Virus coat proteins efficiently encapsulate their native RNAs but are also able to encapsulate foreign RNAs, synthetic polyelectrolytes and functionalised nanoparticles. The question arises what physical principles dictate the efficiency of encapsulation. Known is that the genome size M scales linearly with the number of positive charges Q on the RNA binding domains: M ≈ 1.6 × Q, and that M also increases with the radius R (nm) of the capsid: M ≈ 0.65 × R2.6. Recently, it was found that viral RNAs are topologically more compact and have a higher degree of branching in free solution than random or non-viral RNAs, suggesting that branching could enhance the packing efficiency. We propose a simple Flory model that shows that optimal loading increases indeed linearly with Q, but that the prefactor is larger for more strongly branched polymers. So, indeed, branched objects are packaged more efficiently. We also find that solvent quality has a large impact on packaging efficiently and may offset the advantages of stronger branching.
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