Arjan van der Vaart

New developments in applying quantum mechanics to proteins

Algorithmic improvements of quantum mechanical methodologies have increased our ability to study the electronic structure of fragments of a biomolecule (e.g. an enzyme active site) or entire biomolecules. Three main strategies have emerged as ways in which quantum mechanics can be applied to biomolecules. The supermolecule approach continues to be utilized, but it is slowly being replaced by the so-called coupled quantum mechanical/molecular mechanical methodologies. An exciting new direction is the continued development and application of linear-scaling quantum mechanical approaches to biomolecular systems.

Linear scaling molecular orbital calculations of biological systems using the semiempirical divide and conquer method

A “linear‐scaling revolution” is occurring in quantum chemistry. This development is allowing for the first time the routine examination of large molecular assembles (e.g., proteins and DNA in water) using electronic structure methods. One of these approaches is the divide and conquer method and, in this article, we review the implementation of this approach for semiempirical Hamiltonians. This is then followed by brief reviews of three application areas. First, we will discuss the charge distribution of biological molecules in solution as described by quantum mechanics. In particular, the role polarization and charge transfer plays in affecting the charge distribution of proteins will be discussed. Next, we will examine the energetic consequences of charge transfer and polarization on biomolecular solvation. The final section will describe the computation of solvation free energies using a combined divide and conquer/Poisson–Boltzmann approach. The application of linear scaling quantum mechanical methods to biology is only just beginning, but the future is very bright, and it is our opinion that quantum mechanics will have a profound influence on our understanding of biological systems in the coming years.

Charge transfer in small hydrogen bonded clusters

High level ab initio and density functional calculations on clusters of water with acetate, methylammonium, and dimethylphosphate show that charge is transferred from the hydrogen bond acceptor to the hydrogen bond donor. The amounts of charge transferred are small, between 0.01 and 0.05 electron per hydrogen bond, but increase nearly linearly with the number of hydrogen bonds. The transfer of charge is not an artifact of the computation, since charge is also transferred in the limit of zero basis set superposition error. Calculations on a number of hydrogen bonded clusters show that the semiempirical AM1 and PM3 methods give excellent agreement with high level MP2 charge transfer effects, especially for AM1. Our results indicate the importance of charge transfer in hydrogen bond interactions.

Extracting the Causality of Correlated Motions from Molecular Dynamics Simulations

The information theory measure of transfer entropy is used to extract the causality of correlated motions from molecular dynamics simulations. For each pair of correlated residues, the method quantifies which residue drives the correlated motions, and which residue responds. The measure reveals how correlated motions are used to transmit information through the system, and helps to clarify the link between correlated motions and biological function in biomolecular systems. The method is illustrated by its application to the Ets-1 transcription factor, which partially unfolds upon binding DNA. The calculations show dramatic changes in the direction of information flow upon DNA binding, and elucidate how the presence of DNA is communicated from the DNA binding H1 and H3 helices to inhibitory helix HI-1. Helix H4 is shown to act as a relay, which is attenuated in the apo state.

Gaussian-mixture umbrella sampling.

We introduce the Gaussian-mixture umbrella sampling method (GAMUS) , a biased molecular dynamics technique based on adaptive umbrella sampling that efficiently escapes free energy minima in multidimensional problems. The prior simulation data are reweighted with a maximum likelihood formulation, and the new approximate probability density is fit to a Gaussian-mixture model, augmented by information about the unsampled areas. The method can be used to identify free energy minima in multidimensional reaction coordinates. To illustrate GAMUS , we apply it to the alanine dipeptide (2D reaction coordinate) and tripeptide (4D reaction coordinate).

Multiple scaling replica exchange for the conformational sampling of biomolecules in explicit water

A multiple scaling replica exchange method for the efficient conformational sampling of biomolecular systems in explicit solvent is presented. The method is a combination of the replica exchange with solute tempering (REST) technique and a Tsallis biasing potential. The Tsallis biasing increases the sampling efficiency, while the REST minimizes the number of replicas needed. Unbiased statistics can be obtained by reweighting of the data using a weighted histogram analysis technique. The method is illustrated by its application to a ten residue peptide in explicit water.

Modeling, synthesis and biological evaluation of potential retinoid X receptor (RXR) selective agonists: novel analogues of 4-[1-(3,5,5,8,8-pentamethyl-5,6,7,8-tetrahydro-2-naphthyl)ethynyl]benzoic acid (bexarotene).

This report describes the synthesis of analogues of 4-[1-(3,5,5,8,8-pentamethyl-5,6,7,8-tetrahydro-2-naphthyl)ethynyl]benzoic acid (1), commonly known as bexarotene, and their analysis in acting as retinoid X receptor (RXR)-specific agonists. Compound 1 has FDA approval to treat cutaneous T-cell lymphoma (CTCL); however, its use can cause side effects such as hypothyroidism and increased triglyceride concentrations, presumably by disruption of RXR heterodimerization with other nuclear receptors. The novel analogues in the present study have been evaluated for RXR activation in an RXR mammalian-2-hybrid assay as well as an RXRE-mediated transcriptional assay and for their ability to induce apoptosis as well as for their mutagenicity and cytotoxicity. Analysis of 11 novel compounds revealed the discovery of three analogues that best induce RXR-mediated transcriptional activity, stimulate apoptosis, have comparable K(i) and EC(50) values to 1, and are selective RXR agonists. Our experimental approach suggests that rational drug design can develop new rexinoids with improved biological properties.

DNA Bending through Large Angles Is Aided by Ionic Screening.

We used adaptive umbrella sampling on a modified version of the roll angle to simulate the bending of DNA dodecamers. Simulations were carried out with the AMBER and CHARMM force fields for 10 sequences in which the central base pair step was varied. On long length scales, the DNA behavior was found to be consistent with the worm-like chain model. Persistence lengths calculated directly from the simulated structures and indirectly through the use of sequence-independent coarse-grained models based on simulation data were similar to literature values. On short length scales, the free energy cost of bending DNA was found to be consistent with the worm-like chain model for small and intermediate bending angles. At large angles, the bending free energy as a function of the roll angle became linear, suggesting a relative increase in flexibility at larger roll angles. Counterions congregated on the concave side of the highly bent DNA and screened the repulsion of the phosphate groups, facilitating the bending.

Critical assessment of the performance of the semiempirical divide and conquer method for single point calculations and geometry optimizations of large chemical systems

We present a detailed analysis of the performance of the semiempirical divide and conquer method as compared with standard semiempirical MO calculations. The influence of different subsetting schemes involving dual buffer regions on the magnitude of the errors in energies and computational cost of the calculations are discussed. In addition, the results of geometry optimizations on several protein systems (453 to 4088 atoms) driven by a quasi-Newton algorithm are also presented. These results indicate that the divide and conquer approach gives reliable energies and gradients and suggest that protein geometry optimization using semiempirical methods can be routinely feasible using current computational resources.

Charge transfer in biologically important molecules: comparison of high‐level ab initio and semiempirical methods

Recent observations in both experimental and theoretical chemistry indicate the importance of charge transfer on the energetics and charge distribution of biomolecular systems. Here the authors present a detailed analysis of hydrogen-bonded complexes to assess the quality of Hartree-Fock (HF) and semiempirical methods in predicting the amount of charge transferred. The authors find that both HF and semiempirical methods systematically overestimate charge transfer when compared to MP2/6-311++G** calculations. Although inclusion of electron correlation is important for a proper assessment of charge transfer, both HG/6-311++G** and AM1 can serve as good approximations to charge transfer in biomolecular systems.