Jiří Černý

Benchmark database of accurate (MP2 and CCSD(T) complete basis set limit) interaction energies of small model complexes, DNA base pairs, and amino acid pairs

MP2 and CCSD(T) complete basis set (CBS) limit interaction energies and geometries for more than 100 DNA base pairs, amino acid pairs and model complexes are for the first time presented together. Extrapolation to the CBS limit is done by using two-point extrapolation methods and different basis sets (aug-cc-pVDZ - aug-cc-pVTZ, aug-cc-pVTZ - aug-cc-pVQZ, cc-pVTZ - cc-pVQZ) are utilized. The CCSD(T) correction term, determined as a difference between CCSD(T) and MP2 interaction energies, is evaluated with smaller basis sets (6-31G** and cc-pVDZ). Two sets of complex geometries were used, optimized or experimental ones. The JSCH-2005 benchmark set, which is now available to the chemical community, can be used for testing lower-level computational methods. For the first screening the smaller training set (S22) containing 22 model complexes can be recommended. In this case larger basis sets were used for extrapolation to the CBS limit and also CCSD(T) and counterpoise-corrected MP2 optimized geometries were sometimes adopted.

Density functional theory augmented with an empirical dispersion term. Interaction energies and geometries of 80 noncovalent complexes compared with ab initio quantum mechanics calculations

Standard density functional theory (DFT) is augmented with a damped empirical dispersion term. The damping function is optimized on a small, well balanced set of 22 van der Waals (vdW) complexes and verified on a validation set of 58 vdW complexes. Both sets contain biologically relevant molecules such as nucleic acid bases. Results are in remarkable agreement with reference high‐level wave function data based on the CCSD(T) method. The geometries obtained by full gradient optimization are in very good agreement with the best available theoretical reference. In terms of the standard deviation and average errors, results including the empirical dispersion term are clearly superior to all pure density functionals investigated—B‐LYP, B3‐LYP, PBE, TPSS, TPSSh, and BH‐LYP—and even surpass the MP2/cc‐pVTZ method. The combination of empirical dispersion with the TPSS functional performs remarkably well. The most critical part of the empirical dispersion approach is the damping function. The damping parameters should be optimized for each density functional/basis set combination separately. To keep the method simple, we optimized mainly a single factor, sR, scaling globally the vdW radii. For good results, a basis set of at least triple‐ζ quality is required and diffuse functions are recommended, since the basis set superposition error seriously deteriorates the results. On average, the dispersion contribution to the interaction energy missing in the DFT functionals examined here is about 15 and 100% for the hydrogen‐bonded and stacked complexes considered, respectively.

On the Structure and Geometry of Biomolecular Binding Motifs (Hydrogen-Bonding, Stacking, X-H···π): WFT and DFT Calculations.

The strengths of noncovalent interactions are generally very sensitive to a number of geometric parameters. Among the most important of these parameters is the separation between the interacting moieties (in the case of an intermolecular interaction, this would be the intermolecular separation). Most works seeking to characterize the properties of intermolecular interactions are mainly concerned with binding energies obtained at the potential energy minimum (as determined at some particular level of theory). In this work, in order to extend our understanding of these types of noncovalent interactions, we investigate the distance dependence of several types of intermolecular interactions, these are hydrogen bonds, stacking interactions, dispersion interactions, and X-H···π interactions. There are several methods that have traditionally been used to treat noncovalent interactions as well as many new methods that have emerged within the past three or four years. Here we obtain reference data using estimated CCSD(T) values at the complete basis set limit (using the CBS(T) method); potential energy curves are also produced using several other methods thought to be accurate for intermolecular interactions, these are MP2/cc-pVTZ, MP2/aug-cc-pVDZ, MP2/6-31G*(0.25), SCS(MI)-MP2/cc-pVTZ, estimated MP2.5/CBS, DFT-SAPT/aug-cc-pVTZ, DFT/M06-2X/6-311+G(2df,2p), and DFT-D/TPSS/6-311++G(3df,3pd). The basis set superposition error is systematically considered throughout the study. It is found that the MP2.5 and DFT-SAPT methods, which are both quite computationally intensive, produce potential energy curves that are in very good agreement to those of the reference method. Among the MP2 techniques, which can be said to be of medium computational expense, the best results are obtained with MP2/cc-pVTZ and SCS(MI)-MP2/cc-pVTZ. DFT-D/TPSS/6-311++G(3df,3pd) is the DFT-based method that can be said to give the most well-balanced description of intermolecular interactions.

The X3LYP extended density functional accurately describes H-bonding but fails completely for stacking

The performance of the recently introduced X3LYP density functional which was claimed to significantly improve the accuracy for H-bonded and van der Waals complexes was tested for extended H-bonded and stacked complexes (nucleic acid base pairs and amino acid pairs). In the case of planar H-bonded complexes (guanine...cytosine, adenine...thymine) the DFT results nicely agree with accurate correlated ab initio results. For the stacked pairs (uracil dimer, cytosine dimer, adenine...thymine and guanine...cytosine) the DFT fails completely and it was even not able to localize any minimum at the stacked subspace of the potential energy surface. The geometry optimization of all these stacked clusters leads systematically to the planar H-bonded pairs. The amino acid pairs were investigated in the crystal geometry. DFT again strongly underestimates the accurate correlated ab initio stabilization energies and usually it was not able to describe the stabilization of a pair. The X3LYP functional thus behaves similarly to other current functionals. Stacking of nucleic acid bases as well as interaction of amino acids was described satisfactorily by using the tight-binding DFT method, which explicitly covers the London dispersion energy.

Increasing Affinity of Interferon-γReceptor 1 to Interferon-γby Computer-Aided Design

We describe a computer-based protocol to design protein mutations increasing binding affinity between ligand and its receptor. The method was applied to mutate interferon-γ receptor 1 (IFN-γ-Rx) to increase its affinity to natural ligand IFN-γ, protein important for innate immunity. We analyzed all four available crystal structures of the IFN-γ-Rx/IFN-γ complex to identify 40 receptor residues forming the interface with IFN-γ. For these 40 residues, we performed computational mutation analysis by substituting each of the interface receptor residues by the remaining standard amino acids. The corresponding changes of the free energy were calculated by a protocol consisting of FoldX and molecular dynamics calculations. Based on the computed changes of the free energy and on sequence conservation criteria obtained by the analysis of 32 receptor sequences from 19 different species, we selected 14 receptor variants predicted to increase the receptor affinity to IFN-γ. These variants were expressed as recombinant proteins in Escherichia coli, and their affinities to IFN-γ were determined experimentally by surface plasmon resonance (SPR). The SPR measurements showed that the simple computational protocol succeeded in finding two receptor variants with affinity to IFN-γ increased about fivefold compared to the wild-type receptor.

Double-Helical -Ladder Structural Transition in the B-DNA is Induced by a Loss of Dispersion Energy

The role of the dispersion energy and electrostatic energy on the geometry and stability of the B-DNA helix was investigated. Both molecular dynamics simulations with empirical force field and hybrid quantum mechanical/molecular mechanics molecular dynamics simulations, where the dispersion or electrostatics term is suppressed/increased, on the one hand and an ab initio minimization procedure on the other have shown that the lack of the dispersion term leads to an increase of the vertical separation of the bases as well as to a loss of helicity, thus resulting in a ladder-like structure. A decrease of the electrostatic term produces a separation of the DNA strands. The biological consequences of both electrostatic and dispersion forces in DNA are enormous, and without either of them, DNA would become unstable and unable to provide the storage and transfer of genetic information.

Novel high‐affinity binders of human interferon gamma derived from albumin‐binding domain of protein G

Recombinant ligands derived from small protein scaffolds show promise as robust research and diagnostic reagents and next generation protein therapeutics. Here, we derived high‐affinity binders of human interferon gamma (hIFNγ) from the three helix bundle scaffold of the albumin‐binding domain (ABD) of protein G from Streptococcus G148. Computational interaction energy mapping, solvent accessibility assessment, and in silico alanine scanning identified 11 residues from the albumin‐binding surface of ABD as suitable for randomization. A corresponding combinatorial ABD scaffold library was synthesized and screened for hIFNγ binders using in vitro ribosome display selection, to yield recombinant ligands that exhibited Kd values for hIFNγ from 0.2 to 10 nM. Molecular modeling, computational docking onto hIFNγ, and in vitro competition for hIFNγ binding revealed that four of the best ABD‐derived ligands shared a common binding surface on hIFNγ, which differed from the site of human IFNγ receptor 1 binding. Thus, these hIFNγ ligands provide a proof of concept for design of novel recombinant binding proteins derived from the ABD scaffold. Proteins 2011.

Theoretical study of the ground and excited states of 7-methyl guanine and 9-methyl guanine: comparison with experiment

The keto-enol tautomerization of 7-methyl-guanine and 9-methyl-guanine in the excited state was investigated using the time-dependent DFT (TDDFT) method. For both species, the potential energy surfaces of the ground state and two lowest singlet excited states (due to pi-->pi* and n-->pi* transitions) have been investigated and their features discussed in terms of consequences on the excited state dynamics. The findings suggest that, for both species, the state due to the n-->pi* transition, suspected to be an intermediate in the excited state deactivation, exhibits two minima with the second minimum characterized by an elongated N1-H distance. This structure, intermediate between enol and keto tautomers, might play a role in the excited state relaxation. The existence of this second well, however, is observed in both 7- and 9-methyl-guanine, which suggests that it cannot account alone for the different photophysical behavior of these species.

Local dynamics of proteins and DNA evaluated from crystallographic B factors

Distributions of scaled B factors from 704 protein–DNA complexes reflect primarily the neighbourhood of amino-acid and nucleotide residues: their flexibility grows from the protein core to protein–protein and protein–DNA interfaces, to solvent-exposed residues. Some of the findings clearly observed at higher resolution structures can no longer be observed for structures at low resolution indicating problems in refinement protocols.

Complete Basis Set Extrapolation and Hybrid Schemes for Geometry Gradients of Noncovalent Complexes.

In this paper, we focus on the performance of popular WFT (MP2, MP2.5, MP3, SCS(MI)-MP2, CCSD(T)) and DFT (M06-2X, TPSS-D) methods in optimizations of geometries of noncovalent complexes. Apart from the straightforward comparison of the accuracy of the resulting geometries with respect to the most accurate, computationally affordable, reference method, we have also attempted to determine the most efficient utilization of the information contained in the gradient of a particular method and basis set. Essentially, we have transferred the ideas successfully used for noncovalent interaction energy calculations to geometry optimizations. We have assessed the performance of the hybrid gradients (for instance, MP2 and CCSD(T) calculated in different basis sets), investigated the possibility of extrapolating gradients calculated with a particular method in a series of systematically built basis sets, and finally compared the extrapolated gradients with the counterpoise(CP)-corrected optimizations, in order to determine which of these approaches is more efficient, in terms of their convergence toward the CBS geometry for the respective calculation cost. Further, we compared the efficiency of the CP-corrected, extrapolated, and hybrid gradients in terms of the rate of convergence with respect to basis set size. We have found that CCSD(T) geometries are most faithfully reproduced by the MP2.5 and MP3 methods, followed by the comparably well performing SCS(MI)-MP2 and MP2 methods, and finally by the worst performing DFT-D and M06 methods. Basis set extrapolation of gradients was shown to improve the results and can be considered as a low-cost alternative to the use of CP-corrected gradients. A hybrid gradient scheme was shown to deliver geometries close to the regular gradient reference. Analogously to a similar hybrid scheme, which nowadays is routinely used for the calculation of interaction energies, such a hybrid gradient scheme can save a huge amount of computer time, when high accuracy is desired.