diff --git a/bionet/1-cyclic-error-correction.ipynb b/bionet/1-cyclic-error-correction.ipynb new file mode 100644 index 0000000..690bfa9 --- /dev/null +++ b/bionet/1-cyclic-error-correction.ipynb @@ -0,0 +1,123 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 8, + "id": "3b5b09c5-9188-49d8-a6c8-2f89ea1c7d7a", + "metadata": {}, + "outputs": [], + "source": [ + "from random import random\n", + "import numpy as np\n", + "\n", + "\n", + "def decide (prob):\n", + " return True if random() <= prob else False\n" + ] + }, + { + "cell_type": "markdown", + "id": "6e68a721", + "metadata": {}, + "source": [ + "Question A: Try to simulate Figure. 1.11, assuming that probability to return to start if right is 0.9 while probability to return to start if attempt is wrong is 0.99. Assume that right and wrong are produced equally often and start 100000 times and for each time count how many end in right, respectively wrong state with 1 sorting step, and with 2 sorting steps." + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "56a4b642-2454-4021-98dd-dc95b07ae5bf", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "244509.0\n", + "270193.0\n", + "485298\n" + ] + } + ], + "source": [ + "N = int(1e6)\n", + "\n", + "isright = True\n", + "n = 0\n", + "\n", + "n_wrong = np.zeros(N)\n", + "n_right = np.zeros(N)\n", + "n_0 = 0\n", + "\n", + "for i in range(0,N):\n", + " if n == 0:\n", + " isright = decide(.5)\n", + " n += 1\n", + " n_0 += 1\n", + " \n", + " elif isright:\n", + " n_right[n] += 1\n", + " if decide(0.9):\n", + " n = 0\n", + " else:\n", + " n += 1\n", + " else:\n", + " n_wrong[n] += 1\n", + " if decide(0.99):\n", + " n = 0\n", + " else:\n", + " n += 1\n", + " \n", + " \n", + "print(np.sum(n_wrong))\n", + "print(np.sum(n_right))\n", + "print(n_0)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "8b1131fa-c7f8-4ff6-81cd-5ae6eec2d03c", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "81e08034-a023-4309-8314-44bcca4b052c", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3356adc3-ef39-4e63-8f2c-d1e4cec9c503", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "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": "3.7.3" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/bionet/10-combined-feedback.ipynb b/bionet/10-combined-feedback.ipynb new file mode 100644 index 0000000..5882a5d --- /dev/null +++ b/bionet/10-combined-feedback.ipynb @@ -0,0 +1,201 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#8.5.1\n", + "\n", + "dt = .01\n", + "p = 10\n", + "D = 1\n", + "tau = 5\n", + "xmax = 100\n", + "tmaxs = 50\n", + "tmax = int(tmaxs / dt)\n", + "\n", + "deltaT = np.zeros(xmax)\n", + "deltaR = np.zeros(xmax)\n", + "T = np.zeros((xmax, tmax))\n", + "R = np.zeros((xmax, tmax))\n", + "\n", + "\n", + "S = np.zeros(xmax)\n", + "S[int(xmax / 2) - 1] = 1\n", + "\n", + "for t in range(0, tmax):\n", + "\n", + " if t > 0:\n", + " for x in range(0,xmax):\n", + " T[x,t] = T[x, t-1]\n", + " R[x,t] = R[x, t-1]\n", + "\n", + " for x in range(0,xmax):\n", + " deltaT = S[x] + p*T[x,t]**2 / (1 + T[x,t]**2) - R[x,t] * T[x,t] / (0.1 + T[x,t]) - T[x,t] \n", + " if x > 0 and x < xmax - 1:\n", + " deltaT += D*(T[x-1,t] + T[x+1,t] - 2*T[x,t])\n", + "\n", + " deltaR= T[x,t] - R[x,t] / tau\n", + "\n", + " T[x,t] += deltaT* dt\n", + " R[x,t] += deltaR* dt\n", + "\n", + "plt.title(\"T\")\n", + "plt.imshow(T, cmap='viridis', interpolation='nearest', extent=[0, tmaxs, xmax, 0])\n", + "plt.xlabel(\"Time\")\n", + "plt.ylabel(\"Position\")\n", + "plt.colorbar()\n", + "plt.show()\n", + "\n", + "plt.title(\"R\")\n", + "plt.imshow(R, cmap='viridis', interpolation='nearest', extent=[0, tmaxs, xmax, 0])\n", + "plt.xlabel(\"Time\")\n", + "plt.ylabel(\"Position\")\n", + "plt.colorbar()\n", + "plt.show()\n" + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#8.5.6\n", + "\n", + "dt = .001\n", + "D = 1\n", + "xmax = 20\n", + "tmaxs = 100\n", + "tmax = int(tmaxs / dt)\n", + "\n", + "a = np.zeros((xmax, tmax))\n", + "b = np.zeros((xmax, tmax))\n", + "\n", + "a[:,0] = .1 # influences number of stripes\n", + "b[:,0] = .1\n", + "a[xmax - 1,0] = 1\n", + "\n", + "for t in range(0, tmax):\n", + "\n", + " if t > 0:\n", + " for x in range(0,xmax):\n", + " a[x,t] = a[x, t-1]\n", + " b[x,t] = b[x, t-1]\n", + "\n", + " for x in range(0,xmax):\n", + "\n", + " delta_a = a[x,t] ** 2 / b[x,t] - a[x,t]\n", + " delta_b = a[x,t] ** 2 - b[x,t]\n", + " \n", + " if x > 0 and x < xmax - 1:\n", + " delta_b += D*(b[x-1,t] + b[x+1,t] - 2*b[x,t])\n", + "\n", + " if x == 0:\n", + " delta_b += D*(b[x+1,t] - b[x,t])\n", + "\n", + " if x == xmax - 1:\n", + " delta_b += D*(b[x-1,t] - b[x,t])\n", + " \n", + " a[x,t] += delta_a * dt\n", + " b[x,t] += delta_b * dt\n", + "\n", + "plt.title(\"a\")\n", + "plt.imshow(a, cmap='viridis', interpolation='nearest', extent=[0, tmaxs, xmax, 0])\n", + "plt.xlabel(\"Time\")\n", + "plt.ylabel(\"Position\")\n", + "plt.colorbar()\n", + "plt.show()\n", + "\n", + "plt.title(\"b\")\n", + "plt.imshow(b, cmap='viridis', interpolation='nearest', extent=[0, tmaxs, xmax, 0])\n", + "plt.xlabel(\"Time\")\n", + "plt.ylabel(\"Position\")\n", + "plt.colorbar()\n", + "plt.show()\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "venv", + "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": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/bionet/11-feedback.ipynb b/bionet/11-feedback.ipynb new file mode 100644 index 0000000..d4acf55 --- /dev/null +++ b/bionet/11-feedback.ipynb @@ -0,0 +1,263 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "import numpy as np" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# 8.2.3\n", + "\n", + "dt = .005\n", + "h = 3\n", + "epsilon = .01\n", + "\n", + "t = np.linspace(0,20,int(20 / dt))\n", + "A = np.zeros_like(t)\n", + "B = np.zeros_like(t)\n", + "C = np.zeros_like(t)\n", + "\n", + "A[0] = 1\n", + "for i in range (0, int(20 / dt) - 1):\n", + " A[i+1] = A[i] + dt * (epsilon + 1/(1+ (5*C[i])**h) - A[i])\n", + " B[i+1] = B[i] + dt * (epsilon + 1/(1 + (5*A[i])**h) - B[i])\n", + " C[i+1] = C[i] + dt * (epsilon + 1/(1 + (5*B[i])**h) - C[i])\n", + "\n", + "plt.title(\"Rock Paper Scissor Oscillation\")\n", + "plt.plot(t, A, label=\"A\")\n", + "plt.plot(t, B, label=\"B\")\n", + "plt.plot(t, C, label=\"C\")\n", + "plt.legend()\n", + "plt.show()\n" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# 8.2.6\n", + "\n", + "tau = 1 # can give positive interference!\n", + "dt = .05\n", + "\n", + "t = np.linspace(0,20,int(20 / dt))\n", + "x = np.zeros_like(t)\n", + "\n", + "offset = int(tau / dt)\n", + "\n", + "for i in range (0, offset):\n", + " x[i] = 1\n", + "\n", + "for i in range (offset, int(20 / dt)):\n", + " x[i] = x[i-1] - dt * (x[i-offset])\n", + "\n", + "plt.title(\"Feedback with time delay\")\n", + "plt.plot(t, x, label=\"x\")\n", + "plt.legend()\n", + "plt.show()\n" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "sigma=1.0: found steady state after 32 iterations\n", + "E=0.0008160259005519703, T=0.0008160259005519703, s=0.0003664319324821372\n", + "sigma=2.0: found steady state after 0 iterations\n", + "E=0.000825264980790624, T=0.000825264980790624, s=0.000898694121382238\n", + "sigma=4.0: found steady state after 0 iterations\n", + "E=0.0008341652124493052, T=0.0008341652124493052, s=0.0018085373673978136\n", + "sigma=8.0: found steady state after 0 iterations\n", + "E=0.0008431183386114386, T=0.0008431183386114386, s=0.0036383427481339204\n", + "sigma=16.0: found steady state after 1 iterations\n", + "E=0.0008636293267295821, T=0.0008636293267295821, s=0.007323625346980424\n", + "sigma=32.0: found steady state after 77 iterations\n", + "E=0.0013020147363979543, T=0.0013020147363979543, s=0.018017347245352085\n", + "sigma=64.0: found steady state after 117 iterations\n", + "E=0.0033454690108945984, T=0.0033454690108945984, s=0.04922756580256679\n", + "sigma=128.0: found steady state after 94 iterations\n", + "E=0.014637594938958297, T=0.014637594938958297, s=0.1198080342996902\n", + "sigma=256.0: failed after 99999 iterations with\n", + "E=0.48076128531418244, T=0.48076128531418244, s=0\n", + "sigma=512.0: failed after 99999 iterations with\n", + "E=0.497995855519903, T=0.497995855519903, s=0\n", + "sigma=1024.0: failed after 99999 iterations with\n", + "E=0.504135476436683, T=0.504135476436683, s=0\n", + "sigma=2048.0: failed after 99999 iterations with\n", + "E=0.4813457484199005, T=0.4813457484199005, s=51.87861540862928\n", + "sigma=4096.0: failed after 99999 iterations with\n", + "E=0.48239510709524136, T=0.48239510709524136, s=103.98345045590045\n", + "sigma=8192.0: failed after 99999 iterations with\n", + "E=0.48288654803214515, T=0.48288654803214515, s=208.17878955154384\n", + "sigma=16384.0: failed after 99999 iterations with\n", + "E=0.4831239913608507, T=0.4831239913608507, s=416.5623302345357\n", + "sigma=32768.0: failed after 99999 iterations with\n", + "E=0.4832406474709451, T=0.4832406474709451, s=833.3258492804173\n", + "sigma=65536.0: failed after 99999 iterations with\n", + "E=0.48329845958357714, T=0.48329845958357714, s=1666.8511077510166\n", + "sigma=131072.0: failed after 99999 iterations with\n", + "E=0.48332723670880345, T=0.48332723670880345, s=3333.900735257699\n", + "sigma=262144.0: failed after 99999 iterations with\n", + "E=0.4833415930453797, T=0.4833415930453797, s=6667.999545646739\n", + "sigma=524288.0: failed after 99999 iterations with\n", + "E=0.4833487631579967, T=0.4833487631579967, s=13336.196944135778\n", + "sigma=1048576.0: failed after 99999 iterations with\n", + "E=0.483352346200491, T=0.483352346200491, s=26672.591629975057\n" + ] + }, + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# 8.4.1\n", + "\n", + "R = 1\n", + "gamma = 1000\n", + "epsilon = .001\n", + "K = 10\n", + "KE = .1\n", + "KT = .1\n", + "\n", + "sigmas = 2 ** np.linspace(0,20,21)\n", + "Ts = np.zeros_like(sigmas)\n", + "Es = np.zeros_like(sigmas)\n", + "ss = np.zeros_like(sigmas)\n", + "\n", + "for n in range(0,21):\n", + " sigma = sigmas[n]\n", + " \n", + " if n == 0:\n", + " E = 0\n", + " T = 0\n", + " else:\n", + " E = Es[n-1]\n", + " T = Ts[n-1]\n", + " \n", + " s = sigma * T / (gamma * E + 1)\n", + "\n", + "\n", + " for i in range (int(1e5)):\n", + " Rs = R * (s / K) / (1 + (s / K))\n", + " \n", + " Enew = E + dt * (epsilon + Rs**2 / (Rs**2 + KE**2) - E)\n", + " Tnew = T + dt * (epsilon + Rs**2 / (Rs**2 + KT**2) - T)\n", + " snew = s + dt * (sigma * T - gamma * E * s - s)\n", + " \n", + " if snew < 0:\n", + " snew = 0\n", + " \n", + " if np.abs(Enew - E) < 1e-5 and np.abs(Tnew - T) < 1e-5 and np.abs(snew - s) < 1e-5:\n", + " print(f\"sigma={sigma}: found steady state after {i} iterations\")\n", + " print(f\"E={Enew}, T={Tnew}, s={snew}\")\n", + " Es[n] = Enew\n", + " Ts[n] = Tnew\n", + " ss[n] = snew\n", + " break\n", + " else:\n", + " E = Enew\n", + " T = Tnew\n", + " s = snew\n", + " \n", + " if (i == int(1e5) -1):\n", + " print(f\"sigma={sigma}: failed after {i} iterations with\")\n", + " print(f\"E={Enew}, T={Tnew}, s={snew}\")\n", + " Es[n] = Enew\n", + " Ts[n] = Tnew\n", + " ss[n] = snew\n", + " \n", + " \n", + "plt.title(\"Consumer motif\")\n", + "plt.xlabel(\"$\\sigma$\")\n", + "plt.xscale(\"log\")\n", + "plt.yscale(\"log\")\n", + "plt.plot(sigmas, Es, label=\"E\")\n", + "plt.plot(sigmas, Ts, label=\"T\")\n", + "plt.plot(sigmas, ss, label=\"s\")\n", + "plt.legend()\n", + "plt.show()\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "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": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/bionet/2-ribosome-traffic.ipynb b/bionet/2-ribosome-traffic.ipynb new file mode 100644 index 0000000..7962425 --- /dev/null +++ b/bionet/2-ribosome-traffic.ipynb @@ -0,0 +1,184 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Consider a traffic model of ribosomes on RNA. The length of the RNA is 1000 steps\n", + "\n", + "and 100 randomly assigned steps are slow-moving steps, where the speed to move is 1/10 of typical speed.\n", + "\n", + "Feed in ribosomes at one end with some frequency, say 1/2 of the time it takes to move one step. but never allowing a ribosome to occupy more than one step.\n", + "\n", + " In practice move ribosomes stochastically, with a probability of 0.5 at a typical step and 0.05 at a slow step.\n", + "\n", + "Investigate the times it takes a ribosome to reach the end with and without the rule that there can only be one ribosome at each step. \n", + "\n", + "Change the frequency of adding a new ribosome at the start site by a factor of 2 up or down.\n", + "\n", + "It is illustrative to make a space-time plot with a dot for each ribosome along the x-axis, and the y-axis representing subsequent timesteps." + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from random import random\n", + "\n", + "def decide (prob):\n", + " return True if random() <= prob else False\n", + "\n", + "ribosomes = np.zeros(1000)\n", + "is_slow_step = np.zeros(1000)\n", + "starts = np.zeros(10000)\n", + "finishes = np.zeros(10000)\n", + "\n", + "def move_ribosome(i, global_step):\n", + " if i < 999:\n", + " ribosomes[i+1] += 1\n", + " else: \n", + " finishes[global_step] += 1\n", + " ribosomes[i] -= 1\n", + "\n", + "random_indices = np.random.choice(1000, 100, replace=False)\n", + "is_slow_step[random_indices] = 1\n", + "\n", + "for step in range(0,10000):\n", + " for i in range(0,1000):\n", + " i = 1000 - i - 1\n", + " x = int(ribosomes[i])\n", + " for j in range(0, x):\n", + " if is_slow_step[i]:\n", + " if decide(.05):\n", + " move_ribosome(i, step)\n", + " else:\n", + " if decide(.5):\n", + " move_ribosome(i, step)\n", + " if decide(.5):\n", + " ribosomes[0] += 1\n", + " starts[step] += 1\n", + "\n", + "plt.title(\"Multiple ribosomes per step\")\n", + "plt.plot(np.cumsum(starts))\n", + "plt.plot(np.cumsum(finishes))\n" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from random import random\n", + "\n", + "def decide (prob):\n", + " return True if random() <= prob else False\n", + "\n", + "ribosomes = np.zeros(1000)\n", + "is_slow_step = np.zeros(1000)\n", + "starts = np.zeros(10000)\n", + "finishes = np.zeros(10000)\n", + "\n", + "def move_ribosome(i, global_step):\n", + " if i < 999:\n", + " if ribosomes[i+1] < 1:\n", + " ribosomes[i+1] += 1\n", + " ribosomes[i] -= 1\n", + " else: \n", + " finishes[global_step] += 1\n", + " ribosomes[i] -= 1\n", + "\n", + "random_indices = np.random.choice(1000, 100, replace=False)\n", + "is_slow_step[random_indices] = 1\n", + "\n", + "for step in range(0,10000):\n", + " for i in range(0,1000):\n", + " i = 1000 - i - 1\n", + " x = int(ribosomes[i])\n", + " for j in range(0, x):\n", + " if is_slow_step[i]:\n", + " if decide(.05):\n", + " move_ribosome(i, step)\n", + " else:\n", + " if decide(.5):\n", + " move_ribosome(i, step)\n", + " if decide(.5):\n", + " ribosomes[0] += 1\n", + " starts[step] += 1\n", + "\n", + "plt.title(\"Single ribosome per step\")\n", + "plt.plot(np.cumsum(starts))\n", + "plt.plot(np.cumsum(finishes))\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "venv", + "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": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/bionet/3-transcription-regulation.ipynb b/bionet/3-transcription-regulation.ipynb new file mode 100644 index 0000000..ea181c9 --- /dev/null +++ b/bionet/3-transcription-regulation.ipynb @@ -0,0 +1,169 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "from math import sqrt\n", + "\n", + "def pq (a,b,c):\n", + " return (-b + sqrt(b**2 - 4*a*c)) / 2*a" + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "-3.792751279232142\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Transcription regulation\n", + "# Question 3.2.1, 3.2.2\n", + "\n", + "dt = 0.01\n", + "t = np.linspace(0,20,int(20 / dt))\n", + "C1 = np.zeros_like(t)\n", + "C2 = np.zeros_like(t)\n", + "C3 = np.zeros_like(t)\n", + "C4 = np.zeros_like(t)\n", + "m = np.zeros_like(t)\n", + "C5 = np.zeros_like(t)\n", + "tau = 10\n", + "\n", + "R = np.where(t <= 10, .1, 10)\n", + "\n", + "C1[0] = tau / (R[0] + 1)\n", + "C2[0] = 1 / (R[0] + 1 / tau)\n", + "C3[0] = tau * R[0] / (R[0] + 1)\n", + "C4[0] = pq(10,1,-2 * tau * R[0]/(R[0] + 1))\n", + "\n", + "print((R[0] / (R[0] + 1) * 2 / (10 * C4[0] + 1) - C4[0] / tau))\n", + "\n", + "m[0] = 1 / (R[0] + 1 / tau)\n", + "C5[0] = R[0] * m[0]\n", + "\n", + "for i in range (0, int(20 / dt) -1):\n", + " C1[i+1] = C1[i] + (1 / (1 + R[i]) - C1[i] / tau) * dt\n", + " C2[i+1] = C2[i] + (1 - (R[i] + 1 / tau) * C2[i]) * dt\n", + " C3[i+1] = C3[i] + (R[i] / (R[i] + 1) - C3[i] / tau) * dt\n", + " C4[i+1] = C4[i] + (R[i] / (R[i] + 1) * 2 / (10 * C4[i] + 1) - C4[i] / tau) * dt\n", + " m[i+1] = m[i] + (1 - m[i] / tau - R[i] * m[i]) * dt\n", + " C5[i+1] = C5[i] + (R[i] * m[i] - C5[i] ) * dt\n", + "\n", + "\n", + "plt.title(\"R increases by factor 100\")\n", + "plt.plot(t, C1, label=\"transcriptional repression\")\n", + "plt.plot(t, C2, label=\"protein degradation\")\n", + "plt.plot(t, C3, label=\"transcriptional activation\")\n", + "#plt.plot(t, C4, label=\"self repression\")\n", + "plt.plot(t, C5, label=\"activated reservoir\")\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 50, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# sRNA regulation\n", + "# Questions 3.3.1, 3.3.2, 3.3.3, 3.3.4\n", + "\n", + "dt = 0.01\n", + "t = np.linspace(0,20,int(20 / dt))\n", + "\n", + "m = np.zeros_like(t)\n", + "s = np.zeros_like(t)\n", + "tau = 1\n", + "\n", + "gamma = 10\n", + "alpha = np.where(t <= 10, .1, 4)\n", + "\n", + "\n", + "m[0] = pq(- gamma / tau, (gamma - alpha[0] * gamma - 1 / tau), 1)\n", + "s[0] = alpha[0] / (1 + gamma * m[0])\n", + "\n", + "\n", + "for i in range (0, int(20 / dt) -1):\n", + " m[i+1] = m[i] + (1 - gamma * alpha[i] * s[i] - m[i] / tau) * dt\n", + " s[i+1] = s[i] + (alpha[i] - gamma * alpha[i] * s[i] - s[i]) * dt\n", + "\n", + "plt.plot(t, m)\n", + "plt.plot(t, s)\n", + "\n", + "# FIXME\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "venv", + "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": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/bionet/4-phage-statmech.ipynb b/bionet/4-phage-statmech.ipynb new file mode 100644 index 0000000..74579b1 --- /dev/null +++ b/bionet/4-phage-statmech.ipynb @@ -0,0 +1,121 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "from math import exp" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'\\nK = exp(-11.1 / .62)\\nC1 = 1/16 * (2 * K - 8 * C1 - np.sqrt(K * (K - 8*C1)))\\n\\nZtot = Z(0,0,0) + Z(1,0,0) + Z(0,1,0) + Z(0,0,1) + Z(1,1,0) + Z(0,1,1) + Z(1,1,1)\\nPR = (Z(0,0,0) + Z(0,0,1)) / Ztot\\nPRM = (Z(0,0,0) + Z(1,0,0) + 9 * (Z(0,1,0) + Z(1,1,0))) / Ztot \\n\\nplt.xlabel(\"C1 concentration\")\\nplt.ylabel(\"Activity\")\\nplt.yscale(\"log\")\\nplt.plot(C1, PR, label=\"PR -> Cro\")\\nplt.plot(C1, PRM, label=\"PRM -> C1\")\\nplt.legend()\\n\\n'" + ] + }, + "execution_count": 36, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Question 4.1.1\n", + "# only dimers\n", + "\n", + "C1 = np.logspace(1,5)\n", + "\n", + "def Z (or1, or2, or3):\n", + " G = 0\n", + " \n", + " if not or1 and not or2 and not or3:\n", + " return 1\n", + "\n", + " if or1:\n", + " G += 12.8\n", + " if or2:\n", + " G += 11.0\n", + " if or3:\n", + " G += 9.7\n", + " \n", + " if or1 and or2 and or3:\n", + " G += 3.3 + 2.6\n", + " elif or1 and or2:\n", + " G += 2.6\n", + " elif or2 and or3:\n", + " G += 3.3\n", + " \n", + " return C1**(or1 + or2 + or3) * exp(G / 0.62)\n", + "\n", + "\n", + "Ztot = Z(0,0,0) + Z(1,0,0) + Z(0,1,0) + Z(0,0,1) + Z(1,1,0) + Z(0,1,1) + Z(1,1,1)\n", + "PR = (Z(0,0,0) + Z(0,0,1)) / Ztot\n", + "PRM = (Z(0,0,0) + Z(1,0,0) + 9 * (Z(0,1,0) + Z(1,1,0))) / Ztot \n", + "\n", + "plt.xlabel(\"C1 concentration\")\n", + "plt.ylabel(\"Activity\")\n", + "plt.xscale(\"log\")\n", + "plt.plot(C1, PR, label=\"PR -> Cro\")\n", + "plt.plot(C1, PRM, label=\"PRM -> C1\")\n", + "plt.legend()\n", + "\n", + "# --------------------\n", + "\"\"\"\n", + "K = exp(-11.1 / .62)\n", + "C1 = 1/16 * (2 * K - 8 * C1 - np.sqrt(K * (K - 8*C1)))\n", + "\n", + "Ztot = Z(0,0,0) + Z(1,0,0) + Z(0,1,0) + Z(0,0,1) + Z(1,1,0) + Z(0,1,1) + Z(1,1,1)\n", + "PR = (Z(0,0,0) + Z(0,0,1)) / Ztot\n", + "PRM = (Z(0,0,0) + Z(1,0,0) + 9 * (Z(0,1,0) + Z(1,1,0))) / Ztot \n", + "\n", + "plt.xlabel(\"C1 concentration\")\n", + "plt.ylabel(\"Activity\")\n", + "plt.yscale(\"log\")\n", + "plt.plot(C1, PR, label=\"PR -> Cro\")\n", + "plt.plot(C1, PRM, label=\"PRM -> C1\")\n", + "plt.legend()\n", + "\n", + "\"\"\"\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "venv", + "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": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/bionet/5-lattice-polymer.ipynb b/bionet/5-lattice-polymer.ipynb new file mode 100644 index 0000000..6f370dc --- /dev/null +++ b/bionet/5-lattice-polymer.ipynb @@ -0,0 +1,453 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "from random import random\n", + "\n", + "def choose012 ():\n", + " rand = random()\n", + " if rand <= 1/3:\n", + " return 0\n", + " elif rand <= 2/3:\n", + " return 1\n", + " else:\n", + " return 2\n", + "\n", + "def choosedir ():\n", + " return 1 if random() <= .5 else -1\n" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.41\n" + ] + } + ], + "source": [ + "# Question 4.5.5\n", + "# No self interaction\n", + "\n", + "M = int(1e4)\n", + "N = 20\n", + "\n", + "back_at_origin = 0\n", + "\n", + "for m in range(0,M):\n", + " current = np.zeros(3) \n", + "\n", + " for n in range(0,N):\n", + " current[choose012()] += choosedir()\n", + " \n", + " if not np.all(current):\n", + " back_at_origin += 1\n", + "\n", + "print(round(back_at_origin / M,2))" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "-1\n", + "[array([0., 0., 0.]), array([0., 0., 1.])]\n", + "1\n", + "[array([0., 0., 0.]), array([-2., -6., -3.])]\n", + "[array([0., 0., 0.]), array([ 0., -1., 0.])]\n", + "1\n", + "[array([0., 0., 0.]), array([ 2., 8., -7.])]\n", + "[array([0., 0., 0.]), array([1., 0., 0.])]\n", + "1\n", + "[array([0., 0., 0.]), array([7., 2., 0.])]\n", + "[array([0., 0., 0.]), array([1., 0., 0.])]\n", + "1\n", + "[array([0., 0., 0.]), array([2., 3., 4.])]\n", + "[array([0., 0., 0.]), array([1., 0., 0.])]\n", + "1\n", + "[array([0., 0., 0.]), array([-2., 0., 7.])]\n", + "[array([0., 0., 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6.])]\n", + "[array([0., 0., 0.]), array([ 0., -1., 0.])]\n", + "1\n", + "[array([0., 0., 0.]), array([-4., -4., -1.])]\n", + "[array([0., 0., 0.]), array([ 0., -1., 0.])]\n", + "1\n", + "[array([0., 0., 0.]), array([1., 0., 8.])]\n", + "[array([0., 0., 0.]), array([-1., 0., 0.])]\n", + "1\n", + "[array([0., 0., 0.]), array([-3., 6., 0.])]\n", + "[array([0., 0., 0.]), array([0., 1., 0.])]\n", + "1\n", + "[array([0., 0., 0.]), array([-2., -7., -6.])]\n", + "[array([0., 0., 0.]), array([0., 0., 1.])]\n", + "1\n", + "[array([0., 0., 0.]), array([ 0., -9., 10.])]\n", + "[array([0., 0., 0.]), array([1., 0., 0.])]\n", + "1\n", + "[array([0., 0., 0.]), array([-4., 1., 4.])]\n", + "0.0\n", + "1.0\n" + ] + } + ], + "source": [ + "# With self interaction\n", + "\n", + "M = int(1e2)\n", + "N = 12\n", + "\n", + "back_at_origin = 0\n", + "aborted = 0\n", + "\n", + "\n", + "def simulate_walk (): \n", + " current = np.zeros(3) \n", + " walk = [np.zeros(3)]\n", + "\n", + " for n in range(0,N-1):\n", + " newcurrent = current\n", + " max_attempts = 100\n", + " attempts = 0\n", + "\n", + " while np.any([np.array_equal(newcurrent, arr) for arr in walk]):\n", + " attempts += 1\n", + " if attempts > max_attempts:\n", + " print(n)\n", + " print(walk)\n", + " return False\n", + " newcurrent = current\n", + " newcurrent[choose012()] += choosedir()\n", + " \n", + " current = newcurrent\n", + " walk.append(current) \n", + " print(walk) \n", + " \n", + " current[choose012()] += choosedir()\n", + " walk.append(current)\n", + "\n", + " return current\n", + " \n", + "\n", + "\n", + "for m in range(0,M):\n", + " walked = simulate_walk()\n", + " if walked and not np.all(walked):\n", + " back_at_origin += 1\n", + " elif not walked:\n", + " aborted += 1\n", + "\n", + "print(back_at_origin / M)\n", + "print(aborted / M)\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "venv", + "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": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/bionet/6-promoter-interference.ipynb b/bionet/6-promoter-interference.ipynb new file mode 100644 index 0000000..288300d --- /dev/null +++ b/bionet/6-promoter-interference.ipynb @@ -0,0 +1,119 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "from random import random\n", + "import matplotlib.pyplot as plt\n", + "from matplotlib.animation import FuncAnimation\n", + "\n", + "def decide (prob):\n", + " return 1 if random() <= prob else 0\n" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "pS activity: 0.016666666666666666\n", + "pA activity: 0.06666666666666667\n" + ] + } + ], + "source": [ + "# Question 5.3.5\n", + "\n", + "L = 100\n", + "dt = .01\n", + "T = 60\n", + "\n", + "pA_rate = .1\n", + "pS_rate = .05\n", + "\n", + "pA = np.zeros(L)\n", + "pS = np.zeros(L)\n", + "\n", + "pS_counts = 0\n", + "pA_counts = 0\n", + "\n", + "\n", + "def check_collisions ():\n", + " collisions = np.where((pA == 1) & (pS == 1))\n", + " pA[collisions] = 0\n", + " pS[collisions] = 0\n", + "\n", + "\n", + " \n", + "for n in range(0,int(T / dt)):\n", + " if pA[0] == 0:\n", + " pA[0] = decide(dt * pA_rate)\n", + "\n", + " if pS[L-1] == 0:\n", + " pS[L-1] = decide(dt * pS_rate)\n", + "\n", + "\n", + " if pA[L-1] == 1 and decide(.4):\n", + " pA[L-1] = 0\n", + " pA_counts += 1\n", + " \n", + " if pS[0] == 1 and decide(.4):\n", + " pS[0] = 0\n", + " pS_counts += 1\n", + "\n", + " for i in range(1,L):\n", + " if pA[L-1-i] == 1 and decide(.4) and pA[L-i] == 0:\n", + " pA[L-1-i] = 0\n", + " pA[L-i] = 1\n", + " check_collisions()\n", + " \n", + " if pS[i] == 1 and decide(.4) and pS[i-1] == 0:\n", + " pS[i-1] = 1\n", + " pS[i] = 0\n", + " check_collisions()\n", + "\n", + "\n", + "print(f\"pS activity: {pS_counts / T}\")\n", + "print(f\"pA activity: {pA_counts / T}\")\n", + " \n", + " " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "venv", + "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": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/bionet/7-gillespie.ipynb b/bionet/7-gillespie.ipynb new file mode 100644 index 0000000..21ae3bc --- /dev/null +++ b/bionet/7-gillespie.ipynb @@ -0,0 +1,261 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "from random import random" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# 6.1.3 \n", + "\n", + "M = 0\n", + "P = 0\n", + "steps = 1000\n", + "\n", + "Omega = .02\n", + "omega = .1\n", + "gamma_m = .01\n", + "gamma_p = .002\n", + "\n", + "P_history = np.zeros(steps)\n", + "M_history = np.zeros(steps)\n", + "time = np.zeros(steps)\n", + "\n", + "\n", + "for n in range(0,steps):\n", + "\n", + " t = np.zeros(4)\n", + " t[0] = - 1 / Omega * np.log(random())\n", + " \n", + " if M > 0:\n", + " t[1] = - 1 / (omega * M) * np.log(random())\n", + " t[2] = - 1 / (gamma_m * M) * np.log(random())\n", + " else:\n", + " t[1] = np.inf\n", + " t[2] = np.inf\n", + " \n", + " if P > 0:\n", + " t[3] = - 1 / (gamma_p * P) * np.log(random())\n", + " else:\n", + " t[3] = np.inf\n", + "\n", + "\n", + " min = np.argmin(t)\n", + "\n", + " if min == 0:\n", + " M += 1 \n", + " elif min == 1:\n", + " P += 1\n", + " elif min == 2:\n", + " M -= 1\n", + " elif min == 3:\n", + " P -= 1\n", + "\n", + " if n == 0:\n", + " time[n] = 0\n", + " else:\n", + " time[n] = time[n-1] + t[min]\n", + " P_history[n] = P\n", + " M_history[n] = M\n", + "\n", + "\n", + "plt.title(\"Protein and mRNA production / decay\")\n", + "plt.plot(time, M_history, label=\"mRNA\")\n", + "plt.plot(time, P_history, label=\"proteins\")\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# 6.1.4\n", + "\n", + "u = 0\n", + "v = 0\n", + "steps = 10000\n", + "\n", + "a = 10\n", + "b = 10\n", + "\n", + "u_history = np.zeros(steps)\n", + "v_history = np.zeros(steps)\n", + "time = np.zeros(steps)\n", + "\n", + "\n", + "for n in range(0,steps):\n", + "\n", + " t = np.zeros(4)\n", + " t[0] = - 1 / (a / (1 + v**2)) * np.log(random())\n", + " t[1] = - 1 / (b / (1 + u**2)) * np.log(random())\n", + " if u > 0:\n", + " t[2] = - 1 / (u) * np.log(random())\n", + " else:\n", + " t[2] = np.inf\n", + " if v > 0:\n", + " t[3] = - 1 / (v) * np.log(random())\n", + " else:\n", + " t[3] = np.inf\n", + "\n", + " min = np.argmin(t)\n", + "\n", + " if min == 0:\n", + " u += 1 \n", + " elif min == 1:\n", + " v += 1\n", + " elif min == 2:\n", + " u -= 1\n", + " elif min == 3:\n", + " v -= 1\n", + " \n", + " if n == 0:\n", + " time[n] = 0\n", + " else:\n", + " time[n] = time[n-1] + t[min]\n", + " u_history[n] = u\n", + " v_history[n] = v\n", + "\n", + "\n", + "plt.title(\"Toggle switch\")\n", + "plt.plot(time, u_history, label=\"u\")\n", + "plt.plot(time, v_history, label=\"v\")\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# 6.2.2\n", + "\n", + "C1 = 0\n", + "Cro = 0\n", + "steps = 100000\n", + "\n", + "delta_prod = .1\n", + "delta_decay = .01\n", + "\n", + "time = np.zeros(steps)\n", + "C1_history = np.zeros(steps)\n", + "Cro_history = np.zeros(steps)\n", + "\n", + "for n in range(0,steps):\n", + "\n", + " t = np.zeros(4)\n", + " t[0] = - 1 / ( (.1 + (C1 / .2)**2) / (delta_prod * (1 + (C1 / .2)**2)*(1 + (Cro / .5)**2)) ) * np.log(random())\n", + " t[1] = - 1 / ( 1 / (delta_prod * (1 + (C1 / .2)**2))) * np.log(random())\n", + " if C1 > 0:\n", + " t[2] = - 1 / (C1 / delta_decay) * np.log(random())\n", + " else:\n", + " t[2] = np.inf\n", + " if Cro > 0:\n", + " t[3] = - 1 / (Cro / delta_decay) * np.log(random())\n", + " else:\n", + " t[3] = np.inf\n", + "\n", + " min = np.argmin(t)\n", + "\n", + " if min == 0:\n", + " C1 += delta_prod \n", + " elif min == 1:\n", + " Cro += delta_prod\n", + " elif min == 2:\n", + " C1 -= delta_decay \n", + " elif min == 3:\n", + " Cro -= delta_decay \n", + " \n", + " if n == 0:\n", + " time[n] = 0\n", + " else:\n", + " time[n] = time[n-1] + t[min]\n", + " C1_history[n] = C1\n", + " Cro_history[n] = Cro\n", + "\n", + "\n", + "plt.title(\"CI and Cro\")\n", + "plt.plot(time, C1_history, label=\"CI\")\n", + "plt.plot(time, Cro_history, label=\"Cro\")\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "venv", + "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": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/bionet/8-nucleosomes.ipynb b/bionet/8-nucleosomes.ipynb new file mode 100644 index 0000000..03ad8ee --- /dev/null +++ b/bionet/8-nucleosomes.ipynb @@ -0,0 +1,293 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from random import random\n", + "\n", + "L = 60\n", + "\n", + "def rand_i ():\n", + " return int(random() * L)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Start with simulating the basic 3-state nucleosome model for a system with N=60 nucleosomes.\n", + "\n", + "Then do variants Q7.2.1, Q7.2.2.\n", + "\n", + "First where U-->M and U-->A local (only acting on nearest neighbors), whereas recruitments A--> U and M-->U are global (act randomly in entire system). This local-global model variant needs two parameters:\n", + "the parameter alpha for how often one chose recruitment (should be around 90 for random conversions), and a parameter beta=0.5 for the probability that a given recruitment attempt should be global. When attempting a global attempt, select one recruiting nucleosome and another that it acts on anywhere in the system. The move can only be performed if the two chosen nuleosomes are of type M and A, or A and M. Similarly a local move involves selection of two neighbor nucleosomes where the nucleosome to be changed have to start in U state. Use again an L=60 system" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "steps = 100000\n", + "alpha = .9\n", + "\n", + "nuc = np.zeros(L)\n", + "nucs_A = np.zeros(steps)\n", + "nucs_M = np.zeros(steps)\n", + "\n", + "for n in range(steps):\n", + " i = rand_i()\n", + "\n", + " if (random() <= alpha):\n", + " # Recruited conversion\n", + " j = i\n", + " while j == i:\n", + " j = rand_i()\n", + " \n", + " nuc[i] += nuc[j]\n", + " \n", + " else:\n", + " # Noisy change\n", + " if nuc[i] == 0:\n", + " if random() < 0.5:\n", + " nuc[i] = 1\n", + " else:\n", + " nuc[i] = -1\n", + " else:\n", + " nuc[i] = 0\n", + " \n", + " if nuc[i]:\n", + " nuc[i] = nuc[i] / np.abs(nuc[i])\n", + " \n", + " nucs_A[n] = np.count_nonzero(nuc == -1)\n", + " nucs_M[n] = np.count_nonzero(nuc == 1)\n", + "\n", + "\n", + "plt.title(\"Global\")\n", + "plt.plot(nucs_A, label=\"A\")\n", + "plt.plot(nucs_M, label=\"M\")\n", + "plt.legend()\n", + "plt.show()\n", + "\n", + "\n", + " \n", + " \n" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "steps = 100000\n", + "alpha = .9\n", + "beta = .5\n", + "\n", + "nuc = np.zeros(L)\n", + "nucs_A = np.zeros(steps)\n", + "nucs_M = np.zeros(steps)\n", + "\n", + "for n in range(steps):\n", + " i = rand_i()\n", + "\n", + " if random() <= alpha:\n", + " # Recruited conversion\n", + "\n", + " if random() <= beta:\n", + " # global\n", + " j = i\n", + " while j == i:\n", + " j = rand_i()\n", + " \n", + " # only A->U, M->U\n", + " if nuc[i] + nuc[j] == 0:\n", + " nuc[i] = 0\n", + " else:\n", + " # local\n", + " if i == 0:\n", + " j = 1\n", + " elif i == L-1:\n", + " j = L-2\n", + " elif random() < .5:\n", + " j = i+1\n", + " else:\n", + " j = i-1\n", + "\n", + " # only U->A, U->M\n", + " if np.abs(nuc[i] + nuc[j]) == 1:\n", + " nuc[i] += nuc[j]\n", + "\n", + " \n", + " else:\n", + " # Noisy change\n", + " if nuc[i] == 0:\n", + " if random() < 0.5:\n", + " nuc[i] = 1\n", + " else:\n", + " nuc[i] = -1\n", + " else:\n", + " nuc[i] = 0\n", + " \n", + " if nuc[i]:\n", + " nuc[i] = nuc[i] / np.abs(nuc[i])\n", + " \n", + " nucs_A[n] = np.count_nonzero(nuc == -1)\n", + " nucs_M[n] = np.count_nonzero(nuc == 1)\n", + "\n", + "\n", + "plt.title(\"A->U, M->U global and U->A, U->M local\")\n", + "plt.plot(nucs_A, label=\"A\")\n", + "plt.plot(nucs_M, label=\"M\")\n", + "plt.legend()\n", + "plt.show()\n", + "\n", + "\n", + " \n", + " \n" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "steps = 100000\n", + "alpha = .9\n", + "beta = .5\n", + "\n", + "nuc = np.zeros(L)\n", + "nucs_A = np.zeros(steps)\n", + "nucs_M = np.zeros(steps)\n", + "\n", + "for n in range(steps):\n", + " i = rand_i()\n", + "\n", + " if random() <= alpha:\n", + " # Recruited conversion\n", + "\n", + " if random() <= beta:\n", + " # global\n", + " j = i\n", + " while j == i:\n", + " j = rand_i()\n", + " \n", + " # only U->A, U->M\n", + " if np.abs(nuc[i] + nuc[j]) == 1:\n", + " nuc[i] += nuc[j]\n", + " \n", + " \n", + " else:\n", + " # local\n", + " if i == 0:\n", + " j = 1\n", + " elif i == L-1:\n", + " j = L-2\n", + " elif random() < .5:\n", + " j = i+1\n", + " else:\n", + " j = i-1\n", + " \n", + " # only A->U, M->U\n", + " if nuc[i] + nuc[j] == 0:\n", + " nuc[i] = 0\n", + "\n", + " \n", + " else:\n", + " # Noisy change\n", + " if nuc[i] == 0:\n", + " if random() < 0.5:\n", + " nuc[i] = 1\n", + " else:\n", + " nuc[i] = -1\n", + " else:\n", + " nuc[i] = 0\n", + " \n", + " if nuc[i]:\n", + " nuc[i] = nuc[i] / np.abs(nuc[i])\n", + " \n", + " nucs_A[n] = np.count_nonzero(nuc == -1)\n", + " nucs_M[n] = np.count_nonzero(nuc == 1)\n", + "\n", + "\n", + "plt.title(\"U->A, U->M global and A->U, M->U local\")\n", + "plt.plot(nucs_A, label=\"A\")\n", + "plt.plot(nucs_M, label=\"M\")\n", + "plt.legend()\n", + "plt.show()\n", + "\n", + "\n", + " \n", + " \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "venv", + "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": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/bionet/combined-feedback-plots/highS_R.png b/bionet/combined-feedback-plots/highS_R.png new file mode 100644 index 0000000..dc7a221 Binary files /dev/null and b/bionet/combined-feedback-plots/highS_R.png differ diff --git a/bionet/combined-feedback-plots/highS_T.png b/bionet/combined-feedback-plots/highS_T.png new file mode 100644 index 0000000..d8d7e8d Binary files /dev/null and b/bionet/combined-feedback-plots/highS_T.png differ diff --git a/bionet/combined-feedback-plots/hightau_R.png b/bionet/combined-feedback-plots/hightau_R.png new file mode 100644 index 0000000..df8e7f0 Binary files /dev/null and b/bionet/combined-feedback-plots/hightau_R.png differ diff --git a/bionet/combined-feedback-plots/hightau_T.png b/bionet/combined-feedback-plots/hightau_T.png new file mode 100644 index 0000000..ee6f4e9 Binary files /dev/null and b/bionet/combined-feedback-plots/hightau_T.png differ diff --git a/bionet/combined-feedback-plots/normal_R.png b/bionet/combined-feedback-plots/normal_R.png new file mode 100644 index 0000000..cf86db7 Binary files /dev/null and b/bionet/combined-feedback-plots/normal_R.png differ diff --git a/bionet/combined-feedback-plots/normal_T.png b/bionet/combined-feedback-plots/normal_T.png new file mode 100644 index 0000000..3d3e3c3 Binary files /dev/null and b/bionet/combined-feedback-plots/normal_T.png differ