Cheng-Wen Liu

From thermodynamics to kinetics: enhanced sampling of rare events.

Despite great advances in molecular dynamics simulations, there remain large gaps between the simulations and experimental observations in terms of the time and length scales that can be approached. Developing fast and accurate algorithms and methods is of ultimate importance to bridge these gaps. In this Account, we briefly summarize recent efforts in such directions. In particular, we focus on integrated tempering sampling. The efficiency of this sampling method has been demonstrated by applications to a range of chemical and biological problems: protein folding, molecular cluster structure searches, and chemical reactions. The combination of integrated tempering sampling and a trajectory sampling method allows the calculation of rate constants and reaction pathways without predefined collective coordinates.

Inhibitory Mechanism of Caspase-6 Phosphorylation Revealed by Crystal Structures, Molecular Dynamics Simulations, and Biochemical Assays

Background: Caspase-6 is a drug target against neurodegenerative diseases and is suppressed by phosphorylation at Ser257. Results: S257E mutation inhibits caspase-6 activation by locking the protein in the “inhibited state” and inhibits caspase-6 activity by steric hindrance. Conclusion: Phosphorylation inhibits caspase-6 through the same mechanism. Significance: The study revealed the inhibition mechanism of caspase-6 phosphorylation and provided new strategies for drug discovery. The apoptotic effector caspase-6 (CASP6) has been clearly identified as a drug target due to its strong association with neurodegeneration and axonal pruning events as well as its crucial roles in Huntington disease and Alzheimer disease. CASP6 activity is suppressed by ARK5-mediated phosphorylation at Ser257 with an unclear mechanism. In this work, we solved crystal structures of ΔproCASP6S257E and p20/p10S257E, which mimicked the phosphorylated CASP6 zymogen and activated CASP6, respectively. The structural investigation combined with extensive biochemical assay and molecular dynamics simulation studies revealed that phosphorylation on Ser257 inhibited self-activation of CASP6 zymogen by “locking” the enzyme in the TEVD193-bound “inhibited state.” The structural and biochemical results also showed that phosphorylation on Ser257 inhibited the CASP6 activity by steric hindrance. These results disclosed the inhibition mechanism of CASP6 phosphorylation and laid the foundation for a new strategy of rational CASP6 drug design.

Photoelectron Spectroscopy and ab initio Calculations of Li(H2O)n– and Cs(H2O)n– (n = 1–6) Clusters

The Li(H2O)n(-) and Cs(H2O)n(-) (n = 0-6) clusters were studied using anion photoelectron spectroscopy combined with ab initio calculations. It was found that Li tends to be surrounded by water molecules with no water-water H-bonds being formed in the first hydration shell; while Cs sticks on the surface of water-water H-bonds network. The Li atom in its anionic or neutral state is surrounded by four water molecules through Li-O interactions within the first hydration shell; while the case of Cs is different. For the anionic Cs(H2O)n(-) clusters, two types of structures, namely H-end and O-end structures, were identified, with nearly degenerate energies. For the neutral Cs(H2O)n clusters, only O-end structures exist and the first hydration shell of the Cs atom has four water molecules. The different hydration nature of Li and Cs atoms can be ascribed to the delicate balance between the alkali metal-water interactions and the water-water interactions as well as the effect of excess electron.

Emergence of Solvent-Separated Na+–Cl– Ion Pair in Salt Water: Photoelectron Spectroscopy and Theoretical Calculations

Solvation of salts in water is a fundamental physical chemical process, but the underlying mechanism remains unclear. We investigated the contact ion pair (CIP) to solvent-separated ion pair (SSIP) transition in NaCl(H2O)n clusters with anion photoelectron spectroscopy and ab initio calculations. It is found that the SSIP type of structures show up at n = 2 for NaCl-(H2O)n anions. For neutral NaCl(H2O)n, the CIP structures are dominant at n < 9. At n = 9-12, the CIP structures and SSIP structures of NaCl(H2O)n are nearly degenerate in energy, coincident to the H2O:NaCl molar ratio of NaCl saturated solution and implying that the CIP and SSIP structures can coexist in concentrated solutions. These results are useful for understanding the solvation of salts at the molecular level.

Capturing Many-Body Interactions with Classical Dipole Induction Models

The nonadditive many-body interactions are significant for structural and thermodynamic properties of condensed phase systems. In this work we examined the many-body interaction energy of a large number of common organic/biochemical molecular clusters, which consist of 18 chemical species and cover nine common organic elements, using the Møller–Plesset perturbation theory to the second order (MP2) [Møller et al. Phys. Rev.1934, 46, 618.]. We evaluated the capability of Thole-based dipole induction models to capture the many-body interaction energy. Three models were compared: the original model and parameters used by the AMOEBA force field, a variation of this original model where the damping parameters have been reoptimized to MP2 data, and a third model where the damping function form applied to the permanent electric field is modified. Overall, we find the simple classical atomic dipole models are able to capture the 3- and 4-body interaction energy across a wide variety of organic molecules in various intermolecular configurations. With modified Thole models, it is possible to further improve the agreement with MP2 results. These models were also tested on systems containing metal/halogen ions to examine the accuracy and transferability. This work suggests that the form of damping function applied to the permanent electrostatic field strongly affects the distance dependence of polarization energy at short intermolecular separations.

Study of interactions between metal ions and protein model compounds by energy decomposition analyses and the AMOEBA force field

The interactions between metal ions and proteins are ubiquitous in biology. The selective binding of metal ions has a variety of regulatory functions. Therefore, there is a need to understand the mechanism of protein-ion binding. The interactions involving metal ions are complicated in nature, where short-range charge-penetration, charge transfer, polarization, and many-body effects all contribute significantly, and a quantitative description of all these interactions is lacking. In addition, it is unclear how well current polarizable force fields can capture these energy terms and whether these polarization models are good enough to describe the many-body effects. In this work, two energy decomposition methods, absolutely localized molecular orbitals and symmetry-adapted perturbation theory, were utilized to study the interactions between Mg2+/Ca2+ and model compounds for amino acids. Comparison of individual interaction components revealed that while there are significant charge-penetration and charge-transfer effects in Ca complexes, these effects can be captured by the van der Waals (vdW) term in the AMOEBA force field. The electrostatic interaction in Mg complexes is well described by AMOEBA since the charge penetration is small, but the distance-dependent polarization energy is problematic. Many-body effects were shown to be important for protein-ion binding. In the absence of many-body effects, highly charged binding pockets will be over-stabilized, and the pockets will always favor Mg and thus lose selectivity. Therefore, many-body effects must be incorporated in the force field in order to predict the structure and energetics of metalloproteins. Also, the many-body effects of charge transfer in Ca complexes were found to be non-negligible. The absorption of charge-transfer energy into the additive vdW term was a main source of error for the AMOEBA many-body interaction energies.

Many-body effect determines the selectivity for Ca2+ and Mg2+ in proteins

Significance Metal ions have important biological functions and are associated with diseases including cancer and neurodegenerative disorders. The fundamental question of metal ion selectivity in proteins has received continued interest over the past decades. Compared with Na+/K+, the selectivity for Mg2+/Ca2+ is less well understood. Although Mg2+ is a better charge acceptor, calcium-binding proteins with highly charged binding pockets can selectively bind Ca2+ against a much higher concentration of Mg2+. Here we show that this selectivity is dictated by the many-body polarization effect, which is a cost arising from the dense packing of multiple residues around the metal ion. By combining geometric constraint and the many-body effect, it is possible to fine-tune the selectivity for metal ions of different sizes. Calcium ion is a versatile messenger in many cell-signaling processes. To achieve their functions, calcium-binding proteins selectively bind Ca2+ against a background of competing ions such as Mg2+. The high specificity of calcium-binding proteins has been intriguing since Mg2+ has a higher charge density than Ca2+ and is expected to bind more tightly to the carboxylate groups in calcium-binding pockets. Here, we showed that the specificity for Ca2+ is dictated by the many-body polarization effect, which is an energetic cost arising from the dense packing of multiple residues around the metal ion. Since polarization has stronger distance dependence compared with permanent electrostatics, the cost associated with the smaller Mg2+ is much higher than that with Ca2+ and outweighs the electrostatic attraction favorable for Mg2+. With the AMOEBA (atomic multipole optimized energetics for biomolecular simulation) polarizable force field, our simulations captured the relative binding free energy between Ca2+ and Mg2+ for proteins with various types of binding pockets and explained the nonmonotonic size dependence of the binding free energy in EF-hand proteins. Without electronic polarization, the smaller ions are always favored over larger ions and the relative binding free energy is roughly proportional to the net charge of the pocket. The many-body effect depends on both the number and the arrangement of charged residues. Fine-tuning of the ion selectivity could be achieved by combining the many-body effect and geometric constraint.

Elucidating the Phosphate Binding Mode of Phosphate-Binding Protein: The Critical Effect of Buffer Solution

Phosphate is an essential component of cell functions, and the specific transport of phosphorus into a cell is mediated by phosphate-binding protein (PBP). The mechanism of PBP-phosphate recognition remains controversial: on the basis of similar binding affinities at acidic and basic pHs, it is believed that the hydrogen network in the binding site is flexible to adapt to different protonation states of phosphates. However, only hydrogen (1H) phosphate was observed in the sub-angstrom X-ray structures. To address this inconsistency, we performed molecular dynamics simulations using the AMOEBA polarizable force field. Structural and free energy data from simulations suggested that 1H phosphate was the preferred bound form at both pHs. The binding of dihydrogen (2H) phosphate disrupted the hydrogen-bond network in the PBP pocket, and the computed affinity was much weaker than that of 1H phosphate. Furthermore, we showed that the discrepancy in the studies described above is resolved if the interaction between phosphate and the buffer agent is taken into account. The calculated apparent binding affinities are in excellent agreement with experimental measurements. Our results suggest the high specificity of PBP for 1H phosphate and highlight the importance of the buffer solution for the binding of highly charged ligands.

Molecular dynamics simulation, ab initio calculation, and size-selected anion photoelectron spectroscopy study of initial hydration processes of calcium chloride

To understand the initial hydration processes of CaCl2, we performed molecular simulations employing the force field based on the theory of electronic continuum correction with rescaling. Integrated tempering sampling molecular dynamics were combined with ab initio calculations to overcome the sampling challenge in cluster structure search and refinement. The calculated vertical detachment energies of CaCl2(H2O)n- (n = 0-8) were compared with the values obtained from photoelectron spectra, and consistency was found between the experiment and computation. Separation of the Cl-Ca ion pair is investigated in CaCl2(H2O)n- anions, where the first Ca-Cl ionic bond required 4 water molecules, and both Ca-Cl bonds are broken when the number of water molecules is larger than 7. For neutral CaCl2(H2O)n clusters, breaking of the first Ca-Cl bond starts at n = 5, and 8 water molecules are not enough to separate the two ion pairs. Comparing with the observations on magnesium chloride, it shows that separating one ion pair in CaCl2(H2O)n requires fewer water molecules than those for MgCl2(H2O)n. Coincidentally, the solubility of calcium chloride is higher than that of magnesium chloride in bulk solutions.

A physically grounded damped dispersion model with particle mesh Ewald summation

Accurate modeling of dispersion is critical to the goal of predictive biomolecular simulations. To achieve this accuracy, a model must be able to correctly capture both the short-range and asymptotic behavior of dispersion interactions. We present here a damped dispersion model based on the overlap of charge densities that correctly captures both regimes. The overlap damped dispersion model represents a classical physical interpretation of dispersion: the interaction between the instantaneous induced dipoles of two distinct charge distributions. This model is shown to be an excellent fit with symmetry adapted perturbation theory dispersion energy calculations, yielding an RMS error on the S101x7 database of 0.5 kcal/mol. Moreover, the damping function used in this model is wholly derived and parameterized from the electrostatic dipole-dipole interaction, making it not only physically grounded but transferable as well.