Tao Yu

Dynamics connect substrate recognition to catalysis in protein kinase A

Atomic resolution studies of protein kinases have traditionally been carried out in the inhibitory state, limiting our current knowledge on the mechanisms of substrate recognition and catalysis. Using NMR, X-ray crystallography and thermodynamic measurements, we analyzed the substrate recognition process of cAMP-dependent protein kinase (PKA), finding that entropy and protein dynamics play a prominent role. The nucleotide acts as a dynamic and allosteric activator by coupling the two lobes of apo PKA, enhancing the enzyme dynamics synchronously and priming it for catalysis. The formation of the ternary complex is entropically driven, and NMR spin relaxation data reveal that both substrate and PKA are dynamic in the closed state. Our results show that the enzyme toggles between open and closed states, which indicates that a conformational selection rather than an induced-fit mechanism governs substrate recognition.

Practical methods for including torsional anharmonicity in thermochemical calculations on complex molecules: the internal-coordinate multi-structural approximation.

Many methods for correcting harmonic partition functions for the presence of torsional motions employ some form of one-dimensional torsional treatment to replace the harmonic contribution of a specific normal mode. However, torsions are often strongly coupled to other degrees of freedom, especially other torsions and low-frequency bending motions, and this coupling can make assigning torsions to specific normal modes problematic. Here, we present a new class of methods, called multi-structural (MS) methods, that circumvents the need for such assignments by instead adjusting the harmonic results by torsional correction factors that are determined using internal coordinates. We present three versions of the MS method: (i) MS-AS based on including all structures (AS), i.e., all conformers generated by internal rotations; (ii) MS-ASCB based on all structures augmented with explicit conformational barrier (CB) information, i.e., including explicit calculations of all barrier heights for internal-rotation barriers between the conformers; and (iii) MS-RS based on including all conformers generated from a reference structure (RS) by independent torsions. In the MS-AS scheme, one has two options for obtaining the local periodicity parameters, one based on consideration of the nearly separable limit and one based on strongly coupled torsions. The latter involves assigning the local periodicities on the basis of Voronoi volumes. The methods are illustrated with calculations for ethanol, 1-butanol, and 1-pentyl radical as well as two one-dimensional torsional potentials. The MS-AS method is particularly interesting because it does not require any information about conformational barriers or about the paths that connect the various structures.

Energy landscapes and functions of supramolecular systems

By means of two supramolecular systems - peptide amphiphiles engaged in hydrogen-bonded β-sheets, and chromophore amphiphiles driven to assemble by π-orbital overlaps - we show that the minima in the energy landscapes of supramolecular systems are defined by electrostatic repulsion and the ability of the dominant attractive forces to trap molecules in thermodynamically unfavourable configurations. These competing interactions can be selectively switched on and off, with the order of doing so determining the position of the final product in the energy landscape. Within the same energy landscape, the peptide-amphiphile system forms a thermodynamically favoured product characterized by long bundled fibres that promote biological cell adhesion and survival, and a metastable product characterized by short monodisperse fibres that interfere with adhesion and can lead to cell death. Our findings suggest that, in supramolecular systems, function and energy landscape are linked, superseding the more traditional connection between molecular design and function.

Simultaneous covalent and noncovalent hybrid polymerizations

Doubling down on polymerization In biology, structural polymers such as cytoskeletal fibers assemble from covalently polymerized monomers through weaker supramolecular interactions such as hydrogen bonds. Yu et al. report the synthesis of cylindrical fibers when three monomers react, two covalently and one in a supramolecular fashion. When the reaction proceeded stepwise, lower-molecular-weight flat tapes formed instead, which suggests that supramolecular interactions helped to catalyze the covalent polymerization. Science, this issue p. 497 Cylindrical fibers of uniform diameter form after simultaneous covalent and supramolecular polymerization reactions. Covalent and supramolecular polymers are two distinct forms of soft matter, composed of long chains of covalently and noncovalently linked structural units, respectively. We report a hybrid system formed by simultaneous covalent and supramolecular polymerizations of monomers. The process yields cylindrical fibers of uniform diameter that contain covalent and supramolecular compartments, a morphology not observed when the two polymers are formed independently. The covalent polymer has a rigid aromatic imine backbone with helicoidal conformation, and its alkylated peptide side chains are structurally identical to the monomer molecules of supramolecular polymers. In the hybrid system, covalent chains grow to higher average molar mass relative to chains formed via the same polymerization in the absence of a supramolecular compartment. The supramolecular compartments can be reversibly removed and re-formed to reconstitute the hybrid structure, suggesting soft materials with novel delivery or repair functions.

Multi-structural variational transition state theory. Kinetics of the 1,4-hydrogen shift isomerization of the pentyl radical with torsional anharmonicity

We present a new formulation of variational transition state theory (VTST) called multi-structural VTST (MS-VTST) and the use of this to calculate the rate constant for the 1,4-hydrogen shift isomerization reaction of 1-pentyl radical and that for the reverse reaction. MS-VTST uses a multi-faceted dividing surface and provides a convenient way to include the contributions of many structures (typically conformers) of the reactant and the transition state in rate constant calculations. In this particular application, we also account for the torsional anharmonicity. We used the multi-configuration Shepard interpolation method to efficiently generate a semi-global portion of the potential energy surface from a small number of high-level electronic structure calculations using the M06 density functional in order to compute the energies and Hessians of Shepard points along a reaction path. The M06-2X density functional was used to calculate the multi-structural anharmonicity effect, including all of the structures of the reactant, product and transition state. To predict the thermal rate constant, VTST calculations were performed to obtain the canonical variational rate constant over the temperature range 200–2000 K. A transmission coefficient is calculated by the multidimensional small-curvature tunneling (SCT) approximation. The final MS-CVT/SCT thermal rate constant was determined by combining a reaction rate calculation in the single-structural harmonic oscillator approximation (including tunneling) with the multi-structural anharmonicity torsional factor. The calculated forward rate constant agrees very well with experimentally-based evaluations of the high-pressure limit for the temperature range 300–1300 K, although it is a factor of 2.5–3.0 lower than the single-structural harmonic oscillator approximation over this temperature range. We anticipate that MS-VTST will be generally useful for calculating the reaction rates of complex molecules with multiple torsions.

cAMP-Dependent Protein Kinase A Selects the Excited State of the Membrane Substrate Phospholamban

Phosphorylation of membrane proteins is a central regulatory and signaling mechanism across cell compartments. However, the recognition process and phosphorylation mechanism of membrane-bound substrates by kinases are virtually unknown. cAMP-dependent protein kinase A (PKA) is a ubiquitous enzyme that phosphorylates several soluble and membrane-bound substrates. In cardiomyocytes, PKA targets phospholamban (PLN), a membrane protein that inhibits the sarcoplasmic reticulum Ca(2+)-ATPase (SERCA). In the unphosphorylated state, PLN binds SERCA, reducing the calcium uptake and generating muscle contraction. PKA phosphorylation of PLN at S16 in the cytoplasmic helix relieves SERCA inhibition, initiating muscle relaxation. Using steady-state kinetic assays, NMR spectroscopy, and molecular modeling, we show that PKA recognizes and phosphorylates the excited, membrane-detached R-state of PLN. By promoting PLN from a ground state to an excited state, we obtained a linear relationship between rate of phosphorylation and population of the excited state of PLN. The conformational equilibrium of PLN is crucial to regulate the extent of PLN phosphorylation and SERCA inhibition.

Multipath Variational Transition State Theory: Rate Constant of the 1,4-Hydrogen Shift Isomerization of the 2-Cyclohexylethyl Radical

We propose a new formulation of variational transition state theory called multipath variational transition state theory (MP-VTST). We employ this new formulation to calculate the forward and reverse thermal rate constant of the 1,4-hydrogen shift isomerization of the 2-cyclohexylethyl radical in the gas phase. First, we find and optimize all the local-minimum-energy structures of the reaction, product, and transition state. Then, for the lowest-energy transition state structures, we calculate the reaction path by using multiconfiguration Shepard interpolation (MSCI) method to represent the potential energy surface, and, from this representation, we also calculate the ground-state vibrationally adiabatic potential energy curve, the reaction-path curvature vector, and the generalized free energy of activation profile. With this information, the path-averaged generalized transmission coefficients are evaluated. Then, thermal rate constant containing the multiple-structure anharmonicity and torsional anharmonicity effects is calculated using multistructural transition state theory (MS-TST). The final MP-VTST thermal rate constant is obtained by multiplying k(MS-T)(MS-TST) by . In these calculations, the M06 density functional is utilized to compute the energy, gradient, and Hessian at the Shepard points, and the M06-2X density functional is used to obtain the structures (conformers) of the reactant, product, and the saddle point for computing the multistructural anharmonicity factors.

Steered molecular dynamics studies of the potential of mean force for peptide amphiphile self-assembly into cylindrical nanofibers.

Steered molecular dynamics (SMD) simulations were applied to determine the potential of mean force for the self-assembly of peptide amphiphile (PA) nanofibers, specifically considering a single PA adding to a growing cylindrical nanofiber at 310 K. It is found that the free energy, enthalpy, and entropy differences for this assembly process are -67 kcal/mol, -71.5 kcal/ml, and -14.5 cal/(mol K), respectively, and therefore that enthalpy provides the driving force for self-assembly to form a fiber. A pairwise interaction analysis shows that both electrostatic and van der Waals interactions play important roles in the self-assembly process, with the van der Waals interaction being the larger effect. The mechanistic picture that emerges from this work is that as the PA is pulled from the fiber, the interaction evolves through three stages: (1) initially electrostatic interactions between the charged head of the pulled PA and other PAs, and between the pulled PA and solvent are dominant, (2) after the charged head emerges, the rest of the peptide comes out, with both PA-solvent electrostatic interactions and van der Waals interactions being significant, and (3) in the last step, the alkane tail emerges, dominated by van der Waals interactions with either peptide or solvent.

Biofuel combustion. Energetics and kinetics of hydrogen abstraction from carbon-1 in n-butanol by the hydroperoxyl radical calculated by coupled cluster and density functional theories and multistructural variational transition-state theory with multidimensional tunneling.

Multistructural canonical variational transition-state theory with small-curvature multidimensional tunneling (MS-CVT/SCT) is employed to calculate thermal rate constants for hydrogen-atom abstraction from carbon-1 of n-butanol by the hydroperoxyl radical over the temperature range 250-2000 K. The M08-SO hybrid meta-GGA density functional was validated against CCSD(T)-F12a explicitly correlated wave function calculations with the jul-cc-pVTZ basis set. It was then used to compute the properties of all stationary points and the energies and Hessians of a few nonstationary points along the reaction path, which were then used to generate a potential energy surface by the multiconfiguration Shepard interpolation (MCSI) method. The internal rotations in the transition state for this reaction (like those in the reactant alcohol) are strongly coupled to each other and generate multiple stable conformations, which make important contributions to the partition functions. It is shown that neglecting to account for the multiple-structure effects and torsional potential anharmonicity effects that arise from the torsional modes would lead to order-of-magnitude errors in the calculated rate constants at temperatures of interest in combustion.

Dependence of Vibronic Coupling on Molecular Geometry and Environment: Bridging Hydrogen Atom Transfer and Electron-Proton Transfer.

The rate constants for typical concerted proton-coupled electron transfer (PCET) reactions depend on the vibronic coupling between the diabatic reactant and product states. The form of the vibronic coupling is different for electronically adiabatic and nonadiabatic reactions, which are associated with hydrogen atom transfer (HAT) and electron–proton transfer (EPT) mechanisms, respectively. Most PCET rate constant expressions rely on the Condon approximation, which assumes that the vibronic coupling is independent of the nuclear coordinates of the solute and the solvent or protein. Herein we test the Condon approximation for PCET vibronic couplings. The dependence of the vibronic coupling on molecular geometry is investigated for an open and a stacked transition state geometry of the phenoxyl-phenol self-exchange reaction. The calculations indicate that the open geometry is electronically nonadiabatic, corresponding to an EPT mechanism that involves significant electronic charge redistribution, while the stacked geometry is predominantly electronically adiabatic, corresponding primarily to an HAT mechanism. Consequently, a single molecular system can exhibit both HAT and EPT character. The dependence of the vibronic coupling on the solvent or protein configuration is examined for the soybean lipoxygenase enzyme. The calculations indicate that this PCET reaction is electronically nonadiabatic with a vibronic coupling that does not depend significantly on the protein environment. Thus, the Condon approximation is shown to be valid for the solvent and protein nuclear coordinates but invalid for the solute nuclear coordinates in certain PCET systems. These results have significant implications for the calculation of rate constants, as well as mechanistic interpretations, of PCET reactions.