The effect of electron transport on the kinetics of the manganese-containing superoxide dismutase from Bacillus stearothermophilus

A reaction mechanism for the enzyme-dimer is presented based on the intramolecular electron transfer between two active centers and the Mn ion placed in the region of a contact of two subunits. It is shown that the enzyme would exhibit the property of co-operativity. Numerical solutions of the kinetic equations are obtained and compared to the experimental data and the theoretical model of McAdam et al. (1977a).     

Minimal models of multi-site ligand-binding kinetics

Mathematical models based on the current understanding of co-operativity in ligand binding to the (macro) molecule and relating the dose-response (saturation) curve of the (macro) molecule ligation to intrinsic dissociation constants characterizing the affinities of ligand for binding sites of both unliganded and partly liganded (macro) molecule have been developed. The simplified models disregarding the structural properties and considerations concerning conformational changes of the (macro) molecule retain the ability to yield sigmoid curves of ligand binding and reflect the co-operativity. Model 1 contains only three parameters, parameter κ (a multiplier characterising the change in the affinity) reflects also the existence and type of co-operativity of ligand binding: κ<1 corresponds to positive co-operativity, κ>1 to the negative and κ=1 to the absence of any co-operativity. Model 2 contains an extra parameter, ω, equilibrium constant for the T₀↔R₀ transition but fails to produce dose-response, which would suggest negative co-operativity. For any fixed n>1, the deviation of the dose-response (saturation) curve from the Henri hyperbola depends either solely on parameter κ (Model 1) or also on parameter ω (Model 2). The (macro) molecule being a receptor, both models yield a diversity of dose-response curves due to possible variety of efficacies of the (macro) molecule. The models may be considered as extensions of the Henri model: in case the dissociation constants remain unchanged, the proposed models are reduced to the latter.     

Mixed and uniform co-operativity of ligand binding to multisite proteins: the co-operativity types allowed by the adair equation and conditions for them

It is proved for the first time that the macroscopic co-operativity of binding to a protein with q binding sites may change signs over a single binding curve any number of times from 0 to (q-2), but no more than (q-2). n changes of sign of macroscopic co-operativity requires as a necessary condition at least n changes of sign of microscopic co-operativity, but this necessary condition is not a sufficient one. The necessary and sufficient condition that decides whether there are two changes of sign in a four-site protein is obtained. There are no changes when K₁K₃(K₂-K₄)+K₁K₂(K₃-K₂)+K₂K₃(K₄-K₃) is positive, and two changes when it is negative, presuming the above mentioned necessary conditions to be satisfied. The K's of this formula are the “intrinsic” per-site Adair constants. As a result, the conditions for all six co-operativity types possible with a four-site protein are now known.     

Allosteric kinetics of pyruvate kinase of Saccharomyces carlsbergensis

The allosteric model of Monod et al. (1965) has been used to analyse the steadystate kinetics of pyruvate kinase from Saccharomyces carlsbergensis. The dissociation constants for the substrate phosphoenolpyruvate, the inhibitor ATP as well as the activator fructose-1, 6-diphosphate from the R and T state were calculated using a series of computer programs. On the basis of a crucial relation (derived in the Appendix), which correlates the Hill coefficient and the half-saturating concentration of substrate saturation curves with the parameters of the model of Monod et al., it is possible to differentiate between exclusive and non-exclusive ligand binding. On the other hand, this relation makes it possible to fit the experimental data to an extended model assuming only partially concerted transitions in each enzyme molecule.The physical data of yeast pyruvate kinase point to a tetrameric structure, whereas the steady-state kinetics favour a trimeric one. This discrepancy in the number of protomers can be overcome by the use of an extended model, which permits the occurrence of hybrid states R_tT_n?t. The introduction of one symmetrical hybrid state R₂T₂ into the model explains the kinetic data of yeast pyruvate kinase on the basis of four, probably identical, protomers. The equilibrium constants between the states are given.In the Appendix the derivation of the equation describing the occurrence of hybrid states is reported.     

Conformational analysis of the beta sheet structure of poly-L-alanine and poly(L-alanine-glycine).

The β pleated sheet structures of poly-l-alanine and the polydipeptide (Ala-Gly)_n are analysed by conformational energy calculations, and the results are compared with the structures previously determined by X-ray methods. Structural parameters calculated for β poly-l-alanine using two different sets of potentials are in close agreement (within 5% or less) with the results of X-ray structure analysis (Arnott et al., 1967). For (Ala-Gly)_n, the alanyl and glycyl-glycyl intersheet distances calculated by assuming the model of Fraser et al. (1965) are comparable to those observed in the polydipeptide, but differ significantly from those of (Gly)_n and (Ala)_n. These calculations help establish the structural details of both the polydipeptide and the closely related Bombyx mori silk protein in their β form.     

Conditions for the various types of co-operativity allowed by the adair,equation and their relation with the algebraic character of binding polynomials

A convenient way to obtain for any number, n, of sites, the functions of the constants of the Adair equation that decide the type of co-operativity of ligand binding to a non-dissociating protein is given and is illustrated by the examples n = 4 and n = 5. These functions are invariants of the binding polynomial and various of its derivatives.Although there are some simple sufficient conditions (inequalities relating successive Adair constants) for some co-operativity types, the full necessary and sufficient conditions even for uniform positive and negative co-operativity depend on very complicated functions of the constants for n > 4.However there are alternative ways of writing binding polynomials known as canonical forms. Up to at least n = 5, and probably beyond, the conditions that are complicated in terms of Adair constants are very simple in terms of the constants of canonical forms. For instance any fourth-degree polynomial can be written in the form p(x - α)⁴ + q(x - β)⁴ + 6μ (x - α)²(x - β)² although in three different ways. For one of these ways, the sign of μ distinguishes between mixed and uniform co-operativity. For any kind of mixed co-operativity μ > 0, while μ < 0 corresponds to uniform co-operativity. Advantages of the use of canonical forms are briefly commented on.     

Molecular and Genetic Analyses of Four Nonfunctional S Haplotype Variants Derived from a Common Ancestral S Haplotype Identified in Sour Cherry (Prunus cerasus L.)

Tetraploid sour cherry (Prunus cerasus) has an S-RNase-based gametophytic self-incompatibility (GSI) system; however, individuals can be either self-incompatible (SI) or self-compatible (SC). Unlike the situation in the Solanaceae, where self-compatibility accompanying polyploidization is often due to the compatibility of heteroallelic pollen, the genotype-dependent loss of SI in sour cherry is due to the compatibility of pollen containing two nonfunctional S haplotypes. Sour cherry individuals with the S₄S₆S_36aS_36b genotype are predicted to be SC, as only pollen containing both nonfunctional S_36a and S_36b haplotypes would be SC. However, we previously found that individuals of this genotype were SI. Here we describe four nonfunctional S₃₆ variants. Our molecular analyses identified a mutation that would confer loss of stylar S function for one of the variants, and two alterations that might cause loss of pollen S function for all four variants. Genetic crosses showed that individuals possessing two nonfunctional S₃₆ haplotypes and two functional S haplotypes have reduced self-fertilization due to a very low frequency of transmission of the one pollen type that would be SC. Our finding that the underlying mechanism limiting successful transmission of genetically compatible gametes does not involve GSI is consistent with our previous genetic model for Prunus in which heteroallelic pollen is incompatible. This provides a unique case in which breakdown of SI does not occur despite the potential to generate SC pollen genotypes.GAMETOPHYTIC self-incompatibility (GSI) is a widespread mechanism in flowering plants that prevents self-fertilization and promotes out-crossing (De Nettancourt 2001). In GSI plants, pollen tube growth is arrested if there is a match between the genes at the S-locus that control pollen and stylar specificity. The gene controlling stylar specificity in the Solanaceae, Rosaceae, and Plantaginaceae is known to encode a ribonuclease (S-RNase) (for a review see McClure 2009), while the gene controlling pollen specificity encodes an F-box protein [S haplotype-specific F-box protein (SFB) or S-locus F-box protein (SLF)] (Lai et al. 2002; Entani et al. 2003; Ushijima et al. 2003; Sijacic et al. 2004). As these two specificity genes are tightly linked and recombination between these two genes has never been observed (Ikeda et al. 2005), these two S-locus specificity genes are collectively termed the S haplotype.Characterization of the S haplotype is most advanced in Prunus (Rosaceae) due to the small physical size of the S haplotype region and the close proximity of the stylar S (S-RNase) and pollen S (SFB) genes (Entani et al. 2003; Ushijima et al. 2003; Yamane et al. 2003b; Ikeda et al. 2005). Within Prunus, sweet cherry (Prunus avium) and sour cherry (P. cerasus) represent a model diploid–tetraploid series that has been used to investigate the effects of polyploidy on GSI. Tetraploid sour cherry is considered to have arisen through hybridization between sweet cherry and tetraploid ground cherry (P. fruticosa) (Olden and Nybom 1968). Like sweet cherry, sour cherry exhibits an S-RNase-based GSI system (Yamane et al. 2001; Hauck et al. 2002; Tobutt et al. 2004) and interspecific crossing studies have demonstrated that sour cherry shares eight sweet cherry S haplotypes: S₁, S₄, S₆, S₉, S₁₂, S₁₃, S₁₄, and S₁₆ (Bošković et al. 2006; Hauck et al. 2006a,b; Tsukamoto et al. 2006, 2008). However, in contrast to sweet cherry, natural sour cherry selections include both self-incompatible (SI) and self-compatible (SC) types. A genetic model demonstrating that the genotype-dependent loss of SI in sour cherry is due to the accumulation of a minimum of two nonfunctional S haploytpes within a single individual was developed and validated (Hauck et al. 2006b). These nonfunctional S haplotypes were characterized as either pollen-part mutants or stylar-part mutants, depending on whether the pollen S or stylar S specificity was disrupted. In Prunus, pollen-part and stylar-part mutants are denoted by a prime symbol “′” or a subscribed “m,” respectively, following the S haplotype number (Tsukamoto et al. 2006). Molecular characterizations of five of the nonfunctional S haplotypes from sour cherry characterized to date support the genetic results because mutations were identified that affected the S-RNase and/or SFB. These changes in coding or regulatory regions included mutations within the S-RNase and/or SFB causing premature stop codons, transposable element insertions within SFB and upstream of the S-RNase, and a 23-bp deletion in a conserved region of the S-RNase (Yamane et al. 2003a; Hauck et al. 2006a; Tsukamoto et al. 2006).According to the genetic model, termed the “one-allele-match model,” sour cherry pollen is rejected if one or both of the functional S haplotypes in the 2x pollen grain match an S haplotype in the style (Hauck et al. 2006b). Therefore, only pollen containing two nonfunctional S haplotypes would be SC; thus, a sour cherry genotype is SC if it has a minimum of two nonfunctional S haplotypes. We previously tested the one-allele-match model using 92 sour cherry selections from four progeny populations (Hauck et al. 2006b). For all the progeny except three, their S genotype correctly predicted whether they were SI or SC. The three progeny individuals that were the exception all had the same genotype: S₄S₆S_aS_d. These individuals were predicted to be SC as the S_a and S_d haplotypes were shown to be nonfunctional in genetic studies and therefore S_aS_d pollen should be SC. However, these progeny were classified as SI on the basis of observations of self-pollen tube growth in the styles. The S_a and S_d haplotypes were originally distinguished on the basis of different RFLP fragment sizes using an S-RNase probe; the HindIII fragment sizes for S_a and S_d differed by ∼200 bp, 6.4-kb and 6.2-kb, respectively (Yamane et al. 2001; Hauck et al. 2002). However, partial S-RNase and SFB sequences from the S_a and S_d haplotypes were identical (N. R. Hauck and A. F. Iezzoni, unpublished results), suggesting that S_a and S_d represented different mutations of the same S haplotype. Therefore, we hypothesized that the SI phenotype of the S₄S₆S_aS_d individuals resulted from complementary pistil S and pollen S mutations in the nonfunctional S_a and S_d haplotypes, thus behaving genetically as one functional S haplotype.We previously reported that heteroallelic sour cherry pollen containing two different functional pollen S haplotypes is incompatible (Hauck et al. 2006b). This finding is counter to the well-documented phenomenon in the Solanaceae where SC accompanying polyploidization is frequently due to the SC of heteroallelic pollen (Lewis 1943; Golz et al. 1999, 2001; Tsukamoto et al. 2005; Xue et al. 2009). Therefore, models explaining the molecular basis of self-recognition in Prunus and the Solanaceae must be consistent with these differing genetic expectations. Recently, Huang et al. (2008) reported competitive interaction in a SC selection of tetraploid P. pseudocerasus, raising the possibility that the SC mechanism between these two tetraploid Prunus species could be different. However, although the data in Huang et al. (2008) are consistent with heteroallelic pollen being SC, homoallelic pollen (e.g., S₁S₁, S₅S₅, or S₇S₇) was not shown to be successful in compatible crosses and unsuccessful in incompatible ones. Therefore, it is possible that the SC in P. pseudocerasus could be caused by mutations in other genes critical for the SI reaction. Because of the importance of these differing genetic expectations for understanding S-RNase-based GSI, we sought to investigate our previously identified exceptions to the one-allele-match model. Specifically, our objective was to test our prior hypothesis that the nonfunctional S_a and S_d haplotypes interact in a complementary manner and therefore behave together genetically as a single functional S haplotype. In this work, the S_a and S_d haplotypes were renamed S_36a and S_36b, respectively, following the order of previously published S haplotypes (Tsukamoto et al. 2008; Vaughan et al. 2008) for reasons explained in the results.     

Parameterization of the CO2 and H2O gas exchange of several temperate deciduous broad-leaved trees at the leaf scale considering seasonal changes

A combined model to simulate CO₂ and H₂O gas exchange at the leaf scale was parameterized using data obtained from in situ leaf‐scale observations of diurnal and seasonal changes in the CO₂ and H₂O gas exchange of four temperate deciduous broad‐leaved trees using a porometric method. The model consists of a Ball et al. type stomatal conductance submodel [Ball, Woodrow & Berry, pp. 221–224 in Progress in Photosynthesis Research (ed. I. Biggins), Martinus‐Nijhoff Publishers, Dordrecht, The Netherlands, 1987] and a Farquhar et al. type biochemical submodel of photosynthesis (Farquhar, von Caemmerer & Berry, Planta 149, 78–90, 1980). In these submodels, several parameters were optimized for each tree species as representative of the quantitative characteristics related to gas exchange. The results show that the seasonal physiological changes of V_cmax25 in the biochemical model of photosynthesis should be used to estimate the long‐term CO₂ gas exchange. For R_d25 in the biochemical model of photosynthesis and m in the Ball et al. type stomatal conductance model, the difference should be counted during the leaf expansion period.     

The Impact of Genetic Architecture on Genome-Wide Evaluation Methods

The rapid increase in high-throughput single-nucleotide polymorphism data has led to a great interest in applying genome-wide evaluation methods to identify an individual''s genetic merit. Genome-wide evaluation combines statistical methods with genomic data to predict genetic values for complex traits. Considerable uncertainty currently exists in determining which genome-wide evaluation method is the most appropriate. We hypothesize that genome-wide methods deal differently with the genetic architecture of quantitative traits and genomes. A genomic linear method (GBLUP), and a genomic nonlinear Bayesian variable selection method (BayesB) are compared using stochastic simulation across three effective population sizes and a wide range of numbers of quantitative trait loci (N_QTL). GBLUP had a constant accuracy, for a given heritability and sample size, regardless of N_QTL. BayesB had a higher accuracy than GBLUP when N_QTL was low, but this advantage diminished as N_QTL increased and when N_QTL became large, GBLUP slightly outperformed BayesB. In addition, deterministic equations are extended to predict the accuracy of both methods and to estimate the number of independent chromosome segments (M_e) and N_QTL. The predictions of accuracy and estimates of M_e and N_QTL were generally in good agreement with results from simulated data. We conclude that the relative accuracy of GBLUP and BayesB for a given number of records and heritability are highly dependent on M_e, which is a property of the target genome, as well as the architecture of the trait (N_QTL).THE rapid progress and reducing costs of genome sequencing and high-throughput DNA techniques have led to a great interest in applying genome-wide evaluation methods to identify individuals of high genetic merit. Genome-wide evaluation uses associations of a large number of SNP (single nucleotide polymorphism) markers across the whole genome with phenotypes to produce accurate estimates of breeding values (EBVs) for candidates to selection (Meuwissen et al. 2001). The accuracy of genome-wide selection (i.e., selection based on genomic EBVs) is expected to be substantially higher than that of traditional best linear unbiased prediction (BLUP) selection, which is based on pedigree and phenotypic data (Daetwyler et al. 2008; Goddard 2009; Hayes et al. 2009c). In addition, genome-wide selection has the potential to reduce inbreeding rates because of the increased emphasis on own rather than family information (Woolliams et al. 2002; Daetwyler et al. 2007; Dekkers 2007). Furthermore, the application of genome-wide evaluation approaches can significantly aid our understanding of quantitative trait genetic architecture.The genome-wide evaluation methods suggested to date can be broadly categorized into groups according to whether there is an assortment of the SNP by magnitude of effect or contribution to the variance. One group treats SNP homogeneously and includes variants of genomic best linear unbiased prediction (GBLUP). This group includes a form of ridge regression (Meuwissen et al. 2001) and the use of a realized relationship matrix computed from the markers instead of the traditional pedigree matrix (NejatiJavaremi et al. 1997; Villanueva et al. 2005; Hayes et al. 2009c). Both approaches have been shown to be equivalent (Habier et al. 2007; Goddard 2009). A second group provides for heterogeneity among SNP contributions to the variance, with some contributions permitted to be large while the remainder are small, possibly zero. This assortment is helped by Bayesian approaches, which place priors on numbers of SNP with major contributions (e.g., BayesA and BayesB; see Meuwissen et al. 2001, 2009; Lee et al. 2008), or with some penalty based on functions of the magnitude of effect for each SNP (e.g., Lasso; see Tibshirani 1996; Yi and Xu 2008) or with other smoothing metrics (Long et al. 2007). A third group attempts to reduce dimensionality by using principal components or partial least squares (Raadsma et al. 2008; Solberg et al. 2009) to identify an informative subset of SNP genotypes. The main two methods currently used in real data sets are a linear prediction method, GBLUP, and variants of nonlinear Bayesian variable selection approaches such as BayesB.In most simulated published data, the accuracy of BayesB outperformed that of GBLUP (e.g., Meuwissen et al. 2001; Habier et al. 2007; Lund et al. 2009). However, real data results have not consistently supported this conclusion. Two reviews of empirical results in dairy cattle to date have shown that GBLUP and BayesB result in very similar accuracies for most traits (Hayes et al. 2009a; Vanraden et al. 2009). One reason for the disagreement between simulated and real data results could be that the genetic architecture simulated is significantly different from what is found in real populations. Most studies published to date that compare methods using simulated architectures have considered only 50 or fewer QTL affecting the trait (e.g., Meuwissen et al. 2001; Habier et al. 2007; Lund et al. 2009). In this article we hypothesize that the relative utility of genome-wide evaluation methods depends significantly on both the genomic structure of the population and the genetic trait architecture.The main objective of this study was to compare a linear method, GBLUP, and a nonlinear variable selection method, BayesB, using simulated data across a range of population and trait genetic architectures to further understand the mechanics of genome-wide evaluation methods. An important secondary objective was to extend deterministic prediction models to predict the accuracy of both methods. Theoretical models complement stochastic simulation by helping the understanding of the factors involved in genome-wide evaluation performance and, in return, stochastic simulation is used to confirm theoretical derivations.     

Cooperative response of chemically excitable membrane. II. Two-state models and their limitations

Various types of two-state models, classified by the type of direct receptorionophore coupling, were formulated based on the previously presented generalized two-state model of cooperativity (Kijima &; Kijima, 1978) and their dose-response relationships were examined. Hill coefficient at the mid-point of dose-response curve n_H^o the measure of the cooperativity of curves, is restricted for partial agonists in any two-state models because n_H^o is expressed by the product of two terms, one of which decreases when the other increases. In the independent gating unit model in which the channel opens only when the independent gating units are all in the activated state, the restriction of n_H^o is the most stringent: it never exceeds 2. In 2 ÷ 1·39 even for full agonist. It appears to be incompatible with most of the cooperative responses observed on chemically excitable membrane. In the basic model or one protomer-one channel model, n_H^o never exceeds 2·0 when 〈p〉_∞, the maximum fraction of open-channel, is less than $\text{2}\text{3}$. In the cooperative gating unit model, n_H^o is the least restricted, which is less than 2·8 when 〈p〉_∞ ≤ 0·5, but if the number of gating units, N in a receptor is practically reasonably small (N ≤ 12), n_H^o ≤ 2·0 when 〈p〉_∞ ≤ 0·58. It is discussed whether or not several representative drug-receptive membranes can be accounted for by two-state models. Response of the insect sugar receptor is out of the above limitations of two-state models and can be accounted for by three-state model. The origin of cooperative interaction can be inferred by the shapes of dose-response curves. Cooperative dose-response curves of two dimensional lattices or oligomerc systems with large number of protomers weakly interacting by long range forces bend upward more markedly at lower region than the curves of strongly interacting oligomers, when curves with the same n_H^o are compared.     

Genome-Wide Association Studies and the Problem of Relatedness Among Advanced Intercross Lines and Other Highly Recombinant Populations

Model organisms offer many advantages for the genetic analysis of complex traits. However, identification of specific genes is often hampered by a lack of recombination between the genomes of inbred progenitors. Recently, genome-wide association studies (GWAS) in humans have offered gene-level mapping resolution that is possible because of the large number of accumulated recombinations among unrelated human subjects. To obtain analogous improvements in mapping resolution in mice, we used a 34th generation advanced intercross line (AIL) derived from two inbred strains (SM/J and LG/J). We used simulations to show that familial relationships among subjects must be accounted for when analyzing these data; we then used a mixed model that included polygenic effects to address this problem in our own analysis. Using a combination of F₂ and AIL mice derived from the same inbred progenitors, we identified genome-wide significant, subcentimorgan loci that were associated with methamphetamine sensitivity, (e.g., chromosome 18; LOD = 10.5) and non-drug-induced locomotor activity (e.g., chromosome 8; LOD = 18.9). The 2-LOD support interval for the former locus contains no known genes while the latter contains only one gene (Csmd1). This approach is broadly applicable in terms of phenotypes and model organisms and allows GWAS to be performed in multigenerational crosses between and among inbred strains where familial relatedness is often unavoidable.SUSCEPTIBILITY to diseases such as drug abuse is partially determined by genetic factors. The identification of the alleles that underlie disease susceptibility is an immensely important goal that promises to revolutionize both the diagnosis and the treatment of human disease. Genome-wide association studies (GWAS) in humans can locate common alleles with great precision. However, GWAS may be unable to identify the bulk of the heritable variability for common genetic diseases; some of this “missing heritability” is thought to be due to rare alleles (Manolio et al. 2009). Model organisms are complementary to human genetic studies and offer unique advantages including the ability to control the environment, perform dangerous or invasive procedures, and test hypotheses by manipulating genes via genetic engineering; a final advantage is that crosses between two inbred strains avoid many of the difficulties associated with rare alleles.Studies in model organisms have frequently employed intercrosses (F₂''s) to identify quantitative trait loci (QTL) that underlie phenotypic variability. F₂ crosses are easy to produce and easy to analyze; however, due to a lack of recombination they can identify only larger genomic regions and are thus unsuitable for identifying the genes that cause QTL (Flint et al. 2005; Peters et al. 2007). This is a serious limitation that can be addressed by using populations with greater numbers of accumulated recombinations. Darvasi and Soller (1995) suggested the creation of advanced intercross lines (AILs) by successive generations of random mating after the F₂ generation to produce additional recombinations. An AIL offers vastly improved mapping resolution while maintaining the desirable property that all polymorphic alleles are common.We used an AIL to study sensitivity to methamphetamine, which is a genetically complex trait that may be useful for identifying genetic factors influencing the subjectively euphoric response to stimulant drugs and susceptibility to drug abuse (Palmer et al. 2005; Phillips et al. 2008; Bryant et al. 2009). For example, a prior study suggested that the gene Casein Kinase 1 Epsilon (Csnk1e) might influence sensitivity to the acute locomotor response to methamphetamine in mice (Palmer et al. 2005). This conclusion has been bolstered by additional pharmacological (Bryant et al. 2009) and genetic studies. In addition, we have shown that polymorphisms in this gene are associated with sensitivity to the euphoric effects of amphetamine in humans (Veenstra-Vanderweele et al. 2006). Another group has subsequently reported that this same gene is associated with heroine addiction (Levran et al. 2008). Thus, genes that modulate the acute locomotor response to a drug in mice may also be important for sensitivity to similar drugs in humans as well as the risk for developing drug abuse.The purpose of this study was to develop a framework for rapid identification of high precision QTL and ideally specific genes that influence sensitivity to methamphetamine in mice by employing an AIL. We produced an F₂ cross (n = 490) and a corresponding 34th generation AIL (n = 688) derived from the inbred strains SM/J and LG/J. This allowed us to compare and integrate the results from F₂ and AIL mice. We examined the locomotor stimulant response to a 2-mg/kg dose of methamphetamine, which is extremely disparate in the two progenitor strains. We performed a GWAS using either simple regression, which ignored relatedness, or a mixed model that accounted for relatedness by using identity coefficients that were calculated from the pedigree. We also explored two methods to estimate significance: simple permutation and gene dropping. We discuss the performance of a mixed model that includes polygenic effects vs. simple regression and the performance of permutation vs. gene dropping. The methods used in this study are applicable to a variety of other phenotypes and populations.     

Kinetic manifestations of allosteric interactions in models of regulatory enzymes with "indirect" co-operativity

The shape of the plots of initial reaction rate (ν) versus initial substrate concentration ([S]₀) and versus initial concentration of allosteric effector ([F]₀) for the model of allosteric enzyme of Monod, Wyman &; Changeux (1965) and for the model of dissociating regulatory enzyme has been analysed by means of the inconstant exponent (q) for substrate or effector concentration, respectively. It has been shown that allosteric interactions in above-mentioned models with “indirect” co-operativity may be manifested not only by the sigmoidal shape of the plot of ν versus [S]₀ or ν versus [F]₀ (with one point of inflexion) but also by the increase in the magnitude of exponent q in progress of saturation process of the enzyme by the substrate or by the effector in the absence of the sigmoidal shape of these plots. It has been shown also that the plot of ν versus [S]₀ has two inflexion points when the parameters have certain definite values. One of these inflexion points (or even both at definite values of the parameters) is hardly discernible. At certain definite values of the parameters two inflexion points may be kinetically manifested by such phenomenon as “negative” co-operativity (q < 1). This is possible if one of the interconvertable enzyme forms exceeds another not only in the affinity to the substrate but also in the value of the rate constant for catalytic breakdown of the enzyme-substrate complex.     

Protein symmetry and the co-operative ligand-binding behaviour predicted by allosteric Koshland models

It is shown that the nearest-neighbour interaction two-conformation allosteric models of Koshland, Nemethy & Filmer (1966) predict binding curves with a centre of symmetry when the protein is also symmetrical and induced-fit is assumed. When nonexclusive binding to both conformations is assumed, the models predict that the family of homotropic binding curves obtained by varying the heterotropic ligand has a centre of symmetry. It is argued that the symmetry or asymmetry of binding curves is the main experimentally verifiable prediction of allosteric models insofar as they are models of interaction between protein subunits.Symmetry in a binding curve greatly simplifies the analysis of cooperative behaviour. The co-operative features possible with a symmetric binding curve for a four-site protein are analysed. The sign of co-operativity may either be uniform or change twice as saturation increases; the conditions for the various possibilities are given. For example, in terms of the intrinsic binding constants per site A^∥₁, A2, etc. the necessary and sufficient condition for positive macroscopic co-operativity over the whole symmetric binding curve is A^∥₁≤ A2, A ^∥₁ ≤ A3 which should be contrasted with the obvious A^∥₁ ≤ Al, AZ ≤A^∥₃ (positive microscopic co-operativity) which is only a sufficient but not a necessary condition. A symmetric curve may have one or three, but no more, extrema of the “Hill coefficient” h. For three extrema a change of sign of microscopic (but not necessarily macroscopic) co-operativity is necessary but not sufficient. In the case where there are off-centre maxima of h, then h < 2 everywhere on the curve.The Koshland models predict qualitative and quantitative restrictions on the forms of binding curves additional to that of symmetry. In tetrameric induced fit models, negative co-operativity in the mid-region of the curve and positive co-operativity in the outside regions is possible, but not the opposite, and three extrema of h are possible with uniform positive but not with uniform negative co-operativity.Thus by recognising the importance of symmetry it has been possible to describe and categorise all the co-operativity behaviour possible with the most plausible Koshland tetrameric models. Several experimental examples of probable non-exclusive binding to proteins and enzymes are discussed, and it is shown how the symmetry point of view illuminates their interpretation.     

Cooperativity in viral fusion

A simple model for membrane fusion mediated by vial spike glycoproteins is presented. The viral proteins are considered to be allosteric proteins that undergo concerted conformational transitions when they bind the ligand. The ligand in this case is H⁺. The effect of the conformational transition is to bring membranes together and induce their fusion. An equation is derived for the dependence of fusion rates on ligand concentration, for a given dissociation constant (K _d), equilibrium constant for the conformational change (L), and number of cooperating subunits (n). Curves generated by this equation provide a reasonable fit to data on the rates of fusion of Vesicular Stomatitis virus with cells for a pK _d of 6.3,L=1000 andn=6.     

Prediction of Genetic Values of Quantitative Traits in Plant Breeding Using Pedigree and Molecular Markers

The availability of dense molecular markers has made possible the use of genomic selection (GS) for plant breeding. However, the evaluation of models for GS in real plant populations is very limited. This article evaluates the performance of parametric and semiparametric models for GS using wheat (Triticum aestivum L.) and maize (Zea mays) data in which different traits were measured in several environmental conditions. The findings, based on extensive cross-validations, indicate that models including marker information had higher predictive ability than pedigree-based models. In the wheat data set, and relative to a pedigree model, gains in predictive ability due to inclusion of markers ranged from 7.7 to 35.7%. Correlation between observed and predictive values in the maize data set achieved values up to 0.79. Estimates of marker effects were different across environmental conditions, indicating that genotype × environment interaction is an important component of genetic variability. These results indicate that GS in plant breeding can be an effective strategy for selecting among lines whose phenotypes have yet to be observed.PEDIGREE-BASED prediction of genetic values based on the additive infinitesimal model (Fisher 1918) has played a central role in genetic improvement of complex traits in plants and animals. Animal breeders have used this model for predicting breeding values either in a mixed model (best linear unbiased prediction, BLUP) (Henderson 1984) or in a Bayesian framework (Gianola and Fernando 1986). More recently, plant breeders have incorporated pedigree information into linear mixed models for predicting breeding values (Crossa et al. 2006, 2007; Oakey et al. 2006; Burgueño et al. 2007; Piepho et al. 2007).The availability of thousands of genome-wide molecular markers has made possible the use of genomic selection (GS) for prediction of genetic values (Meuwissen et al. 2001) in plants (e.g., Bernardo and Yu 2007; Piepho 2009; Jannink et al. 2010) and animals (Gonzalez-Recio et al. 2008; VanRaden et al. 2008; Hayes et al. 2009; de los Campos et al. 2009a). Implementing GS poses several statistical and computational challenges, such as how models can cope with the curse of dimensionality, colinearity between markers, or the complexity of quantitative traits. Parametric (e.g., Meuwissen et al. 2001) and semiparametric (e.g., Gianola et al. 2006; Gianola and van Kaam 2008) methods address these problems differently.In standard genetic models, phenotypic outcomes, , are viewed as the sum of a genetic value, , and a model residual, ; that is, . In parametric models for GS, is described as a regression on marker covariates (j = 1,  …  , p molecular markers) of the form , such that(or , in matrix notation), where is the regression of on the jth marker covariate .Estimation of via multiple regression by ordinary least squares (OLS) is not feasible when p > n. A commonly used alternative is to estimate marker effects jointly using penalized methods such as ridge regression (Hoerl and Kennard 1970) or the Least Absolute Shrinkage and Selection Operator (LASSO) (Tibshirani 1996) or their Bayesian counterpart. This approach yields greater accuracy of estimated genetic values and can be coupled with geostatistical techniques commonly used in plant breeding to model multienvironments trials (Piepho 2009).In ridge regression (or its Bayesian counterpart) the extent of shrinkage is homogeneous across markers, which may not be appropriate if some markers are located in regions that are not associated with genetic variance, while markers in other regions may be linked to QTL (Goddard and Hayes 2007). To overcome this limitation, many authors have proposed methods that use marker-specific shrinkage. In a Bayesian setting, this can be implemented using priors of marker effects that are mixtures of scaled-normal densities. Examples of this are methods Bayes A and Bayes B of Meuwissen et al. (2001) and the Bayesian LASSO of Park and Casella (2008).An alternative to parametric regressions is to use semiparametric methods such as reproducing kernel Hilbert spaces (RKHS) regression (Gianola and van Kaam 2008). The Bayesian RKHS regression regards genetic values as random variables coming from a Gaussian process centered at zero and with a (co)variance structure that is proportional to a kernel matrix K (de los Campos et al. 2009b); that is, , where , are vectors of marker genotypes for the ith and jth individuals, respectively, and is a positive definite function evaluated in marker genotypes. In a finite-dimensional setting this amounts to modeling the vector of genetic values, , as multivariate normal; that is, where is a variance parameter. One of the most attractive features of RKHS regression is that the methodology can be used with almost any information set (e.g., covariates, strings, images, graphs). A second advantage is that with RKHS the model is represented in terms of n unknowns, which gives RKHS a great computational advantage relative to some parametric methods, especially when p ≫ n.This study presents an evaluation of several methods for GS, using two extensive data sets. One contains phenotypic records of a series of wheat trials and recently generated genomic data. The other data set pertains to international maize trials in which different traits were measured in maize lines evaluated under severe drought and well-watered conditions.     

Functional properties of the hemoglobin from the South American snake Mastigodryas bifossatus

The hemolysate of Mastigodryas bifossatus shows two major hemoglobins with very close isoelectric points, and four different globin chains. The stripped hemolysate exhibits a low alkaline Bohr effect (Δlog P₅₀/ΔpH = −0.30 between pH7 and 8) and a decrease of the co-operativity from 2.3 to unity when the pH increases from 6.15 to 8.5. In the presence of ATP, large changes in the oxygen affinity and co-operativity are observed. The Bohr effect rises to −0.46 and the n₅₀ values stay at around 3 in the pH range 6–9. An increase in temperature induces a large decrease in the oxygen affinity for the stripped hemolysate. In the pH range between 7.5 and 8.5, the values of AH in kcal/M are around 10 fold larger for the stripped protein than for the protein in the presence of ATP. Measurements of rapid kinetics of oxygen dissociation and carbon monoxide binding reflect the ATP sensitivity observed in equilibrium experiments.     

Bayesian Inference of Genetic Parameters Based on Conditional Decompositions of Multivariate Normal Distributions

It is widely recognized that the mixed linear model is an important tool for parameter estimation in the analysis of complex pedigrees, which includes both pedigree and genomic information, and where mutually dependent genetic factors are often assumed to follow multivariate normal distributions of high dimension. We have developed a Bayesian statistical method based on the decomposition of the multivariate normal prior distribution into products of conditional univariate distributions. This procedure permits computationally demanding genetic evaluations of complex pedigrees, within the user-friendly computer package WinBUGS. To demonstrate and evaluate the flexibility of the method, we analyzed two example pedigrees: a large noninbred pedigree of Scots pine (Pinus sylvestris L.) that includes additive and dominance polygenic relationships and a simulated pedigree where genomic relationships have been calculated on the basis of a dense marker map. The analysis showed that our method was fast and provided accurate estimates and that it should therefore be a helpful tool for estimating genetic parameters of complex pedigrees quickly and reliably.MUCH effort in genetics has been devoted to revealing the underlying genetic architecture of quantitative or complex traits. Traditionally, the polygenic model has been used extensively to estimate genetic variances and breeding values of natural and breeding populations, where an infinite number of genes is assumed to code for the trait of interest (Bulmer 1971; Falconer and Mackay 1996). The genetic variance of a quantitative trait can be decomposed into an additive part that corresponds to the effects of individual alleles and a part that is nonadditive because of interactions between alleles. Attention has generally been focused on the estimation of additive genetic variance (and heritability), since additive variation is directly proportional to the response of selection via the breeder''s equation (Falconer and Mackay 1996, Chap. 11). However, to estimate additive genetic variation and heritability accurately, it can be important to identify potential nonadditive sources in genetic evaluations (Misztal 1997; Ovaskainen et al. 2008; Waldmann et al. 2008), especially if the pedigree being analyzed contains a large proportion of full-sibs and clones, as these in particular give rise to nonadditive genetic relationships (Lynch and Walsh 1998, pp. 145). The polygenic model using pedigree and phenotypic information, i.e., the animal model (Henderson 1984), has been the model of choice for estimating genetic parameters in breeding and natural populations (Abney et al. 2000; Sorensen and Gianola 2002; O′Hara et al. 2008).Recent breakthroughs in molecular techniques have made it possible to create genome-wide, single nucleotide polymorphism (SNP) maps. These maps have helped to uncover a vast amount of new loci responsible for trait expression and have provided general insights into the genetic architecture of quantitative traits (e.g., Valdar et al. 2006; Visscher 2008; Flint and Mackay 2009). These insights can help when calculating disease risks in humans, when attempting to increase the yield from breeding programs, and when estimating relatedness in conservation programs. High-density SNPs of many species of importance to science and agriculture can now be scored quickly and relatively cheaply, for example, in mice (Valdar et al. 2006), chickens (Muir et al. 2008), and dairy cattle (VanRaden et al. 2009).In the analysis of populations of breeding stock, the inclusion of dense marker data has improved the predictive ability (i.e., reliability) of genetic evaluations compared to the traditional phenotype model, both in simulations (Meuwissen et al. 2001; Calus et al. 2008; Hayes et al. 2009) and when using real data (Legarra et al. 2008; VanRaden et al. 2009; González-Recio et al. 2009). Meuwissen et al. (2001) suggested that the effect of all markers should first be estimated, and then summed, to obtain genomic estimated breeding values (GEBVs). An alternative procedure, where all markers are used to compute the genomic relationship matrix (in place of the additive polygenic relationship matrix) has also been suggested (e.g., Villanueva et al. 2005; VanRaden 2008; Hayes et al. 2009); this matrix is then incorporated into the statistical analysis to estimate GEBVs. A comparison of both procedures (VanRaden 2008) yielded similar estimates of GEBVs in cases where the effect of an individual allele was small. In addition, if not all pedigree members have marker information, a combined relationship matrix derived from both genotyped and ungenotyped individuals could be computed; this has been shown to increase the accuracy of GEBVs (Legarra et al. 2009; Misztal et al. 2009). Another plausible option to incorporate marker information is to use low-density SNP panels within families and to trace the effect of SNPs from high-density genotyped ancestors, as suggested by Habier et al. (2009) and Weigel et al. (2009). However, fast and powerful computer algorithms, which can use the marker information as efficiently as possible in the analysis of quantitative traits, are needed to obtain accurate GEBVs from genome-wide marker data.This study describes the development of an efficient Bayesian method for incorporating general relationships into the genetic evaluation procedure. The method is based on expressing the multivariate normal prior distribution as a product of one-dimensional normal distributions, each conditioned on the descending variables. When evaluating the genetic parameters of natural and breeding populations, high-dimensional distributions are often used as prior distributions of various genetic effects, such as the additive polygenic effect (Wang et al. 1993), multivariate additive polygenic effects (Van Tassell and Van Vleck 1996), and quantitative trait loci (QTL) effects via the identical-by-decent matrix (Yi and Xu 2000). A Bayesian framework is adopted to obtain posterior distributions of all unknown parameters, estimated by using Markov chain Monte Carlo (MCMC) sampling algorithms in the software package WinBUGS (Lunn et al. 2000, 2009). By performing prior calculations in the form of the factorized product of simple univariate conditional distributions, the computational time of the MCMC estimation procedure is reduced considerably. This feature permits rapid inference for both the polygenic model and the genomic relationship model. Moreover, the decomposition allows for inbreeding of varying degree, since the correct genetic covariance structure can be inferred into the analysis. In this article, we test the method on two previously published pedigree data sets: phenotype data from a large pedigree of Scots pine, incorporation of information on both additive and dominance genetic relationships (Waldmann et al. 2008); and genomic information obtained from a genome-wide scan of a simulated animal population (Lund et al. 2009).