Equivalence of truncated count mixture distributions and mixtures of truncated count distributions

This article is about modeling count data with zero truncation. A parametric count density family is considered. The truncated mixture of densities from this family is different from the mixture of truncated densities from the same family. Whereas the former model is more natural to formulate and to interpret, the latter model is theoretically easier to treat. It is shown that for any mixing distribution leading to a truncated mixture, a (usually different) mixing distribution can be found so that the associated mixture of truncated densities equals the truncated mixture, and vice versa. This implies that the likelihood surfaces for both situations agree, and in this sense both models are equivalent. Zero-truncated count data models are used frequently in the capture-recapture setting to estimate population size, and it can be shown that the two Horvitz-Thompson estimators, associated with the two models, agree. In particular, it is possible to achieve strong results for mixtures of truncated Poisson densities, including reliable, global construction of the unique NPMLE (nonparametric maximum likelihood estimator) of the mixing distribution, implying a unique estimator for the population size. The benefit of these results lies in the fact that it is valid to work with the mixture of truncated count densities, which is less appealing for the practitioner but theoretically easier. Mixtures of truncated count densities form a convex linear model, for which a developed theory exists, including global maximum likelihood theory as well as algorithmic approaches. Once the problem has been solved in this class, it might readily be transformed back to the original problem by means of an explicitly given mapping. Applications of these ideas are given, particularly in the case of the truncated Poisson family.     

Dissection of the functional structure of aptamer17, which specifically recognizes differentiated PC12 cells

A specific single-stranded DNA (ssDNA) aptamer (aptamer17) that specifically recognizes differentiated PC12 cells had been previously obtained after 6 rounds of whole cell-based subtractive systematic evolution of ligands by exponential enrichment selection from a random ssDNA library. To further investigate the relationship between the structure and function of this aptamer, 3 truncated ssDNA aptamers were designed according to the predicted secondary structure of aptamer17. Our results show that the stem-loop is the core structure of the aptamers required for specific binding to differentiated PC12 cells, specifically loops I and II. Aptamer17 and the truncated aptamers with this basic structure could bind specifically to differentiated PC12 cells and identify these cells from a mixture of differentiated and undifferentiated PC12 cells. Therefore, truncated forms of aptamer17 may be useful in the clinic to identify undifferentiated and differentiated PC12 cells from a mixture of cells.     

Recombinant and truncated tetanus neurotoxin light chain: cloning, expression, purification, and proteolytic activity

Tetanus neurotoxin (TeNT) consists of two disulfide-linked polypeptide chains, heavy (H) and light (L). The L chain is a zinc endopeptidase protein highly specific for vesicle-associated membrane protein (VAMP), which is an essential component of the exocytosis apparatus. Here we describe the cloning of the L chain of TeNT from Clostridium tetani strain Y-IV-3 (WS 15) and its expression in Escherichia coli as a glutathione S-transferase fusion protein. The full-length recombinant L chain, corresponding to residues 1-457, was obtained as a mixture of proteins of slightly different mass with identical N-terminal ends. To obtain a product useful for structural analysis and crystallization, a COOH-terminally truncated L chain (residues 1-427) was cloned, expressed, and purified with high yield. This truncated L chain is more active than the full-length and wild-type proteins in the hydrolysis of VAMP. Preliminary experiments of crystallization of the truncated recombinant L chain gave encouraging results.     

Detection of two-component mixtures of lognormal distributions in grouped, doubly truncated data: analysis of red blood cell volume distributions

We have examined the statistical requirements for the detection of mixtures of two lognormal distributions in doubly truncated data when the sample size is large. The expectation-maximization algorithm was used for parameter estimation. A bootstrap approach was used to test for a mixture of distributions using the likelihood ratio statistic. Analysis of computer simulated mixtures showed that as the ratio of the difference between the means to the minimum standard deviation increases, the power for detection also increases and the accuracy of parameter estimates improves. These procedures were used to examine the distribution of red blood cell volume in blood samples. Each distribution was doubly truncated to eliminate artifactual frequency counts and tested for best fit to a single lognormal distribution or a mixture of two lognormal distributions. A single population was found in samples obtained from 60 healthy individuals. Two subpopulations of cells were detected in 25 of 27 mixtures of blood prepared in vitro. Analyses of mixtures of blood from 40 patients treated for iron-deficiency anemia showed that subpopulations could be detected in all by 6 weeks after onset of treatment. To determine if two-component mixtures could be detected, distributions were examined from untransfused patients with refractory anemia. In two patients with inherited sideroblastic anemia a mixture of microcytic and normocytic cells was found, while in the third patient a single population of microcytic cells was identified. In two family members previously identified as carriers of inherited sideroblastic anemia, mixtures of microcytic and normocytic subpopulations were found. Twenty-five patients with acquired myelodysplastic anemia were examined. A good fit to a mixture of subpopulations containing abnormal microcytic or macrocytic cells was found in two. We have demonstrated that with large sample sizes, mixtures of distributions can be detected even when distributions appear to be unimodal. These statistical techniques provide a means to characterize and quantify alterations in erythrocyte subpopulations in anemia but could also be applied to any set of grouped, doubly truncated data to test for the presence of a mixture of two lognormal distributions.     

A modified method for the purification of active large enzymes using the glutathione S-transferase expression system

The glutathione S-transferase (GST) fusion protein system is widely used for high-level expression and efficient purification of recombinant proteins from bacteria. However many GST-tagged proteins are insoluble, and the existing procedures, which employ a mixture of detergents to solubilize the molecules, frequently compromise their functional activity. A further limitation is that large proteins (>80 kDa) are poorly isolated by the current methods and are contaminated by truncated forms. To overcome these problems, we provide here an improved method for efficient purification of active large GST-tagged enzymes such as the 180-kDa GST-fused mitochondrial RNA polymerase.     

Determination of the disulfide structure of sillucin, a highly knotted, cysteine-rich peptide, by cyanylation/cleavage mass mapping

The disulfide structure of sillucin, a highly knotted, cysteine-rich, antimicrobial peptide, isolated from Rhizomucor pusillus, has been determined to be Cys2--Cys7, Cys12--Cys24, Cys13--Cys30, and Cys14--Cys21 by disulfide mass mapping based on partial reduction and CN-induced cleavage enabled by cyanylation. The denatured 30-residue peptide was subjected to partial reduction by tris(2-carboxyethyl)phosphine hydrochloride at pH 3 to produce a mixture of partially reduced sillucin species; the nascent sulfhydryl groups were immediately cyanylated by 1-cyano-4-(dimethylamino)pyridinium tetrafluoroborate. The cyanylated species, separated and collected during reversed phase high-performance liquid chromatography, were treated with aqueous ammonia, which cleaved the peptide chain on the N-terminal side of cyanylated cysteine residues. The CN-induced cleavage mixture was analyzed by matrix-assisted laser desorption ionization time-of-flight mass spectrometry before and after complete reduction of residual disulfide bonds in partially reduced and cyanylated species to mass map the truncated peptides to the sequence. Because the masses of the CN-induced cleavage fragments of both singly and doubly reduced and cyanylated sillucin are related to the linkages of the disulfide bonds in the original molecule, the presence of certain truncated peptide(s) can be used to positively identify the linkage of a specific disulfide bond or exclude the presence of other possible linkages.     

A novel glycosyltransferase with a polyglutamine repeat; a new candidate for GD1alpha synthase (ST6GalNAc V)(1)

Cystatin C with the 11 N-terminal amino acids truncated shows a much lower affinity for cysteine proteinases than the intact inhibitor. Such truncation of cystatin C is recorded after action of glycyl endopeptidase and cathepsin L. Incubation of cystatin C with papain, cathepsin B or cathepsin H led to no changes in the cystatin C molecule. Isoelectric focusing of the cathepsin L and cystatin C mixture showed the formation of two new bands. One of them appeared whether E-64 or PMSF was added or not, evidently representing a cystatin C/cathepsin L complex. The other band is the truncated cystatin C molecule. N-terminal sequencing after separation by HPLC showed that cystatin C is cleaved by cathepsin L at the Gly11-Gly12 bond. The action of cathepsin L on cystatin C may be explained by the cleavage of the scissile bond in an inappropriate complex.     

The one‐inflated positive Poisson mixture model for use in population size estimation

The one‐inflated positive Poisson mixture model (OIPPMM) is presented, for use as the truncated count model in Horvitz–Thompson estimation of an unknown population size. The OIPPMM offers a way to address two important features of some capture–recapture data: one‐inflation and unobserved heterogeneity. The OIPPMM provides markedly different results than some other popular estimators, and these other estimators can appear to be quite biased, or utterly fail due to the boundary problem, when the OIPPMM is the true data‐generating process. In addition, the OIPPMM provides a solution to the boundary problem, by labelling any mixture components on the boundary instead as one‐inflation.     

ENmix: a novel background correction method for Illumina HumanMethylation450 BeadChip

The Illumina HumanMethylation450 BeadChip is increasingly utilized in epigenome-wide association studies, however, this array-based measurement of DNA methylation is subject to measurement variation. Appropriate data preprocessing to remove background noise is important for detecting the small changes that may be associated with disease. We developed a novel background correction method, ENmix, that uses a mixture of exponential and truncated normal distributions to flexibly model signal intensity and uses a truncated normal distribution to model background noise. Depending on data availability, we employ three approaches to estimate background normal distribution parameters using (i) internal chip negative controls, (ii) out-of-band Infinium I probe intensities or (iii) combined methylated and unmethylated intensities. We evaluate ENmix against other available methods for both reproducibility among duplicate samples and accuracy of methylation measurement among laboratory control samples. ENmix out-performed other background correction methods for both these measures and substantially reduced the probe-design type bias between Infinium I and II probes. In reanalysis of existing EWAS data we show that ENmix can identify additional CpGs, and results in smaller P-value estimates for previously-validated CpGs. We incorporated the method into R package ENmix, which is freely available from Bioconductor website.     

Short-chain dolichols of defined chain length as cofactors in reactions of the microsomal dolichyl-phosphate cycle and transglycosylations.

1) The biological cofactor and carrier activities of dolichyl phosphates of low isoprene multiplicity (n) and defined geometry, (synthesized according to L. Jaenicke and H.-U. Siegmund, Chem. Phys. Lipids 51 (1989) 159-170), were assayed in different transfer reactions of the microsomal dolichyl-phosphate cycle against natural pig liver dolichyl phosphate (n = 18 to 20). 2) The apparent Michaelis constants and maximal velocities were determined from initial reaction rates for the transfer from GDP-mannose, UDP-N-acetylglucosamine, and UDP-glucose to the synthetic truncated dolichyl phosphates. They afford quantitative comparison and show increasing biological activities from dolichyl-6 phosphate to dolichyl-11 phosphate, which is about as active as the natural mixture. This is in accord with previous findings on the starting reactions of the cycle. 3) Truncated dolichyl diphosphochitobioses, biosynthesized in vitro from synthetic dolichyl phosphates, were used as acceptors for nucleoside diphosphohexoses in solubilized membranes. All of them show about the same activity. The kinetics and yield were determined for each of the transfers. Activity is increased by adding UDP-glucose. The inactive very short-chain dolichol compounds do not interfere with the transfer to active longer chain dolichols. 4) The oligosaccharides produced by transfer of mannose and glucose to truncated dolichyl diphosphate-bound chitobiose were isolated and analysed for sugar multiplicity. The heptasaccharide and the un-decasaccharide are accumulated most, pointing to the transport across the endoplasmic membranes (ER) as the rate limiting reaction. 5) The truncated dolichyl-diphosphate-bound oligosaccharides are transferred to protein(s) by the crude, solubilized microsomal preparation independent of chain length of the cofactor/carrier, yet with increasing yield as shown by enzyme immunoblot analysis.     

Bacillus subtilis secretes a foreign protein by the signal sequence of Bacillus amyloliquefaciens neutral protease

Summary We constructed a secretion plasmid in which a truncated penicillinase gene of Bacillus licheniformis was introduced at the end of the signal peptide coding region of a Bacillus amyloliquefaciens neutral protease gene. A Bacillus subtilis recombinant secreted about 140 mg/liter of the penicillinase into the medium. Analysis of the purified product revealed that it was a mixture of two penicillinases containing one or two additional amino acids at the NH₂-terminus of B. licheniformis exo-small penicillinase.     

Domain architecture of the heme-independent yeast cystathionine beta-synthase provides insights into mechanisms of catalysis and regulation

Cystathionine beta-synthase from yeast (Saccharomyces cerevisiae) provides a model system for understanding some of the effects of disease-causing mutations in the human enzyme. The mutations, which lead to accumulation of L-homocysteine, are linked to homocystinuria and cardiovascular diseases. Here we characterize the domain architecture of the heme-independent yeast cystathionine beta-synthase. Our finding that the homogeneous recombinant truncated enzyme (residues 1-353) is catalytically active and binds pyridoxal phosphate stoichiometrically establishes that the N-terminal residues 1-353 compose a catalytic domain. Removal of the C-terminal residues 354-507 increases the specific activity and alters the steady-state kinetic parameters including the K(d) for pyridoxal phosphate, suggesting that the C-terminal residues 354-507 compose a regulatory domain. The yeast enzyme, unlike the human enzyme, is not activated by S-adenosyl-L-methionine. The truncated yeast enzyme is a dimer, whereas the full-length enzyme is a mixture of tetramer and octamer, suggesting that the C-terminal domain plays a role in the interaction of the subunits to form higher oligomeric structures. The N-terminal catalytic domain is more stable and less prone to aggregate than full-length enzyme and is thus potentially more suitable for structure determination by X-ray crystallography. Comparisons of the yeast and human enzymes reveal significant differences in catalytic and regulatory properties.     

Isolation and characterization of the circulating truncated form of PCSK9

Proprotein convertase subtilisin-kexin type 9 (PCSK9) is a secreted protein which regulates serum LDL cholesterol. It circulates in human and rodent serum in an intact form and a major truncated form. Previous in vitro studies involving the expression of human PCSK9 genetic variants and in vivo studies of furin knockout mice suggest that the truncated form is a furin cleavage product. However, the circulating truncated form of PCSK9 has not been isolated and characterized. Utilizing antibodies which bind to either the catalytic domain or the C-terminal domain of PCSK9, the truncated PCSK9 was isolated from serum. MS was used to determine that this form of PCSK9 is a product of in vivo cleavage at Arg218 resulting in pyroglutamic acid formation of the nascent N terminus corresponding to Gln219 of intact PCSK9. We also determined that the truncated PCSK9 in serum lacked the N-terminal segment which contains amino acids critical for LDL receptor binding. A truncated PCSK9, expressed and purified from HEK293 cells with identical composition as the circulating truncated protein, was not active in inhibition of LDL uptake by HepG2 cells. These studies provide a definitive characterization of the composition and activity of the truncated form of PCSK9 found in human serum.     

Functional expression and characterization of Aedes aegypti dopachrome conversion enzyme.

A full-length mosquito dopachrome conversion enzyme (DCE) and its truncated form lacking the last 54 carboxyl-terminal amino acid residues are expressed using a baculovirus/insect cell expression system. The full-length recombinant DCE displayed multiple bands during native PAGE with substrate staining, but only one active band was detected when the truncated recombinant DCE was analyzed under identical analysis conditions. Our data suggest that the last 50 some carboxyl-terminal residues are involved in the polymerization of the DCE molecules and that the proposed DCE isozymes likely reflect the presence of multimers of the same DCE molecules. The significance of the recombinant DCE in accelerating the melanization pathway is demonstrated by a rapid production of melanin in a dopa and tyrosinase reaction mixture in the presence of recombinant DCE. The DCE sequence data obtained in our previous study, together with results of functional expression and biochemical characterization achieved in this study, provide a necessary reference for the study of other insect DCEs.     

A novel Bacillus thuringiensis (PS149B1) containing a Cry34Ab1/Cry35Ab1 binary toxin specific for the western corn rootworm Diabrotica virgifera virgifera LeConte forms ion channels in lipid membranes

The binary Bacillus thuringiensis PS149B1 insecticidal crystal (Cry) protein is comprised of two components, Cry34Ab1, a 14-kDa protein, and Cry35Ab1, a 44-kDa protein, the combination of which forms a novel binary toxin active on western corn rootworm larvae. The permeabilizing behavior of the native binary toxin and its two individual components expressed as recombinant proteins was studied using calcein efflux determination in liposomes and by ion channel activity measurements in planar lipid bilayers (PLBs). Data obtained with solubilized native PS149B1 binary protein revealed it to be a pore-forming toxin that can permeabilize liposomes and form ion channels ( approximately 300-900 pS) in PLBs at pH 5.5 but not pH 9.0. The 14-kDa component of the toxin also formed ion channels ( approximately 15-300 pS) at pH 5.5 but did not insert easily in PLBs. While the 44-kDa moiety did seldomly form resolvable ion channels ( approximately 15-750 pS) in PLBs, it did destabilize the membranes. It showed pH-dependent truncation to a stable 40-kDa protein. The purified 40-kDa truncated product formed channels ( approximately 10-450 pS) in PLBs at pH 5.5. At that same pH, while a 3:1 molar mixture (14:44 kDa) of the individual components of the toxin induced channel activity that resembled that of the 14-kDa component alone, the 3:1 molar mixture of the 14-kDa component and 40-kDa truncated product induced channel activity ( approximately 20-800 pS) similar to that of PS149B1 in planar lipid bilayers. We conclude that the overall membrane permeabilization process of Cry34Ab1/Cry35Ab1 is a result of ion channel formation.     

Construction of a deletion library using a mixture of 5'-truncated primers for inverse PCR (IPCR).

A quick in vitro mutagenesis method for the construction of nested deletion libraries was developed. Many deletions can be obtained in a single inverse PCR (IPCR) by replacing one of the two primers with a mixture of 5'-truncated oligodeoxynucleotides. Since chemical DNA synthesis proceeds from the 3'to the 5'end, such a mixture of 5'-truncated oligodeoxynucleotides can easily be obtained in a single automated DNA synthesis under reduced coupling efficiency. This deletion mutagenesis method yields many different deletions in a defined short DNA segment and is, therefore, best suited for a deletion analysis at base pair level. Applications might include functional analysis of regulatory DNA segments and protein engineering work that requires libraries for the expression of N-terminal, C-terminal or internal truncated proteins as well as fusion proteins having different splice sites.     

Structural and functional studies of FkpA from Escherichia coli, a cis/trans peptidyl-prolyl isomerase with chaperone activity

The protein FkpA from the periplasm of Escherichia coli exhibits both cis/trans peptidyl-prolyl isomerase (PPIase) and chaperone activities. The crystal structure of the protein has been determined in three different forms: as the full-length native molecule, as a truncated form lacking the last 21 residues, and as the same truncated form in complex with the immunosuppressant ligand, FK506. FkpA is a dimeric molecule in which the 245-residue subunit is divided into two domains. The N-terminal domain includes three helices that are interlaced with those of the other subunit to provide all inter-subunit contacts maintaining the dimeric species. The C-terminal domain, which belongs to the FK506-binding protein (FKBP) family, binds the FK506 ligand. The overall form of the dimer is V-shaped, and the different crystal structures reveal a flexibility in the relative orientation of the two C-terminal domains located at the extremities of the V. The deletion mutant FkpNL, comprising the N-terminal domain only, exists in solution as a mixture of monomeric and dimeric species, and exhibits chaperone activity. By contrast, a deletion mutant comprising the C-terminal domain only is monomeric, and although it shows PPIase activity, it is devoid of chaperone function. These results suggest that the chaperone and catalytic activities reside in the N and C-terminal domains, respectively. Accordingly, the observed mobility of the C-terminal domains of the dimeric molecule could effectively adapt these two independent folding functions of FkpA to polypeptide substrates.     

Analysis of conditional gene deletion using probe based Real-Time PCR

Background  

Conditional gene deletion using Cre-lox recombination is frequently used in mouse genetics; however recombination is frequently incomplete, resulting in a mixture of cells containing the functional (2lox) allele and the truncated (1lox) allele. Conventional analysis of 1lox/2lox allele ratios using Southern Blotting is time consuming, requires relatively large amounts of DNA and has a low sensitivity. We therefore evaluated the utility of Real-Time PCR to measure 1lox/2lox allele ratios.