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For a given polynomial P with simple zeros, and a given semiclassical weight w, we present a construction that yields a linear second-order differential equation (ODE), and in consequence, an electrostatic model for zeros of P. The coefficients of this ODE are written in terms of a dual polynomial that we call the electrostatic partner of P. This construction is absolutely general and can be carried out for any polynomial with simple zeros and any semiclassical weight on the complex plane. An additional assumption of quasi-orthogonality of P with respect to w allows us to give more precise bounds on the degree of the electrostatic partner. In the case of orthogonal and quasi-orthogonal polynomials, we recover some of the known results and generalize others. Additionally, for the Hermite–Padé or multiple orthogonal polynomials of type II, this approach yields a system of linear second-order differential equations, from which we derive an electrostatic interpretation of their zeros in terms of a vector equilibrium. More detailed results are obtained in the special cases of Angelesco, Nikishin, and generalized Nikishin systems. We also discuss the discrete-to-continuous transition of these models in the asymptotic regime, as the number of zeros tends to infinity, into the known vector equilibrium problems. Finally, we discuss how the system of obtained second-order ODEs yields a third-order differential equation for these polynomials, well described in the literature. We finish the paper by presenting several illustrative examples. [ABSTRACT FROM AUTHOR]

We study the sequence of monic polynomials { S n } n ⩾ 0 , orthogonal with respect to the Jacobi-Sobolev inner product 〈 f , g 〉 s = ∫ − 1 1 f (x) g (x) d μ α , β (x) + ∑ j = 1 N ∑ k = 0 d j λ j , k f (k) (c j) g (k) (c j) , where N , d j ∈ Z + , λ j , k ⩾ 0 , d μ α , β (x) = (1 − x) α (1 + x) β d x , α , β > − 1 , and c j ∈ R ∖ (− 1 , 1) . A connection formula that relates the Sobolev polynomials S n with the Jacobi polynomials is provided, as well as the ladder differential operators for the sequence { S n } n ⩾ 0 and a second-order differential equation with a polynomial coefficient that they satisfied. We give sufficient conditions under which the zeros of a wide class of Jacobi-Sobolev polynomials can be interpreted as the solution of an electrostatic equilibrium problem of n unit charges moving in the presence of a logarithmic potential. Several examples are presented to illustrate this interpretation. [ABSTRACT FROM AUTHOR]

We study the sequence of monic polynomials {Sn}n⩾0, orthogonal with respect to the Jacobi-Sobolev inner product ⟨f,g⟩s=∫−11f(x)g(x)dμα,β(x)+∑j=1N∑k=0djλj,kf(k)(cj)g(k)(cj), where N,dj∈Z+, λj,k⩾0, dμα,β(x)=(1−x)α(1+x)βdx, α,β>−1, and cj∈R∖(−1,1). A connection formula that relates the Sobolev polynomials Sn with the Jacobi polynomials is provided, as well as the ladder differential operators for the sequence {Sn}n⩾0 and a second-order differential equation with a polynomial coefficient that they satisfied. We give sufficient conditions under which the zeros of a wide class of Jacobi-Sobolev polynomials can be interpreted as the solution of an electrostatic equilibrium problem of n unit charges moving in the presence of a logarithmic potential. Several examples are presented to illustrate this interpretation.

Knowledge of the isoelectric points (pIs) of viruses is beneficial for predicting virus behavior in environmental transport and physical/chemical treatment applications. However, the empirically measured pIs of many viruses have thus far defied simple explanation, let alone prediction, based on the ionizable amino acid composition of the virus capsid. Here, we suggest an approach for predicting the pI of nonenveloped viruses by excluding capsid regions that stabilize the virus polynucleotide via electrostatic interactions. This method was applied first to viruses with known polynucleotide-binding regions (PBRs) and/or three-dimensional (3D) structures. Then, PBRs were predicted in a group of 32 unique viral capsid proteome sequences via conserved structures and sequence motifs. Removing predicted PBRs resulted in a significantly better fit to empirical pI values. After modification, mean differences between theoretical and empirical pI values were reduced from 2.1-2.4 to 0.1-1.7 pH units. [ABSTRACT FROM AUTHOR]

Quantum cellular automata (QCA) enables performing logic operations at the sub‐nm scale. The clock field provides energy gain in QCA circuits, and the energy is dissipated while data flow from inputs to outputs during clock time slots. The authors start from a quantum mechanical model and end in a simple electrostatic model for energy calculation of molecular QCA systems, where the cells are fully polarised, and the tunnelling energy is neglectable compared to the Kink energy. The electrostatic model does not utilise Hartree–Fock approximation and projects asymmetric energy dissipation when the order of inputs are changed. The non‐adiabatic energy dissipations of basic QCA logic devices are analysed utilising electrostatic and thermodynamic models in subsequent clock time interval transitions. Essential considerations in designing low power QCA devices emerge. [ABSTRACT FROM AUTHOR]

The effectiveness of electrokinetic remediation for soils depends on several factors such as the arrangement and shape of electrodes. This paper presents a numerical study on external electrostatic field generated by seven different electrode configurations in any unbounded two-dimensional domain. The boundary condition at infinity for the voltage is approximated by the iterative algorithm that expands the domain till the limit of the specified tolerance (threshold value). The numerical results indicate that there is no unique configuration with larger effective area for all spacings between the oppositely charged electrodes. In addition, the configuration with the smallest inactive electric field strength spots for all spacings between the electrodes is not unique. Moreover, the voltage profile for all electrode configurations is nonlinear, and the external electric field strength varies widely near the electrodes. Only in the intermediate region between the electrodes the external electric field strength approaches a constant value. [ABSTRACT FROM AUTHOR]

The chalcogen bond, the noncovalent, electrostatic attraction between covalently bonded atoms in group 16 and Lewis bases, is present in protein−ligand interactions based on X-ray structures deposited in the Protein Data Bank (PDB). Discovering protein−ligand chalcogen bonding in the PDB employed a strategy that focused on searching the database for protein complexes of five-membered, heterocyclic ligands containing endocyclic sulfur with endo electron-withdrawing groups (isothiazoles; thiazoles; 1,2,3-, 1,2.4-, 1,2,5-, 1,3,4-thiadiazoles) and thiophenes with exo electron-withdrawing groups, e.g., 2-chloro, 2-bromo, 2-amino, 2-alkylthio. Out of 930 ligands investigated, 33 or 3.5% have protein−ligand S---O interactions of which 31 are chalcogen bonds and two appear to be S---HO hydrogen bonds. The bond angles for some of the chalcogen bonds found in the PDB are less than 90°, and an electrostatic model is proposed to explain this phenomenon. [ABSTRACT FROM AUTHOR]

The present study numerically investigates the feasibility of using multiple dielectric barrier discharge (multi-DBD) plasma actuators as a novel approach for active flow control over a large horizontal axis wind turbine rotor. The National Renewable Energy Laboratory 5 MW offshore wind turbine is used as the baseline case. This turbine uses pitch control system to adjust the generated power above its rated wind speeds, but at lower speeds, this system remains inactive. In this paper, the operational condition speed is considered lower than the rated wind speed. The mathematical electro-static model is implemented to simulate the effects of plasma actuator on the external flow and the results are incorporated into Navier-Stokes equations as a body force vector. A configuration of multi-DBD plasma actuators was located at inboard part of the blade along the span that produced a chord-wise body force. Three different cases have been considered based on the number of active actuators. It is revealed that the use of multi-DBD actuators placed parallelly one behind the other could enhance the induced velocity; this affects the pressure distribution and increases the aerodynamic torque. Results showed that, for the cases studied, the turbine power increments are respectively 0.85%, 0.77%, and 0.66%. [ABSTRACT FROM AUTHOR]

We use a two-dimensional electrostatic model to explore Van der Pauw (VdP) method on samples with holes. Results of electrostatic simulation based on the model are consistent with the experimental results. The quantitative investigation of VdP method on sample with one hole indicate the value of f , i.e. the right hand side of VdP equation, is depend on the position of contacts and the size of holes. We also quantitatively explore the VdP method used on sample with two holes in special position of contacts and sample geometry. According to the guidance of simulation and experiment, we find proper position of contacts, which make VdP equation f = 1 valid again on sample with holes. It is helpful for the optimization of VdP method and measuring the resistivity of sample with holes. [ABSTRACT FROM AUTHOR]

The environment of a solute molecule in an ionic liquid is likely to have large fluctuating electrostatic fields, and so the electrostatic properties of such a solute including its charge distribution and its polarizability may make a difference to both its static and dynamic properties. We have developed a new model for the static electrostatic distribution in the CS molecule with 7 charged sites and anisotropic polarizability on the carbon site and isotropic polarizability on the sulfurs. We have investigated static and dynamic properties of the neat liquid and solutions of CS in an ionic liquid, [dmim][NTf]. [ABSTRACT FROM AUTHOR]

Sulfonated polyacrylate copolymer (also known as vinyl sulfonated co-polymer; VS-Co) have been widely used in mineral scale control. However, the speciation chemistry of such polymers in solution is not fully understood. In this paper, the acid-base and calcium complex solution chemistry of a VS-Co has been determined from 0.01 to 2 m ionic strength and from 25 to 90 °C by combining electrostatic theory with potentiometric titrations. To process the titration data, VS-Co is treated as a hypothetical, averaged monoacid, HA, with the same concentration of the active carboxylic functional groups of VS-Co. The acid and calcium dissociation reactions of this acid are simply considered as 1:1 type hypothetical reactions, namely HA↔H + + A − and Ca(A⋯A)↔Ca 2+ + (A⋯A) 2− , with (A⋯A) 2− as an arbitrary combinations of two dissociated A − units. The microconstants of the acid dissociation reaction are fitted with a linear electrostatic model with p K a = p K a , intr + b e l e c θ A − , where p K a , intr is an intrinsic constant referring to the condition of zero dissociation, θ A − is the deprotonated fraction of carboxylic functional groups and b elec is an electrostatic factor based on polyelectrolyte theory. Similarly, the microconstants of the Ca 2+ dissociation reaction are fitted with p K CaA 2 = p K CaA 2 , intr + 2 b elec θ A − with doubled electrostatic effect since the complexation of Ca 2+ with the polymer is considered to neutralize two negative charges. To quantitatively describe the speciation of VS-Co at various conditions, the p K a , intr , p K CaA 2 , intr , and b elec values are fitted empirically as a function of temperature ( T , K), and ionic strength ( I , m): p K a , intr = 5.068 − 128.398 T − 0.924 × I 1 / 2 + 0.311 × I p K CaA 2 , intr = 5.754 − 888.644 T − 5.749 × I 1 / 2 + 2.221 × I b e l e c = 3.234 − 1.321 × I 1 / 2 + 0.399 × I . Fitted results suggests no significant effect of temperature on the electrostatic factor b elec , which is consistent with electrostatic theory. Results from this study can be used to predict the equilibria of VS-Co in a solution, at various temperature, ionic strength, pH, and metal concentrations. [ABSTRACT FROM AUTHOR]

Background. The selectivity of biological cation channels is defined by a short, narrow selectivity filter, having a negative net fixed charge Qf. Voltage gated bacterial channels (NaChBac and some others) are frequently used in biophysics as simplified models of mammalian calcium and sodium channels. We report an experimental, analytic and numerical study of the effects of Qf and bulk ionic concentrations of Ca2+ and Na+ on conduction and selectivity of NaChBac channels, wild type and Qf-varied mutants. Methods. Site-directed mutagenesis and voltage clamp recordings were used to investigate the Na+/Ca2+ selectivity, divalent blockade and anomalous mole fraction effect (AMFE) for different NaChBac wild type/ mutants channels and the properties dependence on Qf. Experimental results were compared with Brownian dynamics simulations and with analytic predictions of the ionic Coulomb blockade (ICB) model, which was extended to encompass bulk concentration effects. Results. It was shown that changing of Qf from -4e (for LESWAS wild type) to -8e (for LEDWAS mutant) leads to strong divalent blockade of the Na+ current by micromolar amounts of Ca2+ ions, similar to the effects seen in mammalian calcium channels. The BD simulations revealed a concentration-related logarithmic shift of the conduction bands. These results were shown to be consistent with ICB model predictions. Conclusions. The extended ICB model explains the experimental (divalent blockade and AMFE) and simulated (multi-ion bands and their concentration-related shifts) selectivity phenomena of NaChBac channel and its charge-varied mutants. These results extend the understanding of ion channel selectivity and may also be applicable to biomimetic nanopores with charged walls. [ABSTRACT FROM AUTHOR]

An electrostatic model is proposed to calculate the formation energy ΔЕ of linear HCCH...Х (X = F, Cl, Br, I) hydrogen-bonded anionic complexes between a halide ion and an acetylene molecule. The potential energy surface (PES) in this model includes four kinds of interaction in the HCCH...Х system, namely, electrostatic (Coulombic), polarization, dispersive, and exchange repulsion interactions. An analytical expression for the formation energy ΔЕ of the complexes is obtained, and the PES parameters necessary for calculating ΔЕ are determined. The calculated ΔЕ values are in good agreement with ab initio data from the literature. The relative contributions from the different types of interactions to ΔЕ are estimated and analyzed. The electrostatic (Coulombic) interaction makes the main contribution to the formation energy of HCCH...Х clusters. [ABSTRACT FROM AUTHOR]

A microelectromechanical system capacitive pressure sensor with a differential configuration (patent pending), including a reference and sensitive capacitor, is presented. A single cavity includes both reference and sensitive electrodes. This implementation is achieved by a size reduction of the sensitive electrode. A reduction of the 40% on the sensible electrode area represents a decrease in the sensor sensitivity of only 12.5%, and allows the reference capacitor implementation in the area commonly used only for the sensitive capacitor. A tridimensional model of the sensor was simulated using a finite‐element solver considering coupled mechanical and electrostatic models. The simulations show that this pressure sensor has a sensitivity of 4.2 fF/bar. The proposed pressure sensor designs use only materials available in complementary metal oxide silicon (CMOS) standard processes. A CMOS compatible post‐process, based on the sacrificial material technique and its restrictions is presented. [ABSTRACT FROM AUTHOR]

Two models (partition and electrostatic) were utilized to explain the retention data of four polar compounds with guanidine or tertiary amine moieties (metformin, phenformin, tolylformin, and ranitidine) in ion-pairing liquid chromatography based on C18 stationary phase (Zorbax Eclipse XDB column). Mobile phase composition, concentration of the ion-pairing (alkylsulphonates with 5 – 8 carbon atoms), and pH of the aqueous component were varied to determine the corresponding dependence of the retention factors and explanation by one model. Good correlations were found for retention factor versus concentration of ion pairing alkyl sulfonates concentration with a slope similar to the predicted values by the electrostatic model and between retention factor and the content of methanol used as organic modifier in mobile phase. Some extrapolations of the linear dependences were used in estimating the hydrophobic character of the pair between analyte and alkyl sulfonate ions in accordance to the partition model. [ABSTRACT FROM PUBLISHER]

Abstract: The capabilities of three simplified analytical equations to accurately model electrostatic interactions during proton binding and release by linear anionic polyelectrolytes in aqueous solution were evaluated. The impermeable sphere (IS), Donnan (DN), and cylindrical (CY) electrostatic models were fit to experimental acid–base titration curves of linear polyacrylamide-co-acrylate having ionizable site densities ranging from ca. 10–35%. The titrations were conducted in 0.003–0.12M NaCl solutions and the sum of squared errors from modeled and experimental data was used as a comparative index of each model’s capability. In addition, the relative size of each polyelectrolyte was estimated from its measured specific viscosity and then compared against the values obtained from the fitting procedure for the size parameter that each model contained. Although the IS and DN electrostatic models could be used to obtain reasonably good fits to each titration curve, the size parameter values obtained by each model were not reflective of the actual polyelectrolyte sizes, indicating that the models had limited physical meaning and that the size parameter was essentially just an additional fitting parameter in each model. In contrast, the CY model was not only more effective in its ability to fit the titration data but also provided a better physical representation of the polyelectrolyte size. Therefore, for polyelectrolytes that remain essentially linear or are only loosely coiled such that counter ions are free to travel throughout the polymer structure, we conclude that the CY model and its morphological representation of a cylindrical polyelectrolyte are more valid and realistic than the IS and DN models and their representation of polyelectrolytes as spheres. [ABSTRACT FROM AUTHOR]

We introduce a new global approach for image dithering, stippling, screening and sampling. It is inspired by the physical principles of electrostatics. Repelling forces between equally charged particles create a homogeneous distribution in flat areas, while attracting forces from the image brightness values ensure a high approximation quality. Our model is transparent and uses only two intuitive parameters: One steers the granularity of our halftoning approach, and the other its regularity. We evaluate two versions of our algorithm: A discrete version for dithering that ties points to grid positions, as well as a continuous one which does not have this restriction, and can thus be used for stippling or sampling density functions. Our methods create very few visual artefacts, reveal favourable blue-noise behaviour in the frequency domain, and have a lower approximation error under Gaussian convolution than state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Abstract: Gordy identified electronegativity of an atom with the electrostatic potential felt by one of its valence electrons and suggested an ansatz, χ = Z eff/r cov where χ is the electronegativity, Z eff is the effective nuclear charge and r cov is the radial distance equal to atom’s single bond covalent radius. In this report we have elucidated that the use of covalent radius in evaluating the electronegativity, (χ), of atoms through Gordy’s formula, χ = Z eff/r cov, is not justified. Armed with this knowledge and relying upon the electronegativity equalization principle, we have argued that the most probable radius (Slater radius), and not the covalent radius, is the fundamental size descriptor of atoms in mathematical formulation of electronegativity property of atoms. We have also suggested that the electronegativity, χ, is not equal to Z eff/r according to Gordy’s original formula rather it is proportional to Z eff/r and the new electronegativity ansatz is χ =[a(Z eff/r)+ b], where a and b are constants and r is the Slater (most probable) radius of atoms. We have taken care so that the electronegativity is evaluated in proper unit i.e. energy unit. We have computed the electronegativity of 103 elements of the periodic table through the new suggested ansatz and using Slater radii and effective nuclear charge computed by us. The evaluated new electronegativities are found to satisfy the sine qua non of a reasonable scale of electronegativity by exhibiting periodicity of periods and groups, and observing silicon rule and correlating many physico-chemical properties of elements. The intrinsic inertness of Hg atom is revealed in the present scale. [Copyright &y& Elsevier]

The effect of pH and ionic strength on the interaction between pesticides (paraquat and MCPA) and humic substances (soil extracted humic acid and fulvic acid) was interpreted with a simple electrostatic model. Potentiometric titrations were carried out, the charge curves for the humic substances were obtained for three values of ionic strength, and the parameters that define proton binding to humic and fulvic acid were calculated by application of the NICA¿Donnan model. The binding isotherms were obtained for paraquat¿humic acid and paraquat¿fulvic acid at three different pH values and two ionic strengths, and the MCPA¿fulvic acid binding isotherms for two pH values and two ionic strengths. Binding experiments were carried out by use of a membrane dialysis technique and the concentrations of pesticide were measured by HPLC. The amount of paraquat bound to the humic substances increased with pH, decreased with increasing ionic strength, decreased in the presence of Ca2+ and was greater for humic acid than for fulvic acid. Much less binding was observed with MCPA than with paraquat, and therefore the isotherms were not well defined. The application of a simple electrostatic model enabled us to conclude that the effect of pH and ionic strength on binding of paraquat to humic substances is due to the effect that these parameters have on the humic substance charge, and the model provided an excellent reproduction of the experimental binding isotherms. [Copyright &y& Elsevier]

Abstract: We give a survey concerning both very classical and recent results on the electrostatic interpretation of the zeros of some well-known families of polynomials, and the interplay between these models and the asymptotic distribution of their zeros when the degree of the polynomials tends to infinity. The leading role is played by the differential equation satisfied by these polynomials. Some new developments, applications and open problems are presented. [Copyright &y& Elsevier]

Abstract: We performed the first-principles calculation to investigate the electronic structure and polarization behaviors in PbTiO3/SrTiO3 (PST) superlattices. The DOS (density of state) profiles show that there are strong hybridizations of atom Ti–O and Pb–O which play very important roles on ferroelectricity of the PbTiO3/SrTiO3 superlattices. Comparing to the corresponding paraelectric phase, we find the electrons of the PT (PbTiO3) layers occupy lower energy states and electrons of the ST (SrTiO3) layer occupy higher energy states. It is shown that the polarizations of the superlattices decrease with proportion of SrTiO3 increasing. The constant polarization of local layer indicates that PST superlattices with small modulation lengthen can be approximately considered as a single ferroelectric material. Furthermore, according to electrostatic model, we find that directions of internal electric fields in PT and ST layers are opposite. In PST superlattices, internal electric field in PT layer leads to the loss of polarization of this layer, but the polarization of ST layer is induced by internal electric field of this layer. Compared to the value of the polarization in bulk PbTiO3, polarization of PST is smaller. [Copyright &y& Elsevier]

Abstract: The heats of protonation of n-pentylamine, dipentylamine, tributylamine and heats for the first protonation step of 1,8-diamino-3,6-dioxaoctan, diazacrownether 22 and cryptand 222 in pure acetonitril and propylene carbonate and of diazacrownether 22 and dibenzosubstituted ligand 22BB in water+acetonitrile mixtures have been measured at 298.15K using calorimetric titrations. The values of the reaction enthalpies in the solvents as well as the data in aqueous and methanol solutions reported in literature are analysed in terms of the simple electrostatic model and thermodynamic parameters of transfer (solvation) of the reactants. Estimation of the electrostatic and covalent contributions to standard enthalpy of transfer of the reactions from water to non-aqueous and mixed solvents has been made. [Copyright &y& Elsevier]

A model based on the solution of the electrostatic potential for a geometry of three dielectric regions associated with a gramicidin A channel (GA) is presented. The model includes a cylindrical dielectric layer to represent the peptide backbone and dipole rings to account for dipolar side chains. Image potential and dipolar contributions for different orientations and positions along the channel are analyzed. The conductance of GA and two analogues obtained by substituting the amino acid at position 1 are studied. The numerical simulation reproduces experimental results (Barrett et al. 1986, Biophys J 49, 673-686) and supports the idea that electrostatic dipole-ion interactions are of primary importance in gramicidin channel function. [ABSTRACT FROM AUTHOR]

This paper reports on a laboratory experiment to study the effect of vehicle net charge on the inception of a positive leader from an aircraft exposed to high atmospheric electric fields. The experiment models the first stage of aircraft‐triggered lightning in which a positive leader typically develops from the vehicle and is shortly afterwards followed by a negative leader. This mechanism of lightning initiation amounts to around 90% of strikes to aircraft. Aircraft can acquire net charge levels of the order of a millicoulomb from a number of sources including corona emission, charged particles in the engine exhaust, and charge transfer by collisions with particles in the atmosphere. In addition, aircraft could potentially be artificially charged through controlled charge emission from the surface. Experiments were performed on a model aircraft with a 1m wingspan, which was suspended between two parallel electrodes in a 1.45m gap with voltage difference of a few hundred kilovolts applied across it. In this configuration, it is found that the breakdown field can vary by as much as 30% for the range of charging levels tested. The experimental results show agreement with an electrostatic model of leader initiation from aircraft, and the model indicates that the effect can be substantially stronger if additional negative charge is added to the aircraft. The results from this work suggest that flying uncharged is not optimal in terms of lightning avoidance and open up the possibility of developing risk‐reduction strategies based on net charge control. Plain Language Summary: Commercial aircraft are typically struck by lightning around once per year, and the vast majority of these events are triggered by the aircraft itself. The lightning discharge originates on the surface of the aircraft in areas with sharp edges. Whether a discharge develops is in part due to the net electric charge of the aircraft, which can be acquired both naturally or artificially. Previous work has shown that it is theoretically possible to reduce the likelihood of a lightning strike occurring by manipulating the net charge of the aircraft. In this paper, the authors perform laboratory experiments to validate this hypothesis. These experiments demonstrate that the threshold for lightning could be increased by 30% by charging the aircraft negatively, which means that an aircraft could fly safely through ambient electric fields that are around 30% higher than those of an uncharged baseline. Theoretical estimates suggest that further improvement may be possible if the aircraft were charged to a more negative state than those tested. This work gives laboratory scale experimental evidence that it is possible to reduce the frequency of lightning strikes on aircraft by manipulating their charge and encourages further investigation of the proposed lightning strike risk reduction strategy. Key Points: Aircraft‐triggered lightning is influenced by the net charge of the floating bodyPositive leader inception from an aircraft requires higher amplitude external fields when negatively biasing the vehicleExperimental results validate a proposed method of aircraft‐triggered lightning strike risk reduction [ABSTRACT FROM AUTHOR]

A fast, empirical method, Mut-pKa, is presented for predicting the pKa values of ionizable residues in proteins based on mutation. The method compares the effect of mutating each residue that may act as a hydrogen bond donor or acceptor for the ionizable residue. The energetic effect of each type of mutation, along with a desolvation measure and the overall background charge, is fit against pKa data for histidine and carboxyl residues. A total of 214 residues from 35 different proteins were used in the dataset. Using 11 parameters for each type of ionizable residue, a root mean squared error (RMSE) of 0.78 and 1.12 pH units were obtained for carboxyl and histidines residues, respectively, using leave one out cross validation (LOOCV). The results were particularly promising for buried residues, which had RMSE values of 0.99 and 1.13 for carboxyl and histidine residues, respectively. A number of desolvation measures were tested. The simplest measure, the number of atoms surrounding the residue, was found to work best. The effect of using dynamics was also studied using short molecular dynamics runs, followed by minimization of the structures. Mut-pKa has significantly fewer parameters than, but similar performance to, other empirical methods. Because of this and the LOOCV results, we believe the model is robust and that overfitting is not a problem., (Copyright © 2011 Wiley Periodicals, Inc.)