Showing papers by "Federico Morán published in 2007"

Functional, fractal nonlinear response with application to rate processes with memory, allometry, and population genetics

Abstract: We give a functional generalization of fractal scaling laws applied to response problems as well as to probability distributions. We consider excitations and responses, which are functions of a given state vector. Based on scaling arguments, we derive a general nonlinear response functional scaling law, which expresses the logarithm of a response at a given state as a superposition of the values of the logarithms of the excitations at different states. Such a functional response law may result from the balance of different growth processes, characterized by variable growth rates, and it is the first order approximation of a perturbation expansion similar to the phase expansion. Our response law is a generalization of the static fractal scaling law and can be applied to the study of various problems from physics, chemistry, and biology. We consider some applications to heterogeneous and disordered kinetics, organ growth (allometry), and population genetics. Kinetics on inhomogeneous reconstructing surfaces leads to rate equations described by our nonlinear scaling law. For systems with dynamic disorder with random energy barriers, the probability density functional of the rate coefficient is also given by our scaling law. The relative growth rates of different biological organs (allometry) can be described by a similar approach. Our scaling law also emerges by studying the variation of macroscopic phenotypic variables in terms of genotypic growth rates. We study the implications of the causality principle for our theory and derive a set of generalized Kramers–Kronig relationships for the fractal scaling exponents.

Species connectivities and reaction mechanisms from neutral response experiments.

Abstract: We develop a new method for obtaining connectivity data for nonlinear reaction networks, based on linear response experiments. In our approach the linear response is not the result of an approximation procedure but is due to the appropriate design of the response experiments, that is (1) they are carried out with the preservation of constant values for the total (labeled plus unlabeled) input and output fluxes and (2) the labeled compounds obey a neutrality condition (i.e., they have practically the same kinetic and transport properties as the unlabeled compounds). Under these circumstances the linear response equations hold even though the kinetics of the process is highly nonlinear. On the basis of this linear response law, we develop a method for evaluating reaction connectivities in biochemical networks from stationary response experiments. Given a system in a stationary regime, a pulse of a labeled species is introduced (with conservation of the total flux) and then the response of all the species of the network is recorded. The mechanistic information is contained in a connectivity matrix, K, which can be evaluated from the response data by means of differential as well as integral methods. The approach does not require any prior knowledge of the reaction mechanism. We carried out a numerical study of the method, based on a two-step procedure. Starting from a known reaction mechanism, we generated response data sets, to which we add noise; then, we use the noisy data sets for retrieving the connectivity matrix. The calculations were done with two programs written in Mathematica: the urea cycle and the upper part of glycolysis are used as sample biochemical networks. Given enough computer power, there are no limitations concerning the number of species involved in the response experiments; on current desktop systems processing responses of teens of species would take a few hours. The method is limited by the occurrence of experimental errors: if experimental errors in the evaluation of fluxes are larger than 10%, the method may fail to reproduce the correct values of some elements of the connectivity matrix.