Session H55: Polymer Physics in Very Strongly Confined Environments I : Knots and Nanopores

Anomalous Dynamics of a Polymer Chain Confined in a Static Porous Environment

Understanding polymer dynamics through a porous environment is relevant to many areas of biology, materials engineering, and physics. Porous environments have been repeatedly employed to separate and characterize synthetic and biological polymers, such as in chromatography and gel electrophoresis. Additionally, the motion of macromolecules through the dense cellular environment is crucial to many biological processes and drug delivery. Even with such a broad range of applicability, single chain dynamics under such confinement remains elusive. In this work, we employ Langevin dynamics simulations in conjunction with statistical mechanical theory to understand chain dynamics in a porous environment. As a simple model of a porous environment, we choose a one dimensional network of spherical cavities connected by small pores. Theoretically we model dynamics by constructing the free energy due to partitioning the chain between different chambers. In both simulations and theory we calculate the anomalous diffusion as a function of the chamber size and the chain length at the segmental and center of mass scales. These studies provide a foundation for understanding dynamics of polymers in more complex porous environments.   

Polymer folding in confined and crowded environments

A flexible homopolymer chain with sufficiently short-range interactions undergoes a first-order-like transition from an expanded coil to a compact crystallite analogous to the all-or-none folding exhibited by many small proteins [1]. Here we investigate this polymer folding transition under geometric confinement and in the presence of macromolecular crowders. One anticipates that both confinement and crowding will lead to entropic stabilization of the folded state. We use a Wang-Landau simulation approach to construct the partition function of a flexible square-well-sphere chain (monomer size d) that is (A) confined within a hard-wall slit [2] and (B) immersed in a hard-sphere solvent with solvent size D ≥ d and solvent volume fraction 0 < vf ≤ 0.4 [3]. Entropic stabilization is found in all cases. For the confined chain, isothermal reduction of the slit width can induce folding, unfolding, or crystallite restructuring. In the crowded environment an isothermal increase in the crowder density can induce folding. This crowding behavior is sensitive to the size of the crowder with larger crowders producing a smaller effect. [1] J. Chem. Phys. 145, 174903 (2016); [2] Macromolecules 50, 6967 (2017); [3] J. Chem. Phys. 147, 166101 (2017).   

Sequence-dependent persistence length of long DNA

DNA is a common model system for studying polymer physics at the single molecule level, making an accurate measurement of the DNA persistence length important for interpreting experimental data. While it well known that the bending energy at short length scales (around 100 base pairs) is a strong function of the underlying sequence, how this behavior propagates into the persistence length of the chain at long length scales remains unclear. Using a high-throughput genome mapping technique, we have obtained over 50 million measurements of the extension of human DNA segments in a 41 nm x 41 nm nanochannel. The analyzed DNA segments are between 2.5 and 393 kilobase pairs in size with % GC content ranging from 32.5% to 60%. While the fractional extension of the chain only changes by a small amount as a function of % GC content, Odijk’s theory for stretching of a wormlike chain in channel confinement implies that the underlying persistence length increases by 20% over this range. We have developed a statistical terpolymer model, which contains no adjustable parameters, that captures the experimental phenomena.   

DNA knots in confinement

Knots are practical constructs which predate the discovery of fire, have been exploited for centuries by sailors, and are commonplace in our everyday life. Knots occur spontaneously in long polymers and play an important role in biological/biotechnological processes such as viral DNA packaging and release, protein stability and DNA sequencing. In many of these processes, the DNA is highly confined or passes through confined spaces. In my group, we have been pursuing a multipronged approach to study knots which includes single molecule experiments, mesoscale simulations, and theory. Here I will discuss some recent findings on DNA knots regarding a universal correlation between knotting probability and complexity, and also studies of DNA knot dynamics in microfluidic flow devices.
  

Prevalence of loose and tight knots in DNA investigated by a nanopore sensor

The knotting of long DNA chains is an important effect in fundamental biological processes such as DNA replication, viral DNA packaging, and transcription. Knots also become a technological challenge in the single molecule sequencing of long DNA segments. Despite being ubiquitous, there is no consensus in the literature regarding basic physical properties of equilibrium knots due to limitations of the existing experimental methods. Nanopore sensing is a new technique for investigating knots that affords high-throughput, single molecule interrogation of molecular conformations at a wide range of length-scales. Here we report a new implementation of nanopore sensing and a classification scheme, which allows us to map transient current data during knotted DNA translocation to molecular conformations and topological states. Using this methodology and a large sampling of single-molecule events, we demonstrate for the first time the co-existence of both loose and tight knots on equilibrium DNA chains. In addition, we are able to sample rare composite knot events, investigate knot localization and probe different modes of translocation.

Keywords: Solid-state nanopores, DNA knots, polymers, DNA sequencing, topology   

Translation and untying of DNA knots in extensional fields

Knots occur naturally in biological DNA, a phenomenon relevant for cellular genome organization as well as genetic sequencing technology. Knotted DNA molecules serve as a model experimental system for polymer entanglement, where fluorescent microscopy can be used to study polymer dynamics on the individual chain level. To study the dynamics of knots in DNA, we induce knotting in viral DNA using an electrohydrodynamic instability and stretch the molecules with a divergent electric field in a microfluidic channel, analogous to elongational flow. The knots appear as bright spots of excess fluorescent intensity along the stretched molecule. With sufficiently long observation time, the knots are seen to translate along the molecule and eventually reach the chain ends and untie. The mobility of the knots can be controlled by modifying the applied strain rate, and can be jammed and re-started through step-function changes in the elongational field. The untying is a complex process that induces a temporary contraction of the molecule, which elongates as the knot unties, and produces several transient knots of lower topological complexity before completely untying.   

Fabricating sub 5 nm nanopores via tip-controlled electric breakdown using an atomic force microscope

We have developed a new approach for fabrication of sub 5 nm pores via local dielectric breakdown induced by a conductive AFM tip across an ~10nm nitride membrane. In our approach, a conductive AFM tip is brought into contact with a nitride membrane sitting on top of an electrolyte reservoir. Application of a voltage pulse leads within seconds to formation of a nanoscale pore that can be detected by a subsequent AFM scan. This approach combines the ease of classic dielectric breakdown with the nanoscale pore positioning capability of high energy particle milling techniques such as TEM and FIB. Note that nm pore positioning is critical to ensure integration of nanopores with nanoscale electrodes (e.g. transverse electrode designs) and nanofluidic channels. Moreover, unlike the classic breakdown approach, our technique does not require that both the top and bottom surfaces of the membrane be immersed in electrolyte solution, significantly simplifying the fabrication process. We report measurements of pore size as a function of pulse duration, DNA translocation blockades and pore noise characteristics.
  

Different solid-state nanopore translocation dynamics and times of dsDNA and ssDNA

By performing all-atomic molecular dynamics simulations of 22-nucleotides-long double stranded (ds) and single stranded (ss) DNA molecules near an aluminum oxide nanopore, we observe that the electrophoretic translocation of dsDNA molecules is significantly faster than their melted ssDNA counterparts. We attribute this phenomenon to vdW attraction between the high-permittivity surface and the nucleic acid aromatic rings, which are more exposed and freer to rotate for ssDNAs. With a scaling theory that captures the larger enthalpy of adsorption due to these vdW contacts at the rings, we are able to develop a transition state theory for the stick-slip translocation dynamics of both molecules. The difference in the translocation time is further enhanced by a normal electric field component, which enhances the vdW attractive interaction by electro-statically attracting the molecules to the surface. We also capture this field-effect on the translocation time by appropriately reducing the barrier to produce a scaling theory that collapses the experimental translocation time data at different voltage for tailor-designed sharp-tip nanopores with a large normal field leakage. This peculiar chromatograph separation between ssDNA and dsDNA is being exploited for biosensing applications.   

Effects of nanopore charge decorations on the translocation dynamics of DNA

We have investigated the dynamics of single-stranded DNA as it translocates through charge mutated protein nanopores. Translocation of DNA is a crucial step in nanopore-based sequencing platforms, where control over translocation speed remains as one of the main challenges. Taking advantage of the interactions between negatively charged DNA and positively charged amino acid residues, the translocation speed of DNA can be manipulated by deliberate charge decorations inside the nanopore. We employed coarse grained Langevin dynamics simulations to monitor the step-by-step movement of the DNA through different mutations of α-hemolysin protein nanopores. We found that although the average translocation time per nucleotide is longer in agreement with experiments, the DNA nucleotides do not translocate with a uniform speed. Furthermore, the location and the spacing of the charge decorations can alter the translocation dynamics significantly, trapping DNA in some cases. Our findings can give insights when designing charge patterns in nanopores.
  

Unfolding of RNA via Translocation Through a Nanopore

RNA unfolding and refolding are important biological phenomena occuring during RNA translation. During these processes, RNA is found in single stranded, secondary and tertiary structures which can comprise complex secondary conformations like hairpins and pseudoknots. Understanding the diverse conformations of RNA and how these influence the dynamics of unfolding and refolding is crucial to gain insight of fundamental biological processes. In this work, we employ atomistic molecular dynamics simulations to study the mechanism of unfolding when RNA is passing through a nanopore under the application of an electric field. We monitor the kinetics of unzipping of individual base pairs during the translocation event.