Global Analysis of Dynamical Decision-Making Models through Local Computation around the Hidden Saddle

Bistable dynamical switches are frequently encountered in mathematical modeling of biological systems because binary decisions are at the core of many cellular processes. Bistable switches present two stable steady-states, each of them corresponding to a distinct decision. In response to a transient signal, the system can flip back and forth between these two stable steady-states, switching between both decisions. Understanding which parameters and states affect this switch between stable states may shed light on the mechanisms underlying the decision-making process. Yet, answering such a question involves analyzing the global dynamical (i.e., transient) behavior of a nonlinear, possibly high dimensional model. In this paper, we show how a local analysis at a particular equilibrium point of bistable systems is highly relevant to understand the global properties of the switching system. The local analysis is performed at the saddle point, an often disregarded equilibrium point of bistable models but which is shown to be a key ruler of the decision-making process. Results are illustrated on three previously published models of biological switches: two models of apoptosis, the programmed cell death and one model of long-term potentiation, a phenomenon underlying synaptic plasticity

Spatial order as a source of kinetic cooperativity in organized bound enzyme systems.

When enzyme molecules are distributed within a negatively charged matrix, the kinetics of the conversion of a negatively charged substrate into a product depends on the organization of fixed charges and bound enzyme molecules. Organization is taken to mean the existence of macroscopic heterogeneity in the distribution of fixed charge density, or of bound enzyme density, or of both. The degree of organization is quantitatively expressed by the monovariate moments of charge and enzyme distributions as well as by the bivariate moments of these two distributions. The overall reaction rate of the bound enzyme system may be expressed in terms of the monovariate moments of the charge density and of the bivariate moments of charge and enzyme densities. The monovariate moments of enzyme density do not affect the reaction rate. With respect to the situation where the fixed charges and enzyme molecules are randomly distributed in the matrix, the molecular organization, as expressed by these two types of moments, generates an increase or decrease of the overall reaction rate as well as a cooperativity of the kinetic response of the system. Thus both the alteration of the rate and the modulation of cooperativity are the consequence of a spatial organization of charges with respect to the enzyme molecules. The rate equations have been derived for different types of organization of fixed charges and enzyme molecules, namely, clustered charges and homogeneously distributed enzyme molecules, clustered enzyme molecules and homogeneously distributed charges, clusters of charges and clusters of enzymes that partly overlap, and clusters of enzymes and clusters of charges that are exactly superimposed. Computer simulations of these equations show how spatial molecular organization may modulate the overall reaction rate

COMPARATIVE STUDY OF OXYHEMOGLOBIN RADIOLYSIS AND THERMOLYSIS BY MÖSSBAUER SPECTROSCOPY

L'étude des modifications en fonction de la dose du spectre Mössbauer de globules rouges artériels irradiés aux rayons X montre que l'irradiation de l'oxyhémoglobine globulaire entraîne la production d'une forme déoxy ligand free probablement quickly reacting comme dans le cas, bien connu, de la photodissociation ainsi que d'une hémoglobine ferrique high spin. Pour des doses de radiation croissantes, l'hème de ces radioproduits est détruit et un composé final du type ferrique high spin à environnement rhomboédrique est produit. Ces résultats sont obtenus par comparaison avec les spectres RPE. La spectrométrie Mössbauer montre que les mêmes composés sont produits sous l'action de la chaleur, à l'exclusion de la forme déoxy ligand free.The study of variations in the Mössbauer spectrum of X-irradiated arterial red cells as a function of dose shows that irradiation of red cells oxyhemoglobin leads to the production of a ligand free deoxy form, probably fast-reacting as in the well-known case of photodissociation, and of a high spin ferric hemoglobin. For increasing radiation doses the heme of these radioproducts is destroyed and a final compound of the type high spin ferric in rhombic environment is produced. These results are obtained by comparison with EPR spectra. Mössbauer spectrometry shows that these same compounds, excluding the «ligand free» deoxy form, are formed by the action of heat