def do_potentials(name_x, name_y, plates, plates_mf, dg0_arr, h_arr):
print("Calculating %s-%s potentials, explicit tethers..." %
(name_x, name_y))
potentials = calc_potentials(plates, dg0_arr, h_arr)
print("Calculating %s-%s potentials, mean field..." % (name_x, name_y))
potentials_mf = calc_potentials(plates_mf, dg0_arr, h_arr)
with open(
os.path.join('results',
'%s_%s_plate_potentials.txt' % (name_x, name_y)),
'w') as f:
f.write('# DeltaG0 (kT)\t'
'h (nm)\t'
'Explicit pair potential (kT / nm^2)\t'
'Mean field pair potential (kT / nm^2)\n')
for dg0 in dg0_arr:
for (h, V, Vmf) in zip(h_arr, potentials[dg0], potentials_mf[dg0]):
f.write("%g\t%g\t%g\t%g\n" % (dg0, h / nm, V, Vmf))
f.write("\n")
try:
with working_directory('gp'):
subprocess.call([
'gnuplot',
'plot_%s_%s_plate_potentials.gp' % (name_x, name_y)
])
except Exception:
pass
with open(
os.path.join('results',
'%s_%s_sphere_potentials.txt' % (name_x, name_y)),
'w') as f:
f.write('# DeltaG0 (kT)\t'
'h (nm)\t'
'Explicit + Derjaguin Pair potential (kT)\t'
'Mean field + Derjaguin Pair potential (kT)\n')
for dg0 in dg0_arr:
V_sphere = dnacc.calc_spheres_potential(h_arr, potentials[dg0], R)
V_sphere_mf = dnacc.calc_spheres_potential(h_arr,
potentials_mf[dg0], R)
for (h, V, Vmf) in zip(h_arr, V_sphere, V_sphere_mf):
f.write("%g\t%g\t%g\t%g\n" % (dg0, h / nm, V, Vmf))
f.write("\n")
try:
with working_directory('gp'):
subprocess.call([
'gnuplot',
'plot_%s_%s_sphere_potentials.gp' % (name_x, name_y)
])
except Exception:
pass
def do_potentials(name_x, name_y, plates, plates_mf, dg0_arr, h_arr):
print("Calculating %s-%s potentials, explicit tethers..." %
(name_x, name_y))
potentials = calc_potentials(plates, dg0_arr, h_arr)
print("Calculating %s-%s potentials, mean field..." %
(name_x, name_y))
potentials_mf = calc_potentials(plates_mf, dg0_arr, h_arr)
with open(os.path.join(
'results',
'%s_%s_plate_potentials.txt' % (name_x, name_y)), 'w') as f:
f.write('# DeltaG0 (kT)\t' 'h (nm)\t'
'Explicit pair potential (kT / nm^2)\t'
'Mean field pair potential (kT / nm^2)\n')
for dg0 in dg0_arr:
for (h, V, Vmf) in zip(h_arr, potentials[dg0],
potentials_mf[dg0]):
f.write("%g\t%g\t%g\t%g\n" % (dg0, h / nm, V, Vmf))
f.write("\n")
try:
with working_directory('gp'):
subprocess.call(['gnuplot', 'plot_%s_%s_plate_potentials.gp' %
(name_x, name_y)])
except Exception:
pass
with open(os.path.join(
'results',
'%s_%s_sphere_potentials.txt' % (name_x, name_y)), 'w') as f:
f.write('# DeltaG0 (kT)\t' 'h (nm)\t'
'Explicit + Derjaguin Pair potential (kT)\t'
'Mean field + Derjaguin Pair potential (kT)\n')
for dg0 in dg0_arr:
V_sphere = dnacc.calc_spheres_potential(
h_arr, potentials[dg0], R)
V_sphere_mf = dnacc.calc_spheres_potential(
h_arr, potentials_mf[dg0], R)
for (h, V, Vmf) in zip(h_arr, V_sphere, V_sphere_mf):
f.write("%g\t%g\t%g\t%g\n" % (dg0, h / nm, V, Vmf))
f.write("\n")
try:
with working_directory('gp'):
subprocess.call(['gnuplot', 'plot_%s_%s_sphere_potentials.gp' %
(name_x, name_y)])
except Exception:
pass
def do_it(beta_DeltaG0Mid):
print 'Working on beta_DeltaG0Mid = %g' % beta_DeltaG0Mid
# and various energy gaps
for beta_Delta in xrange(0, 10):
plates.beta_DeltaG0['alpha', 'beta1'] = \
beta_DeltaG0Mid - 0.5 * beta_Delta
plates.beta_DeltaG0['alpha', 'beta2'] = \
beta_DeltaG0Mid + 0.5 * beta_Delta
# and various total strand coverage
for S in 0.75, 0.25:
sigma = 1 / (S * L) ** 2
ts[ALPHA]['sigma'] = sigma * 0.5
with open('walk-S%0.2f-G0Mid%.1f-delta%.1f.dat' %
(S, beta_DeltaG0Mid, beta_Delta), 'w') as f:
f.write('c\t' 'F_rep (kT)\n')
offset = 0
for c in np.linspace(1.0, 0.0, 21):
ts[BETA_1]['sigma'] = c * sigma
ts[BETA_2]['sigma'] = (1 - c) * sigma
# Calculate effective plate-plate potential
hArr = np.linspace(0.05 * L, 2.00 * L, 40)
VArr = [plates.at(h).free_energy_density
for h in hArr]
# and the resulting plate-sphere potential
Rplt = 1000.0 * R
betaF = dnacc.calc_spheres_potential(
hArr, VArr, R, Rplt)
# Find its minimum
minH, minBetaF = min(zip(hArr, betaF),
key=operator.itemgetter(1))
if offset == 0:
offset = -minBetaF
f.write('%.2f\t%.4f\t%.4f\n' %
(c, minBetaF + offset, minH / nm))
def do_it(beta_DeltaG0Mid):
print 'Working on beta_DeltaG0Mid = %g' % beta_DeltaG0Mid
# and various energy gaps
for beta_Delta in xrange(0, 10):
plates.beta_DeltaG0['alpha', 'beta1'] = \
beta_DeltaG0Mid - 0.5 * beta_Delta
plates.beta_DeltaG0['alpha', 'beta2'] = \
beta_DeltaG0Mid + 0.5 * beta_Delta
# and various total strand coverage
for S in 0.75, 0.25:
sigma = 1 / (S * L)**2
ts[ALPHA]['sigma'] = sigma * 0.5
with open(
'walk-S%0.2f-G0Mid%.1f-delta%.1f.dat' %
(S, beta_DeltaG0Mid, beta_Delta), 'w') as f:
f.write('c\t' 'F_rep (kT)\n')
offset = 0
for c in np.linspace(1.0, 0.0, 21):
ts[BETA_1]['sigma'] = c * sigma
ts[BETA_2]['sigma'] = (1 - c) * sigma
# Calculate effective plate-plate potential
hArr = np.linspace(0.05 * L, 2.00 * L, 40)
VArr = [plates.at(h).free_energy_density for h in hArr]
# and the resulting plate-sphere potential
Rplt = 1000.0 * R
betaF = dnacc.calc_spheres_potential(hArr, VArr, R, Rplt)
# Find its minimum
minH, minBetaF = min(zip(hArr, betaF),
key=operator.itemgetter(1))
if offset == 0:
offset = -minBetaF
f.write('%.2f\t%.4f\t%.4f\n' %
(c, minBetaF + offset, minH / nm))
# Make plate potential first
with open('plates-S%0.2f-G%.1f.dat' % (S, betaDeltaG0), 'w') as f:
f.write('\t'.join([
'h / L', "F_rep (kT/L^2)", "F_att (kT/L^2)", "F_plate (kT/L^2)"
]) + '\n')
for h, V in zip(hArr, betaFPlate):
betaFRep = plates.at(h).rep_free_energy_density
betaFAtt = V - betaFRep
f.write('%.7g\t%.7g\t%.7g\t%.7g\n' %
(h / L, betaFRep / (1 / L**2), betaFAtt / (1 / L**2),
(betaFRep + betaFAtt) / (1 / L**2)))
# Now sphere potentials
# (don't decompose into attractive and repulsive contributions,
# although it's not hard to do)
for R in 6.7, 25.0:
betaFSphere = dnacc.calc_spheres_potential(hArr, betaFPlate, R * L)
with open('spheres-R%.1f-S%0.2f-G%.1f.dat' % (R, S, betaDeltaG0),
'w') as f:
f.write('\t'.join([
'h / L', "[ignore: F_rep (kT)]", "[ignore: F_att (kT)]",
"F_sphere (kT)"
]) + '\n')
for h, V in zip(hArr, betaFSphere):
f.write('%.7g\t%.7g\t%.7g\t%.7g\n' % (h / L, 0, 0, V))
)
# Now compute a similar plate potential using the Poisson approximation
badBetaFPlate = [-plates.at(h).sigma_bound[ALPHA, ALPHA_P] + plates.rep_free_energy_density for h in hArr]
with open("bad-plates-A_B-T%.1f-G%.1f.txt" % (T, beta_DeltaG0), "w") as f:
f.write("# h (nm)\t" "F_rep (kT/nm^2)\t" "F_att (kT/nm^2)\t" "F_plate (kT/nm^2)\n")
for h, betaF, betaFRep in zip(hArr, badBetaFPlate, betaFRepPlate):
betaFAtt = betaF - betaFRep
f.write(
"%g\t%g\t%g\t%g\n" % (h / nm, betaFRep / (1 / nm ** 2), betaFAtt / (1 / nm ** 2), betaF / (1 / nm ** 2))
)
# Now for sphere-sphere potentials
betaFSpheres = dnacc.calc_spheres_potential(hArr, betaFPlate, R)
betaFRepSpheres = dnacc.calc_spheres_potential(hArr, betaFRepPlate, R)
with open("spheres-A_B-T%.1f-G%.1f.txt" % (T, beta_DeltaG0), "w") as f:
f.write("# h (nm)\t" "F_rep (kT)\t" "F_att (kT)\t" "F_spheres (kT)\n")
for h, betaF, betaFRep in zip(hArr, betaFSpheres, betaFRepSpheres):
betaFAtt = betaF - betaFRep
f.write("%g\t%g\t%g\t%g\n" % (h / nm, betaFRep, betaFAtt, betaF))
# Same, but with the Poisson approximation
badBetaFSpheres = dnacc.calc_spheres_potential(hArr, badBetaFPlate, R)
with open("bad-spheres-A_B-T%.1f-G%.1f.txt" % (T, beta_DeltaG0), "w") as f:
f.write("# h (nm)\t" "F_rep (kT)\t" "F_att (kT)\t" "F_spheres (kT)\n")
for h, betaF, betaFRep in zip(hArr, badBetaFSpheres, betaFRepSpheres):
betaFAtt = betaF - betaFRep
# along with this program. If not, see <http://www.gnu.org/licenses/>.
import dnacc
from dnacc.units import nm
import numpy as np
plates = dnacc.PlatesMeanField()
plates.add_tether_type(plate='lower',
sticky_end='alpha',
L=20 * nm,
sigma=1 / (20 * nm) ** 2)
plates.add_tether_type(plate='upper',
sticky_end='alphap',
L=20 * nm,
sigma=1 / (20 * nm) ** 2)
plates.beta_DeltaG0['alpha', 'alphap'] = -8 # in kT
plates.at(41 * nm).set_reference_now()
h_arr = np.linspace(1 * nm, 40 * nm, 40)
V_plate_arr = [plates.at(h).free_energy_density for h in h_arr]
R = 500 * nm
V_sphere_arr = dnacc.calc_spheres_potential(h_arr, V_plate_arr, R)
print("# h (nm) V (kT)")
for (h, V) in zip(h_arr, V_sphere_arr):
print (h / nm), V
def test_potential_1(self):
if (self.__dnacc):
try:
import dnacc
from dnacc.units import nm
except:
pass
else:
self.__params = {
"r1": 500,
"r2": 500,
"lengths": {
"A": 20,
"B": 20
},
"sigma1": {
"A": 1 / 20.**2
},
"sigma2": {
"B": 1 / 20.**2
},
"beta_DeltaG0": {
("A", "A"): 0,
("A", "B"): -8,
("B", "B"): 0
}
}
res = potential.DNACC(**self.__params)
r = numpy.linspace(41 / 1000., 41, 1000) + 500. + 500.
u, f = res.evaluate_array(r)
# Example from documentation
plates = dnacc.PlatesMeanField()
plates.add_tether_type(plate='lower',
sticky_end='alpha',
L=20 * nm,
sigma=1 / (20 * nm)**2)
plates.add_tether_type(plate='upper',
sticky_end='alphap',
L=20 * nm,
sigma=1 / (20 * nm)**2)
plates.beta_DeltaG0['alpha', 'alphap'] = -8
plates.at(41 * nm).set_reference_now()
V_plate_arr = [
plates.at(rv - 1000.).free_energy_density for rv in r
]
R = 500 * nm
V_sphere_arr = dnacc.calc_spheres_potential(
r - 1000., V_plate_arr, R)
# Compare results over the domain of the theory
self.assertTrue(numpy.allclose(V_sphere_arr, u))
# Check that potential is zero beyond cutoff
self.assertEqual(res.evaluate(r[-1] + 0.00001), (0.0, 0.0))
# Check that WCA-esque potential wall is used at contact and below
rep_wallu, rep_wallf = res.evaluate_array(
numpy.linspace(0, r[0], 1000))
# Wall is monotonically decreasing
self.assertEqual(res.evaluate(0), (numpy.inf, numpy.inf))
self.assertTrue(
numpy.all(rep_wallu[1:] < numpy.inf)
and numpy.all(rep_wallu[1:] > 0))
self.assertTrue(
numpy.all(x > y for x, y in zip(rep_wallu, rep_wallu[1:])))
self.assertTrue(
numpy.all(rep_wallf[1:] < numpy.inf)
and numpy.all(rep_wallf[1:] > 0))
self.assertTrue(
numpy.all(x > y for x, y in zip(rep_wallf, rep_wallf[1:])))
# Wall connects continuously
self.assertTrue(numpy.isclose(rep_wallu[-1], u[0]))
self.assertTrue(numpy.isclose(rep_wallf[-1], f[0]))
f.write('\t'.join(['h / L',
"F_rep (kT/L^2)",
"F_att (kT/L^2)",
"F_plate (kT/L^2)"]) + '\n')
for h, V in zip(hArr, betaFPlate):
betaFRep = plates.at(h).rep_free_energy_density
betaFAtt = V - betaFRep
f.write('%.7g\t%.7g\t%.7g\t%.7g\n'
% (h / L, betaFRep / (1 / L ** 2),
betaFAtt / (1 / L ** 2),
(betaFRep + betaFAtt) / (1 / L ** 2)))
# Now sphere potentials
# (don't decompose into attractive and repulsive contributions,
# although it's not hard to do)
for R in 6.7, 25.0:
betaFSphere = dnacc.calc_spheres_potential(
hArr, betaFPlate, R * L)
with open('spheres-R%.1f-S%0.2f-G%.1f.dat'
% (R, S, betaDeltaG0), 'w') as f:
f.write('\t'.join(['h / L',
"[ignore: F_rep (kT)]",
"[ignore: F_att (kT)]",
"F_sphere (kT)"]) + '\n')
for h, V in zip(hArr, betaFSphere):
f.write('%.7g\t%.7g\t%.7g\t%.7g\n'
% (h / L, 0, 0, V))
# along with this program. If not, see <http://www.gnu.org/licenses/>.
import dnacc
from dnacc.units import nm
import numpy as np
plates = dnacc.PlatesMeanField()
plates.add_tether_type(plate='lower',
sticky_end='alpha',
L=20 * nm,
sigma=1 / (20 * nm)**2)
plates.add_tether_type(plate='upper',
sticky_end='alphap',
L=20 * nm,
sigma=1 / (20 * nm)**2)
plates.beta_DeltaG0['alpha', 'alphap'] = -8 # in kT
plates.at(41 * nm).set_reference_now()
h_arr = np.linspace(1 * nm, 40 * nm, 40)
V_plate_arr = [plates.at(h).free_energy_density for h in h_arr]
R = 500 * nm
V_sphere_arr = dnacc.calc_spheres_potential(h_arr, V_plate_arr, R)
print("# h (nm) V (kT)")
for (h, V) in zip(h_arr, V_sphere_arr):
print(h / nm), V