arXiv subjects

Madalena Chaves

Publications and source records attributed to Madalena Chaves.

7 recordsLinked to original sources

arXiv2025

Circadian Clock Model with Sequestration Repression Motif: Existence of Periodic Orbits and Entrainment Properties

Protein sequestration motifs appear in many biological regulatory networks and introduce special properties into the network dynamics. Sequestration can be described as a mode of inactivation of a given protein by its binding to a second protein to form a new complex. In this complexed form, the original protein is prevented from performing its specific functions and is thus rendered inactive. We study a mathematical model of the mammalian circadian clock with a protein sequestration motif, which generates one of the negative feedback loops that guarantees periodic behavior. First, the motif permits a time-scale separation, which can be used to simplify the model. We show that the simplified model admits a periodic orbit over a fairly large region of parameters. Second, we are able to show that the sequestration motif induces a phase response curve with a very specific form, implying that external perturbations can affect the system only in a narrow window of the periodic orbit. Finally, we compare our model with a classic Goodwin oscillator, to illustrate the dynamical and robustness properties induced by the protein sequestration motif.

math.DS↗

arXiv2007

Bistability preserving model reduction in apoptosis

Biological systems are typically very complex and need to be reduced before they are amenable to a thorough analysis. Also, they often possess functionally important dynamic features like bistability. In model reduction, it is sometimes more desirable to preserve the dynamic features only than to recover a good quantitative approximation. We present an approach to reduce the order of a bistable dynamical system significantly while preserving bistability and the switching threshold. These properties are important for the operation of the system in the context of a larger network. As an application example, a bistable model for caspase activation in apoptosis is considered.

q-bio.MN↗

arXiv2006

Methods of robustness analysis for Boolean models of gene control networks

As a discrete approach to genetic regulatory networks, Boolean models provide an essential qualitative description of the structure of interactions among genes and proteins. Boolean models generally assume only two possible states (expressed or not expressed) for each gene or protein in the network as well as a high level of synchronization among the various regulatory processes. In this paper, we discuss and compare two possible methods of adapting qualitative models to incorporate the continuous-time character of regulatory networks. The first method consists of introducing asynchronous updates in the Boolean model. In the second method, we adopt the approach introduced by L. Glass to obtain a set of piecewise linear differential equations which continuously describe the states of each gene or protein in the network. We apply both methods to a particular example: a Boolean model of the segment polarity gene network of Drosophila melanogaster. We analyze the dynamics of the model, and provide a theoretical characterization of the model's gene pattern prediction as a function of the timescales of the various processes.

q-bio.MN↗

arXiv2005

Robustness and fragility of Boolean models for genetic regulatory networks

Interactions between genes and gene products give rise to complex circuits that enable cells to process information and respond to external signals. Theoretical studies often describe these interactions using continuous, stochastic, or logical approaches. We propose a new modeling framework for gene regulatory networks, that combines the intuitive appeal of a qualitative description of gene states with a high flexibility in incorporating stochasticity in the duration of cellular processes. We apply our methods to the regulatory network of the segment polarity genes, thus gaining novel insights into the development of gene expression patterns. For example, we show that very short synthesis and decay times can perturb the wild type pattern. On the other hand, separation of timescales between pre- and posttranslational processes and a minimal prepattern ensure convergence to the wild type expression pattern regardless of fluctuations.

q-bio.MN↗

arXiv2004

Computation of amplification for systems arising from cellular signaling pathways

A commonly employed measure of the signal amplification properties of an input/output system is its induced L2 norm, sometimes also known as "H infinity" gain. In general, however, it is extremely difficult to compute the numerical value for this norm, or even to check that it is finite, unless the system being studied is linear. This paper describes a class of systems for which it is possible to reduce this computation to that of finding the norm of an associated linear system. In contrast to linearization approaches, a precise value, not an estimate, is obtained for the full nonlinear model. The class of systems that we study arose from the modeling of certain biological intracellular signaling cascades, but the results should be of wider applicability.

q-bio.QM↗

arXiv2003

Optimal length and signal amplification in weakly activated signal transduction cascades

Weakly activated signaling cascades can be modeled as linear systems. The input-to-output transfer function and the internal gain of a linear system, provide natural measures for the propagation of the input signal down the cascade and for the characterization of the final outcome. The most efficient design of a cascade for generating sharp signals, is obtained by choosing all the off rates equal, and a ``universal'' finite optimal length.

math.OC↗

arXiv2000

State-estimators for chemical reaction networks of Feinberg-Horn-Jackson zero deficiency type

One of the most interesting questions in control theory is that of constructing observers. Observers compute estimates of the internal states of a dynamical system, using data provided by measurement probes or partial state information. For linear systems, Luenberger observers (also known as "deterministic Kalman filters" since they amount to Kalman filters designed without regard to the statistics of measurement noise) provide a general solution, but, for nonlinear systems, establishing generally applicable conditions for existence and convergence of observers is an open and active area of research. This paper provides a necessary and sufficient condition for detectability, and an explicit construction of observers when this condition is satisfied, for chemical reaction networks of the Feinberg-Horn-Jackson zero deficiency type.

math.OC↗