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...

Parametrization and testing of a new all-atom force field for organic molecules and peptides with fixed bond lengths and bond angles are described. The van der Waals parameters for both the organic molecules and the peptides were taken from J. Phys. Chem. B 2003, 107, 7143 and J. Phys. Chem. B 2004, 108, 12181. First, the values of the 1-4 nonbonded and electrostatic scale factors appropriate to the new force field were determined by computing the conformational energies of six model molecules, namely, ethanol, ethylamine, propanol, propylamine, 1,2-ethanediol, and 1,3-propanediol with different values of these factors. The partial atomic charges of these molecules were obtained by fitting to the electrostatic potentials calculated with the HF/6-31G quantum-mechanical method. Two different charge models (single- and multiple-conformation-derived) were also considered. We demonstrated that the charge model has a stronger effect on the conformational energies than the 1-4 scaling. The choice of a charge model affected the conformational energies of even the smallest molecules considered, whereas the effect of the 1-4 electrostatic or nonbonded scaling was apparent only for 1,3-propanediol. The best agreement with high-level ab initio data was obtained with the multiple-conformation-derived charges and with no scaling of the 1-4 nonbonded or electrostatic interactions (scale factors of 1.0). Next, the torsional parameters of a large number of neutral and charged organic molecules, assumed to be models of the side chains of the 20 naturally occurring amino acids, were computed by fitting to rotational energy profiles obtained from ab initio MP2/6-31G calculations. The quality of the fits was high with average errors for torsional profiles of less than 0.2 kcal/mol. To derive the torsional parameters for the peptide backbone, the partial atomic charges of the 20 neutral and charged amino acids were obtained by fitting to the electrostatic potentials of terminally blocked amino acids using the HF/6-31G quantum-mechanical method. Then, the phi-psi energy maps of Ac-Ala-NMe and Ac-Gly-NMe were computed using MP2/6-31G//HF/6-31G quantum-mechanical methods. The phi-psi energy map of Ac-Ala-NMe was used for refinement of the nonbonded parameters for the backbone nitrogen and hydrogen bonded to it. Subsequently, the main-chain torsional parameters were obtained by fitting the molecular mechanics energies to the phi-psi energy maps of Ac-Ala-NMe and Ac-Gly-NMe. The transferability of the entire force field was demonstrated by reproducing the main energy minima of terminally blocked Ala3 from the literature. The performance of the force field was also evaluated by simulating crystal structures of small peptides. By comparison of simulated and experimental data, examination of the torsional-angle and atom-positional root-mean-square deviations of the energy-minimized crystal structures from the corresponding X-ray model structures demonstrated high accuracy of the force field.

The N-terminal cysteine-rich somatomedin B (SMB) domain (residues 1-44) of the human glycoprotein vitronectin contains the high-affinity binding sites for plasminogen activator inhibitor-1 (PAI-1) and the urokinase receptor (uPAR). We previously showed that the eight cysteine residues of recombinant SMB (rSMB) are organized into four disulfide bonds in a linear uncrossed pattern (Cys(5)-Cys(9), Cys(19)-Cys(21), Cys(25)-Cys(31), and Cys(32)-Cys(39)). In the present study, we use an alternative method to show that this disulfide bond arrangement remains a major preferred one in solution, and we determine the solution structure of the domain using NMR analysis. The solution structure shows that the four disulfide bonds are tightly packed in the center of the domain, replacing the traditional hydrophobic core expected for a globular protein. The few noncysteine hydrophobic side chains form a cluster on the outside of the domain, providing a distinctive binding surface for the physiological partners PAI-1 and uPAR. The hydrophobic surface consists mainly of side chains from the loop formed by the Cys(25)-Cys(31) disulfide bond, and is surrounded by conserved acidic and basic side chains, which are likely to contribute to the specificity of the intermolecular interactions of this domain. Interestingly, the overall fold of the molecule is compatible with several arrangements of the disulfide bonds. A number of different disulfide bond arrangements were able to satisfy the NMR restraints, and an extensive series of conformational energy calculations performed in explicit solvent confirmed that several disulfide bond arrangements have comparable stabilization energies. An experimental demonstration of the presence of alternative disulfide conformations in active rSMB is provided by the behavior of a mutant in which Asn(14) is replaced by Met. This mutant has the same PAI-1 binding activity as rVN1-51, but its fragmentation pattern following cyanogen bromide treatment is incompatible with the linear uncrossed disulfide arrangement. These results suggest that active forms of the SMB domain may have a number of allowed disulfide bond arrangements as long as the Cys(25)-Cys(31) disulfide bond is preserved.

One of the greatest challenges in protein structure prediction is the refinement of low-resolution predicted models to high-resolution structures that are close to the native state. Although contemporary structure prediction methods can assemble the correct topology for a large fraction of protein domains, such approximate models are often not of the resolution required for many important applications, including studies of reaction mechanisms and virtual ligand screening. Thus, the development of a method that could bring those structures closer to the native state is of great importance. We recently optimized the relative weights of the components of the Amber ff03 potential on a large set of decoy structures to create a funnel-shaped energy landscape with the native structure at the global minimum. Such an energy function might be able to drive proteins toward their native structure. In this work, for a test set of 47 proteins, with 100 decoy structures per protein that have a range of structural similarities to the native state, we demonstrate that our optimized potential can drive protein models closer to their native structure. Comparing the lowest-energy structure from each trajectory with the starting decoy, structural improvement is seen for 70% of the models on average. The ability to do such systematic structural refinements by using a physicsbased all-atom potential represents a promising approach to highresolution structure prediction.Amber force field ͉ force field optimization ͉ protein structure prediction ͉ all-atom potential T he past several years have witnessed significant progress in the field of protein structure prediction (1-10), with contemporary methods being able to assemble the correct topology for a large fraction of protein domains. Such approximately correct models typically vary in their structural similarity to the native state, with a rmsd (root mean square deviation) from native that ranges from 1 Å to Ϸ6 Å. Models with a rmsd to native of 1-2 Å are comparable to experimentally obtained structures and can be used in a broad range of applications, including studies of reaction mechanisms and virtual ligand screening (2). In contrast, the range of applicability of lower-resolution models (with a 3-to 6-Å rmsd from native) is smaller (2). Structure prediction methods often use a coarse-grained protein representation to enhance the conformational search efficiency. To further improve model quality, it is possible that additional structural details need to be included. A tempting approach is to use an all-atom detailed protein representation for the final stages of structure prediction, but despite considerable effort, all-atom refinement has seen little success (11-13). Over the years, there have been individual examples of successful refinement (11-16), with the best improvement of Ϸ2 Å (12, 16) and the largest refinement benchmarks consisting of a small set of proteins (12,13,(17)(18)(19). Although isolated examples of refinement have been reported, the methods are far from routin...

Differentiation of oligodendrocyte progenitor cells (OPC) to oligodendrocytes and subsequent axon myelination are critical steps in vertebrate central nervous system (CNS) development and regeneration. Growing evidence supports the significance of mechanical factors in oligodendrocyte biology. Here, we explore the effect of mechanical strains within physiological range on OPC proliferation and differentiation, and strain-associated changes in chromatin structure, epigenetics, and gene expression. Sustained tensile strain of 10–15% inhibited OPC proliferation and promoted differentiation into oligodendrocytes. This response to strain required specific interactions of OPCs with extracellular matrix ligands. Applied strain induced changes in nuclear shape, chromatin organization, and resulted in enhanced histone deacetylation, consistent with increased oligodendrocyte differentiation. This response was concurrent with increased mRNA levels of the epigenetic modifier histone deacetylase Hdac11. Inhibition of HDAC proteins eliminated the strain-mediated increase of OPC differentiation, demonstrating a role of HDACs in mechanotransduction of strain to chromatin. RNA sequencing revealed global changes in gene expression associated with strain. Specifically, expression of multiple genes associated with oligodendrocyte differentiation and axon-oligodendrocyte interactions was increased, including cell surface ligands (Ncam, ephrins), cyto- and nucleo-skeleton genes (Fyn, actinins, myosin, nesprin, Sun1), transcription factors (Sox10, Zfp191, Nkx2.2), and myelin genes (Cnp, Plp, Mag). These findings show how mechanical strain can be transmitted to the nucleus to promote oligodendrocyte differentiation, and identify the global landscape of signaling pathways involved in mechanotransduction. These data provide a source of potential new therapeutic avenues to enhance OPC differentiation in vivo.

Myelination is critical for transduction of neuronal signals, neuron survival and normal function of the nervous system. Myelin disorders account for many debilitating neurological diseases such as multiple sclerosis and leukodystrophies. The lack of experimental models and tools to observe and manipulate this process in vitro has constrained progress in understanding and promoting myelination, and ultimately developing effective remyelination therapies. To address this problem, we developed synthetic mimics of neuronal axons, representing key geometric, mechanical, and surface chemistry components of biological axons. These artificial axons exhibit low mechanical stiffness approaching that of a human axon, over unsupported spans that facilitate engagement and wrapping by glial cells, to enable study of myelination in environments reflecting mechanical cues that neurons present in vivo. Our 3D printing approach provides the capacity to vary independently the complex features of the artificial axons that can reflect specific states of development, disease, or injury. Here, we demonstrate that oligodendrocytes’ production and wrapping of myelin depend on artificial axon stiffness, diameter, and ligand coating. This biofidelic platform provides direct visualization and quantification of myelin formation and myelinating cells’ response to both physical cues and pharmacological agents.