Monte Carlo simulations of single- and multistep enzyme-catalyzed reaction sequences: effects of diffusion, cell size, enzyme fluctuations, colocalization, and segregation

Following the discovery of slow fluctuations in the catalytic activity of an enzyme in single-molecule experiments, it has been shown that the classical Michaelis-Menten (MM) equation relating the average enzymatic velocity and the substrate concentration may hold even for slowly fluctuating enzymes. In many cases, the average velocity is that given by the MM equation with time-averaged values of the fluctuating rate constants and the effect of enzyme fluctuations is simply averaged out. The situation is quite different for a sequence of reactions. For colocalization of a pair of enzymes in a sequence to be effective in promoting reaction, the second must be active when the first is active or soon after. If the enzymes are slowly varying and only rarely active, the product of the first reaction may diffuse away before the second enzyme is active, and colocalization may have little value. Even for single-step reactions the interplay of reaction and diffusion with enzyme fluctuations leads to added complexities, but for multistep reactions the interplay of reaction and diffusion, cell size, compartmentalization, enzyme fluctuations, colocalization, and segregation is far more complex than for single-step reactions. In this paper, we report the use of stochastic simulations at the level of whole cells to explore, understand, and predict the behavior of single- and multistep enzyme-catalyzed reaction systems exhibiting some of these complexities. Results for single-step reactions confirm several earlier observations by others. The MM relationship, with altered constants, is found to hold for single-step reactions slowed by diffusion. For single-step reactions, the distribution of enzymes in a regular grid is slightly more effective than a random distribution. Fluctuations of enzyme activity, with average activity fixed, have no observed effects for simple single-step reactions slowed by diffusion. Two-step sequential reactions are seen to be slowed by segregation of the enzymes for each step, and results of the calculations suggest limits for cell size. Colocalization of enzymes for a two-step sequence is seen to promote reaction, and rates fall rapidly with increasing distance between enzymes. Low frequency fluctuations of the activities of colocalized enzymes, with average activities fixed, can greatly reduce reaction rates for sequential reactions.

Linear-scaling method for calculating nuclear magnetic resonance chemical shifts using gauge-including atomic orbitals within Hartree-Fock and density-functional theory

Details of a new density matrix-based formulation for calculating nuclear magnetic resonance chemical shifts at both Hartree-Fock and density functional theory levels are presented. For systems with a nonvanishing highest occupied molecular orbital-lowest unoccupied molecular orbital gap, the method allows us to reduce the asymptotic scaling order of the computational effort from cubic to linear, so that molecular systems with 1000 and more atoms can be tackled with today's computers. The key feature is a reformulation of the coupled-perturbed self-consistent field (CPSCF) theory in terms of the one-particle density matrix (D-CPSCF), which avoids entirely the use of canonical MOs. By means of a direct solution for the required perturbed density matrices and the adaptation of linear-scaling integral contraction schemes, the overall scaling of the computational effort is reduced to linear. A particular focus of our formulation is to ensure numerical stability when sparse-algebra routines are used to obtain an overall linear-scaling behavior.

Helical Packing of Discotic Hexaphenyl Hexa-peri-hexabenzocoronenes: Theory and Experiment

The arrangement of discotic hexa-peri-hexabenzocoronenes (HBCs) into columnar helical superstructures has been investigated in relation to their molecular architecture. The supramolecular structure of two hexaphenyl-substituted HBC derivatives, differing only in the chiral/achiral nature of the attached alkyl side chains, was studied by circular dichroism and temperature-dependent wide-angle X-ray diffraction on oriented filaments. A structural model in agreement with the experimental observations was developed on the basis of accompanying quantum-chemical calculations. The helical organization along the self-assembled columnar structures was induced by the steric requirements of the bulky phenyl rings near the aromatic core, i.e., by their rotation out-of-plane with respect to the aromatic core. On the other hand, a uniform handedness of the twist was generated by chiral alkyl substituents. At higher temperatures the degree of helical organization decreases due to lateral and longitudinal dynamics of the discotic molecules. Annealing at ambient conditions improved the long-range arrangement of the discs along the columnar structures. This reorganization indicated a self-healing of the plastic material which is desirable for application of discotics as active layers in electronic devices. The helical packing resulted in a considerable stability of the mesophase up to 500 degrees C, which has not been reported for a discotic so far.

Structure of Molecular Tweezer Complexes in the Solid State: NMR Experiments, X-ray Investigations, and Quantum Chemical Calculations

The structure of supramolecular complexes formed by a naphthalene-spaced tweezer molecule as host and 1,4-dicyanobenzene (DCNB), 1,2,4,5-tetracyanobenzene (TCNB), and 7,7,8,8-tetracyano-p-quinodimethane (TCNQ) as aromatic, electron-deficient guests is investigated by solid-state NMR and X-ray diffraction measurements. Quantum chemical calculations using linear scaling methods are applied to predict and to assign the 1H NMR chemical shifts of the complexes. By combining experiment and theory, insights into intra- and intermolecular effects influencing the proton chemical shifts of the host-guest system are provided in the solid state.

Molecular recognition in molecular tweezers systems: quantum-chemical calculation of NMR chemical shifts

Quantum-chemical calculations for molecular tweezers systems are presented, where the focus is not only on the recognition process in the host-guest systems, but on the self aggregation of the tweezers host as well. Such intermolecular interactions influence the corresponding NMR spectra strongly by up to 6 ppm for proton chemical shifts, since ring-current effects are particularly important. The quantum-chemical results allow one to reliably assign the spectra and to gain information both on the structure and on the importance of intra- and intermolecular interactions. In addition, we study the accuracy of a variety of density functionals for describing the present host-guest systems, where we observe a considerable underestimation of ring-current effects on (1)H NMR chemical shifts at the density functional theory (DFT) level using smaller basis sets such as 6-31G**, so that larger bases like TZP are required. This stands in contrast to the behavior of the Hartree-Fock scheme, where small basis sets, such as 6-31G**, provide reliable (1)H NMR shieldings for molecular tweezers systems.

Advances in methods and algorithms in a modern quantum chemistry program package

Advances in theory and algorithms for electronic structure calculations must be incorporated into program packages to enable them to become routinely used by the broader chemical community. This work reviews advances made over the past five years or so that constitute the major improvements contained in a new release of the Q-Chem quantum chemistry package, together with illustrative timings and applications. Specific developments discussed include fast methods for density functional theory calculations, linear scaling evaluation of energies, NMR chemical shifts and electric properties, fast auxiliary basis function methods for correlated energies and gradients, equation-of-motion coupled cluster methods for ground and excited states, geminal wavefunctions, embedding methods and techniques for exploring potential energy surfaces.