Belfast-8: first draft

user-doc/tutorials/belfast-8.txt

 /**
 \page belfast-8 Belfast tutorial: Replica exchange II and Multiple walkers
 
+\section Aims
+
+The aim of this tutorial is to introduce the users to the use of Bias-Exchange Metadynamics. We will go through the writing of
+the input files for BEMETA for a simple case of three alanines and we will use METAGUI to to analyse them. We will compare
+the results of WT-BEMETA and STANDARD-BEMETA with four independent runs on the four Collective Variables. Finally we will
+use a simplified version of BEMETA that is Multiple Walkers Metadynamics.
+
+\section belfast-1-lo Learning Outcomes
+
+Once this tutorial is completed students will:
+
+- Know how to run a Bias-Exchange simulation using PLUMED and GROMACS 
+- Know how to analyse the results of BEMETA with the help of METAGUI
+- Know how to run a Multiple Walker simulation 
+
+\section Resources
+
+The <a href="tutorial-resources/belfast-8.tar.gz" download="belfast-8.tar.gz"> tarball </a> for this project contains the following files:
+
+- trajectory-short.xyz : a (short) trajectory for a 16 residue protein in xyz format. All calculations with plumed driver use this trajectory.
+- template.pdb : a single frame from the trajectory that can be used in conjuction with the \ref MOLINFO command
+
+\section Instructions
+
+\subsection bemeta Bias-Exchange Metadynamics
+
+In all variants of metadynamics the free-energy landscape of the system is reconstructed by gradually
+filling the local minima with gaussian hills. The dimensionality of the landscape is equal to the
+number of CVs which are biased, and typically a number of CVs smaller than three is employed.
+The reason for this is that qualitatively, if the CVs are not correlated among them, the simulation time
+required to fill the free-energy landscape grows exponentially with the number of CVs.
+This limitation can be severe when studying complex transformations or reactions in which
+more than say three relevant CVs can be identified.
+
+A possible technique to overcome this limitation is parallel-tempering metadynamics, \ref belfast-7.
+A different solution is performing a bias-exchange simulation:
+in this approach a relatively large number N of CVs  is chosen to describe the possible transformations
+of the system (e.g., to study the conformations of a peptide one may consider all the dihedral angles between amino acids).
+Then, N metadynamics simulations (replicas) are run on the same system at the same temperature, biasing a different
+CV in each replica. 
+
+Normally, in these conditions, each bias profile would converge very slowly to the
+equilibrium free-energy, due to hysteresis. Instead, in the bias-exchange approach every fixed number of steps
+(say 10,000) an exchange is attempted between a randomly selected pair of replicas \f$ a \f$ and \f$ b \f$.
+The probability to accept the exchange is given by a Metropolis rule:
+
+\f[
+\begin{eqnarray}
+\min\left( 1, \exp \left[ \beta ( V_G^a(x^a,t)+V_G^b(x^b,t)-V_G^a(x^b,t)-V_G^b(x^a,t) ) \right] \right)
+\end{eqnarray}
+\f]
+
+where \f$ x^{a} \f$ and \f$ x^{b} \f$ are the coordinates of replicas \f$a \f$ and \f$ b \f$
+and \f$ V_{G}^{a(b)}\left(x,t\right) \f$ is the metadynamics potential acting on the replica \f$ a \f$( \f$ b \f$).
+Each trajectory evolves through the high dimensional free energy landscape in the space of the CVs sequentially biased by
+different metadynamics potentials acting on one CV at each time. 
+The results of the simulation are N one-dimensional projections of the free energy.
+
+In the following example, a bias-exchange simulation is performed on a Ala-Ala-Ala peptide (zwitterionic form, in vacuum with 
+\f$ \epsilon=80 \f$, force field amber03), using the four backbone dihedral angles as CVs. 
+
+Four replicas of the system are employed, each one biased on a different CV,
+thus four similar Plumed input files are prepared as follows:
+
+\verbatim
+
+\endverbatim
+
+The four replicas start from the same GROMACS topology file replicated four times: topol0.tpr, topol1.tpr, topol2.tpr, topol3.tpr.
+Finally, GROMACS is launched as a parallel run on 4 cores, with one replica per core, with the command 
+
+\verbatim
+mpirun -np 4 mdrun -plumed plumed -multi 4 -replex 10000
+\endverbatim
+
+where -replex 10000 indicates that every 10000 molecular-dynamics steps
+all replicas are randomly paired (e.g. 0-2 and 1-3) and exchanges are attempted
+between each pair (as printed in the GROMACS *.log files).
+
 */
 
 link: @subpage belfast-8