def degradation_experiment():
"""Determine whether linear or pairwise models are more resistant to degradation"""
L = 10
N = 50
Ne = 5
nu = Ne - 1
sigma = 1
mu = -10
matrix = sample_matrix(L, sigma)
code = sample_code(L, sigma)
li_motif = sample_motif_cftp(matrix, mu, Ne, N)
pw_motif = sample_pw_motif_mh(code, N, Ne, mu, iterations=100000)[-1]
def li_log_fitness(motif):
eps = [score_seq(matrix, site) for site in motif]
return sum(-nu * log((1 + exp(ep - mu))) for ep in eps)
def pw_log_fitness(motif):
eps = map(lambda x: -log(x), pw_prob_sites(motif, code))
return sum(log(1 / (1 + exp(ep - mu))**nu) for ep in eps)
li_base_fit = li_log_fitness(li_motif)
li_mut_fits = [li_log_fitness(mutate_motif(li_motif)) for i in range(100)]
pw_base_fit = pw_log_fitness(pw_motif)
pw_mut_fits = [pw_log_fitness(mutate_motif(pw_motif)) for i in range(100)]
def prop((code, motif)):
code_p = [d.copy() for d in code]
i = random.randrange(len(code))
b1, b2 = random.choice("ACGT"), random.choice("ACGT")
code_p[i][(b1, b2)] += random.gauss(0, sigma)
motif_p = mutate_motif(motif)
return (code_p, motif_p)
def propose(matrix,motif,motif_prob=0.5):
"""Return a candidate (S,R) system by mutating either the motif or
the matrix"""
if random.random() < motif_prob:
return matrix,mutate_motif(motif)
else:
return mutate_matrix(matrix),motif
def match_ic_mi(N,
L,
des_ic,
des_mi,
iterations=50000,
take_stock=None,
eta=0.01,
alpha=1,
beta=0):
if take_stock is None:
take_stock = int((N * L) * log(N * L))
x = random_motif(L, N)
xs = [None] * iterations
ics = [0.0] * iterations
mis = [0.0] * iterations
alphas = [0.0] * iterations
betas = [0.0] * iterations
ic = motif_ic(x)
mi = total_motif_mi(x)
accepts = 0
for i in xrange(iterations):
# if i == iterations/2:
# eta *= 0.1
xp = mutate_motif(x)
icp = motif_ic(xp)
mip = total_motif_mi(xp)
log_y = (alpha * ic + beta * mi)
log_yp = (alpha * icp + beta * mip)
if log(random.random()) < log_yp - log_y:
accepts += 1
x = xp
ic = icp
mi = mip
ics[i] = (ic)
mis[i] = (mi)
xs[i] = (x)
#print sum(site.count("A") for site in x)
alphas[i] = (alpha)
betas[i] = (beta)
if i > 0 and i % take_stock == 0:
if i < iterations / 10:
mean_ic = mean(ics[i - take_stock:i])
mean_mi = mean(mis[i - take_stock:i])
alpha += eta * (des_ic - mean_ic) * exp(
-i / (10 * float(iterations)))
beta += eta * (des_mi - mean_mi) * exp(
-i / (10 * float(iterations)))
else:
mean_ic = mean(ics[i - take_stock:i])
mean_mi = mean(mis[i - take_stock:i])
alpha = poly1d(polyfit(ics[:i], alphas[:i], 1))(des_ic)
beta = poly1d(polyfit(mis[:i], betas[:i], 1))(des_mi)
fmt_string = (
"mean ic: % 1.2f, mean mi: % 1.2f, alpha: % 1.2f, beta: % 1.2f"
% (mean_ic, mean_mi, alpha, beta))
print i, "AR:", accepts / (i + 1.0), fmt_string
return xs, ics, mis, alphas, betas
def mutate((tf,motif)):
L = len(tf)
if random.random() < 0.5:
tfp = tf[:]
i = random.randrange(L)
tfp[i] = 1 - tf[i]
return (tfp,motif)
else:
return tf,mutate_motif(motif)
def degrade_motif(L,n):
motif = ["A"*L for i in range(n)]
#motif = random_motif(L,n)
column_ics = []
total_ics = []
for iteration in trange(n*L):
col_ic = motif_ic(motif,correct=False)
column_ics.append(col_ic)
total_ics.append(col_ic + pairwise_motif_mi(motif))
motif = mutate_motif(motif)
plt.plot(total_ics,column_ics)
plt.plot([0,2*L],[0,2*L],linestyle='--',color='b')
plt.xlabel("Total IC")
plt.ylabel("Column IC")
plt.title("n=%s, L=%s" % (n,L))
def flux_prob(motif, a, b, trials=10000):
"""determine probability of mutation pushing motif out of interval [a,b]"""
ic = motif_ic(motif)
lesser = 0
same = 0
greater = 0
for i in trange(trials):
icp = motif_ic(mutate_motif(motif))
if icp < a:
lesser += 1
elif a <= icp < b:
same += 1
else:
greater += 1
return lesser, same, greater
def propose_motif(matrix,motif):
return matrix,mutate_motif(motif)