def two_subs_one_prod_random_rev():
"""Reversible two substrates, one product random order mechanism."""
print("Two substrates, one product random reversible mechanism.")
crn = from_react_file(
os.path.join(input_reactions, "two_subs_one_prod_rand_rev"))
crn.remove(rapid_eq = [('ea', 'e+a'), ('eb', 'e+b')], \
qss = ['eab'], \
cons_law = ('e', ConsLaw('e + ea + eb + eab', 'et')))
constants = dict(
Vf=parse_expr("et*k5"),
Vr=parse_expr("et*(k_3+k_4)"),
kia=parse_expr("k_1/k1"),
kib=parse_expr("k_2/k2"),
Kmb=parse_expr("k1*k_2*(k5 + k_3 + k_4)/(k1*k3*k_2 + k2*k4*k_1)"),
Kmp=parse_expr("(k5 + k_3 + k_4)/k_5"))
rateab = parse_expr(
"Vf/(kia*Kmb)/(1+a/kia+b/kib+a*b/(kia*Kmb)+p/Kmp)").subs(constants)
ratep = parse_expr("Vr/Kmp/(1+a/kia+b/kib+a*b/(kia*Kmb)+p/Kmp)").subs(
constants)
rateab = rateab.expand().factor().factor()
ratep = ratep.expand().factor().factor()
indab = crn.complexes.index(parse_complex('a + b'))
indp = crn.complexes.index(parse_complex('p'))
diffab = crn.laplacian[indab, indab] - rateab
diffab = diffab.factor()
diffp = crn.laplacian[indp, indp] - ratep
diffp = diffp.factor()
fail_if_not_equal(diffab, 0)
fail_if_not_equal(diffp, 0)
def two_subs_one_prod_compulsory_rev():
"""Reversible two substrate, one product compulsory order mechanism.
Rates compared to http://www.cogsys.cs.uni-tuebingen.de/software/SBMLsqueezer/doc/KineticLaws2.pdf."""
print("Two substrates, one product compulsory reversible mechanism.")
crn = from_react_file(
os.path.join(input_reactions, "two_subs_one_prod_compul_rev"))
crn.qss(cons_law=('e', ConsLaw('e + ea + eab', 'et')))
constants = dict(kpluscat=parse_expr("k3"),
kminuscat=parse_expr("k_1*k_2/(k_1+k_2)"),
kia=parse_expr("k_1/k1"),
kip=parse_expr("k3/k_3"),
Kma=parse_expr("k3/k1"),
Kmb=parse_expr("(k_2+k3)/k2"),
Kmp=parse_expr("k_1*(k_2+k3)/(k_3*(k_1+k_2))"))
rateab = parse_expr(
"kpluscat*et/(kia*Kmb)/(1+a/kia+Kma*b/(kia*Kmb)+a*b/(Kmb*kia)+Kma*b*p/(kia*Kmb*kip)+p/Kmp)"
).subs(constants)
indab = crn.complexes.index(parse_complex('a + b'))
diffab = (rateab - crn.laplacian[indab, indab]).factor()
ratep = parse_expr(
"kminuscat*et/Kmp/(1+a/kia+Kma*b/(kia*Kmb)+a*b/(Kmb*kia)+Kma*b*p/(kia*Kmb*kip)+p/Kmp)"
).subs(constants)
indp = crn.complexes.index(parse_complex('p'))
diffp = (ratep - crn.laplacian[indp, indp]).factor()
fail_if_not_equal(diffab, 0)
fail_if_not_equal(diffp, 0)
def two_subs_two_prods_compulsory():
"""Irreversible and reversible two substrates, two products compulsory order mechanism."""
print("Two substrates, two products compulsory mechanism.")
# Full version, without using conservation law
crn = from_react_file(
os.path.join(input_reactions, "two_subs_two_prods_compul"))
crn.qss('eab')
crn.qss('ea')
crn.remove_all_constants()
# Full version
crn = from_react_file(
os.path.join(input_reactions, "two_subs_two_prods_compul"))
crn.qss(cons_law=('e', ConsLaw('e + ea + eab', 'et')))
rate = parse_expr(
"k3*et*a*b/(k_1*(k_2+k3)/(k1*k2)+(k_2+k3)/k2*a+k3/k1*b+a*b)")
fail_if_not_equal((crn.rates[0] - rate).factor(), 0)
# Cornish-Bowden version, 6.3
crn = from_react_file(
os.path.join(input_reactions, "two_subs_two_prods_compul_ternary"))
crn.qss(cons_law=('e', ConsLaw('e + ea + eq + eab', 'et')))
constants = dict(Vf=parse_expr("k3*k4*et/(k3+k4)"),
Vr=parse_expr("k_1*k_2*et/(k_1+k_2)"),
kia=parse_expr("k_1/k1"),
kib=parse_expr("(k_1+k_2)/k2"),
kip=parse_expr("(k3+k4)/k_3"),
kiq=parse_expr("k4/k_4"),
Kma=parse_expr("k3*k4/k1/(k3+k4)"),
Kmb=parse_expr("(k_2+k3)*k4/k2/(k3+k4)"),
Kmp=parse_expr("k_1*(k_2+k3)/(k_1+k_2)/k_3"),
Kmq=parse_expr("k_1*k_2/(k_1+k_2)/k_4"))
rateab = parse_expr(
"Vf/(kia*Kmb)/(1+a/kia+b*Kma/(kia*Kmb)+p*Kmq/(kiq*Kmp)+q/kiq+a*b/(kia*Kmb)+Kmq*a*p/(kia*Kmp*kiq)+\
Kma*b*q/(kia*Kmb*kiq)+p*q/(Kmp*kiq)+a*b*p/(kia*Kmb*kip)+b*p*q/(kib*Kmp*kiq))"
).subs(constants)
ratepq = parse_expr(
"Vr/(kiq*Kmp)/(1+a/kia+b*Kma/(kia*Kmb)+p*Kmq/(kiq*Kmp)+q/kiq+a*b/(kia*Kmb)+Kmq*a*p/(kia*Kmp*kiq)+\
Kma*b*q/(kia*Kmb*kiq)+p*q/(Kmp*kiq)+a*b*p/(kia*Kmb*kip)+b*p*q/(kib*Kmp*kiq))"
).subs(constants)
rateab = rateab.factor()
ratepq = ratepq.factor()
indab = crn.complexes.index(parse_complex('a + b'))
indpq = crn.complexes.index(parse_complex('p + q'))
diffab = crn.laplacian[indab, indab] - rateab
diffab = diffab.factor()
diffpq = crn.laplacian[indpq, indpq] - ratepq
diffpq = diffpq.factor()
fail_if_not_equal(diffab, 0)
fail_if_not_equal(diffpq, 0)
def two_subs_one_prod_random_irr():
"""Irreversible two substrates, one product random order mechanism.
(random order bi-uni mechanism, http://www.ebi.ac.uk/sbo/main/SBO:0000432)."""
print("Two substrates, one product random irreversible mechanism.")
crn = from_react_file(
os.path.join(input_reactions, "two_subs_one_prod_rand_irr"))
crn.remove(rapid_eq = [('ea', 'e+a'), ('eb', 'e+b')], \
qss = ['eab'], \
cons_law = ('e', ConsLaw('e + ea + eb + eab', 'et')))
constants = dict(
Vf=parse_expr("et*k5"),
Vr=parse_expr("et*(k_3+k_4)"),
kia=parse_expr("k_1/k1"),
kib=parse_expr("k_2/k2"),
Kmb=parse_expr("k1*k_2*(k5 + k_3 + k_4)/(k1*k3*k_2 + k2*k4*k_1)"),
Kmp=parse_expr("(k5 + k_3 + k_4)/k_5"))
rateab = parse_expr("Vf/(kia*Kmb)/(1+a/kia+b/kib+a*b/(kia*Kmb))").subs(
constants)
indab = crn.complexes.index(parse_complex('a + b'))
diff = crn.laplacian[indab, indab] - rateab
diff = diff.factor()
fail_if_not_equal(diff, 0)
def ternary_compulsory():
"""Transfer of a radioactive atom (a_s -> p_s), in a ternary compulsory mechanism. Cornish-Bowden, 6.8."""
print("Example of transfer of a radioactive atom.")
# Exchange requires a_s to bind to e. Inhibited by high concentrations of a and q, as they also bind to e.
crn = from_react_file(os.path.join(input_reactions, "ternary_compulsory"))
with warnings.catch_warnings(record=True) as w:
# Use 'e + ea + eab + eq' instead of proper conservation 'e + ea + ea_s + eab + ea_sb + eq')
crn.remove(rapid_eq = [('eab', 'ea + b'), ('ea', 'e + a'), ('eq', 'e + q')], \
cons_law = ('e' , ConsLaw('e + ea + eab + eq', 'et')))
crn.remove(qss=['ea_sb', 'ea_s'])
# unlabelled species assumed constant
for s in ['a', 'p', 'b', 'q']:
crn.remove_constant(s)
for ws in w:
assert "not constant." in str(ws.message)
# page 122
ratea_s = parse_expr(
'k1*k2*k3*et*b/((1+k1*a/k_1+k1*k2*a*b/(k_1*k_2)+k_4*q/k4)*(k_1*(k_2+k3)+k2*k3*b))'
)
ratep_s = parse_expr(
'k_1*k_2*k_3*k_4/k4*et*q/((1+k1*a/k_1+k1*k2*a*b/(k_1*k_2)+k_4*q/k4)*(k_1*(k_2+k3)+k2*k3*b))'
)
ratea_s = ratea_s.expand().factor().factor()
ratep_s = ratep_s.expand().factor().factor()
inda_s = crn.complexes.index(parse_complex('a_s'))
indp_s = crn.complexes.index(parse_complex('p_s'))
diffa_s = crn.laplacian[inda_s, inda_s] - ratea_s
diffa_s = diffa_s.factor()
diffp_s = crn.laplacian[indp_s, indp_s] - ratep_s
diffp_s = diffp_s.factor()
fail_if_not_equal(diffa_s, 0)
fail_if_not_equal(diffp_s, 0)
# Full version
crn = from_react_file(os.path.join(input_reactions, "ternary_compulsory"))
#for c in ['a', 'p', 'b', 'q']: crn.remove_constant(c)
crn.remove(rapid_eq = [('eab', 'ea + b'), ('ea', 'e + a'), ('eq', 'e + q')], \
qss = ['ea_sb', 'ea_s'], \
cons_law = ('e' , ConsLaw('e + ea + ea_s + eab + ea_sb + eq', 'et')))
def allosteric_activation():
"""Allosteric activation (Ingalls 3.7.8)."""
print("Allosteric activation.")
crn = from_react_file(
os.path.join(input_reactions, "allosteric_activation"))
crn.qss(cons_law = ('E', ConsLaw('E + ER + ERS', 'Etot')), \
remove_const = True, merge_reacts = True)
#crn.remove_all_constants()
inds = crn.complexes.index(parse_complex('S'))
fail_if_not_equal(
sp.factor(crn.laplacian[inds, inds] - parse_expr(
"R*k3*Etot/(R * (k_2 + k3)/k2 + k_1*(k_2 + k3)/(k1*k2) + S*R)")),
0)
def two_subs_one_prod_compulsory_irr():
"""Irreversible two substrate, one product compulsory order mechanism.
Rates compared to http://www.cogsys.cs.uni-tuebingen.de/software/SBMLsqueezer/doc/KineticLaws2.pdf."""
print("Two substrates, one product compulsory irreversible mechanism.")
# Irreversible
crn = from_react_file(
os.path.join(input_reactions, "two_subs_one_prod_compul_irr"))
crn.qss(cons_law=('e', ConsLaw('e + ea + eab', 'et')))
rateab = parse_expr("k3*et/(kia*Kmb)/(1+a/kia+Kma*b/(kia*Kmb)+a*b/(Kmb*kia))").subs("kia", parse_expr("k_1/k1")) \
.subs("Kma", parse_expr("k3/k1")) \
.subs("Kmb", parse_expr("(k_2+k3)/k2"))
indab = crn.complexes.index(parse_complex('a + b'))
fail_if_not_equal((rateab - crn.laplacian[indab, indab]).factor(), 0)
def two_subs_two_prods_subs_enzyme():
"""Substituted-enzyme (ping-pong) mechanism. From Cornish-Bowden, section 6.1."""
print("Substituted enzyme mechanism.")
crn = from_react_file(
os.path.join(input_reactions, "two_subs_two_prods_subs_enzyme"))
crn.qss(cons_law=('e', ConsLaw('e + e1 + ea + e1b', 'et')))
constants = dict(Vf=parse_expr("k2*k4*et/(k2+k4)"),
Vr=parse_expr("k_1*k_3*et/(k_1+k_3)"),
kia=parse_expr("k_1/k1"),
kib=parse_expr("k_3/k3"),
kip=parse_expr("k2/k_2"),
kiq=parse_expr("k4/k_4"),
Kma=parse_expr("(k_1+k2)*k4/k1/(k2+k4)"),
Kmb=parse_expr("k2/k3*(k_3+k4)/(k2+k4)"),
Kmp=parse_expr("k_3/k_2*(k_1+k2)/(k_1+k_3)"),
Kmq=parse_expr("k_1/k_4*(k_3+k4)/(k_1+k_3)"))
rateab = parse_expr(
"Vf/(kia*Kmb)/(a/kia+b*Kma/(kia*Kmb)+p/kip+q*Kmp/(kip*Kmq)+a*b/(kia*Kmb)+a*p/(kia*kip)+\
Kma*b*q/(kia*Kmb*kiq)+p*q/(Kmq*kip))"
).subs(constants)
ratepq = parse_expr(
"Vr/(kip*Kmq)/(a/kia+b*Kma/(kia*Kmb)+p/kip+q*Kmp/(kip*Kmq)+a*b/(kia*Kmb)+a*p/(kia*kip)+\
Kma*b*q/(kia*Kmb*kiq)+p*q/(Kmq*kip))"
).subs(constants)
rateab = rateab.expand().factor().factor()
ratepq = ratepq.expand().factor().factor()
indab = crn.complexes.index(parse_complex('a + b'))
indpq = crn.complexes.index(parse_complex('p + q'))
diffab = crn.laplacian[indab, indab] - rateab
diffab = diffab.factor()
diffpq = crn.laplacian[indpq, indpq] - ratepq
diffpq = diffpq.factor()
fail_if_not_equal(diffab, 0)
fail_if_not_equal(diffpq, 0)
def two_subs_two_prods_random():
"""Reversible two substrates, two products random order mechanism."""
print("Two substrates, two products random mechanism.")
# Cornish-Bowden version, section 6.1
crn = from_react_file(
os.path.join(input_reactions, "two_subs_two_prods_rand"))
crn.remove(rapid_eq = [('ea', 'e+a'), ('ep', 'e+p'), ('eb', 'e+b'), ('eq', 'e+q')], \
qss = ['eab', 'epq'], \
cons_law = ('e', ConsLaw('e + ea + eb + ep + eq + eab + epq', 'et')), \
merge_reacts = True)
constants = dict(
Vf=parse_expr("et*k9*(k5 + k6)/(k5 + k6 + k9 + k_9)"),
Vr=parse_expr("et*k_9*(k_3 + k_4)/(k9 + k_3 + k_4 + k_9)"),
kia=parse_expr("k_1/k1"),
kib=parse_expr("k_2/k2"),
kip=parse_expr("k7/k_7"),
kiq=parse_expr("k8/k_8"),
Kmb=parse_expr(
"k1*k_2*(k5*k9 + k5*k_3 + k5*k_4 + k6*k9 + k6*k_3 + k6*k_4 + k_3*k_9 + k_4*k_9)/((k1*k3*k_2 + k2*k4*k_1)*(k5 + k6 + k9 + k_9))"
),
Kmp=parse_expr(
"k7*k_8*(k5*k9 + k5*k_3 + k5*k_4 + k6*k9 + k6*k_3 + k6*k_4 + k_3*k_9 + k_4*k_9)/((k8*k_6*k_7 + k7*k_5*k_8)*(k9 + k_3 + k_4 + k_9))"
))
rateab = parse_expr(
"Vf/(kia*Kmb)/(1+a/kia+b/kib+p/kip+q/kiq+a*b/(kia*Kmb)+p*q/(Kmp*kiq))"
).subs(constants)
ratepq = parse_expr(
"Vr/(Kmp*kiq)/(1+a/kia+b/kib+p/kip+q/kiq+a*b/(kia*Kmb)+p*q/(Kmp*kiq))"
).subs(constants)
indab = crn.complexes.index(parse_complex('a + b'))
indpq = crn.complexes.index(parse_complex('p + q'))
diffab = crn.laplacian[indab, indab] - rateab
diffab = diffab.factor()
diffpq = crn.laplacian[indpq, indpq] - ratepq
diffpq = diffpq.factor()
fail_if_not_equal(diffab, 0)
fail_if_not_equal(diffpq, 0)
# Simplified version
crn = from_react_file(
os.path.join(input_reactions, "two_subs_two_prods_rand_v2"))
crn.remove(rapid_eq = [('ea', 'e+a'), ('ep', 'e+p'), ('eb', 'e+b'), ('eq', 'e+q')], \
qss = ['eab'], \
cons_law = ('e', ConsLaw('e + ea + eb + ep + eq + eab', 'et')))
constants = dict(
Vf=parse_expr("et*(k5+k6)"),
Vr=parse_expr("et*(k_3+k_4)"),
kia=parse_expr("k_1/k1"),
kib=parse_expr("k_2/k2"),
kip=parse_expr("k7/k_7"),
kiq=parse_expr("k8/k_8"),
Kmb=parse_expr("k1*k_2*(k5 + k6 + k_3 + k_4)/(k1*k3*k_2 + k2*k4*k_1)"),
Kmp=parse_expr(
"k7*k_8*(k5 + k6 + k_3 + k_4)/(k8*k_6*k_7 + k7*k_5*k_8)"))
rateab = parse_expr(
"Vf/(kia*Kmb)/(1+a/kia+b/kib+p/kip+q/kiq+a*b/(kia*Kmb)+p*q/(Kmp*kiq))"
).subs(constants)
ratepq = parse_expr(
"Vr/(Kmp*kiq)/(1+a/kia+b/kib+p/kip+q/kiq+a*b/(kia*Kmb)+p*q/(Kmp*kiq))"
).subs(constants)
indab = crn.complexes.index(parse_complex('a + b'))
indpq = crn.complexes.index(parse_complex('p + q'))
diffab = crn.laplacian[indab, indab] - rateab
diffab = diffab.factor()
diffpq = crn.laplacian[indpq, indpq] - ratepq
diffpq = diffpq.factor()
fail_if_not_equal(diffab, 0)
fail_if_not_equal(diffpq, 0)
