{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Loopless FBA\n", "\n", "The goal of this procedure is identification of a thermodynamically consistent flux state without loops, as implied by the name.\n", "\n", "Usually, the model has the following constraints.\n", "$$ S \\cdot v = 0 $$\n", "$$ lb \\le v \\le ub $$\n", "\n", "However, this will allow for thermodynamically infeasible loops (referred to as type 3 loops) to occur, where flux flows around a cycle without any net change of metabolites. For most cases, this is not a major issue, as solutions with these loops can usually be converted to equivalent solutions without them. However, if a flux state is desired which does not exhibit any of these loops, loopless FBA can be used. The formulation used here is modified from [Schellenberger et al.](http://dx.doi.org/10.1016/j.bpj.2010.12.3707)\n", "\n", "We can make the model irreversible, so that all reactions will satisfy\n", "$$ 0 \\le lb \\le v \\le ub \\le \\max(ub) $$\n", "\n", "We will add in boolean indicators as well, such that\n", "$$ \\max(ub) \\cdot i \\ge v $$\n", "$$ i \\in \\{0, 1\\} $$\n", "\n", "We also want to ensure that an entry in the row space of S also exists with negative values wherever v is nonzero. In this expression, $1-i$ acts as a not to indicate inactivity of a reaction.\n", "\n", "$$ S^\\mathsf T x - (1 - i) (\\max(ub) + 1) \\le -1 $$\n", "\n", "We will construct an LP integrating both constraints.\n", "\n", "$$ \\left(\n", "\\begin{matrix}\n", "S & 0 & 0\\\\\n", "-I & \\max(ub)I & 0 \\\\\n", "0 & (\\max(ub) + 1)I & S^\\mathsf T\n", "\\end{matrix}\n", "\\right)\n", "\\cdot\n", "\\left(\n", "\\begin{matrix}\n", "v \\\\\n", "i \\\\\n", "x\n", "\\end{matrix}\n", "\\right)\n", "\\begin{matrix}\n", "&=& 0 \\\\\n", "&\\ge& 0 \\\\\n", "&\\le& \\max(ub)\n", "\\end{matrix}$$\n", "\n", "Note that these extra constraints are not applied to boundary reactions which bring metabolites in and out of the system." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "%matplotlib inline\n", "import plot_helper\n", "\n", "import cobra.test\n", "from cobra import Reaction, Metabolite, Model\n", "from cobra.flux_analysis.loopless import construct_loopless_model\n", "from cobra.flux_analysis import optimize_minimal_flux\n", "from cobra.solvers import get_solver_name" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will demonstrate with a toy model which has a simple loop cycling A -> B -> C -> A, with A allowed to enter the system and C allowed to leave. A graphical view of the system is drawn below:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "application/pdf": 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eg965GEtI13sw2Y1evoz3m6X4Ir4oNeP9ly/Pnb0sSHmzhReSLwMnequixmuz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\nkXCOJxn6PgNqlMA1I69WqIg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gbmZtkpxJV/PBTGral65ip9UkkB1f6VKZyGUsujWVURw1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\nekpzytYUaZNpk3mTZZN1k32Tt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n8NdA3ndYhfkLXYxWWD8uTXa3QdpStEdHuW/n5Lf7Po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\n", 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pMtCp71WzeNQuIh5LmSbpsMwcz5RyE339rvg91bsyc0VmHgdsCewLXEK5gnWs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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_helper.plot_loop()" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "test_model = Model()\n", "test_model.add_metabolites([Metabolite(i) for i in \"ABC\"])\n", "test_model.add_reactions([Reaction(i) for i in\n", " [\"EX_A\", \"DM_C\", \"v1\", \"v2\", \"v3\"]])\n", "\n", "test_model.reactions.EX_A.add_metabolites({\"A\": 1})\n", "test_model.reactions.DM_C.add_metabolites({\"C\": -1})\n", "test_model.reactions.DM_C.objective_coefficient = 1\n", "\n", "test_model.reactions.v1.add_metabolites({\"A\": -1, \"B\": 1})\n", "test_model.reactions.v2.add_metabolites({\"B\": -1, \"C\": 1})\n", "test_model.reactions.v3.add_metabolites({\"C\": -1, \"A\": 1})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "While this model contains a loop, a flux state exists which has no flux through reaction v3, and is identified by loopless FBA." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "loopless solution: status = optimal\n", "loopless solution: v3 = 0.0\n" ] } ], "source": [ "solution = construct_loopless_model(test_model).optimize()\n", "print(\"loopless solution: status = \" + solution.status)\n", "print(\"loopless solution: v3 = %.1f\" % solution.x_dict[\"v3\"])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If there there is no forced flux through a loopless reaction, parsimonious FBA will also have no flux through the loop." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "parsimonious solution: status = optimal\n", "parsimonious solution: v3 = 0.0\n" ] } ], "source": [ "solution = optimize_minimal_flux(test_model)\n", "print(\"parsimonious solution: status = \" + solution.status)\n", "print(\"parsimonious solution: v3 = %.1f\" % solution.x_dict[\"v3\"])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "However, if flux is forced through v3, then there is no longer a feasible loopless solution, but the parsimonious solution will still exist." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "loopless solution: status = infeasible\n" ] } ], "source": [ "test_model.reactions.v3.lower_bound = 1\n", "solution = construct_loopless_model(test_model).optimize()\n", "print(\"loopless solution: status = \" + solution.status)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "parsimonious solution: status = optimal\n", "parsimonious solution: v3 = 1.0\n" ] } ], "source": [ "solution = optimize_minimal_flux(test_model)\n", "print(\"parsimonious solution: status = \" + solution.status)\n", "print(\"parsimonious solution: v3 = %.1f\" % solution.x_dict[\"v3\"])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Loopless FBA is also possible on genome scale models, but it requires a capable MILP solver. If one is installed, cobrapy can detect it automatically using the get_solver_name function" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "cplex\n" ] } ], "source": [ "mip_solver = get_solver_name(mip=True)\n", "print(mip_solver)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "salmonella = cobra.test.create_test_model(\"salmonella\")\n", "construct_loopless_model(salmonella).optimize(solver=mip_solver)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ecoli = cobra.test.create_test_model(\"ecoli\")\n", "construct_loopless_model(ecoli).optimize(solver=mip_solver)" ] } ], "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": "3.4.3" } }, "nbformat": 4, "nbformat_minor": 0 }