Monte Carlo and modified Tanford-Kirkwood results for macromolecular electrostatics calculations

The understanding of electrostatic interactions is an essential aspect of the complex correlation between structure and function of biological macromolecules. It is also important in protein engineering and design. Theoretical studies of such interactions are predominantly done within the framework of Debye-Huckel theory. A classical example is the Tanford-Kirkwood (TK) model. Besides other limitations, this model assumes an infinitesimally small macromolecule concentration. By comparison to Monte Carlo (MC) simulations, it is shown that TK predictions for the shifts in ion binding constants upon addition of salt become less reliable even at moderately macromolecular concentrations. A simple modification based on colloidal literature is suggested to the TK scheme. The modified TK models suggested here satisfactorily predict MC and experimental shifts in the calcium binding constant as a function of protein concentration for the calbindin D-9k mutant and calmodulin.

Lamé differential equations and electrostatics

The problem of existence and uniqueness of polynomial solutions of the Lamé differential equation A(x)y″ + 2B(x)y′ + C(x)y = 0, where A(x),B(x) and C(x) are polynomials of degree p + 1,p and p - 1, is under discussion. We concentrate on the case when A(x) has only real zeros aj and, in contrast to a classical result of Heine and Stieltjes which concerns the case of positive coefficients rj in the partial fraction decomposition B(x)/A(x) = ∑j p=0 rj/(x - aj), we allow the presence of both positive and negative coefficients rj. The corresponding electrostatic interpretation of the zeros of the solution y(x) as points of equilibrium in an electrostatic field generated by charges rj at aj is given. As an application we prove that the zeros of the Gegenbauer-Laurent polynomials are the points of unique equilibrium in a field generated by two positive and two negative charges. © 2000 American Mathematical Society.

Uma breve biografia de Stephen Gray (1666-1736)

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Podolsky's higher-order electromagnetism from first principles

Podolsky's higher-order field equations are obtained by generalizing the laws of Podolsky's electrostatics, which follow from Coulomb's generalized law and superposition, to be consistent with special relativity. In addition, it is necessary to take into account the independence of the observed charge of a particle on its speed. It is also shown that the gauge-independent term concerning the Feynman propagator for Podolsky's generalized electrodynamics has a good ultraviolet behaviour at the expense of a negative metric massive ghost which, contrary to what is currently assumed in the literature, is non-tachyonic. A brief discussion on Podolsky's characteristic length is presented as well.

THE B-FORM TO Z-FORM TRANSITION OF POLY(DG-M(5)DC) IS SENSITIVE TO NEUTRAL SOLUTES THROUGH AN OSMOTIC-STRESS

Several neutral solutes, ranging in size from methanol to a tetrasaccharide, stachyose, are shown to stabilize the left-handed Z form of the methylated polynucleotide poly(dG-m(5)dC). The action of these solutes is consistent with an osmotic stress, that is, with their effect on water chemical potentials coupled to a difference in the number of-associated water molecules between the B and Z conformations. The apparent difference in hydration between the two forms is, however, dependent on the particular solute used to probe the reaction. The effect of solutes is not consistent either with a direct binding of solute or with an indirect effect on electrostatics or ion binding through changes in the solution dielectric constant. The interplay of NaCl and neutral solute in modulating the B-Z transition suggests that salt also could be stabilizing the Z form through an osmotic stress.

Zeros of orthogonal polynomials generated by canonical perturbations of measures

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Polyacids self-dissociation model

This work deals with a model to interpret pH measurements of solutions of weak rodlike polyacids, in the absence of added salts or titrating base. The polyacid is modeled as a series of point charges discretely distributod in a straight line with a distance of closest approach for the protons and an average distance between dissociable monomers, projected in the polymer chain axis. Aside from these two geometrical parameters, the dissociation constant for the isolated monomer that describes the proton dissociated monomer interaction forms the basis of the model. The assumption of cylindrical symmetry and the adoption of the cell model lead to a form written in terms of elementary functions for the mean electrostatic potential. Values of pH (related to the proton concentration in a region beyond the influence of the polyacid) as a function of polymer concentration are displayed graphically for some values of the geometrical parameters and of the dissociation, constant. Theoretical predictions of pH values as a function of polymeric concentration are compared with measured values for poly-L-glutamic and polygalacturonic acids, and a good agreement is found. Theoretical values for the dissociation degree in terms of polymeric concentration are shown for the two experimentally investigated systems. These values are in a range appreciably smaller than what is usually studied as a result of titration.

Structure of tick anticoagulant peptide at 1.6 Å resolution complexed with bovine pancreatic trypsin inhibitor

The structure of tick anticoagulant peptide (TAP) has been determined by X-ray crystallography at t.6 Å resolution complexed with bovine pancreatic trypsin inhibitor (BPTI). The TAP-BPTI crystals are tetragonal, a = b = 46.87, c = 50.35 Å, space group P41, four complexes per unit cell. The TAP molecules are highly dipolar and form an intermolecular helical array along the c-axis with a diameter of about 45 Å. Individual TAP units interact in a head-to-tail fashion, the positive end of one molecule associating with the distal negative end of another, and vice versa. The BPTI molecules have a uniformly distributed positively charged surface that interacts extensively through 14 hydrogen bonds and two hydrogen bonded salt bridges with the helical groove around the helical TAP chains. Comparing the structure of TAP in TAP-BPTI with TAP bound to factor Xa(Xa) suggests a massive reorganization in the N-terminal tetrapeptide and the first disulfide loop of TAP (CyS5(T)- Cys 15(T)) upon binding to Xa. The Tyr1(T)OH atom of TAP moves 14.2 Å to interact with Asp189 of the S1 specificity site, Arg3(T)CZ moves 5.0 Å with the guanidinium group forming a cation-π-electron complex in the S4 subsite of Xa, while Lys7(T)NZ differs in position by 10.6 Å in TAP-BPTI and TAP-Xa, all of which indicates a different pre-Xa-bound conformation for the N- terminal of TAP in its native state. In contrast to TAP, the BPTI structure of TAP-BPTI is practically the same as all those of previously determined structures of BPTI, only arginine and lysine side-chain conformations showing significant differences.

Ensino de eletrostática: a história da ciência contribuindo para a aquisição de subsunções

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Experimentos de baixo custo para o ensino de eletrostática no nível fundamental

The experimentation in the teaching of physics has been extensively studied over the years because of its potential as a tool demonstration of physics phenomena studied in classroom. In such a perspective view of the action of apprentice student involving teaching future teachers of physics, under the Program PIBID CAPES, developed since 2009, seeks ways to improve the teaching of physics experiments using the theme chosen for the electrostatic work was . In this particular work, we report the development of the project in a State School located in the city of Rio Claro, in two rooms in the 9th grade in elementary school. It is planned with the activities of teaching physics at this level of education, look at how two different ways of displaying the contents of electrostatics in a playful way for elementary students and implement a library of experiments so that students can take the experiments to their homes

O ensino e a surpresa: experimentos surpreendentes e suas possibilidades no ensino de Física

Some experiments in Physics teaching have an amazing effect among the students, that is, generally be characterized by counteracting the initial expectations of students. This characteristic may contribute to the emergence of learning situations extremely promising. However, the privilege, by the teacher, the description of certain results shortens the involvement that the student could establish on teaching situations favor a more careful observation that can be done. We discuss in this paper, the that surprise may be manifested in the student on an experimental demonstration and its ability to mobilize the interest and curiosity of this student. We intend to observe the pedagogic value that represents the amazing effect such in situations of teaching and learning, particularly for the Teaching of Physics, as well as the possibilities for educational approaches.Through an extensive analysis of several authors who address about experimental learning activities, Epistemology of Science and Education, we found some results that lead us to understand some of the possibilities that the surprise element can propose. We describe a demonstration activity that we consider amazingly from our point of view and that was realized in a regular classroom in a of Rio Claro Public High School in the year of 2011

O uso de experimentos didáticos como ferramenta para o ensino de física nos anos iniciais da educação básica

When it comes to teaching physics in the early years of elementary school, the first question is: but there are opportunities to teach concepts to children of such complexity? This study sought to examine approaches and strategies to enter the Basic Education in Physics. To this end, we used low cost materials testing, taking as its starting point the work of Ferreira (1978) instrumentation for Teaching Physics, particularly with the theme electrostatics. The present study was made from the use of prototypes developed with the materials cited. Observations were made in the classroom looking for, from the records of teaching, analyzing the behavior of children and their arguments, possibilities for Physics Teaching this age group as well as some evidence of their cognitive development. In teaching discussions were held with students of the early years of elementary school involving conceptual and phenomenological aspects, adapting such knowledge at the level of logical and mathematical thinking that was still under development. The work shows that it is possible to work on electrostatic physical concepts with children belonging to the age group of nine to ten years. With the support of the group Pibid Physics city of Rio Claro, I realize my observations and practices at the Municipal School Marcelo Schmidt, which proved to be available and open for acceptance of this proposal

O experimento e o lúdico: reflexões sobre atividades didáticas experimentais para o ensino de Física e a ludicidade

In this work, is discussed the importance of experimental activities in Education of Physics in Basic Education from the experience of Supervised Stage and the work with the Initiation of Teaching in the Program PIBID CAPES, in this case linked to the Department of Education of the Institute of Biosciences, Campus Rio Claro, São Paulo State, in partnership with three schools of basic education in the city. At first, based on the work of Ferreira with Instrumentation for Teaching Physics, consider the electrostatic theme. The focus is the searching for equipments constructed with low cost materials and easy access. Were developed and promoted strategies of the use of such materials in Physics’ Teaching, with a view to reintroducing experimental teaching activities in Public Basic Education, in the form Workshop Learning and Teaching of Physics, as well as lessons of Laboratory with the help of script and also in the form of an Experiments Library. These experimental activities were critically analyzed with a focus on playfulness. The focus of work in experimental activities for the Physics’ Teaching allowed to redeem, critically, didactic materials. From the standpoint of playfulness, playful moments and interaction of individuals with the knowledge that provides the experimental material when used strategically, they seem to be of great relevance to the Physics’ Teaching in Basic Education. It is possible to use experiments in Physics’ Teaching in public schools