Transmembrane segment 3 of the Glut1 glucose transporter is an outer helix

A model has been proposed for the structure of the Glut1 glucose transporter based on the results of mutagenesis studies and homology modeling in which eight transmembrane segments form an inner helical bundle surrounded by four outer helices. The role of transmembrane segment 3 in this structural model was investigated using cysteine-scanning mutagenesis in conjunction with the membrane-impermeant, sulfhydryl-specific reagent, p-chloromercuribenzenesulfonate (pCMBS). Twenty-one Glut1 mutants were created from a fully functional, cysteine-less, parental Glut1 molecule by successively changing each residue along transmembrane helix 3 to a cysteine. The single cysteine mutants were then expressed in Xenopus oocytes, and their expression levels, transport activities, and sensitivities to pCMBS were determined. Cysteine substitution at methionine 96 abolished transport activity, whereas substitutions at the other positions resulted in either modest reductions or no significant effect on transport activity. In striking contrast to all other helices that have been examined to date, only one of the 21 helix 3 single-cysteine mutants was inhibited by pCMBS, suggesting that only a small portion of this helix is exposed to the external solvent. This result is consistent with predictions based on our current structural model, in which helix 3 is one of four outer helices that surround the inner helical bundle that comprises the aqueous substrate-binding cavity. An updated two-dimensional model for the orientation of the 12 transmembrane helices and the conformation of the exofacial glucose-binding site of Glut1 is presented that is consistent with existing experimental data.     

The L49F mutation in alpha erythroid spectrin induces local disorder in the tetramer association region: Fluorescence and molecular dynamics studies of free and bound alpha spectrin

The bundling of the N‐terminal, partial domain helix (Helix C′) of human erythroid α‐spectrin (αI) with the C‐terminal, partial domain helices (Helices A′ and B′) of erythroid β‐spectrin (βI) to give a spectrin pseudo structural domain (triple helical bundle A′B′C′) has long been recognized as a crucial step in forming functional spectrin tetramers in erythrocytes. We have used apparent polarity and Stern–Volmer quenching constants of Helix C′ of αI bound to Helices A′ and B′ of βI, along with previous NMR and EPR results, to propose a model for the triple helical bundle. This model was used as the input structure for molecular dynamics simulations for both wild type (WT) and αI mutant L49F. The simulation output structures show a stable helical bundle for WT, but not for L49F. In WT, four critical interactions were identified: two hydrophobic clusters and two salt bridges. However, in L49F, the region downstream of Helix C′ was unable to assume a helical conformation and one critical hydrophobic cluster was disrupted. Other molecular interactions critical to the WT helical bundle were also weakened in L49F, possibly leading to the lower tetramer levels observed in patients with this mutation‐induced blood disorder.     

Disorder influence on linear dichroism analyses of smectic phases

Linear dichroism, the unequal absorption of parallel and perpendicular linear polarized light, is often used to determine the anisotropic ordering of rodlike polymers in a smectic phase, such as helices in a lipid bilayer. It is a measure of two properties of the sample: 1), orientation of the chromophore transition dipole moment (TDM) and 2), disorder. Since it is the orientation of the chromophore TDM that is needed for high resolution structural studies, it is imperative to either deconvolve sample disorder, or at a minimum, estimate its effect upon the calculated TDM orientation. Herein, a rigorous analysis of the effects of disorder is undertaken based on the recently developed Gaussian disorder model implemented in linear dichroism data. The calculation of both the rod tilt and rotational pitch angles as a function of the disorder and dichroism, yield the following conclusions: Disorders smaller than 5 degrees have a vanishingly small effect on the calculated polymer orientation, whereas values smaller than 10 degrees have a negligible effect on the calculated parameters. Disorders larger than 10 degrees have an appreciable effect on the calculated orientational parameters and as such must be estimated before any structural characterization. Finally the theory is tested on the HIV vpu transmembrane domain, employing experimental mosaicity measurements from x-ray reflectivity rocking scans and linear dichroism.     

Flexibility of beta-sheets: principal component analysis of database protein structures

Protein folds are built primarily from the packing together of two types of structures: alpha-helices and beta-sheets. Neither structure is rigid, and the flexibility of helices and sheets is often important in determining the final fold (e.g., coiled coils and beta-barrels). Recent work has quantified the flexibility of alpha-helices using a principal component analysis (PCA) of database helical structures (J. Mol. Bio. 2003, 327, pp. 229-237). Here, we extend the analysis to beta-sheet flexibility using PCA on a database of beta-sheet structures. For sheets of varying dimension and geometry, we find two dominant modes of flexibility: twist and bend. The distributions of amplitudes for these modes are found to be Gaussian and independent, suggesting that the PCA twist and bend modes can be identified as the soft elastic normal modes of sheets. We consider the scaling of mode eigenvalues with sheet size and find that parallel beta-sheets are more rigid than antiparallel sheets over the entire range studied. Finally, we discuss the application of our PCA results to modeling and design of beta-sheet proteins.     

Crystallographic analysis of acrosomal bundle from Limulus sperm

The acrosomal process of Limulus sperm contains a bundle of filaments composed of actin and a 102 kDa protein in a 1:1 molar ratio. The structure of the bundle in true discharge was investigated by electron cryomicroscopy, X-ray scattering and crystallographic image analysis. A bundle can be characterized as a quasi-crystal with continuously varying views along the bundle axis. Each segment of the bundle is found to obey the symmetry of space group P1, with a = b = 147 A, c = 762 A, alpha = 90 degrees, beta = 90.6 degrees, gamma = 120 degrees. A unit cell contains a helical repeat of the filament with a selection rule following that of an actin filament. A 24 A projection map based on the h0l view was reconstructed after averaging 5300 unit cells from six electron images. Filaments in this projection are well separated and clearly display a 21 screw symmetry. This screw symmetry results from the helical parameters of the bundle filament and is found to be a non-crystallographic symmetry element present in the unit cell. Our structural analysis has led to the proposal that the assembly of a stable bundle with a defined maximum diameter can be controlled by the crystallographic packing of the twisted filaments.     

Mechanistic analytical models for long-distance seed dispersal by wind

We introduce an analytical model, the Wald analytical long-distance dispersal (WALD) model, for estimating dispersal kernels of wind-dispersed seeds and their escape probability from the canopy. The model is based on simplifications to well-established three-dimensional Lagrangian stochastic approaches for turbulent scalar transport resulting in a two-parameter Wald (or inverse Gaussian) distribution. Unlike commonly used phenomenological models, WALD's parameters can be estimated from the key factors affecting wind dispersal--wind statistics, seed release height, and seed terminal velocity--determined independently of dispersal data. WALD's asymptotic power-law tail has an exponent of -3/2, a limiting value verified by a meta-analysis for a wide variety of measured dispersal kernels and larger than the exponent of the bivariate Student t-test (2Dt). We tested WALD using three dispersal data sets on forest trees, heathland shrubs, and grassland forbs and compared WALD's performance with that of other analytical mechanistic models (revised versions of the tilted Gaussian Plume model and the advection-diffusion equation), revealing fairest agreement between WALD predictions and measurements. Analytical mechanistic models, such as WALD, combine the advantages of simplicity and mechanistic understanding and are valuable tools for modeling large-scale, long-term plant population dynamics.     

Multiple helical conformations of the helix‐turn‐helix region revealed by NOE‐restrained MD simulations of tryptophan aporepressor,TrpR

The nature of flexibility in the helix‐turn‐helix region of E. coli trp aporepressor has been unexplained for many years. The original ensemble of nuclear magnetic resonance (NMR structures showed apparent disorder, but chemical shift and relaxation measurements indicated a helical region. Nuclear Overhauser effect (NOE) data for a temperature‐sensitive mutant showed more helical character in its helix‐turn‐helix region, but nevertheless also led to an apparently disordered ensemble. However, conventional NMR structure determination methods require all structures in the ensemble to be consistent with every NOE simultaneously. This work uses an alternative approach in which some structures of the ensemble are allowed to violate some NOEs to permit modeling of multiple conformational states that are in dynamic equilibrium. Newly measured NOE data for wild‐type aporepressor are used as time‐averaged distance restraints in molecular dynamics simulations to generate an ensemble of helical conformations that is more consistent with the observed NMR data than the apparent disorder in the previously reported NMR structures. The results indicate the presence of alternating helical conformations that provide a better explanation for the flexibility of the helix‐turn‐helix region of trp aporepressor. Structures representing these conformations have been deposited with PDB ID: 5TM0. Proteins 2017; 85:731–740. © 2016 Wiley Periodicals, Inc.     

Bayesian mixture model based clustering of replicated microarray data

MOTIVATION: Identifying patterns of co-expression in microarray data by cluster analysis has been a productive approach to uncovering molecular mechanisms underlying biological processes under investigation. Using experimental replicates can generally improve the precision of the cluster analysis by reducing the experimental variability of measurements. In such situations, Bayesian mixtures allow for an efficient use of information by precisely modeling between-replicates variability. RESULTS: We developed different variants of Bayesian mixture based clustering procedures for clustering gene expression data with experimental replicates. In this approach, the statistical distribution of microarray data is described by a Bayesian mixture model. Clusters of co-expressed genes are created from the posterior distribution of clusterings, which is estimated by a Gibbs sampler. We define infinite and finite Bayesian mixture models with different between-replicates variance structures and investigate their utility by analyzing synthetic and the real-world datasets. Results of our analyses demonstrate that (1) improvements in precision achieved by performing only two experimental replicates can be dramatic when the between-replicates variability is high, (2) precise modeling of intra-gene variability is important for accurate identification of co-expressed genes and (3) the infinite mixture model with the 'elliptical' between-replicates variance structure performed overall better than any other method tested. We also introduce a heuristic modification to the Gibbs sampler based on the 'reverse annealing' principle. This modification effectively overcomes the tendency of the Gibbs sampler to converge to different modes of the posterior distribution when started from different initial positions. Finally, we demonstrate that the Bayesian infinite mixture model with 'elliptical' variance structure is capable of identifying the underlying structure of the data without knowing the 'correct' number of clusters. AVAILABILITY: The MS Windows based program named Gaussian Infinite Mixture Modeling (GIMM) implementing the Gibbs sampler and corresponding C++ code are available at http://homepages.uc.edu/~medvedm/GIMM.htm SUPPLEMENTAL INFORMATION: http://expression.microslu.washington.edu/expression/kayee/medvedovic2003/medvedovic_bioinf2003.html     

Mixture-of-Experts Variational Autoencoder for clustering and generating from similarity-based representations on single cell data

Clustering high-dimensional data, such as images or biological measurements, is a long-standing problem and has been studied extensively. Recently, Deep Clustering has gained popularity due to its flexibility in fitting the specific peculiarities of complex data. Here we introduce the Mixture-of-Experts Similarity Variational Autoencoder (MoE-Sim-VAE), a novel generative clustering model. The model can learn multi-modal distributions of high-dimensional data and use these to generate realistic data with high efficacy and efficiency. MoE-Sim-VAE is based on a Variational Autoencoder (VAE), where the decoder consists of a Mixture-of-Experts (MoE) architecture. This specific architecture allows for various modes of the data to be automatically learned by means of the experts. Additionally, we encourage the lower dimensional latent representation of our model to follow a Gaussian mixture distribution and to accurately represent the similarities between the data points. We assess the performance of our model on the MNIST benchmark data set and challenging real-world tasks of clustering mouse organs from single-cell RNA-sequencing measurements and defining cell subpopulations from mass cytometry (CyTOF) measurements on hundreds of different datasets. MoE-Sim-VAE exhibits superior clustering performance on all these tasks in comparison to the baselines as well as competitor methods.     

Induction of Peptide Bond Dipoles Drives Cooperative Helix Formation in the (AAQAA)3 Peptide

Cooperativity is a central feature in the formation of secondary structures in proteins. However, the driving forces behind this cooperativity are poorly understood. The present work shows that the cooperativity of helix formation in the acetyl-(AAQAA)₃-NH₂ peptide is significantly enhanced using an empirical force field that explicitly includes the treatment of electronic polarizability. Polarizable simulations yield helical content consistent with experimental measurements and indicate that the dependence of helical content on temperature is improved over additive models, though further sampling is required to fully validate this conclusion. Cooperativity is indicated by the peptide sampling either the coiled state or long helices with relatively low populations of short helices. The cooperativity is shown to be associated with enhanced dipole moments of the peptide backbone upon helix formation. These results indicate the polarizable force field to more accurately model peptide-folding cooperativity based on its physically realistic treatment of electronic polarizability.     

Induction of Peptide Bond Dipoles Drives Cooperative Helix Formation in the (AAQAA)3 Peptide

Cooperativity is a central feature in the formation of secondary structures in proteins. However, the driving forces behind this cooperativity are poorly understood. The present work shows that the cooperativity of helix formation in the acetyl-(AAQAA)₃-NH₂ peptide is significantly enhanced using an empirical force field that explicitly includes the treatment of electronic polarizability. Polarizable simulations yield helical content consistent with experimental measurements and indicate that the dependence of helical content on temperature is improved over additive models, though further sampling is required to fully validate this conclusion. Cooperativity is indicated by the peptide sampling either the coiled state or long helices with relatively low populations of short helices. The cooperativity is shown to be associated with enhanced dipole moments of the peptide backbone upon helix formation. These results indicate the polarizable force field to more accurately model peptide-folding cooperativity based on its physically realistic treatment of electronic polarizability.     

Deconvolution of isotope signals from bundles of multiple hairs

Segmental analysis of hair has been used in diverse fields ranging from forensics to ecology to measure the concentration of substances such as drugs and isotopes. Multiple hairs are typically combined into a bundle for segmental analysis to obtain a high-resolution series of measurements. Individual hair strands cycle through multiple phases of growth and grow at different rates when in the growth phase. Variation in growth of hair strands in a bundle can cause misalignment of substance concentration between hairs, attenuating the primary body signal. We developed a mathematical model based on the known physiology of hair growth to describe the signal averaging caused by bundling multiple hairs for segmental analysis. The model was used to form an inverse method to estimate the primary body signal from measurements of a hair bundle. The inverse method was applied to a previously described stable oxygen isotope chronology from the hair of a murder victim and provides a refined interpretation of the data. Aspects of the reconstruction were confirmed when the victim was later identified.     

Determination of the resonant harmonics of the error field from dynamic magnetic measurements in a tokamak

The possibility is discussed of determining the amplitude and phase of a static resonant error field in a tokamak by means of dynamic magnetic measurements. The method proposed assumes measuring the plasma response to a varying external helical magnetic field with a small (a few gauss) amplitude. The case is considered in which the plasma is probed by square pulses with a duration much longer than the time of the transition process. The plasma response is assumed to be linear, with a proportionality coefficient being dependent on the plasma state. The analysis is carried out in a standard cylindrical approximation. The model is based on Maxwell’s equations and Ohm’s law and is thus capable of accounting for the interaction of large-scale modes with the conducting wall of the vacuum chamber. The method can be applied to existing tokamaks.     

The adipophilin C terminus is a self-folding membrane-binding domain that is important for milk lipid secretion

Cytoplasmic lipid droplets (CLD) in mammary epithelial cells undergo secretion by a unique membrane envelopment process to produce milk lipids. Adipophilin (ADPH/Plin2), a member of the perilipin/PAT family of lipid droplet-associated proteins, is hypothesized to mediate CLD secretion through interactions with apical plasma membrane elements. We found that the secretion of CLD coated by truncated ADPH lacking the C-terminal region encoding a putative four-helix bundle structure was impaired relative to that of CLD coated by full-length ADPH. We used homology modeling and analyses of the solution and membrane binding properties of purified recombinant ADPH C terminus to understand how this region possibly mediates CLD secretion. Homology modeling supports the concept that the ADPH C terminus forms a four-helix bundle motif and suggests that this structure can form stable membrane bilayer interactions. Circular dichroism and protease mapping studies confirmed that the ADPH C terminus is an independently folding α-helical structure that is relatively resistant to urea denaturation. Liposome binding studies showed that the purified C terminus binds to phospholipid membranes through electrostatic dependent interactions, and cell culture studies documented that it localizes to the plasma membrane. Collectively, these data provide direct evidence that the ADPH C terminus forms a stable membrane binding helical structure that is important for CLD secretion. We speculate that interactions between the four-helix bundle of ADPH and membrane phospholipids may be an initial step in milk lipid secretion.     

Mean-square amplitudes of the longitudinal vibrational of helical polymers

A simple model for the longitudinal acoustical vibrations of helical polymers has been developed. This model consists of a linear string of masses, M, connected by springs. The mass must be taken as that of one helical turn of the true helix. It has been found that all of the previously observed or calculated frequencies for the longitudinal acoustical modes of helical polymers can be calculated from this model using only one adjustable parameter, the force constant f, between the turns, for each type of helix. Using this simplified model it has been possible to obtain the rms amplitudes of the changes in the overall end-to-end length of helical polymers as a function of their chain length and temperature. At room temperatures the rms end-to-end length is found to vary from a few tenths of an angstrom for hydrocarbon chains of the length found in phospholipid membrane bilayers to several angstroms in a rigid α-helix of 100 peptide residues. The damping of these α-helical modes is not considered but may be appreciable in solution.     

Mean geometry of the thiopeptide unit and conformational features of dithiopeptides and polythiopeptides

The mean geometry of the thiopeptide [Ca-N-C(=S)-Ca] unit has been derived from an analysis of X-ray crystal structure data, as well as MM2 and Gaussian 80/82 calculations. The conformational flexibilities of dithiopeptides with glycl- and alanyl-side chains have been investigated by molecular mechanics. Minimum energy conformations were examined using interactive computer graphics molecular modeling techniques. Alanyl-dithiopeptide substitution within an oligopeptide results in considerable restriction of conformational freedom whereas the effect is minimal for glycyl-dithiopeptide substitution. Polyglycyl-thiopeptide adopts a left-handed three or fourfold or right-handed threefold helical structure with favorable interchain C = S...H-N hydrogen bond interactions. A poly-L-alanyl-thiopeptide prefers a left-handed threefold poly-L-proline-like helical structure.     

The structure of the M2 channel-lining segment from the nicotinic acetylcholine receptor

The structures of functional peptides corresponding to the predicted channel-lining M2 segment of the nicotinic acetylcholine (AChR) were determined using solution NMR experiments on micelle samples, and solid-state NMR experiments on bilayer samples. The AChR M2 peptide forms a straight transmembrane alpha-helix, with no kinks. M2 inserts in the lipid bilayer at an angle of 12 degrees relative to the bilayer normal, with a rotation about the helix long axis such that the polar residues face the N-terminus of the peptide, which is assigned to be intracellular. A molecular model of the AChR channel pore, constructed from the solid-state NMR 3-D structure of the AChR M2 helix in the membrane assuming a pentameric organization, results in a funnel-like architecture for the channel with the wide opening on the N-terminal intracellular side. A central narrow pore has a diameter ranging from about 3.0 A at its narrowest, to 8.6 A at its widest. Nonpolar residues are predominantly on the exterior of the bundle, while polar residues line the pore. This arrangement is in fair agreement with evidence collected from permeation, mutagenesis, affinity labeling and cysteine accessibility measurements. A pentameric M2 helical bundle may, therefore, represent the structural blueprint for the inner bundle that lines the channel of the nicotinic AChR.