**Universality in conformations and transverse fluctuations of a semi-
flexible polymer in a crowded environment**

J Bair and S Seth and A Bhattacharya, JOURNAL OF CHEMICAL PHYSICS, 158, 204902 (2023).

DOI: 10.1063/5.0143814

We study the universal aspects of polymer conformations and transverse
fluctuations for a single swollen chain characterized by a contour
length L and a persistence length lp in two dimensions (2D) and three
dimensions (3D) in the bulk, as well as in the presence of excluded
volume (EV) particles of different sizes occupying different area/volume
fractions. In the absence of the EV particles, we extend the previously
established universal scaling relations in 2D **Huang et al., J. Chem.
140, 214902 (2014)** to include 3D and demonstrate that the scaled endto-
end distance < R-N(2) >/(2Ll(p)) and the scaled transverse fluctuation
root < l(perpendicular to)(2)>/L as a function of L/l(p) collapse onto
the same master curve, where.R2 N. and.l2 -. are the mean-square end-to-
end distance and transverse fluctuations. However, unlike in 2D, where
the Gaussian regime is absent due to the extreme dominance of the EV
interaction, we find that the Gaussian regime is present, albeit very
narrow in 3D. The scaled transverse fluctuation in the limit L/l p << 1
is independent of the physical dimension and scales as root <
l(perpendicular to)(2)>/L similar to (L/l(p))(nu-1), where zeta = 1.5 is
the roughening exponent. For L/ lp >> 1, the scaled fluctuation scales
as root < l(perpendicular to)(2)>/L similar to (L/l(p))(nu-1), where. is
the Flory exponent for the corresponding spatial dimension (nu(2D) =
0.75 and nu(3D) = 0.58). When EV particles of different sizes for
different area or volume fractions are added into 2D and 3D systems, our
results indicate that the crowding density either does not or does only
weakly affect the universal scaling relations. We discuss the
implications of these results in living matter by showing the
experimental result for a dsDNA on the master plot.

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