Usefulness of single nucleotide polymorphism data for estimating population parameters

Single nucleotide polymorphism (SNP) data can be used for parameter estimation via maximum likelihood methods as long as the way in which the SNPs were determined is known, so that an appropriate likelihood formula can be constructed. We present such likelihoods for several sampling methods. As a test of these approaches, we consider use of SNPs to estimate the parameter Theta = 4N(e)micro (the scaled product of effective population size and per-site mutation rate), which is related to the branch lengths of the reconstructed genealogy. With infinite amounts of data, ML models using SNP data are expected to produce consistent estimates of Theta. With finite amounts of data the estimates are accurate when Theta is high, but tend to be biased upward when Theta is low. If recombination is present and not allowed for in the analysis, the results are additionally biased upward, but this effect can be removed by incorporating recombination into the analysis. SNPs defined as sites that are polymorphic in the actual sample under consideration (sample SNPs) are somewhat more accurate for estimation of Theta than SNPs defined by their polymorphism in a panel chosen from the same population (panel SNPs). Misrepresenting panel SNPs as sample SNPs leads to large errors in the maximum likelihood estimate of Theta. Researchers collecting SNPs should collect and preserve information about the method of ascertainment so that the data can be accurately analyzed.     

A note on the rationale for estimating genealogical coancestry from molecular markers

Background

Genetic relatedness or similarity between individuals is a key concept in population, quantitative and conservation genetics. When the pedigree of a population is available and assuming a founder population from which the genealogical records start, genetic relatedness between individuals can be estimated by the coancestry coefficient. If pedigree data is lacking or incomplete, estimation of the genetic similarity between individuals relies on molecular markers, using either molecular coancestry or molecular covariance. Some relationships between genealogical and molecular coancestries and covariances have already been described in the literature.

Methods

We show how the expected values of the empirical measures of similarity based on molecular marker data are functions of the genealogical coancestry. From these formulas, it is easy to derive estimators of genealogical coancestry from molecular data. We include variation of allelic frequencies in the estimators.

Results

The estimators are illustrated with simulated examples and with a real dataset from dairy cattle. In general, estimators are accurate and only slightly biased. From the real data set, estimators based on covariances are more compatible with genealogical coancestries than those based on molecular coancestries. A frequently used estimator based on the average of estimated coancestries produced inflated coancestries and numerical instability. The consequences of unknown gene frequencies in the founder population are briefly discussed, along with alternatives to overcome this limitation.

Conclusions

Estimators of genealogical coancestry based on molecular data are easy to derive. Estimators based on molecular covariance are more accurate than those based on identity by state. A correction considering the random distribution of allelic frequencies improves accuracy of these estimators, especially for populations with very strong drift.     

The molecular chaperone, ClpA, has a single high affinity peptide binding site per hexamer

Substrate recognition by Clp chaperones is dependent on interactions with motifs composed of specific peptide sequences. We studied the binding of short motif-bearing peptides to ClpA, the chaperone component of the ATP-dependent ClpAP protease of Escherichia coli in the presence of ATPgammaS and Mg2+ at pH 7.5. Binding was measured by isothermal titration calorimetry (ITC) using the peptide, AANDENYALAA, which corresponds to the SsrA degradation motif found at the C terminus of abnormal nascent polypeptides in vivo. One SsrA peptide was bound per hexamer of ClpA with an association constant (K(A)) of 5 x 10(6) m(-1). Binding was also assayed by changes in fluorescence of an N-terminal dansylated SsrA peptide, which bound with the same stoichiometry of one per ClpA hexamer (K(A) approximately 1 x 10(7) m(-1)). Similar results were obtained when ATP was substituted for ATPgammaS at 6 degrees C. Two additional peptides, derived from the phage P1 RepA protein and the E. coli HemA protein, which bear different substrate motifs, were competitive inhibitors of SsrA binding and bound to ClpA hexamers with K(A)' > 3 x 10(7) m(-1). DNS-SsrA bound with only slightly reduced affinity to deletion mutants of ClpA missing either the N-terminal domain or the C-terminal nucleotide-binding domain, indicating that the binding site for SsrA lies within the N-terminal nucleotide-binding domain. Because only one protein at a time can be unfolded and translocated by ClpA hexamers, restricting the number of peptides initially bound should avoid nonproductive binding of substrates and aggregation of partially processed proteins.     

Chemical basis for the affinity maturation of a camel single domain antibody

Affinity maturation of classic antibodies supposedly proceeds through the pre-organization of the reactive germ line conformational isomer. It is less evident to foresee how this can be accomplished by camelid heavy-chain antibodies lacking light chains. Although these antibodies are subjected to somatic hypermutation, their antigen-binding fragment consists of a single domain with restricted flexibility in favor of binding energy. An antigen-binding domain derived from a dromedary heavy-chain antibody, cAb-Lys3, accumulated five amino acid substitutions in CDR1 and CDR2 upon maturation against lysozyme. Three of these residues have hydrophobic side chains, replacing serines, and participate in the hydrophobic core of the CDR1 in the mature antibody, suggesting that conformational rearrangements might occur in this loop during maturation. However, transition state analysis of the binding kinetics of mature cAb-Lys3 and germ line variants show that the maturation of this antibody relies on events late in the reaction pathway. This is reflected by a limited perturbation of k(a) and a significantly decreased k(d) upon maturation. In addition, binding reactions and the maturation event are predominantly enthalpically driven. Therefore, maturation proceeds through the increase of favorable binding interactions, or by the reduction of the enthalpic penalty for desolvation, as opposed to large entropic penalties associated with conformational changes and structural plasticity. Furthermore, the crystal structure of the mutant with a restored germ line CDR2 sequence illustrates that the matured hydrophobic core of CDR1 in cAb-Lys3 might be compensated in the germ line precursor by burying solvent molecules engaged in a stable hydrogen-bonding network with CDR1 and CDR2.     

Method for estimating bioburden of nonsterile cotton gauze

In new hygienically controlled plants, products often have a low level of microbial contamination, so that current methods for estimating bioburden appear to be inadequate. The adoption of efficient procedures giving consistent and reproducible results could contribute to the improvement of conventional methods for evaluating microbiological quality of products with low bioburden. The effectiveness of a washing procedure and mechanical shaking for the removal of Bacillus subtilis spores from pre-inoculated cotton gauze samples was tested in combination with a membrane filtration technique. A 45-min agitation in the presence of surfactant and glass beads improved recovery up to 70.5%, with satisfactory reproducibility. In order to compare the procedure with the current standard method, uncontaminated samples were processed to extinction by applying a repetitive treatment. When exhaustive rinses were performed in order to calculate a conversion factor, permanent entrapment of a high percentage of organisms in the cotton microfibers was highlighted: this fact may play a role in an overestimation of the extrapolated removal efficiency. Received 18 June 1996/ Accepted in revised form 22 August 1996     

Method for estimating the decomposition of hexadecane in the marine environment.

A method, based on quantitating 14CO2 produced from [14C]hexadecane, has been developed for estimating the rate of hexadecane decomposition in seawater of Tokyo Bay during the summer stagnation period. The rate of hexadecane decomposition was from 0.1 to 1.3 mug/h per liter of seawater at the surface layer in the polluted gyre of the inner part of Tokyo Bay during the summer of 1974. A similar horizontal distribution pattern was seen for the density of hexadecane-decomposing bacteria.     

Constrained global optimization for estimating molecular structure from atomic distances.

Finding optimal three-dimensional molecular configurations based on a limited amount of experimental and/or theoretical data requires efficient nonlinear optimization algorithms. Optimization methods must be able to find atomic configurations that are close to the absolute, or global, minimum error and also satisfy known physical constraints such as minimum separation distances between atoms (based on van der Waals interactions). The most difficult obstacles in these types of problems are that 1) using a limited amount of input data leads to many possible local optima and 2) introducing physical constraints, such as minimum separation distances, helps to limit the search space but often makes convergence to a global minimum more difficult. We introduce a constrained global optimization algorithm that is robust and efficient in yielding near-optimal three-dimensional configurations that are guaranteed to satisfy known separation constraints. The algorithm uses an atom-based approach that reduces the dimensionality and allows for tractable enforcement of constraints while maintaining good global convergence properties. We evaluate the new optimization algorithm using synthetic data from the yeast phenylalanine tRNA and several proteins, all with known crystal structure taken from the Protein Data Bank. We compare the results to commonly applied optimization methods, such as distance geometry, simulated annealing, continuation, and smoothing. We show that compared to other optimization approaches, our algorithm is able combine sparse input data with physical constraints in an efficient manner to yield structures with lower root mean squared deviation.     

On the maximum likelihood method for estimating molecular trees: Uniqueness of the likelihood point

Summary Studies are carried out on the uniqueness of the stationary point on the likelihood function for estimating molecular phylogenetic trees, yielding proof that there exists at most one stationary point, i.e., the maximum point, in the parameter range for the one parameter model of nucleotide substitution. The proof is simple yet applicable to any type of tree topology with an arbitrary number of operational taxonomic units (OTUs). The proof ensures that any valid approximation algorithm be able to reach the unique maximum point under the conditions mentioned above. An algorithm developed incorporating Newton's approximation method is then compared with the conventional one by means of computers simulation. The results show that the newly developed algorithm always requires less CPU time than the conventional one, whereas both algorithms lead to identical molecular phylogenetic trees in accordance with the proof. Contribution No. 1780 from the National Institute of Genetics, Mishima 411, Japan     

Method for determining the temporal response of microbial phosphate transport affinity

Nutrient transport affinities of nutrient-starved microbial populations were measured as initial slopes of plots of limiting-nutrient transport rates versus extracellular limiting-nutrient concentrations. A method was devised for the determination of soluble reactive phosphate (Pi) affinity in Pi-limited continuous culture (aT), which was then used as an indicator of the effects of light/dark cycle (LD) perturbations on the temporal Pi transport abilities of three species of freshwater algae. Cell division was asynchronous for the green alga Selenastrum capricornutum grown in continuous cultures exposed to LD cycles. An apparent rhythm in aT for Pi was greatly affected by the population size parameter. Cell division was phased for the green alga Scenedesmus quadricauda grown in LD continuous culture. A rhythm in aT for Pi was not greatly affected by the biomass parameter. Cell division was also phased in LD continuous culture for the blue-green alga (cyanobacterium) Synechococcus N?geli, but rhythms in other parameters could not be detected. Synechococcus N?geli was an extremely efficient Pi transporter at low Pi concentrations in LD continuous culture, and so aT could not be calculated. The results demonstrate that aT is well suited to describing the temporal response of Pi transport in LD-perturbed, Pi-limited continuous culture.     

GENIE: estimating demographic history from molecular phylogenies

GENIE implements a statistical framework for inferring the demographic history of a population from phylogenies that have been reconstructed from sampled DNA sequences. The methods are based on population genetic models known collectively as coalescent theory. AVAILABILITY: GENIE is available from http://evolve.zoo.ox.ac.uk. All popular operating systems are supported.     

Bootstrap approaches to estimating confidence intervals for molecular dissimilarities and resultant trees

Varied approaches to estimating confidence intervals for immunological and hybridization distances can be uniformly applied to any matrix of distances. One procedure bootstraps the pairwise dissimilarities between the distances of every pair of taxa to all others, creating a derived matrix of distances for which dispersions can be estimated. Another approach bootstraps the sample of differences between pairwise homologous branch lengths concerning each pair of taxa and between asymmetric halves of the matrix, to find a standard error of the dispersions. This allows comparison of the robustness of trees among different sources of data. DNA hybridization, transferrin immunology and protein immunodiffusion matrices all yield much the same result once standard deviations of dissimilarities are acknowledged: namely, unresolvable trichotomies among the human-chimp-gorilla clade and among this clade with orang and gibbon; conventional relationships among hominoids, cercopithecoids, ceboids and strepsirhines; and a polychotomy among anthropoids, strepsirhines, tarsiers, tupaiids and dermopterans.     

Improving the affinity of antigens for mutated antibodies by use of statistical molecular design

We demonstrate the use of statistical molecular design (SMD) in the selection of peptide libraries aimed to systematically investigate antigen-antibody binding spaces. Earlier, we derived two novel antibodies by mutating the complementarity-determining region of the anti-p24 (HIV-1) single chain Fv antibody, CB4-1 that had lost their affinity for a p24 epitope-homologous peptide by 8- and 60-fold. The present study was devoted to explore how peptide libraries can be designed under experimental design criteria for effective screening of peptide antigens. Several small peptide-antigen libraries were selected using SMD principles and their activities were evaluated by their binding to SPOT-synthesized peptide membranes and by fluorescence polarization (FP). The approach was able to reveal the most critical residues required for antigen binding, and finally to increase the binding activity by proper modifications of amino acids in the peptide antigen. A model of the active peptide binding pocket formed by the mutated scFv and the antigen was compatible with the information gained from the experimental data. Our results suggest that SMD approaches can be used to explore peptide antigen features essential for their interactions with antibodies.     

Optimizing the affinity and specificity of proteins with molecular display

Affinity maturation of receptor-ligand interactions represents an important area of academic and pharmaceutical research. Improving affinity and specificity of proteins can tailor potency for both in vivo and in vitro applications. A number of different display platforms including phage display, bacterial and yeast display, ribosome display, and mRNA display can optimize protein affinity and specificity. Here, we will review the advantages and disadvantages of these molecular display methods with a focus on their suitability for protein affinity maturation.     

A statistical procedure for estimating Grey seal pup production from a single census

The variable start and duration of the Grey seal breeding season makes the estimation of total pup production from a single census very difficult. Classifying the count into morphological age classes enables the form and timing of the birth rate curve and estimates of pup mortality rates to be elucidated. A simulation technique is described which enables the duration of each morphological stage to be determined from a series of such classified counts taken over one season. A further statistical technique uses these estimates to calculate the mean timing and duration of the breeding season from a single classified count taken from similar populations in subsequent years. This information allows total pup production to be calculated for any appropriate breeding colony. Some guidance is given as to the optimal timing of that single census which would yield the best estimate of production, although the precise date is not critical to the success of the technique. Results from single census estimates obtained in this way are compared with known production data from more detailed surveys for a number of different colonies.     

Method for determining the temporal response of microbial phosphate transport affinity.

Nutrient transport affinities of nutrient-starved microbial populations were measured as initial slopes of plots of limiting-nutrient transport rates versus extracellular limiting-nutrient concentrations. A method was devised for the determination of soluble reactive phosphate (Pi) affinity in Pi-limited continuous culture (aT), which was then used as an indicator of the effects of light/dark cycle (LD) perturbations on the temporal Pi transport abilities of three species of freshwater algae. Cell division was asynchronous for the green alga Selenastrum capricornutum grown in continuous cultures exposed to LD cycles. An apparent rhythm in aT for Pi was greatly affected by the population size parameter. Cell division was phased for the green alga Scenedesmus quadricauda grown in LD continuous culture. A rhythm in aT for Pi was not greatly affected by the biomass parameter. Cell division was also phased in LD continuous culture for the blue-green alga (cyanobacterium) Synechococcus Nägeli, but rhythms in other parameters could not be detected. Synechococcus Nägeli was an extremely efficient Pi transporter at low Pi concentrations in LD continuous culture, and so aT could not be calculated. The results demonstrate that aT is well suited to describing the temporal response of Pi transport in LD-perturbed, Pi-limited continuous culture.     

Measuring antibody affinity and performing immunoassay at the single molecule level

Fluorescence correlation spectroscopy (FCS) enables direct observation of the translational diffusion of single fluorescent molecules in solution. When fluorescent hapten binds to antibody, analysis of FCS data yields the fractional amounts of free and bound hapten, allowing determination of the equilibrium binding constant. Equilibrium dissociation constants of anti-digoxin antibodies and corresponding fluorescein-labeled digoxigenin obtained by FCS and fluorescence polarization measurements are identical. It is also possible to follow a competitive displacement of the tracer from the antibody by unlabeled hapten using FCS in an immunoassay format. The fluorescence polarization immunoassay for vancomycin detection was used to test the FCS approach. Fitting of the FCS data for the molar fractions of free and bound fluorescein-labeled vancomycin yielded a calibration curve which could serve for determination of the vancomycin concentration in biological samples.     

A viral sampling design for testing the molecular clock and for estimating evolutionary rates and divergence times

MOTIVATION: The high pace of viral sequence change means that variation in the times at which sequences are sampled can have a profound effect both on the ability to detect trends over time in evolutionary rates and on the power to reject the Molecular Clock Hypothesis (MCH). Trends in viral evolutionary rates are of particular interest because their detection may allow connections to be established between a patient's treatment or condition and the process of evolution. Variation in sequence isolation times also impacts the uncertainty associated with estimates of divergence times and evolutionary rates. Variation in isolation times can be intentionally adjusted to increase the power of hypothesis tests and to reduce the uncertainty of evolutionary parameter estimates, but this fact has received little previous attention. RESULTS: We provide approximations for the power to reject the MCH when the alternative is that rates change in a linear fashion over time and when the alternative is that rates differ randomly among branches. In addition, we approximate the standard deviation of estimated evolutionary rates and divergence times. We illustrate how these approximations can be exploited to determine which viral sample to sequence when samples representing different dates are available.     

Oscillations of IgM antibody affinity at the level of single immunocytes

IgM antibody affinity was measured by hemolytic plaque inhibition assays on spleen cells from mice immunized with a single injection of DNP-dextran. Maturation of affinity was found to occur with time after 1 to 1000 microgram of immunogen and to be characterized by rapid oscillations independent from changes inFC number/spleen and in antibody secretion rate. Analysis of affinity heterogeneity showed that such oscillations occur in higher affinity PFC subpopulations. The origin of affinity oscillations was discussed in terms of interactions among antigen and the elements of the immune network.