Protein Electrostatics: Rapid Multigrid-Based Newton Algorithm for Solution of the Full Nonlinear Poisson-Boltzmann Equation

Abstract

A new method for solving the full nonlinear Poisson-Boltzmann equation is outlined. This method is robust and efficient, and uses a combination of the multigrid and inexact Newton algorithms. The novelty of this approach lies in the appropriate combination of the two methods, neither of which by themselves are capable of solving the nonlinear problem accurately. Features of the Poisson-Boltzmann equation are fully exploited by each component of the hybrid algorithm to provide robustness and speed. The advantages inherent in this method increase with the size of the problem. The efficacy of the method is illustrated by calculations of the electrostatic potential around the enzyme Superoxide Dismutase. The CPU time required to solve the full nonlinear equation is less than half that needed for a conjugate gradient solution of the corresponding linearized Poisson-Boltzmann equation. The solutions reveal that the field around the active sites is significantly reduced as compared to that obtained by solving the corresponding linearized Poisson-Boltzmann equation. This new method for the nonlinear Poisson-Boltzmann equation will enable fast and accurate solutions of large protein electrostatics problems.     

Revisiting the Association of Cationic Groove-Binding Drugs to DNA Using a Poisson-Boltzmann Approach

Proper modeling of nonspecific salt-mediated electrostatic interactions is essential to understanding the binding of charged ligands to nucleic acids. Because the linear Poisson-Boltzmann equation (PBE) and the more approximate generalized Born approach are applied routinely to nucleic acids and their interactions with charged ligands, the reliability of these methods is examined vis-à-vis an efficient nonlinear PBE method. For moderate salt concentrations, the negative derivative, SK_pred, of the electrostatic binding free energy, ΔG_el, with respect to the logarithm of the 1:1 salt concentration, [M⁺], for 33 cationic minor groove drugs binding to AT-rich DNA sequences is shown to be consistently negative and virtually constant over the salt range considered (0.1-0.4 M NaCl). The magnitude of SK_pred is approximately equal to the charge on the drug, as predicted by counterion condensation theory (CCT) and observed in thermodynamic binding studies. The linear PBE is shown to overestimate the magnitude of SK_pred, whereas the nonlinear PBE closely matches the experimental results. The PBE predictions of SK_pred were not correlated with ΔG_el in the presence of a dielectric discontinuity, as would be expected from the CCT. Because this correlation does not hold, parameterizing the PBE predictions of ΔG_el against the reported experimental data is not possible. Moreover, the common practice of extracting the electrostatic and nonelectrostatic contributions to the binding of charged ligands to biopolyelectrolytes based on the simple relation between experimental SK values and the electrostatic binding free energy that is based on CCT is called into question by the results presented here. Although the rigid-docking nonlinear PB calculations provide reliable predictions of SK_pred, at least for the charged ligand-nucleic acid complexes studied here, accurate estimates of ΔG_el will require further development in theoretical and experimental approaches.     

Dependence of the Electrophoretic Mobility of DNA in Gels on Field Intermittency

Abstract

The electrophoretic mobility of double helical DNA in agarose and Polyacrylamide gels increases as a function of time after the electric field is applied to the gel and decreases after the field is terminated. The changes are large for long (more than 10 kb) molecules. The effects of other variables are indicated.     

On a Nonlinear Master Equation and the Haken-Kelso-Bunz Model

A nonlinear master equation (NLME) is proposed basedon general information measures.Classical and cut-off solutions of the NLME are considered.In the former case, the NLME exhibits uniquely defined stationary distributions. In the latter case, there are multiple stationary distributions.In particular, for classical solutions, it is shown that transient solutions converge to stationary distributions that maximize information measures (H-theorem). Cut-off distributions arestudied numerically for the Haken-Kelso-Bunz model. The Haken-Kelso-Bunz modelis known to describe multistable human motor control systems. It is shownthat a stochastic Haken-Kelso-Bunz model based on a NLME can exhibit multiplestationary cut-off distributions.In doing so, we illustrate that multistability in stochastic biological systems can beestablished by means of cut-off distributions.     

Design of a Fluorescent Electrophoretic Mobility Shift Assay Improved for the Quantitative and Multiple Analysis of Protein-DNA Complexes

We describe a protocol for the fluorescent electrophoretic mobility shift assay improved for the quantitative analysis of protein-DNA complexes. Fluorescent-labeled oligonucleotide probes incubated with nuclear proteins were followed by electrophoresis. The signals for protein-DNA complexes were measured and normalized with fluorescent-labeled marker using fragment analysis software. This assay proved reliable measurement and multiple detection of DNA binding proteins.     

A Multiparametric Equation for Calculation of the Animal Lifespan

Biophysics - Abstract—We propose a multiparametric equation for calculation of the average natural lifespan of various vertebrate species, including well-known mammalian...     

一个生物种群非线性泛函微分方程模型整体解的聚集性

自然界的种群,如鱼类、鸟类和有蹄兽类有聚集成群的现象,研究种群的聚集性是生物数学中的一个有趣的课题．本文讨论了一个有关生物种群的非线性泛函微分方程模型整体解的聚集性和稳定性问题．     

Electrophoretic Plugging of Nuclear Pores by Using the Nuclear Hourglass Technique

The nuclear hourglass technique (NHT) was recently introduced as a novel technique that measures the electrical nuclear envelope (NE) conductance of isolated Xenopus laevis oocyte nuclei. The main conclusion drawn from NHT work so far is that nuclear pore complexes (NPCs) of oocytes are in an electrically open state under physiological conditions, with a mean conductance of 1.7 nS per NPC. Since nuclear patch-clamp data indicate that usually NPCs are electrically closed, our work has been challenged by the notion that NHT cannot assure a high resistance seal (``gigaseal') between glass wall and NE like that required for patch-clamp experiments. Thus, NHT could have dramatically underestimated NE electrical resistance. Here we demonstrate that NHT does not require a gigaseal for accurate NE conductance measurements. In addition, we present experimental conditions where mean single NPC electrical conductance is reduced 26-fold due to electrophoretic plugging by negatively charged nucleoplasmic macromolecules. In addition, data indicate that under physiological conditions (i.e., when macromolecules are offered in the cytosolic solution) the nuclear surface is heavily folded, underestimating ``true' NE surface by a factor of 2.6. When ``true' NE surface area is taken into consideration, modified values of mean single NPC conductances of 654 pS for electrically open conditions and 25 pS for electrically plugged conditions can be calculated. We conclude that the large overall NE conductance detected with the nuclear hourglass technique in intact Xenopus laevis oocyte nuclei can be explained by the sum of single NPC conductances in the pS range, as long as open probability is high. This confirms previous patch-clamp work concerning single NPC conductance, but disagrees with the view that mean open probability of NPC channels is usually low. Received: 27 March 2001/Revised: 3 July 2001     

Effect of pH on the Electrophoretic Mobility of Spores of Bacillus anthracis and Its Surrogates in Aqueous Solutions

The electrophoretic mobility (EPM) of endospores of Bacillus anthracis and surrogates was measured in aqueous solution across a broad pH range and several ionic strengths. EPM values trended around phylogenetic clustering based on the 16S rRNA gene. Measurements reported here provide new insight for Bacillus anthracis surrogate selection and for attachment/detachment and transport studies.     

Direct Calculation of a Tree Length Using a Distance Matrix

Comparative studies of tree-building methods have shown minimum evolution to be in general an accurate criterion for selecting a true tree. To improve the use of this criterion, this paper proposes a method for rapidly and directly calculating a length of a dichotomous tree without having to resort to branch length calculations. This direct calculation (DC) method applies to the complete final topology, giving equal importance to each branch after a dichotomy. According to this method, the tree length S _DC is S _DC =∑ _i ∑ _j (D _ij /2 ^Bij ) = (∑ _i<j ∑D _ij 2 ^Bmax−Bij )/2 ^{Bmax −1} where D _ij is the observed distance between taxa i and j, B _ij is the number of branches connecting i and j, Bmax is the greatest B _ij in the tree, and the powers of two are due to the dichotomy of the tree. This tree length expression may be used as a rapid method for selecting the shortest tree from a set of hypothetical or subobtimal trees. Received: 2 March 2000 / Accepted: 24 March 2000     

人口动力学中非线性发展方程解的爆破现象

讨论描述人口发展规律的一类非线性发展方程具有第三类非线性边界条件的混合问题．在已知函数满足某些假设条件下,证明了其解在有限时间内爆破．     

Deletion of New Covalently Linked Cell Wall Glycoproteins Alters the Electrophoretic Mobility of Phosphorylated Wall Components of Saccharomyces cerevisiae

The incorporation of radioactive orthophosphate into the cell walls of Saccharomyces cerevisiae was studied. 33P-labeled cell walls were extensively extracted with hot sodium dodecyl sulfate (SDS). Of the remaining insoluble radioactivity more than 90% could be released by laminarinase. This radioactive material stayed in the stacking gel during SDS-polyacrylamide gel electrophoresis but entered the separating gel upon treatment with N-glycosidase F, indicating that phosphate was linked directly or indirectly to N-mannosylated glycoproteins. The phosphate was bound to covalently linked cell wall proteins as mannose-6-phosphate, the same type of linkage shown previously for soluble mannoproteins (L. Ballou, L. M. Hernandez, E. Alvarado, and C. E. Ballou, Proc. Natl. Acad. Sci. USA 87:3368-3372, 1990). From the phosphate-labeled glycoprotein fraction released by laminarinase, three cell wall mannoproteins, Ccw12p, Ccw13p and Ccw14p, were isolated and identified by N-terminal sequencing. For Ccw13p (encoded by DAN1 [also called TIR3]) and Ccw12p the association with the cell wall has not been described before; Ccw14p is identical with cell wall protein Icwp (I. Moukadiri, J. Armero, A. Abad, R. Sentandreu, and J. Zueco, J. Bacteriol. 179:2154-2162, 1997). In ccw12, ccw13, or ccw14 single or double mutants neither the amount of radioactive phosphate incorporated into cell wall proteins nor its position in the stacking gel was changed. However, the triple mutant brought about a shift of the 33P-labeled glycoprotein components from the stacking gel into the separating gel. The disruption of CCW12 results in a pronounced sensitivity of the cells to calcofluor white and Congo red. In addition, the ccw12 mutant shows a decrease in mating efficiency and a defect in agglutination.     

一类三阶非线性递归差分方程的全局渐近稳定性与振动性(英文)

研究了一类三阶方程x_(n+1)=x_nx_(n-2)+a/x_n+x_(n-2)+b,n=0,1,…的解的振动性和正解的全局渐近稳定性,证明了正平衡解的全局渐近稳定,非平衡解具有规律的振动性.