def getRates(self, source=None, sink=None):
""" Get the rates between two states
Parameters
----------
source : int, optional
The state index to use as source
sink : int, optional
The state index to use as sink
Returns
-------
rates : :class:`Rates` object
A Rates object containing the rates
Example
-------
>>> kin = Kinetics(model, temperature=300, concentration=0.015)
>>> r = kin.getRates()
>>> print(r)
>>> dg = r.g0eq
"""
actset = self.model.hmm.active_set
if source is None:
source = self.source
else:
source = np.where(actset == source)[0]
if sink is None:
sink = self.sink
else:
sink = np.where(actset == sink)[0]
logger.info('Calculating rates between source: {} and sink: {} states.'.format(actset[source], actset[sink]))
if source == sink:
logger.info('Calculating rates between state and itself gives 0')
r = Rates(); r.mfpton = 0; r.mfptoff=0; r.koff=0; r.kon=0; r.g0eq=0; r.kdeq=0;
return r
if source == self.source: # Apply concentration only on the bulk state
conc = self.concentration
elif sink == self.source:
conc = 1 / self.concentration
else:
conc = 1
model = self.model
from msmtools.analysis import mfpt
r = Rates()
r.mfpton = model.data.fstep * model.hmm.lag * mfpt(self.model.hmm.transition_matrix, origin=source, target=sink)
r.mfptoff = model.data.fstep * model.hmm.lag * mfpt(self.model.hmm.transition_matrix, origin=sink, target=source)
r.koff = 1E9 / r.mfptoff
r.kon = 1E9 / (r.mfpton * conc)
eq = model.hmm.stationary_distribution
sinkeq = np.sum(eq[sink])
sourceeq = np.sum(eq[source])
if conc != 1:
logger.info('Concentration correction of {:.2f} kcal/mol.'.format(-self._kBT * np.log(1 / conc)))
r.g0eq = -self._kBT * np.log(sinkeq / (conc * sourceeq))
r.kdeq = np.exp(r.g0eq / self._kBT)
return r
def getRates(self, source=None, sink=None, states='macro'):
""" Get the rates between two states
Parameters
----------
source : int, optional
The state index to use as source
sink : int, optional
The state index to use as sink
states : ['macro','micro'], optional
The state type of the states given before
Returns
-------
rates : :class:`Rates` object
A Rates object containing the rates
Example
-------
>>> kin = Kinetics(model, temperature=300, concentration=0.015)
>>> r = kin.getRates()
>>> print(r)
>>> dg = r.g0eq
"""
self._intergrityCheck()
if source is None:
source = self.source
if sink is None:
sink = self.sink
if source == sink:
logger.info('Calculating rates between state and itself gives 0')
r = Rates(); r.mfpton = 0; r.mfptoff=0; r.koff=0; r.kon=0; r.g0eq=0; r.kdeq=0;
return r
if source == self.source: # Apply concentration only on the bulk state
conc = self.concentration
elif sink == self.source:
conc = 1 / self.concentration
else:
conc = 1
model = self.model
from msmtools.analysis import mfpt
r = Rates()
r.mfpton = model.data.fstep * model.lag * mfpt(self.model.P, origin=source, target=sink)
r.mfptoff = model.data.fstep * model.lag * mfpt(self.model.P, origin=sink, target=source)
r.koff = 1E9 / r.mfptoff
r.kon = 1E9 / (r.mfpton * conc)
eq = model.hmm.stationary_distribution
sinkeq = eq[sink]
sourceeq = eq[source]
r.g0eq = -self._kBT * np.log(sinkeq / (conc * sourceeq))
r.kdeq = np.exp(r.g0eq / self._kBT)
return r
def getRates(self, source=None, sink=None):
""" Get the rates between two states
Parameters
----------
source : int, optional
The state index to use as source
sink : int, optional
The state index to use as sink
Returns
-------
rates : :class:`Rates` object
A Rates object containing the rates
Example
-------
>>> kin = Kinetics(model, temperature=300, concentration=0.015)
>>> r = kin.getRates()
>>> print(r)
>>> dg = r.g0eq
"""
if source is None:
source = self.source
if sink is None:
sink = self.sink
logger.info('Calculating rates between source: {} and sink: {} states.'.format(source, sink))
if source == sink:
logger.info('Calculating rates between state and itself gives 0')
r = Rates(); r.mfpton = 0; r.mfptoff=0; r.koff=0; r.kon=0; r.g0eq=0; r.kdeq=0;
return r
if source == self.source: # Apply concentration only on the bulk state
conc = self.concentration
elif sink == self.source:
conc = 1 / self.concentration
else:
conc = 1
model = self.model
from msmtools.analysis import mfpt
r = Rates()
r.mfpton = model.data.fstep * model.hmm.lag * mfpt(self.model.hmm.transition_matrix, origin=source, target=sink)
r.mfptoff = model.data.fstep * model.hmm.lag * mfpt(self.model.hmm.transition_matrix, origin=sink, target=source)
r.koff = 1E9 / r.mfptoff
r.kon = 1E9 / (r.mfpton * conc)
eq = model.hmm.stationary_distribution
sinkeq = np.sum(eq[sink])
sourceeq = np.sum(eq[source])
if conc != 1:
logger.info('Concentration correction of {:.2f} kcal/mol.'.format(-self._kBT * np.log(1 / conc)))
r.g0eq = -self._kBT * np.log(sinkeq / (conc * sourceeq))
r.kdeq = np.exp(r.g0eq / self._kBT)
return r
def test_mfpt_between_sets(self):
x = mfpt(self.P, [1, 2], origin=0)
assert_allclose(x, self.o0t12)
x = mfpt(self.P, [0, 1], origin=2)
assert_allclose(x, self.o2t01)
x = mfpt(self.P, 2, origin=[0, 1])
assert_allclose(x, self.o01t2)
x = mfpt(self.P, 0, origin=[1, 2])
assert_allclose(x, self.o12t0)
def test_mfpt(self):
x = mfpt(self.P, 0)
assert_allclose(x, self.m0)
x = mfpt(self.P, 1)
assert_allclose(x, self.m1)
x = mfpt(self.P, 2)
assert_allclose(x, self.m2)
x = mfpt(self.P, [0, 1])
assert_allclose(x, self.m01)
x = mfpt(self.P, [1, 2])
assert_allclose(x, self.m12)
def test_time_units(self):
dtraj = np.random.randint(0, 4, 1000)
tau = 12
dt = 0.456
msmobj = estimate_markov_model(dtraj, lag=tau, dt_traj='%f ns' % dt)
# check MFPT consistency
mfpt_ref = msmobj.mfpt([0], [1])
tptobj = tpt(msmobj, [0], [1])
assert_allclose(tptobj.mfpt, mfpt_ref)
assert_allclose(msmana.mfpt(msmobj.P, [1], [0], tau=tau) * dt, mfpt_ref)
assert_allclose(np.dot(msmobj.stationary_distribution, tptobj.backward_committor) / tptobj.total_flux, mfpt_ref)
# check flux consistency
total_flux_ref = tptobj.total_flux
A = tptobj.A
B = tptobj.B
I = tptobj.I
assert_allclose(tptobj.gross_flux[A, :][:, B].sum() + tptobj.gross_flux[A, :][:, I].sum(),
total_flux_ref)
assert_allclose(tptobj.net_flux[A, :][:, B].sum() + tptobj.net_flux[A, :][:, I].sum(), total_flux_ref)
assert_allclose(tptobj.flux[A, :][:, B].sum() + tptobj.flux[A, :][:, I].sum(), total_flux_ref)
mf = tptobj.major_flux(1.0)
assert_allclose(mf[A, :][:, B].sum() + mf[A, :][:, I].sum(), total_flux_ref)
# check that the coarse-grained version is consistent too
_, tptobj2 = tptobj.coarse_grain([A, I, B])
assert_allclose(tptobj2.total_flux, total_flux_ref)
assert_allclose(tptobj2.mfpt, mfpt_ref)
def mfpt_all(T, mss):
Nmss = mss.shape[0]
m_t = []
for i in range(Nmss):
for j in range(Nmss):
if ( i != j ):
m_t.append( mfpt(T,mss[j],origin=mss[i]) )
return np.array(m_t)
def setUpClass(cls):
# 5-state toy system
cls.P = np.array([[0.8, 0.15, 0.05, 0.0, 0.0],
[0.1, 0.75, 0.05, 0.05, 0.05],
[0.05, 0.1, 0.8, 0.0, 0.05],
[0.0, 0.2, 0.0, 0.8, 0.0],
[0.0, 0.02, 0.02, 0.0, 0.96]])
cls.A = [0]
cls.B = [4]
cls.P_mfpt = np.zeros_like(cls.P)
for ii in np.arange(cls.P.shape[0]):
for jj in np.arange(cls.P.shape[1]):
cls.P_mfpt[ii, jj] = mfpt(cls.P, [ii], [jj])
return cls
def getRates(self, source=None, sink=None, states='macro', _logger=True):
""" Get the rates between two (sets of) states
Parameters
----------
source : int, optional
The state index to use as source
sink : int, optional
The state index to use as sink
states : ['macro','micro'], optional
The state type of the states given before
Returns
-------
rates : :class:`Rates` object
A Rates object containing the rates
Example
-------
>>> kin = Kinetics(model, temperature=300, concentration=0.015)
>>> r = kin.getRates()
>>> print(r)
>>> dg = r.g0eq
>>> r = kin.getRates(source=4, sink=[0,1,2,3])
"""
import numbers
self._intergrityCheck()
if source is None:
source = self.source
if sink is None:
sink = self.sink
if isinstance(source, numbers.Integral):
source = [
source,
]
if isinstance(sink, numbers.Integral):
sink = [
sink,
]
if _logger:
logger.info(
'Calculating rates between source: {} and sink: {} states.'.
format(source, sink))
if len(np.intersect1d(source, sink)) != 0:
if _logger:
logger.info(
'Calculating rates between state and itself gives 0')
r = Rates()
return r
if self.source in source: # Apply concentration only on the bulk state
conc = self.concentration
elif self.source in sink: # Invert concentration is bulk state is in sink
if _logger:
logger.info(
'Bulk state detected in sink. Applying concentration correction to sink instead of source.'
)
conc = 1 / self.concentration
else:
conc = 1
model = self.model
if states == 'macro': # Finding the microstates of the macrostates
eq = model.eqDistribution(
plot=False
) # If macro, use the membership probs to calculate eq prob
sinkeq = np.sum(
eq[sink]
) # sink and source might be multiple macros so we have to sum them
sourceeq = np.sum(eq[source])
sourcemicros = []
for s in source:
sourcemicros += list(np.where(model.macro_ofmicro == s)[0])
sinkmicros = []
for s in sink:
sinkmicros += list(np.where(model.macro_ofmicro == s)[0])
elif states == 'micro':
eq = model.msm.stationary_distribution
sinkeq = np.sum(eq[sink])
sourceeq = np.sum(eq[source])
sourcemicros = source
sinkmicros = sink
from msmtools.analysis import mfpt
r = Rates()
r.mfpton = model.data.fstep * model.lag * mfpt(
self.model.P, origin=sourcemicros, target=sinkmicros)
r.mfptoff = model.data.fstep * model.lag * mfpt(
self.model.P, origin=sinkmicros, target=sourcemicros)
r.koff = 1E9 / r.mfptoff
r.kon = 1E9 / (r.mfpton * conc)
if conc != 1:
if _logger:
logger.info(
'Concentration correction of {:.2f} kcal/mol.'.format(
-self._kBT * np.log(1 / conc)))
r.g0eq = -self._kBT * np.log(sinkeq / (conc * sourceeq))
r.kdeq = np.exp(r.g0eq / self._kBT)
return r
def getRates(self, source=None, sink=None, states='macro', _logger=True):
""" Get the rates between two (sets of) states
Parameters
----------
source : int, optional
The state index to use as source
sink : int, optional
The state index to use as sink
states : ['macro','micro'], optional
The state type of the states given before
Returns
-------
rates : :class:`Rates` object
A Rates object containing the rates
Example
-------
>>> kin = Kinetics(model, temperature=300, concentration=0.015)
>>> r = kin.getRates()
>>> print(r)
>>> dg = r.g0eq
>>> r = kin.getRates(source=4, sink=[0,1,2,3])
"""
import numbers
self._intergrityCheck()
if source is None:
source = self.source
if sink is None:
sink = self.sink
if isinstance(source, numbers.Integral):
source = [source, ]
if isinstance(sink, numbers.Integral):
sink = [sink, ]
if _logger: logger.info('Calculating rates between source: {} and sink: {} states.'.format(source, sink))
if len(np.intersect1d(source, sink)) != 0:
if _logger: logger.info('Calculating rates between state and itself gives 0')
r = Rates()
return r
if self.source in source: # Apply concentration only on the bulk state
conc = self.concentration
elif self.source in sink: # Invert concentration is bulk state is in sink
if _logger: logger.info('Bulk state detected in sink. Applying concentration correction to sink instead of source.')
conc = 1 / self.concentration
else:
conc = 1
model = self.model
if states == 'macro': # Finding the microstates of the macrostates
eq = model.eqDistribution(plot=False) # If macro, use the membership probs to calculate eq prob
sinkeq = np.sum(eq[sink]) # sink and source might be multiple macros so we have to sum them
sourceeq = np.sum(eq[source])
sourcemicros = []
for s in source:
sourcemicros += list(np.where(model.macro_ofmicro == s)[0])
sinkmicros = []
for s in sink:
sinkmicros += list(np.where(model.macro_ofmicro == s)[0])
elif states == 'micro':
eq = model.msm.stationary_distribution
sinkeq = np.sum(eq[sink])
sourceeq = np.sum(eq[source])
sourcemicros = source
sinkmicros = sink
from msmtools.analysis import mfpt
r = Rates()
r.mfpton = model.data.fstep * model.lag * mfpt(self.model.P, origin=sourcemicros, target=sinkmicros)
r.mfptoff = model.data.fstep * model.lag * mfpt(self.model.P, origin=sinkmicros, target=sourcemicros)
r.koff = 1E9 / r.mfptoff
r.kon = 1E9 / (r.mfpton * conc)
if conc != 1:
if _logger: logger.info('Concentration correction of {:.2f} kcal/mol.'.format(-self._kBT * np.log(1 / conc)))
r.g0eq = -self._kBT * np.log(sinkeq / (conc * sourceeq))
r.kdeq = np.exp(r.g0eq / self._kBT)
return r
