Oscar M. Sorarrain

A theoretical conformational analysis of morpholine

Abstract The CNDO and INDO methods were used for a theoretical conformational analysis of morpholine. The agreement between the methods is very satisfactory. Some results are also compared with the available experimental data.

Semiempirical CNDO/2 calculation of the electronic structure of the DNA molecule I. Ground state potential curves; Tunneling and tautomeric equilibrium in the NHN and OHN bonds of the adenine-thymine base pair

Abstract The ground electronic state structure of the double hydrogen bond in the adenine-thymine nucleotide base pair has been investigated in the semi-empirical CNDO/2 approximation. Potential curves are obtained for several nuclear configurations characterizing both, single and simultaneous tautomeric rearrangements of the NHN and NHO bonds. The results indicate two relative minima corresponding to the normal and tautomeric forms for the coupled motion of the two protons. For the single displacement, the bond energy analysis shows that W A-T (R, r) is repulsive in such a way that W A−T (R, r) + W A−H (R, r) -I- W T−H (R, r) shows only one minimum. These results are in agreement with earlier studies on the hydrogen bond in the guanine-cytosine base pair utilizing ab initio techniques. The atom-atom bond index curves for several pairs of atoms are given and some molecular orbitals have been correlated in the normal and tautomeric forms. Estimates are made within the WKB approximation of the tunneling rate and tunneling probability. The magnitude of the equilibrium distribution between the normal and tautomeric proton positions of minimum energy is consistent with the idea that simultaneous double proton tunneling in the ground state is not significant, thus ruling out a possibility for an error mechanism in the genetic code.

Continuous and discontinuous Markov-chain models for mastitis infection

Abstract Mastitis infection has been analysed with the theory of finite Markov chains, considering two models for the infection process: discrete in space and continuous in time, and discrete in space and time. The predictions of the two models are in full agreement, and the transition matrices approach the same limit for both models. For the Markov chain discontinuous in time we have also calculated the average and variance matrices for the first passage time between any pair of states. The obtained results are discussed.

Application of finite absorbent Markov chains to sib mating populations with selection.

The general theory of Markov chains has been described by several authors: Kemeny and Snell [1960], Bharucha Reid [1960], Feller [1959], Takdcs [1960], among others. Although the treatment given by Bharucha Reid is undoubtedly the most complete among those mentioned, Kemeny and Snells approach is quite adequate for discrete chains in space and time when the number of possible states is finite, as is the case for several genetic models. Examples of application of the formalism developed by Kemeny and Snell to sib mating populations with selection are presented here. Kemeny and Snell give expressions for moments up to the second order in finite absorbing chains. New expressions for moments of the third and the fourth orders have been derived for these chaiTis and are included in this paper as an appendix.

The ring puckering potential function of trimethylene sulfide and trimethylene selenide

Abstract The rotational constants A , B and C are functions of the vibrational quantum numbers for the out-of-plane bending modes of trimethylene sulfide and trimethylene selenide. Infrared and microwave spectroscopy have been used to determine the dependence between these parameters. The height and shape of the barrier arising from combination of the ring bending modes is also determined. CNDO/2 calculations are used to predict the position of the hydrogen atoms of the methylene groups in trimethylene sulfide and trimethylene selenide. The four-membered rings are non-planar for several vibrational states of the ring bending modes.

Molecular orbital theory of the electronic structure of organic compounds—II: Transannular interactions in dioxodiazacycloalkanes

Abstract The CNDO/2 MO and INDO MO methods were used to study the molecular electronic structure of the bicyclic molecules derived by transannular interaction of the amide groups in two isomeric dioxodiazacyclo-decanes. A physical model based on the invariance of the MOs with respect to linear transformation of the basis set allowed to determine a functional relation between the bond atomic population M C-N and r C-N (transannular) in a set of closely related lactams (dioxodiazacycloalkanes). Further, the stabilities of a set of cyclopeptides as determined by Shemyakin et al. allowed to calculate a minimum value of M C-N and a maximum transannular distance r C-N beyond which is not possible the transannular interaction between the amide groups in this kind of molecules. These approaches were used together to provide quantitative results which enable to account for the different behaviour of 6,10-dioxo-l,5-diazacyclodecane and 4,10-dioxo-1,5-diazacyclodecane towards ring contraction reactions.

Application of absorbent markov chains for a selling model of two independent logi

We have considered self-fertilization with selection for a pair of independent diallelic loci. The average, variance and third order moment about the mean have been calculated for the distribution representing the number of generations needed to reach an absorption beginning in any one of the transient states. We have analysed four cases: no selection and those arising from the combination of advantage selective values for the heterozygous and homozygous genotypes for both genes. All cases have been compared. For the calculations we have used the theory of absorbent Markov chains. The formalism employed, which arises from a transition matrix P, was previously developed by Kemeny & Snell (1960) and Bosso, Sorarrain & Favret (1969).

Application of absorbing Markov chains to sib mating populations with selection for a pair of independent diallelic loci

Abstract In this paper we consider a sib mating population with a pair of independent diallelic loci. The average, variance, and third order moment about the mean have been calculated for the distribution representing the number of generations needed to reach an absorbing state beginning in any one of the trnsient states. Four cases are analysed: the no selection one and those cases arising from the combination of favorable selective values for the homozygous and heterozygous genotypes for both genes. The different cases are considered separately and compared, but only some typical starting cases have been reported so as to save space. No selective differences were assumed between the two sexes. The formalism of absorbing Markov chains have been used for the calculations.

A mathematical model for the evolution of a host-pathogen system

Abstract A mathematical model of a particular host-pathogen system has been constructed, considering the expression for the interaction between two and four independent loci in the host and pathogen organisms, assuming a continous generation pattern for its evolution. For this pattern we have found a set of coupled differential equations corresponding to the rate of change in the genetic frequencies of the system. The differential equations have been solved using the Runge-Kutta–Gill numerical method. The solutions are discussed, analyzing the simultaneous attack of one to four virulent races.

Some remarks about the ring puckering potential function of 3-methyleneoxetane

Abstract The rotational constants A, B, C are functions from the vibrational quantum numbers for the out-of-plane ring bending vibration of 3-methyleneoxetane. Gibson and Harris [1] using microwave spectroscopy had given the dependence between quantum vibrational numbers for the out-of-plane bending mode and rotational constants. In this paper, the agreement between experimental results from the microwave measurements and theoretical ones from the CNDO/2 is analysed. The planarity for the strained four-member ring is confirmed from the information available. The position corresponding to the methylene groups is also predicted from CNDO/2 calculations.