{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "*Write your name(s) here.*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##
CS341 Project 1 (due Thursday September, 10, 2020)
\n", "\n", "## Part 1. Units and Degradation\n", "\n", "To model the degradation of protein $P1$, we use the following ODE \n", "\n", "(∗) $\\frac{d}{dt}P1(t) = -d1\\cdot P1(t)$\n", " \n", "where $P1$ has units of nM and $t$ has units of seconds (s)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\n", "(1) What units must d1 have? Show your work." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*Remove this line and use this cell for your solution.*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\n", "This is a linear differential equation, which has an analytic solution \n", "\n", "(†) $P1(t) = e^{-d1\\cdot t}\\cdot P1_0$\n", "\n", "where the initial condition is $P1(0) = P1_0$.\n", "\n", "We can confirm that it is a solution by differentiating both sides of (†):\n", "\n", "$\\frac{d}{dt}(P1(t)) = \\frac{d}{dt}(e^{-d1\\cdot t}\\cdot P1_0) $\n", "\n", "And since the $e^t$ is isn't own derivative, we have\n", "\n", "$\\frac{d}{dt}(P1(t)) = -d1\\cdot e^{-d1\\cdot t}\\cdot P1_0 $\n", "\n", "and substituting the definition of $P1(t)$\n", "\n", "$\\frac{d}{dt}(P1(t)) = -dt\\cdot P1(t)$\n", "\n", "(2) Using initial condition $P1(0) = 2 nM$ and kinetic parameter $d1=2 s^{-1}$, simulate the system from time $t=0s$ to $t=10$s with a time step of $0.01$s. (Use sciyp.integrate.solve_ivp.)\n", "\n", "Plot the simulation result along with the analytic result on the same graph. Be sure to label your axes and to supply a legend. (use matplotlib.pyplot's plot command).\n", "\n", "Next, demonstrate that the slope of the solution really is $-d1 P1(t)$ by selecting several points on the solution curve and drawing a short line with slope $-d1 P1(t)$ centered at $P1(t)$. We expect these lines to be tangent lines, if the solution is correct.\n", "\n", "Finally, add a new Markdown cell to act as a caption for the figure. It should describe the content of the figure (i.e. it should include that one line is the numerical solution to a simulation, one is the analytic solution, and that there are short lines computed using the RHS of the ODE). It should also explain any conclusions we should draw from this figure. In this case, explain why these short lines demonstrate the curve is the solution." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# Write code here" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\n", "(3) The half-life of a protein is the amount of time it takes for the concentration\n", "to halve. What is the half-life of protein P1 (in terms of d1)? Show your work." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*Remove this line and use this cell for your solution.*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\n", "(4) Demonstrate that your calculation of the half-life is correct by re-plotting the numerical solution from above and plotting a vertical line at the half-life and a horizontal line at $P1(0)/2$. Add a new Markdown cell below the figure to describe what it contains and why it shows your calculation is correct." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "# Write code here" ] }, { "attachments": { "dimerNetwork.png": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAWcAAADQCAYAAADbAKD0AAAJJmlDQ1BpY2MAAEiJlZVnUJNZF8fv8zzphUASQodQQ5EqJYCUEFoo0quoQOidUEVsiLgCK4qINEWQRQEXXJUia0UUC4uCAhZ0gywCyrpxFVFBWXDfGZ33HT+8/5l7z2/+c+bec8/5cAEgiINlwct7YlK6wNvJjhkYFMwE3yiMn5bC8fR0A9/VuxEArcR7ut/P+a4IEZFp/OW4uLxy+SmCdACg7GXWzEpPWeGjy0wPj//CZ1dYsFzgMt9Y4eh/eexLzr8s+pLj681dfhUKABwp+hsO/4b/c++KVDiC9NioyGymT3JUelaYIJKZttIJHpfL9BQkR8UmRH5T8P+V/B2lR2anr0RucsomQWx0TDrzfw41MjA0BF9n8cbrS48hRv9/z2dFX73kegDYcwAg+7564ZUAdO4CQPrRV09tua+UfAA67vAzBJn/eqiVDQ0IgALoQAYoAlWgCXSBETADlsAWOAAX4AF8QRDYAPggBiQCAcgCuWAHKABFYB84CKpALWgATaAVnAad4Dy4Aq6D2+AuGAaPgRBMgpdABN6BBQiCsBAZokEykBKkDulARhAbsoYcIDfIGwqCQqFoKAnKgHKhnVARVApVQXVQE/QLdA66At2EBqGH0Dg0A/0NfYQRmATTYQVYA9aH2TAHdoV94fVwNJwK58D58F64Aq6HT8Id8BX4NjwMC+GX8BwCECLCQJQRXYSNcBEPJBiJQgTIVqQQKUfqkVakG+lD7iFCZBb5gMKgaCgmShdliXJG+aH4qFTUVlQxqgp1AtWB6kXdQ42jRKjPaDJaHq2DtkDz0IHoaHQWugBdjm5Et6OvoYfRk+h3GAyGgWFhzDDOmCBMHGYzphhzGNOGuYwZxExg5rBYrAxWB2uF9cCGYdOxBdhK7EnsJewQdhL7HkfEKeGMcI64YFwSLg9XjmvGXcQN4aZwC3hxvDreAu+Bj8BvwpfgG/Dd+Dv4SfwCQYLAIlgRfAlxhB2ECkIr4RphjPCGSCSqEM2JXsRY4nZiBfEU8QZxnPiBRCVpk7ikEFIGaS/pOOky6SHpDZlM1iDbkoPJ6eS95CbyVfJT8nsxmpieGE8sQmybWLVYh9iQ2CsKnqJO4VA2UHIo5ZQzlDuUWXG8uIY4VzxMfKt4tfg58VHxOQmahKGEh0SiRLFEs8RNiWkqlqpBdaBGUPOpx6hXqRM0hKZK49L4tJ20Bto12iQdQ2fRefQ4ehH9Z/oAXSRJlTSW9JfMlqyWvCApZCAMDQaPkcAoYZxmjDA+SilIcaQipfZItUoNSc1Ly0nbSkdKF0q3SQ9Lf5RhyjjIxMvsl+mUeSKLktWW9ZLNkj0ie012Vo4uZynHlyuUOy33SB6W15b3lt8sf0y+X35OQVHBSSFFoVLhqsKsIkPRVjFOsUzxouKMEk3JWilWqUzpktILpiSTw0xgVjB7mSJleWVn5QzlOuUB5QUVloqfSp5Km8oTVYIqWzVKtUy1R1WkpqTmrpar1qL2SB2vzlaPUT+k3qc+r8HSCNDYrdGpMc2SZvFYOawW1pgmWdNGM1WzXvO+FkaLrRWvdVjrrjasbaIdo12tfUcH1jHVidU5rDO4Cr3KfFXSqvpVo7okXY5upm6L7rgeQ89NL0+vU++Vvpp+sP5+/T79zwYmBgkGDQaPDamGLoZ5ht2GfxtpG/GNqo3uryavdly9bXXX6tfGOsaRxkeMH5jQTNxNdpv0mHwyNTMVmLaazpipmYWa1ZiNsulsT3Yx+4Y52tzOfJv5efMPFqYW6RanLf6y1LWMt2y2nF7DWhO5pmHNhJWKVZhVnZXQmmkdan3UWmijbBNmU2/zzFbVNsK20XaKo8WJ45zkvLIzsBPYtdvNcy24W7iX7RF7J/tC+wEHqoOfQ5XDU0cVx2jHFkeRk4nTZqfLzmhnV+f9zqM8BR6f18QTuZi5bHHpdSW5+rhWuT5z03YTuHW7w+4u7gfcx9aqr01a2+kBPHgeBzyeeLI8Uz1/9cJ4eXpVez33NvTO9e7zofls9Gn2eedr51vi+9hP0y/Dr8ef4h/i3+Q/H2AfUBogDNQP3BJ4O0g2KDaoKxgb7B/cGDy3zmHdwXWTISYhBSEj61nrs9ff3CC7IWHDhY2UjWEbz4SiQwNCm0MXwzzC6sPmwnnhNeEiPpd/iP8ywjaiLGIm0iqyNHIqyiqqNGo62ir6QPRMjE1MecxsLDe2KvZ1nHNcbdx8vEf88filhICEtkRcYmjiuSRqUnxSb7JicnbyYIpOSkGKMNUi9WCqSOAqaEyD0tandaXTlz/F/gzNjF0Z45nWmdWZ77P8s85kS2QnZfdv0t60Z9NUjmPOT5tRm/mbe3KVc3fkjm/hbKnbCm0N39qzTXVb/rbJ7U7bT+wg7Ijf8VueQV5p3tudATu78xXyt+dP7HLa1VIgViAoGN1tubv2B9QPsT8M7Fm9p3LP58KIwltFBkXlRYvF/OJbPxr+WPHj0t6ovQMlpiVH9mH2Je0b2W+z/0SpRGlO6cQB9wMdZcyywrK3BzcevFluXF57iHAo45Cwwq2iq1Ktcl/lYlVM1XC1XXVbjXzNnpr5wxGHh47YHmmtVagtqv14NPbogzqnuo56jfryY5hjmceeN/g39P3E/qmpUbaxqPHT8aTjwhPeJ3qbzJqamuWbS1rgloyWmZMhJ+/+bP9zV6tua10bo63oFDiVcerFL6G/jJx2Pd1zhn2m9az62Zp2WnthB9SxqUPUGdMp7ArqGjzncq6n27K7/Ve9X4+fVz5ffUHyQslFwsX8i0uXci7NXU65PHsl+spEz8aex1cDr97v9eoduOZ67cZ1x+tX+zh9l25Y3Th/0+LmuVvsW523TW939Jv0t/9m8lv7gOlAxx2zO113ze92D64ZvDhkM3Tlnv296/d5928Prx0eHPEbeTAaMip8EPFg+mHCw9ePMh8tPN4+hh4rfCL+pPyp/NP637V+bxOaCi+M24/3P/N59niCP/Hyj7Q/Fifzn5Ofl08pTTVNG02fn3Gcufti3YvJlykvF2YL/pT4s+aV5quzf9n+1S8KFE2+Frxe+rv4jcyb42+N3/bMec49fZf4bmG+8L3M+xMf2B/6PgZ8nFrIWsQuVnzS+tT92fXz2FLi0tI/QiyQvpNzTVQAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAAAZiS0dEAP8A/wD/oL2nkwAAAAlwSFlzAAAASAAAAEgARslrPgAAQr9JREFUeNrtnXl4FFXWxt9bHRIgJIRAAFGCLKIou4yioDi4LyNuLIqo4zrq6KCOI44LuOsM4zoygt+4jCufM34qjAiyCAgBAQVBBRFEXEBkhwQIXfd+f9y1qjskgXSqk5zf8xRVXXXr1u20vn363HPOZWPHjhUgCIIg0gov6gEQBEEQiZA4EwRBpCEkzgRBEGkIiTNBEEQaQuJMEASRhpA4EwRBpCEkzgRBEGkIiTNBEEQaQuJMEASRhpA4EwRBpCEkzgRBEGkIiTNBEEQaQuJMEASRhpA4EwRBpCEkzgRBEGkIiTNBEEQaQuJMEASRhpA4EwRBpCEkzgRBEGkIiTNBEEQakpGKTjnn+Pbbb7Fu3Trs3r076vdY7cRiMTRu3BgdO3ZEo0aNoh4OQRA1kCoX56KiIrz73nvYubMYrdu0R4PsnKjfY7Xjx+PYsP57bNm8Eb1798bAiy5CdnZ21MMiCKIGUaXi/L//+xbmFhXhyuEP4rQBw5CRVR8QAAMgGMAE5IsQAgATAoIxQIgkPTPdyr1D7ZO1ZhBMgAkGMN2/HIO8JXx/5fovvz2Dx4AVyxZh3Og/4eFHHsXtf7wNeXl5VfnnJgiiFsPGjh0rDrwbYMGCBXj1tdcx+qVpaHd4Z4ABjAExxsDDTwhpmdZkxpJeTpBC7Lu7/WjPICDAyhDbSkk1AwSXr7kA4nv34oFbBmP7L2tx2623VMWfmiCIOkCVTQi+P2kShlw7Am07dgYYk0InpNjFGEPMAzwP8Fho70lR1nvG5DW990LntIAzR3k99cJjDB5jqj3bR3u7l/0Ks5cbnD0CfcoNzl62yfBkm/C3QkZGPfxh1D/w7erVWLVqVdSfN0EQNYQqcWvs2LEDP/34I0449UKlTUqhmADgSatUADGPwfMYfM7BGINQLgx9zFhyW1db1cI1jZ29vMYcAQ41KIeE/stzmzCm7mHmvqTeGAgIBjRp2gJH9TweK1asQPv27aviT04QRC2nysQZAJq2aKVcA66jWbeSB0IIxLS5qS8KIU1nUZafI6Seya57ZfmrK0BYy5kaC/Oc53vB/tXzuBAQgtlmzpeO9HEIAAJNmx+MHTvWVd0nRxBEraZKxFm4ogln5k29ZsaKZgH3QgxS83wRElvn3kC/Fb6eMEI1CiHvYMxMQDL5BuSxEAHfsd4JV7z1M7huy6zvmqm/haPhDAwcAszz4HOe6s+TIIhaQpWH0ukpNBY4J0ykhtFgIYwKZriiB3kuuC/ruKzrYYLthRBgnuNWUcfMK/t52nWiLWWhxi7dMQDnjosG1s8hGABeUQcLQRCEpMrFWepsMOzCWM6Op0CGuDET4sYA5e6Q9wnHkk4IXFP+aWuxBxuEoy9CdjOS+DGCe8eNov3L3HVVGMGVX0JcQLVH0KUB/YNBYD8dLgRB1FFSkiGorWIt0jrOGJ7rvdAOgaCNrVUsI8aMNardEAGxZjLUxLgpEHRTsFDMNHPkMTwBGRZ7OdEnn+dr9wVz3puwvdlfCswRcPOuIZiAIMuZIIhKkgJxtpOAQr823lndhCVrDn2k5/ZiMaZcBizkZUgSH5fsWIt5MjH2vJCvXO51Wz3JZy15d4zBCUobvSGvC+586QhjVBMEQVSYFPicpWXJjL9CBK552l0AWFcA04JsfcGe4/+NeQIeAO7cKxzLW/9rr4SvC+sLBpRuioAbRDs/uBFc6cowLhKjxeGvHOnW0EIvtC9dtdUWNVnOBEFUhtT4nAORE8piZlo8ASih1OLmNA1FbTi9MoDHSzHm8fsTzNDMzCzk5Obh8CO74ujeJ4J5TPl6mTsCs39l3FM4pE1b/Pq0c60LOeCRsPIe8DVbJ3rgBmMZC/fLQXdFwkwQROVJjc/Z/R2vJsOYYHYyUEU4aBHX+ue5PuWAx0Fao3E/jhfHjN7nowsP7YDnx3+Alq1aWx8yrJU7/l/P4fGH7sAVv7sFJ585QIbRcXfCUFnRwgn9E1qk3ZATmGMhHCHXSSlu24DHmyAIonxSUM/ZTRaR/zBtbToKJeAkoQQQ4Aimaht7XN3f41fHY86y9Zi7bD2KvliPWYu/x7vTP8OAiy7F2jXf4PbrL0EGA+p5DPU8hgyPwRMcr4x7Ao+NvC3JOF2fdjDaQgut9ieb9vqi0zYQeu28N+c3A0EQRIVIgeXspG4rn7OJ1nAnzoQzU8b0oVBSnjyKQ2tiLJaB3MZ58DwrgQXNm+Oxp1/A0sUL8fmnn2DL5l/QtFkBAGDN6pW4/cbLsWzJIvT81fH4dMFcQPmhdUSItpTDPhMbxeFccyYCueBq77Rx0sCDGYMEQRAVo4otZ21ZOsHL0HHOIduRhYWM2dRvx0o2vYbuD4a+2ToXR3buCgD4bvVKeAyIMWDm1Pfx0w9rMfLRZ/DY319yehGOvzs4HmscB4Pm3ItWtFVgoPuLwU1SAcitQRBEpahiy9mmNKuXKg5ZqBwUBs/xOwvmpnMLW0wIQS029ZgdxRZCGB+1UA12lRRjxtRJAID27TvAY9IGP+WMczHo0mtRv0ED/PjDd04fQDBWzibLmHfDQsIrgl8eJlrDjegIFFACgk4OgiCI8klBtIaaJGOORat8zq6VyiDD44K1j6RQcgCecDINVTstcXv3lmLThvWAcmuU7tmNn35ci9f++SyKd+7AKWeci2bNW5h5u0MK21rtDYSGAG5onIu8104OWvdyoqVsw+yC4m4mF0EZggRBVI7U+JxNph5CE23K56yy+dwUa1e4PSR6QazjGliyaB5OOvrQpE8/6eQzMeovz8APhLrJuGufBzu0lq4ciQi4WdS9yeKchRVmebsT7RFyT+tMRbKcCYKoDFUrzkabktdztpZrqKSmm7kHmOWqAlYus1l7rQ5pg/MGDTOPrd+gAVod3AZt23dEp87dACBBiMuGBYzoQLizsG4ak5wSEmuTFVhWPWdlUZPlTBBEZahacWbWFWAKYATC4XQdC33OFWbr1gBCLg3YLgEpzjfceg9c8dNfCz5HSDiDtTO4Y1G7GX9uCJxwx8CFzTBUYu1GT7up3knrOas7yHImCKIypMatUcF6zoGqGqGoieDKJjYNW+PzsgsXhaoSqWP5QmtzmbX8dfU8FhRbdzKSMV0/w5Zv0kNPqOeswuzIciYIojJEWs9ZMCeATsCumA2ELO7EKndcCIDDXJOZK+H46ETcNG0/VC1O+skdizhgRQd9zvpXAi+vnrNAwOoniKh45513sHPnzqiHUaPIzMzEBRdcgIyM1CRT74tI6znLyA7r/TBRHXDdBFLofQH4vjV7fS3Mzi5oniZPKtEiygUQ94PCqxd21a4SMyYk1nMW6vmmzEZZ9ZzVzChZzkSUFBUVYfbHH+P8C4dEPZQaxdQp76PehAk4//zzq/3ZkdZzDoVzQM/IccjC+7pcqK6JbL0WTC2qGigxZPZWbK31qs+5bo1A6LKzB2x7MynInPcmmDti7LOeswrDI8uZiIqSkhL83//9H/5870P47dXXRz2cGsX8oo9x4W9OQdeuXat9cebI6jmzxObQRx5TIsq1T0CaqvWyGmLeN7sAIRDnABM8+ZqAXN2jU7OdURS0bI153+ySk4NGlEPF9mHD/DzG4LtxzrogacLq4U7kBg9+6VA9ZyJK3nnnXbRu0xaXX3ld1EOpcRx7XF9cd+MtePnll3HXXXchKyur2p5d5YWPhImg0BNjInDN+JuVT9eE36nJNC4E4lzA50K6MgTssXOe67177N7n3M8FM3su5Oomei83OHv9TJj79cSgfhcuxl8erues2hrhrraPlCAsa9aswccfz8Zfn/wHPC8Fdc7qAHfcdR/ymjTFv//972p9bpV/Wqp+nFPpjRmfs1vP2S0EZ1wOXG76WLseyts4F2bvHts2wtnrNsK0BxAKsbNCGxBdqLKm4SWwnFoa9l/bFyNlJiKAc4433nwTl15xDbr36BX1cGosmZmZGPP8KygqKsLSpUur7bmp+SrVv+OV5WxXR1HXTWiZTNU2FiukJexzu0+2xZWVG+fKyhYw+4DVW8b9Ycs43L68/uXEJguG8ul0bvPWXdcGJaEQ1c/MmTOxffsO3HnPA1EPpcZzZOeu+NOf78Orr75abREvVSvOuoBFReo5CyDOZQSG7yv3gt6Xs3HlhijL0vaV1Vzm/eoaFwgc6+tuH0JFiei9HCOH7wtwzuFOau6rnnMw45EgUsv27dvx3nvv4f6H/4bGjfOiHk6t4Iabb0OHw47A62+8US3PqxJxbtSoEQBg6+ZfEKznDFjLWaqWtoo5t8Y1F3bvHuvr5W0+t3v3uMz+nb0InUu2hccT7s+s1hKcCYX2OQPAlo3rzd+JIFLNv//zH3Tp1hMXDrok6qHUGjzPw7PP/wtffvEl5s2bl/rnVUUnjRs3RvPmLVA0Y4I8kaSes2AyrjjpBFzgXOKm74v7weOyLOG4L8xeHtu9e2yv23uSWdLh55fVXofxhes5F+/YimWfzkGHDh1S/oESxIoVK7Bo4UL85YkxUQ+l1lHYpi0eePRxjB8/Hps3b07ps6rMrXHaaafitTEP4KfvV8O1IKXvliPuQ4ljovgluhmCPmf3XHKfdFDcubB7rhJW9D5Zf3HOzT7OuRlzxZ8f3LhJ4ZYTiv945FYc1LIlOnbsmNIPkyDi8TjefPNNXP/7W9Hx8E5RD6dWMvSyq3BcnxPxyiuvpHSVoyoT5759+6LzkZ3wx8v7Y/bktxGP+yoaAhBcJY3ofTjaQgBCizMXSTY4e4TOJW6CM2z8Zb16HlP9M+NOCd8vODN797is/ssbj7533dpv8cDwQfhs7hRcddWVFMpEpJwpU6ZAgGH47XdFPZRazRN//x/89NM6TJ8+PWXPYGPHjq0y6RdCYOrUqXh/0gfIyKiHth27oGGjnKoYJoLZhMlTs12+XDwfrdsdjpzcvJT0vy/8+F78/NNarF29Al26dsUlF1+MJk2aVMHfgSDKZuPGjbjvvvvw/EvjcdqZ50Q9nFrP+xPfwfVXDcVdd92Fli1bVnn/VSrOmj179mD58uVYv349du3aVS1/KJft27djzpw5aNKkCXr37l3tz4/FYsjLy8Phhx+O5s2bV/vzibrJmDFjUNDiYLwy/t1K31taWopvV63Eli2b69yCxLFYDE2bFaBtuw6V/nX7++sux6cLinD77bcjFotV6bhSUlsjKysL3bp1Q7du3VLRfbm89NJLAIAtW7agsLAQPXv2jGQcBFFdLF68GMtXrMDz//pPpe776ccfMPrR+/Hu2/+LkpJiNMxuVOdCPn3fx+5dJWiS3xRDL7sKf7h1BBrlVOwX/yN/fQb9enfB1KlTcfrpp1fpuKq/Dl6K2bZtGz755BPz+u2330a3bt2q/FuNINKJZcuWYcD5g9C6sE2F71n4SREuHTwA7Tv1wF1PvInO3Y9DLDPLRsKyMsoO6GtiX46/irsKzbocOk0C9vlVk71V/lh2F+/AonnTMP75xzDx3bfx7/em4OBDWpfbc05uLk45/WysWbW8KgYaoNbNUM2YMQO+75vXv/zyCz766KOoh0UQKacyRXk2/rIBlw4egNMvuhoP/OM99Dj216hXvz4yYgwZMQYvxhDzGDxPFv8ye8YQiwExtc+IQb4u4zijjM1t48WADI/Bi8lqlBkeQywm93o8sr16tjnHkBHzVJ9emf0n20ybDPns7Jxc9D3lPPzt1Zlo1e5IDLv4/ICOREGtEufS0lLMmjUr4fzEiRNRUlIS9fAIIm149qnROKTtEbjs9/dC1iMQUgyEFIUMxpDBgBgDYp6z92R9Gb33GJNCnXAMs5cLNquFm8HgMQ+e2seYF7jXU9a63utj2V59KTCoY8BjQo1DmPF4pk/dP5w9zBhjjMnFPZitipNZLxN/uO85rF+3Du++/b+Rfka1SpyLiopQXFyccL6kpATvv/9+1MMjiLRh8gcTcdr5Vyjfgcma0qtlyFWJGJDBPCV4dtUifewxOIIY3HS5XQamhFntVVnfmGf70v0bsffs3j0us3/A2Sdu+pluP2W51QUYshvloM+pF+DDyf+N9DOqNeIshMC0adPKvD59+nRs3Lgx6mESRFqw7qcf0LJ1O+XoBeyizHBcsdIR7HlAzPOQkcGQkeEF3ArSmlZCqlwOMY8hI0O5KLTrICbPZWQw5VJQe2//Nn2v7N+ze/c45rTLkGMNlDAOlAKGffOCoVVhe/z044+Rfka1RpyXLl2Kn3/+uczrvu/j7bffjnqYBJEW+PG4WhdPKbJgdp6MCb2yp/nJzyDFIsaAGJhaPk5aw4wJ+xrOMZO1ZZjbHvqc2ifdYMoKI3Cc/Lp6acbI3HP6HiECy84ByRZk1iMU8GIx+H480s+o1kRrTJ06tdw2ixYtwurVq9GuXbuoh0sQkWMWxUAoKEKoxZbNsS16y8DAPMATrsVZmWOW5FqYcBu9LpFwRqHPJX+WFF4GrtoJFRKi66uXuSBzBUZXXdQKy3nt2rVYsWJFhdq+9dZbUQ+XINICuzSEW2sdypthfdAm6Iwxu7gRk4s1xzKke8PzAE9HeTh7fc208WR0htkrF4feu8f6uqeiNAJ9OnvzbPMcNU5nAQxwAEJOegq99BIYggsyWx92OqTh1ApxrojVrFm9ejUWLVoU9ZAJIk3Qflb5ijleDn1ZanEZMcpC3i9D7YS1sLUvW4k4IPeMWetbu0WMG4XJvvSy0HZSj9n7GAu6TYx7RI5BLuQhoBcscgqsyzK/Tt/BTEhtOQeXyYiSGu/W2Lp1KxYuXLjvN5mRgQYNGiArKwtZWVlYsmQJjj766KiHThARE4rSgBViFlrJJ9DMUS5hhFP5d2OyExHIYGHKNcJMYotwrXXTv+PgTsgZsask63uFEnnzPNjElfCCzG7SSbkLMiM9LOcaL87xeBzXXXedEd7MzExznJWVhenTp2PLli24+OKLox4qQaQXTqSGEI7/golAGxvkwGwmnwdj4SIQK6xC15hIWBRJIJlUlqXFzNqw2gJmWtZtOyEArqxoLuxEpl3m01nrU21cJFmQWddjB1P9RE+NF+dmzZqhWbNmZV4/6qijMHbs2KiHSRDph+NADljEIQe0UC4HlmhIq9fCuUfdp+KWZ3/0AT6d/3HgsZ7noWF2I+Q3bY4TTz4T+QXNVTKIMxZYoX1l3FM4pE1b/Pq0c82zuXAkXdhpQi7KkPzQgszyrVuxd76mlBsmenmu8eJcHq1bt0ZpaSk2bNhAFeIIIgHHX2EUShg3hLwkHItaL2oMJZTWH8IZ4GkXhLJ2FxbNxMtjnyjz6RkZGbhu+N249g93hqxs2fP4f43F4w+NwBW/uwUnn3meHBtPdD2Ye9VkJhc6YFu19KDCBYVZkJkLa90Lt62wcSFRUismBMuje/fu1bLmF0HULByJCwQtyIw+jbAXkvZgLGVzQqiJOdv+mRffxtxl6zH3i/WYs3QdPpz3NZ56fjzy8pvh2dGjMG/mFNTzGOqp2hqe4Hhl3BN4bORt6jkhHwlzrWZnrEpoWfCngPGBMGfU+1qQOXq7uY6I8ymnnIKZM2di9+7dUQ+FINKIkPfXZAgKcCeKw0QAi+BtDFDtwlImQyXcs9nZjZCb1wSN85qgSX4+Dilsg1PPOg933vc3AMCMKRNMhMV3367EJeeegNEP3oluPY9VjxRmIg+wE4Dmy0A/2fW9uO9Tfelw7Y8ua0HmCsVhVw91QpybN2+Oww8/HLNnz456KASRPhhhY0EXrXFXhJJImEjowDOugEBitAqxCz9MR0uoQkgew5GduwAA1qxeqdLEgVnT3sdPP6zFyEefwWN/f8kOFUG/t+tT1udteJwIPttYztp2dmKczVtlxuomt0Y1csYZZ2Dq1KmIx6NNySSItMFmagTOCa5FzqZvG6dyqDG3zueQrcocd4ju2PqrVd4ePpggSyq0bdcBGSrV+5QzzsW0+SsxeNi1gaEKd7z6WLhfCWq8CfUyQqMOuD50505bwdLAbq4DE4KawsJCHHTQQZg/fz769OkT9XAIIg0I+pyFqlfBPAR8zjKETth5PidRJcYcy9l1ZRjLVva/betmbPxlvTLABbZu2YQli+bj5eefhud5GDzsKnkbAw5p0xbgKkKPWUvXDNSOCoLpST6b1C3UazMQYVqbZxihD6wYIN+LSAu7uQ6JMyCt5zfeeAPHHXccrYRNEK7flQXdtzqITgc261A34xjQnhDtAgmH1wkZSqe55dohSUeQ1yQfDz8+Dp269IDvJol4Qqfzqe6c2GWh/d2JJI1zVi/0PTpaQ9j0x9DEYHpMCNYpcT7iiCNMhmCPHj2iHg5BRI9JlXN9z8wWPnJDGlyTWasX12FqiZazO1k4YOAwHNxaLqHlMYZmBS1wcOs26NrzGOTm5oEHFh1JUowJTsdM2bZCZ/fpt6Kn+Wy8s1suyZTUAINI2rkI1hCJmDolzoC0nidNmoRu3bqR9UzUcYIp1ghptPbpWi0OTh5at4MIRWck5gEOGHgZjjn+BNmLm0ACIM6tq0HXwxBCZf0FxBdw/cKAdMEIZUIzJsXaRnYIx7EiZZoLYVO9BUy7wLhFsN5dVNQ5derevTvq1auH6dOnRz0UgogW5giom7Phng+4KxzBcv3Pyq8bsDZ5eIJQwBcMXCWICGXd6s3ndu9zqGNpmANWuLWnJDCZ59Tp0D5qt6iRGyO973rOWsIpWiOaN+x5uOKKKzBp0qR9FucniNrOPus5uxOF5sDxxerzwhF2twMvmMMnBCB8Ae7LyTq9r8im4VxuAYylLQKiytyBAqYKv6mhpMXayWbUk4Gm24ipc+IMAAUFBTjnnHPw4osvgnN+4B0SRA3EZsvtRz1n3YcpSefWq5CiKi1l2c4XAnEAcQjE9bEQiAvsc/PV/Vyf43LzEyrPuWsJstA1UD3nmsRJJ52EzMxMfPjhh1EPhSAixGYCAnb+r6L1nF3zVs4LCnAB6ZLwbb+Cy9VHuI+ETai2ggOCK+ta7bXPWVvbnKvNHMtBukkoVM+5hsMYw2WXXYZHHnkEXbp0QatWraIeEkFUM04WoJPbUZl6zvqagLSOpfoxgMlA5RvveBg33vGQXDKKCxNfzBg3k35S4PU97jiAgpatUbRyFxiTPujwhKHpT6W16PUCecByDk5O1pR6znXWcgZkudEBAwbgpZdegu/7B94hQdQkAvWczSGCfgsBD1ZAzWWl176ZxJPi6Qt9zr0WnOCzx+597v3SHeJOIPqcmfZxX94b92H6jKu9L+SeBWcM5VtRmzT2tUUu4DrStUskHSznOi3OAHDiiSciOzsb7777btRDIYjqxVFaYxGrAkGuxWkWSHUNaS2EXKV7c13EvgIbl5at0C4K95wSTrtXLg6952rij9t4CldoA6ILnQgTtIXNqUCNOv0nSZ96znVenAHgyiuvxJIlS/DBBx9EPRSCqGYcf4WOuhBBzyuDUEa2POtzOTnHHWtVC7WfZItzSIuXA3EuJwF9vVf3xfd1v9MmWfu4sr7jXNhjxxKX74GpCBInQ1DXczbvTPt2qJ5z2pCTk4NbbrkFH3/8McU/E3WIYG0NcypJPWcBPYEXnpArfxNq4k5wNemnZuZ0KrZQvmhR1v0CZu8eu9d1H6Y/Z3KR+1y28zkSKtkF0rb1+02P9G0SZ0VeXh5uueUWfPjhh/j4448PvEOCSGNychujZOc2lFfPWQjr1/XVfB+HPfZdyxkV23wO+HCsaudcsr5dXzIPndPHcfcc1HGS/riThbives7FO3cgJzc30s+IxNmhadOmGD58ON577z188sknUQ+HIFJG567dseSTjxBOyTb1nNWkXFxZyHEVCqcFVZ/zHQs3ricGfXXsC8TdY64zAWH25hlqL4/t3j221+09bl96YjLu2/2+2psQvCT1nJcumIkuXaOtv0PiHKJFixYYPnw43nrrLXz22WdRD4cgUsKVV9+AiePH4sfvvgmcFyoKIs55MAKCC2mVKiHW55L6nPWxtnZ52CctnL0WVu5EcrhiCxs3rcVcTRBKHzNXXxjc+KjD7d1zyTZuSoxKE3rBrMlYumg2Lhn220g/IxLnJLRq1Qo33XQTXnvtNVo9haiVnH7WbzDg/IG4+9qz8fmCWYBQgiuYysjW+8SNK3cHh7VuEzc4e4TOBTeZuKJqMYOpY6gwusT7hVDtVREj7uz3Zyy2D2DGxDfx2B2XYeT9j+HQtu0j/YzqbBJKeRQWFuL222/HmDFj8P3332Pw4MGIxWJRD4sgqoy/PT0Wf330ftxzwwC0P6IrOnU/HrmN893CFMkJFpVLqCgqjwNl5pwbRNKXFXpGmf0n6awS/QvOsfmX9fh8/gxs2fQzHv7Lk7j40mitZoDEeZ+0aNECI0aMwD//+U88/vjjuOqqq5Cfnx/1sGok48aNw6JFi1CvXr1K37t3717ceuutOPzww6N+G7WKWCyGEXfdh2GXX4333nkLS5d8hh/WfV3n6s3EYjE0bVaAm/5wC849fyAaN86LekgASJzLpUGDBrjhhhvwwQcf4KGHHsK5556LE088MbROGVEeGzduxGeffYYjjjii0vf+9a9/RVFRUZ0S58WLF6NBgwbV8p4PPqQ1rv/9rVG/ZSIEiXMF8DwPZ511Frp3746XX34ZCxcuxKBBg9C6deuoh1ZjkKste6hfv36l762LiyJ8//33mDhxIg477DD85je/qVNfTISk7v1XfwC0atUKd9xxB3r06IGnn34azz33HH788ceoh0XUYlauXInHH38co0ePxooVK6IeDlGNkOVcSTzPQ//+/dG3b1/MmDEDTzzxBAoLC3H88cejW7du++VTJYjy0CJNlnTdgcR5P8nMzMTpp5+OX//61/j0008xe/ZsvP766+jatSvat2+Pdu3a4aCDDqqTP8mJ1EEiXXcgcT5AMjMz0bt3b/Tu3RubN2/G0qVLsXLlSkyZMgVbt25Fbm4usrOzkZ2djYyMsv/csVisUltGRgbq1auHevXqITMzExkZGcjMzEzY6tevj/r169MEZi0jLNJE7YPEuQrJz89Hv3790K9fPwDArl27sGPHDhQXF2Pnzp2Ix+Nl3ss5h+/7+9zi8Tj27t0bONZbaWmpOd6zZw9KS0tRWlpqjhs2bIjs7Gzk5OSgSZMmaNq0KVq1aoXs7GwAcsJOb/o1YCfj3PPhdsleh68daL3sPXv2YNu2bQc8zmTX9sXu3buxa9cu7NmzB3v37jWlKOPxOOLxOHzfl0kRnJu9e6zLWIbPudeStfnmm2/KHRtgRTo3NxeHtq98JAyRvpA4p5AGDRqgQYMGUQ8Dvu+juLgYJSUl2LZtG7Zu3YqFCxfiyy+/RG5ubkAgAFsLV8e7huvllvc62bXdu3cf0HuYM2cOPvnkkwMap9smTDIxb9u2LdasWYOGDRuaXyL6mv71EovFTCSK3vRrd1/WuWSvGWMoLS2N5L+V3bt3g9e1hScYQ8OGDaMeRQIkznWAWCyG3Nxc5ObmomXLlti9ezcmTpyIwYMHo3PnztUyhkceeeSA7u/fvz/OO++8KhtPeV8yGi3I1c2ECROwevXqcttpt8aCBQv2+1mT/vsu/vXCOCyYPxfFxTsjeb9Rk5mZiSO7dMfAQZdg6OVXIysrK+ohkTjXNdatW4fnnnsORx55ZLUJczpSUbdGuhKeENwfcd61axd+d9VQzJk9E2dcdCXuGvIHNCk4CF4sBk8AnKlY24TUaVWwnpVVlD6Ue63TrPWXXkJqtl4P0K7IYm5B4gCE0142F3qBqTKHsK98cCEEdmzdgi8XF+Hppx7Hv176H7zy5jtoXdgm0s+YxLmOUFpailmzZmHSpEm44IIL0KdPn6iHROwHVRmlceN1l2PlN6sx5j+foKDlwapyppK48mpbVDXV/TwXAeBQoFO3Y3DWoGvw+N1XY8iFZ2PqrAWRuiVJnGs5e/fuxaxZszB58mS0bdsWt912G600XgOp6tC52TOnY/qHH+Afby9EsxaHBIQx5iEo0LDXwqtalVmXCJXTWga1ALduz+y5pG0TVggPWdflPU9dFNqgVw3rN2iI2x99CTcNPBb/HPsMfj/8T1Xy994fSJxrIb7vY8WKFVi4cCEWL16MDh064KabbqJ08xpIquKZ3/nPeJxw6gUoaFUIQPoQGGwVOU+t4srUslXJJlJZkuNk50y3elVro8RBcWVaTpO2D3ZuXRjuuOxXgxZuZs7bDpkqiQoml7MKvieBehn1cPag6/DO26+SOBMHzs6dO7Fy5Up88cUX+Oyzz9C0aVP06tULd999N1XSq4G0bt06pZX4vl39DY489kwwI5KwTl7lS/agaqJA+Z+ZZ0U6JJjM8fwCslayx2SdZLnQCoNg9jo8AQjPPjupvCenPBc2EJB6OToG8zxdV58j0boW6syhhx2FV5+tWDhjqiBxrqFs2bIFa9aswddff40VK1Zg48aNaN++PY444giMGDECBQUFUQ8xwKZNm3DttdeiY8eOlb73p59+QuPGjaN+C9VK9+7dU9p/aWkp6mVlOdarCPoVmBQqD/J0DHJ20FPLVQsBJbBanUVA6GPKMo3BXof7RSBY8P4EXMcEc+53+vKE9b+414Vtw5i7XKtaG1FPJAqAMwa1ZpWFMWTWr4/S0j0p/QzKg8Q5TRFCYMeOHdi2bRs2bdqE9evXY926dVi3bh3Wr1+PevXqobCwEB07dsTQoUNx6KGHpvViACNGjMDy5cv3695WrVrRBGYKsNKnlmly/BDMcTtY3ZMy53l2tRQd8KKPtRDq44peD2Mt35BA65HrLxXXcnf81IwxZVlLm55zHdnhqcVrtYYLqdV6TUHArPIdNSTOKcb3fWzcuBE7d+7Ezp07UVxcHMjgc7fi4mJs3boV27Ztw44dO5CVlYW8vDzk5+ejZcuWOOyww3DCCSfgoIMOMpl9NYVmzZqhb9++UQ+DcAjoT2WiCpVbgQHwmPXquiufJEwI6tC7CrpFbHBc8gm+gFfZsZQBOQQuBJgHCL6vgI/qCgfZP0icU8CaNWuwbNkyrFy5Et9++y0aNWqEnJwcNGrUCNnZ2cjKyjIZZw0bNkTjxo2RlZWF7OxsNG7c2GxU4Y5INVpKmWucsuB8nWBubeFgjITHhPUweI4jOBRNoS1kaynvY0LQnDV2ttMuSXSG8mmDCbPuoR6K6c28FuZrAAlR2naaMR1C4Emcq4jt27ejqKgIRUVF2Lt3L3r06IH+/fujQ4cONc7KJeoaNixCaKFz1/8TUOqsxZA5d0phZ6aJEkIg4MOWiSOwiSPMnoPbtiwfNCu7P+Y0EkzO9HF9j2yMwE8DM/GpGpkvFDcxJerPhMT5gNm+fTsmT56MuXPnonv37rjkkktw2GGH1ejsM6JuwJx/EfI52ytCTQLaAOeAu1eJuGByH2MmVk26FfYVjFFmLF5ogk9P4pkJQGfYKmxDR8Qx4djFJn7ZjYzWwivM+K0QM3NfOvzvS+K8n8Tjcbz//vuYMWMGjjnmGIwcORJ5eXlRD4sgKkXQt2tD6VzPr1AREkxb13AMaX3NWMHSjPZU3PTHMyfj0/kfq96Uhe15aJidg/ymBTjh5DOR36yFTd9WfWzetBEzJr+L779bjZzcxjiqay8ce0J/1b0Ub64ySFS0HgTcuij2S0LHTms8FaAhtJA7xrOAkA3SABLn/WDNmjV46aWX0Lx5c9xzzz0UR0zUSKyxLCfrXMtZKCE23t5APLTrfWCuNwCCac+xjHNeWDQTL499oswxZGRk4Lrhd+Oam0aAKUfxtEnv4t4/XoPinTvQrHlLbNn0C3zfR5+TTsPj495C/aysUPSbfrgwro6gN1k5zZUTWoigv1oEtTvJiWigZToqgRACEyZMwN///neceeaZuOGGG0iYiVqAEljHDcBc3zAAq1bC7gQcC1vrt45DC1qfz7z4NuYsXY85y9ZjzufrMKXoazw5bjzy8pvh2dGjMG/Wh4gx4Jeff8Q9t12NJk0L8M/xkzF90RpMW7gGQ397I+Z8NAVjRo+UT2PuhKMwjhjtsjAFm8x4hbW6wznosO+jMskwqYbEuYLs3r0b//jHP7B8+XLcc889OPbYY6MeEkEcEMGgN/ekUNl8ImhECiVsjqBxRyClsc2SOmyzGzVC4yZ5yGvSBE2a5uPgwjY47ezzcOd9fwMAzPhwAjwPmD3tfZQU78TgS6/GcX1PQsxjKGjeHDePuB85uY0x9YN3TQxH8EtDjcmE9jHrvzbjkmko2nXCEgTYOcOiN53JrVEBNm3ahGeffRZt2rTBtddeu8/lpgiiZuHE0DlRDEwwG0Kn9ZeFLGKV2m2EzsQbI1GglUWu451jkBOGnY7qAgD4bvVKxBjQpVtP3DHqLzjn/CGyrKsQ8AXQsGEj5OU3w45tW62t7DqLZfcQPGThm+dry9kzXyhCiISmul+K1qgBbN68GaNHj0b//v1x6qmnRj0cgqhCQjHDru/YszHGRma5iphw06GFk4hiPALMBFkEcZJMlFU7eeLbAIBD23WAxxi69eiFbj16gUO6EbWrZOH8Ofh+zSqc0P8M+3zH8Wzs/4TwuGALN1ojMVPG3kvRGmnO9u3b8eSTT5IwE7USYWI0WLC0hrKcAZ0KrSb6dOEiE2sMxDzr82WOxWwsW8XWrZuxccN6KdxCYOvmTVj86Ty8/PzT8DwPQy69CkwX8tCTdqqLkt278LcHRyAWi+HGP46Cdni7GYeuexlChF7rnRyrjtYwvxh48K9i3njEkDiXQUlJCZ566in06tWLhJmotZisPBNSzEyIHHPcFbqcqJtibb0gapqNhfp1jNdbrx2S9Pl5TfLxyBPj0KlrD2kpq/MeY+BMYOeOnbj5qkFYungBbrv7UXTq0h3gZQdU2DRw2JoZugiS+hLhbrRGKC/ctorer0HinIQ9e/bgmWeeQceOHXHuuedGPRyCSAluEknwZCgUjTnqlZA9KEzQs3DOhy3nAQOH4eDWbVR3DM0KWuCQ1m3QtccxyM3LA09YU1bglw3rcd2wAfhq2WIMv/NBXH7dcCegxMbABUt+BoXXTlU6wu8xcJ68sobpOw0gcQ6xd+9ejBkzBi1btsSgQYOiHg5BpAwT/pasLKdyUeiCRlavHAF2i1gwHSkRduRKBgwchmOO74dgip9s5/PEsf2wdjWuGnwmfl73Ax5+8p/4zYWXSnlN4kp2c03sQbDWhmzKIMBNhTr5XRJeSKCMCc0IIHEO8cILLyA7OxvDhg2jFGyiViOl1Pl5b30bylWh9ix8lzpyElEEgsLOQmapgAy7k+nViVXqmGOQr/r6K1x7yVnYs3sXnnvtvzjm+H7qXifuOmQVM0DV0mcQXASEXKZk2y8D57sHnAcF37g10iBcg8TZYe7cudiwYQP+/Oc/w/MoBJyo3bjFOEXI2hVOnK/xVug8aTiWMxMhK9P6pgMFkjik68IpGSq4yWIxp0tKSnDDZQOwq6QYL7w1DR07dQHnznhdLWX2Rm3hB+xy5tzkMeenghVfs4J4IKouPYwyEmfF1q1b8Z///AfDhw9P66L1BFGVaGm21eFgozWYY9UCpraGG+5sJwwZ9FqD2iKPOwaoDyDu1r3Qk3IhA/X5vz+GdT+uxWGduuDNf41NOuY7H3wajHnWZmbW8rcGe0jFuT7SoXRqwYCQS8PU6Ij6gwGJs+HVV19Fv379aBFUok5hsgS1KJtqbzbnRJhaQHpizc2tE+Z2T7ucfcD3BBh3vANcLaYqko1ByFA9ITDtvzLueeVXS7Hyq6VJx3z7qCeREWNqDUBr64pAEorrArGJJQJ20lAkDIbqOacd8+bNw+bNm3H99ddHPRSCiADrrrBxz+EojnBEh77T1nPmqitASFMZwI13PIIb73gYANTEn7ZL9R3620Aej/9wSRljDE40+m44nHNd+7GDE4TuvbqN9nSwUFah+gJKA9O5zovztm3b8O9//xs333wzuTOIOgVz/g1oHXOsUQhZo9n4ip1VUxisEIb9AaG+ElbMVpEUzCz4Csc9oackrZUunAVkrXAKxx8OM58pu1I1pp1sFNcFbZwfbr1RquecXrz++uvo27cvCgsLox4KQVQ7Wv50konE1nM2P/VVhqA+a5aBSoyMg2nk7hEMgJCTgY7VqlfBdpzfwuwFwBkEc5Y4ccL+TDq2cKOZbYahECwo0mbsbryH81Sq5xw9n3/+OX7++Wdcc801UQ+FIKodq6VujBqkdarcHJ6JrtOuDwEOJr0QCNziGspJnpVkwVY3I1BlUXsi2b32wIxZuM8N9i1HHspm9KxIC6G91cKIe+CxaVLPuU6L8+TJk3H22WdTlTmijuMUPQpFZAjhlJng2pWcmPZcMYKTd7oPnVItmPYlJw7Pfjm4rghrCfNQsSKuLGKufS0mhE53qFZE4fYRwTcVvfVcZ1Xp22+/xebNm3H00UdHPRSCqHbq16+P0t27EBAjx0+sy4UylcHnJokAVisdV3SlfLVC98md+3mof+2yEEmu831fDzxLJD4r4GR3Qu70n2DPnhI0aNAw0s+ozorzhx9+iJNPPpmSTYg6yWGHd8I3Xy6Cm+rsrm7NhCw8xLm2dnUMs55AFOacvB7wfCQYqqHuYWpxKNNZZw9ynQounFgOfSxUNTkVh80RHI/u08wt2ppOJsMQzMY2m/UD9ZC0z5oxrPziU3ToeESkn1GdVKaNGzdi+fLl6Nu3b9RDIYgqIScnB4sWzgfnvELtBw4eirnTJ2DNyi8Q8D4L+VM/LgS4L485B3xfmL17bK/bva+yAX11jbvnzCbsngvVRiRvH+rPV219H4ir8cSdPt37OQ/e7ztj0NeD2doMxdu3YsLrz+KiwUPL/TsKIfDFsiWoX79+lX+mdVKcp06dir59+6bkD0oQUXDqqafih7Vr8OrL/1Oh9j17HYuhw67CfTddiFXLl8rQZCVSvlrR2hcCHEi6+cLuD3wTqi8BDvc4eXuuVkfhQgSOD2QMXKnz1k0/4/6bL0JhYSGGXVF+oMCLz4/ByhXLcdppp1X5Z1rn3BrFxcWYP38+Ro4cGfVQCKLKaNiwIc477zw8fN9dOGfAhcjPb1ruPQ/95Ul4sRhuGXoC+pwyAD2OOwX5Ba0QS+LqC8z/hd0UyfNByp5TK28yMVlYXmX6R2JcdcIjmNtGYPvWzfhy8VzMmPgGev2qN5574bVyAwW+W7MaD4y8E8OGXYrc3NwD/xDDYxw7dmwaBI1UH5MmTcLPP/+MK664IuqhEESVIoTAX/86Gr37nIjRT42t8H2fL/kUr738T3wyby42btwA3/crfG9tgDGGxnlN0KVrd1w0aChOPePscu8RQuC8s34NP74H16YoFLfOWc4LFy7ExRdfHPUwCKLKYYxhyJDBeOTRR3HpFdege49eFbqva7ee6Pp4z6iHX6N48fkx+OqLpRg58t6UPaNO+Zy3bduGzZs3o127dlEPhSBSQmFhIU7oewLuuPXGUMU1oqrQ7owhQwYjJycnZc+pVZZzcXExXn75ZWRmZiIrKyth+/7779GiRQt8+eWXgfNNmzalRBSi1jBgwLkYOXIUXn/lBQy97Kqoh1OrEELg5uuvxFGdj0KvXhX7ZbK/1CpFys7Ohu/7WLBgwT7bPfPMM+a4oKAAo0aNinroBFFlZGdn47zzBuDBkXfirN+cjyZN8qMeUq3hhXHPYvmXS3HvvalzZ2hqnVvjlFNOqVT7Cy64gKxmotbRp08f5Ofn4+H774p6KLWG79asxoOj/owhQ4ak1J2hqXXi3KlTJxx88MEVatu+fXv07EkTIUTtgzGGwYMH4Y1XXsTnSz6Nejg1HiEEbvrdb9G581HVVvKh1okzIAPyK8LAgQOjHipBpIxDDz0Uffr0wR230OTggfLCuGex4qtlGDJkSLU9s1aK869+9atyg8J79eqFtm3bRj1UgkgpAwYMwKpvVuDN116Keig1ljXfrsIDo+6sNneGplaKc0ZGBk466aR9Xj///POjHiZBpJxGjRrh3HPPxQP3jsC2bVujHk6NQ0dndOncudorWNbambB+/fph0qRJ2Lt3b8K1/v37o1mzZlEPkSCqhb59+2Lu3Lm4/OLz0fHwTlEPp0axYcN6rPhqWbVEZ4SpteLcqFEj9O7dG7Nnz044f9ZZZ0U9PIKoNjzPwyWXXIJZs2ZhzarlUQ+nxvHb3/62Wt0ZmlorzoAMqwuL8znnnIMGDRpEPTSCqFYKCwtx6aWXRj0MohLUSp+zpmXLlujcubN53aJFC5x44olRD4sgCKJcqsVyjsfj2LBhA4qLi6s9pOeII47AsmXLAAC9e/fGqlWrqvX5nuchJycHBQUFtOoKQRAVJqUlQ7ds2YIJEyZg4cJF2LNnN+rXbwBW0UXGqpDdu3eBMYasrOovrs85x549u9GoUQ769u2DM888k4r8EwRRLimznFetWoVnnx2Dw7r0wr1Pv4XO3Y9DLDOrjPXEHMLrjyWlvGrcwZZTJ76OQ9sfiQ5Hdk9YX+zAKX8su4t3YNG8aXjjuUfw6cOP4Jbhf0B+PtU7IAiibFJiOW/fvh2jRt2Hs4dcj8tvGqlXW4enll4PeDZCWsaYgBAMjAlzGQgvhMDk4oxlCKIot30QfU0tDenIrVwaUrrmudPe7T9RnM3zGADOzNLvpXtL8Zc/XY4fVi3Fn+8cQW4OgiDKJCXqMGXKFBR2OAqX3XQv5PK3Qj5IyAdmMIYMBsQYEPOcvQd4jJm9xxhiagsew+w9yDoCehl3j3nw1D7GvMC9nrLW9V4fy/ZQ/UMdAx4TahzCjMczfer+4exhxhhjDEz9PJCyzZBZLxPDHxiH7Tt2YuHChVF/9gRBpDEpEefPP/8cZ1x4pfId6E0fMggmrcoM5inBk8JqhVMJrxHE4Cavy70UZrVnso+YZ/vS/Rux9+zePS6zf8DZJ276mW4/ZbnVBRiyG+XghNMH4vPPP4/6sycIIo1Jic95y5YtaNm6nXTu6p/9jMlf/8YDIB3LUow9ew6OQ1qvJgnYvsJOYwbrpNY+k32t7FhZmKf6VN9j+tjtXz1PruBrl5hnjDnRKWovGFoVtsfyhdNS8acnCKKWkBJx9n1f1Uh2xBbqJRPWq8tCFqkSWq6F1iztC9uXI+wJwq2/BMw+GUEPc6JHOuyBRsDw128lcEG4PanLalVfOy+oPdgCXiwGzuvWIpoEQVSOlEVrSL0KTurpF4IJo7vSSLbixjzAE66wVuaYJbkWJtymPLFOfJYUXgau2gml2kJIdw3nqiemehWJk5sEQRD7ImXizNx/3aAKD2qiTBjjWEALmTWCGQM8T7oxhLCWcEJshBBB90Gowb7tYqBsYXesYuW2kM+RkRcBM5rLnj0AvoBx4ViXhvvXEKgihwtBELWYFGcIWj+rFlzXpayPvQTJlTAhhczz5HWhfNDMCZQ2XgxPP44BXvAhzAmc1gIZsIpZkkHpQGsmjxljEFyYU7Ib634RQgfbSfHnSeIFhesqIQiC2AcpFOdQlAZs7DALSBQLNnOUSygXgvRHM7AYlEXqZrAwpavMmUd0IyaY7VgPKSFnhNnvEe22UC4W8zzYOUjh+JETop6Vdc3UMwUPynGV5b4QBFGrSZ04MxulINzoCyYCbXT8sxFZ7fpQ9yIQK6xC15RLJJknIzEBJZkWO9N92lpmWtZtO2kNy+dxYScybTCIfS9a97njzhDG/QG4FjVZzgRBlEfqxNmIFwtaxAEHNJNyqOKeodoFxIuFIy+EyjZkmP3RB/h0/seBx3qeh4bZjZDftDlOPPlM5Bc0t24NNZbNmzZgxuT38P13q5GT0xhHde+F3n36m2dz4Ui6E4nBRRmS77gwjBEurNg7X1MqIo/kmSCIfZNin7Mbg6ZOCWHcEPKScCxqGyMMpw0EwJUr2fg5ILCwaCZeHvtE2W8uIwPXDb8b1/7hTqOf0ya9g3tvuwbFO3egWfOW2LLpF/i+jz4nnY4nxo1HZmb9BNeDsdCZnMyUIu3Y6B6kGAshJyi1kCttF25b4U5GEgRBJCeFxR0ciXMNTpXRp7H1KVjSHoylbE5Ip6/rHHjmxbcxd9l6zP1iPeYsXYcP532Np54fj7z8Znh29CjMmzkF9TyGTet/xD23Xo38pgV4YfxkzPx0DaYvWoOhV96IOR9NxrOjR5lYbGs1O2NVQsuCPwWMDyQhQsW4Xdz3S24NgiDKJ4XiHK5oBCNiXKcKmhwN4f72t+6FpLENzCSvaLKzGyE3rwka5zVBk/x8HFLYBqeedR7uvO9vAIAZUyaAMWDmtPdRUrwTg4ddg959TwJjDE2bFeCmO+5HTm5jTP3gXTkEN2nG9Su7vhf3faovHa790QGXh23HkOx+giCIRFInzkbYWNBFa9wVoSQSJhI6MCF2gfKhAkyIJA/T0RJSRD2P4cjOXQAAa1avhOcBXbr1xIhRf8GAgUMD0RyNsrORl98MxTu2J44d1uWdkIqtGxvLWdvOobhrHbkREG+CIIiySfGEIEs4JzjsBCCzqSHSqRxszIWc+AtPEooEC9RGdQjlv/YAfDDhbQBA23YdkMEYuvX4Fbr2+JVJJBHKbbFw/sf4fs0qnND/zODYhfuVIMwXS1Ckg+/RdX0Y17TtFBCM7GaCIMolxXHO1ucsVLU25iHgc5YhdMLO8zmJKjHmWM6uK8NYtrL/bVs3Y+Mv65UBLrB1yyYsWTQfLz//NDzPw+BhV8nbmMruc+KQS0pK8LcH70QsFsONfxzpjgqC6Uk+m2kohAjGOQvT2jxDJ8sEVwxQiTRkNxMEUQFSKM6BHOqA+1YH0enAZh3qZhwD2hOiXSDh8DptUStuuXZI0hHkNcnHw4+PQ6cuPeC7SSKeTOcrLt6Jm68ahKWfLcBtdz+KTp27Q3Dt704kaZyzTu1W9+hoDWGiUOz7Nven7o9OEEQtIbWhdCZVzvU9M1v4yA1pcE1mrV5ch6klWs7uZOGAgcNwcOs2AKRoNytogYNbt0HXnscgNzcPwQJw8nkbNqzH74YNwFfLFmP4nQ/i8uuGq2QZZdsKnd2n34pdJ4U7sc/aDrZp3ayMaqWqJWNkORMEUS6pdWuEU6jdpDzl07VaHJw8FExHR9jSoqavkEk6YOBlOOb4E2QvbgIJgDi3rgamzPfvv1uDq4ecgZ/X/YCHn3wBv7noEnAOuH5hQLpghDKhbW0NW2jJOlakTEs/to3VDtZztrnf5HUmCKI8Upy+7SgtEIwhTiq69tCGErMEgxocpvY9IG1SX020JVSpkw3MftXXX+G6oWdh9+5deO61/+KY4/uBczciA6HJPKbWNVRfFmYiUQ/VPmvf9ZyV1U1eZ4IgKkD61HPW4ueed5NAmNOBF8zhEwIQvnYbQLojkhinu3aV4MbLB2BXSTFeeGsaOnbqoixmJHdFSLVXVnKyST81PpUhSPWcCYKoKtK2njPgJn3oDG/lExaADwbtEvaFQFy3CoTBBWXw+b8/hnU/rsVhnbrgzX+NTTruEQ88DS/mhaIs7L+y9kZIZqmeM0EQVUxa13N2i1rIeUGhqr4pq1p3z5W1mkT1tHuBMYZp/5Vxzyu/WoqVXy1NOuLbRz0ZGoeNzjCTgswdn42vpnrOBEFUFWldz9kIH6R1LNWPAYwDguHGOx7GjXc8JJeM4m4xfg4hdFF+/W3AMX7KEmcczmQeE6q9vOpzGD+zjcmQK3wzIcADVnWoN6rnTBBEFZDW9Zx9kcwa1ufca8mOy7oettL1hKXQwRRSmE2UhhvpEY7CcCcGVXy0486ges4EQewv6VnPWQC+amJaswq6A4TM7NNLXEEfu6ni7l6H8zntwW37gNCaR8hjjzHpYw4UR9Jv3SacOF9TVM+ZIIgKkVb1nAUYfI7kv/3L8AVYb66bLu6IpUg02BPudwzrcPuka3ObrEbYc2o2kOo5EwRRFVRDbQ0WqEinJ/c0RrN991XlCASq6ZIW2pOivgwgypBE5rgfYI+Dq3mLffQXytF2IlRsF27UCbk1CIIon5SIc4OGDVGycxsS0gIFACFMATohZDhccr9uMPaYVVDRhM4IdH3GvOy+mT4H5zrKvi4bOYfh/oywWz+2vklb4MU7d6BBgwap+NMTBFFLSIk4F7YuxJJPPkKP4/sjnLotLVuVKceVM0L5hWFinW1FuASfs62XZEKaXUs5HOMsuDCp10ASsU4Qc2bukQ2E02cZYsxFKLxODtRZ1Nu4MxgDlsyfjtatW0fwcRMEUVNISbH9k07qhwlvPocfv/smcF4IgbgPxDlHnMvIBl/IGGVfAD4X5phzYa7L14DPnWMh7+c8dJ0LZ6/64Fy2Fe452U4eq74EEOeyRkacC8Q5h89h9snau+eSbdyUGJUyvWDWZCz7dA769u0b9WdPEEQakxJx7tatG47u2RN3Xn0mPl8wCxBKcAVTE2R6n7hxCJXQIUUy+QZnj9C54CYTV3QCCFPHcizJ7hdCtVdFjLiz35+x2D6AGRPfxKN/uhQXXXghCgoKov7sCYJIY9jYsWNTEjrAOceECRMwecoUtOvYGUcdfQJyG+eX7zxOEoYcOA8kOqnDk3LhObqKPKPM/pN0Von+BefY/Mt6fFY0FVs2rsfAiy5Cnz59UvEnJwiiFpEycdZs3rwZixYtwtq1a1FSUgLO+YF3WoPwPA85OTlo164devXqhYYNG0Y9JIIgagApjnMG8vPzceqpp0b9PgmCIGoUqVt9myAIgthvSJwJgiDSEBJngiCINITEmSAIIg0hcSYIgkhDSJwJgiDSEBJngiCINITEmSAIIg0hcSYIgkhDSJwJgiDSEBJngiCINITEmSAIIg0hcSYIgkhDSJwJgiDSEBJngiCINOT/AfHai0F3pilqAAAAJXRFWHRkYXRlOmNyZWF0ZQAyMDIwLTA4LTEzVDIxOjM5OjI0LTA0OjAwHQ0DAQAAACV0RVh0ZGF0ZTptb2RpZnkAMjAyMC0wOC0xM1QyMTozOToyNC0wNDowMGxQu70AAAAgdEVYdHBkZjpIaVJlc0JvdW5kaW5nQm94ADM1OXgyMDgrMCswWvOJfAAAACB0RVh0cGRmOlZlcnNpb24AUERGLTEuNCAgMSAwIG9iaiA8PCDilXZ9AAAAAElFTkSuQmCC" } }, "cell_type": "markdown", "metadata": {}, "source": [ "## Part 2. Dimerization\n", "\n", "Consider a system in which two proteins can bind to form a dimer, and unbind to\n", "unform the dimer.\n", "\n", "![dimerNetwork.png](attachment:dimerNetwork.png)" ] }, { "attachments": { "dimerizationChemicalReaction.png": { "image/png": "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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "Proteins P1 and P2 can bind to form a dimer and the dimer can unbind to release P1 and P2. In addtion, P1, P2, and the dimer are degraded.\n", "\n", "For each process (indicated by the white square), we write the corresponding reaction. Since we are using mass action kinetics, we know that the mathematical expression for each reaction is dependent on the substrates and a kinetic rate constant. To be as informative as possible, we include in our reactions the kinetic rate constant associated with each reaction, i.e. \n", "\n", "![dimerizationChemicalReaction.png](attachment:dimerizationChemicalReaction.png)\n", "\n", "where $k1$ is the rate constant for binding and $k2$ is the rate constant for unbinding.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\n", "(1) Write down the set of ODEs that describe the dynamics of this system." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*Remove this line and use this cell for your solution.*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\n", "(2) Using initial conditions $P1(0) = 2 nM$, $P2(0) = 3 nM$, and $P1P2(0) = 1 nM$ and kinetic parameters $k1= 1nM^{-1}s^{-1}$ and $k2=2 s^{-1}$, simulate the system from time $t=0s$ to $t=10s$ with a time step of $0.01s$.\n", "\n", "Plot the results, being sure to label your axes and to supply a legend. Add a new Markdown cell below the figure to describe what it contains and why the basic trajectories of the curves makes sense, given the ODEs." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# Write code here" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\n", "(3) Steady-state is achieved when the rates are at zero. What is the steady-state for this system? Explain the relationships between the steady-states of $P1$, $P2$, and $P1P2$. Why are they in such a relationship? (i.e. relate the parameters to the steady-states)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*Remove this line and use this cell for your solution.*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\n", "(4) Re-run the simulation with $k1=1nM^{-1}s^{-1}$ and $k2=1s^{-1}$ and plot the results. Add a new Markdown cell below the figure to describe what it contains." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "# Write code here." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\n", "(5) The rate constants for binding and unbinding are identical. But this does not mean that the system begins in steady-state. Why not?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*Remove this line and use this cell for your solution.*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\n", "(6) Explain what has changed in the relationship between the steady-states of the molecular concentrations. Why have those changes occurred?\n", "\n", "*Opportunity for thoroughness: Please feel free to add additional code and Markdown cells to make your explanation as complete as possible. You could demonstrate the calculation for extreme values of k1 and k2, produce annotated figures, and demonstrate the relationship between simulation output and calculations you perform.*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*Remove this line and use this cell for your solution.*" ] }, { "attachments": { "dimerNetworkWithDegrad.png": { "image/png": "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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "# Part 3. Dimerization with Degradation\n", "\n", "We add to our system the process of degradation.\n", "\n", "![dimerNetworkWithDegrad.png](attachment:dimerNetworkWithDegrad.png)" ] }, { "attachments": { "dimerizationWithDegradationChemicalReaction.png": { "image/png": "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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "Proteins P1 and P2 can bind to form a dimer and the dimer can unbind to release P1 and P2. In addtion, P1, P2, and the dimer are degraded.\n", "\n", "For each process (indicated by the white square), we write the corresponding reaction (including rate constants), i.e. \n", "\n", "![dimerizationWithDegradationChemicalReaction.png](attachment:dimerizationWithDegradationChemicalReaction.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\n", "(1) Write down the set of ODEs that describe the dynamics of this system." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*Remove this line and use this cell for your solution.*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\n", "(2) Using initial conditions $P1(0) = 2 nM$, $P2(0) = 3 nM$, and $P1P2(0) = 1 nM$ and kinetic parameters $k1= 1nM^{-1}s^{-1}$, $k2=2 s^{-1}$ and $d1=d2=d3=1 s^{-1}$, simulate the system from time $t=0s$ to $t=10s$ with a time step of $0.01s$.\n", "\n", "Plot the results, being sure to label your axes and to supply a legend." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "# Write code here." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\n", "(3) Describe the interesting features of the data. For example, is there a steady-state? If so, what is it and why did the system approach it? Are there any peaks? If so, why are they there?\n", "\n", "*Opportunity for thoroughness: Please feel free to add additional code and Markdown cells to make your explanation as complete as possible.*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*Remove this line and use this cell for your solution.*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\n", "(4) Find a set of parameter values (all $\\ge10^{-12}$) for which the dimer's apparent steady-state concentration is higher than the steady-states of $P1$ and $P2$. What intuition did you use to find these values?\n", "\n", "Note: By \"apparent steady-state\", I mean the value that $P1P2$ seems to remain at during the time-period of the simulation (i.e. its value from say 5s to 10s). Given that degradation is included in the model, the steady-state as time goes to infinity will always be zero for all three proteins. But I am interested in the behavior on the timescale of seconds -- not years. \n", "\n", "*Opportunity for thoroughness: Please feel free to add additional code and Markdown cells to make your explanation as complete as possible.*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*Remove this line and use this cell for your solution.*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\n", "Acknowledgements\n", "\n", "*Replace this text with links to external resources and thanks to people you worked with.*" ] } ], "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": "3.8.5" } }, "nbformat": 4, "nbformat_minor": 4 }