Protein Structure and Function. Application of Bioinformatics Methods - John Rigden 2014

Ab Initio Protein Structure Prediction
Conformational Search Methods
Monte Carlo Modeling

The Simulated Annealing (SA) algorithm (Kirkpatrick et al. 1983) is arguably the most popular method for conformational searching. The principles of SA are straightforward and intuitive, making the method easy to apply to a wide range of structural optimization problems. Typically, SA employs the Monte Carlo (MC) algorithm proposed by N. Metropolis to generate a set of conformational states that obey the classical Boltzmann energy distribution at a given Temperature. The initial stage of SA involves calculations at a high temperature, followed by a series of runs with a gradually decreasing temperature (hence the name, simulated annealing). Precisely because of its simplicity, the efficiency of conformational searching via SA is relatively low compared to other, more sophisticated Methods discussed below.

In cases where the potential energy surface of the studied system is rugged due to numerous energy barriers, standard MC calculations tend to get trapped in metastable states. This ultimately distorts the distribution of sampled states and violates the ergodicity of the sampling. To overcome this limitation, various techniques have been developed. One such approach relies on using a generalized ensemble instead of the canonical ensemble typically used in simulations. Originally, the method went by several names, including the multicanonical ensemble (Berg and Neuhaus 1992) and the entropic ensemble (Lee 1993). The underlying idea is to accelerate transitions between states separated by energy barriers. This is achieved by modifying the transition probabilities so that the resulting energy distribution profile shifts from bell-shaped to nearly flat.

Another popular and closely related approach is the replica exchange Monte Carlo (REM) method (Kihara et al. 2001), which simultaneously performs a series of MC calculations across a selected temperature range. Periodically, attempts are made to swap the structures (or equivalently, the temperatures) of neighboring runs to sample states over a broad energy range, thereby facilitating the crossing of energy barriers. Parallel hyperbolic sampling (PHS) (Zhang et al. 2002) is an extension of the REM method designed to lower energy barriers by introducing a dynamically deformed energy surface via the inverse hyperbolic sine function.

Monte Carlo with Minimization (MCM), originally developed by Li and Scheraga (Li and Scheraga 1987), has been successfully applied to conformational searches within the high-resolution energy function of the ROSETTA software. In this method, perturbed protein structures are mapped onto local energy minima following local energy minimization. For a given Structure A residing in a local energy minimum, a test structure B is generated through a random perturbation followed by subsequent local energy minimization. To determine whether structure B is acceptable relative to structure A, the standard Metropolis criterion is applied by calculating the energy difference between the two states.