Elasticity Theory and Shape Transitions of Viral Shells

Recently, continuum elasticity theory has been applied to explain the shape transition of icosahedral viral capsids - single-protein-thick crystalline shells - from spherical to buckled/faceted as their radius increases through a critical value determined by the competition between stretching and bending energies of a closed 2D elastic network. In the present work we generalize this approach to capsids with non-icosahedral symmetries, e.g., spherocylindrical and conical shells. One key new physical ingredient is the role played by nonzero spontaneous curvature. Another is associated with the special way in which the energy of the twelve topologically-required five-fold sites depends on the background local curvature of the shell in which they are embedded. Systematic evaluation of these contributions leads to a shape phase diagram in which transitions are observed from icosahedral to spherocylindrical capsids as a function of the ratio of stretching to bending energies and of the spontaneous curvature of the 2D protein network. We find that the transition from icosahedral to spherocylindrical symmetry is continuous or weakly first-order near the onset of buckling, leading to extensive shape degeneracy. These results are discussed in the context of experimentally observed variations in the shapes of a variety of viral capsids.Comment: 53 pages, 17 figure

Transfer matrix solution of the Wako-Sait\^o-Mu\~noz-Eaton model augmented by arbitrary short range interactions

The Wako-Sait{\^o}-Mu\~noz-Eaton (WSME) model, initially introduced in the theory of protein folding, has also been used in modeling the RNA folding and some epitaxial phenomena. The advantage of this model is that it admits exact solution in the general inhomogeneous case (Bruscolini and Pelizzola, 2002) which facilitates the study of realistic systems. However, a shortcoming of the model is that it accounts only for interactions within continuous stretches of native bonds or atomic chains while neglecting interstretch (interchain) interactions. But due to the biopolymer (atomic chain) flexibility, the monomers (atoms) separated by several non-native bonds along the sequence can become closely spaced. This produces their strong interaction. The inclusion of non-WSME interactions into the model makes the model more realistic and improves its performance. In this study we add arbitrary interactions of finite range and solve the new model by means of the transfer matrix technique. We can therefore exactly account for the interactions which in proteomics are classified as medium- and moderately long-range ones.Comment: 15 pages, 2 figure

Computational Design and Study of Structural and Dynamic Nucleic Acid Systems

abstract: DNA and RNA are generally regarded as one of the central molecules in molecular biology. Recent advancements in the field of DNA/RNA nanotechnology witnessed the success of usage of DNA/RNA as programmable molecules to construct nano-objects with predefined shapes and dynamic molecular machines for various functions. From the perspective of structural design with nucleic acid, there are basically two types of assembly method, DNA tile based assembly and DNA origami based assembly, used to construct infinite-sized crystal structures and finite-sized molecular structures. The assembled structure can be used for arrangement of other molecules or nanoparticles with the resolution of nanometers to create new type of materials. The dynamic nucleic acid machine is based on the DNA strand displacement, which allows two nucleic acid strands to hybridize with each other to displace one or more prehybridized strands in the process. Strand displacement reaction has been implemented to construct a variety of dynamic molecular systems, such as molecular computer, oscillators, in vivo devices for gene expression control. This thesis will focus on the computational design of structural and dynamic nucleic acid systems, particularly for new type of DNA structure design and high precision control of gene expression in vivo. Firstly, a new type of fundamental DNA structural motif, the layered-crossover motif, will be introduced. The layered-crossover allow non-parallel alignment of DNA helices with precisely controlled angle. By using the layered-crossover motif, the scaffold can go through the 3D framework DNA origami structures. The properties of precise angle control of the layered-crossover tiles can also be used to assemble 2D and 3D crystals. One the dynamic control part, a de-novo-designed riboregulator is developed that can recognize single nucleotide variation. The riboregulators can also be used to develop paper-based diagnostic devices.Dissertation/ThesisDoctoral Dissertation Chemistry 201

Design of DNA origami

The generation of arbitrary patterns and shapes at very small scales is at the heart of our effort to miniaturize circuits and is fundamental to the development of nanotechnology. Here I review a recently developed method for folding long single strands of DNA into arbitrary two-dimensional shapes using a raster fill technique - 'scaffolded DNA origami'. Shapes up to 100 nanometers in diameter can be approximated with a resolution of 6 nanometers and decorated with patterns of roughly 200 binary pixels at the same resolution. Experimentally verified by the creation of a dozen shapes and patterns, the method is easy, high yield, and lends itself well to automated design and manufacture. So far, CAD tools for scaffolded DNA origami are simple, require hand-design of the folding path, and are restricted to two dimensional designs. If the method gains wide acceptance, better CAD tools will be required

Predicting RNA Secondary Structures By Folding Simulation: Software and Experiments

We present a new method for predicting the secondary structure of RNA sequences. Using our method, each RNA nucleotide of an RNA Sequence is represented as a point on a 3D triangular lattice. Using the Simulated Annealing technique, we manipulate the location of the points on the lattice. We explore various scoring functions for judging the relative quality of the structures created by these manipulations. After near optimal configurations on the lattice have been found, we describe how the lattice locations of the nucleotides can be used to predict a secondary structure for the sequence. This prediction can be further improved by using a greedy, 2-interval post-processing step to find the maximum independent set of the helices predicted by the lattice. The complete method, DeltaIS, is then compared with HotKnot, a popular secondary structure prediction program. We evaluate the relative effectiveness of DeltaIS and HotKnot by predicting 252 sequences from the Pseudobase Database. The predictions of each method are then scored against the true structures. We show DeltaIS to be superior to HotKnot for shorter RNA sequences, and in the number of perfectly predicted structures