Two important lines of research in the behavior of proteins are - Given the sequence : predict the structure of the protein - Given the structure : predict the function of the protein Want to study the functioning of a protein given the structure The behavior depends on the surrounding molecules To explicitly deal with sufficient number of solvent molecules is difficult due to computational costs We want to parameterize the state of water molecules near a protein As a basic model we will use A is the drift vector and B is the diffusion tensor; these need to be determined, dW is white noise There are two approaches we use - We guess the correct form of the coefficients - We use MD data to determine the coefficients We start by considering a simple solute: specifically, we consider a Buckyball (C 60 ), as this has approximate spherical symmetry Once we have a good parameterization for water around this simple solute, we shall consider more complex solutes that mimic the geometric and chemical properties of a protein We shall then use the appropriate parameterization when simulating the dynamics of an actual protein We use inputs obtained from MD simulations to develop our parameterization The MD simulation was performed with a Buckyball (C 60 ) hydrated by 1380 water molecules A 3.5 x 3.5 x 3.5 cubic box was used, which was periodic in all dimensions The interactions were –LJ (Lennard Jones) cutoff 1nm –Particle Mesh Ewald (PME) The simulation parameters were –Integrator time step 2fs –Temperature 300K (using Nose Hoover thermostat) To benchmark our code we use two exactly solvable processes The Ornstein Uhlenbeck process governed by The Langevin process with quadratic potential, which is governed by the equation We are interested in the overdamped case which corresponds to a>>1 The OU process can be considered a coarse-grained version of the Langevin process A measure of diffusivity which is used in the literature is We calculate this for our test models and compare the results to the exact solutions We are interested in the regime where the V dynamics are coarse-grained, i.e. we want a value of  such that  v <<  <<  X where is the momentum relaxation time and is the characteristic time for the X dynamics We also use the two aformentioned exact systems to understand how to calculate the best value of  for our models As a first model (following Garde et.al), we guess the correct form to be We use Monte Carlo methods to simulate this SDE We calculate the diffusivity and compare it with the diffusivity obtained directly from the MD data We next use a more general drift-diffusion parameterization The parameters U long D long & D lat are calculated directly from the MD data We then calculate the diffusivity, and compare it to the value obtained directly from the MD data We note that the DD-II model does better than DD-I model in capturing the features of the diffusivity We shall now use the DD-II model with input from MD simulation of water around more complex solutes We hope to construct effective models for the dynamics of water around different types of proteins, using these simulations 2. OUR APPROACH 3. GENERAL PROGRAM 4. MD SIMULATION 5. BENCHMARKING 6. THE DD-I MODEL 7. THE DD-II MODEL 8. CONCLUSIONS & FUTURE WORK PARAMETERIZATION OF SOLVENT MOLECULES AROUND A SOLUTE Adnan Khan 1 Peter Kramer 1 & Rahul Godawat 2 1 Department of Mathematical Sciences 2 Department of Chemical Engineering Rensselaer Polytechnic institute 1.THE PROBLEM Initial configuration for the Buckyball Water system Numerical vs Exact Diffusivity for OU and Langevin systems