Related papers: The determinism and boundedness of self-assembling…
Protein structure prediction can be shown to be an NP-hard problem; the number of conformations grows exponentially with the number of residues. The native conformations of proteins occupy a very small subset of these, hence an exploratory,…
DNA nanostructures with programmable shape and interactions can be used as building blocks for the self-assembly of crystalline materials with prescribed nanoscale features, holding a vast technological potential. Structural rigidity and…
Formation of highly ordered structures usually needs to overcome a high free-energy barrier that is greatly beyond the ability of thermodynamic fluctuation, such that the system would be easily trapped into a state with many defects and the…
Proteins are the common constituents of all living cells. They are molecular machines that interact with each other as well as with other cell products and carry out a dizzying array of functions with distinction. These interactions follow…
The ability to design and synthesize ever more complicated colloidal particles opens the possibility of self-assembling a zoo of complex structures, including those with one or more self-limited length scales. An undesirable feature of…
We use simple analytic arguments and lattice-based computer simulations to study the growth of structures made from a large number of distinct component types. Components possess 'designed' interactions, chosen to stabilize an equilibrium…
Small-angle scattering (SAS) of X-rays, neutrons or light from ensembles of randomly oriented and placed deterministic fractal structures are studied theoretically. In the standard analysis, a very few parameters can be determined from SAS…
Protein aggregation is of great importance in biology, e.g., in amyloid fibrillation. The aggregation processes that occur at the cellular scale must be highly stochastic in nature because of the statistical number fluctuations that arise…
We use a coarse-grained model of DNA-functionalized particles to understand the role of DNA chain length on their self-assembly. We find that the increasing chain length for a given particle size decreases the propensity to form ordered…
We study the entanglement structure, i.e., the structure of quantum composite system from operational aspects. The structure is not uniquely determined in General Probabilistic Theories (GPTs) even if we impose reasonable postulate about…
The cornerstone of structural biology is the unique relationship between protein sequence and the 3D structure at equilibrium. Although intrinsically disordered proteins (IDPs) do not fold into a specific 3D structure, breaking this…
Many algorithms for processing probabilistic networks are dependent on the topological properties of the problem's structure. Such algorithms (e.g., clustering, conditioning) are effective only if the problem has a sparse graph captured by…
Multiple phenotypic protein expressions arising from one genome represent variations in the protein relative abundance and their stoichiometry. A lack of definite compositional parts challenges the modeling of protein megacomplexes and…
Pattern formation often occurs in confined systems, yet how boundaries shape patterning dynamics is unclear. We develop techniques to analyze confinement effects in nonlocal advection-diffusion equations, which generically capture the…
We apply a simple model system of patchy particles to study monodisperse self-assembly, using the Platonic solids as target structures. We find marked differences between the assembly behaviours of the different systems. Tetrahedra,…
We present an analytical method for determining the designability of protein structures. We apply our method to the case of two-dimensional lattice structures, and give a systematic solution for the spectrum of any structure. Using this…
Motivated by the hinge structure present in protein chains and other molecular conformations, we study the singularities of certain maps associated to body-and-hinge and panel-and-hinge chains. These are sequentially articulated systems…
Accurately modeling and designing protein complex structures is a central problem in computational structural biology, with broad implications for understanding cellular function and developing therapeutics. This thesis investigates two…
Two distinct structures of aggregates of atoms connected by anisotropic bonds with a network configuration are discussed from the viewpoint of a point set topology. A specific topological space connects the two types of topological…
Since the 1920s, packing arguments have been used to rationalize crystal structures in systems ranging from atomic mixtures to colloidal crystals. Packing arguments have recently been applied to complex nanoparticle structures, where they…