Edit Figure: Figure 3.26: The repressilator genetic regulatory network

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[[Image:figure-3.26-repressilator_dynamics.png|320px]] Figure 3.26: The repressilator genetic regulatory network. (b) A simulation of a simple model for the repressilator, showing the oscillation of the individual protein concentrations. <nowiki> # example-3.18-repressilator.py - Transcriptional regulation # RMM, 29 Aug 2021 # # Figure 3.26: The repressilator genetic regulatory network. (a) A schematic # diagram of the repressilator, showing the layout of the genes in the # plasmid that holds the circuit as well as the circuit diagram # (center). (b) A simulation of a simple model for the repressilator, # showing the oscillation of the individual protein concentrations. # import control as ct import numpy as np import matplotlib.pyplot as plt # # Repressilator dynamics # # This function implements the basic model of the repressilator All # parameter values were taken from Nature. 2000 Jan 20; 403(6767):335-8. # # This model was developed by members of the 2003 Synthetic Biology Class # on Engineered Blinkers. # # Dynamics for the repressilator def repressilator(t, x, u, params): # store the state variables under more meaningful names mRNA_cI = x[0] mRNA_lacI = x[1] mRNA_tetR = x[2] protein_cI = x[3] protein_lacI = x[4] protein_tetR = x[5] # # set the parameter values # # set the max transcription rate in transcripts per second k_transcription_cI = params.get('k_transcription_cI', 0.5) k_transcription_lacI = params.get('k_transcription_lacI', 0.5) k_transcription_tetR = params.get('k_transcription_tetR', 0.5) # set the leakage transcription rate (ie transcription rate if # promoter region bound by repressor) in transcripts per second k_transcription_leakage = params.get('k_transcription_leakage', 5e-4) # Set the mRNA and protein degradation rates (per second) mRNA_half_life = params.get('mRNA_half_life', 120) # in seconds k_mRNA_degradation = np.log(2)/mRNA_half_life protein_half_life = params.get('protein_half_life', 600) # in seconds k_protein_degradation = np.log(2)/protein_half_life # proteins per transcript lifespan translation_efficiency = params.get('translation_efficiency', 20) average_mRNA_lifespan = 1/k_mRNA_degradation # proteins per transcript per sec k_translation = translation_efficiency/average_mRNA_lifespan # set the Hill coefficients of the repressors n_tetR = params.get('n_tetR', 2) n_cI = params.get('n_cI', 2) n_lacI = params.get('n_lacI', 2) # Set the dissociation constant for the repressors to their target promoters # in per molecule per second KM_tetR = params.get('KM_tetR', 40) KM_cI = params.get('KM_cI', 40) KM_lacI = params.get('KM_lacI', 40) # the differential equations governing the state variables: # mRNA concentration = transcription given repressor concentration - # mRNA degradation + transcription leakage dxdt = np.empty(6) dxdt[0] = k_transcription_cI/(1 + (protein_tetR / KM_tetR) ** n_tetR) - \ k_mRNA_degradation * mRNA_cI + k_transcription_leakage dxdt[1] = k_transcription_lacI/(1 + (protein_cI / KM_cI)**n_cI) - \ k_mRNA_degradation * mRNA_lacI + k_transcription_leakage dxdt[2] = k_transcription_tetR/(1 + (protein_lacI / KM_lacI) ** n_lacI) - \ k_mRNA_degradation * mRNA_tetR + k_transcription_leakage # protein concentration = translation - protein degradation dxdt[3] = k_translation*mRNA_cI - k_protein_degradation*protein_cI dxdt[4] = k_translation*mRNA_lacI - k_protein_degradation*protein_lacI dxdt[5] = k_translation*mRNA_tetR - k_protein_degradation*protein_tetR return dxdt # Define the system as an I/O system sys = ct.nlsys( updfcn=repressilator, outfcn=lambda t, x, u, params: x[3:], states=6, inputs=0, outputs=3) # Set up the plotting grid to match the layout in the book fig = plt.figure(constrained_layout=True) gs = fig.add_gridspec(2, 2) # # (b) A simulation of a simple model for the repressilator, showing the # oscillation of the individual protein concentrations. # fig.add_subplot(gs[0, 1]) # first row, second column # Initial conditions and time t = np.linspace(0, 20000, 1000) x0 = [1, 0, 0, 200, 0, 0] # Integrate the differential equation response = ct.input_output_response(sys, t, 0, x0) # Plot the results (protein concentrations) plt.plot(response.time/60, response.outputs[0], '-') plt.plot(response.time/60, response.outputs[1], '--') plt.plot(response.time/60, response.outputs[2], '-.') plt.axis([0, 300, 0, 5000]) plt.legend(("cI", "lacI", "tetR"), loc='upper right') plt.xlabel("Time [min]") # Axis labels plt.ylabel("Proteins per cell") plt.title("Repressilator simulation") # Plot title # Save the figure plt.savefig("figure-3.26-repressilator_dynamics.png", bbox_inches='tight') </nowiki>

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