A P-stable exponentially-fitted method for the numerical integration of the Schrödinger equation

In this paper we present a P-stable exponentially-fitted four-step method for the numerical integration of the radial Schrödinger equation. More specifically we present a method than satisfies the property of P-stability and also integrates exactly any linear combination of the functions {1, x, exp( ± w x), x exp( ± w x), x ²exp( ± w x)}. We tested the efficiency of our newly developed scheme against well known methods, with excellent results. The numerical illustration showed that our method is considerably more efficient compared to well‐known methods used for the numerical integration of resonance problem of the radial Schrödinger equation.     

A Förster-resonance-energy transfer-based method for fluorescence detection of the protein redox state

A method for fluorescence detection of a protein's redox state based on resonance energy transfer from an attached fluorescence label to the prosthetic group of the redox protein is described and tested for proteins containing three types of prosthetic groups: a type-1 copper site (azurin, amicyanin, plastocyanin, and pseudoazurin), a heme group (cytochrome c550), and a flavin mononucleotide (flavodoxin). This method permits one to reliably distinguish between reduced and oxidized proteins and to perform potentiometric titrations at submicromolar concentrations.     

Bound state solutions of Schrödinger equation with modified Mobius square potential (MMSP) and its thermodynamic properties

We solved the Schrödinger equation with the modified Mobius square potential model using the modified factorization method. Within the framework of the Greene–Aldrich approximation for the centrifugal term and using a suitable transformation scheme, we obtained the energy eigenvalues equation and the corresponding eigenfunction in terms of the hypergeometric function. Using the resulting eigenvalues equation, we calculated the vibrational partition function and other relevant thermodynamic properties. We also showed that the modified Mobius square potential can be reduced to the Hua potential model using appropriate potential constant values.     

High Algebraic Order Methods for the Numerical Solution of the Schrödinger Equation

Abstract

A family of new hybrid four-step tenth algebraic order methods with phase-lag of order 16(2)22 is developed for the numerical solution of the Schrödinger equation. Based on the new methods a variable-step procedure is introduced. Numerical illustrations obtained for the approximation of the phase shift problem for the well known case of the Lenard-Jones potential and for the numerical solution of the coupled equations arising from the Schrödinger equation show that these new methods are better than other finite difference methods.     

Three–dimensional effective mass Schrödinger equation: harmonic and Morse-type potential solutions

In this work, a scheme to generate exact wave functions and eigenvalues for the spherically symmetric three-dimensional position-dependent effective mass Schrödinger equation is presented. The methodology is implemented by means of separation of variables and point canonical transformations that allow to recognize a radial dependent equation with important differences as compared with the one-dimensional position dependent mass problem, which has been widely studied. This situation deserves to consider the boundary conditions of the emergent problem. To obtain specific exact solutions, the methodology requires known solutions of ordinary one-dimensional Schrödinger equations. We have preferred those applications that use the harmonic oscillator and the Morse oscillator solutions.     

A thermodynamical study of the clockwork hypothesis proposed by E. Schrödinger

In the present study, the 'clockwork' hypothesis proposed by Schr?dinger was examined from the viewpoint of thermodynamics. Firstly, noticing a unidirectional transfer of entropy in a heat engine, the logic was briefly explained about a close relation between this entropy transfer and an irreversible cycle performed by a working body. Next, paying attention to two fundamental differences between a heat engine and a biological system, we considered an isolated system Asigma consisting of three one-component systems (Ai, A, Ao) and noted a case that the same molecules as the component ones flowed quasistatically into Ai from the outside. Then, the unidirectional flows of the molecules, energy and entropy, which were induced by the above inflow in Asigma, were formulated on the basis of the equilibrium thermodynamics for an open system. Furthermore, it was clarified that the fundamental equation for these flows is the Schr?dinger inequality and that the necessary-sufficient condition for this inequality is the existence of an irreversible cycle performed by A. Here A corresponds to a working body in a heat engine. It was, thus, concluded that the 'clockwork' hypothesis by Schr?dinger is considered to be reasonable for a biological system composed of various irreversible subsystems.     

Bringing physics to bear on the phenomenon of life: the divergent positions of Bohr, Delbrück, and Schrödinger

The received view on the contributions of the physics community to the birth of molecular biology tends to present the physics community as sharing a basic level consensus on how physics should be brought to bear on biology. I argue, however, that a close examination of the views of three leading physicists involved in the birth of molecular biology, Bohr, Delbrück, and Schr?dinger, suggests that there existed fundamental disagreements on how physics should be employed to solve problems in biology even within the physics community. In particular, I focus on how these three figures differed sharply in their assessment of the relevance of complementarity, the potential of chemical methods, and the relative importance of classical physics. In addition, I assess and develop Roll-Hansen's attempt to conceptualize this history in terms of models of scientific change advanced by Kuhn and Lakatos. Though neither model is fully successful in explaining the divergence of views among these three physicists, I argue that the extent and quality of difference in their views help elucidate and extend some themes that are left opaque in Kuhn's model.     

Role of enzyme-ribofuranosyl contacts in the ground state and transition state for orotidine 5'-phosphate decarboxylase: a role for substrate destabilization?

The crystal structure of yeast orotidine 5'-monophosphate decarboxylase (ODCase) complexed with the inhibitor 6-hydroxyuridine 5'-phosphate (BMP) reveals the presence of a series of strong interactions between enzyme residues and functional groups of this ligand. Enzyme contacts with the phosphoribofuranosyl moiety of orotidine 5'-phosphate (OMP) have been shown to contribute at least 16.6 kcal/mol of intrinsic binding free energy to the stabilization of the transition state for the reaction catalyzed by yeast ODCase. In addition to these enzyme-ligand contacts, active site residues contributed by both subunits of the dimeric enzyme are positioned to form hydrogen bonds with the 2'- and 3'-OH groups of the ligand's ribosyl moiety. These involve Thr-100 of one subunit and Asp-37 of the opposite subunit, respectively. To evaluate the contributions of these ribofuranosyl contacts to ground state and transition state stabilization, Thr-100 and Asp-37 were each mutated to alanine. Elimination of the enzyme's capacity to contact individual ribosyl OH groups reduced the k(cat)/K(m) value of the T100A enzyme by 60-fold and that of the D37A enzyme by 300-fold. Removal of the 2'-OH group from the substrate OMP decreased the binding affinity by less than a factor of 10, but decreased k(cat) by more that 2 orders of magnitude. Upon removal of the complementary hydroxymethyl group from the enzyme, little further reduction in k(cat)/K(m) for 2'-deoxyOMP was observed. To assess the contribution made by contacts involving both ribosyl hydroxyl groups at once, the ability of the D37A mutant enzyme to decarboxylate 2'-deoxyOMP was measured. The value of k(cat)/K(m) for this enzyme-substrate pair was 170 M(-1) s(-1), representing a decrease of more than 7.6 kcal/mol of binding free energy in the transition state. To the extent that electrostatic repulsion in the ground state can be tested by these simple alterations, the results do not lend obvious support to the view that electrostatic destabilization in the ground state enzyme-substrate complex plays a major role in catalysis.     

A method for the separation of peptides and α-amino acids

1. Peptides and alpha-amino acids, occurring in mixtures from various sources, can be separated into one fraction containing the amino acids and several peptide fractions. This is achieved by chelation of the mixture with Cu(2+) ions and subsequent chromatography of these chelates over the acetate form of diethylaminoethylcellulose or triethylaminoethylcellulose. 2. The amino acid fraction is obtained by elution with 0.01m-collidine-acetate buffer, pH8.0. 3. Peptide fractions are eluted with 0.01m-collidine-acetate buffer, pH4.5, 0.17n-acetic acid and 0.1n-hydrochloric acid respectively. 4. With the exception of aspartic acid and glutamic acid, which are partly found in the acidic peptide fraction, the amino acids are completely separated from the peptides. 5. Contamination of the acidic peptide fraction with glutamic acid and aspartic acid can be largely avoided by previous addition of an excess of arginine. 6. Copper is removed from the eluates by extraction with 8-hydroxyquinoline in chloroform.     

Reversible dehydration of trehalose and anhydrobiosis: from solution state to an exotic crystal?

Physico-chemical properties of the trehalose-water system are reviewed with special reference to the transformations that may shed light on the mechanism of trehalose bio-protection. Critical analysis of solution thermodynamics is made in order to scrutinize trehalose properties often called 'anomalous' and to check the consistency of literature results. Discussion on the conversion between the solid state polymorphic forms is given, with a special emphasis of the transformations involving the newly identified anhydrous crystalline form of alpha,alpha-trehalose, TRE(alpha). This exotic crystal is almost 'isomorphous' with the dihydrate crystal structure, and possesses the unique feature of reversibly absorbing water to produce the dihydrate, without changing the main structural features. The reversible process could play a functional role in the well-known ability of this sugar to protect biological structures from damage during desiccation. The final aim of the paper is to add some new insights into and to reconcile previous hypotheses for the peculiar 'in vivo' action of trehalose.     

Sclerotization of insect cuticle: A new method for studying the ratio of quinone and β-sclerotization

Sclerotized cuticle upon hydrolysis yields conventional amino acids, ketocatechols and/or aryl amino acid adduct(s) depending on the mode of sclerotization. In the absence of structural details of the bridged hydrolysis products, the two modes of sclerotization have been assessed by differential labelling and chromatography. Insect cuticle labelled with either DOPA or tyrosine was hydrolyzed and chromatographed on dihydroxyboryl cellulose and Dowex 50 columns. Dihydroxyboryl cellulose specifically and quantitatively retained all catechols, while Dowex 50 separated basic aryl amino acid adduct(s) from amino acids. Hydrolysates of cuticles labelled with DOPA were resolved into non-catecholic and catecholic fractions; the ratio of radioactivity present in these two fractions reflected the ratio of quinone tanning and β-sclerotization. However, cuticle labelled with tyrosine required additional chromatography of the non-catecholic fraction on Dowex 50 to determine this ratio.     

A simple method for fitting Bělehrádek's equation to embryonic development data of zooplankton

A method is described whereby a Bělehrádek function is fitted to experimentally derived data for embryonic development duration at a range of temperatures. The method is applied to data for the freshwater copepods Cyclops abyssorum and Eudiaptomus gracilis from Lough Neagh, Northern Ireland. Differences in duration of embryonic development of Lough Neagh populations and that of previously published data for these species are discussed.     

A rapid and simple electrophoretic method for the detection of mutations involving small insertion or deletion: application to β-thalassemia

Summary The 1.8-kb -globin gene fragments of DNAs from individuals heterozygous for nine different -thalassemia mutations involving 1, 2, 3, 4, or 25 basepair (bp) insertions or deletions were amplified by the polymerase chain reaction (PCR). The PCR products were subjected to electrophoresis on aqueous 8% polyacrylamide gel. In each heterozygote with either a 2 to 25 bp deletion, but not with a 1 bp insertion, two slower migrating bands representing heteroduplexes in addition to the 1.8-kb homoduplex band were seen. The electrophoretic positions of these slower migrating bands were characteristic of each mutation studied. By co-amplification with known normal DNA, it was also possible to distinguish DNAs from normal individuals and from individuals who are homozygous for the small insertion/deletion mutations. These studies demonstrate that the heteroduplex formation generated in PCR can be applied as a simple method in the diagnosis of insertion/deletion mutations involving 2 to 25 bp in -thalassemias as well as in other genetic disorders.     

A method for the determination of confidence limits for the P/2e − ratio for chosen values of Y ATP max from the results of continuous culture experiments

A model is described, which allows the determination of 95% confidence limits for the maintenance coefficient and the efficiency of oxidative phosphorylation for chosen values of the growth yield for ATP corrected for energy maintenance (Y _ATP ^max ). As experimental data the specific rates of substrate consumption, product formation and oxygen uptake in chemostat cultures at various growth rates are used.     

A simpler iterative steady state solution of münch pressure-flow systems applied to long and short translocation paths

A simple steady state iterative solution of Münch pressure-flow in unbranched sieve tubes containing only water and sucrose is derived. The iterative equations can be solved on a programmable desk calculator. Solutions are presented for steady state transport with specific mass transfer rates up to 1.5 × 10⁻⁵ mole second⁻¹ centimeters⁻² (= 18.5 grams hour⁻¹ centimeters⁻²) over distances in excess of 50 meters. The calculations clearly indicate that a Münch pressure-flow system can operate over long distances provided (a) the sieve tube is surrounded by a semipermeable membrane; (b) sugars are actively loaded in one region and unloaded at another; (c) the sieve pores are unblocked so that the sieve tube hydraulic conductivity is high (around 4 centimeters² second⁻¹ bar⁻¹); (d) the sugar concentration is kept high (around one molar in the source region); and (e) the average sap velocity is kept low (around 20-50 centimeters hour⁻¹). The dimensions of sieve cells in several species of plants are reviewed and sieve tube hydraulic conductivities are calculated; the values range from 0.2 to 20 centimeters² second⁻¹ bar⁻¹. For long distance pressure-flow to occur, the hydraulic conductivity of the sieve cell membranes must be about 5 × 10⁻⁷ centimeters second⁻¹ bar⁻¹ or greater.     

A robust method to estimate the largest Lyapunov exponent of noisy signals: A revision to the Rosenstein’s algorithm

This study proposed a revision to the Rosenstein’s method of numerical calculation of the largest Lyapunov exponent (LyE) to make it more robust to noise. To this aim, the effect of increasing number of initial neighboring points on the LyE value was investigated and compared to values obtained by filtering the time series. Both simulated (Lorenz and passive dynamic walker) and experimental (human walking) time series were used to calculate the LyE. The number of initial neighbors used to calculate LyE for all time series was 1 (the original Rosenstein’s method), 2, 3, 4, 5, 10, 15, 20, 25, and 30 data points. The results demonstrated that the LyE graph reached a plateau at the 15-point neighboring condition implying that the LyE values calculated using at least 15 neighboring points were consistent. The proposed method could be used to calculate more consistent LyE values in experimental time series acquired from biological systems where noise is omnipresent.     

Semiquinone-iron complex of photosystem II: EPR signals assigned to the low-field edge of the ground state doublet of QA•-Fe2+ and QB•-Fe2+

The quinone-iron complex of the electron acceptor complex of Photosystem II was studied by EPR spectroscopy in Thermosynechococcus elongatus. New g ～ 2 features belonging to the EPR signal of the semiquinone forms of the primary and secondary quinone, i.e., Q(A)(?-)Fe(2+) and Q(B)(?-)Fe(2+), respectively, are reported. In previous studies, these signals were missed because they were obscured by the EPR signal arising from the stable tyrosyl radical, TyrD(?). When the TyrD(?) signal was removed, either by chemical reduction or by the use of a mutant lacking TyrD, the new signals dominated the spectrum. For Q(A)(?-)Fe(2+), the signal was formed by illumination at 77 K or by sodium dithionite reduction in the dark. For Q(B)(?-)Fe(2+), the signal showed the characteristic period-of-two variations in its intensity when generated by a series of laser flashes. The new features showed relaxation characteristics comparable to those of the well-known features of the semiquinone-iron complexes and showed a temperature dependence consistent with an assignment to the low-field edge of the ground state doublet of the spin system. Spectral simulations are consistent with this assignment and with the current model of the spin system. The signal was also present in Q(B)(?-)Fe(2+) in plant Photosystem II, but in plants, the signal was not detected in the Q(A)(?-)Fe(2+) state.