Journal of Biological Physics

, Volume 44, Issue 2, pp 133–145 | Cite as

Confining annealed branched polymers inside spherical capsids

  • Alexander Y. Grosberg
  • Robijn Bruinsma


The Lifshitz equation for the confinement of a linear polymer in a spherical cavity of radius R has the form of the Schrödinger equation for a quantum particle trapped in a potential well with flat bottom and infinite walls at radius R. We show that the Lifshitz equation of a confined annealed branched polymer has the form of the Schrödinger equation for a quantum harmonic oscillator. The resulting confinement energy has a 1/R4 dependence on the confinement radius R, in contrast to the case of confined linear polymers, which have a 1/R2 dependence. We discuss the application of this result to the problem of the confinement of single-stranded RNA molecules inside spherical capsids.


Branched polymers Confinement Viral RNA 



RB would like to acknowledge support from the National Science Foundation under DMR Grant 1309423. The work of AYG was supported partially by the MRSEC Program of the National Science Foundation under Award Number DMR-1420073. RB and AYG thank the Aspen Center for Physics where part of this work was done with the support of the National Science Foundation under Grant No. PHY-1066293.

Compliance with Ethical Standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Authors and Affiliations

  1. 1.Department of Physics and Center for Soft Matter ResearchNew York UniversityNew YorkUSA
  2. 2.Department of Physics and AstronomyUniversity of CaliforniaLos AngelesUSA
  3. 3.Department of Chemistry and BiochemistryUniversity of CaliforniaLos AngelesUSA

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