{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" }, "tags": [] }, "source": [ "# Kinetics of Protein Folding" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "In a simplistic model of protein folding, a protein can exist in either the unfolded or the folded state. This model ignores possible intermediate, partially folded states. We will use this simple model to study the transition between the unfolded and folded states." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "source": [ "Let us assume that unfolded proteins will transition to the folded state at rate $k_f$, and folded proteins will transition to the unfolded state at rate $k_u$. If we denote the unfolded and folded states by $U$ and $F$, respectively, then the transitions can be represented by the reactions:\n", "\\begin{align}\n", "U \\xrightarrow{k_f} F \\\\\n", "F \\xrightarrow{k_u} U\n", "\\end{align}\n", "Note that the rates $k_f$ and $k_u$ are *per capita*, so the overall rate of transitions will be proportional to the number of reactants." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "By now you already know how to simulate such stochastic processes using the Gillespie algorithm. Here, however, we are interested in the *kinetics* of the reactions, e.g., how fast the numbers of reactants approach their equilibrium values. For that purpose, it suffices to study the *average* behavior of the numbers of reactants, i.e., to use a **deterministic approximation** of their dynamics. (Arguably, this is even simpler than the stochastic simulations.)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "Let $N_U$ and $N_F$ be the numbers of unfolded and folded proteins, respectively. We will derive the dynamical equations that they obey. Note that $N_U$ and $N_F$ should in principle be discrete integers, but in the deterministic approximation we will treat them as if they are continuous real numbers. In a short time period $dt$, there will be, on average, $N_U k_f dt$ unfolded proteins that transition to the folded state, and $N_F k_u dt$ folded proteins that become unfolded. (Recall that the number of transition events should really be a Poisson distributed random number, with the mean given by those expressions.) Therefore, the number of unfolded proteins will change by $dN_U = N_F k_u dt - N_U k_f dt$, and the number of folded proteins will change by the opposite. Dividing by $dt$, we arrive at the differential equations:\n", "\\begin{align}\n", "\\frac{dN_U}{dt} &= + k_u N_F - k_f N_U \\\\\n", "\\frac{dN_F}{dt} &= - k_u N_F + k_f N_U\n", "\\end{align}" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "At equilibrium, we expect both time derivatives to be 0. That implies $k_u N_F^{eq} = k_f N_U^{eq}$, hence:\n", "\\begin{equation}\n", "\\frac{N_F^{eq}}{N_U^{eq}} = \\frac{k_f}{k_u} \\equiv K\n", "\\end{equation}\n", "That is, the ratio of the folded and unfolded proteins is given by the ratio of the transition rates, which is called the equilibrium constant $K$. Since the total number of unfolded and folded proteins is conserved, $N_U + N_F = N_{tot}$, their equilibrium numbers would be:\n", "\\begin{equation}\n", "N_U^{eq} = \\frac{1}{1+K} N_{tot} \\,, \\quad N_F^{eq} = \\frac{K}{1+K} N_{tot}\n", "\\end{equation}" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "When the numbers of unfolded and folded proteins are not at equilibrium, their dynamics are approximately described by the rate equations above. To see that such dynamics do represent the *average* behavior of the underlying stochastic processes, we will first simulate these processes like before. Then we will numerically solve those differential equations and compare the solutions to the simulation results." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" }, "tags": [] }, "source": [ "## Stochastic simulations" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "Let us first define a simulation class using the `StochSimulation` base class that we had before." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from Gillespie import StochSimulation # import the base class saved in the script `Gillespie.py`" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "outputs": [], "source": [ "class FoldingUnfolding(StochSimulation):\n", " \"\"\"\n", " define a derived class to model the folding and unfolding of proteins.\n", " \"\"\"\n", " \n", " def __init__(self, rates, init, record=True): # decorate base method\n", " \"\"\"\n", " modify the initialization to specify the stoichiometry matrices.\n", " the chemical species are U and F in that order; the reactions are U -> F and F -> U.\n", " \"\"\"\n", " reactants = [[1, 0],\n", " [0, 1]]\n", " products = [[0, 1],\n", " [1, 0]]\n", " StochSimulation.__init__(self, (reactants, products), rates, init, record=record)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "Now we choose the parameters and initial values, then run the simulation multiple times." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "outputs": [], "source": [ "kf = 9. # folding rate\n", "ku = 1. # unfolding rate\n", "\n", "NU0 = 100 # initial number of unfolded proteins\n", "NF0 = 0 # initial number of folded proteins\n", "N_tot = NU0 + NF0 # total number of proteins\n", "\n", "K = kf / ku # equilibrium constant\n", "NUeq = 1/(1+K) * N_tot # equilibrium number of unfolded proteins\n", "NFeq = K/(1+K) * N_tot # equilibrium number of folded proteins" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "current time = 1.0047517408322153, current numbers of unfolded and folded protein = [ 8 92]\n", "current time = 1.0028892526832816, current numbers of unfolded and folded protein = [10 90]\n", "current time = 1.0133952655437546, current numbers of unfolded and folded protein = [11 89]\n", "current time = 1.0188621737864618, current numbers of unfolded and folded protein = [ 5 95]\n", "current time = 1.0023558104035135, current numbers of unfolded and folded protein = [ 8 92]\n", "current time = 1.0018249014117626, current numbers of unfolded and folded protein = [17 83]\n", "current time = 1.004495906909637, current numbers of unfolded and folded protein = [ 9 91]\n", "current time = 1.0035735466468143, current numbers of unfolded and folded protein = [ 7 93]\n", "current time = 1.0045166804604957, current numbers of unfolded and folded protein = [13 87]\n", "current time = 1.0018275857342773, current numbers of unfolded and folded protein = [ 8 92]\n" ] } ], "source": [ "T = 1. # total amount of time to simulate\n", "trials = 10 # number of simulations to repeat\n", "fu_list = [] # list of simulations\n", "\n", "for i in range(trials):\n", " fu1 = FoldingUnfolding([kf, ku], [NU0, NF0], record=True)\n", " fu1.run(T)\n", " print(f'current time = {fu1.time}, current numbers of unfolded and folded protein = {fu1.numbers}')\n", " fu_list.append(fu1)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "Here are the simulated trajectories. Note that the codes are very similar to the simulations we did before for the protein production and degradation model, with slight modifications." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1,2, figsize=(12,4))\n", "for fu1 in fu_list:\n", " time_hist = np.asarray(fu1.time_hist) # extract time history\n", " num_hist = np.asarray(fu1.numbers_hist) # extract number history of all species\n", " ax[0].plot(time_hist, num_hist[:,0], drawstyle='steps-post') # number of unfolded proteins\n", " ax[1].plot(time_hist, num_hist[:,1], drawstyle='steps-post') # number of folded proteins\n", "ax[0].axhline(NUeq, color='k', linewidth=2, label='equilibrium') # expected number at equilibrium\n", "ax[1].axhline(NFeq, color='k', linewidth=2, label='equilibrium') # expected number at equilibrium\n", "ax[0].set_xlabel('time')\n", "ax[0].set_ylabel('#unfolded')\n", "ax[0].legend(loc='upper right')\n", "ax[1].set_xlabel('time')\n", "ax[1].set_ylabel('#folded')\n", "ax[1].legend(loc='lower right')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "notes" }, "tags": [] }, "source": [ "As expected, the folded and unfolded protein numbers approach their equilibrium values, and we see stochastic fluctuations over time and between trajectories." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" }, "tags": [] }, "source": [ "## Deterministic equations" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "Let us numerically solve the deterministic equations derived above. To do that properly, we will use the `odeint` function from the `scipy.integrate` package. First, we need to define a function that takes as input the vector of numbers $(N_U, N_F)$ and outputs a vector of time derivatives $(dN_U/dt, dN_F/dt)$ according to the rate equations." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "outputs": [], "source": [ "import scipy.integrate as intgr" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "outputs": [], "source": [ "def dNdt(x, t):\n", " \"\"\"\n", " calculate the time derivatives of the numbers of unfolded and folded proteins.\n", " inputs:\n", " x: 1-d array, numbers of unfolded and folded proteins, [N_U, N_F].\n", " t: float, time (in case the equations depend on time explicitly, not used here).\n", " outputs:\n", " dxdt: 1-d array, time derivatives, [dN_U/dt, dN_F/dt]\n", " \"\"\"\n", " NU, NF = x # parse the vector x into components NF, NU\n", " dNUdt = ku * NF - kf * NU # calculate dN_U/dt\n", " dNFdt = - ku * NF + kf * NU # calculate dN_F/dt\n", " dxdt = [dNUdt, dNFdt] # combine derivatives into a vector\n", " return dxdt" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "Now we can integrate our differential equations using `odeint`. We specify a set of time points at which we would like to know the values of the variables. Then we ask the function `odeint` to return these values at given time points." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "outputs": [], "source": [ "time_points = np.linspace(0, T, 101) # selected time points\n", "x0 = [NU0, NF0] # initial values as a vector\n", "sol = intgr.odeint(dNdt, x0, time_points) # solve ODE" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "source": [ "The solution is an array of shape ($n_t$, $n_v$), where the first axis is the number of time points, and the second axis is the number of variables. We can now plot these solutions on top of the simulation results." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1,2, figsize=(12,4))\n", "for fu1 in fu_list:\n", " time_hist = np.asarray(fu1.time_hist) # extract time history\n", " num_hist = np.asarray(fu1.numbers_hist) # extract number history of all species\n", " ax[0].plot(time_hist, num_hist[:,0], drawstyle='steps-post', alpha=0.5) # number of unfolded proteins\n", " ax[1].plot(time_hist, num_hist[:,1], drawstyle='steps-post', alpha=0.5) # number of folded proteins\n", "ax[0].axhline(NUeq, color='k', linewidth=2, label='equilibrium') # expected number at equilibrium\n", "ax[1].axhline(NFeq, color='k', linewidth=2, label='equilibrium') # expected number at equilibrium\n", "ax[0].plot(time_points, sol[:,0], 'k--', label='solution') # solution to the rate equations\n", "ax[1].plot(time_points, sol[:,1], 'k--', label='solution') # solution to the rate equations\n", "ax[0].set_xlabel('time')\n", "ax[0].set_ylabel('#unfolded')\n", "ax[0].legend(loc='upper right')\n", "ax[1].set_xlabel('time')\n", "ax[1].set_ylabel('#folded')\n", "ax[1].legend(loc='lower right')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "We see that the solutions do a great job tracing out the *average* behavior of the stochastic trajectories. Mathematically, since the equations are linear in $(N_U, N_F)$, they can be solved easily and the solutions are:\n", "\\begin{align}\n", "N_U(t) &= N_U^{eq} + \\big( N_U(0) - N_U^{eq} \\big) \\, \\mathrm{e}^{-k t} \\\\\n", "N_F(t) &= N_F^{eq} - \\big( N_F^{eq} - N_F(0) \\big) \\, \\mathrm{e}^{-k t}\n", "\\end{align}\n", "That is, the numbers of unfolded and folded proteins approach their equilibrium values exponentially, e.g., $N_F^{eq} - N_F(t) \\sim \\mathrm{e}^{-k t}$, where $k = k_f + k_u$. This can be better seen by plotting $(N_F^{eq} - N_F)$ on the log scale." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "num_points = (NFeq - NF0) * np.exp(-(kf+ku) * time_points) # theoretical solution\n", "\n", "plt.figure()\n", "for fu1 in fu_list:\n", " time_hist = np.asarray(fu1.time_hist) # extract time history\n", " num_hist = np.asarray(fu1.numbers_hist) # extract number history of all species\n", " plt.plot(time_hist, NFeq - num_hist[:,1], drawstyle='steps-post', alpha=0.5) # number of folded proteins\n", "plt.plot(time_points, num_points, 'k--', label='theory') # plot theoretical solution\n", "plt.ylim(0.1, 100)\n", "plt.yscale('log') # change to log scale\n", "plt.xlabel('time')\n", "plt.ylabel(r'$N_F^{eq} - N_F$')\n", "plt.legend(loc='upper right')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" }, "tags": [] }, "source": [ "## Inferring rate constants from data" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "If we had the (numerical) experimental data but did not know the parameter values $k_f$ and $k_u$, we can infer these values from the equilibrium constant and the relaxation rate." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "outputs": [], "source": [ "def collect_data(time_points, time_hist, num_hist):\n", " \"\"\"\n", " collect data from history of time and numbers, assuming no events happen between consecutive times in history.\n", " inputs:\n", " time_points: list (or 1-d array), time points at which to collect numbers.\n", " time_hist: list (or 1-d array), full history of time of events, assuming no events between times.\n", " num_hist: list (or 1-d array), full history of number after each event.\n", " outputs:\n", " num_points: list, collected numbers at given time points.\n", " \"\"\"\n", " num_points = [] # to collect number at every time point\n", " if (time_hist[0] > time_points[0]) or (time_hist[-1] < time_points[-1]): # check if data contain all time points\n", " raise RuntimeError('time history does not contain all time points') # if not, report error\n", " for t in time_points:\n", " i = np.argmin(np.asarray(time_hist) <= t) - 1 # index of time point just before given time\n", " num_points.append(num_hist[i]) # get number at the time point\n", " return num_points" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "First, the equilibrium constant $K$ can be estimated by finding the average numbers of folded and unfolded proteins and calculating their ratio. For this we will collect data from time points *after* the trajectories have reached equilibrium, say $t > 0.5$." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "estimated equilibrium constant = 8.906759906759907\n", "true equilibrium constant = kf / ku = 9.0\n" ] } ], "source": [ "time_points = np.linspace(0.5, T, 51) # choose time points\n", "numF_all = [] # collect N_F data from all simulations\n", "\n", "for fu1 in fu_list:\n", " time_hist = np.asarray(fu1.time_hist) # extract time history\n", " num_hist = np.asarray(fu1.numbers_hist) # extract numbers history\n", " numF_points = collect_data(time_points, time_hist, num_hist[:,1]) # collect numbers of folded proteins\n", " numF_all.extend(numF_points)\n", "\n", "numF_eq = np.mean(numF_all) # estimate equilibrium number of folded proteins\n", "K_eq = numF_eq / (N_tot - numF_eq) # estimated equilibrium constant\n", "print(f'estimated equilibrium constant = {K_eq}')\n", "print(f'true equilibrium constant = kf / ku = {K}')" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "Then, we can estimate the relaxation rate $k$ from the slope of the trajectories by fitting the data to a straight line in log scale. For this we will collect data from time points *before* the equilibrium is reached, say $t < 0.1$." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "estimated relaxation rate = 9.765429679446495\n", "true relaxation rate = kf + ku = 10.0\n" ] } ], "source": [ "time_points = np.linspace(0, 0.1, 11) # choose time points\n", "numF_all = [] # collect N_F data from all simulations\n", "\n", "for fu1 in fu_list:\n", " time_hist = np.asarray(fu1.time_hist) # extract time history\n", " num_hist = np.asarray(fu1.numbers_hist) # extract numbers history\n", " numF_points = collect_data(time_points, time_hist, num_hist[:,1]) # collect numbers of folded proteins\n", " numF_all.extend(numF_points)\n", "\n", "time_all = np.tile(time_points, trials) # use `np.tile()` to repeat an array multiple times\n", "numF_all = np.array(numF_all)\n", "slope, intercept = np.polyfit(time_all, np.log(NFeq - numF_all), 1) # fit data in log scale to a line\n", "k_relax = -slope # estimated relaxation rate\n", "print(f'estimated relaxation rate = {k_relax}')\n", "print(f'true relaxation rate = kf + ku = {kf+ku}')" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "From these two combinations $K = k_f / k_u$ and $k = k_f + k_u$, we can eventually infer the values of $k_f$ and $k_u$ by\n", "\\begin{equation}\n", "k_f = \\frac{K k}{1+K} \\,, \\quad k_u = \\frac{k}{1+K}\n", "\\end{equation}" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "estimated kf = 8.779695718862367, ku = 0.9857339605841284\n", "true kf = 9.0, ku = 1.0\n" ] } ], "source": [ "kf_est = K_eq/(1+K_eq) * k_relax\n", "ku_est = 1/(1+K_eq) * k_relax\n", "print(f'estimated kf = {kf_est}, ku = {ku_est}')\n", "print(f'true kf = {kf}, ku = {ku}')" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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 }