Origin of parameter degeneracy and molecular shape relationships in geometric-flow calculations of solvation free energies

Abstract

Implicit solvent models are important tools for calculating solvation free energies for chemical and biophysical studies since they require fewer computational resources but can achieve accuracy comparable to that of explicit-solvent models. In past papers, geometric flow-based solvation models have been established for solvation analysis of small and large compounds. In the present work, the use of realistic experiment-based parameter choices for the geometric flow models is studied. We find that the experimental parameters of solvent internal pressure p = 172 MPa and surface tension γ = 72 mN/m produce solvation free energies within 1 RT of the global minimum root-mean-squared deviation from experimental data over the expanded set. Our results demonstrate that experimental values can be used for geometric flow solvent model parameters, thus eliminating the need for additional parameterization. We also examine the correlations between optimal values of p and γ which are strongly anti-correlated. Geometric analysis of the small molecule test set shows that these results are inter-connected with an approximately linear relationship between area and volume in the range of molecular sizes spanned by the data set. In spite of this considerable degeneracy between the surface tension and pressure terms in the model, both terms are important for the broader applicability of the model. © 2013 AIP Publishing LLC. [http://dx

Improvements to the APBS biomolecular solvation software suite

“…This section contains additional information about the geometric flow equation implementation in APBS introduced in the section "Geometric flow." The geometric flow methods used by APBS have been described extensively in previous publications [54][55][56][57]101 ; this section focuses on the configuration and use of these methods in APBS.…”

“…Three additional parameters are needed for geometric flow calculations to specify how nonpolar solvation is linked to the polar implicit solvent models: gamma htensioni: Specify the surface tension of the solvent in units of kJ mol 21 Å 22 . Based on Daily et al, 57 a recommended value for small molecules is 0.431 kJ mol 21 Å 22 . press hpressurei: Specify the internal pressure of the solvent in units of kJ mol 21 Å 23 .…”

“…press hpressurei: Specify the internal pressure of the solvent in units of kJ mol 21 Å 23 . Based on Daily et al, 57 a recommended value for small molecules is 0.104 kJ mol 21 Å 23 . bconc hconcentrationi: Specify the bulk concentration of solvent in Å 23 .…”

Variational Methods for Biomolecular Modeling

“…Recently, differential geometry based implicit solvent model has been tested extensively via solvation analysis [27,26,28,39,132,138]. The differential geometry based nonpolar model was found to deliver some of the best nonpolar solvation predictions [28].…”

Modeling Zika Virus Spread in Colombia Using Google Search Queries and Logistic Power Models

“…A sampling of the parameter values R and a obtained using the Monte Carlo 175 algorithm is given in Fig 4. These results imply that not only are these parameters 176 highly sensitive to the initial guesses used in the LMA fitting procedure, but they are 177 also impossible to be determined uniquely for a given data set. Sets of R, a, and p that 178 differ significantly but give the same best-fit curve are given in Table 1, and the fits are 179 plotted in Fig 5. This problem is not uncommon in the context of highly parameterized 180 models, and is referred to in the literature as "parameter degeneracy" [15,16]. This 181 PLOS 6/20 occurs when two or more parameters in a model are affected by the same physical 182 process in such a way that they cannot uniquely determined.…”