def Invn(n=5, sigma=-0.3, mode="inverse"):
"""
spin inversion in a n coupled spins system in linear geometry
sigma is the interspin cross relaxation, can be positive or negative
mode can be "inverse" or "saturate"
"""
# set-up equilibrium
eq1 = NMR(1, n)
# add spin systems
R1E = 1.0
# sigma = 0.2
# Relax = np.matrix([[R1E,sigma],[sigma,R1E]])
Relax = R1E * np.eye(n) + sigma * (np.diag(np.ones(n - 1), 1) +
np.diag(np.ones(n - 1), -1))
Relax = np.matrix(Relax)
print(Relax)
eq1.set_spin(0, SpinSys(n, Relax))
if mode == "inverse":
eq1.set_magnetization(-1.0, 0, 0) # inverse first spin
else:
eq1.saturate(0, 0) # or saturate it
# eq1.report()
dt = 1e-2 # one step every 10msec.
maxtime = 10. # for 10 sec
(t, res) = eq1.solve(maxtime=maxtime, step=maxtime / dt,
trajectory=True) #,verbose=True)
for i in range(1, n + 1):
plt.plot(t, [r[i] for r in res], label="spin %d" % i)
plt.title("$\sigma = %f$" % sigma)
plt.legend()
plt.show()
def S2():
"""
NOE in a 2 coupled spins system
"""
# set-up equilibrium
eq1 = NMR(1, 2)
# add spin systems
R1E = 1.0
sigma = -0.2
Relax = np.matrix([[R1E, sigma], [sigma, R1E]])
eq1.set_spin(0, SpinSys(2, Relax))
eq1.saturate(0, 0)
eq1.report()
print()
cf = eq1.solve(maxtime=1) # maxtime=1E-4, step=100,verbose=True)
print("saturate one spin, look at transfer after 1sec")
print("sigma/rho: %.2f noe: %.2f" % (sigma / R1E, cf[2] - 1.0))
def Inv2():
"""
spin inversion in a 2 coupled spins system
"""
# set-up equilibrium
eq1 = NMR(1, 2)
# add spin systems
R1E = 1.0
# sigma = 0.2
for sigma in (-0.5, ): #0.25, 0.0, -0.25, -0.5, -0.8, -0.9, -0.95):
Relax = np.matrix([[R1E, sigma], [sigma, R1E]])
eq1.set_spin(0, SpinSys(2, Relax))
eq1.set_magnetization(-1.0, 0, 0) # inverse one spin
eq1.report()
st = 10. / 1e-2
(t, res) = eq1.solve(maxtime=30.0, step=st,
trajectory=True) #,verbose=True)
plt.plot(t, [r[1] for r in res], label="$\sigma = %f$" % sigma)
plt.plot(t, [r[2] for r in res])
plt.legend()
plt.show()
def EL_STD_3s(Khigh=1 / 45E-6,
Ltot=1E-3,
Etot=1E-4,
time=5.0,
verbose=False,
trajectory=False):
"""
STD exp on
E + L <-> EL equilibrium
L (1 spin) + E (1 spin saturated) <--> EL (two spins)
Same as EL_STD, but here a three spin model is used for the protein-ligand complex :
EL : (L - E1 - E2) where only E2 is saturated
"""
# set-up equilibrium
print("K=", Khigh)
eq1 = NMR(("E", "L", "EL"), 6)
L = 0
E = 1
EL = 2
eq1.set_K3(Khigh, L, E, EL)
eq1.set_concentration(Ltot, L)
eq1.set_concentration(Etot, E)
eq1.set_massconserv(Ltot, [1, 0, 1]) # in L
eq1.set_massconserv(Etot, [0, 1, 1]) # in E
# then add spin systems
R1L = R1E = 1.0
sigma = -0.99
RelaxE = np.matrix([[R1E, sigma], [sigma, R1E]])
RelaxEL = np.matrix([[R1E, sigma, 0.0], [sigma, R1E, sigma],
[0.0, sigma, R1E]])
eq1.set_spin(L, SpinSys(1, R1L)) #L
eq1.set_spin(E, SpinSys(2, RelaxE)) #E
eq1.set_spin(EL, SpinSys(3, RelaxEL)) #EL
eq1.set_spinflux(E, 0, EL, 1) # which is which
eq1.set_spinflux(E, 1, EL, 2) # which is which
eq1.set_spinflux(L, 0, EL, 0)
if verbose:
print("\nDepart\n")
eq1.report()
print("state_dic", eq1.state_dic)
print("dic_state", eq1.dic_state)
print("species2spins")
for i in range(eq1.Nspecies):
print(i, list(eq1.species2spins(i)))
print("spin2species")
for i in range(eq1.Nspins):
print(i, eq1.spin2species(i))
# compute equilibrium
cf = eq1.solve(maxtime=1E-2, step=100)
# then apply saturation
eq1.conc = cf[0:3]
eq1.saturate(E, 1) # we saturate the protein
eq1.saturate(EL, 2)
if verbose:
print("\nsaturation\n")
eq1.report()
st = max(1, time / 1E-3) # computes at 1ms resolution
res = eq1.solve(maxtime=time,
step=st,
trajectory=trajectory,
verbose=verbose)
if trajectory:
(t, cf3) = res
plt.plot(t, cf3[:, 3])
(t, cf) = EL_STD(trajectory=True, time=time)
plt.plot(t, cf[:, 3])
plt.show()
return res
def EL_STD(Khigh=1 / 3E-4,
Ltot=1E-3,
Etot=1E-4,
time=1.0,
step=10,
verbose=False,
trajectory=False):
"""
Saturation Difference Difference experience on the equilibrium
E + L <-> EL
L (1 spin) + E (1 spin saturated) <--> EL (two spins - E spin saturated)
"""
# set-up equilibrium
Dprint("K=", Khigh)
eq1 = NMR(("E", "L", "EL"), 4)
L = 0
E = 1
EL = 2
eq1.set_K3(Khigh, L, E, EL)
eq1.set_concentration(Ltot, L)
eq1.set_concentration(Etot, E)
eq1.set_massconserv(Ltot, [1, 0, 1]) # in L
eq1.set_massconserv(Etot, [0, 1, 1]) # in E
# then add spin systems
R1L = 1.0
R1E = 10.0
sigma = -0.5 * R1E
eq1.set_spin(L, SpinSys(1, R1L)) #L
eq1.set_spin(E, SpinSys(1, R1E)) #E
Relax = np.matrix([[R1E, sigma], [sigma, R1E]])
eq1.set_spin(EL, SpinSys(2, Relax)) #EL
eq1.set_spinflux(E, 0, EL, 1) # which is which
eq1.set_spinflux(L, 0, EL, 0)
if verbose:
print(r"\Starting\n")
eq1.report()
# compute equilibrium
cf = eq1.solve(maxtime=1E-3, step=10)
# eq1.Integrator = "odeint"
# then apply saturation
eq1.saturate(E, 0) # we saturate the protein
eq1.saturate(EL, 1) # in both binding states !
if verbose:
print("\nsaturation\n")
eq1.report()
res = eq1.solve(maxtime=time,
step=step,
trajectory=trajectory,
verbose=verbose)
finale = eq1.get_concentration_array()
if verbose:
print("\n final concentrations:")
eq1.showconc()
print("\n final magnetizations:")
eq1.showmagn()
print("fraction occupied %f %%" % (100 * finale[EL] /
(finale[E] + finale[EL])))
if not trajectory:
print("EL_STD: Kd %.2g STD : %.2f %%" % (1 / Khigh, 100 *
(1 - res[3])))
return res
def T1n(n=5):
"""
compares selective and global T1 in n coupled spins system
"""
# set-up equilibrium
eq1 = NMR(1, n)
# add spin systems
R1E = 0.5 * (n + 1) # non selectif T1 : spin-lattice relaxation
sigma = -0.5 # strong sigma, corresponding to a large prot
Relax = np.matrix(sigma * np.ones((n, n))) # set sigma everywhere
for i in range(n):
Relax[i, i] = R1E # set diagonal to T1
eq1.set_spin(0, SpinSys(n, Relax))
eq1.set_magnetization(0.0, 0, 0) # pulse on one spin
eq1.report()
st = 10. / 1e-2
(t, res) = eq1.solve(maxtime=10.0, step=st,
trajectory=True) #,verbose=True)
plt.plot(t, [r[1] for r in res], label="selective pulse")
# second exp
for i in range(n):
eq1.set_magnetization(0.0, 0, i) # pulse on all spin
eq1.report()
st = 10. / 1e-2
(t, res) = eq1.solve(maxtime=10.0, step=st,
trajectory=True) #,verbose=True)
plt.plot(t, [r[1] for r in res], label="global excitation")
plt.title("magnetization recovery\nin a %d coupled spin system" % n)
plt.legend()
plt.show()
def T1():
"""
compares selective and global T1 in 2 coupled spins system
"""
# set-up equilibrium
eq1 = NMR(1, 2)
# add spin systems
R1E = 1.0 # non selectif T1 : spin-lattice relaxation
sigma = -0.5 # strong sigma, corresponding to a large prot
Relax = np.matrix([[R1E, sigma], [sigma, R1E]])
eq1.set_spin(0, SpinSys(2, Relax))
eq1.set_magnetization(0.0, 0, 0) # pulse on one spin
eq1.report()
st = 10. / 1e-2
(t, res) = eq1.solve(maxtime=10.0, step=st,
trajectory=True) #,verbose=True)
plt.plot(t, [r[1] for r in res], label="selective pulse")
# second exp
eq1.set_magnetization(0.0, 0, 0) # pulse on both spin
eq1.set_magnetization(0.0, 0, 1) # pulse on both spin
eq1.report()
st = 10. / 1e-2
(t, res) = eq1.solve(maxtime=10.0, step=st,
trajectory=True) #,verbose=True)
plt.plot(t, [r[1] for r in res], label="global excitation")
plt.title("magnetization recovery\nin a two coupled spin system")
plt.legend()
plt.show()