Fast Tree Search for Enumeration of a Lattice Model of Protein Folding

Using a fast tree-searching algorithm and a Pentium cluster, we enumerated all the sequences and compact conformations (structures) for a protein folding model on a cubic lattice of size $4\times3\times3$. We used two types of amino acids -- hydrophobic (H) and polar (P) -- to make up the sequences, so there were $2^{36} \approx 6.87 \times 10^{10}$ different sequences. The total number of distinct structures was 84,731,192. We made use of a simple solvation model in which the energy of a sequence folded into a structure is minus the number of hydrophobic amino acids in the ``core'' of the structure. For every sequence, we found its ground state or ground states, i.e., the structure or structures for which its energy is lowest. About 0.3% of the sequences have a unique ground state. The number of structures that are unique ground states of at least one sequence is 2,662,050, about 3% of the total number of structures. However, these ``designable'' structures differ drastically in their designability, defined as the number of sequences whose unique ground state is that structure. To understand this variation in designability, we studied the distribution of structures in a high dimensional space in which each structure is represented by a string of 1's and 0's, denoting core and surface sites, respectively.Comment: 18 pages, 10 figure

Charge Blinking Statistics of Semiconductor Nanocrystals Revealed by Carbon Nanotube Single Charge Sensors

We demonstrate the relation between the optical blinking of colloidal semiconductor nanocrystals (NCs) and their electrical charge blinking for which we provide the first experimental observation of power-law statistics. To show this, we harness the performance of CdSe/ZnS NCs coupled with carbon nanotube field-effect transistors (CNTFETs), which act as single charge-sensitive electrometers with submillisecond time resolution, at room temperature. A random telegraph signal (RTS) associated with the NC single-trap charging is observed and exhibits power-law temporal statistics (τ^–α, with α in the range of ∼1–3), and a Lorentzian current noise power spectrum with a well-defined 1/<i>f</i>² corner. The spectroscopic analysis of the NC–CNTFET devices is consistent with the charging of NC defect states with a charging energy of <i>E</i>_c ≥ 200 meV. These results pave the way for a deeper understanding of the physics and technology of nanocrystal-based optoelectronic devices