On the existence of atomic models

1993 ◽  
Vol 58 (4) ◽  
pp. 1189-1194 ◽  
Author(s):  
M. C. Laskowski ◽  
S. Shelah
Keyword(s):  
Atomic Model ◽  
Atomic Models ◽  
Countable Theory

AbstractWe give an example of a countable theory T such that for every cardinal λ ≥ ℵ2 there is a fully indiscernible set A of power λ such that the principal types are dense over A, yet there is no atomic model of T over A. In particular, T(A) is a theory of size λ where the principal types are dense, yet T(A) has no atomic model.

scholarly journals THE NUMBER OF ATOMIC MODELS OF UNCOUNTABLE THEORIES

2018 ◽  
Vol 83 (1) ◽  
pp. 84-102
Author(s):  
DOUGLAS ULRICH
Keyword(s):  
Atomic Model ◽  
Complete Theory ◽  
Atomic Models ◽  
Image Position

AbstractWe show there exists a complete theory in a language of size continuum possessing a unique atomic model which is not constructible. We also show it is consistent with $ZFC + {\aleph _1} < {2^{{\aleph _0}}}$ that there is a complete theory in a language of size ${\aleph _1}$ possessing a unique atomic model which is not constructible. Finally we show it is consistent with $ZFC + {\aleph _1} < {2^{{\aleph _0}}}$ that for every complete theory T in a language of size ${\aleph _1}$, if T has uncountable atomic models but no constructible models, then T has ${2^{{\aleph _1}}}$ atomic models of size ${\aleph _1}$.

CONSTRUCTING MANY ATOMIC MODELS IN ℵ1

2016 ◽  
Vol 81 (3) ◽  
pp. 1142-1162 ◽  
Author(s):  
JOHN T. BALDWIN ◽  
MICHAEL C. LASKOWSKI ◽  
SAHARON SHELAH
Keyword(s):  
Order Theory ◽  
Atomic Model ◽  
First Order ◽  
Atomic Models ◽  
First Order Theory ◽  
Image Position

AbstractWe introduce the notion of pseudoalgebraicity to study atomic models of first order theories (equivalently models of a complete sentence of ${L_{{\omega _1},\omega }}$). Theorem: Let T be any complete first-order theory in a countable language with an atomic model. If the pseudominimal types are not dense, then there are 2ℵ0 pairwise nonisomorphic atomic models of T, each of size ℵ1.

scholarly journals Building a pseudo-atomic model of the anaphase-promoting complex

2013 ◽  
Vol 69 (11) ◽  
pp. 2236-2243 ◽  
Author(s):  
Kiran Kulkarni ◽  
Ziguo Zhang ◽  
Leifu Chang ◽  
Jing Yang ◽  
Paula C. A. da Fonseca ◽  
...  
Keyword(s):  
Cell Cycle ◽  
Homology Modelling ◽  
Active Form ◽  
Protein Crystallography ◽  
Hybrid Approach ◽  
Atomic Model ◽  
Anaphase Promoting Complex ◽  
Atomic Models ◽  
Entire Complex ◽  
Cell Cycle Regulatory Proteins

The anaphase-promoting complex (APC/C) is a large E3 ubiquitin ligase that regulates progression through specific stages of the cell cycle by coordinating the ubiquitin-dependent degradation of cell-cycle regulatory proteins. Depending on the species, the active form of the APC/C consists of 14–15 different proteins that assemble into a 20-subunit complex with a mass of approximately 1.3 MDa. A hybrid approach of single-particle electron microscopy and protein crystallography of individual APC/C subunits has been applied to generate pseudo-atomic models of various functional states of the complex. Three approaches for assigning regions of the EM-derived APC/C density map to specific APC/C subunits are described. This information was used to dock atomic models of APC/C subunits, determined either by protein crystallography or homology modelling, to specific regions of the APC/C EM map, allowing the generation of a pseudo-atomic model corresponding to 80% of the entire complex.

scholarly journals Near-atomic model of microtubule-tau interactions

Science ◽  
2018 ◽  
Vol 360 (6394) ◽  
pp. 1242-1246 ◽  
Author(s):  
Elizabeth H. Kellogg ◽  
Nisreen M. A. Hejab ◽  
Simon Poepsel ◽  
Kenneth H. Downing ◽  
Frank DiMaio ◽  
...  
Keyword(s):  
Electron Microscopy ◽  
Alzheimer’S Disease ◽  
Alzheimer's Disease ◽  
Atomic Model ◽  
Developmentally Regulated ◽  
Computational Approaches ◽  
Atomic Models ◽  
Cryo Electron Microscopy ◽  
Tubulin Binding ◽  
Axonal Protein

Tau is a developmentally regulated axonal protein that stabilizes and bundles microtubules (MTs). Its hyperphosphorylation is thought to cause detachment from MTs and subsequent aggregation into fibrils implicated in Alzheimer’s disease. It is unclear which tau residues are crucial for tau-MT interactions, where tau binds on MTs, and how it stabilizes them. We used cryo–electron microscopy to visualize different tau constructs on MTs and computational approaches to generate atomic models of tau-tubulin interactions. The conserved tubulin-binding repeats within tau adopt similar extended structures along the crest of the protofilament, stabilizing the interface between tubulin dimers. Our structures explain the effect of phosphorylation on MT affinity and lead to a model of tau repeats binding in tandem along protofilaments, tethering together tubulin dimers and stabilizing polymerization interfaces.

An Atomic Model of Cellulose Network in Wood Cell Wall

2008 ◽  
Author(s):  
Ying Wang ◽  
Youping Chen
Keyword(s):  
Hydrogen Bond ◽  
Cell Wall ◽  
Molecular Mechanisms ◽  
Mechanical Performance ◽  
Atomic Model ◽  
Crystalline Cellulose ◽  
First Principle Calculation ◽  
Atomic Models ◽  
Water Solvent ◽  
Assembly Method

Wood is composed of parallel columns of long hollow cells which are made up of layered composite of semi-crystalline cellulose fibrils embedded in an amorphous matrix of hemicellulose and lignin. The extraordinary mechanical performance of wood is believed to result from a molecular mechanism operated through hydrogen bond connection. However, the molecular interactions, the assembly method of cell-wall components, as well as the molecular mechanisms responsible for the deformation of wood, are not well understood yet. Progress in studying the superior mechanical properties of wood cell is severely hindered because of this fact. To overcome this barrier, the foremost step is to build up an atomic model of the native cellulose fibril network, which is the dominant polysaccharide in wood cell walls. Then, in this work, we proposed the atomic models to study the cellulose network which includes a single cellulose microfibril (MF), and a thin film which is built up by first secondary layers (S1) and second secondary layers (S2) composed of cellulose MF with periodic boundary conditions. Additionally, we investigated the length effect of the microfibril and compared the effect of explicit water solvent environment with the vacuum environment. Moreover, the spatial arrangements of these atomic models have been determined by molecular mechanics simulation (energy minimization). The hydrogen bond length of the crystalline part of the inner cellulose was evaluated using first principle calculation.

Prime and atomic models

1978 ◽  
Vol 43 (3) ◽  
pp. 385-393 ◽  
Author(s):  
Julia F. Knight
Keyword(s):  
Model Theory ◽  
Existence Results ◽  
Atomic Model ◽  
Elementary Embedding ◽  
Prime Model ◽  
Atomic Models ◽  
Large Model

This paper gives some simple existence results on prime and atomic models over sets. It also contains an example in which there is no prime model over a certain set even though there is an atomic model over the set. The existence results are “local” in that they deal with just one set rather than all sets contained in models of some theory. For contrast, see the “global” results in [6] or [7, p. 200].Throughout the paper, L is a countable language, and T is a complete L-theory with infinite models. There is a “large” model of T that contains the set X and any other sets and models to be used in a particular construction of a prime or atomic model over X.A model is said to be prime over X if and every elementary monomorphism on X can be extended to an elementary embedding on all of . This notion is used in a variety of ways in model theory. It aids in distinguishing between models that are not isomorphic, as in Vaught [10]. It also aids in showing that certain models are isomorphic, as in Baldwin and Lachlan [1].

scholarly journals Refined atomic model of glutamine synthetase at 3.5 Å resolution

1989 ◽  
Vol 264 (30) ◽  
pp. 17681-17690
Author(s):  
M M Yamashita ◽  
R J Almassy ◽  
C A Janson ◽  
D Cascio ◽  
D Eisenberg
Keyword(s):  
Glutamine Synthetase ◽  
Atomic Model

scholarly journals 2P013 A new approach to build 3D atomic model from single electron microsope image(01A. Protein: Structure,Poster)

2013 ◽  
Vol 53 (supplement1-2) ◽  
pp. S161
Author(s):  
Atsushi Matsumoto ◽  
Junichi Takagi ◽  
Kenji Iwasaki
Keyword(s):  
Protein Structure ◽  
Single Electron ◽  
Atomic Model ◽  
New Approach
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