Relaxation oscillations and hierarchy of feedbacks in MAPK signaling

We formulated a computational model for a MAPK signaling cascade downstream of the EGF receptor to investigate how interlinked positive and negative feedback loops process EGF signals into ERK pulses of constant amplitude but dose-dependent duration and frequency. A positive feedback loop involving RAS and SOS, which leads to bistability and allows for switch-like responses to inputs, is nested within a negative feedback loop that encompasses RAS and RAF, MEK, and ERK that inhibits SOS via phosphorylation. This negative feedback, operating on a longer time scale, changes switch-like behavior into oscillations having a period of 1 hour or longer. Two auxiliary negative feedback loops, from ERK to MEK and RAF, placed downstream of the positive feedback, shape the temporal ERK activity profile but are dispensable for oscillations. Thus, the positive feedback introduces a hierarchy among negative feedback loops, such that the effect of a negative feedback depends on its position with respect to the positive feedback loop. Furthermore, a combination of the fast positive feedback involving slow-diffusing membrane components with slower negative feedbacks involving faster diffusing cytoplasmic components leads to local excitation/global inhibition dynamics, which allows the MAPK cascade to transmit paracrine EGF signals into spatially non-uniform ERK activity pulses.Peer reviewe

Gene switching rate determines response to extrinsic perturbations in the self-activation transcriptional network motif

International audienc

Innovations in early childhood teacher education: Reflections on practice: Developmentally appropriate technology use and early childhood teacher education

Early childhood teacher education methods classes often emphasize the application of developmentally appropriate practices (DAP). In today\u27s digital age, it is important for teacher educators and their students to think about how to extend DAP to technology use. In this article, two contrasting classroom scenarios are provided to illustrate developmentally appropriate technology use (DATU), a new educational term coined by the authors. Briefly, DATU is defined as use that both respects the unique challenges presented by children\u27s levels of development and capitalizes on children\u27s natural desire to actively, collaboratively construct knowledge and solve problems. A five-element framework for guiding teachers toward DATU is explained. © National Association of Early Childhood Teacher Educators

Additional file 5 of Genetic toggle switch controlled by bacterial growth rate

Figure S5. Stationary distributions of protein level based on stochastic simulations for different doubling times and different repression levels. (PDF 59 kb

Additional file 4 of Genetic toggle switch controlled by bacterial growth rate

Figure S4. MFPT between the two states of the toggle switch. (PDF 97 kb

Additional file 2 of Genetic toggle switch controlled by bacterial growth rate

Figure S2. Gene copy numbers as a function of the doubling time. (PDF 77 kb

Additional file 1 of Genetic toggle switch controlled by bacterial growth rate

Figure S1. Genome replication model. (PDF 54 kb