A description of the semi-flexible polymer configuration inside the nanosphere and how it ejection

Abstract

The ejection of the polymer from the nanosphere has been of interest due to its connection with various fundamental sciences and applications, such as the gene ejection from its capsid in gene therapy or the ejection of the genetic substance of the virus from its capsule. To investigate the dynamics of the ejection of these confined chains, one can consider a semi-flexible polymer chain confined inside a nano-sphere. Sakaue described static configurations of a semi-flexible polymer chain with length L and width b confined in a nanosphere with diameter D in a wide range of persistence lengths l within five different regimes [1]. In our past studies, we presented a theory to describe the ejection dynamics of a semi-flexible polymer chain from the sphere. Accordingly, the ejection times of a semi-flexible polymer were calculated for the five regimes [2]. In the present study, a description of the configuration of the semi-flexible polymer inside the nano-sphere in each regime and how it ejects is given. In the first regime (I), which is called Fluctuating Semi-dilute regime, the polymer can move freely inside the nano-sphere and is divided into blobs that do not have significant overlap. In the second regime (II), or Mean-field Semi-dilute regime, the polymer becomes much more compact and can no longer move freely. In the third regime (III), which is Liquid Crystalline regime, with a further increase in the polymer density, the blobs size becomes comparable to the persistence length. Thus, the polymer configuration is like a spool, inside which there are smaller spools, which are formed to increase the entropy. In the fourth regime (IV) or Ideal Chain regime, the size of the sphere becomes very small, which is comparable to the size of the blob. In this case, asymmetry occurs. And finally, in the fifth regime (V), which is called Bending regime, the size of the nano-sphere becomes smaller than the persistence length, and the behavior of the polymer is affected by the bending energy and takes a spool-like shape. The polymer ejection is different in the five regimes. The ejection of the polymer in the regimes I, IV and V happens by a transition to a state where a small length of the polymer remains inside the sphere. This small length does not feel confined and is affected by the connection of the polymer to the wall of the sphere which reduces its available configurations. However, in the regimes II and III, the polymer experiences several regimes during the ejection. In the regime III, the polymer first passes to the regime II and then to the regime I or IV, and finally it continues to complete ejection due to the attachment force. This change of regime causes the polymer configuration to change over time, during ejection.