The optimal particle-mesh interpolation basis

A formula and numerical study on Ewald 1D summation

Ewald summation is famous for its successful applications in molecular simulations for systems under 2 dimensional periodic boundary condition (2D PBC, e.g., planar interfaces) and systems under 3D PBC (e.g., bulk). However, the extension to systems under 1D PBC (like porous structures and tubes) is largely hindered by the special functions in the formula. In this work, a simple approximation of Ewald 1D sum is introduced with its error rigorously controlled. To investigate the impacts on the efficiency and accuracy by different parts, a pairwise potential is calculated for a series of screening parameters ( α ) and radial distances ( ρ ) between two point charges. A mapping between the sum of trigonometric functions in Ewald 1D method and the sum of specific vectors further reveals the different converging speeds of different Fourier parts. When choosing α = 0.2 Å^-1 , it is appropriate to ignore the insignificant parts in the sum to accelerate the method.

Reading and erasing of the phosphonium analogue of trimethyllysine by epigenetic proteins

N ε-Methylation of lysine residues in histones plays an essential role in the regulation of eukaryotic transcription. The 'highest' methylation mark, N ε-trimethyllysine, is specifically recognised by N ε-trimethyllysine binding 'reader' domains, and undergoes demethylation, as catalysed by 2-oxoglutarate dependent JmjC oxygenases. We report studies on the recognition of the closest positively charged N ε-trimethyllysine analogue, i.e. its trimethylphosphonium derivative (KPme3), by N ε-trimethyllysine histone binding proteins and Nε-trimethyllysine demethylases. Calorimetric and computational studies with histone binding proteins reveal that H3KP4me3 binds more tightly than the natural H3K4me3 substrate, though the relative differences in binding affinity vary. Studies with JmjC demethylases show that some, but not all, of them can accept the phosphonium analogue of their natural substrates and that the methylation state selectivity can be changed by substitution of nitrogen for phosphorus. The combined results reveal that very subtle changes, e.g. substitution of nitrogen for phosphorus, can substantially affect interactions between ligand and reader domains / demethylases, knowledge that we hope will inspire the development of highly selective small molecules modulating their activity.

Midtown splines: An optimal charge assignment for electrostatics calculations

Transferring particle charges to and from a grid plays a central role in the particle-mesh algorithms widely used to evaluate the electrostatic energy in molecular dynamics (MD) simulations. The computational cost of this transfer process represents a substantial part of the overall time required for simulation and is primarily determined by the size of the support (the set of grid nodes at which the transfer function is evaluated). The accuracy of the resulting approximation depends on the form of the transfer function, of which several have been proposed, as well as the size and shape of its support. Here, we show how to derive the transfer function that yields maximal asymptotic accuracy for a given support in the limit of fine grid resolution, finding that all such functions are splines, and we determine these functions (which we refer to as midtown splines) for a variety of choices of support to find optimally efficient transfer functions at accuracy levels relevant to MD simulations. We describe midtown splines that achieve fourth- and sixth-order accuracy in the grid spacing while requiring a support size of 32 and 88 grid nodes, respectively, compared to the 64 and 216 nodes required by the most widely used transfer functions (B-splines). At accuracy levels typically used in MD simulations, the use of midtown splines thus cuts the time required for charge spreading by roughly a factor of two.

Mechanism of biomolecular recognition of trimethyllysine by the fluorinated aromatic cage of KDM5A PHD3 finger

The understanding of biomolecular recognition of posttranslationally modified histone proteins is centrally important to the histone code hypothesis. Despite extensive binding and structural studies on the readout of histones, the molecular language by which posttranslational modifications on histone proteins are read remains poorly understood. Here we report physical-organic chemistry studies on the recognition of the positively charged trimethyllysine by the electron-rich aromatic cage containing PHD3 finger of KDM5A. The aromatic character of two tryptophan residues that solely constitute the aromatic cage of KDM5A was fine-tuned by the incorporation of fluorine substituents. Our thermodynamic analyses reveal that the wild-type and fluorinated KDM5A PHD3 fingers associate equally well with trimethyllysine. This work demonstrates that the biomolecular recognition of trimethyllysine by fluorinated aromatic cages is associated with weaker cation-π interactions that are compensated by the energetically more favourable trimethyllysine-mediated release of high-energy water molecules that occupy the aromatic cage.

Comparison of Molecular Recognition of Trimethyllysine and Trimethylthialysine by Epigenetic Reader Proteins

Gaining a fundamental insight into the biomolecular recognition of posttranslationally modified histones by epigenetic reader proteins is of crucial importance to understanding the regulation of the activity of human genes. Here, we seek to establish whether trimethylthialysine, a simple trimethyllysine analogue generated through cysteine alkylation, is a good trimethyllysine mimic for studies on molecular recognition by reader proteins. Histone peptides bearing trimethylthialysine and trimethyllysine were examined for binding with five human reader proteins employing a combination of thermodynamic analyses, molecular dynamics simulations and quantum chemical analyses. Collectively, our experimental and computational findings reveal that trimethylthialysine and trimethyllysine exhibit very similar binding characteristics for the association with human reader proteins, thereby justifying the use of trimethylthialysine for studies aimed at dissecting the origin of biomolecular recognition in epigenetic processes that play important roles in human health and disease.