It is nontrivial whether the average size of a ring polymer should become smaller or larger under a topological constraint. Making use of some knot invariants, we numerically evaluate the mean-square radius of gyration for ring polymers having a fixed knot type, where the ring polymers are given by self-avoiding polygons consisting of freely jointed hard cylinders. We obtain plots of the gyrati...

Cationic latex microgel particles were studied in dilute aqueous suspensions of varying ionic strengths. Static light scattering indicates a Gaussian distribution of polymer density over the length scales probed. The measured radius of gyration is up to 50% larger than that obtained from TEM measurements of dried precursor particles. This radius of gyration is observed to be weak function of io...

It is traced out a parallel between the cosmological constant problem and the polymer physics. The time evolution of the universe world line is compared with the growing of a polymer chain. An equivalent Flory free energy and a modification of it are used as a means to evaluate two versions for the “radius of gyration” of the universe. It is proposed a link between this radius of gyration and t...

The radius of gyration is a fundamental structural parameter that is particularly useful for describing polymers. It has been known since Flory's seminal work in the mid-20th century that polymers show a power-law dependence, where the radius of gyration is proportional to the number of residues raised to a power. The power-law exponent has been measured experimentally for denatured proteins an...

The first algorithm for sampling the space of thick equilateral knots, as a function of thickness, will be described. This algorithm is based on previous algorithms of applying random reflections. To prove the existence of the algorithm, we describe a method for turning any knot into the regular planar polygon using only thickness non-decreasing moves. This approach ensures that the algorithm h...

Changes in volume play a significant but often under-emphasized role in governing the stability of proteins in the cell.1!6 When proteins fold from extended unfolded state to a compact or folded native state, there is a concomitant decrease in the characteristic volume occupied by the protein as probed by osmolyte particles, and thus an increase in the volume available to osmolytes or crowding ...

We determine the density expansion of the radius of gyration, of the hydrodynamic radius, and of the end-to-end distance for a monodisperse polymer solution in good-solvent conditions. We consider the scaling limit (large degree of polymerization), including the leading scaling corrections. Using the expected large-concentration behavior, we extrapolate these low-density expansions outside the ...

Using small angle x-ray scattering from solutions of yeast phosphoglycerate kinase, we have measured the radius of gyration of the enzyme both in the presence and in the abscence of ligands. We find that the radius of gyration decreases by 1.09 +/- 0.34 A upon binding both substrates MgATP and 3-phosphoglycerate to form the ternary complex. Smaller decreases, at the limit of the precision of th...