Unitarized VenezianoππScattering Amplitude Consistent with Positivity and Crossing-Symmetry Constraints

1971 ◽  
Vol 4 (10) ◽  
pp. 3005-3011 ◽  
Author(s):  
Kyungsik Kang ◽  
M. Lacombe ◽  
R. Vinh Mau
Keyword(s):  
Crossing Symmetry ◽  
Symmetry Constraints

scholarly journals Crossing-symmetry constraints on partial-wave amplitudes and their physical content

1969 ◽  
Vol 64 (3) ◽  
pp. 585-602 ◽  
Author(s):  
J. L. Basdevant ◽  
G. Cohen-Tannoudji ◽  
A. Morel
Keyword(s):  
Partial Wave ◽  
Physical Content ◽  
Crossing Symmetry ◽  
Symmetry Constraints

scholarly journals Chiral symmetry constraints on resonant amplitudes

2018 ◽  
Vol 778 ◽  
pp. 43-47 ◽  
Author(s):  
Peter C. Bruns ◽  
Maxim Mai
Keyword(s):  
Chiral Symmetry ◽  
Symmetry Constraints

Duality and crossing symmetry of the narrow resonance model

1970 ◽  
Vol 48 (12) ◽  
pp. 1426-1429 ◽  
Author(s):  
K. Nakazawa
Keyword(s):  
Finite Energy ◽  
Complex Variables ◽  
Narrow Resonance ◽  
Veneziano Amplitude ◽  
Resonance Model ◽  
Sum Rule ◽  
Crossing Symmetry ◽  
The One

In the narrow resonance approximation, conditions of duality and crossing symmetry are derived using the finite energy sum rule for an amplitude which is completely determined as a function of two complex variables by its meromorphic part in one of these variables. As an example, the one term Veneziano amplitude is discussed.

scholarly journals Chirality-induced spin polarization places symmetry constraints on biomolecular interactions

2017 ◽  
Vol 114 (10) ◽  
pp. 2474-2478 ◽  
Author(s):  
Anup Kumar ◽  
Eyal Capua ◽  
Manoj K. Kesharwani ◽  
Jan M. L. Martin ◽  
Einat Sitbon ◽  
...  
Keyword(s):  
Spin Polarization ◽  
Noncovalent Interactions ◽  
Electronic Charge ◽  
Biological Processes ◽  
Interaction Energies ◽  
Hall Voltage ◽  
Charge Redistribution ◽  
Chiral Molecules ◽  
Quantum Chemistry Calculations ◽  
Symmetry Constraints

Noncovalent interactions between molecules are key for many biological processes. Necessarily, when molecules interact, the electronic charge in each of them is redistributed. Here, we show experimentally that, in chiral molecules, charge redistribution is accompanied by spin polarization. We describe how this spin polarization adds an enantioselective term to the forces, so that homochiral interaction energies differ from heterochiral ones. The spin polarization was measured by using a modified Hall effect device. An electric field that is applied along the molecules causes charge redistribution, and for chiral molecules, a Hall voltage is measured that indicates the spin polarization. Based on this observation, we conjecture that the spin polarization enforces symmetry constraints on the biorecognition process between two chiral molecules, and we describe how these constraints can lead to selectivity in the interaction between enantiomers based on their handedness. Model quantum chemistry calculations that rigorously enforce these constraints show that the interaction energy for methyl groups on homochiral molecules differs significantly from that found for heterochiral molecules at van der Waals contact and shorter (i.e., ∼0.5 kcal/mol at 0.26 nm).

scholarly journals Flaviviruses have imperfect icosahedral symmetry

2018 ◽  
Vol 115 (45) ◽  
pp. 11608-11612 ◽  
Author(s):  
Matthew D. Therkelsen ◽  
Thomas Klose ◽  
Frank Vago ◽  
Wen Jiang ◽  
Michael G. Rossmann ◽  
...  
Keyword(s):  
Lipid Membrane ◽  
Viral Assembly ◽  
Icosahedral Symmetry ◽  
Proximal Pole ◽  
The Core ◽  
Cryo Electron Microscopy ◽  
Symmetry Constraints ◽  
Conformational Rearrangements ◽  
Mature Virus ◽  
Concentric Organization

Flaviviruses assemble initially in an immature, noninfectious state and undergo extensive conformational rearrangements to generate mature virus. Previous cryo-electron microscopy (cryo-EM) structural studies of flaviviruses assumed icosahedral symmetry and showed the concentric organization of the external glycoprotein shell, the lipid membrane, and the internal nucleocapsid core. We show here that when icosahedral symmetry constraints were excluded in calculating the cryo-EM reconstruction of an immature flavivirus, the nucleocapsid core was positioned asymmetrically with respect to the glycoprotein shell. The core was positioned closer to the lipid membrane at the proximal pole, and at the distal pole, the outer glycoprotein spikes and inner membrane leaflet were either perturbed or missing. In contrast, in the asymmetric reconstruction of a mature flavivirus, the core was positioned concentric with the glycoprotein shell. The deviations from icosahedral symmetry demonstrated that the core and glycoproteins have varied interactions, which likely promotes viral assembly and budding.

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