{ "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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", 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" ] }, "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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", 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" ] }, "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 }