def oppg_2_4():
N = 15
T = 10**(-6)
d = 10000
# Number of protein plots
calculations = 10
mean_energy = np.zeros(calculations)
for i in range(len(mean_energy)):
protein = Protein(N, T)
energy = np.zeros(d)
for j in range(d):
protein.twist()
energy[j] = protein.energy()
mean_energy[i] = np.mean(energy)
plt.figure('exercise-2-4')
plt.title('Mean energy at $T = 0$')
plt.grid()
plt.xlabel('Calculation #')
plt.ylabel('$<$E$>$')
plt.xticks(np.arange(0, calculations, 1))
plt.plot(np.arange(calculations),
mean_energy,
color='#000000',
markerfacecolor='#000000',
linestyle='None',
marker='o')
plt.show()
def oppg_4_3(return_protein):
T_step = -30 # increase the temp by this amount each iteration
N = 15
T_max = 1500
d = 600
N_T = (T_max // abs(T_step))
count = 0
# Matrix with all diameters for all twists and temp
length = np.zeros((N_T, d))
# Vector with mean energy for each temp
L_mean = np.zeros(N_T)
# Calculate energy
protein = Protein(N, T_max)
for j in range(T_max, -T_step, T_step):
print(j)
protein.change_temp(j)
for i in range(0, d):
protein.twist()
length[count][i] = protein.diameter()
L_mean[count] = np.mean(length[count])
count += 1
protein.change_temp(10**(-6))
for i in range(0, d):
protein.twist()
length[N_T - 1] = protein.diameter()
L_mean[N_T - 1] = np.mean(length[N_T - 1])
L_mean = L_mean[::-1]
# Create temp vector for plotting the mean diameter
x = np.arange(0, T_max, -T_step)
# Plot the mean diameter
plt.figure('exercise-4-3')
plt.title('Mean diameter')
plt.grid()
plt.xlabel('T')
plt.ylabel('$<$L$>$')
plt.plot(x, L_mean, color='#000000', linestyle='-')
plt.show()
if return_protein:
return protein, N
def oppg_4_1():
T_step = -30 # increase the temp by this amount each iteration
N = 15
T_max = 1500
d = 600
N_T = (T_max // abs(T_step)) * d
count = 0
# Vector with energy
energy = np.zeros(N_T)
# Calculate energy
protein = Protein(N, T_max)
for j in range(T_max, -T_step, T_step):
print(j)
protein.change_temp(j)
for i in range(0, d):
protein.twist()
energy[count] = protein.energy()
count += 1
protein.change_temp(10**(-6))
for i in range(0, d):
protein.twist()
energy[count] = protein.energy()
count += 1
# Create temp vector for plotting the energy
x = np.arange(0, N_T)
# Plot the energy
plt.figure('exercise-4-1')
plt.title('Protein energy')
plt.grid()
plt.xlabel('# twists')
plt.ylabel('Energy')
labels = []
for i in range(0, N_T, d):
if (i % (N_T / 10)) == 0:
labels.append(str(i))
else:
labels.append("")
plt.xticks(np.arange(0, N_T, d), labels)
plt.plot(x, energy, color='#000000', linestyle='-', linewidth=0.3)
plt.show()
def oppg_4_2():
T_step = -30 # increase the temp by this amount each iteration
N = 30
T_max = 1500
d = 600
N_T = (T_max // abs(T_step))
count = 0
# Matrix with all energies for all twists and temp
epsilon = np.zeros((N_T, d))
# Vector with mean energy for each temp
e_mean = np.zeros(N_T)
# Calculate energy
protein = Protein(N, T_max)
for j in range(T_max, -T_step, T_step):
print(j)
protein.change_temp(j)
for i in range(0, d):
protein.twist()
epsilon[count][i] = protein.energy()
e_mean[count] = np.mean(epsilon[count])
count += 1
protein.change_temp(10**(-6))
for i in range(0, d):
protein.twist()
epsilon[N_T - 1] = protein.energy()
e_mean[N_T - 1] = np.mean(epsilon[N_T - 1])
e_mean = e_mean[::-1]
# Create temp vector for plotting the mean energy
x = np.arange(0, T_max, -T_step)
# Plot the mean energy
plt.figure('exercise-4-2')
plt.title('Mean energy')
plt.grid()
plt.xlabel('T')
plt.ylabel('$<$E$>$')
plt.plot(x, e_mean, color='#000000', linestyle='-')
plt.show()
def oppg_3():
T_step = 5 # Increase the temp by this amount each iteration
N = 15
T = 10**(-6) # Define temperature CLOSE to zero to avoid division by zero
s = 0.003
d_max = 10000
T_max = 1500
N_T = T_max // T_step
# Matrix with all diameters for all twists and temps
length = np.zeros((N_T, d_max))
# Vector with mean energy for each temp
L_mean = np.zeros(N_T)
# Calculate mean diameter for temp close to zero
protein = Protein(N, T)
for i in range(0, d_max):
protein.twist()
length[0][i] = protein.diameter()
L_mean[0] = np.mean(length[0][:d_max])
# Calculate mean diameter for all other temps up to T_max
for j in range(1, N_T):
print(j)
protein = Protein(N, j * T_step)
d = int(np.ceil(d_max * np.exp(-s * (j * T_step))))
for i in range(0, d):
protein.twist()
length[j][i] = protein.diameter()
L_mean[j] = np.mean(length[j][:d])
# Create temp vector for plotting the mean diameter
x = np.arange(0, T_max, T_step)
# Plot the mean diameter
plt.figure('exercise-3')
plt.title('Mean diameter')
plt.grid(color='#ffffff', linestyle='-')
plt.xlabel('T')
plt.ylabel('$<L>$')
plt.plot(x, L_mean, color='#000000', linestyle='-')
plt.show()
def oppg_2_2():
N = 15
T_0 = 10**(-6)
T_500 = 500
d = 5000
x = np.arange(0, d)
protein1 = Protein(N, T_0)
protein2 = Protein(N, T_500)
energy1 = np.zeros(d)
energy2 = np.zeros(d)
for i in range(d):
protein1.twist()
protein2.twist()
energy1[i] = protein1.energy()
energy2[i] = protein2.energy()
plt.figure('exercise-2-2')
plt.suptitle('Binding energy')
# Plot for T = 0 Kelvin
plt.subplot(121)
plt.title('$T = 0$')
plt.grid()
plt.xlabel('$\log$ # twists')
plt.ylabel('E')
plt.semilogx(x, energy1, color='#000000', linestyle='-')
# Plot for T = 500 Kelvin
plt.subplot(122)
plt.title('$T = 500$')
plt.xlabel('# twists')
plt.ylabel('E')
plt.grid()
plt.plot(x, energy2, color='#000000', linestyle='-', linewidth=0.7)
plt.show()
def oppg_1():
N = 10
T = 100
# Create the protein object
protein = Protein(N, T)
# Start subplot - 1 twist
plt.figure('exercise-1')
plt.suptitle('Protein folding')
plt.subplot(131)
# Create vectors for plotting the protein
x1 = []
y1 = []
for i in range(N):
x1.append(int(protein.matrix[i][0]))
y1.append(int(protein.matrix[i][1]))
# Plot the unfolded protein
plt.grid()
plt.xlim(0, N - 1)
plt.ylim(0, N - 1)
plt.xticks(np.arange(0, N, 1))
plt.yticks(np.arange(0, N, 1))
plt.plot(x1, y1)
plt.plot(x1,
y1,
color='#000000',
linestyle='-',
marker='o',
markerfacecolor='#aeaeae',
markersize='12')
for i in range(1, N + 1):
plt.annotate(i, (x1[i - 1], y1[i - 1]),
xytext=(x1[i - 1] + 0.1, y1[i - 1] + 0.1))
plt.subplot(132)
# Perform the first twist
protein.twist()
x2 = []
y2 = []
for i in range(N):
x2.append(int(protein.matrix[i][0]))
y2.append(int(protein.matrix[i][1]))
# Plot the once-folded protein
plt.grid()
plt.xlim(0, N - 1)
plt.ylim(0, N - 1)
plt.xticks(np.arange(0, N, 1))
plt.yticks(np.arange(0, N, 1))
plt.plot(x2, y2)
plt.plot(x2,
y2,
color='#000000',
linestyle='-',
marker='o',
markerfacecolor='#aeaeae',
markersize='12')
for i in range(1, N + 1):
plt.annotate(i, (x2[i - 1], y2[i - 1]),
xytext=(x2[i - 1] + 0.1, y2[i - 1] + 0.1))
plt.subplot(133)
# Perform the second twist
protein.twist()
x3 = []
y3 = []
for i in range(N):
x3.append(int(protein.matrix[i][0]))
y3.append(int(protein.matrix[i][1]))
# Plot the twice-folded protein
plt.grid()
plt.xlim(0, N - 1)
plt.ylim(0, N - 1)
plt.xticks(np.arange(0, N, 1))
plt.yticks(np.arange(0, N, 1))
plt.plot(x3, y3)
plt.plot(x3,
y3,
color='#000000',
linestyle='-',
marker='o',
markerfacecolor='#aeaeae',
markersize='12')
for i in range(1, N + 1):
plt.annotate(i, (x3[i - 1], y3[i - 1]),
xytext=(x3[i - 1] + 0.1, y3[i - 1] + 0.1))
plt.show()