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.     

Functional comparision between truncated MTT1 and truncated MTT2 from Tetrahyemna thermophila

Metallothioneins (MTs) are low-molecular-weight proteins with high Cys content and high metal-chelating ability. CdMT and CuMT subfamilies present different characteristics in Tetrahymena. To explore the effect of the cysteine arrangement and sequence length of MTs for binding different metal ions, MTT1, truncated MTT1 (TM1), MTT2, and truncated MTT2 (TM2) were expressed in E. coli. The half-maximal inhibiting concentrations (IC₅₀) of Cd²⁺ and Cu⁺ for the recombinant strains were different. Furthermore, E. coli cells expressing MTT1 and TM1 exhibited higher accumulating ability for Cd²⁺ than cells expressing MTT2 and TM2. However, the opposite is true for Cu⁺. The binding ability of the different recombinant proteins to Cd²⁺ and Cu⁺ were also different. MTT1 and truncated mutant TM1 were the preference for Cd²⁺, whereas MTT2 and truncated mutant TM2 were the preference for Cu⁺ coordination. These results showed that metal ion tolerance and accumulation ability not only depended on cysteine arrangement pattern but also on sequence length of MT in Tetrahymena.     

Modeling truncated hemoglobin vibrational dynamics

We present a study on the near equilibrium dynamics of two small proteins in the family of truncated hemoglobins, developed under the framework of a Gaussian network approach. Effective beta carbon atoms are taken into account besides Calphas for all residues but glycines in the coarse-graining procedure, without leading to an increase in the degrees of freedom (beta Gaussian Model). Normalized covariance matrix and deformation along slowest modes with collective character are analyzed, pointing out anticorrelations between functionally relevant sites for the proteins under study. In particular, we underline the functional motions of an extended tunnel-cavity system running inside the protein matrix, which provide a pathway for small ligands binding with the iron in the heme group. We give a rough estimate of the order of magnitude of the relaxation times of the slowest two overdamped modes and compare results with previous studies on globins.     

The truncated hemoglobin from Mycobacterium leprae

Truncated hemoglobins (trHb's) form a family of low molecular weight O2 binding hemoproteins distributed in eubacteria, protozoa, and plants. TrHb's branch in a distinct clade within the hemoglobin (Hb) superfamily. A unique globin gene has recently been identified from the complete genome sequence of Mycobacterium leprae that is predicted to encode a trHb (M. leprae trHbO). Sequence comparison and modelling considerations indicate that monomeric M. leprae trHbO has structural features typical of trHb's, such as 20-40 fewer residues than conventional globin chains, Gly-based sequence consensus motifs, likely assembling into a 2-on-2 alpha-helical sandwich fold, and hydrophobic residues recognized to build up the protein matrix ligand diffusion tunnel. The ferrous heme iron atom of deoxygenated M. leprae trHbO appears to be hexacoordinated, like in Arabidopsis thaliana trHbO-3 (A. thaliana trHbO-3). Accordingly, the value of the second-order rate constant for M. leprae trHbO carbonylation (7.3 x 10(3) M(-1) s(-1)) is similar to that observed for A. thaliana trHbO-3 (1.4 x 10(4) M(-1) s(-1)) and turns out to be lower than that reported for carbon monoxide binding to pentacoordinated Mycobacterium tuberculosis trHbN (6.7 x 10(6) M(-1) s(-1)). The lower reactivity of M. leprae trHbO as compared to M. tuberculosis trHbN might be related to the higher susceptibility of the leprosy bacillus to toxic nitrogen and oxygen species produced by phagocytic cells.     

Two-sample Kolmogorov-Smirnov test for truncated data

A nonparametric statistical test to compare two cumulative frequency distribution functions is presented that can be used even when both samples include censored data, as is often the case when comparing the survival of two groups of laboratory animals under conditions in which the experiment is terminated before all the animals die. (Such a design can produce considerable savings and is to be recommended.) The program calculates exact probabilities for both the one-sided and two-sided alternatives to the null hypothesis, applicable to the case of equal group size, as well as the corresponding general asymptotic values; a continuity correction is employed that markedly improves the asymptotic approximation. Expressions are stated in terms of two different but related statistics, and the one that utilizes more information in any particular set of data is selected for the probability calculations. All basic equations and definitions are provided.     

Ribosome rescue by tmRNA requires truncated mRNAs

tmRNA targets ribosomes, stalled either on truncated mRNAs or on mRNAs with slowly read sense or stop codons, tags the newly synthesized peptide chains for degradation and allows for their release by a class-1 release factor. We have studied in vitro how the rate of trans-transfer of a peptide from the P-site tRNA to tmRNA and the efficiency by which tmRNA competes with peptide release factors depend on the length of the mRNA downstream from the P-site. We show that the rate and efficiency of tmRNA action decrease rapidly with increasing down stream length and approach zero when it exceeds 15 bases. We demonstrate that tmRNA action is strongly stimulated by RelE cleavage of mRNA in the A site. We conclude that tmRNA action in vivo must always be preceded by mRNA truncation, and suggest that cleavage of ribosome bound mRNAs is a common element in different bacterial stress responses.     

Molecular dynamics simulation of truncated bovine adrenodoxin

The 128 amino acid long soluble protein adrenodoxin (Adx) is a typical member of the ferredoxin protein family that are electron carrier proteins with an iron-sulfur cofactor. Adx carries electrons from adrenodoxin reductase (AdR) to cytochrome P450s. Its binding modes to these proteins were previously characterized by site-directed mutagenesis, by X-ray crystallography for the complex Adx:AdR, and by NMR. However, no clear evidence has been provided for the driving force that promotes Adx detachment from AdR upon reduction. Here, we characterized the conformational dynamics of unbound Adx in the oxidized and reduced forms using 2-20 ns long molecular dynamics simulations. The most noticeable difference between both forms is the enhanced flexibility of the loop (47-51) surrounding the iron-sulfur cluster in the reduced form. Together with several structural displacements at the binding interface, this increased flexibility may be the key factor promoting unbinding of reduced Adx from AdR. This points to an intrinsic property of reduced Adx that drives dissociation.     

Fungicidal activity of truncated analogues of dihydrosphingosine

The minimal fungicidal concentration (MFC) of dihydrosphingosine (DHS), phytosphingosine (PHS), and five short-chain DHS derivatives was determined for Candida albicans and Candida glabrata. In this respect, a C15- and a C17-homologue of DHS showed a 2- to 10-fold decreased MFC as compared to native DHS (i.e. C18-DHS). DHS derivatives that were active, that is, comprising 12, 15, 17, or 18 carbon atoms, induced accumulation of reactive oxygen species (ROS) in C. albicans.     

Heme-ligand tunneling in group I truncated hemoglobins

Truncated hemoglobins (trHbs) are small hemoproteins forming a separate cluster within the hemoglobin superfamily; their functional roles in bacteria, plants, and unicellular eukaryotes are marginally understood. Crystallographic investigations have shown that the trHb fold (a two-on-two alpha-helical sandwich related to the globin fold) hosts a protein matrix tunnel system offering a potential path for ligand diffusion to the heme distal site. The tunnel topology is conserved in group I trHbs, although with modulation of its size/structure. Here, we present a crystallographic investigation on trHbs from Mycobacterium tuberculosis, Chlamydomonas eugametos, and Paramecium caudatum, showing that treatment of trHb crystals under xenon pressure leads to binding of xenon atoms at specific (conserved) sites along the protein matrix tunnel. The crystallographic results are in keeping with data from molecular dynamics simulations, where a dioxygen molecule is left free to diffuse within the protein matrix. Modulation of xenon binding over four main sites is related to the structural properties of the tunnel system in the three trHbs and may be connected to their functional roles. In a parallel crystallographic investigation on M. tuberculosis trHbN, we show that butyl isocyanide also binds within the apolar tunnel, in excellent agreement with concepts derived from the xenon binding experiments. These results, together with recent data on atypical CO rebinding kinetics to group I trHbs, underline the potential role of the tunnel system in supporting diffusion, but also accumulation in multiple copies, of low polarity ligands/molecules within group I trHbs.     

Dolichyl phosphate-dependent glycosyltransferases utilize truncated cofactors.

Synthetic truncated dolichyl phosphates of chain lengths from four to thirteen isoprene units (Jaenicke L. and Siegmund H.-U., Chem. Phys. Lipids 51 (1989) 159-170) were assayed for their cofactor activity in the enzymatic transfer of hexoses and hexosamines. The enzymes were microsomal preparations from the green alga Volvox carteri, baker's yeast, and mammalian liver cells. Under saturating conditions, the acceptor activities of the truncated dolichyl phosphates increased from zero to full strength as compared to the mixture of long-chain dolichyl phosphates from natural sources with growing chain length from five to nine isoprene units. Km determinations confirmed the results. Of the geometric isomers of dolichyl 7-phosphate (35 carbon atoms), the 14-trans compound has unchanged acceptor activity; all-trans dolichyl 7-phosphate, however, was almost inactive. The data suggest that hydrophobicity may be an important, but not the only criterion for the binding of the isoprene moiety to the active sites of the transferase enzyme(s) and that the geometry of more than only one double bond in the dolichols is recognized.     

Crystal structure of truncated human betaB1-crystallin

Crystallins are long-lived proteins packed inside eye lens fiber cells that are essential in maintaining the transparency and refractive power of the eye lens. Members of the two-domain betagamma-crystallin family assemble into an array of oligomer sizes, forming intricate higher-order networks in the lens cell. Here we describe the 1.4 angstroms resolution crystal structure of a truncated version of human betaB1 that resembles an in vivo age-related truncation. The structure shows that unlike its close homolog, betaB2-crystallin, the homodimer is not domain swapped, but its domains are paired intramolecularly, as in more distantly related monomeric gamma-crystallins. However, the four-domain dimer resembles one half of the crystallographic bovine betaB2 tetramer and is similar to the engineered circular permuted rat betaB2. The crystal structure shows that the truncated betaB1 dimer is extremely well suited to form higher-order lattice interactions using its hydrophobic surface patches, linker regions, and sequence extensions.     

Core flexibility of a truncated metazoan mitochondrial tRNA

Secondary and tertiary structures of tRNAs are remarkably preserved from bacteria to humans, the notable exception being the mitochondrial (m) tRNAs of metazoans, which often deviate substantially from the canonical cloverleaf (secondary) or ‘L’-shaped (tertiary) structure. Many metazoan mtRNAs lack either the TψC (T) or dihydrouridine (D) loops of the canonical cloverleaf, which are known to confer structural rigidity to the folded structure. Thus, the absence of canonical TψC–D interactions likely results in greater dispersion of anticodon-acceptor interstem angle than for canonical tRNAs. To test this hypothesis, we have assessed the dispersion of the anticodon-acceptor angle for bovine mtRNA^Ser(AGY), which lacks the canonical D arm and is thus incapable of forming stabilizing interarm interactions. Using the method of transient electric birefringence (TEB), and by changing the helical torsion angle between a core mtRNA bend and a second bend of known angle/rigidity, we have demonstrated that the core of mtRNA^Ser(AGY) has substantially greater flexibility than its well-characterized canonical counterpart, yeast cytoplasmic tRNA^Phe. These results suggest that increased flexibility, in addition to a more open interstem angle, would allow both noncanonical and canonical mtRNAs to utilize the same protein synthetic apparatus.