Involvement of Glu G3(101)beta in the function of hemoglobin. Comparative O2 equilibrium studies of human mutant hemoglobins

The glutamyl residue at G3(101)beta of normal hemoglobin (Hb A) is one of the alpha 1 beta 2 subunit contacts which are vital to O2 binding properties of the molecule. The O2 equilibrium properties of the four mutants with different substitutions at this site are studied in order to elucidate the role of this residue. Under stripped conditions with minimum chloride the order of O2 affinity is: Hb A (Glu) much less than Hb Rush (Gln) less than or equal to Hb British Columbia (Lys) less than or equal to Hb Potomac (Asp) less than or equal to Hb Alberta (Gly). The first Adair constants, K1, for the mutant hemoglobins are greater than that for Hb A whereas the fourth, K4, are similar, indicating that the allosteric constants (L) of these mutants are greatly reduced. Therefore, the G3(101)beta residue contributes intrinsically to the strengthening of the structural constraints that are imposed upon the deoxy (T) forms but not the oxy (R) form. On addition of 0.1 M Cl- and further addition of 2,3-diphosphoglycerate or inositol hexaphosphate, their O2 affinities and cooperativities are altered, reflecting different responses to anionic ligands. Hb Rush exhibits a stronger chloride effect than Hb A and the other variants and, as a result, an increased Bohr effect and a smaller heat of oxygenation at pH 6.5. These changes are consistent with an increased positive net charge in the central cavity of Hb Rush and subsequent extra anion binding in the deoxy form. The tetramer to dimer dissociation constants are estimated to be greater than normal for Hb British Columbia and less than normal for Hb Alberta. This comparative study of the G3(101)beta mutants indicates that the size and the charge of this residue may influence the switching of two neighboring interchain hydrogen bonds that occurs during oxygenation of normal hemoglobin.     

Nonfixed relationship of the Michaelis constant and maximum velocity with their corresponding rate constants

The Michaelis constant (K(m)) and V(mas) (E0k(cat)) values for two mutant sets of enzymes were studied from the viewpoint of their definition in a rapid equilibrium reaction model and in a steady state reaction model. The "AMP set enzyme" had a mutation at the AMP-binding site (Y95F, V67I, and V67I/L76V), and the "ATP set enzyme" had a mutation at a possible ATP-binding region (Y32F, Y34F, and Y32A/Y34A). Reaction rate constants obtained using steady state model analysis explained discrepancies found by the rapid equilibrium model analysis. (i) The unchanged number of bound AMPs for Y95F and the wild type despite the markedly increased K(m) values for AMP of the AMP set of enzymes was explained by alteration of the rate constants of the AMP step (k(+2), k(-2)) to retain the ratio k(+2)/k(-2). (ii) A 100 times weakened selectivity of ATP for Y34F in contrast to no marked changes in K(m) values for both ATP and AMP for the ATP set of enzymes was explained by the alteration of the rate constants of the ATP steps. A similar alteration of the K(m) and k(cat) values of these enzymes resulted from distinctive alterations of their rate constants. The pattern of alteration was highly suggestive. The most interesting finding was that the rate constants that decided the K(m) and k(cat) values were replaced by the mutation, and the simple relationships between K(m), k(cat), and the rate constants of K(m)1 = k(+1)/k(-1) and k(cat) = k(f) were not valid. The nature of the K(m) and k(cat) alterations was discussed.     

Numerical modeling and uncertainties in rate coefficients for methane utilization and TCE cometabolism by a methane-oxidizing mixed culture

The rates of methane utilization and trichloroethylene (TCE) cometabolism by a methanotrophic mixed culture were characterized in batch and pseudo-steady-state studies. Procedures for determination of the rate coefficients and their uncertainties by fitting a numerical model to experimental data are described. The model consisted of a system of differential equations for the rates of Monod kinetics, cell growth on methane and inactivation due to TCE transformation product toxicity, gas/liquid mass transfer of methane and TCE, and the rate of passive losses of TCE. The maximum specific rate of methane utilization (k(CH(4) )) was determined by fitting the numerical model to batch experimental data, with the initial concentration of active methane-oxidizing cells (X(0) (a)) also used as a model fitting parameter. The best estimate of k(CH(4) ) was 2.2 g CH(4)/g cells-d with excess copper available, with a single-parameter 95% confidence interval of 2.0-2.4 mg/mg-d. The joint 95% confidence region for k(CH(4) ) and X(0) (a) is presented graphically. The half-velocity coefficient (K(S,CH(4) )) was 0.07 mg CH(4)/L with excess copper available and 0.47 mg CH(4)/L under copper limitation, with 95% confidence intervals of 0.02-0.11 and 0.35-0.59 mg/L, respectively. Unique values of the TCE rate coefficients k(TCE) and K(S,TCE) could not be determined because they were found to be highly correlated in the model fitting analysis. However, the ratio k(TCE)/K(S,TCE) and the TCE transformation capacity (T(C)) were well defined, with values of 0.35 L/mg-day and 0.21 g TCE/g active cells, respectively, for cells transforming TCE in the absence of methane or supplemental formate. The single-parameter 95% confidence intervals for k(TCE)/K(S,TCE) and T(C) were 0.27-0.43 L/mg-d and 0.18-0.24 g TCE/g active cells, respectively. The joint 95% confidence regions for k(TCE)/K(S,TCE) and T(C) are presented graphically. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 53: 320-331, 1997.     

Obtaining Critical Values for Simultaneous Confidence Intervals and Multiple Testing

There are many situations where it is desired to make simultaneous tests or give simultaneous confidence intervals for linear combinations (contrasts) of population or treatment means. Somerville (1997, 1999) developed algorithms for calculating the critical values for a large class of simultaneous tests and simultaneous confidence intervals. Fortran 90 and SAS‐IML batch programs and interactive programs were developed. These programs calculate the critical values for 15 different simultaneous confidence interval procedures (and the corresponding simultaneous tests) and for arbitrary procedures where the user specifies a combination of one and two sided contrasts. The programs can also be used to obtain the constants for “step‐down” testing of multiple hypotheses. This paper gives examples of the use of the algorithms and programs and illustrates their versatility and generality. The designs need not be balanced, multiple covariates may be present and there may be many missing values. The use of multiple regression and dummy variables to obtain the required variance covariance matrix is illustrated. Under weak normality assumptions the methods are “exact” and make the use of approximate methods or “simulation” unnecessary.     

An Exact Confidence Interval for the Ratio of Two Related Proportions

I propose an exact confidence interval for the ratio of two proportions when the proportions are not independent. One application is to estimate the population prevalence using a screening test with perfect specificity but imperfect sensitivity. The population prevalence is the ratio of the observed prevalence divided by the test's sensitivity. I describe a method to calculate exact confidence intervals for this problem and compare these results with approximate confidence intervals given previously.     

Test-based exact confidence intervals for the difference of two binomial proportions

Confidence intervals are often provided to estimate a treatment difference. When the sample size is small, as is typical in early phases of clinical trials, confidence intervals based on large sample approximations may not be reliable. In this report, we propose test-based methods of constructing exact confidence intervals for the difference in two binomial proportions. These exact confidence intervals are obtained from the unconditional distribution of two binomial responses, and they guarantee the level of coverage. We compare the performance of these confidence intervals to ones based on the observed difference alone. We show that a large improvement can be achieved by using the standardized Z test with a constrained maximum likelihood estimate of the variance.     

Confidence intervals for a variance ratio, or for heritability, in an unbalanced mixed linear model

A procedure is presented for constructing an exact confidence interval for the ratio of the two variance components in a possibly unbalanced mixed linear model that contains a single set of m random effects. This procedure can be used in animal and plant breeding problems to obtain an exact confidence interval for a heritability. The confidence interval can be defined in terms of the output of a least squares analysis. It can be computed by a graphical or iterative technique requiring the diagonalization of an m X m matrix or, alternatively, the inversion of a number of m X m matrices. Confidence intervals that are approximate can be obtained with much less computational burden, using either of two approaches. The various confidence interval procedures can be extended to some problems in which the mixed linear model contains more than one set of random effects. Corresponding to each interval procedure is a significance test and one or more estimators.     

Simultaneous small-sample multivariate Bernoulli confidence intervals

A technique based on the bootstrap is presented for assessing the simultaneous confidence level of k small-sample confidence intervals for multivariate Bernoulli marginal frequencies. The small-sample intervals used are those of Clopper and Pearson (1934, Biometrika 26, 404-413) and require iterative computation. To estimate the simultaneous confidence level, the multivariate Bernoulli vectors are resampled via the bootstrap and the Clopper-Pearson intervals recomputed on each pseudosample. The bootstrap estimate is then the proportion of times (computed via Monte Carlo) that all the k intervals computed by resampling contain the original sample frequencies. The technique is applied to single-sample HLA data.     

Dynamic mechanism of the self-assembly process of tobacco mosaic virus protein studied by rapid temperature-jump small-angle X-ray scattering using synchrotron radiation

The self-assembly process of tobacco mosaic virus protein (TMVP) was observed by rapid temperature-jump time-resolved solution X-ray small-angle scattering using synchrotron radiation. The temperature-jump device used for the X-ray measurements is rapid enough to cope with even the fastest-assembling process of TMVP, and accumulates data of reasonable signal-to-noise ratios with a minimum total counting time of 7.5 seconds. The measurements suggested that the 20 S disk of TMVP polymerized to stacked disks (short rods). The time to complete stacking varied from approximately 25 seconds to approximately 1200 seconds, depending on the solution condition and magnitude of the temperature gap. Higher protein concentration, ionic strength and temperature favoured faster association. The results were analysed in terms of a set of kinetic equations that describe the two-stage aggregation of TMVP with an equilibrium constant K1, and two rate constants k+2 and k-2 for association and dissociation of disks, respectively. The consistency of the analysis suggests that the TMVP assembly proceeds in two steps of: (1) the aggregation of A-proteins into double-layered disks; and (2) the stacking of double-layered disks. The kinetic analysis indicated that the stacking belongs to the lowest range of protein-protein interaction system.     

The efficiency of simulation-based multiple comparisons

A frequently encountered problem in practice is that of simultaneous interval estimation of p linear combinations of a parameter beta in the setting of (or equivalent to) a univariate linear model. This problem has been solved adequately only in a few settings when the covariance matrix of the estimator is diagonal; in other cases, conservative solutions can be obtained by the methods of Scheffé, Bonferroni, or Sidák (1967, Journal of the American Statistical Association 62, 626-633). Here we investigate the efficiency of using a simulated critical point for exact intervals, which has been suggested before but never put to serious test. We find the simulation-based method to be completely reliable and essentially exact. Sample size savings are substantial (in our settings): 3-19% over the Sidák method, 4-37% over the Bonferroni method, and 27-33% over the Scheffé method. We illustrate the efficiency and flexibility of the simulation-based method with case studies in physiology and marine ecology.     

Quaternary interactions in hemoglobin beta subunit tetramers. Kinetics of ligand binding and self-assembly

We have investigated the rates of monomer in equilibrium with tetramer self-association of oxygenated beta SH subunits of human hemoglobin A as well as the influence of self-association on the binding kinetics for O2 and CO. A 4 beta in equilibrium with 2 beta 2 in equilibrium with beta 4 assembly pathway can be used to describe the association equilibria and kinetics. We have determined all four elementary rate constants for this assembly pathway at 15 degrees C in 0.1 M Tris-HCl, 0.1 M NaCl, 1 mM Na2EDTA, pH 7.4. These data imply that a significant amount (approximately 17%) of beta 2 can be present. Laser photolysis kinetic studies of O2 binding indicate that the O2 association rate constant is unaffected by the degree of self-association. In contrast, photolysis of beta CO solutions shows an overall rate of CO binding that increases at higher protein concentrations. These data are consistent with a concentration-dependent equilibrium between two protein species with CO association rates differing by a factor of 2.5, but they do not appear to be compatible with a direct assignment of different CO binding rates to the different assembly states. Rather, we believe the data imply that CO binding to beta oligomers is heterogeneous, with both a fast binding and a slow binding form being present in single association states. The fast binding form predominates (approximately equal to 87%) in beta 4, while the beta monomer has very little or none of the fast binding form. We propose that the slow binding component within beta 4 may be those subunits with rotationally disordered hemes (La Mar, G. N., Yamamoto, Y., Jue, T., Smith, K. M., and Pandey, R. K. (1985) Biochemistry 24, 3826-3831). The implications of these findings for the use of isolated subunits as models for the subunits within "R state" hemoglobin tetramers are discussed.     

Model for population distributions of lymphocyte-target cell conjugates

A quantitative model for the population distributions of the different types of conjugates formed between cytotoxic T lymphocytes and target cells has been developed. The comparison of the theoretical predictions with data of the literature reveals that the transit populations among the different types of conjugates depends on the lymphocyte-to-target ratio, R, and two constants, k and k1. These constants (where k greater than k1) govern, respectively, the transit populations among conjugates of the type LTi (LTn----LTn-1----...LT), and among LjT conjugates (LT----L2T----...----LmT). We have found that high ratios are necessary to obtain conjugates where multiple T lymphocytes are bound to one target cell, and that under these conditions the predominant conjugate, LjT, varies according to j = 1 + k1R. Conversely, for low values of R the predominant population is of the type LTi, where i also shows a linear dependence on R. Our model explains also why the conjugate LT is normally the predominant population under the experimental conditions reported in the literature. A discussion of the influence exerted by the population distributions of lymphocyte-target cell conjugates on the kinetic of the lytic process for these kinds of effector-target systems has also been made.     

Confidence intervals for heritability for two-factor mating design single environment linear models

Summary Precision measurement is an essential part of heritability estimate interpretation. Approximate standard errors are commonly used as measures of precision for heritability on a progeny mean basis (H). Their derivation, however, is not inferred from the distribution theory for H. F-distribution based exact confidence intervals have been derived for some onefactor mating design H estimators. Extension of the confidence interval results from one-factor to twofactor mating designs is reported in this paper. Functions of heritability on a full-sib or half-sib progeny mean basis from nested or factorial mating design parameters were distributed according to the F-distribution. Exact confidence intervals were derived for heritability on a full-sib progeny mean basis. Exact confidence intervals for heritability on a half-sib progeny basis were adapted from previous results. Maize (Zea mays L.) data were used to estimate confidence intervals. Complete equations were given for interpolation in F-tables.Oregon Agricultural Experiment Station Technical Paper No. 7659     

Simultaneous confidence intervals from randomization tests with application in testing bioequivalence with multiple endpoints

We propose a method to construct simultaneous confidence intervals for a parameter vector from inverting a series of randomization tests (RT). The randomization tests are facilitated by an efficient multivariate Robbins–Monro procedure that takes the correlation information of all components into account. The estimation method does not require any distributional assumption of the population other than the existence of the second moments. The resulting simultaneous confidence intervals are not necessarily symmetric about the point estimate of the parameter vector but possess the property of equal tails in all dimensions. In particular, we present the constructing the mean vector of one population and the difference between two mean vectors of two populations. Extensive simulation is conducted to show numerical comparison with four methods. We illustrate the application of the proposed method to test bioequivalence with multiple endpoints on some real data.     

The k partition-distance problem

Many applications of data partitioning (clustering) have been well studied in bioinformatics. Consider, for instance, a set N of organisms (elements) based on DNA marker data. A partition divides all elements in N into two or more disjoint clusters that cover all elements, where a cluster contains a non-empty subset of N. Different partitioning algorithms may produce different partitions. To compute the distance and find the consensus partition (also called consensus clustering) between two or more partitions are important and interesting problems that arise frequently in bioinformatics and data mining, in which different distance functions may be considered in different partition algorithms. In this article, we discuss the k partition-distance problem. Given a set of elements N with k partitions of N, the k partition-distance problem is to delete the minimum number of elements from each partition such that all remaining partitions become identical. This problem is NP-complete for general k?>?2 partitions, and no algorithms are known at present. We design the first known heuristic and approximation algorithms with performance ratios 2 to solve the k partition-distance problem in O(k?·?ρ?·?|N|) time, where ρ is the maximum number of clusters of these k partitions and |N| is the number of elements in N. We also present the first known exact algorithm in O(??·?2(?)·k(2)?·?|N|(2)) time, where ? is the partition-distance of the optimal solution for this problem. Performances of our exact and approximation algorithms in testing the random data with actual sets of organisms based on DNA markers are compared and discussed. Experimental results reveal that our algorithms can improve the computational speed of the exact algorithm for the two partition-distance problem in practice if the maximum number of elements per cluster is less than ρ. From both theoretical and computational points of view, our solutions are at most twice the partition-distance of the optimal solution. A website offering the interactive service of solving the k partition-distance problem using our and previous algorithms is available (see http://mail.tmue.edu.tw/~yhchen/KPDP.html).     

Simultaneous confidence intervals for a success probability and intraclass correlation,with an application to screening mammography

This paper provides asymptotic simultaneous confidence intervals for a success probability and intraclass correlation of the beta‐binomial model, based on the maximum likelihood estimator approach. The coverage probabilities of those intervals are evaluated. An application to screening mammography is presented as an example. The individual and simultaneous confidence intervals for sensitivity and specificity and the corresponding intraclass correlations are investigated. Two additional examples using influenza data and sex ratio data among sibships are also considered, where the individual and simultaneous confidence intervals are provided.     

Quantitative chimeric analysis of six specificity determinants that differentiate Escherichia coli aspartate from tyrosine aminotransferase

The six mutations, referred to as the Hex mutations, that together have been shown to convert Escherichia coli aspartate aminotransferase (AATase) specificity to be substantially like that of E. coli tyrosine aminotransferase (TATase) are dissected into two groups, (T109S/N297S) and (V39L/K41Y/T47I/N69L). The letters on the left and right of the numbers designate AATase and TATase residues, respectively. The T109S/N297S pair has been investigated previously. The latter group, the "Grease" set, is now placed in the AATase framework, and the retroGrease set (L39V/Y41K/I47T/L69N) is substituted into TATase. The Grease mutations in the AATase framework were found primarily to lower K(M)s for both aromatic and dicarboxylic substrates. In contrast, retroGrease TATase exhibits lowered k(cat)s for both substrates. The six retroHex mutations, combining retroGrease and S109T/S297N, were found to invert the substrate specificity of TATase, creating an enzyme with a nearly ninefold preference (k(cat)/K(M)) for aspartate over phenylalanine. The retroHex mutations perturb the electrostatic environment of the pyridoxal phosphate cofactor, as evidenced by a spectrophotometric titration of the internal aldimine, which uniquely shows two pK(a)s, 6.1 and 9.1. RetroHex was also found to have impaired dimer stability, with a K(D) for dimer dissociation of 350 nM compared with the wild type K(D) of 4 nM. Context dependence and additivity analyses demonstrate the importance of interactions of the Grease residues with the surrounding protein framework in both the AATase and TATase contexts, and with residues 109 and 297 in particular. Context dependence and cooperativity are particularly evident in the effects of mutations on k(cat)/K(M)(Asp). Effects on k(cat)/K(M)(Phe) are more nearly additive and context independent.     

Folding of a three-stranded coiled coil

Coiled coils consist of two or more amphipathic a-helices wrapped around each other to form a superhelical structure stabilized at the interhelical interface by hydrophobic residues spaced in a repeating 3-4 sequence pattern. Dimeric coiled coils have been shown to often form in a single step reaction in which association and folding of peptide chains are tightly coupled. Here, we ask whether such a simple folding mechanism may also apply to the formation of a three-stranded coiled coil. The designed 29-residue peptide LZ16A was shown previously to be in a concentration-dependent equilibrium between unfolded monomer (M), folded dimer (D), and folded trimer (T). We show by time-resolved fluorescence change experiments that folding of LZ16A to D and T can be described by 2M (k1)<==>(k(-1)) D and M + D (k2)<==>(k(-2)) T. The following rate constants were determined (25 degrees C, pH 7): k1 = 7.8 x 10(4) M(-1) s(-1), k(-1) = 0.015 s(-1), k2 = 6.5 x 10(5) M(-1) s(-1), and k(-2) = 1.1 s(-1). In a separate experiment, equilibrium binding constants were determined from the change with concentration of the far-ultraviolet circular dichroism spectrum of LZ16A and were in good agreement with the kinetic rate constants according to K(D) = k1/2k(-1) and K(T) = k2/k(-2). Furthermore, pulsed hydrogen-exchange experiments indicated that only unfolded M and folded D and T were significantly populated during folding. The results are compatible with a two-step reaction in which a subpopulation of association competent (e.g., partly helical) monomers associate to dimeric and trimeric coiled coils.     

Unconditional Exact Tests for Equivalence or Noninferiority for Paired Binary Endpoints

Problems of establishing equivalence or noninferiority between two medical diagnostic procedures involve comparisons of the response rates between correlated proportions. When the sample size is small, the asymptotic tests may not be reliable. This article proposes an unconditional exact test procedure to assess equivalence or noninferiority. Two statistics, a sample-based test statistic and a restricted maximum likelihood estimation (RMLE)-based test statistic, to define the rejection region of the exact test are considered. We show the p-value of the proposed unconditional exact tests can be attained at the boundary point of the null hypothesis. Assessment of equivalence is often based on a comparison of the confidence limits with the equivalence limits. We also derive the unconditional exact confidence intervals on the difference of the two proportion means for the two test statistics. A typical data set of comparing two diagnostic procedures is analyzed using the proposed unconditional exact and asymptotic methods. The p-value from the unconditional exact tests is generally larger than the p-value from the asymptotic tests. In other words, an exact confidence interval is generally wider than the confidence interval obtained from an asymptotic test.     

Two MHC surface amino acid differences distinguish foreign peptide recognition from autoantigen specificity

KRN T cells can recognize two self MHC alleles with differing biological consequences. They respond to the foreign peptide RN(42--56) bound to I-A(k) or alternatively initiate autoimmune arthritis by interacting with a self Ag, GPI(282--294), on I-A(g7). Five surface amino acid differences between the two MHC molecules collectively alter which peptide side chains are recognized by the KRN TCR. In this study, it is shown that mutation of only two of these residues, alpha 65 and beta 78, in I-A(k) to their I-A(g7) counterparts is sufficient to allow recognition of the TCR contacts from GPI(282--294). To provide a detailed mechanism for the specificity change, the distinct contributions of each of these two mutations to the global effect on peptide specificity were analyzed. The alpha65 mutation is shown to broaden the spectrum of amino acids permissible at P8 of the peptide. In contrast, the beta 78 mutation alone blocks KRN TCR interaction with I-A(k) and requires the simultaneous presence of the alpha 65 mutation to preserve recognition. In the presence of the alpha 65 mutation, the beta 78 residue broadens peptide recognition at P3 and prevents recognition of the P8 L in RN(42--56), thus producing the observed specificity shift. These results localize the functionally relevant differences between the surfaces of two self-restricted MHC molecules to two residues that have counterbalanced positive and negative contributions to interaction with a single TCR. They highlight how subtle structural distinctions attributable to single amino acids can stand at the interface between foreign Ag responsiveness and pathogenic autoreactivity.