Bound State Asymptotics for Elliptic Operators with Strongly Degenerated Symbols

2002 ◽  
pp. 233-245 ◽  
Author(s):  
Ari Laptev ◽  
Oleg Safronov ◽  
Timo Weidl
Keyword(s):  
Bound State ◽  
Elliptic Operators

CRYO-Electron Microscopy of the Acto-Myosin-ATP Complex

1990 ◽  
Vol 48 (1) ◽  
pp. 248-249
Author(s):  
John Trinickt ◽  
Howard White
Keyword(s):  
Electron Microscopy ◽  
Atp Hydrolysis ◽  
Myosin Head ◽  
Bound State ◽  
Cross Linking ◽  
Weakly Bound ◽  
Cryo Electron Microscopy ◽  
Myosin Subfragment 1 ◽  
Attached State ◽  
High Fraction

The primary force of muscle contraction is thought to involve a change in the myosin head whilst attached to actin, the energy coming from ATP hydrolysis. This change in attached state could either be a conformational change in the head or an alteration in the binding angle made with actin. A considerable amount is known about one bound state, the so-called strongly attached state, which occurs in the presence of ADP or in the absence of nucleotide. In this state, which probably corresponds to the last attached state of the force-producing cycle, the angle between the long axis myosin head and the actin filament is roughly 45°. Details of other attached states before and during power production have been difficult to obtain because, even at very high protein concentration, the complex is almost completely dissociated by ATP. Electron micrographs of the complex in the presence of ATP have therefore been obtained only after chemically cross-linking myosin subfragment-1 (S1) to actin filaments to prevent dissociation. But it is unclear then whether the variability in attachment angle observed is due merely to the cross-link acting as a hinge.We have recently found low ionic-strength conditions under which, without resorting to cross-linking, a high fraction of S1 is bound to actin during steady state ATP hydrolysis. The structure of this complex is being studied by cryo-electron microscopy of hydrated specimens. Most advantages of frozen specimens over ambient temperature methods such as negative staining have already been documented. These include improved preservation and fixation rates and the ability to observe protein directly rather than a surrounding stain envelope. In the present experiments, hydrated specimens have the additional benefit that it is feasible to use protein concentrations roughly two orders of magnitude higher than in conventional specimens, thereby reducing dissociation of weakly bound complexes.

A computer-assisted proof method of the invertibility to elliptic operators

2014 ◽  
Vol 1 ◽  
pp. 816-819
Author(s):  
Akitoshi Takayasu ◽  
Shin'ichi Oishi
Keyword(s):  
Elliptic Operators ◽  
Computer Assisted ◽  
Computer Assisted Proof

Degenerate Diffusion Operators Arising in Population Biology (AM-185)

2017 ◽  
Author(s):  
Charles L. Epstein ◽  
Rafe Mazzeo
Keyword(s):  
Adjoint Operator ◽  
Integral Kernel ◽  
Mathematical Finance ◽  
Elliptic Operators ◽  
Complete Analysis ◽  
Time Behavior ◽  
Degenerate Elliptic Operators ◽  
Regularity Properties ◽  
Degenerate Elliptic ◽  
Mathematical Foundations

This book provides the mathematical foundations for the analysis of a class of degenerate elliptic operators defined on manifolds with corners, which arise in a variety of applications such as population genetics, mathematical finance, and economics. The results discussed in this book prove the uniqueness of the solution to the martingale problem and therefore the existence of the associated Markov process. The book uses an “integral kernel method” to develop mathematical foundations for the study of such degenerate elliptic operators and the stochastic processes they define. The precise nature of the degeneracies of the principal symbol for these operators leads to solutions of the parabolic and elliptic problems that display novel regularity properties. Dually, the adjoint operator allows for rather dramatic singularities, such as measures supported on high codimensional strata of the boundary. The book establishes the uniqueness, existence, and sharp regularity properties for solutions to the homogeneous and inhomogeneous heat equations, as well as a complete analysis of the resolvent operator acting on Hölder spaces. It shows that the semigroups defined by these operators have holomorphic extensions to the right half plane. The book also demonstrates precise asymptotic results for the long-time behavior of solutions to both the forward and backward Kolmogorov equations.

Binding Mechanism and Structural Insights into the Identified Protein Target of Covid-19 with In-Vitro Effective Drug Ivermectin

2020 ◽  
Author(s):  
Parth Sarthi Sen Gupta ◽  
Satyaranjan Biswal ◽  
Saroj Kumar Panda ◽  
Abhik Kumar Ray ◽  
Malay Kumar Rana
Keyword(s):  
Ternary Complex ◽  
Bound State ◽  
Molecular Target ◽  
Cooperative Interaction ◽  
Effective Drug ◽  
Rna Dependent Rna Polymerase ◽  
Protein Target ◽  
Ternary Complex Formation ◽  
Structural Insights

<p>While an FDA approved drug Ivermectin was reported to dramatically reduce the cell line of SARS-CoV-2 by ~5000 folds within 48 hours, the precise mechanism of action and the COVID-19 molecular target involved in interaction with this in-vitro effective drug are unknown yet. Among 12 different COVID-19 targets studied here, the RNA dependent RNA polymerase (RdRp) with RNA and Helicase NCB site show the strongest affinity to Ivermectin amounting -10.4 kcal/mol and -9.6 kcal/mol, respectively. Molecular dynamics of corresponding protein-drug complexes reveals that the drug bound state of RdRp with RNA has better structural stability than the Helicase NCB site, with MM/PBSA free energy of -135.2 kJ/mol, almost twice that of Helicase (-76.6 kJ/mol). The selectivity of Ivermectin to RdRp is triggered by a cooperative interaction of RNA-RdRp by ternary complex formation. Identification of the target and its interaction profile with Ivermectin can lead to more powerful drug designs for COVID-19 and experimental exploration. </p>

Functional characterization and structural modelling of peptidoglycan degrading β-N-acetyl-glucosaminidase from a dental isolate of Serratia marcescens

2020 ◽  
Vol 23 ◽  
Author(s):  
Aditi Rathee ◽  
Anil Panwar ◽  
Seema Kumari ◽  
Sanjay Chhibber ◽  
Ashok Kumar
Keyword(s):  
Functional Characterization ◽  
Major Change ◽  
Crystal Form ◽  
Bound State ◽  
Dynamics Simulation ◽  
Gram Positive ◽  
Structural Cell ◽  
Stability Structure ◽  
Arginine Residues ◽  
The Stability

Introduction:: Enzymatic degradation of peptidoglycan, a structural cell wall component of Gram-positive bacteria, has attracted considerable attention being a specific target for many known antibiotics. Methods:: Peptidoglycan hydrolases are involved in bacterial lysis through peptidoglycan degradation. β-N-acetylglucosaminidase, a peptidoglycan hydrolase, acts on O-glycosidic bonds formed by N-acetylglucosamine and N-acetyl muramic acid residues of peptidoglycan. Aim of present study was to study the action of β-N-acetylglucosaminidase, on methicillin- resistant Staphylococcus aureus (MRSA) and other Gram-negative bacteria. Results:: We investigated its dynamic behaviour using molecular dynamics simulation and observed that serine and alanine residues are involved in catalytic reaction in addition to aspartic acid, histidine, lysine and arginine residues. When simulated in its bound state, the RMSD values were found lesser than crystal form in the time stamp of 1000 picoseconds revealing its stability. Structure remained stably folded over 1000 picoseconds without undergoing any major change further confirming the stability of complex. Conclusion:: It can be concluded that enzymes belonging to this category can serve as a tool in eradicating Gram-positive pathogens and associated infections.

Lower Bound for ppK– Quasi-Bound State Energy

2020 ◽  
Vol 51 (5) ◽  
pp. 979-987 ◽  
Author(s):  
I. Filikhin ◽  
B. Vlahovic
Keyword(s):  
Lower Bound ◽  
State Energy ◽  
Bound State ◽  
Bound State Energy ◽  
Quasi Bound State

scholarly journals An event excess observed in the deeply bound region of the 12C (K−, p) missing-mass spectrum

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Yudai Ichikawa ◽  
Junko Yamagata-Sekihara ◽  
Jung Keun Ahn ◽  
Yuya Akazawa ◽  
Kanae Aoki ◽  
...  
Keyword(s):  
Mass Spectrum ◽  
Binding Energy ◽  
Decay Channel ◽  
Peak Shift ◽  
Bound State ◽  
Elastic Peak ◽  
Missing Mass ◽  
Decay Modes ◽  
Kaon Momentum ◽  
First Time

Abstract We have measured, for the first time, the inclusive missing-mass spectrum of the $^{12}$C$(K^-, p)$ reaction at an incident kaon momentum of 1.8 GeV/$c$ at the J-PARC K1.8 beamline. We observed a prominent quasi-elastic peak ($K^-p \rightarrow K^-p$) in this spectrum. In the quasi-elastic peak region, the effect of secondary interaction is apparently observed as a peak shift, and the peak exhibits a tail in the bound region. We compared the spectrum with a theoretical calculation based on the Green’s function method by assuming different values of the parameters for the $\bar{K}$–nucleus optical potential. We found that the spectrum shape in the binding-energy region $-300 \, \text{MeV} &lt; B_{K} &lt; 40$ MeV is best reproduced with the potential depths $V_0 = -80$ MeV (real part) and $W_0 = -40$ MeV (imaginary part). On the other hand, we observed a significant event excess in the deeply bound region around $B_{K} \sim 100$ MeV, where the major decay channel of $K^- NN \to \pi\Sigma N$ is energetically closed, and the non-mesonic decay modes ($K^- NN \to \Lambda N$ and $\Sigma N$) should mainly contribute. The enhancement is fitted well by a Breit–Wigner function with a kaon-binding energy of 90 MeV and width 100 MeV. A possible interpretation is a deeply bound state of a $Y^{*}$-nucleus system.

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