Oscillations in I/O monotone systems under negative feedback

Oscillatory behavior is a key property of many biological systems. The Small-Gain Theorem (SGT) for input/output monotone systems provides a sufficient condition for global asymptotic stability of an equilibrium and hence its violation is a necessary condition for the existence of periodic solutions. One advantage of the use of the monotone SGT technique is its robustness with respect to all perturbations that preserve monotonicity and stability properties of a very low-dimensional (in many interesting examples, just one-dimensional) model reduction. This robustness makes the technique useful in the analysis of molecular biological models in which there is large uncertainty regarding the values of kinetic and other parameters. However, verifying the conditions needed in order to apply the SGT is not always easy. This paper provides an approach to the verification of the needed properties, and illustrates the approach through an application to a classical model of circadian oscillations, as a nontrivial ``case study,'' and also provides a theorem in the converse direction of predicting oscillations when the SGT conditions fail.Comment: Related work can be retrieved from second author's websit

Multi-Stability in Monotone Input/Output Systems

This paper studies the emergence of multi-stability and hysteresis in those systems that arise, under positive feedback, starting from monotone systems with well-defined steady-state responses. Such feedback configurations appear routinely in several fields of application, and especially in biology. Characterizations of global stability behavior are stated in terms of easily checkable graphical conditions. An example of a signaling cascade under positive feedback is presented.Comment: See http://www.math.rutgers.edu/~sontag for related work; to appear in Systems and Control Letter

Monotone Control Systems

Monotone systems constitute one of the most important classes of dynamical systems used in mathematical biology modeling. The objective of this paper is to extend the notion of monotonicity to systems with inputs and outputs, a necessary first step in trying to understand interconnections, especially including feedback loops, built up out of monotone components. Basic definitions and theorems are provided, as well as an application to the study of a model of one of the cell's most important subsystems.Comment: See http://www.math.rutgers.edu/~sontag/ for related wor

Structural instability in an autophosphorylating kinase switch

We analyse a simple kinase model that exhibits bistability when there is no protein turnover, and show analytically that the property of being bistable is not necessarily conserved when degradation and synthesis of the kinase are taken into account

La gestión compartida como modelo de inclusión urbana

Villa Palito nació en 1962 como consecuencia de la compulsiva erradicación de villas en la Capital Federal.\nSus habitantes continuaron en forma precaria su instalación en una zona que se transformó en una de las\nmás estigmatizadas del Conurbano. La experiencia que comenzó a fines de los 90 resultó un modelo de\ngestión inédito de coparticipación para la inclusión. Habitantes, técnicos y el Estado confluyeron a raíz de la\npresión de los grupos sociales marginados, de su participación activa e incesante