Calculation Of Ks Research Articles

Haplotype-resolved genome assembly provides insights into evolutionary history of the Actinidia arguta tetraploid

Actinidia arguta, known as hardy kiwifruit, is a widely cultivated species with distinct botanical characteristics such as small and smooth-fruited, rich in beneficial nutrients, rapid softening and tolerant to extremely low temperatures. It contains the most diverse ploidy types, including diploid, tetraploid, hexaploid, octoploid, and decaploid. Here we report a haplotype-resolved tetraploid genome (A. arguta cv. ‘Longcheng No.2’) containing four haplotypes, each with 40,859, 41,377, 39,833 and 39,222 protein-coding genes. We described the phased genome structure, synteny, and evolutionary analyses to identify and date possible WGD events. Ks calculations for both allelic and paralogous genes pairs throughout the assembled haplotypic individuals showed its tetraploidization is estimated to have formed ~ 1.03 Mya following Ad-α event occurred ~ 18.7 Mya. Detailed annotations of NBS-LRRs or CBFs highlight the importance of genetic variations coming about after polyploidization in underpinning ability of immune responses or environmental adaptability. WGCNA analysis of postharvest quality indicators in combination with transcriptome revealed several transcription factors were involved in regulating ripening kiwi berry texture. Taking together, the assembly of an A. arguta tetraploid genome provides valuable resources in deciphering complex genome structure and facilitating functional genomics studies and genetic improvement for kiwifruit and other crops.Graphical

Design of a Help Tool for the Evaluation of the Permeability of Saturated Soil

The permeability of a soil represents the property of this soil to allow penetration by a fluid, the permeability in the saturated state (ks) of soils is an important parameter to determine before the design of geotechnical works, because it constitutes a factor determining factor in the calculation of the load-bearing capacity of soils. The models for predicting saturated permeability proposed in the literature are numerous (statistical models, empirical models, etc.), and the comparison studies between these models are also numerous; with the aim of facilitating such studies we have attempted to present an expert system which takes care of the evaluation of this parameter based on the methods of (Beyer 1981, Kruger 1992, Terzaghi 1981). Our expert system first allows the calculation of (ks) from the three models studied, as it also allows the comparison between the results of these models on the basis of calculation of the mean square error.

Роль горнообогатительного комбината в образовании техногеохимических аномалий мышьяка в почвах Соймоновской долины (Южный Урал)

Introduction. The heterogeneity of soil cover of mountainous areas carries in itself the specific formation of technogeochemical anomalies in the areas of metallurgical combines, and the remoteness and inaccessibility of these areas requires detailed studies of the processes of pollutants in the soil and mechanisms of their behavior. The aim of the study was to investigate the influence of aero-industrial emissions from the copper smelter on the formation of techno-geochemical anomalies of arsenic in soils and its spatial distribution. Methods and materials of the research. Studies were conducted in the area of the Karabash copper smelter (KMC), located in the southern Urals (Russia), Chelyabinsk region, one of the main pollutants of soils is arsenic, which is formed in the Soymanovskaya Valley and adjacent landscapes techno-geochemical soil anomalies. In the course of works 25 soil sections were laid at different distances and directions from KMC, taking into account the specific geo-morphological features of the territory. In the selected soil samples we determined the acidity of the salt extract, the content of organic matter, granulometric composition, gross content of arsenic and its exchangeable form. Determination of arsenic was carried out by atomic adsorption spectrometry (AA-6800 Shimadzu). To identify the dependence of arsenic concentration in the upper 0-15 cm of the soil thickness with the distance from the CMC was carried out to calculate the Pearson coefficient and the concentration coefficient (Kc). Research results and discussion. The study area was divided into 5 zones depending on the distance from CMC. Excess concentrations of gross arsenic relative to the background content varies from 64 times in the 2 km zone to 3 times at a distance of more than 10 km. Maximum concentrations were recorded in the upper 0-15 cm of the soil thickness in the 2 km zone. The exchangeable form of arsenic has a specific accumulation near the combine, with a distance of more than 10 km from the combine, there is a tendency to reduce the content of this form, to a complete absence. In the intraprofile distribution there is a pattern of accumulation in the upper 0-15 cm of the soil layer, with depth significantly decreasing. Conclusions. Patterns in the spatial distribution of arsenic in soils based on the distance from the emission of aeroindustrial emissions were revealed. Maps of the spatial distribution of gross arsenic and exchange forms in the soils of the study area. It was determined that an important role in the formation of techno-geochemical anomalies plays pH of the environment. During the calculation of Ks revealed local areas that form anomalous halos dispersion, which are confined mainly to places near the CMC and the direction of the prevailing winds. Two local areas were identified for which the Kc values are more than 50. Pearson criterion calculations confirm the dependence of the spatial distribution of arsenic in soils on the wind rose. The results may be useful in the preparation of geochemical maps of arsenic distribution. In the prediction of local and radial differentiation of arsenic in other regions with similar activity of the combine, as well as in the correction of the regional geochemical background of arsenic in soils.

Quantification of Kuramoto Coupling Between Intrinsic Brain Networks Applied to fMRI Data in Major Depressive Disorder.

Organized patterns of system-wide neural activity adapt fluently within the brain to adjust behavioral performance to environmental demands. In major depressive disorder (MD), markedly different co-activation patterns across the brain emerge from a rather similar structural substrate. Despite the application of advanced methods to describe the functional architecture, e.g., between intrinsic brain networks (IBNs), the underlying mechanisms mediating these differences remain elusive. Here we propose a novel complementary approach for quantifying the functional relations between IBNs based on the Kuramoto model. We directly estimate the Kuramoto coupling parameters (K) from IBN time courses derived from empirical fMRI data in 24 MD patients and 24 healthy controls. We find a large pattern with a significant number of Ks depending on the disease severity score Hamilton D, as assessed by permutation testing. We successfully reproduced the dependency in an independent test data set of 44 MD patients and 37 healthy controls. Comparing the results to functional connectivity from partial correlations (FC), to phase synchrony (PS) as well as to first order auto-regressive measures (AR) between the same IBNs did not show similar correlations. In subsequent validation experiments with artificial data we find that a ground truth of parametric dependencies on artificial regressors can be recovered. The results indicate that the calculation of Ks can be a useful addition to standard methods of quantifying the brain's functional architecture.

Spin Splitting Energy of Transition Metals: A New, More Affordable Wave Function Benchmark Method and Its Use to Test Density Functional Theory.

Accurately predicting the spin splitting energy of chemical species is important for understanding their reactivity and magnetic properties, but it is very challenging, especially for molecules containing transition metals. One impediment to progress is the scarcity of accurate benchmark data. Here we report a set of calculations designed to yield reliable benchmarks for simple transition-metal complexes that can be used to test density functional methods that are affordable for large systems of more practical interest. Various wave function methods are tested against experiment for Fe2+, Fe3+, and Co3+, including CASSCF, CASPT2, CASPT3, MRCISD, MRCISD+Q, ACPF, AQCC, CCSD(T), and CASPT2/CCSD(T) and also a new method called CASPT2.5, which is performed by taking the average of the CASPT2 and CASPT3 energies. We find that MRCISD+Q, ACPF, and AQCC require smaller active spaces for good accuracy than are required by CASPT2 and CASPT3, and this aspect may be important for calculations on larger molecules; here we find that CASPT2.5 extrapolated to a complete basis set is the most suitable method-in terms of computational cost and in terms of accuracy on monatomic systems-and therefore we chose this method for molecular benchmarks. Then Kohn-Sham density functional calculations with 60 exchange-correlation functionals are tested for FeF2, FeCl2, and CoF2. We find that MN15-L, M06-SX, and revM06 have very good agreement with CASPT2.5 benchmarks in terms of both the spin splitting energy and the optimized geometry for each spin state. In addition, we recommend def2-TZVP as the most suitable basis set to perform density functional calculations for molecular spin splitting energies; extra polarization functions in the basis set do not help to increase the accuracy of the spin splitting energy in KS calculations.

Laboratory evaluation of falling-head infiltration for saturated soil hydraulic conductivity determination

Falling-head one-dimensional infiltration procedures, such as the simplified falling-head (SFH) technique, yield estimates of saturated soil hydraulic conductivity, Ks, with parsimonious and rapid experiments. Factors that can influence determination of Ks by the SFH technique were tested in the laboratory on three repacked soils differing by particle diameter ranges (0-2000, 0- 105 and 105-2000 mm, respectively). Using the theoretically calculated depth of ponding on the infiltration surface, D, instead of the measured one had a small impact on the Ks calculations (means differing by a factor of 1.1-1.2, depending on the soil). For the finest soil, Ks decreased by 3.1 times as D increased from 40 to 135 mm but D did not affect Ks for the coarsest soil, yielding in general the highest Ks values. The abrupt increase of the infiltration rate close to the end of the run did not influence appreciably Ks calculations since it determined an increase in Ks by a mean factor never exceeding 1.1. The most frequent result of the developed procedure for estimating the α* parameter was failure of the experiment although the valid α* calculations were plausible, being higher for the coarse textured soil (17 m–1) than the finer soils (9.2-9.3 m–1). The depth of the wetting front at the end of the run was 1.1-1.2 times deeper than that calculated theoretically before the run, depending on the soil. In conclusion, the method used to determine D should not affect very much Ks determination but larger D values can yield smaller Ks values in fine-textured soils. Air escapes from the sampled soil volume when almost all water had infiltrated but this circumstance does not have a great impact on calculation of Ks. A falling-head one-dimensional ponded infiltration process is not recommended to estimate α*. The theoretical depth of the wetting front can approximately be predicted before the run. The SFH technique appears a rather robust method to simply and rapidly determine Ks.

Excited-State Potential Energy Surfaces, Conical Intersections, and Analytical Gradients from Ground-State Density Functional Theory.

Kohn-Sham density functional theory (KS-DFT) has been a well-established theoretical foundation for ground-state electronic structure and has achieved great success in practical calculations. Recently, utilizing the eigenvalues from KS or generalized KS (GKS) calculations as an approximation to the quasiparticle energies, our group demonstrated a method to calculate the excitation energies from (G)KS calculation on the ground-state ( N - 1)-electron system. This method is now called QE-DFT (quasiparticle energies from DFT). In this work, we extend this QE-DFT method to describe excited-state potential energy surfaces (PESs), conical intersections, and the analytical gradients of excited-state PESs. The analytical gradients were applied to perform geometry optimization for excited states. In conjunction with several commonly used density functional approximations, QE-DFT can yield PESs in the vicinity of the equilibrium structure with accuracy similar to that from time-dependent DFT (TD-DFT). Furthermore, it describes conical intersection well, in contrast to TD-DFT. Good results for geometry optimization, especially bond length, of low-lying excitations for 14 small molecules are presented. The capability of describing excited-state PESs, conical intersections, and analytical gradients from QE-DFT and its efficiency based on just ground-state DFT calculations should be of great interest for describing photochemical and photophysical processes in complex systems.

Charge transfer excitation energies from ground state density functional theory calculations.

Calculating charge transfer (CT) excitation energies with high accuracy and low computational cost is a challenging task. Kohn-Sham density functional theory (KS-DFT), due to its efficiency and accuracy, has achieved great success in describing ground state problems. To extend to excited state problems, our group recently demonstrated an approach with good numerical results to calculate low-lying and Rydberg excitation energies of an N-electron system from a ground state KS or generalized KS calculations of an (N - 1)-electron system via its orbital energies. In the present work, we explore further the same methodology to describe CT excitations. Numerical results from this work show that performance of conventional density functional approximations (DFAs) is not as good for CT excitations as for other excitations due to the delocalization error. Applying localized orbital scaling correction (LOSC) to conventional DFAs, a recently developed method in our group to effectively reduce the delocalization error, can improve the results. Overall, the performance of this methodology is better than time dependent DFT (TDDFT) with conventional DFAs. In addition, it shows that results from LOSC-DFAs in this method reach similar accuracy to other methods, such as ΔSCF, G0W0 with Bethe-Salpeter equations, particle-particle random phase approximation, and even high-level wavefunction methods like CC2. Our analysis shows that the correct 1/R trend for CT excitation can be captured from LOSC-DFA calculations, stressing that the application of DFAs with the minimal delocalization error is essential within this methodology. This work provides an efficient way to calculate CT excitation energies from ground state DFT.

Accuracy of Saturated Soil Hydraulic Conductivity Estimated from Numerically Simulated Single‐Ring Infiltrations

Core Ideas The accuracy of the PI method in estimating soil Ks was tested by numerical simulations. Estimated Ks using two‐ponding‐depth and multiple‐ponding‐depth infiltration were compared. Transient and steady‐state infiltration data for six soils were used to estimate Ks. The PI should yield more accurate Ks estimates in coarse‐ than fine‐textured soils. The transient method does not solve the Ks inaccuracy problems in fine‐textured soils. The single‐ring pressure infiltrometer (PI) method is widely used to determine saturated soil hydraulic conductivity, Ks, directly in the field. The original and still most common way to analyze the data makes use of the steady‐state model developed by the Canadian School in the 90s and two (two‐ponding‐depth, TPD, approach) or more (multiple‐ponding‐depth, MPD, approach) depths of ponding. The so‐called Wu method based on a generalized infiltration equation allows analysis of the transient infiltration data collected by establishing a single ponding depth of water on the infiltration surface. This investigation, making use of simulated infiltration runs for initially unsaturated sand to silty clay loam soils, showed that, with a run duration of practical interest (e.g., 2 h), the PI can be expected to yield more accurate estimates of Ks in coarse‐textured soils than in fine‐textured soils even if the transient method is used instead of the steady‐state method. Performing a three‐level experiment and analyzing the estimated steady‐state infiltration rates with both the TPD and MPD approaches is a way to predict the reliability of the estimated Ks value. The Ks accuracy should be acceptable if the two approaches yield similar results. Otherwise, the MPD approach should be expected to yield more accurate Ks estimates than the TPD approach. The transient method does not solve the Ks inaccuracy problems in fine‐textured soils because obtaining accurate Ks data requires that the portion of total infiltration varying linearly with time represent a high percentage of total infiltration, but this percentage is small in fine‐textured soils when the run does not exceed a few hours. This investigation opens some new perspective on the use of infiltration data to make predictions on the expected reliability of the Ks calculations with reference to both steady‐state and transient data analysis procedures.

Modeling rice development and field water balance using AquaCrop model under drying-wetting cycle condition in eastern China

Various crop growth models have been developed to simulate the crop development and were used to assess the effects of climate, cultivation and irrigation methods. To evaluate the feasibility of water driven model-AquaCrop in simulating crop development, production and field water balance in paddy soil under drying – wetting cycle condition, the model was calibrated and validated based on data during 2012–2013 rice season in Eastern China. Results showed that the accuracy of this model in simulating canopy cover (CC), evapotranspiration (ET), biomass, yield were generally acceptable, with the root mean square of error (RMSE) less than 10% for CC, 1.0 mm for ET, 0.61t ha−1 for biomass and with relative deviation of 3.6% for yield. Meanwhile, AquaCrop tended to overestimate CC, biomass and yield slightly during the midseason. Yet, its performance in simulating soil moisture content was not as good as expected. It tended to underestimate soil moisture with a RMSE of 14.81%, but overestimated the water deficit coefficient (Ks). The method for Ks calculation incorporated in AquaCrop should be revised for rice under drying-wetting cycle condition.

Identification and functional prediction of stress responsive AP2/ERF transcription factors in Brassica napus by genome-wide analysis

Using homology and domain authentication, 321 putative AP2/ERF transcription factors were identified in Brassica napus, called BnAP2/ERF TFs. BnAP2/ERF TFs were classified into five major subfamilies, including DREB, ERF, AP2, RAV, and BnSoloist. This classification is based on phylogenetic analysis, motif identification, gene structure analysis, and physiochemical characterization. These TFs were annotated based on phylogenetic relationship with Brassica rapa. BnAP2/ERF TFs were located on 19 chromosomes of B. napus. Orthologs and paralogs were identified using synteny-based methods Ks calculation within B. napus genome and between B. napus with other species such as B. rapa, Brassica oleracea, and Arabidopsis thaliana indicated that BnAP2/ERF TFs were formed through duplication events occurred before B. napus formation. Kn/Ks values were between 0 and 1, suggesting the purifying selection among BnAP2/ERF TFs. Gene ontology annotation, cis-regulatory elements and functional interaction networks suggested that BnAP2/ERF TFs participate in response to stressors, including drought, high salinity, heat and cold as well as developmental processes particularly organ specification and embryogenesis. The identified cis-regulatory elements in the upstream of BnAP2/ERF TFs were responsive to abscisic acid. Analysis of the expression data derived from Illumina Hiseq 2000 RNA sequencing revealed that BnAP2/ERF genes were highly expressed in the roots comparing to flower buds, leaves, and stems. Also, the ERF subfamily was over-expressed under salt and fungal treatments. BnERF039 and BnERF245 are candidates for salt-tolerant B. napus. BnERF253-256 and BnERF260-277 are potential cytokinin response factors. BnERF227, BnERF228, BnERF234, BnERF134, BnERF132, BnERF176, and BnERF235 were suggested for resistance against Leptosphaeria maculan and Leptosphaeria biglobosa.

Effects of biological crust coverage on soil hydraulic properties for the Loess Plateau of China

AbstractBiological soil crusts (BSCs) are ubiquitous living covers that have been allowed to grow on abandoned farmlands over the Loess Plateau because the “Grain for Green” project was implemented in 1999 to control serious soil erosion. However, few studies have been conducted to quantify the effects of BSC coverage on soil hydraulic properties. This study was performed to assess the effects of BSC coverage on soil hydraulic properties, which are reflected by the soil sorptivity under an applied pressure of 0 (S0) and −3 (S3) cm, saturated hydraulic conductivity (Ks), wetting front depth (WFD), and mean pore radius (λm), for the Loess Plateau of China. Five classes of BSC coverage (i.e., 1–20%, 20–40%, 40–60%, 60–80%, and 80–100%) and a bare control were selected at both cyanobacteria‐ and moss‐covered sites to measure soil hydraulic properties using a disc infiltrometer under 2 consecutive pressure heads of 0 and −3 cm, allowing the direct calculation of S0, S3, Ks, and λm. The WFD was measured onsite using a ruler immediately after the experiments of infiltration. The results indicated that both cyanobacteria and moss crusts were effective in changing the soil properties and impeding soil infiltration. The effects of moss were greater than those of cyanobacteria. Compared to those of the control, the S0, S3, Ks, WFD, and λm values of cyanobacteria‐covered soils were reduced by 13.7%, 11.0%, 13.3%, 10.6%, and 12.6% on average, and those of moss‐covered soils were reduced by 27.6%, 22.1%, 29.5%, 22.2%, and 25.9%, respectively. The relative soil sorptivity under pressures of 0 (RS0) and −3 (RS3) cm, the relative saturated hydraulic conductivity (RKs), the relative wetting front depth (RWFD), and the relative mean pore radius (Rλm) decreased exponentially with coverage for both cyanobacteria‐ and moss‐covered soils. The rates of decrease in RS0, RS3, RKs, RWFD, and Rλm of cyanobacteria were significantly slower than those of moss, especially for the coverage of 0–40%, with smaller ranges. The variations of soil hydraulic properties with BSC coverage were closely related to the change in soil clay content driven by the BSC coverage on the Loess Plateau. The results are useful for simulating the hydraulic parameters of BSC‐covered soils in arid and semiarid areas.

Comparison between Optimization Method and Experience-Based Method in Soil Conservation

The analysis of the slope stability is important in soil conservation. To analyze the slope stability, optimization methods were coded and compared with the traditional experience-based methods. Furthermore, the results were visualized in the program, so that the user can easily check the results and can designate an area, in which the program seeks the center and radius of the most hazardous slide arc. Moreover, the graphic interaction function was implemented in the program. In addition, the Standard Model One, recommended by ACAD (The Association for Computer Aided Design), was calculated by the program, of which the results (safety factor Ks=0.95~0.96) were smaller than the official recommend value (Ks=1). It is because that the traditional slice method, which neglects the normal stress and shear stress between the slices, was applied for calculation of Ks.

Nonsynonymous substitution rate (Ka) is a relatively consistent parameter for defining fast-evolving and slow-evolving protein-coding genes

BackgroundMammalian genome sequence data are being acquired in large quantities and at enormous speeds. We now have a tremendous opportunity to better understand which genes are the most variable or conserved, and what their particular functions and evolutionary dynamics are, through comparative genomics.ResultsWe chose human and eleven other high-coverage mammalian genome data–as well as an avian genome as an outgroup–to analyze orthologous protein-coding genes using nonsynonymous (Ka) and synonymous (Ks) substitution rates. After evaluating eight commonly-used methods of Ka and Ks calculation, we observed that these methods yielded a nearly uniform result when estimating Ka, but not Ks (or Ka/Ks). When sorting genes based on Ka, we noticed that fast-evolving and slow-evolving genes often belonged to different functional classes, with respect to species-specificity and lineage-specificity. In particular, we identified two functional classes of genes in the acquired immune system. Fast-evolving genes coded for signal-transducing proteins, such as receptors, ligands, cytokines, and CDs (cluster of differentiation, mostly surface proteins), whereas the slow-evolving genes were for function-modulating proteins, such as kinases and adaptor proteins. In addition, among slow-evolving genes that had functions related to the central nervous system, neurodegenerative disease-related pathways were enriched significantly in most mammalian species. We also confirmed that gene expression was negatively correlated with evolution rate, i.e. slow-evolving genes were expressed at higher levels than fast-evolving genes. Our results indicated that the functional specializations of the three major mammalian clades were: sensory perception and oncogenesis in primates, reproduction and hormone regulation in large mammals, and immunity and angiotensin in rodents.ConclusionOur study suggests that Ka calculation, which is less biased compared to Ks and Ka/Ks, can be used as a parameter to sort genes by evolution rate and can also provide a way to categorize common protein functions and define their interaction networks, either pair-wise or in defined lineages or subgroups. Evaluating gene evolution based on Ka and Ks calculations can be done with large datasets, such as mammalian genomes.ReviewersThis article has been reviewed by Drs. Anamaria Necsulea (nominated by Nicolas Galtier), Subhajyoti De (nominated by Sarah Teichmann) and Claus O. Wilke.

FAO-56 methodology for the stress coefficient evaluation under saline environment conditions: Validation on potato and broad bean crops

Abstract This study aims at validating the methodology proposed by Allen et al. (1998) to calculate the stress coefficient Ks (ratio between actual and maximal evapotranspiration) under saline environment conditions not affected by soil water shortage. Validation was performed in Mediterranean region (Bari, southern Italy) on two crops: a winter crop (broad bean) and a spring crop (potato) grown in lysimeters, on clay and loam soils, having different levels of salinity. Preliminary observations were carried out to verify that the conditions established by Allen et al. (1998) for applying this Ks calculation methodology were fulfilled. The measured Ks values showed an evolution during the growing cycle. Ks values were close to 1 after emergence, and decreased at the end of the growing cycle. Contrarily, the calculated Ks values showed steady values during the whole crop cycle, being lower than the measured Ks. Only at the end of the crop cycle the calculated Ks values approached those measured. The various causes of differences between measured and calculated values of Ks are analyzed in this study. The observed differences between calculated and measured values of Ks led to an underestimation of calculated actual evapotranspiration (AET), at different stages in the crop growing cycle, by an average of 12%. The analysis of seasonal evapotranspiration as a function of soil salinity allows for a modulation of this mean value. The underestimation was quite negligible (close to 4%), if the average value of ECe during the crop cycle was close or lower than 3 dS m−1. On the contrary, the underestimation in evapotranspiration was close to 20% when the ECe raised up to 6 dS m−1. An underestimation of calculated AET in saline environment conditions, by the methodology proposed by Allen et al. (1998) , causes the appearance of an additional water stress, mainly when soil salinity, increases due to the combined effect of soil water shortage and water quality. Different solutions are proposed to improve the calculation of AET in this condition.

Ground-State Degeneracies Leave Recognizable Topological Scars in the Electronic Density

In Kohn-Sham density functional theory (KS DFT) a fictitious system of noninteracting particles is constructed having the same ground-state (GS) density as the physical system of interest. A fundamental open question in DFT concerns the ability of an exact KS calculation to spot and characterize the GS degeneracies in the physical system. In this Letter we provide theoretical evidence suggesting that the GS density, as a function of position on a 2D manifold of parameters affecting the external potential, is "topologically scarred" in a distinct way by degeneracies. These scars are sufficiently detailed to enable determination of the positions of degeneracies and even the associated Berry phases. We conclude that an exact KS calculation can spot and characterize the degeneracies of the physical system.

How Do Variable Substitution Rates Influence Ka and Ks Calculations?

The ratio of nonsynonymous substitution rate (Ka) to synonymous substitution rate (Ks) is widely used as an indicator of selective pressure at sequence level among different species, and diverse mutation models have been incorporated into several computing methods. We have previously developed a new γ-MYN method by capturing a key dynamic evolution trait of DNA nucleotide sequences, in consideration of varying mutation rates across sites. We now report a further improvement of NG, LWL, MLWL, LPB, MLPB, and YN methods based on an introduction of gamma distribution to illustrate the variation of raw mutation rate over sites. The novelty comes in two ways: (1) we incorporate an optimal gamma distribution shape parameter a into γ-NG, γ-LWL, γ-MLWL, γ-LPB, γ-MLPB, and γ-YN methods; (2) we investigate how variable substitution rates affect the methods that adopt different models as well as the interplay among four evolutional features with respect to Ka/Ks computations. Our results suggest that variable substitution rates over sites under negative selection exhibit an opposite effect on ω estimates compared with those under positive selection. We believe that the sensitivity of our new methods has been improved than that of their original methods under diverse conditions and it is advantageous to introduce novel parameters for Ka/Ks computation.

Correlation Between Ka/Ks and Ks is Related to Substitution Model and Evolutionary Lineage

In 2005, Wyckoff and coworkers described a surprisingly strong correlation between Ka/Ks and Ks in several data sets using the LPB93 algorithm. This finding indicated the possibility of a paradigm shift in the way selection strength can be measured using the Ka/Ks ratio. We carried out a calculation of Ka and Ks using six different algorithms on three cross-species orthologous data sets and found a highly variable correlation among the algorithms and lineages. Algorithms based on the GY-HKY substitution model exhibit a weaker positive correlation or a stronger negative correlation than those based on the K2P and JC69 substitution model. Even if one algorithm shows a positive correlation between Ka/Ks and Ks in a warm-blooded lineage, it may show no correlation in a cold-blooded lineage. This algorithm-related and evolutionary lineage-related correlation indicates the need for great caution in drawing conclusions when using only one Ka and Ks algorithm in a genomewide analysis of selection strength. Our results indicated that currently used algorithms for Ka and Ks calculations are flawed and need improvements.

Physical interpretation and evaluation of the Kohn–Sham and Dyson components of the ε–I relations between the Kohn–Sham orbital energies and the ionization potentials

Theoretical and numerical insight is gained into the ε–I relations between the Kohn–Sham orbital energies εi and relaxed vertical ionization potentials (VIPs) Ij, which provide an analog of Koopmans’ theorem for density functional theory. The Kohn–Sham orbital energy εi has as leading term −niIi−∑j∈Ωs(i)njIj, where Ii is the primary VIP for ionization (φi)−1 with spectroscopic factor (proportional to the intensity in the photoelectron spectrum) ni close to 1, and the set Ωs(i) contains the VIPs Ij that are satellites to the (φi)−1 ionization, with small but non-negligible nj. In addition to this “average spectroscopic structure” of the εi there is an electron-shell step structure in εi from the contribution of the response potential vresp. Accurate KS calculations for prototype second- and third-row closed-shell molecules yield valence orbital energies −εi, which correspond closely to the experimental VIPs, with an average deviation of 0.08 eV. The theoretical relations are numerically investigated in calculations of the components of the ε–I relations for the H2 molecule, and for the molecules CO, HF, H2O, HCN. The derivation of the ε–I relations employs the Dyson orbitals (the ni are their norms). A connection is made between the KS and Dyson orbital theories, allowing the spin-unrestricted KS xc potential to be expressed with a statistical average of individual xc potentials for the Dyson spin–orbitals as leading term. Additional terms are the correction vc,kin,σ due to the correlation kinetic effect, and the “response” vresp,σ, related to the correction to the energy of (N−1) electrons due to the correlation with the reference electron.

Kinetics of Reaction of SO2 with Marble

In industrial environments, the decay of marble takes place primarily due to atmospheric SO2. In order to predict quantitatively the rate of weathering of marble, we reacted four varieties of marble at 20 °C and 100% relative humidity in atmospheres containing 10 and 300 ppm SO2. The surface rate constant, ks, was calculated from the mass loss of reacted samples upon leaching the reaction product by immersion in water. For application to marble, the grain theory model commonly used to evaluate gas‐solid non‐catalytic reactions was modified to provide for calculation of ks and the diffusion coefficient, Deg. Further, the volumetric rate constant, kv, was determined based upon the x‐ray diffraction data. In both these cases, it was found that the total magnitude of reaction can be determined only through summation of the kinetically controlled initial reaction and the subsequent diffusion‐controlled reaction. The next paper in this issue uses these reaction constants to predict the weathering of marble in natural environments.