Addition theorems for Slater-type orbitals in momentum space and their application to three-center overlap integrals

Using addition theorems for complete orthonormal sets of exponential type orbitals in the momentum representation introduced by the author, the addition theorems are established for Slater type orbitals in momentum space. With the help of these addition theorems, the general series expansion formulae in terms of the product of two-center overlap integrals are established for the three-center overlap integrals that arise in the solution of atomic and molecular problems occurring when explicitly correlated methods are employed. The formulae obtained for addition theorems and three-center overlap integrals are valid for arbitrary location and parameters of orbitals.     

Calculation of multicenter electric field gradient integrals over Slater-type orbitals using unsymmetrical one-range addition theorems

The electric field induced within a molecule by its electrons determines a whole series of important physical properties of the molecule. In particular, the values of the gradient of this field at the nuclei determine the interaction of their quadrupole moments with the electrons. Using unsymmetrical one-range addition theorems introduced by one of the authors, the sets of series expansion relations for multicenter electric field gradient integrals over Slater-type orbitals in terms of multicenter charge density expansion coefficients and two-center basic integrals are presented. The convergence of the series is tested by calculating concrete cases for different values of quantum numbers, parameters and locations of orbitals.     

One-range addition theorems for derivatives of Slater-type orbitals

Using addition theorems for STOs introduced by the author with the help of complete orthonormal sets of -ETOs (Guseinov II (2003) J Mol Model 9:190–194), where =1, 0, –1, –2, ..., a large number of one-range addition theorems for first and second derivatives of STOs are established. These addition theorems are especially useful for computation of multicenter-multielectron integrals over STOs that arise in the Hartree–Fock–Roothaan approximation and also in the Hylleraas function method, which play a significant role for the study of electronic structure and electron–nuclei interaction properties of atoms, molecules, and solids. The relationships obtained are valid for arbitrary quantum numbers, screening constants and location of STOs.     

Calculation of molecular integrals over Slater-type orbitals using recurrence relations for overlap integrals and basic one-center Coulomb integrals

The recurrence relations are established for the basic one-center Coulomb integrals over Slater-type orbitals (STOs). These formulae and the recurrence relations for basic overlap integrals are utilized for the calculation of multicenter electron-repulsion integrals. The calculations of multicenter electron-repulsion integrals are performed by the use of translation formulae for STOs obtained from the Lambda and Coulomb Sturmian exponential-type functions (ETFs). It is shown that these integrals show a faster convergence rate in the case of Coulomb Sturmian ETFs. The accuracy of the results is quite high for the quantum numbers of STOs and for the arbitrary values of internuclear distances and screening constants of atomic orbitals.     

Evaluation of overlap integrals with integer and noninteger n Slater-type orbitals using auxiliary functions

The series expansion formulae are derived for the overlap integrals with arbitrary integer n and noninteger n* Slater-type orbitals (ISTOs and NISTOs) in terms of a product of well-known auxiliary functions A(sigma) and B (k). The series becomes an ordinary closed expression when both principal quantum numbers n* and n'* of orbitals are integer n*= n and n'*= n'. These formulae are especially useful for the calculation of overlap integrals for large quantum numbers. Accuracy of the results is satisfactory for values of integer and noninteger quantum numbers up to n= n'=60, n*= n'*<33 and for arbitrary values of screening constants of orbitals and internuclear distances.     

Addition and expansion theorems for complete orthonormal sets of exponential-type orbitals in coordinate and momentum representations

Analytical properties of new complete orthonormal sets of Psi(alpha) exponential-type orbitals (Psi(alpha)-ETOs where alpha=1, 0, -1, -2, em leader ), introduced by the author as finite linear combinations of Slater-type orbitals (STOs), are studied. Addition and expansion theorems for Psi(alpha)-ETOs are obtained in both coordinate and momentum representations. Using expressions of Psi(alpha)-ETOs in terms of STOs, the new methods are suggested to calculate multicenter multielectron integrals over STOs.     

Development of immune-specific interaction potentials and their application in the multi-agent-system VaccImm

Peptide vaccination in cancer therapy is a promising alternative to conventional methods. However, the parameters for this personalized treatment are difficult to access experimentally. In this respect, in silico models can help to narrow down the parameter space or to explain certain phenomena at a systems level. Herein, we develop two empirical interaction potentials specific to B-cell and T-cell receptor complexes and validate their applicability in comparison to a more general potential. The interaction potentials are applied to the model VaccImm which simulates the immune response against solid tumors under peptide vaccination therapy. This multi-agent system is derived from another immune system simulator (C-ImmSim) and now includes a module that enables the amino acid sequence of immune receptors and their ligands to be taken into account. The multi-agent approach is combined with approved methods for prediction of major histocompatibility complex (MHC)-binding peptides and the newly developed interaction potentials. In the analysis, we critically assess the impact of the different modules on the simulation with VaccImm and how they influence each other. In addition, we explore the reasons for failures in inducing an immune response by examining the activation states of the immune cell populations in detail.In summary, the present work introduces immune-specific interaction potentials and their application to the agent-based model VaccImm which simulates peptide vaccination in cancer therapy.     

Neurophysiological study of short-latency potentials in central structures of visual system and their relations to additional oscillations in retina

In chronic experiments on alert rabbits, the formation of short-latency positive and negative potentials preceding initial responses, in wide range of light intensities in visual structures, were revealed. The observed potentials were registered in retina under light intensity of 100-120 J. In corpus geniculatum laterale, colliculus superior and visual cortex, they were initiated under 30 J, 15-50 J and 50 J, respectively. The relations of these potentials to light stimulus intensities were studied.     

Covalent modification and metabolic control analysis. Modification to the theorems and their application to metabolic systems containing covalently modifiable enzymes

A study of the sensitivity properties of metabolic systems containing covalently modifiable enzymes and cascades has been carried out with the aid of metabolic control analysis. We have considered how the theorems of metabolic control analysis must be modified to take into account covalently modifiable enzymes, and have used these results to investigate the effects of increasing the total amount of modifiable enzyme. The sensitivity of system variables to an effector acting through a covalent-modification cycle has also been investigated.     

Membrane potentials of vallisneria leaf cells and their relation to photosynthesis

A study has been made of the effects of the inhibitors carbonylcyanide m-chlorophenylhydrazone (CCCP), 3-(3,4-dichlorophenyl)-1,1-dimethyl urea (DCMU), and of anoxia on the light-sensitive membrane potential of Vallisneria leaf cells. The present results are compared with the known effects of these inhibitors on ion transport and photosynthesis (Prins 1974 Ph.D thesis). The membrane potential is composed of a diffusion potential plus an electrogenic component. The electrogenic potential is about −13 millivolts in the dark and −80 millivolts in the light. The inhibitory effect of DCMU and CCCP on the electrogenic mechanisms strongly depends on the light intensity used, the inhibition being less at a higher light intensity. This is of significance in view of the often conflicting results obtained with these inhibitors. With ion transport in Vallisneria the electrogenic pump derives its energy from phosphorylation; however, the process which causes the initial light-induced hyperpolarization and the process that keeps the membrane potential at a steady hyperpolarized state in the light have different energy requirements. The action of photosystem I alone is sufficient to induce the initial hyperpolarization. For continuous operation in the light the activity of photosystem II also is needed.     

Structural derivatives of pindolol: relationship between in vivo and in vitro potencies for their interaction with central beta-adrenergic receptors

Although (-)-125I-iodopindolol (IPIN) can be used to label beta-adrenergic receptors in the central nervous system (CNS) in vivo, use of this ligand for receptor imaging studies in humans may be limited due to its relatively poor penetration into the CNS. A series of derivatives related to pindolol was therefore studied in an effort to determine the factors that might influence the penetration and interaction of these compounds with central beta-adrenergic receptors in vivo. Evaluation of the ability of these derivatives to displace the binding of IPIN in the brain upon systemic administration provides an assessment of whether the derivatives penetrate and interact with central beta-adrenergic receptors in vivo. Multiple regression analyses showed that the most important factor which influences the ability of the pindolol derivatives to penetrate into the brain and interact with beta-adrenergic receptors in vivo is the affinity of the derivatives for binding to beta-adrenergic receptors in vitro. Both lipophilicity and the molecular weights of the derivatives are important secondary factors which influence their in vivo potency.     

Cytohistochemical techniques for calcium localization and their application to diseased plants

Lesion delimitation and resistance of old bean (Phaselous vulgaris L., cv. Red Kidney) plants to Rhizoctonia solani Kühn have been suggested to result from increased calcium pectate formation in walls. Ultrastructural histochemistry was used to determine the site of calcium in tissues adjacent to lesions and in older bean hypocotyls. Hypocotyl lesion tissue and uninoculated control tissue were treated with ammonium oxalate or potassium pyroantimonate during fixation. Treatment with potassium pyroantimonate, but not with oxalate, resulted in granular deposits in cell walls of healthy and lesion tissue. Granules also occurred on the plasma membrane of cells adjacent to lesions and in organelles of damaged cells, but wall granule density was not increased. Cell walls from healthy 24-day-old plants had a greater granule density than those for 8-day-old plants. Wall granules were removed from thin sections with ethylene glycol bis(β-aminoethyl ether)-N,N,N′,N′-tetraacetic acid. Energy dispersive analysis of x-rays also suggested that potassium pyroantimonate localized calcium. Chemical analyses showed that some calcium was retained in tissues after fixation. The results suggest that there are different mechanisms for lesion delimitation and age-induced resistance.     

Standard specimens for stain calibration and their application to the Papanicolaou stain

Standardized specimens composed of extracts of biologic objects (nucleoprotamine and bovine liver) were developed as tools for the quantitative evaluation of stain performance on biologic substrates. The specimens are mixtures of proteins and nucleic acids and thus mimic the staining characteristics of cytologic smears. The concentration of each mixture and the specimen thickness can be precisely controlled, ensuring the production of a large number of samples with a nearly identical capability for dye binding. The transmitted light spectra of the standardized specimens varied depending on the extract and the preparation conditions. Spectra similar to those reported from the nuclei and cytoplasm of cell types in Papanicolaou-stained cervicovaginal smears were observed. Light transmission was uniform to +/- 5% across each specimen and from specimen to specimen. The specimen thickness was uniform within +/- 2%. Studies with these standardized samples could reveal the much-needed correlations between the chemical and optical characteristics of dyes and dye solutions and the performance of the dyes on biologic substrates.     

Genetic engineering of cytokinins and their application to agriculture

Cytokinins are master regulators of plant growth and development. They are involved in the regulation of many important physiological and metabolic processes. Recent progress in cytokinin research at the molecular level, including identification of related genes and cytokinin receptors, plus elucidation of signal transduction, has greatly increased our understanding of cytokinin actions. Although still in its infant stage, molecular breeding of crops with altered cytokinin metabolism, when combined with the transgenic approach, has shown very promising potential for application to agriculture. In this review we briefly introduce recent progress in cytokinin molecular biology, discuss applications of cytokinin genetic engineering to agriculture, and present implications and future research directions.     

Phosphine derivatives for selective phosphorylation of nucleoside and their application to oligonucleotide chemistry

Some new phosphorylating reagents have been developed. They were classified into two types; one reacts selectively to the cis-glycol of ribonucleoside and the other has the selective reactivity to the primary alcohol of nucleoside. The application of these selective phosphorylation reactions to the synthesis of oligonucleotides is described.     

Natural and orthogonal interaction framework for modeling gene-environment interactions with application to lung cancer

Objectives: We aimed at extending the Natural and Orthogonal Interaction (NOIA) framework, developed for modeling gene-gene interactions in the analysis of quantitative traits, to allow for reduced genetic models, dichotomous traits, and gene-environment interactions. We evaluate the performance of the NOIA statistical models using simulated data and lung cancer data. Methods: The NOIA statistical models are developed for additive, dominant, and recessive genetic models as well as for a binary environmental exposure. Using the Kronecker product rule, a NOIA statistical model is built to model gene-environment interactions. By treating the genotypic values as the logarithm of odds, the NOIA statistical models are extended to the analysis of case-control data. Results: Our simulations showed that power for testing associations while allowing for interaction using the NOIA statistical model is much higher than using functional models for most of the scenarios we simulated. When applied to lung cancer data, much smaller p values were obtained using the NOIA statistical model for either the main effects or the SNP-smoking interactions for some of the SNPs tested. Conclusion: The NOIA statistical models are usually more powerful than the functional models in detecting main effects and interaction effects for both quantitative traits and binary traits.     

Responses of central auditory neurons to frequency-modulated stimuli and temporal characteristics of inhibitory interaction

Responses to frequency-modulated stimuli of 118 inferior collicular neurons were compared with quantitative characteristics of the frequency — threshold curves and lateral inhibitory zones during time-varying two-tone stimulation in anesthetized albino rats. In one third of neurons high sensitivity to the direction of frequency modulation does not correspond to their spatial characteristics (the shape, width, and arrangement of the lateral inhibitory zones relative to the frequency — threshold curve). The specificity of response of these neurons to a particular direction of frequency modulation is evidently based on differences in the temporal course of inhibition evoked by high-frequency and low-frequency tones.I. M. Sechenov Institute of Evolutionary Physiology and Biochemistry, Academy of Sciences of the USSR, Leningrad. Translated from Neirofiziologiya, Vol. 7, No. 6, pp. 603–607, November–December, 1975.