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We have developed a new simulation algorithm for free-energy calculations. The method is a multidimensional extension of the replica-exchange method. While pairs of replicas with different temperatures are exchanged during the simulation in the original replica-exchange method, pairs of replicas with different temperatures and/or different parameters of the potential energy are exchanged in the new algorithm. This greatly enhances the sampling of the conformational space and allows accurate calculations of free energy in a wide temperature range from a single simulation run, using the weighted histogram analysis method.

In complex systems with many degrees of freedom such as peptides and proteins, there exists a huge number of local‐minimum‐energy states. Conventional simulations in the canonical ensemble are of little use, because they tend to get trapped in states of these energy local minima. A simulation in generalized ensemble performs a random walk in potential energy space and can overcome this difficulty. From only one simulation run, one can obtain canonical‐ensemble averages of physical quantities as functions of temperature by the single‐histogram and/or multiple‐histogram reweighting techniques. In this article we review uses of the generalized‐ensemble algorithms in biomolecular systems. Three well‐known methods, namely, multicanonical algorithm, simulated tempering, and replica‐exchange method, are described first. Both Monte Carlo and molecular dynamics versions of the algorithms are given. We then present three new generalized‐ensemble algorithms that combine the merits of the above methods. The effectiveness of the methods for molecular simulations in the protein folding problem is tested with short peptide systems. © 2001 John Wiley & Sons, Inc. Biopolymers (Pept Sci) 60: 96–123, 2001

Computer simulations are widely used to study molecular systems, especially in biology. As simulations have greatly increased in scale reaching cellular levels there are now significant challenges in managing, analyzing, and interpreting such data in comparison with experiments that are being discussed. Management challenges revolve around storing and sharing terabyte to petabyte scale data sets whereas the analysis of simulations of highly complex systems will increasingly require automated machine learning and artificial intelligence approaches. The comparison between simulations and experiments is furthermore complicated not just by the complexity of the data but also by difficulties in interpreting experiments for highly heterogeneous systems. As an example, the interpretation of NMR relaxation measurements and comparison with simulations for highly crowded systems is discussed.

Chem. Phys. Lett., in press. We propose two efficient algorithms for configurational sampling of systems with rough energy landscape. The first one is a new method for the determination of the multicanonical weight factor. In this method a short replica-exchange simulation is performed and the multicanonical weight factor is obtained by the multiple-histogram reweighting techniques. The second one is a further extension of the first in which a replica-exchange multicanonical simulation is performed with a small number of replicas. These new algorithms are particularly useful for studying the protein folding problem.

Proton-dependent oligopeptide transporters (POTs) are major facilitator superfamily (MFS) proteins that mediate the uptake of peptides and peptide-like molecules, using the inwardly directed H + gradient across the membrane. The human POT family transporter peptide transporter 1 is present in the brush border membrane of the small intestine and is involved in the uptake of nutrient peptides and drug molecules such as β-lactam antibiotics. Although previous studies have provided insight into the overall structure of the POT family transporters, the question of how transport is coupled to both peptide and H + binding remains unanswered. Here we report the high-resolution crystal structures of a bacterial POT family transporter, including its complex with a dipeptide analog, alafosfalin. These structures revealed the key mechanistic and functional roles for a conserved glutamate residue (Glu310) in the peptide binding site. Integrated structural, biochemical, and computational analyses suggested a mechanism for H + -coupled peptide symport in which protonated Glu310 first binds the carboxyl group of the peptide substrate. The deprotonation of Glu310 in the inward open state triggers the release of the bound peptide toward the intracellular space and salt bridge formation between Glu310 and Arg43 to induce the state transition to the occluded conformation.membrane transporter | molecular dynamics simulation | X-ray crystallography

Ca 2؉ -ATPase of sarcoplasmic reticulum is an ATP-powered Ca 2؉ pump but also a H ؉ pump in the opposite direction with no demonstrated functional role. Here, we report a 2.4-Å-resolution crystal structure of the Ca 2؉ -ATPase in the absence of Ca 2؉ stabilized by two inhibitors, dibutyldihydroxybenzene, which bridges two transmembrane helices, and thapsigargin, also bound in the membrane region. Now visualized are water and several phospholipid molecules, one of which occupies a cleft between two transmembrane helices. Atomic models of the Ca 2؉ binding sites with explicit hydrogens derived by continuum electrostatic calculations show how water and protons fill the space and compensate charge imbalance created by Ca 2؉ -release. They suggest that H ؉ countertransport is a consequence of a requirement for maintaining structural integrity of the empty Ca 2؉ -binding sites. For this reason, cation countertransport is probably mandatory for all P-type ATPases and possibly accompanies transport of water as well.2ϩ -ATPase of skeletal muscle sarcoplasmic reticulum (SERCA1a), an integral membrane protein consisting of 994 aa (1), transfers two Ca 2ϩ from the cytoplasm into the lumen of sarcoplasmic reticulum per ATP hydrolyzed and thereby establishes a Ͼ10 4 concentration gradient across the membrane (2). At the same time, Ca 2ϩ -ATPase pumps two or three H ϩ in the opposite direction (3-6) during the reaction cycle. According to the classical E1͞E2 theory (7-9), transmembrane ion-binding sites have high affinity for Ca 2ϩ and face the cytoplasm in E1, whereas they have low affinity and face the lumen of sarcoplasmic reticulum in E2. The opposite applies to H ϩ , which binds to the ATPase in E2 and dissociates in E1, presumably in exchange with Ca 2ϩ . As Na ϩ K ϩ -ATPase and gastric H ϩ K ϩ -ATPase countertransport K ϩ , instead of H ϩ , countertransport of monovalent cations may be a common feature of the P-type ATPase superfamily (2, 10), of which SERCA1a is the best-studied member (11,12). However, the sarcoplasmic reticulum membrane is leaky to monovalent cations including H ϩ (13). As has been pointed out before (14), the membrane potential and pH gradient must be minimized to achieve such a large concentration gradient of Ca 2ϩ . Therefore, the physiological role of H ϩ countertransport has been a puzzle. Although protonation of carboxyls in the Ca 2ϩ -binding site has been suggested from biochemical (15, 16) and mutagenesis studies (17, 18), crystal structures of SERCA1a in various states (19-24) did not clarify the role of countertransport or identify protonation sites.These questions, however, can be addressed computationally by calculating stabilization energy provided by H ϩ binding (25)(26)(27). Protonation probability of a particular residue is related directly to the free energy difference between protonated and unprotonated forms. Such calculations, therefore, should be able to identify residues likely to be protonated in crystal structures and were indeed successful (28) for a Ca 2ϩ -bound form [E1⅐2C...

Biological macromolecules function in highly crowded cellular environments. The structure and dynamics of proteins and nucleic acids are well characterized in vitro, but in vivo crowding effects remain unclear. Using molecular dynamics simulations of a comprehensive atomistic model cytoplasm we found that protein-protein interactions may destabilize native protein structures, whereas metabolite interactions may induce more compact states due to electrostatic screening. Protein-protein interactions also resulted in significant variations in reduced macromolecular diffusion under crowded conditions, while metabolites exhibited significant two-dimensional surface diffusion and altered protein-ligand binding that may reduce the effective concentration of metabolites and ligands in vivo. Metabolic enzymes showed weak non-specific association in cellular environments attributed to solvation and entropic effects. These effects are expected to have broad implications for the in vivo functioning of biomolecules. This work is a first step towards physically realistic in silico whole-cell models that connect molecular with cellular biology.DOI: http://dx.doi.org/10.7554/eLife.19274.001