The implementation of molecular dynamics (MD) with our physics-based protein united-residue (UNRES) force field, described in the accompanying paper, was extended to Langevin dynamics. The equations of motion are integrated by using a simplified stochastic velocity Verlet algorithm. To compare the results to those with all-atom simulations with implicit solvent in which no explicit stochastic and friction forces are present, we alternatively introduced the Berendsen thermostat. Test simulations on the Ala(10) polypeptide demonstrated that the average kinetic energy is stable with about a 5 fs time step. To determine the correspondence between the UNRES time step and the time step of all-atom molecular dynamics, all-atom simulations with the AMBER 99 force field and explicit solvent and also with implicit solvent taken into account within the framework of the generalized Born/surface area (GBSA) model were carried out on the unblocked Ala(10) polypeptide. We found that the UNRES time scale is 4 times longer than that of all-atom MD simulations because the degrees of freedom corresponding to the fastest motions in UNRES are averaged out. When the reduction of the computational cost for evaluation of the UNRES energy function is also taken into account, UNRES (with hydration included implicitly in the side chain-side chain interaction potential) offers about at least a 4000-fold speed up of computations relative to all-atom simulations with explicit solvent and at least a 65-fold speed up relative to all-atom simulations with implicit solvent. To carry out an initial full-blown test of the UNRES/MD approach, we ran Berendsen-bath and Langevin dynamics simulations of the 46-residue B-domain of staphylococcal protein A. We were able to determine the folding temperature at which all trajectories converged to nativelike structures with both approaches. For comparison, we carried out ab initio folding simulations of this protein at the AMBER 99/GBSA level. The average CPU time for folding protein A by UNRES molecular dynamics was 30 min with a single Alpha processor, compared to about 152 h for all-atom simulations with implicit solvent. It can be concluded that the UNRES/MD approach will enable us to carry out microsecond and, possibly, millisecond simulations of protein folding and, consequently, of the folding process of proteins in real time.

Myelination and its regenerative counterpart remyelination represent one of the most complex cell-cell interactions in the central nervous system (CNS). The biochemical regulation of axon myelination via the proliferation, migration, and differentiation of oligodendrocyte progenitor cells (OPCs) has been characterized extensively. However, most biochemical analysis has been conducted in vitro on OPCs adhered to substrata of stiffness that is orders of magnitude greater than that of the in vivo CNS environment. Little is known of how variation in mechanical properties over the physiological range affects OPC biology. Here, we show that OPCs are mechanosensitive. Cell survival, proliferation, migration, and differentiation capacity in vitro depend on the mechanical stiffness of polymer hydrogel substrata. Most of these properties are optimal at the intermediate values of CNS tissue stiffness. Moreover, many of these properties measured for cells on gels of optimal stiffness differed significantly from those measured on glass or polystyrene. The dependence of OPC differentiation on the mechanical properties of the extracellular environment provides motivation to revisit results obtained on nonphysiological, rigid surfaces. We also find that OPCs stiffen upon differentiation, but that they do not change their compliance in response to substratum stiffness, which is similar to embryonic stem cells, but different from adult stem cells. These results form the basis for further investigations into the mechanobiology of cell function in the CNS and may specifically shed new light on the failure of remyelination in chronic demyelinating diseases such as multiple sclerosis.

Recent improvements in the protein-structure prediction method developed in our laboratory, based on the thermodynamic hypothesis, are described. The conformational space is searched extensively at the united-residue level by using our physics-based UNRES energy function and the conformational space annealing method of global optimization. The lowest-energy coarse-grained structures are then converted to an all-atom representation and energyminimized with the ECEPP͞3 force field. The procedure was assessed in two recent blind tests of protein-structure prediction. During the first blind test, we predicted large fragments of ␣ and ␣؉␤ proteins [60 -70 residues with C ␣ rms deviation (rmsd) <6 Å]. However, for ␣؉␤ proteins, significant topological errors occurred despite low rmsd values. In the second exercise, we predicted whole structures of five proteins (two ␣ and three ␣؉␤, with sizes of 53-235 residues) with remarkably good accuracy. In particular, for the genomic target TM0487 (a 102-residue ␣؉␤ protein from Thermotoga maritima), we predicted the complete, topologically correct structure with 7.3-Å C ␣ rmsd. So far this protein is the largest ␣؉␤ protein predicted based solely on the amino acid sequence and a physics-based potential-energy function and search procedure. For target T0198, a phosphate transport system regulator PhoU from T. maritima (a 235-residue mainly ␣-helical protein), we predicted the topology of the whole six-helix bundle correctly within 8 Å rmsd, except the 32 C-terminal residues, most of which form a ␤-hairpin. These and other examples described in this work demonstrate significant progress in physics-based protein-structure prediction.global optimization ͉ thermodynamic hypothesis T o date, the great majority of successful algorithms for proteinstructure prediction are knowledge-based approaches; they make explicit use of homology modeling (1, 2) or fold recognition methods (2-6). This feature even pertains to most of the methods considered as ab initio (7,8), which, in theory, should not make explicit use of structural databases. However, in-depth understanding of the physical principles of formation of protein structure requires the development of physics-based methods for proteinstructure prediction (9). Moreover, such methods will be independent of structural databases used in the training of knowledgebased methods. Furthermore, physics-based methods will enable us to study the structures of proteins that seem to possess a degenerate native state, such as the prion proteins, to simulate protein-folding pathways, to understand the mechanisms of protein folding, and to study interactions of proteins with other biomacromolecules and their assemblies (e.g., nucleic acids, polysaccharides, lipids, etc.). The underlying principle of physics-based methods for proteinstructure prediction is Anfinsen's thermodynamic hypothesis (10), according to which protein molecules adopt the conformations that are the global minima of their potential-energy surfaces. The methods based on this hypoth...