A model for the regulation of apoptosis intrinsic pathway: The potential role of the transcriptional regulator E2F in the point of no return.

Apoptosis has been extensively characterized by both experimental approaches and model simulations. However, it is still not fully understood how the regulation occurs, especially in the intrinsic pathway, which can be activated by a great variety of signals. In addition, the conditions in which a point of no return could be reached remain elusive. In this work, we use differential equations models to approach these issues. Our starting point was the model for caspase activation of Legewie et al. (Legewie S, et al., PLoS Computational Biology 2006, 2(9): e120), which exhibits irreversible bistability. We added an activation module to this model, with the main events related to mitochondrial outer membrane permeabilization, which includes cytochrome C release by the mitochondria and its effects on caspase activation and respiratory chain disruption. This "Extended Legewie Model" (ELM) uses BAK as the apoptotic stimulus and active caspase 3 as a measure of apoptosis activation. Unexpectedly, in the extended model, BAK cannot trigger apoptosis activation using physiologically sound initial values of the variables, due to limitations in apoptosome concentration increase. Therefore, the next step was to find a regulatory mechanism, allowing apoptosis activation in the ELM, starting from physiological initial concentrations. For this aim, we performed a sensitivity analysis on the 61 parameters of the system, finding that those producing the most relevant changes in the qualitative behaviour were the rates of synthesis of caspase 3, caspase 9 and XIAP. Based on these results, the transcription factor E2F was included in the ELM because it directly regulates the rate of synthesis of caspase 3 and 9. Depending on the concentration of E2F, the ELM shows different qualitative behaviours. On one hand, for low E2F apoptosis is impossible and for high E2F apoptosis is inevitable. Therefore, if E2F is sufficiently increased, the point of no return is crossed. On the other hand, for intermediate values of E2F there is a bistable region where the fate of the system also depends on the concentration of BAK and other signalling species.

Exotic equilibria of Harary graphs and a new minimum degree lower bound for synchronization.

This work is concerned with stability of equilibria in the homogeneous (equal frequencies) Kuramoto model of weakly coupled oscillators. In 2012 [R. Taylor, J. Phys. A: Math. Theor. 45, 1-15 (2012)], a sufficient condition for almost global synchronization was found in terms of the minimum degree-order ratio of the graph. In this work, a new lower bound for this ratio is given. The improvement is achieved by a concrete infinite sequence of regular graphs. Besides, non standard unstable equilibria of the graphs studied in Wiley et al. [Chaos 16, 015103 (2006)] are shown to exist as conjectured in that work.

A modular modulation method for achieving increases in metabolite production.

Increasing the production of overproducing strains represents a great challenge. Here, we develop a modular modulation method to determine the key steps for genetic manipulation to increase metabolite production. The method consists of three steps: (i) modularization of the metabolic network into two modules connected by linking metabolites, (ii) change in the activity of the modules using auxiliary rates producing or consuming the linking metabolites in appropriate proportions and (iii) determination of the key modules and steps to increase production. The mathematical formulation of the method in matrix form shows that it may be applied to metabolic networks of any structure and size, with reactions showing any kind of rate laws. The results are valid for any type of conservation relationships in the metabolite concentrations or interactions between modules. The activity of the module may, in principle, be changed by any large factor. The method may be applied recursively or combined with other methods devised to perform fine searches in smaller regions. In practice, it is implemented by integrating to the producer strain heterologous reactions or synthetic pathways producing or consuming the linking metabolites. The new procedure may contribute to develop metabolic engineering into a more systematic practice.

An analog circuit implementation of a Huber-Braun cold receptor neuron model.

We present the design and implementation of an electronic device that, using off the shelf discrete analog components, implements the mathematical model of a cold receptor neuron called Huber-Braun. This model describes the electrical behavior of certain kinds of receptors when interacting with their environment, and it consists of a set of differential equations that has only been solved by numeric simulations. By these means a chaotic behavior has been found. An analog computer can be relevant for further analysis and validation of the model. The results obtained by means of numeric simulations and through our analog circuit simulator are consistent. In particular, temperature and external current bifurcation diagrams were successfully built. Finally, the electronic device allows the observation of all relevant variables and most of the expected behavior (tonic firing, chaotic, burst discharge, subthreshold oscillation and steady state).