Modified Poisson–Boltzmann equations for characterizing biomolecular solvation

2014 ◽  
Vol 13 (03) ◽  
pp. 1440001 ◽  
Author(s):  
Patrice Koehl ◽  
Frederic Poitevin ◽  
Henri Orland ◽  
Marc Delarue
Keyword(s):  
Electrostatic Interactions ◽  
Degrees Of Freedom ◽  
Lattice Gas ◽  
Homogeneous Medium ◽  
Variable Density ◽  
Solvent Density ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
High Dielectric ◽  
Solvation Free Energies

Methods for computing electrostatic interactions often account implicitly for the solvent, due to the much smaller number of degrees of freedom involved. In the Poisson–Boltzmann (PB) approach the electrostatic potential is obtained by solving the Poisson–Boltzmann equation (PBE), where the solvent region is modeled as a homogeneous medium with a high dielectric constant. PB however is not exempt of problems. It does not take into account for example the sizes of the ions in the atmosphere surrounding the solute, nor does it take into account the inhomogeneous dielectric response of water due to the presence of a highly charged surface. In this paper we review two major modifications of PB that circumvent these problems, namely the size-modified PB (SMPB) equation and the Dipolar Poisson–Boltzmann Langevin (DPBL) model. In SMPB, steric effects between ions are accounted for with a lattice gas model. In DPBL, the solvent region is no longer modeled as a homogeneous dielectric media but rather as an assembly of self-orienting interacting dipoles of variable density. This model results in a dielectric profile that transits smoothly from the solute to the solvent region as well as in a variable solvent density that depends on the charges of the solute. We show successful applications of the DPBL formalism to computing the solvation free energies of isolated ions in water. Further developments of more accurately modified PB models are discussed.

scholarly journals Computing Protein pKas Using the TABI Poisson–Boltzmann Solver

2020 ◽  
pp. 2042006
Author(s):  
Jiahui Chen ◽  
Jingzhen Hu ◽  
Yongjia Xu ◽  
Robert Krasny ◽  
Weihua Geng
Keyword(s):  
Boltzmann Distribution ◽  
Dielectric Medium ◽  
Boundary Integral ◽  
Acid Dissociation ◽  
Low Dielectric ◽  
Poisson Boltzmann ◽  
Computing Procedure ◽  
Poisson Boltzmann Equation ◽  
High Dielectric ◽  
Electrostatic Calculations

A common approach to computing protein pKas uses a continuum dielectric model in which the protein is a low dielectric medium with embedded atomic point charges, the solvent is a high dielectric medium with a Boltzmann distribution of ionic charges, and the pKa is related to the electrostatic free energy which is obtained by solving the Poisson–Boltzmann equation. Starting from the model pKa for a titrating residue, the method obtains the intrinsic pKa and then computes the protonation probability for a given pH including site–site interactions. This approach assumes that acid dissociation does not affect protein conformation aside from adding or deleting charges at titratable sites. In this work, we demonstrate our treecode-accelerated boundary integral (TABI) solver for the relevant electrostatic calculations. The pKa computing procedure is enclosed in a convenient Python wrapper which is publicly available at the corresponding author’s website. Predicted results are compared with experimental pKas for several proteins. Among ongoing efforts to improve protein pKa calculations, the advantage of TABI is that it reduces the numerical errors in the electrostatic calculations so that attention can be focused on modeling assumptions.

DelEnsembleElec: Computing Ensemble-Averaged Electrostatics Using DelPhi

2013 ◽  
Vol 13 (1) ◽  
pp. 256-268 ◽  
Author(s):  
Lane W. Votapka ◽  
Luke Czapla ◽  
Maxim Zhenirovskyy ◽  
Rommie E. Amaro
Keyword(s):  
Molecular Dynamics ◽  
Influenza Virus ◽  
Boltzmann Equation ◽  
General Theory ◽  
Electrostatic Interactions ◽  
Biological Interest ◽  
Single Structure ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
Electrostatic Calculations

AbstractA new VMD plugin that interfaces with DelPhi to provide ensemble-averaged electrostatic calculations using the Poisson-Boltzmann equation is presented. The general theory and context of this approach are discussed, and examples of the plugin interface and calculations are presented. This new tool is applied to systems of current biological interest, obtaining the ensemble-averaged electrostatic properties of the two major influenza virus glycoproteins, hemagglutinin and neuraminidase, from explicitly solvated all-atom molecular dynamics trajectories. The differences between the ensemble-averaged electrostatics and those obtained from a single structure are examined in detail for these examples, revealing how the plugin can be a powerful tool in facilitating the modeling of electrostatic interactions in biological systems.

scholarly journals Review and Modification of Entropy Modeling for Steric Effects in the Poisson-Boltzmann Equation

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 632
Author(s):  
Tzyy-Leng Horng
Keyword(s):  
Free Energy ◽  
Lattice Gas ◽  
Steric Effect ◽  
Mean Field ◽  
Boltzmann Distribution ◽  
Experimental Conditions ◽  
Ion Concentrations ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
Ion Size

The classical Poisson-Boltzmann model can only work when ion concentrations are very dilute, which often does not match the experimental conditions. Researchers have been working on the modification of the model to include the steric effect of ions, which is non-negligible when the ion concentrations are not dilute. Generally the steric effect was modeled to correct the Helmholtz free energy either through its internal energy or entropy, and an overview is given here. The Bikerman model, based on adding solvent entropy to the free energy through the concept of volume exclusion, is a rather popular steric-effect model nowadays. However, ion sizes are treated as identical in the Bikerman model, making an extension of the Bikerman model to include specific ion sizes desirable. Directly replacing the ions of non-specific size by specific ones in the model seems natural and has been accepted by many researchers in this field. However, this straightforward modification does not have a free energy formula to support it. Here modifications of the Bikerman model to include specific ion sizes have been developed iteratively, and such a model is achieved with a guarantee that: (1) it can approach Boltzmann distribution at diluteness; (2) it can reach saturation limit as the reciprocal of specific ion size under extreme electrostatic conditions; (3) its entropy can be derived by mean-field lattice gas model.

Reversible - through calmodulin - electrostatic interactions between basic residues on proteins and acidic lipids in the plasma membrane.

2005 ◽  
Vol 72 ◽  
pp. 189-198 ◽  
Author(s):  
Stuart McLaughlin ◽  
Gyöngyi Hangyás-Mihályné ◽  
Irina Zaitseva ◽  
Urszula Golebiewska
Keyword(s):  
Plasma Membrane ◽  
Cell Biology ◽  
Electrostatic Interactions ◽  
Theoretical Calculations ◽  
Cell Types ◽  
Kinase Substrate ◽  
Poisson Boltzmann ◽  
Pkc Protein Kinase C ◽  
Poisson Boltzmann Equation ◽  
Acidic Lipids

The inner leaflet of a typical mammalian plasma membrane contains 20-30% univalent PS (phosphatidylserine) and 1% multivalent PtdIns(4,5)P2. Numerous proteins have clusters of basic (or basic/hydrophobic) residues that bind to these acidic lipids. The intracellular effector CaM (calmodulin) can reverse this binding on a wide variety of proteins, including MARCKS (myristoylated alanine-rich C kinase substrate), GAP43 (growth-associated protein 43, also known as neuromodulin), gravin, GRK5 (G-protein-coupled receptor kinase 5), the NMDA (N-methyl-d-aspartate) receptor and the ErbB family. We used the first principles of physics, incorporating atomic models and the Poisson-Boltzmann equation, to describe how the basic effector domain of MARCKS binds electrostatically to acidic lipids on the plasma membrane. The theoretical calculations show the basic cluster produces a local positive electrostatic potential that should laterally sequester PtdInsP2, even when univalent acidic lipids are present at a physiologically relevant 100-fold excess; four independent experimental measurements confirm this prediction. Ca2+/CaM binds with high affinity (Kd approximately 10nM) to this domain and releases the PtdIns(4,5)P2. MARCKS, a major PKC (protein kinase C) substrate, is present at concentrations comparable with those of PtdIns(4,5)P2 (approx. 10 μM) in many cell types. Thus MARCKS can act as a reversible PtdIns(4,5)P2 buffer, binding PtdIns(4,5)P2 in a quiescent cell, and releasing it locally when the intracellular Ca2+ concentration increases. This reversible sequestration is important because PtdIns(4,5)P2 plays many roles in cell biology. Less is known about the role of CaM-mediated reversible membrane binding of basic/hydrophobic clusters for the other proteins.

scholarly journals Poisson-Boltzmann Calculations: van der Waals or Molecular Surface?

2013 ◽  
Vol 13 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Xiaodong Pang ◽  
Huan-Xiang Zhou
Keyword(s):  
Hydrogen Exchange ◽  
High Dielectric Constant ◽  
Van Der Waals ◽  
Molecular Surface ◽  
Explicit Solvent ◽  
Calculation Results ◽  
Van Der Waals Surface ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
High Dielectric

AbstractThe Poisson-Boltzmann equation is widely used for modeling the electro-statics of biomolecules, but the calculation results are sensitive to the choice of the boundary between the low solute dielectric and the high solvent dielectric. The default choice for the dielectric boundary has been the molecular surface, but the use of the van der Waals surface has also been advocated. Here we review recent studies in which the two choices are tested against experimental results and explicit-solvent calculations. The assignment of the solvent high dielectric constant to interstitial voids in the solute is often used as a criticism against the van der Waals surface. However, this assignment may not be as unrealistic as previously thought, since hydrogen exchange and other NMR experiments have firmly established that all interior parts of proteins are transiently accessible to the solvent.

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