From Protein Structure to Function with Bioinformatics.pdf

234 M.B. Kubitzki et al.conformational flooding is not canonical, restricting analysis to structuralquestions.9.3.2 TEE-REXEnhanced sampling methods such as ED (Amadei et al. 1996) achieve their samplingpower (Amadei et al. 1996; de Groot et al. 1996a, b) primarily from the factthat a small number of internal collective degrees of freedom dominate the configurationaldynamics of proteins. Yet, systems simulated with such methods are alwaysin a non-equilibrium state, rendering it difficult to extract thermodynamic, i.e. equilibriumproperties of the system from such simulations. On the other hand, generalizedensemble algorithms such as REX not only enhance sampling but yield correctstatistical ensembles necessary for the calculation of equilibrium properties whichcan be subjected to experimental verification. However, REX quickly becomescomputationally prohibitive for systems of more than a few thousand particles,limiting its current applicability to smaller peptides (Pitera and Swope 2003;Cecchini et al. 2004; Nguyen et al. 2005; Liu et al. 2005; Seibert et al. 2005). Thenewly developed Temperature Enhanced Essential dynamics Replica EXchange(TEE-REX) algorithm (Kubitzki and de Groot 2007) combines the favourable propertiesof REX with those resulting from a specific excitation of functionally relevantmodes, while at the same time avoiding the drawbacks of both approaches.Figure 9.6 shows a schematic comparison of standard temperature REX (left)and the TEE-REX algorithm (right). TEE-REX builds upon the REX framework,i.e. a number of replicas of the system are simulated independently in parallel withperiodic exchange attempts between neighbouring replicas. In contrast to REX, ineach but the reference replica, only those degrees of freedom are thermally stimulatedthat contribute significantly to the total fluctuations of the system (essentialsubspace {es}). This way, several benefits are combined and drawbacks avoided. Incontrast to standard REX, the specific excitation of collective coordinates promotessampling along these often functionally relevant modes of motion, i.e. the advantagesof ED are used. To counterbalance the disadvantages associated with such aspecific excitation, i.e. the construction of biased ensembles, the scheme is embeddedwithin the REX protocol. Thereby ensembles are obtained having approximateBoltzmann statistics and the enhanced sampling properties of REX are utilized. Theexchange probability (equation 9.1) between two replicas crucially depends on theexcited number of degree of freedom of the system. Since the stimulated number ofdegrees of freedom makes up only a minute fraction of the total number of degreesof freedom of the system, the bottleneck of low exchange probabilities in all-atomREX simulations is bypassed. For given exchange probabilities, large temperaturedifferences ΔT can thus be used, such that only a few replicas are required.Figure 9.9 shows a two-dimensional projection of the free energy landscape ofdialanine, calculated with MD (panel A) and TEE-REX (panel B). The thermodynamicbehaviour of a system is completely known once a thermodynamic potential