half of its original when plants were grown in the long inductive night. Also, the pattern of proteins phosphorylation has changed. After 16-h-long inductive night phosphorylation of endogenous target (specific band of 82 kDa) increased in the presence of calcium ions. It may suggest that Ca(2+)-dependent protein kinase is involved in this process and it is dependent on light/dark conditions.     

Influence of micro-landforms on forest structure,tree death and recruitment in a Japanese temperate mixed forest

The micro-landform unit system offers an effective way of analyzing vegetation–geomorphology relationships at a 10-m scale in areas such as the hilly regions of Japan. We analyzed relationships between micro-landforms and tree population parameters over a 9-year interval to elucidate the influence of geomorphic processes on vegetation dynamics. A 2.16-ha permanent plot was established in a temperate mixed forest. Each 5m×5m quadrat within this plot was classified according to six types of micro-landform units: (i) crest slope (CS); (ii) upper sideslope (US); (iii) head hollow (HH); (iv) lower sideslope (LS); (v) foot slope (FS); and (vi) river bed (RB). All living trees larger than 10cm in diameter at breast height (d.b.h.) were identified, mapped and marked in 1989 and resurveyed in 1998. Almost all of the 23 common tree species persisted in their own core habitats (i.e. the micro-landforms) between the two surveys. The species distribution in both surveys showed that the six micro-landforms could be combined into two larger groups: upper and lower hillslope areas. The upper hillslope area had higher tree densities and larger basal areas than the lower hillslope area. It is possible that these differences result from the longer lifespans of trees on the upper hillslope area rather than from differences in mortality and recruitment rates. In addition, the different ways in which trees die in the different micro-landform units may affect the regeneration process in hilly regions through different gap formation. The effects of different geomorphic processes are reflected in the lifespans of the trees and may result in different forest structure and dynamics among micro-landform units.     

How to track and assess genotyping errors in population genetics studies

Genotyping errors occur when the genotype determined after molecular analysis does not correspond to the real genotype of the individual under consideration. Virtually every genetic data set includes some erroneous genotypes, but genotyping errors remain a taboo subject in population genetics, even though they might greatly bias the final conclusions, especially for studies based on individual identification. Here, we consider four case studies representing a large variety of population genetics investigations differing in their sampling strategies (noninvasive or traditional), in the type of organism studied (plant or animal) and the molecular markers used [microsatellites or amplified fragment length polymorphisms (AFLPs)]. In these data sets, the estimated genotyping error rate ranges from 0.8% for microsatellite loci from bear tissues to 2.6% for AFLP loci from dwarf birch leaves. Main sources of errors were allelic dropouts for microsatellites and differences in peak intensities for AFLPs, but in both cases human factors were non-negligible error generators. Therefore, tracking genotyping errors and identifying their causes are necessary to clean up the data sets and validate the final results according to the precision required. In addition, we propose the outline of a protocol designed to limit and quantify genotyping errors at each step of the genotyping process. In particular, we recommend (i) several efficient precautions to prevent contaminations and technical artefacts; (ii) systematic use of blind samples and automation; (iii) experience and rigor for laboratory work and scoring; and (iv) systematic reporting of the error rate in population genetics studies.     

The distribution of the ancestral haplotype in finite stepping-stone models with population expansion

Recent extensive analyses of human DNA polymorphism reveal that the ancestral haplotype at various genetic loci occurs almost exclusively in African samples. We develop a coalescence-based simulation method in stepping-stone models with population expansion and examine the probability (P(A)) that the ancestral haplotype is found in African samples and the probability (Q(A)) that the most recent common ancestor of sampled genes occurs in Africa. These probabilities and other summary statistics are used to infer the human demographic history. It is shown that the high observed P(A) value cannot be explained simply by sampling bias. Rather, it suggests that the African population has been more strongly subdivided and isolated from each other than the non-African population and that there must have been some African populations which were not directly involved in the Out-of-Africa expansion in the late Pleistocene.     

A model explaining the size distribution of gene and protein families

This article deals with the theoretical size distribution of gene and protein families in complete genomes. A simple evolutionary model for the development of such families in which genes in a family are formed or selected against independently and at random, and in which new families are formed by the random splitting of existing families, is used to derive the resulting size distribution. Mathematically this turns out to be the distribution of the state of a homogeneous birth-and-death process after an exponentially distributed time, which it is shown will under certain conditions exhibit the power-law behaviour observed for gene and protein family sizes.