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    "# Problem 3.7: Design principles for toggles\n",
    "\n",
    "<hr>\n"
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    "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."
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