Global Hopf bifurcation in the ZIP regulatory system

Regulation of zinc uptake in roots of Arabidopsis thaliana has recently been modeled by a system of ordinary differential equations based on the uptake of zinc, expression of a transporter protein and the interaction between an activator and inhibitor. For certain parameter choices the steady state of this model becomes unstable upon variation in the external zinc concentration. Numerical results show periodic orbits emerging between two critical values of the external zinc concentration. Here we show the existence of a global Hopf bifurcation with a continuous family of stable periodic orbits between two Hopf bifurcation points. The stability of the orbits in a neighborhood of the bifurcation points is analyzed by deriving the normal form, while the stability of the orbits in the global continuation is shown by calculation of the Floquet multipliers. From a biological point of view, stable periodic orbits lead to potentially toxic zinc peaks in plant cells. Buffering is believed to be an efficient way to deal with strong transient variations in zinc supply. We extend the model by a buffer reaction and analyze the stability of the steady state in dependence of the properties of this reaction. We find that a large enough equilibrium constant of the buffering reaction stabilizes the steady state and prevents the development of oscillations. Hence, our results suggest that buffering has a key role in the dynamics of zinc homeostasis in plant cells.Comment: 22 pages, 5 figures, uses svjour3.cl

Verbal instructions override the meaning of facial expressions

Psychological research has long acknowledged that facial expressions can implicitly trigger affective psychophysiological responses. However, whether verbal information can alter the meaning of facial emotions and corresponding response patterns has not been tested. This study examined emotional facial expressions as cues for instructed threat-of-shock or safety, with a focus on defensive responding. In addition, reversal instructions were introduced to test the impact of explicit safety instructions on fear extinction. Forty participants were instructed that they would receive unpleasant electric shocks, for instance, when viewing happy but not angry faces. In a second block, instructions were reversed (e.g., now angry faces cued shock). Happy, neutral, and angry faces were repeatedly presented, and auditory startle probes were delivered in half of the trials. The defensive startle reflex was potentiated for threat compared to safety cues. Importantly, this effect occurred regardless of whether threat was cued by happy or angry expressions. Although the typical pattern of response habituation was observed, defense activation to newly instructed threat cues remained significantly enhanced in the second part of the experiment, and it was more pronounced in more socially anxious participants. Thus, anxious individuals did not exhibit more pronounced defense activation compared to less anxious participants, but their defense activation was more persistent

Monotone and near-monotone biochemical networks

Monotone subsystems have appealing properties as components of larger networks, since they exhibit robust dynamical stability and predictability of responses to perturbations. This suggests that natural biological systems may have evolved to be, if not monotone, at least close to monotone in the sense of being decomposable into a “small” number of monotone components, In addition, recent research has shown that much insight can be attained from decomposing networks into monotone subsystems and the analysis of the resulting interconnections using tools from control theory. This paper provides an expository introduction to monotone systems and their interconnections, describing the basic concepts and some of the main mathematical results in a largely informal fashion