A Hidden Markov Model approach to variation among sites in rate of evolution

The method of Hidden Markov Models is used to allow for unequal and unknown evolutionary rates at different sites in molecular sequences. Rates of evolution at different sites are assumed to be drawn from a set of possible rates, with a finite number of possibilities. The overall likelihood of phylogeny is calculated as a sum of terms, each term being the probability of the data given a particular assignment of rates to sites, times the prior probability of that particular combination of rates. The probabilities of different rate combinations are specified by a stationary Markov chain that assigns rate categories to sites. While there will be a very large number of possible ways of assigning rates to sites, a simple recursive algorithm allows the contributions to the likelihood from all possible combinations of rates to be summed, in a time proportional to the number of different rates at a single site. Thus with three rates, the effort involved is no greater than three times that for a single rate. This "Hidden Markov Model" method allows for rates to differ between sites and for correlations between the rates of neighboring sites. By summing over all possibilities it does not require us to know the rates at individual sites. However, it does not allow for correlation of rates at nonadjacent sites, nor does it allow for a continuous distribution of rates over sites. It is shown how to use the Newton-Raphson method to estimate branch lengths of a phylogeny and to infer from a phylogeny what assignment of rates to sites has the largest posterior probability. An example is given using beta-hemoglobin DNA sequences in eight mammal species; the regions of high and low evolutionary rates are inferred and also the average length of patches of similar rates.      

Application of the size-fractionation method to simultaneous estimation of clearance rates by heterotrophic flagellates and ciliates of pico- and nanophytoplankton

To estimate the clearance rates of pico- and nanophytoplankton by heterotrophic nanoflagellates (HNF) and ciliates, the size-fractionation method was employed in combination with a multiple regression analysis. Apparent growth rate of a specific phytoplankton group was decomposed into three terms, net growth rate, grazing rates by HNF and those by ciliates, and the grazing rates were interpreted as a linear function of average cell concentrations of HNF and ciliates. We produced a set of subsamples from a water sample by size-fractionation using three different pore sizes. By measuring phytoplankton and protozoan cell concentrations, apparent growth rate of a specific phytoplankton group was regressed against the average cell concentrations of HNF and ciliates to obtain the net growth rate of the phytoplankton group and the average clearance rates by these two protozoan groups. The estimated values were within the range of those previously reported for cultured and natural protozoan, which supported the feasibility of the present method. The estimated values also suggested that picophytoplankton abundance in Otsuchi Bay in spring is controlled mainly by HNF through active grazing. The present study rediscovered the utility of the size-fractionation method as a method to estimate the clearance rates of different protozoan groups from natural assemblages in a single experiment.     

Estimating recombination rates from single-nucleotide polymorphisms using summary statistics

We describe a novel method for jointly estimating crossing-over and gene-conversion rates from population genetic data using summary statistics. The performance of our method was tested on simulated data sets and compared with the composite-likelihood method of R. R. Hudson. For several realistic parameter values, the new method performed similarly to the composite-likelihood approach for estimating crossing-over rates and better when estimating gene-conversion rates. We used our method to analyze a human data set recently genotyped by Perlegen Sciences.     

Accuracy of the Haldane method as an indirect measure of metabolism

Metabolic rates of barn owls increased as ambient temperature decreased below the thermoneutral zone. The Haldane method was as reliable as an O2 analyzer in measuring the metabolic rates of captive barn owls. However, at lowered ambient temperature (below 5 degrees C) there was a slight disparity in the metabolic rates determined by the two methods. The Haldane method has the potential of being used in a field situation (i.e. it is reliable, portable and relatively inexpensive).     

Determination of division rates of rCHO cells in high density and immobilized fermentation systems by flow cytometry

As most high density and immobilized fermentation systems do not allow the direct quantitative determination of cell density, two flow cytometric methods (the determination of incorporation of bromodeoxyuridine into newly synthesized DNA and the increase in mitotic cells by colchicine blockage) were evaluated as to their suitability to measure true division rates of cells in bioreactors. The BrdU method gave division rates identical to the growth rates measured by cell count, while the colchicine block method gave values that were lower and varied with the cell line. This is due to the cytotoxicity of colchicine and makes a calibration of the method for each cell line necessary. Both methods have been successfully used to measure division rates of rCHO cells immobilized in an alginate matrix as well as in macroporous carriers in a fluidised bed system and in dialysis culture.     

A likelihood approach to character weighting and what it tells us about parsimony and compatibility

The statistical framework of maximum likelihood estimation is used to examine character weighting in inferring phylogenies. A simple probabilistic model of evolution is used, in which each character evolves independently among two states, and different lineages evolve independently. When different characters have different known probabilities of change, all sufficiently small, the proper maximum likelihood method of estimating phylogenies is a weighted parsimony method in which the weights are logarithmically related to the rates of change. When rates of change are taken extremely small, the weights become more equal and unweighted parsimony methods are obtained. When it is known that a few characters have very high rates of change and the rest very low rates, but it is not known which characters are the ones having the high rates, the maximum likelihood criterion supports use of compatibility methods. By varying the fraction of characters believed to have high rates of change one obtains a ‘threshold method’ whose behavior depends on the value of a parameter. By altering this parameter the method changes smoothly from being a parsimony method to being a compatibility method. This provides us with a spectrum of intermediates between these methods. These intermediate methods may be of use in analysing real data.     

Estimation of amino acid residue substitution rates at local spatial regions and application in protein function inference: a Bayesian Monte Carlo approach

The amino acid sequences of proteins provide rich information for inferring distant phylogenetic relationships and for predicting protein functions. Estimating the rate matrix of residue substitutions from amino acid sequences is also important because the rate matrix can be used to develop scoring matrices for sequence alignment. Here we use a continuous time Markov process to model the substitution rates of residues and develop a Bayesian Markov chain Monte Carlo method for rate estimation. We validate our method using simulated artificial protein sequences. Because different local regions such as binding surfaces and the protein interior core experience different selection pressures due to functional or stability constraints, we use our method to estimate the substitution rates of local regions. Our results show that the substitution rates are very different for residues in the buried core and residues on the solvent-exposed surfaces. In addition, the rest of the proteins on the binding surfaces also have very different substitution rates from residues. Based on these findings, we further develop a method for protein function prediction by surface matching using scoring matrices derived from estimated substitution rates for residues located on the binding surfaces. We show with examples that our method is effective in identifying functionally related proteins that have overall low sequence identity, a task known to be very challenging.     

Measurement of Respiration Rates of Methylobacterium extorquens AM1 Cultures by Use of a Phosphorescence-Based Sensor

Respiration rates of bacterial cultures can be a powerful tool in gauging the effects of genetic manipulation and environmental changes affecting overall metabolism. We present an optical method for measuring respiration rates using a robust phosphorescence lifetime-based sensor and off-the-shelf technology. This method was tested with the facultative methylotroph Methylobacterium extorquens AM1 to demonstrate subtle mutant phenotypes.     

A Proposed Method for Specifying the Temperature History of Cells During the Rapid Cool-down of Plant Specimens

Existing methods for defining cool-down rates of plant specimensquenched in cryogenic liquids are considered unsatisfactory. An analytical method is proposed for specifying the temperaturehistory and cool-down rates at particular cell locations withina plant specimen. This method should provide realistic peakcool-down rates when examining cell structures and the survivalrate of cell systems.     

A likelihood approach to character weighting and what it tells us about parsimony and compatibility

The statistical framework of maximum likelihood estimation is used to examine character weighting in inferring phylogenies. A simple probabilistic model of evolution is used, in which each character evolves independently among two states, and different lineages evolve independently. When different characters have different known probabilities of change, all sufficiently small, the proper maximum likelihood method of estimating phylogenies is a weighted parsimony method in which the weights are logarithmically related to the rates of change. When rates of change are taken extremely small, the weights become more equal and unweighted parsimony methods are obtained.
When it is known that a few characters have very high rates of change and the rest very low rates, but it is not known which characters are the ones having the high rates, the maximum likelihood criterion supports use of compatibility methods. By varying the fraction of characters believed to have high rates of change one obtains a 'threshold method' whose behavior depends on the value of a parameter. By altering this parameter the method changes smoothly from being a parsimony method to being a compatibility method. This provides us with a spectrum of intermediates between these methods. These intermediate methods may be of use in analysing real data.     

The oxygen evolution methodology affects photosynthetic rate measurements of microalgae in well‐defined light regimes

Designing photobioreactors correctly is a must for the success of microalgal mass production. Optimal photobioreactor design requires a precise knowledge of photosynthesis dynamics in fluctuating light conditions and hence a method for the measurement of photosynthetic rates in specific light regimes. However, it is not uncommon in literature that experimental protocols used to obtain oxygen generation rates are described ambiguously and the reported rates of photosynthesis vary widely depending on the methodology. Additionally, quite a number of methods overlook certain aspects that can affect the estimated rates significantly, and can therefore affect photobioreactor design. We have developed a method based on oxygen evolution measurements that accurately determines photosynthetic rates under well‐defined light regimes. Our experimental protocol takes into account most of the issues that can affect the rates of oxygen generation, such as depletion of nutrients during the measurements and precision of the measurements. We have focused on the basic applications in photobioreactor design and used a dynamic model of photosynthesis to analyze our results and compare them with available published data. The results suggest that our oxygen evolution method is consistent. Biotechnol. Bioeng. 2010;106: 228–237. © 2010 Wiley Periodicals, Inc.     

Estimation of population parameters and recombination rates from single nucleotide polymorphisms

Some general likelihood and Bayesian methods for analyzing single nucleotide polymorphisms (SNPs) are presented. First, an efficient method for estimating demographic parameters from SNPs in linkage equilibrium is derived. The method is applied in the estimation of growth rates of a human population based on 37 SNP loci. It is demonstrated how ascertainment biases, due to biased sampling of loci, can be avoided, at least in some cases, by appropriate conditioning when calculating the likelihood function. Second, a Markov chain Monte Carlo (MCMC) method for analyzing linked SNPs is developed. This method can be used for Bayesian and likelihood inference on linked SNPs. The utility of the method is illustrated by estimating recombination rates in a human data set containing 17 SNPs and 60 individuals. Both methods are based on assumptions of low mutation rates.     

Measurement of 15N csa/dipolar cross-correlation rates by means of Spin State Selective experiments

We propose a method for the determination of (15)N csa/dipolar cross-correlation rates based on the measurement of the two apparent transverse (or longitudinal) relaxation rates associated with each component of the nitrogen doublet (N(alpha) and N(beta)). This is achieved by inserting a spin state selective scheme in conventional inverse Carr-Purcell-Meiboom-Gill (or inversion-recovery) pulse sequence which allows for the edition of a HSQC-type spectrum for each of the spin states. Transverse cross-correlation rates necessitate two independent sets of measurements (for N(alpha) and N(beta), respectively), whereas for longitudinal cross correlation rates, besides N(alpha) and N(beta) measurements, the method requires the knowledge of both the (15)N longitudinal auto-relaxation rate and the longitudinal two-spin order (2NzHz) auto-relaxation rate. These additional parameters are mandatory because of the non-exponential behavior of the N(alpha) and N(beta) longitudinal decays. Conversely, the present method does not require any complex manipulation of 2D spectra, the cross-correlation rates being obtained from the difference of the two (N(alpha) and N(beta)) apparent relaxation rates. This approach is applied to (15)N-labelled ubiquitin at two different magnetic fields (9.4 T and 14.1 T).     

Theoretical study of a landscape of protein folding-unfolding pathways. Folding rates at midtransition

This paper presents a new method for calculating the folding-unfolding rates of globular proteins. The method is based on solution of kinetic equations for a network of folding-unfolding pathways of the proteins. The rates are calculated in the point of thermodynamic equilibrium between the native and completely unfolded states. The method has been applied to all the proteins listed by Jackson [Jackson, S. E. (1998) Folding Des. 3, R81-R91] and some peptides. Although the studied protein chains differ by more than 1 order of magnitude in size and exhibit two- as well as three-state kinetics in water, and their folding rates cover more than 11 orders of magnitude, the theoretical estimates are reasonable close to the experimentally measured folding rates in midtransition (the correlation coefficient being as high as 0.78). This means that the presented theory (having no adjustable parameters at all) is consistent with the experimental observations.     

Field Evaluation of Alternative Earthen Final Covers

Five methods to assess percolation rate from alternative earthen final covers (AEFCs) are described in the context of the precision with which the percolation rate can be estimated: trend analysis, tracer methods, water balance method, Darcy's Law calculations, and lysimetry. Trend evaluation of water content data is the least precise method because it cannot be used alone to assess the percolation rate. The precision of percolation rates estimated using tracer methods depends on the tracer concentration, percolation rate, and the sensitivity of the chemical extraction and analysis methods. Percolation rates determined using the water balance method have a precision of approximately 100 mm/yr in humid climates and 50 mm/yr in semiarid and drier climates, which is too large to demonstrate that an AEFC is meeting typical equivalency criterion (30 mm/yr or less). In most cases, the precision will be much poorer. Percolation rates computed using Darcy's Law with measured profiles of water content and matric suction typically have a precision that is about two orders of magnitude (or more) greater than the computed percolation rate. The Darcy's Law method can only be used for performance assessment if the estimated percolation rate is much smaller than the equivalency criterion and preferential flow is not present. Lysimetry provides the most precise estimates of percolation rate, but the precision depends on the method used to measure the collected water. The lysimeter used in the Alternative Cover Assessment Program (ACAP), which is described in this paper, can be used to estimate percolation rates with a precision between 0.00004 to 0.5 mm/yr, depending on the measurement method and the flow rates.     

Application of dynamic metabolic flux analysis for process modeling: Robust flux estimation with regularization,confidence bounds,and selection of elementary modes

In macroscopic dynamic models of fermentation processes, elementary modes (EM) derived from metabolic networks are often used to describe the reaction stoichiometry in a simplified manner and to build predictive models by parameterizing kinetic rate equations for the EM. In this procedure, the selection of a set of EM is a key step which is followed by an estimation of their reaction rates and of the associated confidence bounds. In this paper, we present a method for the computation of reaction rates of cellular reactions and EM as well as an algorithm for the selection of EM for process modeling. The method is based on the dynamic metabolic flux analysis (DMFA) proposed by Leighty and Antoniewicz (2011, Metab Eng, 13(6), 745–755) with additional constraints, regularization and analysis of uncertainty. Instead of using estimated uptake or secretion rates, concentration measurements are used directly to avoid an amplification of measurement errors by numerical differentiation. It is shown that the regularized DMFA for EM method is significantly more robust against measurement noise than methods using estimated rates. The confidence intervals for the estimated reaction rates are obtained by bootstrapping. For the selection of a set of EM for a given st oichiometric model, the DMFA for EM method is combined with a multiobjective genetic algorithm. The method is applied to real data from a CHO fed-batch process. From measurements of six fed-batch experiments, 10 EM were identified as the smallest subset of EM based upon which the data can be described sufficiently accurately by a dynamic model. The estimated EM reaction rates and their confidence intervals at different process conditions provide useful information for the kinetic modeling and subsequent process optimization.     

Data analysis of plasmid stability in continuous culture of recombinantSaccharomyces cerevisiae

Summary A simple method using non-linear regression is developed to analyse experimental data from plasmid stability studies of recombinantSaccharomyces cerevisiae grown in continuous cultures with non-selective and selective media. This method simultaneously provides quantitative information on the probability of plasmid loss due to segregation during cell division and the specific growth rates of plasmid-containing and plasmid-free cells at particular dilution rates. The method is applied to a set of experimental data. The three-parameter model, together with the estimated parameter values, provides a good fit to the experimental data.     

Comparing methods for measuring the rate of spread of invading populations

Measuring rates of spread during biological invasions is important for predicting where and when invading organisms will spread in the future as well as for quantifying the influence of environmental conditions on invasion speed. While several methods have been proposed in the literature to measure spread rates, a comprehensive comparison of their accuracy when applied to empirical data would be problematic because true rates of spread are never known. This study compares the performances of several spread rate measurement methods using a set of simulated invasions with known theoretical spread rates over a hypothetical region where a set of sampling points are distributed. We vary the density and distribution (aggregative, random, and regular) of the sampling points as well as the shape of the invaded area and then compare how different spread rate measurement methods accommodate these varying conditions. We find that the method of regressing distance to the point of origin of the invasion as a function of time of first detection provides the most reliable method over adverse conditions (low sampling density, aggregated distribution of sampling points, irregular invaded area). The boundary displacement method appears to be a useful complementary method when sampling density is sufficiently high, as it provides an instantaneous measure of spread rate, and does not require long time series of data.     

Simultaneous hydrolyses of esters and proteins at saturation levels

A direct titration method for the determination of proteolytic activity is discussed. This involves the potentiometric measurement of the volume of 0.08 N NaOH required to maintain a constant pH (8.0) during the time of the hydrolysis. It is a sensitive method which presents several advantages; viz., it measures simultaneously protease and esterase activity, it follows the hydrolysis very closely and from the first stages; the titration is continuous and on the same sample. This method determines a constant fraction of the groups titratable by formol titration. The ratio formol: direct titration is represented by a factor "f" which is presumed to be distinct for each protein-enzyme system. Kinetic studies, using this method, revealed that the rates of hydrolysis of mixtures casein-gelatin on one hand, casein-BAEE or gelatin-BAEE on the other, are always larger than those of the corresponding isolated substrates. In many cases the resulting rates are equal or nearly equal to the sum of the individual rates, even though the mentioned rates have been determined within the saturation zones for every substrate. The former observations are inconsistent with the theory of the formation of an intermediary enzyme-substrate compound, unless it is assumed that the enzyme has a specific active group for each substrate.     

以雾灵山夜蛾科为材料评估进化模型对DNA条码分类的影响

为了探究进化模型对DNA条形码分类的影响, 本研究以雾灵山夜蛾科44个种的标本为材料, 获得COI基因序列。使用邻接法（neighbor-joining）、 最大简约法（maximum parsimony）、 最大似然法（maximum likelihood）以及贝叶斯法（Bayesian inference）构建系统发育树, 并且对邻接法的12种模型、 最大似然法的7种模型、 贝叶斯法的2种模型进行模型成功率的评估。结果表明, 邻接法的12种模型成功率相差不大, 较稳定; 最大似然法及贝叶斯法的不同模型成功率存在明显差异, 不稳定; 最大简约法不基于模型, 成功率比较稳定。邻接法及最大似然法共有6种相同的模型, 这6种模型在不同的方法中成功率存在差异。此外, 分子数据中存在单个物种仅有一条序列的情况, 显著降低了模型成功率, 表明在DNA条形码研究中, 每个物种需要有多个样本。