Concluding remarks

Viewing cluster science as the embryology of the full-grown forms of matter we encounter in our surroundings, makes it appear to a relative newcomer as a highly dynamic discipline. Lines of attack showing marked progress or potential promise are briefly reviewed, and a sketch of the vast field of still-open problems is presented.     

Extracting nucleation rates from current–time transients. Concluding remarks

Some time ago, Abyaneh and Fleischmann submitted several papers to this journal in which they modelled the heterogeneous nucleation of crystals as a first order kinetic process. In an invited response, I argued that such an approach was seriously flawed, because it ignored nucleation rate dispersion. More recently, instead of responding directly to this criticism, Abyaneh and Fleischmann have challenged the validity of the Deutscher–Fletcher experiments that first established the physical reality of nucleation rate dispersion. This note, therefore, serves two purposes. Firstly, it confirms the validity and high rigour of the original Deutscher–Fletcher experiments. Secondly, it identifies the errors in the Abyaneh–Fleischmann papers. In conclusion, it is emphasised that nucleation rate dispersion is real, universal, and must always be taken into account in experiments involving heterogeneous nucleation.     

On the long way from the Coulombic Hamiltonian to the intermolecular energy surfaces: Concluding remarks at the tromsø conference,June 20–22, 1989

After a brief review of the main results given at the conference, the general properties of the Coulombic Hamiltonian for a system of electrons moving in a framework of moving atomic nuclei—considered as point charges—are discussed. Since this Hamiltonian is invariant under translations and rotations, the total momentum and the total angular momentum are constants of motion, which means that it is possible to separate the motion of the center of mass and the rotation of the system as a whole. Even if these separations are simple in principle, they lead to a mixing of the electronic and nuclear coordinates that complicates the transformed Hamiltonian. The general features of this Hamiltonian are discussed both in pure quantum mechanics and general quantum theory dealing with wave functions Ψ respective density matrices ρ or system operators T. The principles of the latter are derived from five simple axioms, and it is shown that pure quantum mechanics is a special case of the general theory and that the analogy between these two approaches is essential for the “economy of thinking.” It is indicated that the general theory of the shape and topology of the energy surface 〈H〉 = TrHΓ and its critical points, as a function of the system operator Γ involving both electronic and nuclear coordinates, is a very difficult mathematical problem and that calculation of this surface even for simple molecular systems represents a formidable computational problem, which has to be solved in order to be able to understand the nature of chemical reactions from first principles.     

Diversification and selection mechanisms for the production of protein repertoires: lessons from the immune system

The physiological mechanism for producing antigen-specific antibodies is based on a two-phase neo-Darwinian process: the first phase consists of diversity generation (formation of the repertoire), and the second phase is antigen-mediated selection. In this article, we consider how the natural immunoglobulin gene-diversification processes can be exploited both in vivo and in vitro in order to allow the generation of novel antibody (and heterologous protein) repertoires.     

Defensins--components of the innate immune system in plants

Plant defensins are small (c.a. 5 kDa), basic, cysteine-rich proteins with antimicrobial activities. They are ubiquitous in plants and form part of the innate immunity arsenal. Plant defensins are encoded by small multigene families and are expressed in various plant tissues, but are best characterized in seeds. They are typically produced as preproteins, however, a small subset are produced as larger precursors with C-terminal prodomains. To date, the three-dimensional solution structures of seven seed- and two floral-derived defensins have been elucidated by (1)H-NMR spectroscopy. Despite limited amino acid sequence identities, these defensins have comparable global folds with features that are characteristic of the cysteine-stabilized alphabeta (CSalphabeta) motif. Interestingly, their structures are remarkably similar to those of insect defensins and scorpion toxins. Functionally, these proteins exhibit a diverse array of biological activities, although they all serve a common function as defenders of their hosts. This review describes the distribution, biosynthesis, structure, function and mode of action of plant defensins and reflects on their potential in agribiotechnological applications.     

Making sense of molecular signatures in the immune system

The development of Functional Genomics technologies has opened new avenues to investigate the complexity of the immune system. Microarray technology has been particularly successful because of its relatively low cost and high genome coverage. Consequently to our ability to monitor the expression of a significant proportion of an organism genome, our understanding of the molecular dynamics behind cell differentiation and cell response has greatly improved. Molecular signatures associated to immune cells have provided important tools to investigate the molecular basis of diseases and have been often associated to diagnostic and prognostic markers. The availability of such large collection of data has stimulated the application of complex machine learning techniques in the attempt to link molecular signatures and cell physiology. Here we review the most recent developments in the analysis of molecular signatures in the immune system.     

Some remarks on the hydrogen atom

The path integral for the Green's function involving the Coulomb potential in combination with the Kustaanheimo-Stiefel transformation is used to generate the atomic orbitals of the nonrelativistic hydrogen atom as various combinations of the product of one-dimensional isotropic harmonic oscillator wave functions. The use of the transformation is justified, by connecting the homogeneous space with the quotient space in the Feynman quantization formalism.     

Some remarks on the Pariser-Parr-Pople method

Basic assumptions which characterize the Pariser-Parr-Pople method of computing molecular electronic wave functions are critically examined. By restricted variational calculation of the valence state of carbon and nitrogen atoms and ions, it is demonstrated that the usual methods of evaluation of one-centre Coulomb integrals and atomic core energies are rather good. A semi-theoretical means of estimating the core resonance integral is proposed and shown to give fair agreement with the empirical values for C-C, O-O, C-N, and C-O bonds.

---

Zusammenfassung Die Grundannahmen der Methode von Pariser-Parr-Pople zur Berechnung molekularer Wellenfunktionen werden kritisch durchleuchtet. Mittels beschränkter Variationsansätze für den Valenzzustand von Kohlenstoff- und Stickstoff-Atomen und -Ionen wird dargelegt, daß die Methoden, wie sie üblicherweise zur Berechnung von Einzentren-Coulombintegralen und atomaren Rumpfenergien angewendet werden, zu recht guten Ergebnissen führen. Ferner wird ein halbtheoretisches Verfahren zur Abschätzung der Rumpfresonanzintegrale vorgeschlagen und nachgewiesen, daß das Resultat gut mit den empirischen Werten für die C-C-, O-O-, C-N- und C-O-Bindung übereinstimmt.

---

Résumé Les hypothèses fondamentales de la méthode de Pariser-Parr-Pople pour le calcul des fonctions d'onde électroniques sont examinées critiquement. Un calcul variationel limité des états de valence des atoms et ions de carbone et de nitrogène montre que les méthodes usuelles pour l'évaluation des intégrales de Coulomb monocentriques et des énergies de coeur atomiques sont assez bonnes. Nous proposons un procédé semithéorique pour évaluer l'intégrale de résonance de coeur, qui s'accorde assez bien aux valeurs expérimentales pour les liaisons C-C, O-O, C-N et C-O.

---

---

The research reported in this paper was sponsored in part by the King Gustaf VI Adolf's 70-Years Fund for Swedish Culture, Knut and Alice Wallenberg's Foundation, the Swedish Natural Science Research Council, and in part by the Aeronautical Research Laboratory, OAR, through the European Office, Aerospace Research, United States Air Force, and also in part by the National Aeronautics and Space Administration Research Grant NsG-512.

---

On leave of absence from the Department of Chemistry, Faculty of Science, Hokkaido, University, Sapporo, Japan.     

Some remarks on propagators and resolvents

Summary The background of the propagator methods introduced into quantum chemistry by Linderberg and Öhrn is briefly reviewed. Emphasis is put on its connection with the superresolvent associated with the Liouvillians superoperator as shown by Goscinskiet al. The paper stresses the importance of the effectiveness of the resolvent approach in general, and points out that, for the ordinary Hamiltonian, this method is not only conceptually important as the basis for infinite-order perturbation theory and rational approximations but also as the foundation for a large-scale computational effort still to come. Even if it may be premature to ask for a similar effort related to the superoperator, it would certainly be of value to carry out some test calculations based on the Hilbert-Schmidt binary product, in which the Liouvillian superoperator is automatically self-adjoint, and to compare the results with those obtained from the more conventional propagator methods. The importance of the use of approximations based on inner projections in both these approaches is also mentioned.     

Effects of solar radiation on the human immune system.

On UV irradiation of the skin, a complex cascade of immunological changes results, initiated by cutaneous chromophores and ending in suppression of some local and systemic immune responses. In this review, the stages in this process are outlined first, concentrating on the roles of DNA and urocanic acid as photoreceptors. Evidence indicating UV-induced immunomodulation of delayed hypersensitivity and resistance to infectious diseases in human subjects follows. Aspects of genetic susceptibility to the immunosuppressive effects of UV exposure and extrapolation of the data obtained in animal models to the human situation are included. Finally uncertain and unknown factors relating to the impact of UV on the human immune system are discussed.     

Concluding the Amyloid Formation Pathway of a Coiled‐Coil‐Based Peptide from the Size of the Critical Nucleus

The size of the critical nucleus acting as intermediate in the amyloid formation of a model peptide is calculated. The theoretical approach is based on experimentally determined amyloid formation rates and gives new insights into the amyloid formation pathway.