Advances in Colloid and Interface Science xxx (2016) xxx–xxx ARTICLE IN PRESS CIS-01613; No of Pages 13 Contents lists available at ScienceDirect Advances in Colloid and Interface Science journal homepage: www.elsevier.com/locate/cis Historical perspective Bundling in semiflexible polymers: A theoretical overview Panayotis Benetatos a , YongSeok Jho b, c , ∗ a Department of Physics, Kyungpook National University, 80 Daehakro, Bukgu, Daegu, 702-701, South Korea b Asia Pacific Center for Theoretical Physics, Pohang, Gyeongbuk, 790-784, South Korea c Department of Physics, Pohang University of Science and Technology, 790-784, South Korea ARTICLE INFO Available online xxxx Keywords: Bundles Semiflexible polymers Polyelectrolytes Order parameters Phase transitions ABSTRACT Supramolecular assemblies of polymers are key modules to sustain the structure of cells and their func- tion. The main elements of these assemblies are charged semiflexible polymers (polyelectrolytes) generally interacting via a long(er)-range repulsion and a short(er)-range attraction. The most common supramolecu- lar structure formed by these polymers is the bundle. In the present paper, we critically review some recent theoretical and computational advances on the problem of bundle formation, and point a few promising directions for future work. © 2016 Elsevier B.V. All rights reserved. Contents 1. Introduction ..................................................... 00 2. Theoretical models of bundle formation .......................................... 00 2.1. Permanent cross-links .............................................. 00 2.2. Reversible cross-links and pairwise interactions .................................... 00 2.3. Electrostatic interaction in polyelectrolytes ...................................... 00 2.3.1. Counterion screening in polyelectrolyte solution-generalized Manning condensation ................. 00 2.3.2. Condensed counterion mediated attraction .................................. 00 2.3.3. Charge renormalization .......................................... 00 2.3.4. Correlated counterions inside the condensation layer .............................. 00 3. System-specific explanations for the finite lateral size of bundles ................................ 00 3.1. Filament helicity ................................................. 00 3.2. Quenched defects ................................................ 00 3.3. Charge fluctuations ............................................... 00 4. Simulations for finite size bundle formation ........................................ 00 5. Conclusions – discussion ................................................ 00 Acknowledgments ...................................................... 00 References ......................................................... 00 * Corresponding author. E-mail address: ysjho@apctp.org (Y. Jho). 1. Introduction Many important biomolecules, including the structural elements of the cytoskeleton (F-actin, microtubules, and intermediate fila- ments), are semiflexible polymers, that is their physical behavior is dominated by their resistance to bending which gives rise to a finite- persistence length of their backbone orientation. These semiflexible polymers form polymorphous supramolecular self-assembled struc- tures resulting from the interplay of energetic and entropic contribu- tions. Prominent among them are the bundles. These are assemblies of relatively closely packed, parallel aligned semiflexible filaments. It has been shown that their conformational and mechanical behav- ior is fundamentally different from that of a single filament [1]. As such, they play an important role in various biological functions, optimizing adaptability and mechanical performance. They may also prove useful in biomimetic applications [2]. Theoretically under- standing their properties and formation is a challenging task because it combines the complexity of the single filament with that of the many-body problem. Another subtlety which complicates the http://dx.doi.org/10.1016/j.cis.2016.01.001 0001-8686/© 2016 Elsevier B.V. All rights reserved. Please cite this article as: P. Benetatos, Y. Jho, Bundling in semiflexible polymers: A theoretical overview, Advances in Colloid and Interface Science (2016), http://dx.doi.org/10.1016/j.cis.2016.01.001