This thesis addresses two different topics. The major part of this thesis deals with the precise evaluation of bridge functions required to yield the integral equation theories up to the second power in density for both bulk and confined hard sphere fluids. We propose two modified Mayer-sampling methods based on Transition Matrix Monte Carlo (TMMC) and overlap sampling for calculating the integrated diagrams appearing in the coefficients of the bridge function. The results from these methods compared with the generic Monte Carlo Mayer-sampling are analyzed in detail for the bulk hard sphere system. Next TMMC Mayer-sampling method is applied to evaluate the bridge function for the hard sphere fluid in a slit-pore. We first construct the slit-fluid bridge function by wall-particle bridge diagrams with h b-bond (i.e. bulk-fluid total correlation function h b). The quantity of the slit-fluid bridge function is assessed by comparing density profiles and reduced normal pressures obtained from the singlet integral equation theory with those from the grand canonical Monte Carlo simulation. The second part of this thesis concerns the 3D structure of human beta defensin (HBD) 28 via homology modeling and molecular dynamics approach. Implementations of these methods are described, as well as the comparison among the resulting models that based on HBD-2 and HBD-3 as templates. The highly probable candidates for HBD-28 are refined through molecular simulations in pure water and 50% trifluoroethanol/water mixture. In comparison with circular dichroism experimental data as well as stabilities of ββ-sheet and α-helix, HBD-28 with a reliable 3D structure was found.