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    "# 15. *It's about time:* time-based regulation in cells\n",
    "\n",
    "(c) 2019 Justin Bois and Michael Elowitz. With the exception of pasted graphics, where the source is noted, this work is licensed under a [Creative Commons Attribution License CC-BY 4.0](https://creativecommons.org/licenses/by/4.0/). All code contained herein is licensed under an [MIT license](https://opensource.org/licenses/MIT).\n",
    "\n",
    "This document was prepared at [Caltech](http://www.caltech.edu) with financial support from the [Donna and Benjamin M. Rosen Bioengineering Center](http://rosen.caltech.edu).\n",
    "\n",
    "<img src=\"figs/caltech_rosen.png\">\n",
    "\n",
    "<hr>\n",
    "<br/>"
   ]
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    "#### Design principle\n",
    "\n",
    "- Time-based regulation enables coordinated regulation of target genes\n",
    "- Frequency Modulated Pulsing can implement time-based regulation\n",
    "\n",
    "#### Concepts\n",
    "\n",
    "- In time-based regulation, as opposed to concentration-based regulation, inputs control the fraction of time a regulator is active, rather than the concentration of the active species.\n",
    "\n",
    "#### Techniques\n",
    "\n",
    "- Autocorrelation and cross-correlation analysis\n",
    "\n",
    "<br />\n",
    "\n",
    "<hr>"
   ]
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import scipy.stats as st\n",
    "import numba\n",
    "\n",
    "import biocircuits\n",
    "\n",
    "import bokeh.io\n",
    "import bokeh.plotting\n",
    "\n",
    "bokeh.io.output_notebook()"
   ]
  },
  {
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    "<hr>"
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    "## Biological circuits can be strikingly dynamic, even in constant conditions\n",
    "\n",
    "Even in a constant environment, biological circuits exhibit surprisingly dynamic behaviors. One can observe proteins activating and deactivating in repetitive pulses or or periodic oscillations across a wide range of timescales. These dynamics are **coherent**, involving simultaneous activation and deactivation of many molecules of a given species. \n",
    "\n",
    "Today we will ask what functional benefits dynamics can provide for a signaling system compared to non-dynamic alternatives. We will see that dynamics allows cells to control targets \"in time\" rather than in concentration, and that this **time-based regulation** can allow coordination of diverse target genes within the cell.\n"
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    "## Electrical systems also use dynamics\n",
    "\n",
    "Electrical circuit design utilizes dynamics for numerous operations. \n",
    "\n",
    "One of the simplest, and most familiar, examples is a classic \"dimmer\" switch. Dimmers control light intensity by rapidly chopping the voltage on and off, varying the fraction of time that the light is on. \n",
    "\n",
    "Our electrical devices are a mix of AC (alternating current) and DC (direct current) designs. In fact, the complementary benefits of the two paradigms are often associated with the legendary conflict between Edison and Tesla, who advocated competing visions for DC and AC power distribution, respectively. The AC model prevailed for power distribution, while DC power is better for many digital electronic systems, such as laptop computers.\n",
    "\n",
    "<center><img src=\"figs/Edison_Tesla.png\" width=\"300px\"></center>"
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    "## AM and FM represent distinct signal encoding paradigms\n",
    "\n",
    "In communications, signals can be encoded either in the amplitude or frequency of oscillations. Car stereos usually offer both Amplitude Modulation (AM) and Frequency Modulation (FM) radio bands. In either case, one can tune the radio to a particular frequency or channel. AM radios encode signals in the amplitude of that frequency, while FM encodes signals in small shifts in frequency\n"
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   "source": [
    "t = np.linspace(0, 25, 1001)\n",
    "\n",
    "# Frequency of carrier signal\n",
    "f = 1\n",
    "\n",
    "# Carrier signal\n",
    "yc = np.sin(2*np.pi*f*t)\n",
    "\n",
    "# Modulation signal\n",
    "m = np.sin(2*np.pi*0.1*f*t)\n",
    "\n",
    "# Phase multiplier\n",
    "pm = 4\n",
    "\n",
    "# Amplitude modulation\n",
    "AM = m * yc;\n",
    "\n",
    "# Modulate phase to give frequency modulated signal\n",
    "FM = np.sin(2*np.pi*(f*t + pm*m))\n",
    "\n",
    "# Collect signals for convenience\n",
    "signals = dict(carrier=yc, signal=m, AM=AM, FM=FM)\n",
    "\n",
    "# Set up plots\n",
    "colors = bokeh.palettes.d3['Category10'][4]\n",
    "plots = [bokeh.plotting.figure(height=150, width=350, \n",
    "                           x_axis_label='time',\n",
    "                           title=key) for key in signals]\n",
    "\n",
    "# Populate glyphs\n",
    "for i, (key, sig) in enumerate(signals.items()):\n",
    "     plots[i].line(t, sig, line_width=2, color=colors[i])\n",
    "\n",
    "bokeh.io.show(bokeh.layouts.gridplot(plots, ncols=1))"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "## Transcription factors can be regulated in concentration or in time\n",
    "\n",
    "Cellular signaling systems can encode inputs in at least two qualitatively distinct ways: \n",
    "\n",
    "* In an AM-like concentration-based encoding system, the input signals controls the concentration of an effector inside the cell. \n",
    "* In a time-based regulation system, the input signal can modulate dynamic aspects of a signal, such as its oscillatory period, or, as we will discuss today, the *fraction of time* that the regulator is active. \n",
    "\n",
    "These two modse are illustrated schematically here:\n",
    "\n",
    "<img src=\"figs/concentration_vs_time_based_regulation.png\" width=\"400px\">\n",
    "\n",
    "Note that this example of time-based regulation involves changing both the frequency and duration of pulses to change the fraction of time that the factor is active. But there are many ways to implement time-based regulation. And any given system may mix both of these or other types of regulation at the same time.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dynamic pulsing is ubiquitous\n",
    "\n",
    "A large, and ever-growing, list of regulatory systems and pathways exhibit repetitive pulses of activity in constant conditions. In bacteria, sigma factors activate in pulses. In yeast, key transcription factors mediating stress response or glucose regulation, such as Msn2, Crz1, and Mig1, exhibit repetitive pulses of nuclear localization. In mammalian cells, core signaling pathways including NF-AT, NF-$\\kappa$B, Erk, p53, and others all exhibit different types of pulsing even when cells are in constant conditions. Examples of these systems are summarized in this image:\n",
    "\n",
    "<img src=\"figs/pulsing_is_ubiquitous.png\" width=\"700px\">\n",
    "<center><i> Image from Levine, Lin, and Elowitz (<a href=\"https://doi.org/10.1126/science.1239999\">Science, 2013</a>)</i></center>\n",
    "\n",
    "Detecting pulsing is not  easy, since it requires making movies of specific regulators in individual cells. For this reason, this list is almost certainly an underestimate of the number and diversity of pulsatile factors. \n",
    "\n",
    "In fact, a recent systematic movie-based survey of all yeast proteins revealed that about 10% of transcription factors show pulsatile dynamics in at least some conditions:\n",
    "\n",
    "<center>\n",
    "<video width=\"768px\" src=\"figs/ten_TFs_pulsing2.mov\" controls loop>\n",
    "Your browser does not support display of this video.\n",
    "</video>\n",
    "</center>\n",
    "<center><i> Movie from C. Dalal et al (<a href=\"https://dx.doi.org/10.1016%2Fj.cub.2014.07.076\">Current Biology, 2014</a>).</i></center>\n",
    "\n",
    "<br/>\n",
    "    \n",
    "This work took advantage of a nice property of many transcription factors. They localize to the nucleus when they are active, and to the cytoplasm when they are inactive. This enables one to infer total transcription factor activity from the degree of nuclear localization.\n",
    "\n",
    "<img src=\"figs/nuclear_cytoplasmic_localization.png\" width=\"250px\">\n",
    "<center><i> \n",
    "</i></center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Crz1 mediates the response to calcium through nuclear localization\n",
    "\n",
    "One of the best examples of this mode of control is the yeast transcription factor Crz1, whose name stands for calcineurin-responsive zinc finger 1, and is pronounced \"crazy one.\" \n",
    "\n",
    "In this system, calcium activates the phosphatase calcineurin, which dephosphorylates Crz1. The desporphorylated form localizes to the nucleus, where it can activae a large regulon of target genes. Crz1 is functionall analogous to the mammalian transcription factor NF-AT. (See Stathopoulos, et al. ([*Genes Dev.*, 1997](https://doi.org/10.1101/gad.11.24.3432), [*Genes Dev., 1999](http://genesdev.cshlp.org/content/13/7/798.long); and Matheos et al. ([*Genes Dev.*, 1997](10.1101/gad.11.24.3445)).)\n",
    "\n",
    "<img src=\"figs/Crz1_diagram.png\" width=\"300px\">\n",
    "<center><i> \n",
    "</i></center>\n"
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    "## Crz1 pulses\n",
    "\n",
    "Crz1 earns its reputation for craziness. By making movies of individual yeast cells after addition of calcium to the media, one cannot help but be struck by the \"twinkling\" of individual cells as Crz1 exhibits coherent, repetitive pulses of nuclear localization. \n",
    "\n",
    "<center>\n",
    "<video width=\"768px\" src=\"figs/FMCoordination-mov.mov\" controls loop>\n",
    "Your browser does not support display of this video.\n",
    "</video>\n",
    "</center>"
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    "## Pulses appear stochastic and (sometimes) repetitive\n",
    "\n",
    "To get a better idea of what is going on in this system, one can plot traces of nuclear localization over time. In the following image you can see a pair of examples from two neighboring cells. \n",
    "\n",
    "<img src=\"figs/Crz1_pulse_examples.png\" width=\"600px\">\n",
    "<center><i>Analysis of Crz1 pulse dynamics in two cells, from L. Cai et al. (<a href=\"https://doi.org/10.1038/nature07292\">Nature, 2008</a>)\n",
    "</i></center>\n",
    "\n",
    "These traces show a number of interesting features:\n",
    "\n",
    "* Nuclear localization occurs in brief pulses (sometimes called spikes or bursts), typically lasting just a couple of minutes. These pulses occur only after calcium is added to the media.\n",
    "\n",
    "* Pulses are unsynchronized between different cells, indicating they are generated in a cell-autonomous way. In fact, pulsing is uncorrelated even between mother-daughter cell pairs.\n",
    "\n",
    "* In many, but not all, cells, one sees an immediate response to sudden addition of calcium. This occurs in the blue trace, above.\n",
    "\n",
    "* One also can frequently observe extended episodes of elevated pulsing rate, termed pulse \"trains\" or \"clusters.\"\n",
    "\n",
    "Averaging over many of these traces reveals a very different population average behavior, in which there is an initial response, evidently due to synchronized response to calcium addition, followed by partial adaptation to an (apparently) constant level. Of course, we know that this seemingly steady behavior conceals the wild pulsing going on in each individual cell. \n",
    "\n",
    "<img src=\"figs/Crz1_averaged_traces.png\" width=\"400px\">\n",
    "<center><i>Average of Crz1 pulse dynamics in 42 cells, from L. Cai et al. (<a href=\"https://doi.org/10.1038/nature07292\">Nature, 2008</a>).\n",
    "</i></center>"
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    "## Dynamic correlation analysis allows extraction of key features of stochastic dynamics\n",
    "\n",
    "These observations present us with a frequently encountered challenge: How to condense a huge number of distinct, individual behaviors, each occurring in a different cell, into a small number of comprehensible parameters. \n",
    "\n",
    "One of the most versatile tools is correlation analysis.\n",
    "\n",
    "Consider the following two signals, which are generated synthetically by creating pulses at different points, and adding noise.\n"
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\",\"dtype\":\"float64\",\"shape\":[2001]},\"y\":{\"__ndarray__\":\"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\",\"dtype\":\"float64\",\"shape\":[2001]}},\"selected\":{\"id\":\"1524\",\"type\":\"Selection\"},\"selection_policy\":{\"id\":\"1525\",\"type\":\"UnionRenderers\"}},\"id\":\"1468\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"line_alpha\":0.1,\"line_color\":\"#1f77b4\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1470\",\"type\":\"Line\"},{\"attributes\":{\"axis_label\":\"time\",\"formatter\":{\"id\":\"1461\",\"type\":\"BasicTickFormatter\"},\"ticker\":{\"id\":\"1432\",\"type\":\"BasicTicker\"}},\"id\":\"1431\",\"type\":\"LinearAxis\"},{\"attributes\":{\"line_color\":\"orange\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1469\",\"type\":\"Line\"},{\"attributes\":{},\"id\":\"1437\",\"type\":\"BasicTicker\"},{\"attributes\":{\"bottom_units\":\"screen\",\"fill_alpha\":{\"value\":0.5},\"fill_color\":{\"value\":\"lightgrey\"},\"left_units\":\"screen\",\"level\":\"overlay\",\"line_alpha\":{\"value\":1.0},\"line_color\":{\"value\":\"black\"},\"line_dash\":[4,4],\"line_width\":{\"value\":2},\"render_mode\":\"css\",\"right_units\":\"screen\",\"top_units\":\"screen\"},\"id\":\"1465\",\"type\":\"BoxAnnotation\"},{\"attributes\":{},\"id\":\"1446\",\"type\":\"HelpTool\"},{\"attributes\":{\"label\":{\"value\":\"signal 1\"},\"renderers\":[{\"id\":\"1457\",\"type\":\"GlyphRenderer\"}]},\"id\":\"1467\",\"type\":\"LegendItem\"},{\"attributes\":{},\"id\":\"1429\",\"type\":\"LinearScale\"},{\"attributes\":{},\"id\":\"1432\",\"type\":\"BasicTicker\"},{\"attributes\":{},\"id\":\"1427\",\"type\":\"LinearScale\"},{\"attributes\":{},\"id\":\"1463\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{\"label\":{\"value\":\"signal 2\"},\"renderers\":[{\"id\":\"1471\",\"type\":\"GlyphRenderer\"}]},\"id\":\"1482\",\"type\":\"LegendItem\"},{\"attributes\":{},\"id\":\"1461\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{\"items\":[{\"id\":\"1467\",\"type\":\"LegendItem\"},{\"id\":\"1482\",\"type\":\"LegendItem\"}]},\"id\":\"1466\",\"type\":\"Legend\"},{\"attributes\":{},\"id\":\"1441\",\"type\":\"PanTool\"},{\"attributes\":{\"text\":\"\"},\"id\":\"1459\",\"type\":\"Title\"},{\"attributes\":{\"ticker\":{\"id\":\"1432\",\"type\":\"BasicTicker\"}},\"id\":\"1435\",\"type\":\"Grid\"},{\"attributes\":{},\"id\":\"1444\",\"type\":\"SaveTool\"},{\"attributes\":{\"axis_label\":\"signal\",\"formatter\":{\"id\":\"1463\",\"type\":\"BasicTickFormatter\"},\"ticker\":{\"id\":\"1437\",\"type\":\"BasicTicker\"}},\"id\":\"1436\",\"type\":\"LinearAxis\"}],\"root_ids\":[\"1422\"]},\"title\":\"Bokeh Application\",\"version\":\"1.1.0\"}};\n",
       "  var render_items = [{\"docid\":\"8a0e66d7-13b7-4a9b-a056-bf558886ef30\",\"roots\":{\"1422\":\"b6764997-b4df-4c0b-a0d4-c51344948ec4\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
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     "output_type": "display_data"
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   ],
   "source": [
    "t = np.linspace(0, 20, 2001)\n",
    "\n",
    "mu_1 = np.array([0.3, 1.4, 6.4, 8.9, 11.4, 15.3])\n",
    "sigma_1 = np.array([0.1, 0.2, 0.15, 0.3, 0.4, 0.1])\n",
    "amp_1 = np.array([0.3, 0.5, 0.3, 0.1, 0.3, 0.34])\n",
    "bg_1 = 0.07\n",
    "noise_1 = 1.5\n",
    "\n",
    "mu_2 = mu_1 + 1.7\n",
    "sigma_2 = sigma_1\n",
    "amp_2 = np.array([0.4, 0.3, 0.2, 0.2, 0.24, 0.1])\n",
    "bg_2 = 0.1\n",
    "noise_2 = 1.0\n",
    "\n",
    "sig_1 = np.zeros_like(t)\n",
    "for i, mu in enumerate(mu_1):\n",
    "    sig_1 += amp_1[i] * np.exp(-(t-mu)**2 / sigma_1[i]**2)\n",
    "sig_1 += bg_1\n",
    "sig_1 += noise_1 * sig_1 * np.random.rand(len(t))\n",
    "\n",
    "sig_2 = np.zeros_like(t)\n",
    "for i, mu in enumerate(mu_2):\n",
    "    sig_2 += amp_2[i] * np.exp(-(t-mu)**2 / sigma_2[i]**2)\n",
    "sig_2 += bg_2\n",
    "sig_2 += noise_2 * sig_2 * np.random.rand(len(t))\n",
    "\n",
    "\n",
    "p = bokeh.plotting.figure(width=600, height=250, x_axis_label='time', y_axis_label='signal')\n",
    "p.line(t, sig_1,legend=\"signal 1\")\n",
    "p.line(t, sig_2, color='orange',legend=\"signal 2\")\n",
    "\n",
    "bokeh.io.show(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Two interesting features we might want to extract are the typical durations of the pulses, and the timing relationship between the two signals. To do so, we can calculate the auto-correlation and cross-correlation functions, respectively.\n",
    "\n",
    "Autocorrelation:\n",
    "\n",
    "\\begin{align}\n",
    "(f \\star f)(\\tau) = \\int_{-\\infty}^{\\infty} {f(t)f(t+\\tau)} dt\n",
    "\\end{align}\n",
    "\n",
    "Cross-correlation:\n",
    "\n",
    "\\begin{align}\n",
    "(f \\star g)(\\tau)  = \\int_{-\\infty}^{\\infty} {f(t)g(t+\\tau)} dt\n",
    "\\end{align}\n",
    "\n",
    "For the signals we generated above, these functions can be easily computed. We can adjust the `np.correlate()` function to compute correlations between two signals (assumed to be sampled at uniform time intervals) and also give the corresponding values of the time lag in units of the time between samples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-05-06T17:58:38.132648Z",
     "start_time": "2019-05-06T17:58:38.121854Z"
    }
   },
   "outputs": [],
   "source": [
    "def correlate(x, y, half=False):\n",
    "    n = len(x)\n",
    "    \n",
    "    if n != len(y):\n",
    "        raise RuntimeError('Can only correlate arrays of equal length.')\n",
    "        \n",
    "    if n % 2:\n",
    "        lengths = np.concatenate((np.arange(n//2+1, n), np.arange(n, n//2, -1)))\n",
    "        lags = np.concatenate((np.arange(-n//2+1, 0), np.arange(n//2+1)))\n",
    "    else:\n",
    "        lengths = np.concatenate((np.arange(n//2, n), np.arange(n, n//2, -1)))\n",
    "        lags = np.concatenate((np.arange(-n//2, 0), np.arange(n//2)))\n",
    "        \n",
    "    # Compute correlation with max correlation being unity\n",
    "    corr = np.correlate(x, y, 'same') / lengths\n",
    "    corr /= corr.max()\n",
    "    \n",
    "    if half:\n",
    "        return lags[n//2:], corr[n//2:]\n",
    "    else:\n",
    "        return lags, corr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With this function in hand, we can compute the autocorrelation function for signal 1, and also the cross-correlation for the two signals (stored respectively as `sig_1` and `sig_2`)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-05-06T17:58:38.296183Z",
     "start_time": "2019-05-06T17:58:38.134937Z"
    }
   },
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\",\"dtype\":\"float64\",\"shape\":[2001]}},\"selected\":{\"id\":\"1650\",\"type\":\"Selection\"},\"selection_policy\":{\"id\":\"1651\",\"type\":\"UnionRenderers\"}},\"id\":\"1624\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"label\":{\"value\":\"cross-correlation\"},\"renderers\":[{\"id\":\"1641\",\"type\":\"GlyphRenderer\"}]},\"id\":\"1652\",\"type\":\"LegendItem\"},{\"attributes\":{\"callback\":null},\"id\":\"1595\",\"type\":\"DataRange1d\"},{\"attributes\":{},\"id\":\"1597\",\"type\":\"LinearScale\"},{\"attributes\":{\"line_alpha\":0.1,\"line_color\":\"#1f77b4\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1626\",\"type\":\"Line\"},{\"attributes\":{},\"id\":\"1651\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"active_drag\":\"auto\",\"active_inspect\":\"auto\",\"active_multi\":null,\"active_scroll\":\"auto\",\"active_tap\":\"auto\",\"tools\":[{\"id\":\"1611\",\"type\":\"PanTool\"},{\"id\":\"1612\",\"type\":\"WheelZoomTool\"},{\"id\":\"1613\",\"type\":\"BoxZoomTool\"},{\"id\":\"1614\",\"type\":\"SaveTool\"},{\"id\":\"1615\",\"type\":\"ResetTool\"},{\"id\":\"1616\",\"type\":\"HelpTool\"}]},\"id\":\"1617\",\"type\":\"Toolbar\"},{\"attributes\":{\"bottom_units\":\"screen\",\"fill_alpha\":{\"value\":0.5},\"fill_color\":{\"value\":\"lightgrey\"},\"left_units\":\"screen\",\"level\":\"overlay\",\"line_alpha\":{\"value\":1.0},\"line_color\":{\"value\":\"black\"},\"line_dash\":[4,4],\"line_width\":{\"value\":2},\"render_mode\":\"css\",\"right_units\":\"screen\",\"top_units\":\"screen\"},\"id\":\"1635\",\"type\":\"BoxAnnotation\"},{\"attributes\":{\"ticker\":{\"id\":\"1602\",\"type\":\"BasicTicker\"}},\"id\":\"1605\",\"type\":\"Grid\"},{\"attributes\":{\"text\":\"\"},\"id\":\"1629\",\"type\":\"Title\"},{\"attributes\":{},\"id\":\"1614\",\"type\":\"SaveTool\"},{\"attributes\":{\"source\":{\"id\":\"1638\",\"type\":\"ColumnDataSource\"}},\"id\":\"1642\",\"type\":\"CDSView\"},{\"attributes\":{\"callback\":null},\"id\":\"1593\",\"type\":\"DataRange1d\"}],\"root_ids\":[\"1592\"]},\"title\":\"Bokeh Application\",\"version\":\"1.1.0\"}};\n",
       "  var render_items = [{\"docid\":\"39b50495-6328-4b20-b23c-13528ccda147\",\"roots\":{\"1592\":\"3dd8704a-2037-4c23-963b-5d90df9103a3\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        embed_document(root);\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "      attempts++;\n",
       "      if (attempts > 100) {\n",
       "        console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
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   "source": [
    "lags, auto_corr = correlate(sig_1, sig_1)\n",
    "lags, cross_corr = correlate(sig_1, sig_2)\n",
    "\n",
    "# Compuet tau in units of time\n",
    "tau = lags * (t[1] - t[0])\n",
    "\n",
    "p = bokeh.plotting.figure(width=600, height=250, x_axis_label='τ', \n",
    "                          y_axis_label='correlation')\n",
    "p.line(tau, auto_corr, legend='signal 1 autocorrelation')\n",
    "p.line(tau, cross_corr, color='orange', legend='cross-correlation')\n",
    "\n",
    "bokeh.io.show(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Many features can be extracted from these functions. Here we highlight:\n",
    "\n",
    "* In the autocorrelation, the width of the central peak indicates the typical pulse duration.\n",
    "\n",
    "* The offset of the central cross-correlation peak reveals the typical separation between a peak in one trace and a peak in the other. Here we can see that the orange pulses typically follow the blue traces after a couple time units. \n",
    "\n",
    "It's worth playing with these functions on real and synthetic data to get a feeling for what they look like for different types of functions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calcium modulates pulse frequency but not duration\n",
    "\n",
    "We can now see how calcium modulates the dynamics. First, we see that it strongly modulates mean pulse frequency but not mean pulse duration:\n",
    "\n",
    "<img src=\"figs/Crz1_pulse_duration_frequency.png\" width=\"400px\">\n",
    "<center><i>Average of Crz1 pulse dynamics in 42 cells, from L. Cai et al. (<a href=\"https://doi.org/10.1038/nature07292\">Nature, 2008</a>)\n",
    "</i></center>\n",
    "\n",
    "In fact, even as pulse frequencies change dramatically, the entire distribution of pulse durations is apparently unaffected by the level of calcium:\n",
    "\n",
    "<img src=\"figs/Crz1_duration_distribution.png\" width=\"400px\">\n",
    "<center><i>Distribution of pulse durations, from L. Cai et al. (<a href=\"https://doi.org/10.1038/nature07292\">Nature, 2008</a>).\n",
    "</i></center><br />\n",
    "\n",
    "And we see a similar behavior at the level of pulse clusters, with calcium modulating their frequency, but not their mean duration. To extract these features, one first notes that the autocorrelation function is well fit by a sum of two exponentials with different timescales, corresponding to individual pulses and pulse clusters:\n",
    "\n",
    "\\begin{align}\n",
    "C_a = A_1 \\mathrm{e}^{- \\left(\\frac{t}{\\tau_{pulse}}\\right)} + A_2 \\mathrm{e}^{-\\left(\\frac{t}{\\tau_{cluster}}\\right)}\n",
    "\\end{align}\n",
    "\n",
    "<img src=\"figs/Crz1_pulse_train_analysis.png\" width=\"500px\">\n",
    "<center><i>Analysis of pulse trains, from L. Cai et al. (<a href=\"https://doi.org/10.1038/nature07292\">Nature, 2008</a>).\n",
    "</i></center><br />\n",
    "\n",
    "Finally, the initial response to calcium does not occur in all cells, but the fraction of cells that exhibit that response is also modulated by calcium:\n",
    "\n",
    "<img src=\"figs/Crz1_initial_response.png\" width=\"300px\">\n",
    "<center><i>Analysis of pulse trains, from L. Cai et al. (<a href=\"https://doi.org/10.1038/nature07292\">Nature, 2008</a>).\n",
    "</i></center><br />\n",
    "\n",
    "To summarize, calcium seems to be modulate the frequency of individual pulses, pulse clusters, and even the appearance of initial responses, while *not* affecting the amplitude or duration of the same features!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## How do we get the observed autocorrelation?\n",
    "\n",
    "To show how pulse trains might give the observed biexponential mean autocorrelation function, we can build a simulated signal. We use the following simplified model. A cell can either be in a cluster state, in which it may have pulsed localization, or out of a cluster state, in which no localization occurs. Entry into a cluster state is a modeled as a Poisson process with time constant $\\tau_1$, and exit from a cluster state is modeled as a Poisson process with time constant $\\tau_2$. While in a cluster state, we may get localization events, also modeled as a Poisson process, with time constant $\\tau_3$. We model each pulse as a Gaussian-like peak in time with width $2\\sigma$. Finally, there is also noise in the signal.\n",
    "\n",
    "First, we'll code up some function to make our signal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-05-06T17:58:38.312222Z",
     "start_time": "2019-05-06T17:58:38.301187Z"
    }
   },
   "outputs": [],
   "source": [
    "def pulse_times(tau_1, tau_2, tau_3, t_max):\n",
    "    t_pulse = []\n",
    "    t = 0\n",
    "    \n",
    "    while t < t_max:\n",
    "        # Wait for pulsing to turn on\n",
    "        t += np.random.exponential(tau_1)\n",
    "\n",
    "        # How long will pulsing last?\n",
    "        t_end = t + np.random.exponential(tau_2)\n",
    "\n",
    "        # Make pulses\n",
    "        while t < t_end:\n",
    "            t += np.random.exponential(tau_3)\n",
    "            t_pulse.append(t)\n",
    "\n",
    "    return np.array(t_pulse)\n",
    "\n",
    "\n",
    "def pulse_signal(pulse_times, base_signal, pulse_amplitude, pulse_amplitude_sigma, \n",
    "                 noise_amplitude, sigma, t_max, n_samples):\n",
    "    t = np.linspace(0, t_max * (1 + 0.02), n_samples)\n",
    "    signal = base_signal + np.random.normal(0, noise_amplitude, len(t))\n",
    "    for tp in pulse_times:\n",
    "        signal += (pulse_amplitude * np.random.normal(1, pulse_amplitude_sigma) \n",
    "                       * st.norm.pdf(t, tp, sigma))\n",
    "\n",
    "    return t, signal\n",
    "\n",
    "\n",
    "def make_signal(tau_1, tau_2, tau_3, base_signal, pulse_amplitude, pulse_amplitude_sigma, \n",
    "                 noise_amplitude, sigma, t_max, n_samples):\n",
    "    t_pulse = pulse_times(tau_1, tau_2, tau_3, t_max)\n",
    "\n",
    "    return pulse_signal(t_pulse, base_signal, pulse_amplitude, pulse_amplitude_sigma, \n",
    "                        noise_amplitude, sigma, t_max, n_samples)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's generate a typical signal and see how it looks."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-05-06T17:58:38.518132Z",
     "start_time": "2019-05-06T17:58:38.314438Z"
    }
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\",\"dtype\":\"float64\",\"shape\":[4096]},\"y\":{\"__ndarray__\":\"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\",\"dtype\":\"float64\",\"shape\":[4096]}},\"selected\":{\"id\":\"1871\",\"type\":\"Selection\"},\"selection_policy\":{\"id\":\"1872\",\"type\":\"UnionRenderers\"}},\"id\":\"1805\",\"type\":\"ColumnDataSource\"},{\"attributes\":{},\"id\":\"1796\",\"type\":\"ResetTool\"},{\"attributes\":{\"bottom_units\":\"screen\",\"fill_alpha\":{\"value\":0.5},\"fill_color\":{\"value\":\"lightgrey\"},\"left_units\":\"screen\",\"level\":\"overlay\",\"line_alpha\":{\"value\":1.0},\"line_color\":{\"value\":\"black\"},\"line_dash\":[4,4],\"line_width\":{\"value\":2},\"render_mode\":\"css\",\"right_units\":\"screen\",\"top_units\":\"screen\"},\"id\":\"1870\",\"type\":\"BoxAnnotation\"},{\"attributes\":{\"line_alpha\":0.1,\"line_color\":\"#1f77b4\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1807\",\"type\":\"Line\"},{\"attributes\":{},\"id\":\"1788\",\"type\":\"BasicTicker\"},{\"attributes\":{},\"id\":\"1778\",\"type\":\"LinearScale\"},{\"attributes\":{},\"id\":\"1871\",\"type\":\"Selection\"},{\"attributes\":{},\"id\":\"1872\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"overlay\":{\"id\":\"1870\",\"type\":\"BoxAnnotation\"}},\"id\":\"1794\",\"type\":\"BoxZoomTool\"},{\"attributes\":{\"axis_label\":\"nuclear fluorescent intensity (a.u.)\",\"formatter\":{\"id\":\"1868\",\"type\":\"BasicTickFormatter\"},\"ticker\":{\"id\":\"1788\",\"type\":\"BasicTicker\"}},\"id\":\"1787\",\"type\":\"LinearAxis\"},{\"attributes\":{},\"id\":\"1793\",\"type\":\"WheelZoomTool\"},{\"attributes\":{},\"id\":\"1866\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{},\"id\":\"1797\",\"type\":\"HelpTool\"},{\"attributes\":{},\"id\":\"1783\",\"type\":\"BasicTicker\"},{\"attributes\":{\"data_source\":{\"id\":\"1805\",\"type\":\"ColumnDataSource\"},\"glyph\":{\"id\":\"1806\",\"type\":\"Line\"},\"hover_glyph\":null,\"muted_glyph\":null,\"nonselection_glyph\":{\"id\":\"1807\",\"type\":\"Line\"},\"selection_glyph\":null,\"view\":{\"id\":\"1809\",\"type\":\"CDSView\"}},\"id\":\"1808\",\"type\":\"GlyphRenderer\"},{\"attributes\":{},\"id\":\"1792\",\"type\":\"PanTool\"},{\"attributes\":{\"active_drag\":\"auto\",\"active_inspect\":\"auto\",\"active_multi\":null,\"active_scroll\":\"auto\",\"active_tap\":\"auto\",\"tools\":[{\"id\":\"1792\",\"type\":\"PanTool\"},{\"id\":\"1793\",\"type\":\"WheelZoomTool\"},{\"id\":\"1794\",\"type\":\"BoxZoomTool\"},{\"id\":\"1795\",\"type\":\"SaveTool\"},{\"id\":\"1796\",\"type\":\"ResetTool\"},{\"id\":\"1797\",\"type\":\"HelpTool\"}]},\"id\":\"1798\",\"type\":\"Toolbar\"},{\"attributes\":{},\"id\":\"1780\",\"type\":\"LinearScale\"},{\"attributes\":{\"axis_label\":\"time (min)\",\"formatter\":{\"id\":\"1866\",\"type\":\"BasicTickFormatter\"},\"ticker\":{\"id\":\"1783\",\"type\":\"BasicTicker\"}},\"id\":\"1782\",\"type\":\"LinearAxis\"},{\"attributes\":{\"ticker\":{\"id\":\"1783\",\"type\":\"BasicTicker\"}},\"id\":\"1786\",\"type\":\"Grid\"},{\"attributes\":{},\"id\":\"1868\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{\"text\":\"\"},\"id\":\"1864\",\"type\":\"Title\"},{\"attributes\":{\"dimension\":1,\"ticker\":{\"id\":\"1788\",\"type\":\"BasicTicker\"}},\"id\":\"1791\",\"type\":\"Grid\"},{\"attributes\":{\"callback\":null},\"id\":\"1774\",\"type\":\"DataRange1d\"},{\"attributes\":{\"callback\":null},\"id\":\"1776\",\"type\":\"DataRange1d\"},{\"attributes\":{\"line_color\":\"#1f77b4\",\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1806\",\"type\":\"Line\"},{\"attributes\":{},\"id\":\"1795\",\"type\":\"SaveTool\"},{\"attributes\":{\"source\":{\"id\":\"1805\",\"type\":\"ColumnDataSource\"}},\"id\":\"1809\",\"type\":\"CDSView\"}],\"root_ids\":[\"1773\"]},\"title\":\"Bokeh Application\",\"version\":\"1.1.0\"}};\n",
       "  var render_items = [{\"docid\":\"858f6ce5-ed3b-48b8-a3e5-cb9b4de900e3\",\"roots\":{\"1773\":\"4f6fbbea-51fa-44fe-b827-88e2b61fb050\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        embed_document(root);\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "      attempts++;\n",
       "      if (attempts > 100) {\n",
       "        console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "1773"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "t, signal = make_signal(tau_1=10,\n",
    "                        tau_2=12,\n",
    "                        tau_3=1,\n",
    "                        base_signal=0.5,\n",
    "                        pulse_amplitude=1.5,\n",
    "                        pulse_amplitude_sigma=0.1,\n",
    "                        noise_amplitude=0.1,\n",
    "                        sigma=0.25,\n",
    "                        t_max=500,\n",
    "                        n_samples=4096)\n",
    "\n",
    "p = bokeh.plotting.figure(width=500, height=250, x_axis_label='time (min)', \n",
    "                          y_axis_label='nuclear fluorescent intensity (a.u.)')\n",
    "p.line(t, signal, line_join='bevel')\n",
    "bokeh.io.show(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see clusters of nuclear localization with quiet periods separating them.\n",
    "\n",
    "We will now generate many of these signals (100 of them) and compute the mean autocorrelation function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-05-06T17:58:44.577234Z",
     "start_time": "2019-05-06T17:58:38.520010Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "  <div class=\"bk-root\" id=\"992507cf-b780-4857-9498-2cede58afd99\" data-root-id=\"1927\"></div>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "(function(root) {\n",
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     "output_type": "display_data"
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   "source": [
    "auto_corrs = np.empty((100, 4096//2))\n",
    "for i in range(100):\n",
    "    _, signal = make_signal(tau_1=10,\n",
    "                            tau_2=12,\n",
    "                            tau_3=1,\n",
    "                            base_signal=0.5,\n",
    "                            pulse_amplitude=1.5,\n",
    "                            pulse_amplitude_sigma=0.1,\n",
    "                            noise_amplitude=0.1,\n",
    "                            sigma=0.25,\n",
    "                            t_max=500,\n",
    "                            n_samples=4096)\n",
    "\n",
    "    tau, auto_corrs[i] = correlate(signal, signal, half=True)\n",
    "\n",
    "mean_autocorr = np.mean(auto_corrs, axis=0)\n",
    "\n",
    "p = bokeh.plotting.figure(width=400, height=250,\n",
    "                          x_axis_label='τ (min)',\n",
    "                          y_axis_label='autocorrelation',\n",
    "                          x_range=[-2, 50])\n",
    "p.line(tau, mean_autocorr)\n",
    "p.circle(tau, mean_autocorr)\n",
    "\n",
    "bokeh.io.show(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, we see two decays, a fast one corresponding to the typical width of spikes, and a second corresponding to the cluster time.\n",
    "\n",
    "This procedure, of generating data with properties we know and then investigating how our analysis technique captures the known properties, is in general very useful for validating data analysis techniques."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Why FM pulsing?\n",
    "\n",
    "These observations provoke the natural question: Why use FM pulsing instead of a seemingly simpler continuous regulation system?\n",
    "\n",
    "In non-biological contexts, FM or pulsatile regulatory systems offer a number of advantages compared to their AM counterparts:\n",
    "\n",
    "* FM radio is less susceptible to transmission noise that predominantly affects signal amplitude.\n",
    "\n",
    "* In neurobiology, transmission of signals through all or none spikes (action potentials) could allow signal propagation with minimal degradation.\n",
    "\n",
    "* \"Bang bang\" control systems work by regulating the fraction of time that a system is \"on\" rather than modulating its level of activity. Bang bang provides simple, intrinsically linear control, and does not require detailed knowledge of the exact input-output behavior of the device. One example where this scheme has been used is rocket thrusters. (A fun example of this is the classic lunar lander video game, in which one uses bang bang control to safely land a spacecraft: http://moonlander.seb.ly/).\n",
    "\n",
    "<img src=\"figs/lunar_lander.png\" width=\"300px\">\n",
    "<center><i>Moonlander screenshot; see <a href=\"http://moonlander.seb.ly/\">http://moonlander.seb.ly/</a>.\n",
    "</i></center><br />\n",
    "\n",
    "Which, if any, of these possible explanations might be relevant for the cell? As we will see, the third example—bang bang control—could provide insight into some of the benefits of FM pulsing.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## FM, but not AM, regulation allows coordinated activation of diverse target genes\n",
    "\n",
    "To think about the different effects of AM and FM-pulse regulation, we consider two hypothetical target genes that have different response functions to Crz1.\n",
    "\n",
    "<img src=\"figs/Crz1_two_targets.png\" width=\"300px\">\n",
    "<center><i>\n",
    "</i></center>\n",
    "\n",
    "Consider two hypothetical Crz1 target genes with different response functions. These targets might have different sensitivities, different amplitudes, and different EC50s with respect to nuclear Crz1 concentration. Let's imagine how these genes would respond to different levels of nuclear Crz1. \n",
    "\n",
    "In an AM regulation system, low and high input levels produce different ratios of A and B expression. As illustrated here, low levels of nuclear Crz1 might produce more of B than of A. Higher levels of Crz1 would move one to the right on the response functions, generating more of both proteins, but shifting the ratio, so that A is now produced at a higher rate than B. In this sense, the ratio of A production to B production depends on the precise concentration of Crz1 in the nucleus.\n",
    "\n",
    "<img src=\"figs/AM_uncoordinated.png\" width=\"500px\">\n",
    "<center><i>\n",
    "</i></center>\n",
    "\n",
    "Now contrast this behavior with what one might expect in the FM pulsing system. Here, increasing input level produces a higher frequency of pulses, but the durations and amplitudes of the pulses are not affected. Therefore, the ratio of A to B expression produced by each pulse (or the distribution of those ratios) remains the same regardless of the mean Crz1 activity. As a result, frequency modulation can vary both A and B expression in concert, maintaining a constant A to B ratio across a wide range of expression levels:\n",
    "\n",
    "<img src=\"figs/FM_coordinated.png\" width=\"500px\">\n",
    "<center><i>\n",
    "</i></center>\n",
    "\n",
    "More generally, if we consider many target genes, one can see that FM pulsing ensures they are all co-regulated in fixed proportions, despite differences in their individual input functions. \n",
    "\n",
    "<img src=\"figs/Crz1_AMFM_summary.png\" width=\"500px\">\n",
    "<center><i>\n",
    "</i></center>\n",
    "\n",
    "These considerations suggest a simple **design principle**: *FM pulsing enables coordinated regulation of diverse target genes.*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Crz1 target genes show coordinated regulation\n",
    "\n",
    "Does the real system in fact exhibit coordination regulation of its targets?  If so, one would certainly expect to see target expression track pulse frequency. \n",
    "\n",
    "<img src=\"figs/Crz1_target_tracks_frequency.png\" width=\"350px\">\n",
    "<center><i>From L. Cai et al. (<a href=\"https://doi.org/10.1038/nature07292\">Nature, 2008</a>).\n",
    "</i></center><br />\n",
    "\n",
    "More generally, we would expect that changing key parameters of the reporter would preserve this relationship. To check this, we constructed synthetic Crz1 target promoters with different numbers of binding sites (CDREs) for Crz1. The mean activity of these promoters varied over a 450-fold range. \n",
    "\n",
    "<img src=\"figs/Crz1_synthetic_promoter_series.png\" width=\"350px\">\n",
    "<center><i>Synthetic target promoters show coordinated regulation. Synthetic promoters varying over 450-fold in their mean activity (inset) produce similar dose-response curves. From L. Cai et al. (<a href=\"https://doi.org/10.1038/nature07292\">Nature, 2008</a>).\n",
    "</i></center><br />\n",
    "\n",
    "Furthermore, the same coordination can be observed with natural genes. The following plots show how diverse Crz1 target genes (black) compare  to pulse frequency (red) in their response to calcium dose.\n",
    "\n",
    "<img src=\"figs/Crz1_many_targets.png\" width=\"550px\">\n",
    "<center><i>Natural target genes (black) and pulse frequency (red) show similar responses to calcium dose. From L. Cai et al. (<a href=\"https://doi.org/10.1038/nature07292\">Nature, 2008</a>). Additional targets shown in paper.\n",
    "</i></center><br />"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## What about \"fine-tuning?\"\n",
    "\n",
    "In a fine-tuned model, all the promoters have the same dependence on Crz1 concentration, at least up to a scale factor for each promoter. That is, $P_i$(Crz1) $= \\alpha_i P_0$(Crz1), where the index i labels each target promoter and $P_0$ refers to a reference promoter. \n",
    "\n",
    "If this were the case, then increasing the concentration of Crz1 should change all promoters to the same extent. Contrary to this expectation, experiments revealed that different promoters were affected to differing extents by Crz1 overexpression, suggesting that the observed coordination results from FM pulsing rather than from fine-tuning of target promoters."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Other \"histogram-preserving\" modulations can also enable coordination.\n",
    "\n",
    "Coordination can occur with multiple types of time-based regulation. It does not require frequency modulation per se. Any type of \"histogram preserving\" modulation in which input signals control only the fraction of time the factor spends in a state, but not the distribution of activities in either the low or high activity states, should work.\n",
    "\n",
    "Here are some examples. In each case, top and bottom illustrations show, schematically, how time traces would be affected by a change in input.\n",
    "\n",
    "<img src=\"figs/Crz1_diverse_modulation.png\" width=\"450px\">\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Multiple pulsers: from frequency to phasing\n",
    "\n",
    "So far we have focused on a single transcription factor, pulsing away in a single condition. But in reality there are likely to be multiple pulsatile transcription factors operating in the same cell at the same time, and potentially co-regulating many common target genes, something like this:\n",
    "\n",
    "<center>\n",
    "<video width=\"768px\" src=\"figs/phase_pulsing_animation.m4v\" controls loop>\n",
    "Your browser does not support display of this video.\n",
    "</video>\n",
    "</center>\n",
    "\n",
    "This leads to the next question: how do multiple pulsatile systems interact *in time* to control targets?\n",
    "Could cells use **relative timing** or **phasing** of dynamics between different transcription factors to control target genes in new ways?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Phasing matters\n",
    "\n",
    "<img src=\"figs/phasing_matters_1.png\" width=\"500px\">\n",
    "<img src=\"figs/phasing_matters_2.png\" width=\"500px\">\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Msn2 and Mig1 pulse and co-regulate common target genes\n",
    "\n",
    "Msn2 and Mig1, two major transcription factors in yeast, respond to overlapping stresses, including glucose limitation, and co-regulate some common target genes:\n",
    "\n",
    "<img src=\"figs/Msn2_Mig1_diagram.png\" width=\"400px\">\n",
    "\n",
    "Msn2 is an activator, while Mig1 is generally a repressor. \n",
    "\n",
    "You can imagine that if only Msn2 is present, it can easily activate the gene, but if both Msn2 and Mig1 are simultaneously present, it is a bit like stepping on both the accelerator (Msn2) and brake (Mig1) at the same time. If you do that, ideally, the brake will dominate and the car (target gene), will not move (activate)."
   ]
  },
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    "## Three-color strains enable simultaneous analysis of two transcription factors and one target\n",
    "\n",
    "To be able to visualize Msn2 and Mig1 dynamics, along with their effects on a target gene, Y. Lin et al. ([*Nature*, 2105](https://doi.org/10.1038/nature15710)) engineered a three color reporter system in yeast.\n",
    "\n",
    "<img src=\"figs/three_color_strain.png\" width=\"500px\">\n",
    "\n",
    "In this system, Msn2 and Mig1 are fused to distinct fluorescent protein colors. In addition, the RNA-binding protein PP7, fused to a third fluorescent protein, enables rapid and direct tracking of target transcription from synthetic and natural target genes; see Larson, et al. ([*Science*, 2011](https://doi.org/10.1126/science.1202142))."
   ]
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    "## Different inputs activate with different relative timing\n",
    "\n",
    "In these movies, we can see that exposure of cells to either salt or ethanol each activate both transcription factors. However, they do so with different relative timing, either \"out of phase\" or \"in phase\". Because M\n",
    "\n",
    "For example, in this movie note that adding NaCl causes a sequential activation (nuclear localization) of Msn2 *followed by* Mig1, leading to increase in target expression.\n",
    "\n",
    "<br/>\n",
    "<center>\n",
    "<video width=\"768px\" src=\"figs/NaCl_out_of_phase.avi\" controls loop>\n",
    "Your browser does not support display of this video.\n",
    "</video>\n",
    "</center>\n",
    "\n",
    "<br/>\n",
    "\n",
    "By contrast, here we can see that adding ethanol to the same cells causes *simultaneous* activation (nuclear localization) of Msn2 and Mig1, producing little or no expression of the target:\n",
    "\n",
    "<br />\n",
    "<center>\n",
    "<video width=\"768px\" src=\"figs/EtOH_in_phase.mov\" controls loop>\n",
    "Your browser does not support display of this video.\n",
    "</video>\n",
    "</center><br />\n",
    "\n",
    "These movies can be summarized with this plot:\n",
    "\n",
    "<img src=\"figs/salt_ethanol_phasing.png\" width=\"600px\">\n",
    "<i>Different stresses activate Msn2 and Mig1 with different relative timing, resulting in distinct target activation patterns. The three target genes in each case so a full combinatorially regulated target as well as controls lacking one or the other set of binding sites. See Lin et al, <a href=\"https://doi.org/10.1038/nature15710\">Nature, 2015</a>.\n",
    "</i>\n",
    "<br /><br/>\n",
    "\n",
    "What we can see here is amazing: Different inputs activate the same transcription factors with different **relative timing** and this in turn determines whether target genes are activated or not. The paper provides many other examples and contexts in which this type of regulation occurs, and provides some indication of genes that may be \n"
   ]
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   "metadata": {},
   "source": [
    "## Relative timing can be continuously modulated by glucose concentration\n",
    "\n",
    "Another way to modulate this system is to vary glucose concentration. If one then tracks the dynamics of the two transcription factors, and computes the cross-correlation functions, one can see the relative amplitude of in phase and out of phase peaks gradually shifting:\n",
    "\n",
    "<img src=\"figs/glucose_titration_ccf.png\" width=\"800px\">\n",
    "<center><i>Glucose concentration determines relative timing of Msn2 and Mig1 pulses. See Lin et al, <a href=\"https://doi.org/10.1038/nature15710\">Nature, 2015</a>.\n",
    "</i></center><br />\n",
    "\n",
    "This shows us that cells can and do encode signals not only in the overall dynamics of a single transcription factor but more generally in the relative timing of multiple transcription factors.\n",
    "\n",
    "Someday, we would like to have a more complete picture in which we could simultaneously image the dynamic responses of all regulators in the same cell over time, while also observing their targets. \n"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusions\n",
    "\n",
    "Today we have seen that cells are organized not only in space but also in time. Perhaps we should not be surprised: just as electrical circuits have long made use of the time domain for complex regulation, so too do living cells. While we have examined a few core regulatory systems in yeast, similar types of dynamic regulatory strategies are likely to be quite general across pathways, cell types, and species.\n",
    "\n",
    "To recap:\n",
    "\n",
    "* Time-based regulation provides a unique regulatory capability: controlling a diverse set of target genes in fixed proportions. \n",
    "\n",
    "* This capability is ideal for ensuring that protein products of multiple targets need to work together in fixed stoichiometries. At the same time, it may also be interesting to think about cases in which coordination is *not* desired. For example, when it is more optimal to trigger qualitatively distinct responses to high levels of input compared to low ones.\n",
    "\n",
    "* In some systems, inputs regulate target through multiple transcription factors, by regulating the **relative timing** with which they activate. \n"
   ]
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