def sample_motif_cftp_param_study():
"""Examine dependence of IC on sigma, Ne"""
grid_points = 10
sigmas = np.linspace(0.5,10,grid_points)
Nes = np.linspace(1,10,grid_points)
trials = 3
n = 20
L = 10
def f(sigma, Ne):
matrix = sample_matrix(L, sigma)
mu = approx_mu(matrix, 10*n)
return motif_ic(sample_motif_cftp(matrix, mu, Ne, n))
ics = [[(mean(f(sigma, Ne) for _ in range(trials)))
for sigma in sigmas] for Ne in tqdm(Nes,desc="ic grid")]
plt.contourf(sigmas, Nes,ics)
plt.colorbar()
#bio_motifs = [getattr(Escherichia_coli,tf) for tf in Escherichia_coli.tfs]
bio_sigmas = [sigma_from_matrix(pssm_from_motif(motif,pc=1))
for motif in bio_motifs]
bio_ics = [motif_ic(motif) for motif in bio_motifs]
#griddata((sigmas,Nes),ics)
interp = interp2d(sigmas,Nes,ics)
bio_Nes = [bisect_interval(lambda Ne:interp(show(bio_sigma),Ne)-bio_ic,0,20)
for bio_sigma, bio_ic in zip(bio_sigmas,bio_ics)]
plt.scatter(sigm)
def spoof_motifs(motif,
num_motifs=10,
trials=1,
sigma=None,
Ne_tol=10**-4,
double_sigma=True):
N = len(motif)
L = len(motif[0])
copies = 10 * N
if sigma is None:
sigma = sigma_from_matrix(pssm_from_motif(motif, pc=1))
epsilon = (1 + double_sigma) * sigma # 15 Jan 2016
print "sigma:", sigma
bio_ic = motif_ic(motif)
def f(Ne):
ps = ps_from_copies(sigma, Ne, L, copies)
motifs = [
sample_motif(epsilon, Ne, L, copies, n, ps=ps)
for i in range(trials)
]
return mean(map(motif_ic, motifs)) - bio_ic
Ne = log_regress_spec2(f, [1, 10], tol=10**-3)
return [sample_motif(sigma, Ne, L, copies, n) for _ in range(num_motifs)]
def spoof_motif_cftp(motif, num_motifs=10, trials=1, sigma=None,Ne_tol=10**-2,verbose=False):
n = len(motif)
L = len(motif[0])
copies = 10*n
if sigma is None: sigma = sigma_from_matrix(pssm_from_motif(motif,pc=1))
print "sigma:", sigma
bio_ic = motif_ic(motif)
matrix = sample_matrix(L, sigma)
mu = approx_mu(matrix, copies=10*n, G=5*10**6)
print "mu:", mu
def f(Ne):
motifs = [sample_motif_cftp(matrix, mu, Ne, n, verbose=verbose)
for i in trange(trials)]
return mean(map(motif_ic,motifs)) - bio_ic
# lb = 1
# ub = 10
# while f(ub) < 0:
# ub *= 2
# print ub
x0s = [2,10]#(lb + ub)/2.0
# print "choosing starting seed for Ne"
# fs = map(lambda x:abs(f(x)),x0s)
# print "starting values:",x0s,fs
# x0 = x0s[argmin(fs)]
# print "chose:",x0
# Ne = bisect_interval_noisy_ref(f,x0,lb=1,verbose=True)
Ne = log_regress_spec2(f,x0s,tol=Ne_tol)
print "Ne:",Ne
return [sample_motif_cftp(matrix, mu, Ne, n) for _ in trange(num_motifs)]
def spoof_motif_ref(motif,
num_motifs=10,
trials=10,
sigma=None,
Ne_tol=10**-4):
n = len(motif)
L = len(motif[0])
copies = 10 * n
if sigma is None:
sigma = sigma_from_matrix(pssm_from_motif(motif, pc=1))
print "sigma:", sigma
bio_ic = motif_ic(motif)
def f(Ne):
ps = ps_from_copies(sigma, Ne, L, copies)
motifs = [
sample_motif(sigma, Ne, L, copies, n, ps=ps) for i in range(trials)
]
return mean(map(motif_ic, motifs)) - bio_ic
lb = 1
ub = 2
while f(ub) < 0:
ub *= 2
ub *= 2 # once more for good measure
x0 = (lb + ub) / 2.0
print "Ne guess:", x0
Nes = [
bisect_interval_noisy(f, x0=x0, tolerance=Ne_tol, lb=1)
for i in range(3)
]
Ne = mean(Nes)
print "Nes:", Nes, Ne
return [sample_motif(sigma, Ne, L, copies, n) for _ in range(num_motifs)]
def resample_from_post_chain(chain, N):
"""given chain of the form [(mat, mu, Ne)], perform reduction:
mat -> sigma -> mat' -> motif'
Conclusion: heavily underestimates IC.
"""
L = len(chain[0][0])
sigmas = [sigma_from_matrix(mat) for (mat, mu, Ne) in chain]
matrices = [sample_matrix(L, sigma) for sigma in sigmas]
motifs = [sample_motif_cftp(matrix, mu, Ne, N) for matrix, (_, mu, Ne) in tqdm(zip(matrices, chain))]
return motifs
def resample_from_post_chain(chain, N):
"""given chain of the form [(mat, mu, Ne)], perform reduction:
mat -> sigma -> mat' -> motif'
Conclusion: heavily underestimates IC.
"""
L = len(chain[0][0])
sigmas = [sigma_from_matrix(mat) for (mat, mu, Ne) in chain]
matrices = [sample_matrix(L, sigma) for sigma in sigmas]
motifs = [
sample_motif_cftp(matrix, mu, Ne, N)
for matrix, (_, mu, Ne) in tqdm(zip(matrices, chain))
]
return motifs
def spoof_motifs(motif, num_motifs=10, trials=1, sigma=None,Ne_tol=10**-4,double_sigma=True):
N = len(motif)
L = len(motif[0])
copies = 10*N
if sigma is None:
sigma = sigma_from_matrix(pssm_from_motif(motif,pc=1))
epsilon = (1+double_sigma)*sigma # 15 Jan 2016
print "sigma:", sigma
bio_ic = motif_ic(motif)
def f(Ne):
ps = ps_from_copies(sigma, Ne, L, copies)
motifs = [sample_motif(epsilon, Ne, L, copies, n,ps=ps)
for i in range(trials)]
return mean(map(motif_ic,motifs)) - bio_ic
Ne = log_regress_spec2(f,[1,10],tol=10**-3)
return [sample_motif(sigma, Ne, L, copies, n) for _ in range(num_motifs)]
def spoof_motifs_occ(motif, num_motifs=10, trials=1, sigma=None,Ne_tol=10**-4,double_sigma=True):
N = len(motif)
L = len(motif[0])
copies = 10*N
if sigma is None:
sigma = sigma_from_matrix(pssm_from_motif(motif,pc=1))
epsilon = (1+double_sigma)*sigma # 15 Jan 2016
print "sigma:", sigma
#bio_ic = motif_ic(motif)
mat = matrix_from_motif(motif)
eps = [score_seq(mat, site) for site in motif]
mu = gle_approx_mu(mat, copies)
bio_occ = mean([1/(1+exp(ep-mu)) for ep in eps])
def f(Ne):
return expected_occupancy(epsilon, Ne, L, copies) - bio_occ
Ne = log_regress_spec2(f,[1,10],tol=10**-3)
return [sample_motif(sigma, Ne, L, copies, N) for _ in range(num_motifs)]
def analyze_bio_motifs(Nes,trials=20):
results = {}
for tf_idx,tf in enumerate(Escherichia_coli.tfs):
Ne = Nes[tf]
bio_motif = getattr(Escherichia_coli,tf)
n,L = len(bio_motif),len(bio_motif[0])
bio_matrix = matrix_from_motif(bio_motif)
sigma = sigma_from_matrix(bio_matrix)
matrix_chains = [sella_hirsch_mh(n=n,L=L,sigma=sigma,Ne=Ne,init='ringer') for i in range(trials)]
ics = [mean(map(motif_ic,chain[-1000:])) for (matrix,chain) in matrix_chains]
ginis = [mean(map(motif_gini,chain[-1000:])) for (matrix,chain) in matrix_chains]
mis = [mean(map(total_motif_mi,chain[-1000:])) for (matrix,chain) in matrix_chains]
print "results for:",tf,tf_idx
print motif_ic(bio_motif),mean(ics),sd(ics)
print motif_gini(bio_motif),mean(ginis),sd(ginis)
print total_motif_mi(bio_motif),mean(mis),sd(mis)
results[tf] = (mean(ics),sd(ics),mean(ginis),sd(ginis),mean(mis),sd(mis))
return results
def spoof_motif_ar(motif, num_motifs=10, trials=1, sigma=None,Ne_tol=10**-4):
n = len(motif)
L = len(motif[0])
copies = 10*n
if sigma is None:
sigma = sigma_from_matrix(pssm_from_motif(motif,pc=1))
print "sigma:", sigma
bio_ic = motif_ic(motif)
matrix = sample_matrix(L, sigma)
mu = approx_mu(matrix, copies=10*n, G=5*10**6)
print "mu:", mu
def f(Ne):
motifs = [sample_motif_ar(matrix, mu, Ne, n)
for i in trange(trials)]
return mean(map(motif_ic,motifs)) - bio_ic
x0 = 2
print "Ne guess:", x0
Ne = bisect_interval_noisy(f,x0=x0,iterations=100,lb=1, verbose=False,w=0.5)
print "Ne:",Ne
return [sample_motif_ar(matrix, mu, Ne, n) for _ in trange(num_motifs)]
def main_experiment(samples=30, iterations=10000, delta_ic=0.1):
results_dict = {}
for tf_idx, tf in enumerate(tfdf.tfs):
print "starting on:", tf
motif = getattr(tfdf, tf)
if motif_ic(motif) < 5:
print "excluding", tf, "for low IC"
continue
bio_ic = motif_ic(motif)
n = len(motif)
L = len(motif[0])
matrix = matrix_from_motif(motif)
sigma = sigma_from_matrix(matrix)
mu = approximate_mu(matrix, n, G)
Ne = estimate_Ne(matrix, mu, n, bio_ic)
spoofs = []
ar = 0
spoof_trials = 0.0
while len(spoofs) < samples:
spoof_trials += 1
matrix, chain = sella_hirsch_mh(Ne=Ne,
mu=mu,
n=1,
matrix=sample_matrix(L, sigma),
init='ringer',
iterations=iterations)
spoof_motif = concat(
[random.choice(chain[iterations / 2:]) for i in range(n)])
if abs(motif_ic(spoof_motif) - bio_ic) < delta_ic:
spoofs.append(spoof_motif)
ar += 1
print "spoof acceptance rate:", ar / spoof_trials, len(
spoofs), samples, spoof_trials
#spoofs = [chain[-1] for (spoof_matrix,chain,Ne) in [spoof_motif(motif,Ne) for i in range(samples)]]
results_dict[tf] = {
fname: map(eval(fname), spoofs)
for fname in "motif_ic motif_gini total_motif_mi".split()
}
print "finished:", tf, "(%s/%s)" % (tf_idx, len(tfdf.tfs))
print bio_ic, mean_ci(results_dict[tf]['motif_ic'])
return results_dict
def spoof_motif(motif, Ne=None, iterations=10000):
matrix = matrix_from_motif(motif)
L = len(motif[0])
n = len(motif)
sigma = sigma_from_matrix(matrix)
spoof_matrix = sample_matrix(L, sigma)
bio_ic = motif_ic(motif)
# this method of reading site_mu, site_sigma off of motif is slightly suspect...
site_mu = site_mu_from_matrix(matrix_from_motif(motif))
site_sigma = site_sigma_from_matrix(matrix_from_motif(motif))
# now need to find mu, nu
n = len(motif)
assumed_copies = 10 * n
mu = approximate_mu(matrix, assumed_copies, G)
spoof_mu = approximate_mu(spoof_matrix, assumed_copies, G)
if Ne is None:
Ne = estimate_Ne(spoof_matrix, spoof_mu, n, bio_ic)
print "chose Ne:", Ne
spoof_matrix, chain = sella_hirsch_mh(Ne=Ne,
matrix=spoof_matrix,
mu=mu,
n=n)
return spoof_matrix, chain, Ne
def spoof_motif_ref(motif, num_motifs=10, trials=10, sigma=None,Ne_tol=10**-4):
n = len(motif)
L = len(motif[0])
copies = 10*n
if sigma is None:
sigma = sigma_from_matrix(pssm_from_motif(motif,pc=1))
print "sigma:", sigma
bio_ic = motif_ic(motif)
def f(Ne):
ps = ps_from_copies(sigma, Ne, L, copies)
motifs = [sample_motif(sigma, Ne, L, copies, n,ps=ps)
for i in range(trials)]
return mean(map(motif_ic,motifs)) - bio_ic
lb = 1
ub = 2
while f(ub) < 0:
ub *= 2
ub *= 2 # once more for good measure
x0 = (lb + ub)/2.0
print "Ne guess:", x0
Nes = [bisect_interval_noisy(f,x0=x0,tolerance=Ne_tol,lb=1) for i in range(3)]
Ne = mean(Nes)
print "Nes:",Nes,Ne
return [sample_motif(sigma, Ne, L, copies, n) for _ in range(num_motifs)]
def spoof_motifs_occ(motif,
num_motifs=10,
trials=1,
sigma=None,
Ne_tol=10**-4,
double_sigma=True):
N = len(motif)
L = len(motif[0])
copies = 10 * N
if sigma is None:
sigma = sigma_from_matrix(pssm_from_motif(motif, pc=1))
epsilon = (1 + double_sigma) * sigma # 15 Jan 2016
print "sigma:", sigma
#bio_ic = motif_ic(motif)
mat = matrix_from_motif(motif)
eps = [score_seq(mat, site) for site in motif]
mu = gle_approx_mu(mat, copies)
bio_occ = mean([1 / (1 + exp(ep - mu)) for ep in eps])
def f(Ne):
return expected_occupancy(epsilon, Ne, L, copies) - bio_occ
Ne = log_regress_spec2(f, [1, 10], tol=10**-3)
return [sample_motif(sigma, Ne, L, copies, N) for _ in range(num_motifs)]