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    "# Problem 1.2: Separation of time scales\n",
    "\n",
    "<hr>"
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    "*This problem is still a draft.*\n",
    "\n",
    "We employed a separation-of-time-scales assumption to simplify our expressions for the rate of production of a gene product. Specifically, we assumed that the binding and unbinding dynamics of a repressor to its target DNA sequence happened at a faster time scale than transcription and translation dynamics.\n",
    "\n",
    "**a)** What happens if you don't assume separation of timescales? Write a set of differential equations to capture the dynamics of mRNA concentration $m$ and protein concentration $x$, as well as the dynamics of the unoccupied promoter concentration $p$ as a function of the repressor concentration $r$ and total promoter concentration $p_\\mathrm{tot}$.\n",
    "\n",
    "**b)** How do you tell if you're in a parameter regime where that assumption is appropriate? Give both theoretical and experimental arguments."
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