Difference between revisions of "Python:Simulating DNA Melting"
From Course Wiki
(→To Do) |
(→Code) |
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import matplotlib.pyplot as plt | import matplotlib.pyplot as plt | ||
− | def quickplot( | + | def quickplot(xvector, yvector, title, xlabel, ylabel): |
""" | """ | ||
− | Wrapper function for | + | Wrapper function for making a simple plot using matplotlib.pyplot |
""" | """ | ||
− | plt.plot( | + | plt.plot(xvector, yvector) |
plt.title(title) | plt.title(title) | ||
plt.xlabel(xlabel) | plt.xlabel(xlabel) | ||
Line 66: | Line 66: | ||
return numpy.array(result) | return numpy.array(result) | ||
− | def | + | def diffedCurve(expt, plot=True): |
""" | """ | ||
− | Takes an Experiment and | + | Takes an Experiment and calculates a differentiated melting curve. |
− | + | Optionally plots it. | |
− | + | ||
""" | """ | ||
expt.dTemp = middles(expt.temp) | expt.dTemp = middles(expt.temp) | ||
expt.diffDsDnaFraction = numpy.diff(expt.dsDnaFraction) | expt.diffDsDnaFraction = numpy.diff(expt.dsDnaFraction) | ||
− | quickplot(expt.dTemp, -1 * expt.diffDsDnaFraction, | + | if plot: |
− | + | quickplot(expt.dTemp, -1 * expt.diffDsDnaFraction, | |
+ | "Inverted Derivative of Melting Curve", | ||
+ | "Temperature (K)", "Delta dsDNA Fraction") | ||
− | def makeIdeal(): | + | def makeIdeal(plot=True): |
""" | """ | ||
Returns an ideal/theoretical DNA melting experiment. | Returns an ideal/theoretical DNA melting experiment. | ||
+ | Optionally plots it. | ||
""" | """ | ||
ideal = Experiment() | ideal = Experiment() | ||
Line 88: | Line 90: | ||
ideal.dsDnaFraction = DnaFraction(ideal.concentration, ideal.temp, | ideal.dsDnaFraction = DnaFraction(ideal.concentration, ideal.temp, | ||
ideal.deltaS, ideal.deltaH) | ideal.deltaS, ideal.deltaH) | ||
+ | if plot: | ||
+ | quickplot(ideal.temp, ideal.dsDnaFraction, | ||
+ | "Ideal DNA Melting Curve", | ||
+ | "Temperature (K)", "dsDNA Fraction") | ||
return ideal | return ideal | ||
Line 247: | Line 253: | ||
# If you run this script, plots will appear one after the other, | # If you run this script, plots will appear one after the other, | ||
# following the sequence of the write-up. | # following the sequence of the write-up. | ||
− | # If you encounter a bug with the script drawing multiple plots in one run | + | # If you encounter a bug with the script drawing multiple plots in one run |
− | # | + | # (may happen on Mac OSX), change plot=True to plot=False as desired to plot |
− | + | # only one thing at a time. | |
+ | # Change other parameters as desired to add or remove noise. | ||
− | # | + | # ideal curve |
− | + | ideal = makeIdeal(plot=True) | |
− | + | diffedCurve(ideal, plot=True) | |
− | + | ||
− | # | + | # simulated realistic data |
sim = makeSimulated() | sim = makeSimulated() | ||
simCooling(sim, plot=True) | simCooling(sim, plot=True) | ||
− | simRTD(sim, plot=True) | + | simRTD(sim, addNoise=True, plot=True) |
− | simFluorescenceSignal(sim, plotFluor=True, plotSignal=True) | + | simFluorescenceSignal(sim, gaussianNoise=True, shotNoise=True, |
+ | photobleaching=True, plotFluor=True, plotSignal=True) | ||
#write out matlab file of sim data | #write out matlab file of sim data |
Revision as of 14:37, 5 April 2011
Hi. I'm not really finished, but I work!
For now, you can copy and run the following Python script, and follow along with the explanatory writeup from the Matlab version while it runs. In addition to Python, you will need to have installed the packages numpy, scipy, and matplotlib.
To Do
- Make the "ideal" part work more like the "sim" part, with the plot=True or False parameter
- Test on 309 lab computers and Athena
- This code was written before TECs were included in the lab, which is why it includes only passive cooling and not forced heating. Add forced heating. If I finish making the heating control circuit work with the H-bridge, also add forced cooling.
Code
# Simulating DNA Melting in Python # 20.309 # Translated from the Matlab by KAD, 4 Apr 2011 import numpy import scipy.io as sio import matplotlib.pyplot as plt def quickplot(xvector, yvector, title, xlabel, ylabel): """ Wrapper function for making a simple plot using matplotlib.pyplot """ plt.plot(xvector, yvector) plt.title(title) plt.xlabel(xlabel) plt.ylabel(ylabel) plt.show() class Experiment: """ Empty class definition -- works like a struct in C or Matlab. """ pass def DnaFraction(Ct, T, DeltaS, DeltaH, R=1.987): """ Returns the fraction of dsDNA in a solution containing equal concentrations of two complementary ssDNA oligos, as a function of total [DNA], temperature, entropy of annealing, and enthalpy of annealing. Default units are mole, calorie, kelvin. For other unit systems, supply the appropriate value for the optional gas constant parameter. T can be a single value or a numpy.array of values. """ # Compute Ct * Keq CtKeq = Ct * numpy.exp(DeltaS/R - DeltaH/(R*T)) # Compute f f = (1 + CtKeq - numpy.sqrt(1 + 2*CtKeq)) / CtKeq return f def middles(arr): """ Returns a new numpy array, 1 element shorter than the input array, whose values come from averaging each two adjacent values in the input. """ result = [] for i in range(0, len(arr) - 1): element = (arr[i] + arr[i+1]) / 2.0 result.append(element) return numpy.array(result) def diffedCurve(expt, plot=True): """ Takes an Experiment and calculates a differentiated melting curve. Optionally plots it. """ expt.dTemp = middles(expt.temp) expt.diffDsDnaFraction = numpy.diff(expt.dsDnaFraction) if plot: quickplot(expt.dTemp, -1 * expt.diffDsDnaFraction, "Inverted Derivative of Melting Curve", "Temperature (K)", "Delta dsDNA Fraction") def makeIdeal(plot=True): """ Returns an ideal/theoretical DNA melting experiment. Optionally plots it. """ ideal = Experiment() ideal.temp = numpy.array(range(0, 100)) + 273.15 ideal.deltaS = -184 ideal.deltaH = -71E3 ideal.concentration = 1E-6 ideal.dsDnaFraction = DnaFraction(ideal.concentration, ideal.temp, ideal.deltaS, ideal.deltaH) if plot: quickplot(ideal.temp, ideal.dsDnaFraction, "Ideal DNA Melting Curve", "Temperature (K)", "dsDNA Fraction") return ideal def makeSimulated(): """ Returns a simulated experimental run, from which we'll produce realistic noisy data. """ sim = Experiment() sim.concentration = 1e-6 sim.deltaS = -184 sim.deltaH = -71e3 sim.initTemp = 363 sim.finalTemp = 293 sim.sampleRate = 1 sim.duration = 900 # create time vector (seconds) sim.time = numpy.array(numpy.arange(0.0, sim.duration, 1.0/sim.sampleRate)) return sim def simCooling(sim, plot=True): """ Accepts a simulated experiment and calculates its temperature over time, simulating exponential passive cooling. """ coolingConst = 180.0 #tau = 180s = 3min # T(t) = (Tf-Ti)e^-(t/tau) + Tf sim.temp = ((sim.initTemp - sim.finalTemp) * numpy.exp(-sim.time / coolingConst)) + sim.finalTemp if plot: quickplot(sim.time, sim.temp, "Simulated Temperature vs. Time", "Time (sec)", "Temperature (K)") def simRTD(sim, addNoise=True, plot=True): """ Simulates RTD voltage (proportional to temp) vs. time, either with or without noise. """ #Fix it so you don't have to run simCooling first. try except # R_RTD = 1000 + 3.85(T-273) (ohms) sim.rRTD = 1000 + 3.85 * (sim.temp - 273) # RTD is in a voltage divider. # V across RTD = total voltage * (RTD / (other+RTD)). vPower = 15 #15V rOther = 20e3 #20kohms sim.vRTD = vPower * (sim.rRTD / (rOther + sim.rRTD)) if addNoise: #gaussian noise with stdev=1mV noise = numpy.random.normal(scale=0.001, size=len(sim.vRTD)) sim.vRTD += noise if plot: quickplot(sim.time, sim.vRTD, "Simulated RTD Voltage vs. Time", "Time (sec)", "RTD Voltage (V)") def simFluorescenceSignal(sim, gaussianNoise=True, shotNoise=True, photobleaching=True, plotFluor=True, plotSignal=True): """ Calculates dsDNA fraction vs. time, scales to obtain fluorescence signal, and optionally adds noise and photobleaching. """ title = "Fluorescence Signal Voltage vs. Time" sim.dsDnaFraction = DnaFraction(sim.concentration, sim.temp, sim.deltaS, sim.deltaH) #simulate photobleaching of signal if photobleaching: #Set bleaching const such that 1/2 of fluorphores fail during experiment BleachingConstant = 0.5**(1.0/900) #compute difference sim.diffDsDnaFraction = numpy.diff(sim.dsDnaFraction) #initialize empty array sim.dsDnaFractionBleached = numpy.empty(len(sim.dsDnaFraction)) #set initial condition for difference eqn sim.dsDnaFractionBleached[0] = 0.05 #For loop to compute difference equation for i in range(1, len(sim.dsDnaFraction)): sim.dsDnaFractionBleached[i] = BleachingConstant * sim.dsDnaFractionBleached[i-1] + sim.diffDsDnaFraction[i-1] title += "\n(+ Photobleaching)" #Moving variable names around to make the other code happy sim.dsDnaFractionUnbleached = sim.dsDnaFraction sim.dsDnaFraction = sim.dsDnaFractionBleached if plotFluor: quickplot(sim.time, sim.dsDnaFraction, "Relative Fluorescence vs. Time", "Time (sec)", "Relative Fluorescence (AU)") #Scale curve to simulate voltage output of photodiode / amplifier. #Amplifier range between 5 and 9 volts output ampRange = numpy.random.uniform(low=5.0, high=9.0) #Minimum between +/- 1 ampMin = numpy.random.uniform(low=-1.0, high=1.0) #Scale output sim.fluorSignal = ampRange * sim.dsDnaFraction + ampMin #gaussian random noise if gaussianNoise: #gaussian noise with stdev=10mV noise = numpy.random.normal(scale=0.01, size=len(sim.fluorSignal)) sim.fluorSignal += noise title += " (+ Gaussian Noise)" #shot (impulse) noise if shotNoise: # Technically this should be poisson-distributed, but generating # poisson noise is actually not trivial. An acceptable substitute is # to make every sample have some probability P(spike) of being a spike # and probability 1-P(spike) of being the actual fluorescence sample. # (See the book "Numerical recipes in $language".) #Uniformly distributed random numbers noise = numpy.random.rand(len(sim.fluorSignal)) #Probability of spike on any given sample spikeProbability = 1.0/75 #Turn list of probabilities into list of zeros and 10V spikes noise = map(lambda i: 10 if i<spikeProbability else 0, noise) #Add in spikes sim.fluorSignal = [max(s, n) for s, n in zip(sim.fluorSignal, noise)] title += " (+ Shot Noise)" if plotSignal: quickplot(sim.time, sim.fluorSignal, title, "Time (sec)", "Fluorescence Signal Voltage (V)") def formatDataForMatlab(rtd, fluor, filename): """ Outputs a .mat file in the exact style of the data you get from running the LabView VM, i.e. an Nx2 matrix with RTD voltages in the first column and fluorescence signal voltages in the second. Inputs: two numpy arrays. """ #Turn 1D numpy arrays into columns in a single matrix simData = numpy.column_stack((rtd, fluor)) #Write matlab file sio.savemat(filename, {"simData": simData}) # If you run this script, plots will appear one after the other, # following the sequence of the write-up. # If you encounter a bug with the script drawing multiple plots in one run # (may happen on Mac OSX), change plot=True to plot=False as desired to plot # only one thing at a time. # Change other parameters as desired to add or remove noise. # ideal curve ideal = makeIdeal(plot=True) diffedCurve(ideal, plot=True) # simulated realistic data sim = makeSimulated() simCooling(sim, plot=True) simRTD(sim, addNoise=True, plot=True) simFluorescenceSignal(sim, gaussianNoise=True, shotNoise=True, photobleaching=True, plotFluor=True, plotSignal=True) #write out matlab file of sim data formatDataForMatlab(sim.vRTD, sim.fluorSignal, "simData.mat")