Calculation of electrostatic free energy for the nonlinear Poisson-Boltzmann model based on the dimensionless potential

The Poisson-Boltzmann (PB) equation governing the electrostatic potential with a unit is often transformed to a normalized form for a dimensionless potential in numerical studies. To calculate the electrostatic free energy (EFE) of biological interests, a unit conversion has to be conducted, because the existing PB energy functionals are all described in terms of the original potential. To bypass this conversion, this paper proposes energy functionals in terms of the dimensionless potential for the first time in the literature, so that the normalized PB equation can be directly derived by using the Euler-Lagrange variational analysis. Moreover, alternative energy forms have been rigorously derived to avoid approximating the gradient of singular functions in the electrostatic stress term. A systematic study has been carried out to examine the surface integrals involved in alternative energy forms and their dependence on finite domain size and mesh step size, which leads to a recommendation on the EFE forms for efficient computation of protein systems. The calculation of the EFE in the regularization formulation, which is an analytical approach for treating singular charge sources of the PB equation, has also been studied. The proposed energy forms have been validated by considering smooth dielectric settings, such as diffuse interface and super-Gaussian, for which the EFE of the nonlinear PB model is found to be significantly different from that of the linearized PB model. All proposed energy functionals and EFE forms are designed such that the dimensionless potential can be simply plugged in to compute the EFE in the unit of kcal/mol, and they can also be applied in the classical sharp interface PB model.

Electrostatics in Computational Biophysics and Its Implications for Disease Effects

This review outlines the role of electrostatics in computational molecular biophysics and its implication in altering wild-type characteristics of biological macromolecules, and thus the contribution of electrostatics to disease mechanisms. The work is not intended to review existing computational approaches or to propose further developments. Instead, it summarizes the outcomes of relevant studies and provides a generalized classification of major mechanisms that involve electrostatic effects in both wild-type and mutant biological macromolecules. It emphasizes the complex role of electrostatics in molecular biophysics, such that the long range of electrostatic interactions causes them to dominate all other forces at distances larger than several Angstroms, while at the same time, the alteration of short-range wild-type electrostatic pairwise interactions can have pronounced effects as well. Because of this dual nature of electrostatic interactions, being dominant at long-range and being very specific at short-range, their implications for wild-type structure and function are quite pronounced. Therefore, any disruption of the complex electrostatic network of interactions may abolish wild-type functionality and could be the dominant factor contributing to pathogenicity. However, we also outline that due to the plasticity of biological macromolecules, the effect of amino acid mutation may be reduced, and thus a charge deletion or insertion may not necessarily be deleterious.

Electrostatic Features for the Receptor Binding Domain of SARS-COV-2 Wildtype and Its Variants. Compass to the Severity of the Future Variants with the Charge-Rule

Electrostatic intermolecular interactions are important in many aspects of biology. We have studied the main electrostatic features involved in the interaction of the receptor-binding domain (RBD) of the SARS-CoV-2 spike protein with the human receptor Angiotensin-converting enzyme 2 (ACE2). As the principal computational tool, we have used the FORTE approach, capable to model proton fluctuations and computing free energies for a very large number of protein-protein systems under different physical-chemical conditions, here focusing on the RBD-ACE2 interactions. Both the wild-type and all critical variants are included in this study. From our large ensemble of extensive simulations, we obtain, as a function of pH, the binding affinities, charges of the proteins, their charge regulation capacities, and their dipole moments. In addition, we have calculated the pK_as for all ionizable residues and mapped the electrostatic coupling between them. We are able to present a simple predictor for the RBD-ACE2 binding based on the data obtained for Alpha, Beta, Gamma, Delta, and Omicron variants, as a linear correlation between the total charge of the RBD and the corresponding binding affinity. This "RBD charge rule" should work as a quick test of the degree of severity of the coming SARS-CoV-2 variants in the future.

The pH Effects on SARS-CoV and SARS-CoV-2 Spike Proteins in the Process of Binding to hACE2

COVID-19 has been threatening human health since the late 2019, and has a significant impact on human health and economy. Understanding SARS-CoV-2 and other coronaviruses is important to develop effective treatments for COVID-19 and other coronavirus-caused diseases. In this work, we applied multi-scale computational approaches to study the electrostatic features of spike (S) proteins for SARS-CoV and SARS-CoV-2. From our results, we found that SARS-CoV and SARS-CoV-2 have similar charge distributions and electrostatic features when binding with the human angiotensin-converting enzyme 2 (hACE2). Energy pH-dependence calculations revealed that the complex structures of hACE2 and the S proteins of SARS-CoV/SARS-CoV-2 are stable at pH values ranging from 7.5 to 9. Three independent 100 ns molecular dynamics (MD) simulations were performed using NAMD to investigate the hydrogen bonds between S proteins RBD and hACE2 RBD. From MD simulations, we found that SARS-CoV-2 forms 19 pairs (average of three simulations) of hydrogen bonds with high occupancy (>50%) to hACE2, compared to 16 pairs between SARS-CoV and hACE2. Additionally, SARS-CoV viruses prefer sticking to the same hydrogen bond pairs, while SARS-CoV-2 tends to have a larger range of selections on hydrogen bonds acceptors. We also labelled key residues involved in forming the top five hydrogen bonds that were found in all three independent 100 ns simulations. This identification is important to potential drug designs for COVID-19 treatments. Our work will shed the light on current and future coronavirus-caused diseases.

Computational Study on DNA Repair: The Roles of Electrostatic Interactions Between Uracil-DNA Glycosylase (UDG) and DNA

Uracil-DNA glycosylase (UDG) is one of the most important base excision repair (BER) enzymes involved in the repair of uracil-induced DNA lesion by removing uracil from the damaged DNA. Uracil in DNA may occur due to cytosine deamination or deoxy uridine monophosphate (dUMP) residue misincorporation during DNA synthesis. Medical evidences show that an abnormal expression of UDG is related to different types of cancer, including colorectal cancer, lung cancer, and liver cancer. Therefore, the research of UDG is crucial in cancer treatment and prevention as well as other clinical activities. Here we applied multiple computational methods to study UDG in several perspectives: Understanding the stability of the UDG enzyme in different pH conditions; studying the differences in charge distribution between the pocket side and non-pocket side of UDG; analyzing the field line distribution at the interfacial area between UDG and DNA; and performing electrostatic binding force analyses of the special region of UDG (pocket area) and the target DNA base (uracil) as well as investigating the charged residues on the UDG binding pocket and binding interface. Our results show that the whole UDG binding interface, and not the UDG binding pocket area alone, provides the binding attractive force to the damaged DNA at the uracil base.