The 1/t Wang-Landau algorithm is tested on simple models of polymers and proteins. It is found that this method resolves the problem of the saturation of the error present in the original algorithm for lattice polymers. However, for lattice proteins, which have a rough energy landscape with an unknown energy minimum, it is found that the density of states does not converge in all runs. A new variant of the Wang-Landau algorithm that appears to solve this problem is described and tested. In the new variant, the optimum modification factor is calculated in the same straightforward way throughout the simulation. There is only one free parameter for which a value of unity appears to give near optimal convergence for all run lengths for lattice homopolymers when pull moves are used. For lattice proteins, a much smaller value of the parameter is needed to ensure rapid convergence of the density of states for energies discovered late in the simulation, which unfortunately results in poor convergence early on in the run.

The phase diagram for a lattice ring polymer under applied force, with variable solvent quality, for different topological knot states, is determined for the first time.In addition to eliminating pseudophases where the polymer is flattened into a single layer, it is found that non-trivial knots result in additional pseudophases under tensile force conditions.

We propose several improvements to the Monte Carlo simulation techniques for lattice peptide adsorption on surfaces. Firstly, we examine the implementation of "pull" moves and discuss the most efficient way of selecting them. Secondly, we explicitly show how Wang-Landau sampling may be used to calculate the appropriate density of states for a peptide chain in contact with a single surface, and how the information from such a simulation may be used to calculate results for slit geometry with a range of wall separations. Lastly, we consider further possible modifications of the simulation method and its application to adsorption on structured and patterned surfaces.