Polymer Translocation and Packaging: Role of Flickering Pores, Time-Dependent Driving, and Capsid Shapes

Abstract

The translocation of biopolymers across nanopores is an ubiquitous process in bi ology. Examples range from the transport of RNA through a nuclear membrane pore complex, viral ejection of DNA into host cells, and protein transport through membrane channels. One of the principal reasons for studying polymer translocation is to create effective biosequencing methods, such as the detection of a DNA sequence. The poly mer is field-driven across the pore, and the translocating polymer segment is mapped from the ionic current perturbations. In order to achieve precise control in the detection process, we need to control the polymer-pore interactions and pore geometry. Within this framework, theoretical models have yielded significant insights into how polymer properties, pore characteristics, interactions between polymers, and external drive af fect translocation dynamics. Polymer translocation also plays a key role in gene therapy and controlled drug delivery. There are various scenarios in biological nanopores, such as the twin pore complex in the inner membrane of mitochondria and the nuclear pore complex (NPC), where the pore size can change during protein translocation. In the realm of synthetic nanopore design, elastomeric nanochannel devices have been utilized to adjust the width of the channels by applying mechanical stresses. To replicate the behavior of these systems, as in our first study, we investigated the driven translocation of a semiflexible polymer through an attractive extended pore with a periodically oscillating width. Theoretical studies of polymer translocation through pores with dynamically changing widths have shown that the translocation can be significantly improved compared to that of a static pore. Comparing the average translocation time for an oscillating pore (τosc) with that of a static pore (τstat), we showed that semiflexible polymers translocate more effi ciently through oscillating pores than through static ones. However, the gain defined as η = τstat/τosc, is highly influenced by the stiffness of the polymer and the attractive properties of the pores. We explored the interplay between the pore-polymer interac tion (parameterized by ϵ) and the stiffness of the polymer (parameterized by κ) on the translocation efficiency. We observed a gain reversal in translocation efficiency. For a lower strength of the pore-polymer interaction, the gain decreases with increasing κ at lower values of κ and saturates at higher values. In contrast, at a higher strength of the pore-polymer interaction, the gain increases with increasing κ at higher values of κ 9 and saturates at lower values. This intriguing reversal, which occurs independently of the dimensionality of the problem, is explored in the parameter space of driving force, chain stiffness, and pore stickiness. In various in vivo situations, translocation involves time-varying processes, such as f luctuations in membrane potential and ionic strengths, and variations in ATP concen trations in molecular motor-assisted translocation events. In such cases, theoretical modeling proceeds by assuming a time-varying driving force. This situation is similar to choosing a fluctuating pore width and shows resonant behavior at an optimal driving frequency. Although theoretical studies have explored the role of pore-polymer inter actions in the translocation of biopolymers under time-dependent driving forces, such studies have considered pores where pore-polymer interactions vary uniformly across them. However, varying pore-polymer interactions along the length of the channel have shown dramatic variations in the translocation time distributions under constant external drive. The translocation time of a polymer through a channel with alternate charged and uncharged sections has been shown to depend nonmonotonically on the length of the charged section. In addition, chain heterogeneity, in which segments of the polymer interact differently with pores, has shown prospects for DNA sequencing using solid-state nanopores with tailored surface properties. Heterogeneity has been introduced as the polymer segments that experience different driving forces, polymers with different friction interactions with pores, polymers with varying pore-polymer in teractions along their lengths, and polymers with periodic varying stiffness. The latter is significant because experimental studies have shown the importance of sequence dependent bending rigidity for DNA-protein interaction and nucleosome positioning. In our second study, we present a detailed picture of the dynamics of polymer translo cation through variously patterned pores in the presence of an external force that pe riodically varies. We consider both homopolymers, which are uniformly semiflexible, and heteropolymers, with alternate stiff and flexible segments. Similarly to previous investigations, the gain in translocation time for homopolymers exhibits oscillations with the frequency of the external periodic force. Although the gain varies significantly with chain stiffness for a uniformly attractive pore, these changes are negligible for pores with varying interactions. This behavior with variably structured pores is further characterized using the mean translocation time and waiting time distributions. For heteropolymers, there are notable differences in the waiting-time distribution between various pores, and for varying oscillation frequencies depending on the block length of the stiff/flexible segment. We employ these differences in a sequencing technique to in 10 vestigate the potential for detecting heteropolymers by allowing them to pass through numerous pores. We demonstrate how the combination of periodic forcing, chain het erogeneity, and pore patterning can help with sequence detection. Bacteriophages house DNA in capsids of various shapes and sizes and eject DNA into host cells once the capsid is opened. Since packed DNA is enclosed in a capsid that is usually smaller than the persistence length of the DNA, it is subject to significant energy and entropic penalties. There is a tremendous build-up of internal pressure that is used by viruses or bacteriophages. Typically, bacteriophages attach themselves to the surface of a bacterium and use the internal pressure that releases the phage’s DNA when its capsid is opened to eject their genome into the cytoplasm of the host. There is a great variation in the shape of viral capsids. Shapes range from spherical or quasi-spherical for phage DNA which infects prokaryotes to more elongated shapes for viruses affecting eukaryotes. Theoretical studies have studied the impact of different capsid geometries on the packaging and ejection dynamics of polymers of different f lexibility. In addition, such situations often involve ATP hydrolysis to facilitate transfer. Therefore, it is necessary to look at the translocation process in the presence of active forces. In our third study, we considered the biomimetic packaging of an active semiflexi ble polymer in spherical and ellipsoidal capsids of the same internal volume. Active polymers show different conformational and dynamical properties compared to those of passive ones. We studied the impact of capsid geometry and activity on the poly mer packaging and ejection dynamics. For a passive polymer, we observe that as the sphericity of the capsid increases, the packing time decreases monotonically, indicating that a spherical capsid is packed more easily than other shapes. A semiflexible poly mer packs slower than a flexible one. Although activity has a minimal effect on the qualitative behavior of packing and unpacking, the rate of packing and unpacking is significantly affected in the presence of activity. Like the packing time, the ejection time increases with capsid sphericity. For the packing of a semiflexible polymer, we observed prominent peaks in the mean waiting times for capsid geometries with low sphericities.