{"cells": [{"cell_type": "markdown", "metadata": {}, "source": ["# Homework 2.1: Design principles for toggles (45 pts)\n", "\n", "<hr>\n"]}, {"cell_type": "markdown", "metadata": {}, "source": ["Consider two components, A and B, which regulate each other. A may activate or repress B, and B may activate or repress A. There are three possible architectures in this scenario, two with positive feedback and one with negative feedback, shown below.\n", "\n", "<div style=\"width: 400px; margin: auto;\">\n", "\n", "![Toggles](toggles.png)\n", "    \n", "</div>\n", "\n", "<br />\n", "\n", "**a)** A circuit can behave like a toggle if it has two stable steady states, one with A high and B low and another with B high and A low. Only one of the above architectures can function as a toggle. Which one? Explain in words and sketches why _only_ the one you chose can be a toggle.\n", "\n", "**b)** A and/or B may have ultrasensitive regulation, which we describe with a Hill coefficient, $n$, greater than one. Show that without ultrasensitive regulation, even the architecture you chose cannot have toggle behavior."]}, {"cell_type": "markdown", "metadata": {}, "source": ["<br />"]}], "metadata": {"anaconda-cloud": {}, "kernelspec": {"display_name": "Python 3", "language": "python", "name": "python3"}, "language_info": {"codemirror_mode": {"name": "ipython", "version": 3}, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.7"}}, "nbformat": 4, "nbformat_minor": 4}