Abstract: The population matrices with a countable infinite number of age-classes introduced by Demetrius is a natural generalization of the Leslie matrix model. The biological significance of infinite population matrices revolve around their applications to the studies of the evolution of clonal plants, mortality plateau and negligible senescence.
This talk explores the relation between the infinite and finite dimensional population models by considering two macroscopic parameters
of these models, the asymptotic growth rate and the generation time, both related to the properties of the Euler-Lotka equation. Earlier studies of infinite population matrices have appealed to the theory of positive operators on partially ordered Banach spaces. This paper addresses the problem using the theory of kneading determinants. The significance of
this methodology rests on its computational power - an important requisite in biological applications of the model.

Abstract: Phosphoinositides are five percent of phospholipids, the building blocks of the cell membranes. They have an inositol ring as their hydrophobic head and it can be phosphorylated in the third, fourth and fifth positions. These phosphorylations give rise to the seven subspecies of phosphoinositides. They are signaling lipids and have diverse functions such to serve as cell membranes identifiers or ion channel regulators. In recent years, much attention was devoted to the phosphoinositides, not only because of their involvement in diseases such as cancer or cystic fibrosis but also due to the emergence of new methods that allowed their study.
Here, we propose an exploratory model based on the current state of knowledge of this pathway. It is a generalized mass action system of differential equations with power-law approximations based on the biochemical system theory framework developed by Savageau and Voit.
The model was implemented in R and links phenomena as cell polarization and pathogen infection strategies with a bistability of PTEN, PI3KI and the phosphoinosidites that these enzymes catalyze and suggests roles for some of the less abundant phosphoinositide sub-species. We are now on the parameter analysis phase and plan to use the model to test hypothesis previously formulated and to search for therapeutic targets in the context of cystic fibrosis.

José Augusto Pereira (ICBAS-Instituto de Ciências Biomédicas de Abel Salazar, Porto)  homepage

Abstract: Since life is composed of complex molecules, hypothesis about its origin and evolution typically propose polymerization of simpler molecules using energy and catalysis under a set of conditions. Computational models of this type of systems are often based on artificial chemistries [1] composed of symbolic strings, interpreted as molecules, and operations on the strings, interpreted as reactions. The characterization of the resulting networks of strings by elementary flux mode (EFM) analysis [2] reveals many biological traits such as reaction coupling, intermediate cycling (molecular markers and ATP-like molecules) and autocatalytic cycles [3]. Looking at the artificial chemistry as a formal system with a specific language and production rules, it is conjectured that the cycles are facilitated by an ambiguous grammar for the language, that is, when more than one string set can be derived from the same set of “reacting” strings.

Maria Filomena Teodoro (CEMAT: Center for Computational and Stochastic Mathematics and CINAV, Portuguese Naval Academy, Almada, Portugal)  homepage

Modelling the Nervous Conduction in a Myelinated Axon.