Emergence of stable and fast folding protein structures

The number of protein structures is far less than the number of sequences. By imposing simple generic features of proteins (low energy and compaction) on all possible sequences we show that the structure space is sparse compared to the sequence space. Even though the sequence space grows exponentially with N (the number of amino acids) we conjecture that the number of low energy compact structures only scales as ln N. This implies that many sequences must map onto countable number of basins in the structure space. The number of sequences for which a given fold emerges as a native structure is further reduced by the dual requirements of stability and kinetic accessibility. The factor that determines the dual requirement is related to the sequence dependent temperatures, T_\theta (collapse transition temperature) and T_F (folding transition temperature). Sequences, for which \sigma =(T_\theta-T_F)/T_\theta is small, typically fold fast by generically collapsing to the native-like structures and then rapidly assembling to the native state. Such sequences satisfy the dual requirements over a wide temperature range. We also suggest that the functional requirement may further reduce the number of sequences that are biologically competent. The scheme developed here for thinning of the sequence space that leads to foldable structures arises naturally using simple physical characteristics of proteins. The reduction in sequence space leading to the emergence of foldable structures is demonstrated using lattice models of proteins.Comment: latex, 18 pages, 8 figures, to be published in the conference proceedings "Stochastic Dynamics and Pattern Formation in Biological Systems

Probing the Mechanisms of Fibril Formation Using Lattice Models

Using exhaustive Monte Carlo simulations we study the kinetics and mechanism of fibril formation using lattice models as a function of temperature and the number of chains. While these models are, at best, caricatures of peptides, we show that a number of generic features thought to govern fibril assembly are present in the toy model. The monomer, which contains eight beads made from three letters (hydrophobic, polar, and charged), adopts a compact conformation in the native state. The kinetics of fibril assembly occurs in three distinct stages. In each stage there is a cascade of events that transforms the monomers and oligomers to ordered structures. In the first "burst" stage highly mobile oligomers of varying sizes form. The conversion to the aggregation-prone conformation occurs within the oligomers during the second stage. As time progresses, a dominant cluster emerges that contains a majority of the chains. In the final stage, the aggregation-prone conformation particles serve as a template onto which smaller oligomers or monomers can dock and undergo conversion to fibril structures. The overall time for growth in the latter stages is well described by the Lifshitz-Slyazov growth kinetics for crystallization from super-saturated solutions.Comment: 27 pages, 6 figure

Dependence of folding rates on protein length

Using three-dimensional Go lattice models with side chains for proteins, we investigate the dependence of folding times on protein length. In agreement with previous theoretical predictions, we find that the folding time grows as a power law with the chain length N with exponent $\lambda \approx 3.6$ for the Go model, in which all native interactions (i.e., between all side chains and backbone atoms) are uniform. If the interactions between side chains are given by pairwise statistical potentials, which introduce heterogeneity in the contact energies, then the power law fits yield large $\lambda$ values that typically signifies a crossover to an underlying activated process. Accordingly, the dependence of folding time is best described by the stretched exponential \exp(\sqrt{N}). The study also shows that the incorporation of side chains considerably slows down folding by introducing energetic and topological frustration.Comment: 6 pages, 5 eps figure

Vapor-Liquid-Solid Growth of Semiconductor SiC Nanowires for Electronics applications

While investigations of semiconductor nanowires (NWs) has a long history, a significant progress is yet to be made in silicon carbide (SiC) NW technologies before they are ready to be utilized in electronic applications. In this dissertation work, SiC NW polytype control, NW axis orientation with respect to the growth substrate and other issues of potential technological importance are investigated. A new method for growing SiC NWs by vapor-liquid-solid mechanism was developed. The method is based on an in-situ vapor phase delivery of a metal catalyst to the growth surface during chemical vapor deposition. This approach is an alternative to the existing seeded catalyst method based on ex-situ catalyst deposition on the target substrate. The new SiC NW growth method provided an improved control of the NW density. It was established that the NW density is influenced by the distance from the catalyst source to the substrate and is affected by both the gas flow rate and the catalyst diffusion in the gas phase. An important convenience of the new method is that it yields NW growth on the horizontal substrate surfaces as well as on titled and vertical sidewalls of 4H-SiC mesas. This feature facilitates investigation of the NW growth trends on SiC substrate surfaces having different crystallographic orientations simultaneously, which is very promising for future NW device applications. It was established that only certain orientations of the NW axes were allowed when growing on a SiC substrate. The allowed orientations of NWs of a particular polytype were determined by the crystallographic orientation of the substrate. This substrate-dependent (i.e., epitaxial) growth resulted in growth of 3C-SiC NWs in total six allowed crystallographic orientations with respect to the 4H-SiC substrate. This NW axis alignment offers an opportunity to achieve a limited number of NW axis directions depending on the surface orientation of the substrate. The ease of controlling the NW density enabled by the vapor-phase catalyst delivery approach developed in this work, combined with the newly obtained knowledge about how to grow unidirectional (wellaligned) NW arrays, offer new opportunities for developing novel SiC NW electronic and photonic devices