The collapse transition in three‐dimensional linear and ring polymers

1986 ◽  
Vol 84 (1) ◽  
pp. 447-448 ◽  
Author(s):  
Marvin Bishop ◽  
J. P. J. Michels
Keyword(s):  
Three Dimensional ◽  
Collapse Transition ◽  
Ring Polymers

Scaling in three‐dimensional linear and ring polymers

1986 ◽  
Vol 84 (1) ◽  
pp. 444-446 ◽  
Author(s):  
Marvin Bishop ◽  
J. P. J. Michels
Keyword(s):  
Three Dimensional ◽  
Ring Polymers

scholarly journals Resolving critical degrees of entanglement in Olympic ring systems

2016 ◽  
Vol 25 (14) ◽  
pp. 1650081 ◽  
Author(s):  
Spencer Igram ◽  
Kenneth C. Millett ◽  
Eleni Panagiotou
Keyword(s):  
Large Scale ◽  
Periodic Boundary ◽  
Three Dimensional ◽  
Small Ring ◽  
Kinetoplast Dna ◽  
Circular Dna ◽  
Linking Number ◽  
Ring Polymers ◽  
Condition Systems ◽  
Insight Into

Olympic systems are collections of small ring polymers whose aggregate properties are largely characterized by the extent (or absence) of topological linking in contrast with the topological entanglement arising from physical movement constraints associated with excluded volume contacts or arising from chemical bonds. First, discussed by de Gennes, they have been of interest ever since due to their particular properties and their occurrence in natural organisms, for example, as intermediates in the replication of circular DNA in the mitochondria of malignant cells or in the kinetoplast DNA networks of trypanosomes. Here, we study systems that have an intrinsic one, two, or three-dimensional character and consist of large collections of ring polymers modeled using periodic boundary conditions. We identify and discuss the evolution of the dimensional character of the large scale topological linking as a function of density. We identify the critical densities at which infinite linked subsystems, the onset of percolation, arise in the periodic boundary condition systems. These provide insight into the nature of entanglement occurring in such course grained models. This entanglement is measured using Gauss linking number, a measure well adapted to such models. We show that, with increasing density, the topological entanglement of these systems increases in complexity, dimension, and probability.

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

Conformation of Ribosomes from Escherichia Coli

1974 ◽  
Vol 32 ◽  
pp. 210-211
Author(s):  
M. Boublik ◽  
W. Hellmann ◽  
F. Jenkins
Keyword(s):  
Binding Sites ◽  
Ribosomal Proteins ◽  
Fluorescent Dyes ◽  
Protein Biosynthesis ◽  
Three Dimensional ◽  
Spatial Arrangement ◽  
Dimensional Structure ◽  
Complete Understanding ◽  
And Function

The present knowledge of the three-dimensional structure of ribosomes is far too limited to enable a complete understanding of the various roles which ribosomes play in protein biosynthesis. The spatial arrangement of proteins and ribonuclec acids in ribosomes can be analysed in many ways. Determination of binding sites for individual proteins on ribonuclec acid and locations of the mutual positions of proteins on the ribosome using labeling with fluorescent dyes, cross-linking reagents, neutron-diffraction or antibodies against ribosomal proteins seem to be most successful approaches. Structure and function of ribosomes can be correlated be depleting the complete ribosomes of some proteins to the functionally inactive core and by subsequent partial reconstitution in order to regain active ribosomal particles.

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