VI Preface simulations.The second paper,by HELMS MCCAMMON,surveys a wide range of different computational techniques for the exploration of conforma- tional transitions of proteins,including the use of stochastic dynamics with the Poisson-Boltzmann approximation as a simple solvent model.The ar- ticle by EICHINGER ET AL.combines several speedup techniques:multiple time stepping algorithms adapted to fit fast multipole methods(see also the last chapter of this book),the previously mentioned SMD technique,and GRUBMULLER's method of "computational flooding",which uses local po- tential modifications in order to successively drive the system to different low-energy basins.The novel approach taken by DEUFLHARD ET AL.em- ploys ideas from the mathematics of dynamical systems to construct certain almost invariant sets in phase space,which can be interpreted as chemical conformations;their algorithm also supplies patterns and rates of conforma- tional changes.In the last paper of this chapter,ToLSTUROKOV VIRNIK describe another use of dynamical systems tools and propose a simplified set of differential equations for the description of an observed hysteresis behavior in water adsorption-desorption of nucleic acids. The second chapter,on Thermodynamic Modelling,is devoted largely to methods for computing free energies and potentials of mean force.The paper by HERMANS ET AL.reviews experimental and theoretical techniques for studying the stability of protein-ligand complexes,including a new method for computing absolute free energies of binding with MD simulations,and summarizes recent applications from their laboratory.MARK ET AL.describe a new method to estimate relative binding free energies of a series of related ligands on the basis of a single simulated trajectory of a reference state in which a specially constructed,artificial ligand is modelled with a special "soft"potential function.KUCZERA describes a multiple-dimension approach by which conformation space is explored,while the potential of mean force is simultaneously computed.The joint paper from the groups of LESYNG and of MCCAMMON reviews an algorithm for the prediction of ionization constants in proteins;calculations of the relevant protein-solvent system are based on the already mentioned Poisson-Boltzmann equation.The paper by STRAUB ANDRICIOAEI employs the Tsallis statistics to speed up phase space sampling. In the final article of this chapter,NEUMAIER ET AL.construct empirical potentials for possible use in off-lattice protein studies. The third chapter,on Enhanced Time-Stepping Algorithms,opens with a personal account on long-timestep integration by SCHLICK.She assesses both the successes and the limitations of various algorithmic approaches including implicit discretization,harmonic/anharmonic separation of modes,and force splitting techniques combined with Langevin dynamics.The second paper, by ELBER ET AL.,describes a large step-size approximation of stochastic path integrals arising from Langevin dynamics -requiring,however,knowl- edge about both initial and final states.On the basis of a detailed case study ASCHER REICH argue that implicit discretizations should not be used with timesteps significantly larger than typical periods of the fast oscilla-