Design of a Protein Potential Energy Landscape by Parameter Optimization

Application of the multiensemble sampling to the equilibrium folding of proteins

MOTIVATION

Conventional Monte Carlo and molecular dynamics simulations of proteins in the canonical ensemble are of little use, because they tend to get trapped in states of energy local minima at low temperatures. One way to surmount this difficulty is to use a non-Boltzmann sampling method in which conformations are sampled upon a general weighting function instead of the conventional Boltzmann weighting function. The multiensemble sampling (MES) method is a non-Boltzmann sampling method that was originally developed to estimate free energy differences between systems with different potential energies and/or at different thermodynamic states. The method has not yet been applied to studies of complex molecular systems such as proteins.

RESULTS

MES Monte Carlo simulations of small proteins have been carried out using a united-residue force field. The proteins at several temperatures from the unfolded to the folded states were simulated in a single MC run at a time and their equilibrium thermodynamic properties were calculated correctly. The distributions of sampled conformations clearly indicate that, when going through states of energy local minima, the MES simulation did not get trapped in them but escaped from them so quickly that all the relevant parts of conformation space could be sampled properly. A two-step folding process consisting of a collapse transition followed by a folding transition is observed. This study demonstrates that the use of MES alleviates the multiple-minima problem greatly.

AVAILABILITY

Available on request from the authors.

Protein structure prediction based on fragment assembly and parameter optimization

We propose a novel method for ab-initio prediction of protein tertiary structures based on the fragment assembly and global optimization. Fifteen residue long fragment libraries are constructed using the secondary structure prediction method PREDICT, and fragments in these libraries are assembled to generate full-length chains of a query protein. Tertiary structures of 50 to 100 conformations are obtained by minimizing an energy function for proteins, using the conformational space annealing method that enables one to sample diverse low-lying local minima of the energy. Then in order to enhance the performance of the prediction method, we optimize the linear parameters of the energy function, so that the native-like conformations become energetically more favorable than the non-native ones for proteins with known structures. We test the feasibility of the parameter optimization procedure by applying it to the training set consisting of three proteins: the 10-55 residue fragment of staphylococcal protein A (PDB ID 1bdd), a designed protein betanova, and 1fsd.

Folding simulations of small proteins

Understanding how a protein folds is a long-standing challenge in modern science. We have used an optimized atomistic model (united-residue force field) to simulate folding of small proteins of various structures: HP-36 (alpha protein), protein A (beta), 1fsd (alpha+beta), and betanova (beta). Extensive Monte Carlo folding simulations (ten independent runs with 10(9) Monte Carlo steps at a temperature) starting from non-native conformations are carried out for each protein. In all cases, proteins fold into their native-like conformations at appropriate temperatures, and glassy transitions occur at low temperatures. To investigate early folding trajectories, 200 independent runs with 10(6) Monte Carlo steps are also performed at a fixed temperature for a protein. There are a variety of possible pathways during non-equilibrium early processes (fast process, approximately 10(4) Monte Carlo steps). Finally, these pathways converge to the point unique for each protein. The convergence point of the early folding pathways can be determined only by direct folding simulations. The free energy surface, an equilibrium thermodynamic property, dictates the rest of the folding (slow process, approximately 10(8) Monte Carlo steps).