A Proposal for the Revision of Molecular Boundary Typology

Kim, Deok-Soo; Won, Chung-In; Bhak, Jong

doi:10.1080/07391102.2010.10507359

Cited by 13 publications

(9 citation statements)

References 118 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Different research groups advocate the use of different surfaces 99 in PB calculations, typically van der Waals 79,80,[100][101][102] or molecular [103][104][105] surfaces, along with different solute permittivity values. [76][77][78][79][80] However, this debate mostly concerns calculations aiming at accounting for the dielectric properties of protein-solvent systems as realistically as possible using the approximate PB approach, usually based on a single system configuration.…”

Section: Choice Of Dielectric Boundary Conditionsmentioning

confidence: 99%

Calculating the binding free energies of charged species based on explicit-solvent simulations employing lattice-sum methods: An accurate correction scheme for electrostatic finite-size effects

Rocklin¹,

Mobley²,

Dill³

et al. 2013

The Journal of Chemical Physics

227

368

View full text Add to dashboard Cite

The calculation of a protein-ligand binding free energy based on molecular dynamics (MD) simulations generally relies on a thermodynamic cycle in which the ligand is alchemically inserted into the system, both in the solvated protein and free in solution. The corresponding ligand-insertion free energies are typically calculated in nanoscale computational boxes simulated under periodic boundary conditions and considering electrostatic interactions defined by a periodic lattice-sum. This is distinct from the ideal bulk situation of a system of macroscopic size simulated under non-periodic boundary conditions with Coulombic electrostatic interactions. This discrepancy results in finite-size effects, which affect primarily the charging component of the insertion free energy, are dependent on the box size, and can be large when the ligand bears a net charge, especially if the protein is charged as well. This article investigates finite-size effects on calculated charging free energies using as a test case the binding of the ligand 2-amino-5-methylthiazole (net charge +1 e) to a mutant form of yeast cytochrome c peroxidase in water. Considering different charge isoforms of the protein (net charges -5, 0, +3, or +9 e), either in the absence or the presence of neutralizing counter-ions, and sizes of the cubic computational box (edges ranging from 7.42 to 11.02 nm), the potentially large magnitude of finite-size effects on the raw charging free energies (up to 17.1 kJ mol(-1)) is demonstrated. Two correction schemes are then proposed to eliminate these effects, a numerical and an analytical one. Both schemes are based on a continuum-electrostatics analysis and require performing Poisson-Boltzmann (PB) calculations on the protein-ligand system. While the numerical scheme requires PB calculations under both non-periodic and periodic boundary conditions, the latter at the box size considered in the MD simulations, the analytical scheme only requires three non-periodic PB calculations for a given system, its dependence on the box size being analytical. The latter scheme also provides insight into the physical origin of the finite-size effects. These two schemes also encompass a correction for discrete solvent effects that persists even in the limit of infinite box sizes. Application of either scheme essentially eliminates the size dependence of the corrected charging free energies (maximal deviation of 1.5 kJ mol(-1)). Because it is simple to apply, the analytical correction scheme offers a general solution to the problem of finite-size effects in free-energy calculations involving charged solutes, as encountered in calculations concerning, e.g., protein-ligand binding, biomolecular association, residue mutation, pKa and redox potential estimation, substrate transformation, solvation, and solvent-solvent partitioning.

show abstract

Section: Choice Of Dielectric Boundary Conditionsmentioning

confidence: 99%

Calculating the binding free energies of charged species based on explicit-solvent simulations employing lattice-sum methods: An accurate correction scheme for electrostatic finite-size effects

Rocklin¹,

Mobley²,

Dill³

et al. 2013

The Journal of Chemical Physics

227

368

View full text Add to dashboard Cite

show abstract

“…Molecular surfaces can be represented analytically as a patch complex of spheres (van der Walls surfaces and Lee-Richards surfaces) [29,24] or as a patch complex of spheres and tori (Connolly surfaces) [14,36] or as a patch complex of spheres and quadratic hyperboloids [17] or as parametric B-spline or NURBs surfaces [2,3] or as level sets resulting from summing up Gaussian atomic electron density functions (Gaussian surfaces) [7,9,16,22,46] or implicit algebraic splines or A-patch surfaces [50]. Of course, linear surface tessellations can be generated from those analytical forms of molecular surfaces [15,42,1,13,28,49,35,37].…”

Section: Related Workmentioning

confidence: 99%

3D molecular assembling of B-DNA sequences using nucleotides as building blocks

Raposo

Gomes

2012

Graphical Models

View full text Add to dashboard Cite

“…For the complete definition of these surfaces and their naming in literature, we recommend readers to refer to Ref. [2].…”

Section: Introductionmentioning

confidence: 99%

Beta‐decomposition for the volume and area of the union of three‐dimensional balls and their offsets

et al. 2012

Self Cite

View full text Add to dashboard Cite

Given a set of spherical balls, called atoms, in three-dimensional space, its mass properties such as the volume and the boundary area of the union of the atoms are important for many disciplines, particularly for computational chemistry/biology and structural molecular biology. Despite many previous studies, this seemingly easy problem of computing mass properties has not been well-solved. If the mass properties of the union of the offset of the atoms are to be computed as well, the problem gets even harder. In this article, we propose algorithms that compute the mass properties of both the union of atoms and their offsets both correctly and efficiently. The proposed algorithms employ an approach, called the Beta-decomposition, based on the recent theory of the beta-complex. Given the beta-complex of an atom set, these algorithms decompose the target mass property into a set of primitives using the simplexes of the beta-complex. Then, the molecular mass property is computed by appropriately summing up the mass property corresponding to each simplex. The time complexity of the proposed algorithm is O(m) in the worst case where m is the number of simplexes in the beta-complex that can be efficiently computed from the Voronoi diagram of the atoms. It is known in ℝ(3) that m = O(n) on average for biomolecules and m = O(n(2)) in the worst case for general spheres where n is the number of atoms. The theory is first introduced in ℝ(2) and extended to ℝ(3). The proposed algorithms were implemented into the software BetaMass and thoroughly tested using molecular structures available in the Protein Data Bank. BetaMass is freely available at the Voronoi Diagram Research Center web site.

show abstract

A Proposal for the Revision of Molecular Boundary Typology

Cited by 13 publications

References 118 publications

Calculating the binding free energies of charged species based on explicit-solvent simulations employing lattice-sum methods: An accurate correction scheme for electrostatic finite-size effects

Calculating the binding free energies of charged species based on explicit-solvent simulations employing lattice-sum methods: An accurate correction scheme for electrostatic finite-size effects

3D molecular assembling of B-DNA sequences using nucleotides as building blocks

Beta‐decomposition for the volume and area of the union of three‐dimensional balls and their offsets

Contact Info

Product

Resources

About