TD6_biochemical_programming.ipynb 286 KB
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1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424 1425 1426 1427 1428 1429 1430 1431 { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# TD6 Biochemical Programming\n", "\n", "* CRN synthesis from\n", " * GPAC circuits\n", " * PIVP definitions of function of time\n", " * PIVP definition of function of input variable\n", "* Trigonometric functions\n", "* Sigmoid functions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# GPAC generating cosine(t)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "compile_wgpac(y::integral integral-1*y)." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "present(y,1)." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "fast*[x2]*[y]for _=[x2+y]=>x1.\r\n", "fast*[x1]for x1=>_.\r\n", "_=[x1]=>x0.\r\n", "_=[x0]=>y.\r\n", "present(x2,-1).\r\n", "present(y,1).\r\n", "parameter(\r\n", " fast = 1000\r\n", ").\r\n" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "list_model." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "\\begin{align*}\n", "y_0 &= 1\\\\\n", "x0_0 &= 0\\\\\n", "x1_0 &= 0\\\\\n", "x2_0 &= -1\\\\\n", "fast &= 1000\\\\\n", "\\frac{dy}{dt} &= x0\\\\\n", "\\frac{dx0}{dt} &= x1\\\\\n", "\\frac{dx1}{dt} &= fast*[x2]*[y]-fast*[x1]\\\\\n", "\\frac{dx2}{dt} &= 0\\\\\n", "\\end{align*}\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "list_ode." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "numerical_simulation." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "application/javascript": [ "\n", "(function(root) {\n", " function now() {\n", " return new Date();\n", " }\n", "\n", " var force = true;\n", "\n", " if (typeof 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"\\begin{align*}\n", "f_p_0 &= 1\\\\\n", "f_m_0 &= 0\\\\\n", "z2_p_0 &= 0\\\\\n", "z2_m_0 &= 0\\\\\n", "fast &= 1000\\\\\n", "\\frac{df_p}{dt} &= z2_p-fast*f_m*f_p\\\\\n", "\\frac{df_m}{dt} &= z2_m-fast*f_m*f_p\\\\\n", "\\frac{dz2_p}{dt} &= f_m-fast*z2_m*z2_p\\\\\n", "\\frac{dz2_m}{dt} &= f_p-fast*z2_m*z2_p\\\\\n", "\\end{align*}\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "list_ode." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "numerical_simulation." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
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y_m+y_p=>_.\r\n", "present(y_p,1).\r\n", "present(x_p,4).\r\n", "parameter(\r\n", " fast = 1000\r\n", ").\r\n" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "list_model." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "\\begin{align*}\n", "y_p_0 &= 1\\\\\n", "y_m_0 &= 0\\\\\n", "z2_p_0 &= 0\\\\\n", "z2_m_0 &= 0\\\\\n", "x_p_0 &= 4\\\\\n", "x_m_0 &= 0\\\\\n", "fast &= 1000\\\\\n", "\\frac{dy_p}{dt} &= z2_m*x_m+z2_p*x_p-fast*y_m*y_p\\\\\n", "\\frac{dy_m}{dt} &= z2_m*x_p+z2_p*x_m-fast*y_m*y_p\\\\\n", "\\frac{dz2_p}{dt} &= y_p*x_m+y_m*x_p-fast*z2_m*z2_p\\\\\n", "\\frac{dz2_m}{dt} &= y_m*x_m+y_p*x_p-fast*z2_m*z2_p\\\\\n", "\\frac{dx_p}{dt} &= x_m-fast*x_m*x_p\\\\\n", "\\frac{dx_m}{dt} &= x_p-fast*x_m*x_p\\\\\n", "\\end{align*}\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "list_ode." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "numerical_simulation." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
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Application\",\"version\":\"0.12.14\"}};\n", " var render_items = [{\"docid\":\"028500a4-68d0-4575-9b45-e89bce6de76c\",\"elementid\":\"e74800ad-ad0f-4ccc-abf2-fb69ffa2ec04\",\"modelid\":\"d1950695-365b-4a69-8996-550ca79098e5\",\"notebook_comms_target\":\"00563e43-9746-4736-8394-3f795fb39426\"}];\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": "d1950695-365b-4a69-8996-550ca79098e5" } }, "output_type": "display_data" } ], "source": [ "plot." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Sigmoid functions" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [], "source": [ "clear_model." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Logistic function 1/(1+e^-t)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "S => 2*S." ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [], "source": [ "S =[S]=> _." ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [], "source": [ "present(S,0.5)." ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "\\begin{align*}\n", "S_0 &= 0.5\\\\\n", "\\frac{dS}{dt} &= S-S^2\\\\\n", "\\end{align*}\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "list_ode." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Hyperbolic tangent" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [], "source": [ "_ => HT." ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [], "source": [ "2*HT => HT." ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "\\begin{align*}\n", "HT_0 &= 0\\\\\n", "S_0 &= 0.5\\\\\n", "\\frac{dHT}{dt} &= 1-HT^2\\\\\n", "\\frac{dS}{dt} &= S-S^2\\\\\n", "\\end{align*}\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "list_ode." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Arc tangent" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [], "source": [ "_ => T." ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [], "source": [ "1/(1+T^2) for /T => AT." ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "\\begin{align*}\n", "AT_0 &= 0\\\\\n", "/T_0 &= 0\\\\\n", "T_0 &= 0\\\\\n", "HT_0 &= 0\\\\\n", "S_0 &= 0.5\\\\\n", "\\frac{dAT}{dt} &= 1/(1+T^2)\\\\\n", "\\frac{d/T}{dt} &= - (1/(1+T^2))\\\\\n", "\\frac{dT}{dt} &= 1\\\\\n", "\\frac{dHT}{dt} &= 1-HT^2\\\\\n", "\\frac{dS}{dt} &= S-S^2\\\\\n", "\\end{align*}\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "list_ode." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Hill function degree 1" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [], "source": [ "MA(1) for NH1 =[NH1]=> _." ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [], "source": [ "MA(1) for _ =[2*NH1]=> H1." ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [], "source": [ "present(NH1,1)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Hill function degree 2" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [], "source": [ "MA(2) for NH2 =[T+NH2]=> _." ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [], "source": [ "MA(2) for _ =[T+2*NH2]=> H2." ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [], "source": [ "present(NH2,1)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Hill function degree 5" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [], "source": [ "MA(5) for NH5 =[4*T+NH5]=> _." ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [], "source": [ "MA(5) for _ =[4*T+2*NH5]=> H5." ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [], "source": [ "present(NH5,1)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Hill function degree n\n", " Hn=t^n/(k+t^n)\n", "\n", " MA(n) for NHn =[(n-1)*t+NHn]=> _.\n", "\n", " MA(n*k) for _ =[(n-1)*t+2*NHn]=> Hn.\n", "\n", " present(NHn,1/k)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Simulations" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "_=[S]=>S.\r\n", "S=[S]=>_.\r\n", "_=>HT.\r\n", "HT=[HT]=>_.\r\n", "_=>T.\r\n", "1/(1+T^2)for/T=>AT.\r\n", "NH1=[NH1]=>_.\r\n", "_=[2*NH1]=>H1.\r\n", "MA(2)for NH2=[T+NH2]=>_.\r\n", "MA(2)for _=[T+2*NH2]=>H2.\r\n", "MA(5)for NH5=[4*T+NH5]=>_.\r\n", "MA(5)for _=[4*T+2*NH5]=>H5.\r\n", "present(S,0.5).\r\n", "present(NH1,1).\r\n", "present(NH2,1).\r\n", "present(NH5,1).\r\n" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" } ], "source": [ "list_model." ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "\\begin{align*}\n", "H5_0 &= 0\\\\\n", "NH5_0 &= 1\\\\\n", "H2_0 &= 0\\\\\n", "NH2_0 &= 1\\\\\n", "H1_0 &= 0\\\\\n", "NH1_0 &= 1\\\\\n", "AT_0 &= 0\\\\\n", "/T_0 &= 0\\\\\n", "T_0 &= 0\\\\\n", "HT_0 &= 0\\\\\n", "S_0 &= 0.5\\\\\n", "\\frac{dH5}{dt} &= 5*T^4*NH5^2\\\\\n", "\\frac{dNH5}{dt} &= - (5*T^4*NH5^2)\\\\\n", "\\frac{dH2}{dt} &= 2*T*NH2^2\\\\\n", "\\frac{dNH2}{dt} &= - (2*T*NH2^2)\\\\\n", "\\frac{dH1}{dt} &= NH1^2\\\\\n", "\\frac{dNH1}{dt} &= -NH1^2\\\\\n", "\\frac{dAT}{dt} &= 1/(1+T^2)\\\\\n", "\\frac{d/T}{dt} &= - (1/(1+T^2))\\\\\n", "\\frac{dT}{dt} &= 1\\\\\n", "\\frac{dHT}{dt} &= 1-HT^2\\\\\n", "\\frac{dS}{dt} &= S-S^2\\\\\n", "\\end{align*}\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "list_ode." ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [], "source": [ "numerical_simulation." ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
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