Sedimentation equilibrium in macromolecular solutions of arbitrary concentration. II. Two protein components

Relations describing sedimentation equilibrium in solutions containing two macromolecular solute components are derived for the following cases: (1) two nonassociating proteins at arbitrary concentration, (2) one dilute self-associating protein in the presence of a second inert protein at arbitrary concentration, and (3) two proteins at arbitrary concentration that can associate to form a single heterocomplex of arbitrary composition. As in earlier work (R. C. Chatelier and A. P. Minton (1987) Biopolymers, 26, 507–524), the relations are obtained by using scaled particle theory to calculate the thermodynamic activity of each species present at a given radial distance in the centrifuge. The results of numerical simulations of sedimentation equilibrium are presented as the dependence of apparent molecular weights, or apparent weight-average molecular weights, upon solution composition. Semiempirical methods are presented, by means of which the weight-average molecular weights of self- and heteroassociating proteins in highly nonideal solutions may be estimated from experimental data. It is found that the semiempirical methods yield reasonably accurate estimates of the true weight-average molecular weight over a broad range of experimental conditions, providing that the partial specific volumes of two components in a heteroassociating system do not differ by more than about 0.05 mL/g.     

Criteria that discriminate between native proteins and incorrectly folded models

Various theoretical concepts, such as free energy potentials, electrostatic interaction potentials, atomic packing, solvent-exposed surface, and surface charge distribution, were tested for their ability to discriminate between native proteins and misfolded protein models. Misfolded models were constructed by introducing incorrect side chains onto polypeptide backbones: side chains of the alpha-helical hemerythrin were modeled on the beta-sheeted backbone of immunoglobulin VL domain, whereas those of the VL domain were similarly modeled on the hemerythrin backbone. CONGEN, a conformational space sampling program, was used to construct the side chains, in contrast to the previous work, where incorrect side chains were modeled in all trans conformations. Capability of the conformational search procedure to reproduce native conformations was gauged first by rebuilding (the correct) side chains in hemerythrin and the VL domain: constructs with r.m.s. differences from the x-ray side chains 2.2-2.4 A were produced, and many calculated conformations matched the native ones quite well. Incorrectly folded models were then constructed by the same conformational protocol applied to incorrect amino acid sequences. All CONGEN constructs, both correctly and incorrectly folded, were characterized by exceptionally small molecular surfaces and low potential energies. Surface charge density, atomic packing, and Coulomb formula-based electrostatic interactions of the misfolded structures and the correctly folded proteins were similar, and therefore of little interest for diagnosing incorrect folds. The following criteria clearly favored the native structures over the misfolded ones: 1) solvent-exposed side-chain nonpolar surface, 2) number of buried ionizable groups, and 3) empirical free energy functions that incorporate solvent effects.     

GAPDOCK: a Genetic Algorithm Approach to Protein Docking in CAPRI round 1

As part of the first Critical Assessment of PRotein Interactions, round 1, we predict the structure of two protein-protein complexes, by using a genetic algorithm, GAPDOCK, in combination with surface complementarity, buried surface area, biochemical information, and human intervention. Among the five models submitted for target 1, HPr phosphocarrier protein (B. subtilis) and the hexameric HPr kinase (L. lactis), the best correctly predicts 17 of 52 interprotein contacts, whereas for target 2, bovine rotavirus VP6 protein-monoclonal antibody, the best model predicts 27 of 52 correct contacts. Given the difficult nature of the targets, these predictions are very encouraging and compare well with those obtained by other methods. Nevertheless, it is clear that there is a need for improved methods for distinguishing between "correct" and "plausible but incorrect" complexes.     

Role of two proline-containing turns in the folding of porcine ribonuclease

Unfolded ribonuclease (RNase) from porcine pancreas consists of a mixture of fast and slow-refolding species. The equilibrium distribution of these species differs strongly from other homologous RNases, because an additional proline residue is present at position 115 of the porcine protein. The major slow-folding species of porcine RNase contains incorrect proline isomers at Pro93 and at Pro114-Pro115. Both positions are presumably part of beta-turn structures in the native protein, as deduced from the structure of the homologous bovine RNase A. The folding kinetics of these molecules depend strongly on the conditions used. Under unfavorable conditions (near the unfolding transition), refolding is virtually blocked by the presence of the incorrect proline peptide bonds and partially folded intermediates with incorrect isomers could not be detected. As a consequence, folding is very slow under such conditions and the re-isomerization of Pro114-Pro115 is the first and rate-limiting step of folding. Under strongly native conditions (such as in the presence of ammonium sulfate), refolding is much faster. A largely folded intermediate accumulates with the turns around Pro93 and Pro114-Pro115 still in the non-native conformation. These results suggest that incorrect proline isomers strongly influence protein folding and that, under favorable conditions, the polypeptide chain can fold with two beta-turns locked into a non-native conformation. We conclude, therefore, that early formation of correct turn structure is not necessarily required for protein folding. However, the presence of incorrect turns, locked-in by non-native proline isomers, strongly decreases the rate of refolding. Alternative pathways of folding exist. The choice of pathway depends on the number and distribution of incorrect proline isomers and on the folding conditions.     

Correct and incorrect vertebrate phylogenies obtained by the entire mitochondrial DNA sequences.

Concatenated sequences of all protein-coding genes in mitochondria recovered a known phylogeny of 11 vertebrate species correctly with statistical significance. However, when it was rooted by lampreys or sea urchins, the root of the vertebrate tree was placed between the mammal cluster and the chicken-frog-fish cluster or between the mammal-chicken cluster and the frog-fish cluster, depending on the tree-making method used. Although the frog-fish or chicken-frog-fish cluster was biologically incorrect, it was again supported with a significantly high bootstrap value. In this study, we investigated the reasons why this happened. It has been suggested that an incorrect phylogeny may be constructed due to a change of amino acid composition in different lineages or due to homoplasies at sites with hydrophobic amino acids. However, our results indicated that these were not the causes of the incorrect rooting of the vertebrate tree. Rather, it was important to take into account an extensive rate variation across sites and different probabilities of substitution among different amino acids. The substitution rates for mitochondrial sequences vary considerably for different vertebrate lineages. In such a case, it is known to be important to use the model that reflects the actual substitution probability to obtain a correct tree topology. The correct rooting of the vertebrate tree was recovered when rate variation across sites was properly accounted for.     

Folding of ribonuclease T1. 2. Kinetic models for the folding and unfolding reactions

The slow refolding of ribonuclease T1 was investigated by different probes. Structural intermediates with secondary structure are formed early during refolding, as indicated by the rapid regain of a native-like circular dichroism spectrum in the amide region. This extensive structure formation is much faster than the slow steps of refolding, which are limited in rate by the reisomerization of incorrect proline isomers. The transient folding intermediates were also detected by unfolding assays, which make use of the reduced stability of folding intermediates relative to that of the native protein. The results of this and the preceding paper [Kiefhaber et al. (1990) Biochemistry (preceding paper in this issue)] were used to propose kinetic models for the unfolding and refolding of ribonuclease T1. The unfolding mechanism is based on the assumption that, after the structural unfolding step, the slow isomerizations of two X-Pro peptide bonds occur independently of each other in the denatured protein. At equilibrium a small amount of fast-folding species coexists with three slow-folding species: two with one incorrect proline isomer each and another, dominant species with both these prolines in the incorrect isomeric state. In the mechanism for refolding we assume that all slow-folding molecules can rapidly regain most of the secondary and part of the tertiary structure early in folding. Reisomerizations of incorrect proline peptide bonds constitute the slow, rate-limiting steps of refolding. A peculiar feature of the kinetic model for refolding is that the major unfolded species with two incorrect proline isomers can enter two alternative folding pathways, depending on which of the two reisomerizes first. The relative rates of reisomerization of the respective proline peptide bonds at the stage of the rapidly formed intermediate determine the choice of pathway. It is changed in the presence of prolyl isomerase, because this enzyme catalyzes these two isomerizations with different efficiency and consequently leads to a shift from the very slow to the intermediate refolding pathway.     

Estimating Treatment Effects of Longitudinal Designs using Regression Models on Propensity Scores

Summary We derive regression estimators that can compare longitudinal treatments using only the longitudinal propensity scores as regressors. These estimators, which assume knowledge of the variables used in the treatment assignment, are important for reducing the large dimension of covariates for two reasons. First, if the regression models on the longitudinal propensity scores are correct, then our estimators share advantages of correctly specified model‐based estimators, a benefit not shared by estimators based on weights alone. Second, if the models are incorrect, the misspecification can be more easily limited through model checking than with models based on the full covariates. Thus, our estimators can also be better when used in place of the regression on the full covariates. We use our methods to compare longitudinal treatments for type II diabetes mellitus.     

An ultracentrifugal study of the self-association of canine apolipoprotein A-I in solution.

The sedimentation behavior of canine apolipoprotein (apo) A-I in 0.02 M EDTA, pH 8.6, was studied as a function of protein concentration by the techniques of sedimentation velocity and sedimentation equilibrium in the analytical ultracentrifuge. At concentrations of less than 1 g/liter, apo-A-I exhibited a monomodal sedimentation pattern, with apparent sedimentation coefficients which varied from 2.3 to 3.5 S with increasing protein concentrations. Above 1.5 g/liter, apo-A-I had two well resolved peaks with s20,w values of 4.15 S and 5.75 S. The proportion of the 5.75 S component increased with increasing apo-A-I concentrations, with a concomitant decrease of the 4.15 S component. By sedimentation equilibrium ultracentrifugation with both the conventional and meniscus-depletion methods, the apparent weight-average molecular weight of apo-A-I was found to be concentration-dependent. At a protein concentration of 5.25 g/liter, an apparent weight average molecular weight of 138,000 was determined, indicating that molecular species larger than a tetramer (monomer molecular weight = 28,000) were present in solution. When analyzed in terms of a reversible self-associating system, the experimental data could best be described according to a monomer-dimer-tetramer-octamer model, as previously reported from human apo-A-I (Vitello, L. B., and Scanu, A. M. (1975) J. Biol. Chem. 251, 1131-1136). The equilibrium constants were: K2 = 4.5 liters/g, K4 = 470 liters3/g3, and K8 = 41,600 liters7/g7, respectively.     

The self-association of chicken-erythrocyte histones.

The self-association of the separate histone fractions isolated from chicken erythrocytes has been studied in solution at a number of different pH values and ionic strengths. The apparent molecular weights of the histones were determined over a range of macromolecular concentrations using the techniques of osmotic pressure and sedimentation equilibrium. Histone F2c (H5) did not associate under any of the conditions investigated whereas the other histone fractions all appeared to undergo self-association forming dimers, dimers of dimers, etc. The degree of association increased with the pH and ionic strength of the medium. The tendency to aggregate increased in the order; histone F2c (H5) (non-aggregating), histone F2b (H2B), histone F2a2 (H2A), histone F3 (H3), histone F2a1 (H4) (highly aggregating). In the case of histone F2a2 (H2A) at pH 3.0 and ionic strength 0.1, the apparent weight-average molecular weight was determined at a number of macromolecular concentrations at five different temperatures. The self-association was analysed according to the method of Adams (published by Beckman Instruments Inc. in 1967) and shown to be a monomer-dimer-tetramer equilibrium. The association constants were evaluated at each of the temperatures studied and from their variation with temperature the values of the enthalpy and entropy of association were calculated. The intermolecular association was characterised by only a small change in enthalpy but a large, positive, change in entropy. This suggests that the association of histones at acid pH is due to hydrophobic interactions between the relatively uncharged segments of like polypeptide chains.     

Requirements for reliable determination of binding affinity constants by saturation analysis approach

Accurate calculation of the equilibrium association constant (K) and binding site concentration (N) related to a receptor (R)/ligand (L) interaction, via R saturation analysis, requires exact determination of the specifically bound L concentration (B(S)) and the unbound L concentration (U) at equilibrium. However, most binding determinations involve a procedure for separation of bound and unbound L. In such situations, it was previously shown that correct calculation of B(S) and U from binding data requires prior determination of alpha, i.e. the procedure parameter representing the proportion of equilibrium B(S) recovered after running the separation process, and of kn, i.e. the equilibrium nonspecific binding coefficient. For the simplest model of R/L interaction, the consequences of alpha neglect and/or kn neglect on determination of K and N, via R saturation analysis, are investigated. When alpha but not kn has been determined, B(S) can be accurately calculated, whereas U is overestimated by factor (kn + 1). Consequently the type (linear or hyperbolic) of theoretic curves obtained by usual representations (such as the Scatchard, the Lineweaver-Burk or the Michaelis-Menten plot) of the R/L binding is unchanged; these curves afford correct N and underestimation of K by factor (kn + 1). When alpha (alpha < 1) has not been determined B(S) and U are underestimated and overestimated, respectively. Then erroneous representations of the R/L binding result (e.g. instead of regular straight line segments, Scatchard plot and Lineweaver-Burk plot involve convex-upward and convex-downward hyperbola portions, respectively, suggestive of positive cooperativity of L binding), which leads to incorrect N and K. Errors in N and K would depend on (i) the binding (K, N and kn) and method (alpha) parameters and (ii) the expressions used to calculate approximate B(S) and U values. Simulations involving variable alpha, KN and kn values indicate that: (1) the magnitude of error in N determination (mainly involving moderate underestimation) directly depends on the alpha value; (2) the magnitude of K underestimation mainly depends on the KN value; it is moderate (usually < two-fold) with KN values < 1, but could become very high (e.g. > 100-fold), when KN > 10(2). In this case, the K underestimation is modulated by the alpha and kn values. Practical situations which afford high KN and thus might result in very marked underestimation of K are discussed. A single R dilution method is proposed to assess the validity of K determinations using the R saturation analysis approach.     

Cold rescue of the thermolabile tailspike intermediate at the junction between productive folding and off-pathway aggregation.

Off-pathway intermolecular interactions between partially folded polypeptide chains often compete with correct intramolecular interactions, resulting in self-association of folding intermediates into the inclusion body state. Intermediates for both productive folding and off-pathway aggregation of the parallel beta-coil tailspike trimer of phage P22 have been identified in vivo and in vitro using native gel electrophoresis in the cold. Aggregation of folding intermediates was suppressed when refolding was initiated and allowed to proceed for a short period at 0 degrees C prior to warming to 20 degrees C. Yields of refolded tailspike trimers exceeding 80% were obtained using this temperature-shift procedure, first described by Xie and Wetlaufer (1996, Protein Sci 5:517-523). We interpret this as due to stabilization of the thermolabile monomeric intermediate at the junction between productive folding and off-pathway aggregation. Partially folded monomers, a newly identified dimer, and the protrimer folding intermediates were populated in the cold. These species were electrophoretically distinguished from the multimeric intermediates populated on the aggregation pathway. The productive protrimer intermediate is disulfide bonded (Robinson AS, King J, 1997, Nat Struct Biol 4:450-455), while the multimeric aggregation intermediates are not disulfide bonded. The partially folded dimer appears to be a precursor to the disulfide-bonded protrimer. The results support a model in which the junctional partially folded monomeric intermediate acquires resistance to aggregation in the cold by folding further to a conformation that is activated for correct recognition and subunit assembly.     

四逆散对疲劳大鼠学习记忆及脑内GABA_B1 表达的影响

目的:探讨四逆散对疲劳大鼠学习记忆及脑内GABA_B1受体的影响。方法:应用游泳训练和睡眠剥夺方法复制疲劳动物模型,运用Y-迷宫检测各组大鼠的学习记忆能力,采用免疫组化方法检测大鼠脑内GABA_B1受体阳性反应物的变化。结果:模型组与正常组相比,大鼠Y-迷宫正确反应率明显下降,错误反应率明显升高,大鼠脑内GABA_B1的阳性反应物数目明显增多;中药治疗组与模型组相比,正确反应率明显升高,错误反应次数明显下降,脑内GABA_B1受体的阳性反应物数目明显减少。结论:四逆散对疲劳大鼠学习记忆能力的下降具有改善作用。     

A comparison of statistical approaches for modelling fish species distributions

SUMMARY 1. The prediction of species distributions is of primary importance in ecology and conservation biology. Statistical models play an important role in this regard; however, researchers have little guidance when choosing between competing methodologies because few comparative studies have been conducted. 2. We provide a comprehensive comparison of traditional and alternative techniques for predicting species distributions using logistic regression analysis, linear discriminant analysis, classification trees and artificial neural networks to model: (1) the presence/absence of 27 fish species as a function of habitat conditions in 286 temperate lakes located in south‐central Ontario, Canada and (2) simulated data sets exhibiting deterministic, linear and non‐linear species response curves. 3. Detailed evaluation of model predictive power showed that approaches produced species models that differed in overall correct classification, specificity (i.e. ability to correctly predict species absence) and sensitivity (i.e. ability to correctly predict speciespresence) and in terms of which of the study lakes they correctly classified. Onaverage, neural networks outperformed the other modelling approaches, although all approaches predicted species presence/absence with moderate to excellent success. 4. Based on simulated non‐linear data, classification trees and neural networks greatly outperformed traditional approaches, whereas all approaches exhibited similar correct classification rates when modelling simulated linear data. 5. Detailed evaluation of model explanatory insight showed that the relative importance of the habitat variables in the species models varied among the approaches, where habitat variable importance was similar among approaches for some species and very different for others. 6. In general, differences in predictive power (both correct classification rate and identity of the lakes correctly classified) among the approaches corresponded with differences in habitat variable importance, suggesting that non‐linear modelling approaches (i.e. classification trees and neural networks) are better able to capture and model complex, non‐linear patterns found in ecological data. The results from the comparisons using simulated data further support this notion. 7. By employing parallel modelling approaches with the same set of data and focusing on comparing multiple metrics of predictive performance, researchers can begin to choose predictive models that not only provide the greatest predictive power, but also best fit the proposed application.     

Sedimentation equilibrium studies of human chymotrypsin II and bovine -chymotrypsin

Sedimentation equilibrium experiments indicate that neither human chymotrypsin II nor bovine δ-chymotrypsin molecules undergo association in the pH range 3–5 where dimerization occurs with α-chymotrypsin. The weight-average molecular weights of human chymotrypsin II and δ-chymotrypsin in a pH 4.4 0.1 ionic strength buffer are 26,200 and 26,400, respectively, using the measured partial specific volumes of 0.722 and 0.727 ml/g at 25 °C. Number-average molecular weight calculations also support the presence of monomeric species at this pH. In the pH range 6–7.6 where sedimentation velocity studies have shown that δ-chymotrypsin associates at concentrations above 3 mg/ml, no association was observed for either the human chymotrypsin II or bovine δ-chymotrypsin in the sedimentation equilibrium experiments where protein concentrations were below 1.2 mg/ml. These studies provide additional evidence that human chymotrypsin II is similar to bovine δ-chymotrypsin.     

Morphological variation among Betula nana (diploid), B. pubescens (tetraploid) and their triploid hybrids in Iceland

BACKGROUND AND AIMS: Introgressive hybridization between two co-existing Betula species in Iceland, diploid dwarf birch B. nana and tetraploid downy birch B. pubescens, has been well documented. The two species are highly variable morphologically, making taxonomic delineation difficult despite stable ploidy levels. Here an analysis is made of morphological variation within each ploidy group with an aim to establishing a reliable means to distinguish the species. METHODS: Plant materials were collected from 14 woodlands in Iceland. The plants were identified based on 2n chromosome numbers. Morphological variation in species-specific characters within each ploidy group was analysed qualitatively and quantitatively. The morphological index was based on eight discrete characters, whereas the multivariate analysis was based on nine leaf variables. KEY RESULTS: Of the 461 plants examined, 9.5 % were found to be triploid hybrids. The three ploidy groups were morphologically distinguishable but their variation overlapped. The diploid, triploid and tetraploid groups had average scores of 1.3, 4.1 and 8.3, respectively, in the morphology index scale from 0 (B. nana) to 13 (B. pubescens). A linear discriminant analysis also revealed significant separation among the three ploidy groups and the model assigned 96 % and 97 % of the B. nana and B. pubescens individuals correctly. The triploid hybrids were difficult to predict since only half of them could be assigned correctly. Leaf length was the most useful variable identifying triploid hybrids. Geographical patterns within the ploidy groups could partly be explained by differences in mean July temperature. CONCLUSIONS: Hybridization between B. nana and B. pubescens is widespread in Iceland. The species can be distinguished from each other morphologically, and from the triploid hybrids. The overlapping morphological variation indicates bidirectional introgression between the two species via triploid hybrids. Iceland could be considered a birch hybrid zone, harbouring genetic variation which may be advantageous in subarctic regions.     

四逆散对疲劳大鼠学习记忆及脑内GABA_B1表达的影响

目的：探讨四逆散对疲劳大鼠学习记忆及脑内GABA_B1受体的影响。方法：应用游泳训练和睡眠剥夺方法复制疲劳动物模型,运用Y-迷宫检测各组大鼠的学习记忆能力,采用免疫组化方法检测大鼠脑内GABA_B1受体阳性反应物的变化。结果：模型组与正常组相比,大鼠Y-迷宫正确反应率明显下降,错误反应率明显升高,大鼠脑内GABA_B1的阳性反应物数目明显增多;中药治疗组与模型组相比,正确反应率明显升高,错误反应次数明显下降,脑内GABA_B1受体的阳性反应物数目明显减少。结论：四逆散对疲劳大鼠学习记忆能力的下降具有改善作用。     

On the relations between error rates in DNA replication and elementary chemical rate constants

A general treatment of the so-called peelback process is presented, where the final rates of errors in a simple model of DNA replication are derived from elementary chemical rate constants for incorporation or removal of correct or incorrect bases, in cases where these constants depend or not on the identity of the preceding base. It is shown that evidences regarding this dependence, for addition as well as for excision or pyrophosphorolysis, can be obtained from experimental determinations of the rate of appearance of various kinds of incorrect doublets in the final material and that these implications hold not only in the simple model case of a homopolynucleotide with a mixture of correct and incorrect substrates, but also in the real case of the four-bases DNA replication with the possibility of incorporation of incorrect bases instead of the correct ones in specific doublets. The connections between the various classes of parameters involved in a peelback process (instantaneous concentrations and lifetimes in final position, probabilities for ultimate fates, final contents of specific bases or doublets or triplets, etc.) are given in the Introduction.     

A kinetic study of the inhibition of human and bovine trypsins and chymotrypsins by the inter-alpha-inhibitor from human plasma.

Human plasma inter-alpha-inhibitor forms 1:1 inactive complexes with human and bovine trypsins (EC 3.4.21.4) and chymotrypsins (EC 3.4.21.1). The association and dissociation rate constants as well as the equilibrium dissociation constants (Ki) of the complexes formed of inter-alpha-inhibitor and the four proteases have been measured. The most stable complexes are those formed with the bovine enzymes. For instance, Ki = 2.1-10-11 M for bovine trypsin whereas Ki = 1.2 - 10-8 M for human trypsin. Whatever the species, the complexes formed with the chymotrypsins are less stable than those formed with the trypsins.     

The high-affinity K+-translocating ATPase complex from Bacillus acidocaldarius consists of three subunits

Cells of the thermoacidophilic bacterium Bacillus acidocaldarius express a high-affinity K+-uptake system when grown at low external K+. A vanadate-sensitive, K+- and Mg2+-stimulated ATPase was partially purified from membranes of these cells by solubilization with a non-ionic detergent followed by ion-exchange chromatography of the extract. Combinations of non-denaturing and denaturing electrophoretic separation methods revealed that the ATPase complex consisted of three subunits with molecular weights almost identical to those of the KdpA, B and C proteins, which together form the Kdp high-affinity, K+-translocating ATPase complex of Escherichia coli. The affinity of the partially purified ATPase from B. acidocaldarius for its substrates K+ (Km 2-3 microM) and ATP (Km 80 microM), its stimulation by various divalent cations, and its inhibition by vanadate (Ki 1-2 microM), bafilomycin A1 (Ki 20 microM), DCCD (Ki 200 microM) or Ca2+ were also similar to those of the E. coli enzyme, indicating that the two K+-translocating ATPases have almost identical properties.