The 3-D structure of the <i>β</i>-adrenergic receptor with a molecular weight of 55,000 daltons is available from crystallographic data. Within one of the seven transmembrane ion channel helices in the <i>β</i><sub>2</sub>-receptor, one loop of a helix ACADL has previously been proposed as the site that explains <i>β</i><sub>2</sub> activity (fights acute bronchitis) whereas ASADL in the <i>β</i><sub>1</sub>-receptor at the corresponding site explains <i>β</i><sub>1</sub>-activity (cardiac stimulation). The <i>α</i>-agonist responsible for this selective reaction is only 0.5% of the receptor molecular weight, and only 1.5% of the weight of the trans-membrane portion of the receptor. The understanding of the mechanism by which a small molecule on binding to a site on one single loop of a helix produces a specific agonist activity on an entire transmembrane ion channel is uncertain. A model of an <i>α</i>-helix is presented in which of pitch occurs at angles both smaller and larger than 180° n. Consequently, atomic coordinates in a peptide backbone <i>α</i>-helix match the data points of individual atom (and atom types) in the backbone. More precisely, eleven atoms in peptide backbone routinely equal one loop of a helix, instead of eleven amino acid residues equaling three loops of a helix; therefore, an <i>α</i>-helix can begin (or end) at any specific atom in a peptide backbone, not just at any specific amino acid. Wavefront Topology System and Finite Element Methods calculate this specific helical shape based only upon circumference, pitch, and phase. Only external forces which specifically affect circumference, pitch and/or phase (e.g. from agonist binding) can/will alter the shape of an <i>α</i>-helix
A 3-D electrostatic density map generated using the Wavefront Topology System and Finite Element Method clearly demonstrates the non-uniformity and periodicity present in even a single loop of an α-helix. The four dihedral angles (N-C*-C-N, C*-C-N-C*, and C-N-C*-C) fully define a helical shape independent of its length: the three dihedral angles, φ = −33.5˚, ω = 177.3˚, and Ψ = −69.4˚, generate the precise (and identical) redundancy in a one loop (or longer) α-helical shape (pitch = 1.59 Å/residue; r = 2.25 Å). Nevertheless the pattern of dihedral angles within an 11 and a 22-peptide backbone atom sequence cannot be distributed evenly because the stoichiometry in fraction of four atoms never divides evenly into 11 or 22 backbone atoms. Thus, three sequential sets of 11 backbone atoms in an α-helix will have a discretely different chemical formula and correspondingly different combinations of molecular forces depending upon the assigned starting atom in an 11-step sequence. We propose that the unit cell of one loop of an α-helix occurs in the peptide backbone sequence C-(N-C*-C)3-N which contains an odd number of C* plus even number of amide groups. A two-loop pattern (C*-C-N) 7-C* contains an even number of C* atoms plus an odd number of amide groups. Dividing the two-loop pattern into two equal lengths, one fraction will have an extra half amide (N-H) and the other fraction will have an extra half amide C=O, i.e., the stoichiometry of each half will be different. Also, since the length of N-C*-C-N, C*-C-N-C*, and C-N-C*-C are unequal, the summation of the number of each in any fraction of n loops of an α-helix in sequence will always have unequal length, depending upon the starting atom (N, C*, or C).
The research provides a computational approach for dynamic allocation of geometric coordinates within a 3DP2P network topology. Deployment of Internet and mobile applications within the network will be achieved with the utilization of a 3D-XML peer node descriptor (3DP2P-XML). The 3DP2P-XML file descriptor generates and deploys enterprise beans, web services, and mobile clients. Boundary conditions and statistical data determine the peer node distribution.The application will demonstrate the procedure for generating network coordinates. The coordinates correlate IP and URL addresses to a metric space. The technique uses a Riemann sum to estimate the number of nodes, volume, and surface boundaries of the 3D-P2P mesh network. The resulting algorithm creates a minimum 3D spanning tree with coordinate indexes. The multi-hop network is visualized as a 3D bouquet ofcomputer nodes.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.