A refinement of a minimal model for protein folding originally proposed by Imamura is presented. The representation of the alpha-helix has been improved by adding in explicit modelling of the entire peptide unit. A four-helix bundle consisting of four alpha-helices and three loop regions is generated with the parallel tempering Monte Carlo scheme. Six native states are found for the given sequence, four U-bundle and two Z-bundle states. All six states have energies of E approx -218ε and all appear equally likely to occur in simulation. The highest probability of folding a native state is found to be at a hydrophobic strength of Ch = 0.8 which agrees with the value of Ch = 0.7 used by Imamura in his studies of alpha to beta structural conversions. Two folding stages are observed in the temperature spectrum dependent on the magnitude of the hydrophobic strength parameter. The two stages observed as temperature decreases are 1) the hydrophobic energy causes the random coil to collapse into a compact globule 2) the secondary structure starts forming below a temperature of about T = 0.52ε/kB. The temperature of the first stage, which corresponds to the characteristic collapse temperature Tθ, is highly dependent on the hydrophobic strength. The temperature of the second stage is constant with respect to hydrophobic strength. Attempts to measure the characteristic folding temperature, Tf , from the structural overlap function proved to be difficult due mostly to the presence of six minima and the complications that arose in the parallel tempering Monte Carlo scheme. However, a rough estimate of Tf is obtained at each hydrophobic strength from a native state density analysis. Tf is found to be significantly lower than Tθ.

This dissertation splits into two distinct halves. The first half is devoted to the study of the holography of higher spin gauge theory in AdS$_3$. We present a conjecture that the holographic dual of $W_N$ minimal model in a 't Hooft-like large $N$ limit is an unusual ``semi-local" higher spin gauge theory on AdS$_3\times $S$^1$. At each point on the S$^1$ lives a copy of three-dimensional Vasiliev theory, that contains an infinite tower of higher spin gauge fields coupled to a single massive complex scalar propagating in AdS$_3$. The Vasiliev theories at different points on the S$^1$ are correlated only through the AdS$_3$ boundary conditions on the massive scalars. All but one single tower of higher spin symmetries are broken by the boundary conditions. This conjecture is checked by comparing tree-level two- and three-point functions, and also one-loop partition functions on both side of the duality. The second half focuses on the holography of higher spin gauge theory in AdS$_4$. We demonstrate that a supersymmetric and parity violating version of Vasiliev's higher spin gauge theory in AdS$_4$ admits boundary conditions that preserve ${\cal N}=0,1,2,3,4$ or $6$ supersymmetries. In particular, we argue that the Vasiliev theory with $U(M)$ Chan-Paton and ${\cal N}=6$ boundary condition is holographically dual to the 2+1 dimensional $U(N)_k\times U(M)_{-k}$ ABJ theory in the limit of large $N,k$ and finite $M$. In this system all bulk higher spin fields transform in the adjoint of the $U(M)$ gauge group, whose bulk t'Hooft coupling is $\frac{M}{N}$. Our picture suggests that the supersymmetric Vasiliev theory can be obtained as a limit of type IIA string theory in AdS$_4\times \mathbb{CP}^3$, and that the non-Abelian Vasiliev theory at strong bulk 't Hooft coupling smoothly turn into a string field theory. The fundamental string is a singlet bound state of Vasiliev's higher spin particles held together by $U(M)$ gauge interactions. / Physics