def gillespie(A, x0, tf, death=0, malthus=0, fs=None):
"""Given an array of fitnesses a mutation matrix and an initial
population vector, sample the system until time t.
Note: agrees with largest_eigenvector :)
"""
K = len(A)
t = 0
x = np.array(x0)
A = np.array(A)
hist = []
hist = [(t, np.copy(x))]
while t < tf:
birth_rates = x.dot(A)
death_rates = x * death
rates = np.hstack([birth_rates, death_rates])
total_rate = 1.0 / np.sum(rates)
dt = random.expovariate(total_rate)
selection = inverse_cdf_sample(range(2 * K), rates, normalized=False)
t += dt
if selection < K: # birth reaction
x[selection] += 1
else:
selection -= K
x[selection] -= 1
if malthus and np.sum(x) > malthus:
choice = inverse_cdf_sample(range(K), x, normalized=False)
x[choice] -= 1
if t < tf:
hist.append((t, np.copy(x)))
if random.random() < 0.0001:
print t, x, x / float(np.sum(x))
last_state = hist[-1][1]
hist.append((tf, last_state))
return hist
def estremo_gibbs(iterations=50000,
verbose=False,
every=1000,
sigma=1,
mu=-10,
Ne=5):
nu = Ne - 1
L = 10
N = 20
code, motif = (sample_code(L=10,
sigma=1), random_motif(length=L, num_sites=N))
def log_f((code, motif)):
eps = map(lambda x: -log(x), pw_prob_sites(motif, code))
return sum(nu * log(1 / (1 + exp(ep - mu))) for ep in eps)
chain = [(code, motif[:])]
print log_f((code, motif))
for iteration in trange(iterations):
for i in range(N):
site = motif[i]
for j in range(L):
b = site[j]
log_ps = []
bps = [bp for bp in "ACGT" if not bp == b]
for bp in bps:
site_p = subst(site, bp, j)
log_ps.append(log_f((code, [site_p])))
log_ps = [p - min(log_ps) for p in log_ps]
bp = inverse_cdf_sample(bps,
map(exp, log_ps),
normalized=False)
motif[i] = subst(site, bp, j)
for k in range(L - 1):
for b1 in "ACGT":
for b2 in "ACGT":
dws = [random.gauss(0, 0.1) for _ in range(10)]
code_ps = [[d.copy() for d in code] for _ in range(10)]
for code_p, dw in zip(code_ps, dws):
code_p[k][b1, b2] += dw
log_ps = [log_f((code_p, motif)) for code_p in code_ps]
log_ps = [p - min(log_ps) for p in log_ps]
code_p = inverse_cdf_sample(code_ps,
map(exp, log_ps),
normalized=False)
code = code_p
print log_f((code, motif))
chain.append((code, motif[:]))
return chain
x0 = (sample_code(L=10, sigma=1), random_motif(length=10, num_sites=20))
chain = mh(log_f,
prop,
x0,
use_log=True,
iterations=iterations,
verbose=verbose,
every=every)
return chain
def update(chromosome,qf,koffs,verbose=False):
"""Do a single iteration of SSA
Given:
chromosome: binary vector describing occupation state of ith site
qf: number of free copies in cytosol
koffs: vector of off-rates
Return:
updated_chromosome
updated_qf
time at which transition chromosome -> updated_chromosome occurs"""
# Determine which reactions can occur
# all free sites can become bound at rate qf * 1
# all bound sites can become unbound at rate koff_i
rates = [koffs[i] if bs else qf for i,bs in enumerate(chromosome)]
sum_rate = sum(rates)
idx = inverse_cdf_sample(range(G),normalize(rates))
time = random.expovariate(sum_rate)
updated_chromosome = chromosome[:]
if chromosome[idx]: # if reaction is an unbinding reaction...
if verbose:
print "unbinding at: ",idx
updated_chromosome[idx] = 0
updated_qf = qf + 1
else: # a binding reaction...
if verbose:
print "binding at: ",idx
updated_chromosome[idx] = 1
updated_qf = qf - 1
return updated_chromosome,updated_qf,time
def sample_path_ref2(qf,koffs,t_final,chromosome=None,verbose=False):
"""Simulate a sample path until time t_final and return the marginal occupancies.
Integrates update, sample_path_ref framework.
"""
if chromosome is None: # then start from empty chromosome
chromosome = [0] * len(koffs)
t = 0
dt = 0
occs = [0 for c in chromosome]
while t < t_final:
rates = [koffs[i] if bs else qf for i,bs in enumerate(chromosome)]
sum_rate = sum(rates)
dt = random.expovariate(sum_rate)
t += dt
if t > t_final:
dt = t_final - t + dt
# update occupancies after deciding dt, before updating chromosome
occs = zipWith(lambda occ,ch:occ + ch*dt,occs,chromosome)
idx = inverse_cdf_sample(range(G),normalize(rates))
if chromosome[idx]: # if reaction is an unbinding reaction...
if verbose:
print "unbinding at: ",idx
chromosome[idx] = 0
qf += 1
else: # a binding reaction...
if verbose:
print "binding at: ",idx
chromosome[idx] = 1
qf -= 1
if verbose:
print "t:",t,"dt:",dt,"q:",qf,"qbound:",sum(chromosome),"mean occ:",sum([occ/t for occ in occs])
return [occ/t_final for occ in occs]
def sample_site_from_copies(sigma, Ne, L, copies, ps=None):
if ps is None:
ps = ps_from_copies(sigma, Ne, L, copies)
k = inverse_cdf_sample(range(L + 1), ps, normalized=False)
return "".join(
permute(["A" for _ in range(L - k)] +
[random.choice("CGT") for _ in range(k)]))
def moran_process(N=1000,
turns=10000,
init=sample_species,
mutate=mutate,
fitness=fitness,
pop=None):
if pop is None:
pop = [(lambda spec: (spec, fitness(spec)))(sample_species())
for _ in trange(N)]
hist = []
for turn in xrange(turns):
fits = [f for (s, f) in pop]
#print fits
birth_idx = inverse_cdf_sample(range(N), fits, normalized=False)
death_idx = random.randrange(N)
#print birth_idx,death_idx
mother, f = pop[birth_idx]
daughter = mutate(mother)
#print "mutated"
pop[death_idx] = (daughter, fitness(daughter))
mean_fits = mean(fits)
hist.append((f, mean_fits))
if turn % 10 == 0:
mean_dna_ic = mean(
[motif_ic(sites, correct=False) for ((sites, eps), _) in pop])
mean_rec_h = mean(
[h_np(boltzmann(eps)) for ((dna, eps), _) in pop])
print turn, "sel_fit:", f, "mean_fit:", mean_fits, "mean_dna_ic:", mean_dna_ic, "mean_rec_h:", mean_rec_h
return pop
def moran_process(N=1000,turns=10000,mean_site_muts=1,mean_rec_muts=1,init=sample_species,mutate=mutate,
fitness=fitness,pop=None,print_modulus=100,hist_modulus=10):
#ringer = (np.array([1]+[0]*(K-1)),sample_eps())
if pop is None:
pop = [(lambda spec:(spec,fitness(spec)))(init())
for _ in trange(N)]
# ringer = make_ringer()
# pop[0] = (ringer,fitness(ringer))
#pop = [(ringer,fitness(ringer)) for _ in xrange(N)]
site_mu = min(1/float(n*L) * mean_site_muts,1)
rec_mu = min(1/float(K) * mean_rec_muts,1)
hist = []
for turn in xrange(turns):
fits = [f for (s,f) in pop]
#print fits
birth_idx = inverse_cdf_sample(range(N),fits,normalized=False)
if birth_idx is None:
return pop
death_idx = random.randrange(N)
#print birth_idx,death_idx
mother,f = pop[birth_idx]
daughter = mutate(mother,site_mu,rec_mu)
#print "mutated"
pop[death_idx] = (daughter,fitness(daughter))
mean_fits = mean(fits)
#hist.append((f,mean_fits))
if turn % hist_modulus == 0:
mean_dna_ic = mean([motif_ic(sites,correct=False) for ((sites,eps),_) in pop])
mean_rec = mean([recognizer_promiscuity(x) for (x,f) in pop])
mean_recced = mean([sites_recognized((dna,rec)) for ((dna,rec),_) in pop])
hist.append((turn,f,mean_fits,mean_dna_ic,mean_rec,mean_recced))
if turn % print_modulus == 0:
print turn,"sel_fit:",f,"mean_fit:",mean_fits,"mean_dna_ic:",mean_dna_ic,"mean_rec_prom:",mean_rec
return pop,hist
def moran_process(mean_rec_muts,
mean_site_muts,
N=1000,
turns=10000,
init=make_ringer2,
mutate=mutate,
fitness=fitness,
pop=None):
site_mu = mean_site_muts / float(n * L)
bd_mu = mean_rec_muts / float(L)
if pop is None:
pop = [(lambda spec: (spec, fitness(spec)))(init()) for _ in trange(N)]
hist = []
for turn in xrange(turns):
fits = [f for (s, f) in pop]
birth_idx = inverse_cdf_sample(range(N), fits, normalized=False)
death_idx = random.randrange(N)
#print birth_idx,death_idx
mother, f = pop[birth_idx]
daughter = mutate(mother, site_mu, bd_mu)
#print "mutated"
pop[death_idx] = (daughter, fitness(daughter))
mean_fits = mean(fits)
hist.append((f, mean_fits))
if turn % 1000 == 0:
mean_dna_ic = mean(
[motif_ic(sites, correct=False) for ((bd, sites), _) in pop])
print turn, "sel_fit:", f, "mean_fit:", mean_fits, "mean_dna_ic:", mean_dna_ic
return pop, hist
def simulate(ks,p,tf=10):
n = len(ks)
X = [1] * n + [0] * n + [p] #state is a vector of n empty sites, n complexes, protein
t = 0
history = [(t,X[:])]
while t < tf:
p = X[-1]
print "X:",X
rates = [p*ks[i]*X[i] for i in range(n)] + [X[n + i] for i in range(n)]
print "rates:",rates
master_rate = float(sum(rates))
dt = expon.rvs(1,1/master_rate)
print "dt:",dt
print "normalized rates:",normalize(rates)
j = inverse_cdf_sample(range(len(X)),normalize(rates))
print "chose reaction:",j
if j < n:
print "forming complex"
#update state for complex formation
X[j] = 0
X[n+j] = 1
X[-1] -= 1
else:
#update state for complex dissociation
print "dissolving complex"
X[j] = 0
X[j-n] = 1
X[-1] += 1
t += dt
history.append((t,X[:]))
return history
def moran(fs, mus, n, t):
"""do moran process of n individuals for t generations"""
K = len(fs)
pop = np.zeros(K)
for i in xrange(n):
pop[random.randrange(K)] += 1
for _ in trange(t):
#print "starting:",pop
b = inverse_cdf_sample(range(K), fs * pop, normalized=False)
m = inverse_cdf_sample(range(K), mus[b, :], normalized=False)
d = inverse_cdf_sample(range(K), pop, normalized=False)
#print "b:",b,"d:",d
pop[d] -= 1
pop[m] += 1
#print pop
return pop / np.sum(pop)
def moran_tracking(fs, mus, tf, init_state=0):
"""Track a single trajectory of a population until tf. Assume mus are
probabilities, i.e. row stochastic"""
t = 0
K = len(fs)
x = np.zeros(K)
i = init_state
x[i] = 1
hist = []
while t < tf:
if False: #random.random() < 0.0001:
print t / tf, x
hist.append((t, np.copy(x)))
lifetime = random.expovariate(fs[i])
t += lifetime
j = inverse_cdf_sample(range(K), mus[i, :])
if random.random() < fs[j] / (
fs[j] + fs[i]): # track new lineage with probability 1/2
x[i] = 0
x[j] = 1
i = j
assert np.sum(x) == 1
last_state = hist[-1][1]
hist.append((tf, last_state))
return hist
def prop(motif):
# determine number of mutations to perform
#k = discrete_exponential_sampler(N,lamb)
k = inverse_cdf_sample(range(N), ps)
#motif_p = mutate_motif_p_exact(ringer,p) # probability of mutation per basepair
motif_p = mutate_motif_k_times(ringer, k)
return motif_p
def entropy_from_ps(ps, N):
K = len(ps)
ns = [0] * K
xs = range(K)
for i in xrange(N):
j = inverse_cdf_sample(xs, ps)
ns[j] += 1
return h([n / float(N) for n in ns])
def random_walk_eigenvector(A, iterations=50000):
K = len(A)
history = np.zeros(K)
state = random.randrange(K)
for _ in xrange(iterations):
history[state] += 1
state = inverse_cdf_sample(range(K), (A[state, :]).tolist())
return history / np.sum(history)
def sample_log_odds(matrix, n, lamb=1):
matrix_probs = [
normalize([exp(-lamb * ep) for ep in row]) for row in matrix
]
return [
"".join([inverse_cdf_sample("ACGT", probs) for probs in matrix_probs])
for i in xrange(n)
]
def entropy_from_ps(ps, N):
K = len(ps)
ns = [0] * K
xs = range(K)
for i in xrange(N):
j = inverse_cdf_sample(xs, ps)
ns[j] += 1
return h([n/float(N) for n in ns])
def sample_site(sigma, mu, Ne, L):
phats = [phat(k, sigma, mu, Ne, L) for k in range(L + 1)]
# Z = sum(phats)
# ps = [ph/Z for ph in phats]
k = inverse_cdf_sample(range(L + 1), phats, normalized=False)
return "".join(
permute(["A" for _ in range(L - k)] +
[random.choice("CGT") for _ in range(k)]))
def weighted_regress_dep(xs,ys, sample_points=100):
regress_points = []
avg_yval = mean(map(abs,ys))
ws = [exp(-abs(y)/avg_yval) for y in ys]
for i in xrange(sample_points):
rx,ry = inverse_cdf_sample(zip(xs,ys),ws,normalized=False)
regress_points.append((rx,ry))
rxs,rys = transpose(regress_points)
return (polyfit(rxs,rys,1))
def random_walk(A, iterations=50000):
K = len(A)
path = np.zeros(iterations)
state = random.randrange(K)
for turn in xrange(iterations):
path[turn] = state
state = inverse_cdf_sample(range(K), (A[state, :]).tolist(),
normalized=False)
return path
def moran_ancestor(fs, mus, n, t):
K = len(fs)
pop = [(i, random.randrange(K)) for i in range(1, n + 1)]
next_idx = n + 1
pop_hist = {idx: (typ, 0) for (idx, typ) in pop}
ancestor_history = np.zeros(K)
for time in trange(t):
bidx, btype = inverse_cdf_sample(pop, [fs[typ] for idx, typ in pop],
normalized=False)
cidx = next_idx
next_idx += 1
ctype = inverse_cdf_sample(range(K), mus[btype, :], normalized=False)
pop_hist[cidx] = (ctype, bidx)
pop[random.randrange(n)] = (cidx, ctype)
anc_idx = find_ancestor(pop, pop_hist)
if anc_idx > 0:
anc_typ, _ = pop_hist[anc_idx]
print time, anc_idx, anc_typ if anc_idx > 0 else None
ancestor_history[anc_typ] += 1
return ancestor_history / np.sum(ancestor_history)
def est_ncp(ps,n,trials,verbose=False):
accs = 0
A = range(len(ps))
for trial in xrange(trials):
if verbose:
if trial % verbose == 0:
print "%s/%s\r" % (trial,trials),
sys.stdout.flush()
xs = [inverse_cdf_sample(ps) for i in range(n)]
if len(set(xs)) == n:
accs += 1
return accs/float(trials)
def mutation_motif_with_ic(n, L, desired_ic, epsilon=0.1):
ringer = ["A" * L] * n
N = L * n
ks_rel_motifs = []
while not ks_rel_motifs:
motifs = [mutate_motif_k_times(ringer, k) for k in range(N + 1)]
ks_rel_motifs = [(k, motif) for k, motif in enumerate(motifs)
if inrange(motif, desired_ic, epsilon)]
ks, rel_motifs = transpose(ks_rel_motifs)
ps = [exp(log_prob_motif_with_mismatch(n, L, k)) for k in ks]
ringified_motif = inverse_cdf_sample(rel_motifs, ks, normalized=False)
return deringify_motif(ringified_motif)
def mh_eigenvector3(fs, mus, iterations=50000):
K = len(mus)
print K
hist = np.zeros(K)
i = random.randrange(K)
for _ in xrange(iterations):
hist[i] += 1
trans_rates = mus[i, :]
j = inverse_cdf_sample(range(K), trans_rates, normalized=False)
if random.random() < fs[j] / fs[i]:
i = j
return hist / np.sum(hist)
def single_moran(fs, mus, iterations=50000):
K = len(mus)
print K
hist = np.zeros(K)
i = random.randrange(K)
for _ in trange(iterations):
hist[i] += 1
trans_rates = mus[i, :]
j = inverse_cdf_sample(range(K), trans_rates, normalized=False)
if random.random() < 1 / 2.0: #fs[j]/(fs[i]+fs[j]):
i = j
return hist / np.sum(hist)
def qs_sampling(fs, mus, iterations=50000):
K = len(mus)
hist = np.zeros(K)
i = random.randrange(K)
for _ in xrange(iterations):
hist[i] += 1
trans_probs = mus[i, :]
fi = fs[i]
offspring = [scipy.stats.poisson(mu * fi).rvs() for mu in trans_probs]
offspring[i] += 1
i = inverse_cdf_sample(range(K), offspring, normalized=False)
return hist / np.sum(hist)
def entropic_sampling(matrix, n=16):
"""sample motifs uniformly wrt fitness"""
L = len(matrix)
ringer = ringer_motif(matrix, n)
N = n * L
ps = [1.0 / N for i in range(N)]
ks = range(N)
replicates = 10000
motifs = [
mutate_motif_k_times(ringer, inverse_cdf_sample(ks, ps))
for i in trange(replicates)
]
log_fs = [log_fitness(matrix, motif, G) for motif in motifs]
def sequential_sample_ref(ks,q):
G = len(ks)
chromosome = [0]*(G+1)
new_ks = ks[:] + [1]
for tf in range(q):
#print "new_ks:",new_ks,"q:",q
Z = float(sum(new_ks))
pos = inverse_cdf_sample([k/Z for k in new_ks])
#print "pos:",pos
chromosome[pos] += 1
if chromosome[pos] > 1 and pos < G:
raise Exception("Chromosome[%s] > 1" % pos)
if pos < G:
new_ks[pos] = 0
return chromosome
def smart_rsa(ks,q,sampler=None,verbose=False,debug_efficiency=False):
"""Perform random sequential adsorption without rejection. Note:
Not a method for sampling from equilibrium distribution! ks is a
vector of the form [k0,k1,kg], i.e. off-rate k0 = 1.
"""
ss = []
N = len(ks)
_ks = ks[:]
for j in range(q):
s = inverse_cdf_sample(normalize(_ks))
ss.append(s)
if s > 0:
_ks[s] = 0
return ss
def maxent_motif_with_ic(n, L, desired_ic, tolerance=10**-2, beta=None):
"""sample motif from max ent distribution with mean desired_ic"""
# first we adjust the desired ic upwards so that when motif_ic is
# called with 1st order correction, we get the desired ic.
if beta is None:
correction_per_col = 3 / (2 * log(2) * n)
desired_ic += L * correction_per_col
beta = find_beta_for_mean_motif_ic(n,
L,
desired_ic,
tolerance=tolerance)
ps = count_ps_from_beta(n, beta)
counts = [inverse_cdf_sample(enumerate_counts(n), ps) for i in range(L)]
cols = [sample_col_from_count(count) for count in counts]
return map(lambda site: "".join(site), transpose(cols))
def sella_hirsch_gibbs_sampler(Ne=1000,
n=16,
L=16,
G=5 * 10**6,
sigma=1,
init="random",
matrix=None,
x0=None,
iterations=50000):
if matrix is None:
matrix = sample_matrix(L, sigma)
if x0 is None:
if init == "random":
x0 = random_motif(L, n)
elif init == "ringer":
x0 = ringer_motif(matrix, n)
else:
x0 = init
nu = Ne - 1
def log_f(motif):
return nu * log_fitness(matrix, motif, G)
def prop(motif):
#return mutate_motif_p(motif,1) # on average, 1 mutation per motif, (binomially distributed)
return mutate_motif_p(
motif,
4) # on average, 4 mutation per motif, (binomially distributed)
motif = x0
chain = [motif]
for iteration in xrange(iterations):
for i in range(n):
for j in range(L):
prop_motifs = [subst_motif(motif, i, j, b) for b in "ACGT"]
log_fs = map(log_f, prop_motifs)
log_f_hat = mean(log_fs)
log_fs_resid = [lf - log_f_hat for lf in log_fs]
ps = normalize(map(exp, log_fs_resid))
idx = inverse_cdf_sample(range(4), ps)
motif = prop_motifs[idx]
chain.append(motif)
if iteration % 10 == 0:
print "iterations:(%s/%s)" % (iteration,
iterations), "log_f:", log_fs[idx]
return matrix, chain
def random_partition(N, K):
part = []
K_ = K
last = N
for _ in range(K_):
#ws = [num_parts(N-i, K-1, i) for i in range(N+1)]
if K == 1:
i = N
else:
ws = [
num_parts(N - i, K - 1, i) if i <= last else 0
for i in range(N + 1)
]
i = inverse_cdf_sample(range(N + 1), ws, normalized=False)
part.append(i)
N -= i
K -= 1
last = i
#print part, N, K
return tuple(part)
def moran_process(fitness,
mutate,
init_species,
N=1000,
turns=10000,
pop=None,
diagnostic_modulus=100,
diagnostics=lambda pop: mean([f for (s, f) in pop])):
if pop is None:
pop = [(lambda spec: (spec, fitness(spec)))(init_species())
for _ in trange(N)]
for turn in xrange(turns):
fits = [f for (s, f) in pop]
birth_idx = inverse_cdf_sample(range(N), fits, normalized=False)
death_idx = random.randrange(N)
mother, f = pop[birth_idx]
daughter = mutate(mother)
pop[death_idx] = (daughter, fitness(daughter))
mean_fits = mean(fits)
if turn % diagnostic_modulus == 0:
print turn, diagnostics(pop)
return pop
def moran_process(N=1000,turns=10000,init=sample_species,mutate=mutate,fitness=fitness,pop=None):
if pop is None:
pop = [(lambda spec:(spec,fitness(spec)))(sample_species())
for _ in trange(N)]
hist = []
for turn in xrange(turns):
fits = [f for (s,f) in pop]
#print fits
birth_idx = inverse_cdf_sample(range(N),fits,normalized=False)
death_idx = random.randrange(N)
#print birth_idx,death_idx
mother,f = pop[birth_idx]
daughter = mutate(mother)
#print "mutated"
pop[death_idx] = (daughter,fitness(daughter))
mean_fits = mean(fits)
hist.append((f,mean_fits))
if turn % 10 == 0:
mean_dna_ic = mean([motif_ic(sites,correct=False) for ((sites,eps),_) in pop])
mean_rec_h = mean([h_np(boltzmann(eps)) for ((dna,eps),_) in pop])
print turn,"sel_fit:",f,"mean_fit:",mean_fits,"mean_dna_ic:",mean_dna_ic,"mean_rec_h:",mean_rec_h
return pop
def moran_process(N=1000,turns=10000,mu=10**-3,ep_sigma=10**-3):
ringer = (np.array([1]+[0]*(K-1)),sample_eps())
# pop = [(lambda spec:(spec,fitness(spec)))(sample_species())
# for _ in xrange(N)]
pop = [(ringer,fitness(ringer)) for _ in xrange(N)]
hist = []
for turn in xrange(turns):
fits = [f for (s,f) in pop]
#print fits
birth_idx = inverse_cdf_sample(range(N),fits,normalized=False)
death_idx = random.randrange(N)
#print birth_idx,death_idx
mother,f = pop[birth_idx]
daughter = mutate(mother,mu,ep_sigma)
#print "mutated"
pop[death_idx] = (daughter,fitness(daughter))
mean_fits = mean(fits)
hist.append((f,mean_fits))
if turn % 100 == 0:
mean_dna_h = mean([h_np(dna) for ((dna,eps),f) in pop])
mean_rec_h = mean([h_np(boltzmann(eps)) for ((dna,eps),f) in pop])
print turn,"mean_fitness:",f,mean_fits,mean_dna_h,mean_rec_h
return hist
def moran_process(mean_rec_muts,mean_site_muts,N=1000,turns=10000,
init=make_ringer2,mutate=mutate,fitness=fitness,pop=None):
site_mu = mean_site_muts/float(n*L)
bd_mu = mean_rec_muts/float(L)
if pop is None:
pop = [(lambda spec:(spec,fitness(spec)))(init())
for _ in trange(N)]
hist = []
for turn in xrange(turns):
fits = [f for (s,f) in pop]
birth_idx = inverse_cdf_sample(range(N),fits,normalized=False)
death_idx = random.randrange(N)
#print birth_idx,death_idx
mother,f = pop[birth_idx]
daughter = mutate(mother,site_mu,bd_mu)
#print "mutated"
pop[death_idx] = (daughter,fitness(daughter))
mean_fits = mean(fits)
hist.append((f,mean_fits))
if turn % 1000 == 0:
mean_dna_ic = mean([motif_ic(sites,correct=False) for ((bd,sites),_) in pop])
print turn,"sel_fit:",f,"mean_fit:",mean_fits,"mean_dna_ic:",mean_dna_ic
return pop,hist
def update(self, final_time):
# Compute propensities
propensities = [propensity(self.state, self.time) for propensity in self.propensities]
self.logging(propensities)
p = sum(propensities) # rate of sum of random variables
# determine time of next reaction
if p == 0:
raise Exception("No possible reactions")
dt = rexp(p)
# optimize next line later
# determine which reaction
new_time = self.time + dt
if new_time < final_time:
v = inverse_cdf_sample(self.stoich_vectors, normalize(propensities))
# update state vector
self.state = zipWith(lambda x, y: x + y, self.state, v)
self.time = new_time
self.logging(str(self.time) + " " + str(self.state))
self.history.append((self.time, self.state))
# print self.state
self.reactions_performed += 1
else:
self.finished_run = True
def sample_site_from_copies(sigma,Ne,L,copies,ps=None):
if ps is None:
ps = ps_from_copies(sigma, Ne, L, copies)
k = inverse_cdf_sample(range(L+1), ps,normalized=False)
return "".join(permute(["A" for _ in range(L-k)] + [random.choice("CGT") for _ in range(k)]))
def sample_site(sigma,mu,Ne,L):
phats = [phat(k,sigma,mu,Ne,L) for k in range(L+1)]
# Z = sum(phats)
# ps = [ph/Z for ph in phats]
k = inverse_cdf_sample(range(L+1), phats,normalized=False)
return "".join(permute(["A" for _ in range(L-k)] + [random.choice("CGT") for _ in range(k)]))
def rpower_law(alpha=2, M=1000):
return inverse_cdf_sample(range(1, M + 1),
[1.0 / (i**alpha) for i in range(1, M + 1)],
normalized=False)
def sample_site_vb(matrix, mu, Ne):
nu = Ne - 1
alpha = nu*exp(-mu)
log_new_mat = [([(-(1+alpha*(exp(ep)))) for ep in row])
for row in matrix]
return "".join(inverse_cdf_sample("ACGT",ps) for ps in new_mat)
def rQ(xs):
"""MFA proposal"""
return [inverse_cdf_sample(range(K), boltzmann(mf_h)) for mf_h in mf_hs]
def sample_from_matrix(matrix, lamb):
return "".join([inverse_cdf_sample("ACGT", [exp(-lamb*ep) for ep in row],
normalized=False)
for row in matrix])
def sample_ps(ps, N):
"""Return a sample from the multinomial distribution given by ps"""
ks = range(N)
return [inverse_cdf_sample(ks, ps) for i in xrange(N)]
def sample_site():
return "".join(inverse_cdf_sample("ACGT",ps) for ps in pss)
def sample_col_ents(ent_dist,L,a,b):
ents = ent_dist.keys()
solutions = interval_subset_sum(ents,L,a,b)
weights = [prod(ent_dist[s] for s in sol) for sol in solutions]
return inverse_cdf_sample(solutions,weights,normalized=False)
def update_spatial(chromosome,qf,koffs,verbose=False):
"""Do a single iteration of SSA with sliding reactions included.
Given:
chromosome: binary vector describing occupation state of ith site.
Each site can be unbound (0), bound non-specifically(1) or bound
specifically(2). Non-specific binding has a free energy of -7
kbt, sequence-specific binding is as usual. A TF bound
non-specifically can slide 1 bp left or right with no change in
free energy.
qf: number of free copies in cytosol
koffs: vector of off-rates
Return:
updated_chromosome
updated_qf
time at which transition chromosome -> updated_chromosome occurs
"""
# Determine which reactions can occur
# free copies can bind non-specifically at rate ep_ns
# non-specifically bound copies can transition to specific binding or slide left or right
# specifically bound copies can transition to non-specific binding
ep_ns = -7
k_ns = exp(-beta*ep_ns)
k1 = 1 # rate for reactions that happen on default simulation timescale
G = len(chromosome)
reactions = [(i,'N',qf*k_ns) for i in xrange(G)]
for i,c in enumerate(chromosome):
# if c == 0 and qf > 0:
# reactions.append((i,'N',qf*k_ns))
if c == 1: # if bound non-specifically
# tf can bind specifically
reactions.append((i,'S',k1))
# tf can fall off
reactions.append((i,'F',k1))
# tf can slide
if chromosome[(i-1)%G] == 0:
reactions.append((i,'L',k1))
if chromosome[(i+1)%G] == 0:
reactions.append((i,'R',k1))
elif c == 2:
reactions.append((i,'U',koffs[i]))
###
rates = [reaction[2] for reaction in reactions]
sum_rate = sum(rates)
chr_idx,rx_type,rate = inverse_cdf_sample(reactions,normalize(rates))
time = random.expovariate(sum_rate)
if verbose:
print chr_idx,rx_type,rate,time
updated_chromosome = chromosome[:]
if rx_type == 'N': # tf binds non-specifically
updated_chromosome[chr_idx] = 1
updated_qf = qf - 1
elif rx_type == 'S': # tf transitions to specific binding
updated_chromosome[chr_idx] = 2
updated_qf = qf
elif rx_type == 'F':
updated_chromosome[chr_idx] = 0
updated_qf = qf + 1
elif rx_type == 'L':
updated_chromosome[chr_idx] = 0
updated_chromosome[(chr_idx-1)%G] = 1
updated_qf = qf
elif rx_type == 'R':
updated_chromosome[chr_idx] = 0
updated_chromosome[(chr_idx+1)%G] = 1
updated_qf = qf
elif rx_type == 'U':
updated_chromosome[chr_idx] = 1
updated_qf = qf
else:
print "Didn't recognize reaction type:",rx_type
assert False
return updated_chromosome,updated_qf,time
def sample_ps(ps, N):
"""Return a sample from the multinomial distribution given by ps"""
ks = range(N)
return [inverse_cdf_sample(ks, ps) for i in xrange(N)]
def rcol(beta, N):
ps = rvector(beta, K=4)
col = [inverse_cdf_sample("ACGT", ps) for _ in xrange(N)]
return col
def rpower_law(alpha=2,M=1000):
return inverse_cdf_sample(range(1,M+1),[1.0/(i**alpha) for i in range(1,M+1)],normalized=False)
def rcol(beta, N):
ps = rvector(beta, K=4)
col = [inverse_cdf_sample("ACGT",ps) for _ in xrange(N)]
return col
def rQ():
return "".join([inverse_cdf_sample("ACGT",qs) for qs in qss])
def rQ():
return "".join([inverse_cdf_sample("ACGT",ps,normalized=False)
for ps in pss])