def validate_sample_motif_neglect_fg2(iterations=50000):
"""compare fg_neglect sampling to MCMC"""
bio_motif = Escherichia_coli.LexA
n = len(bio_motif)
L = len(bio_motif[0])
matrix = [[-ep for ep in row] for row in make_pssm(bio_motif)]
ringer = ringer_motif(matrix,n)
Ne = 2.375
random_motifs = [sample_motif_neglect_fg(matrix,n,Ne) for i in trange(iterations)]
random_rhos = [motif_hamming_distance(ringer,motif) for motif in tqdm(random_motifs)]
random_log_fs = [log_fitness(matrix,motif,G) for motif in tqdm(random_motifs)]
random_ics = map(motif_ic,random_motifs)
_, chain = sella_hirsch_mh(matrix=matrix,init="ringer",Ne=Ne,n=n,iterations=iterations)
chain_rhos = [motif_hamming_distance(ringer,motif) for motif in tqdm(chain)]
chain_log_fs = [log_fitness(matrix,motif,G) for motif in tqdm(chain)]
chain_ics = map(motif_ic,chain)
plt.subplot(1,2,1)
plt.scatter(random_rhos,random_log_fs)
plt.scatter(chain_rhos,chain_log_fs,color='g')
plt.xlabel("rho")
plt.ylabel("log fitness")
plt.subplot(1,2,2)
plt.scatter(random_rhos,random_ics)
plt.scatter(chain_rhos,chain_ics,color='g')
plt.xlabel("rho")
plt.ylabel("IC")
def validate_sample_motif_neglect_fg():
"""compare fg_neglect sampling to random mutation: indeed shows better fitness at given rho"""
bio_motif = Escherichia_coli.LexA
n = len(bio_motif)
L = len(bio_motif[0])
matrix = [[-ep for ep in row] for row in make_pssm(bio_motif)]
ringer = ringer_motif(matrix,n)
random_motifs = [mutate_motif_k_times(ringer,k) for k in range(n*L)]
random_motifs2 = [sample_motif_neglect_fg(matrix,n,Ne) for Ne in np.linspace(1,10,n*L)]
random_rhos = [motif_hamming_distance(ringer,motif) for motif in random_motifs]
random_log_fs = [log_fitness(matrix,motif,G) for motif in random_motifs]
random_rhos2 = [motif_hamming_distance(ringer,motif) for motif in random_motifs2]
random_log_fs2 = [log_fitness(matrix,motif,G) for motif in random_motifs2]
plt.plot(random_rhos,random_log_fs)
plt.plot(random_rhos2,random_log_fs2)
plt.plot(random_rhos3,random_log_fs3)
def entropy_drift_analysis(sigma=2, color='b', color_p='g'):
"""why is convergence so difficult to obtain for, say, sigma = 2? Explore selection/mutation balance."""
n = 16
L = 16
matrix = sample_matrix(L, sigma)
ringer = ringer_motif(matrix, n)
mutants = [
iterate(mutate_motif, ringer, i) for i in trange(256)
for j in range(10)
]
dists = [
motif_hamming_distance(ringer, mutant) for mutant in tqdm(mutants)
]
fs = [log_fitness(matrix, mutant, G) for mutant in tqdm(mutants)]
fps = []
trials = 100
for mutant in tqdm(mutants):
nexts = []
f = log_fitness(matrix, mutant, G)
for i in range(trials):
mutant_p = mutate_motif(mutant)
fp = log_fitness(matrix, mutant_p, G)
if log(random.random()) < fp - f:
nexts.append(fp)
else:
nexts.append(f)
fps.append(mean(nexts))
plt.subplot(3, 1, 1)
plt.scatter(dists, fs, color=color, marker='.')
plt.scatter(dists, fps, color=color_p, marker='.')
#plt.semilogy()
plt.subplot(3, 1, 2)
plt.scatter(dists, [(f - fp) / f for (f, fp) in zip(fs, fps)],
color=color,
marker='.')
plt.plot([0, len(fs)], [0, 0], linestyle='--', color='black')
plt.subplot(3, 1, 3)
diffs = [fp - f for f, fp in zip(fs, fps)]
plt.scatter(fs, diffs, marker='.', color=color)
interpolant = poly1d(polyfit(fs, diffs, 1))
plt.plot(*pl(interpolant, [min(fs), max(fs)]))
plt.plot([min(fs), max(fs)], [0, 0], linestyle='--', color='black')
minx, maxx = min(fs + fs), max(fs + fps)
def plot_matrix_chain_ringer_distance((matrix, chain)):
n = len(chain[0])
ringer = ringer_motif(matrix, n)
plt.plot([motif_hamming_distance(motif, ringer) for motif in tqdm(chain)])
def plot_matrix_chain_distance_from_first((matrix, chain)):
init = chain[0]
plt.plot([motif_hamming_distance(m, init) for m in tqdm(chain)])
def rho_fitness_plot(matrix_chain):
matrix, chain = matrix_chain
n = len(chain[0])
L = len(chain[0][0])
N = n * L
ringer = ringer_motif(matrix, n)
print "fs"
fs = [log10(fitness(matrix, motif, G)) for motif in tqdm(chain)]
print "rhos"
rhos = [motif_hamming_distance(ringer, motif) for motif in tqdm(chain)]
print "ics"
ics = [motif_ic(motif) for motif in tqdm(chain)]
plt.xlabel("Distance from ringer")
plt.ylabel("fitness")
print "perturbations"
perturbations = [
mutate_motif_k_times(ringer, random.randrange(N)) for _ in tqdm(chain)
]
print "fs"
perturb_fs = [
log10(fitness(matrix, motif, G)) for motif in tqdm(perturbations)
]
print "rhos"
perturb_rhos = [
motif_hamming_distance(ringer, motif) for motif in tqdm(perturbations)
]
print "ics"
perturb_ics = [motif_ic(motif) for motif in tqdm(perturbations)]
print "log odds"
log_odds = [
sample_log_odds(matrix, n, 3)
for lamb in tqdm(np.linspace(0.5, 5, 10000))
]
print "fs"
log_odds_fs = [
log10(fitness(matrix, motif, G)) for motif in tqdm(log_odds)
]
print "rhos"
log_odds_rhos = [
motif_hamming_distance(ringer, motif) for motif in tqdm(log_odds)
]
print "ics"
log_odds_ics = [motif_ic(motif) for motif in tqdm(log_odds)]
plt.subplot(1, 3, 1)
plt.scatter(perturb_rhos, perturb_fs, color='g')
plt.scatter(log_odds_rhos, log_odds_fs, color='r')
plt.scatter(rhos, fs, color='b')
plt.xlabel("rho")
plt.ylabel("log f")
plt.subplot(1, 3, 2)
plt.scatter(perturb_rhos, perturb_ics, color='g')
plt.scatter(log_odds_rhos, log_odds_ics, color='r')
plt.scatter(rhos, ics, color='b')
plt.xlabel("rho")
plt.ylabel("IC")
plt.subplot(1, 3, 3)
plt.scatter(perturb_ics, perturb_fs, color='g')
plt.scatter(log_odds_ics, log_odds_fs, color='r')
plt.scatter(ics, fs, color='b')
plt.xlabel("IC")
plt.ylabel("fs")
def log_dprop(motif, _):
k = motif_hamming_distance(ringer,
motif) # number of mutations from ringer
#return log_choose(N,k) + k * log(p) + (N-k)*log(1-p) + k*log(1/3.0)
#return -log(N) + k * log(1/3.0)
return log(ps[k]) - log_choose(N, k) + k * log(1 / 3.0)
def dprop(motif, _):
k = motif_hamming_distance(ringer,
motif) # number of mutations from ringer
#return choose_reference(N,k) * p**k * (1-p)**(N-k) * (1/3.0)**k
#return 1.0/N * (1/3.0)**k
return ps[k] * choose(N, k) * (1 / 3.0)**k
def weight(motif):
k = motif_hamming_distance(ringer,
motif) # number of mutations from ringer
return 4**k
def log_dprop(motif, _):
k = motif_hamming_distance(ringer,
motif) # number of mutations from ringer
### return log(ps[k]) + k * log(1/3.0) ### XXX BE LESS RETARDED ABOUT THIS XXX
# p(k)*(1/choose(N,k)) * (1/3.0)**k
return log(ps[k]) - log_choose(N, k) + k * log(1.0 / 3)
def plot_log_fs_vs_log_dprops(Ne=5,
n=16,
L=16,
G=5 * 10**6,
sigma=1,
matrix=None,
x0=None,
iterations=50000,
lamb=1):
if matrix is None:
matrix = sample_matrix(L, sigma)
nu = Ne - 1
N = n * L
ringer = ringer_motif(matrix, n)
ps = normalize([exp(-lamb * i) for i in range(N)])
#ps = [1.0/N]*N
def log_f(motif):
return log_fitness(matrix, motif, G)
def prop(motif):
k = inverse_cdf_sample(range(N), ps)
motif_p = mutate_motif_k_times(ringer, k)
return motif_p
def log_dprop(motif, _):
k = motif_hamming_distance(ringer,
motif) # number of mutations from ringer
### return log(ps[k]) + k * log(1/3.0) ### XXX BE LESS RETARDED ABOUT THIS XXX
# p(k)*(1/choose(N,k)) * (1/3.0)**k
return log(ps[k]) - log_choose(N, k) + k * log(1.0 / 3)
def weight(motif):
k = motif_hamming_distance(ringer,
motif) # number of mutations from ringer
return 4**k
matrix_probs = [normalize([exp(-ep) for ep in row]) for row in matrix]
def prop_fanciful(motif):
return [
"".join(
[inverse_cdf_sample("ACGT", probs) for probs in matrix_probs])
for i in xrange(n)
]
def dprop(motif, _):
k = motif_hamming_distance(ringer,
motif) # number of mutations from ringer
#return choose_reference(N,k) * p**k * (1-p)**(N-k) * (1/3.0)**k
#return 1.0/N * (1/3.0)**k
return ps[k] * choose(N, k) * (1 / 3.0)**k
def log_dprop(motif, _):
k = motif_hamming_distance(ringer,
motif) # number of mutations from ringer
#return log_choose(N,k) + k * log(p) + (N-k)*log(1-p) + k*log(1/3.0)
#return -log(N) + k * log(1/3.0)
return log(ps[k]) - log_choose(N, k) + k * log(1 / 3.0)
def log_dprop_fanciful(motif, _):
return sum(
log(matrix_probs[i]["ACGT".index(b)]) for site in motif
for i, b in enumerate(site))
motifs = [prop_fanciful(None) for i in trange(iterations)]
log_fs = np.array(map(log_f, tqdm(motifs)))
log_dprops = np.array(
[log_dprop_fanciful(motif, None) for motif in tqdm(motifs)])
ws = np.exp(log_fs - log_dprops)
ws = ws / np.sum(ws)
rhos = np.array(
[motif_hamming_distance(motif, ringer) for motif in motifs])
print "mean log_f:", ws.dot(log_fs)
print "mean rho:", ws.dot(rhos)
plt.subplot(2, 3, 1)
plt.title("log fitness vs proposal")
plt.scatter(log_fs, log_dprops)
minval, maxval = min(log_fs + log_dprops), max(log_fs + log_dprops)
plt.plot([minval, maxval], [minval, maxval], linestyle='--')
plt.subplot(2, 3, 2)
#plt.scatter(exp,log_fs,rhos)
plt.title("ringer dstance vs weight")
plt.scatter(rhos, np.log10(ws))
plt.subplot(2, 3, 3)
#plt.scatter(exp,log_fs,rhos)
plt.title("log fitness vs wieght")
plt.scatter(log_fs, np.log10(ws))
plt.subplot(2, 3, 5)
#plt.scatter(exp,log_fs,rhos)
plt.scatter(rhos, log_fs)
plt.subplot(2, 3, 6)
#plt.scatter(exp,log_fs,rhos)
plt.scatter(log_fs, np.log10(ws))