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Unverified Commit d83c2724 authored by Peter Eastman's avatar Peter Eastman Committed by GitHub
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Added GLYCAM (#3303) 

* Added GLYCAM

* Improved tests and documentation

* Fixed incorrect external bonds
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docs-source/usersguide/application/02_running_sims.rst
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......@@ -499,6 +499,7 @@ File Parameters
:file:`amber14/DNA.bsc1.xml` DNA (alternative)
:file:`amber14/RNA.OL3.xml` RNA
:file:`amber14/lipid17.xml` Lipid
:file:`amber14/GLYCAM_06j-1.xml` Carbohydrates and glycosylated proteins\ :cite:`Kirschner2007`
:file:`amber14/tip3p.xml` TIP3P water model\ :cite:`Jorgensen1983` and ions
:file:`amber14/tip3pfb.xml` TIP3P-FB water model\ :cite:`Wang2014` and ions
:file:`amber14/tip4pew.xml` TIP4P-Ew water model\ :cite:`Horn2004` and ions
......@@ -515,6 +516,18 @@ water model and ions\ :cite:`Wang2014`:
forcefield = ForceField('amber14-all.xml', 'amber14/tip3pfb.xml')
GLYCAM is not included by default, since it is quite large. If your system contains
carbohydrates, include that file as well:
::
forcefield = ForceField('amber14-all.xml', 'amber14/tip3pfb.xml', 'amber14/GLYCAM_06j-1.xml')
Be aware that GLYCAM works somewhat differently from most force fields. It uses
its own nonstandard `naming convention <http://legacy.glycam.org/docs/forcefield/glycam-naming-2/index.html>`_
for carbohydrates, and requires your input file to follow it. If any residues have
names different from what it expects, GLYCAM will be unable to assign parameters
to them.
.. tip:: The solvent model XML files included under the :file:`amber14/` directory
include both water *and* ions compatible with that water model, so if you
mistakenly specify :file:`tip3p.xml` instead of :file:`amber14/tip3p.xml`,
......
docs-source/usersguide/application/03_model_building_editing.rst
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......@@ -67,6 +67,17 @@ If you want more control, it is possible to specify exactly which protonation
state to use for particular residues. For details, consult the API
documentation for the Modeller class.
By default, :class:`Modeller` loads information about hydrogens in standard
amino acids and nucleic acids. You can call :meth:`loadHydrogenDefinitions` to
load definitions for other types of molecules. In particular, if your system
contains carbohydrates that you plan to simulate with the GLYCAM force field, call
::
Modeller.loadHydrogenDefinitions('glycam-hydrogens.xml')
All subsequent calls to :meth:`addHydrogens` will make use of the newly loaded
definitions.
Adding Solvent
**************
......
docs-source/usersguide/references.bib
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......@@ -207,6 +207,17 @@
type = {Journal Article}
}
@article{Kirschner2007
author = {Kirschner, Karl N. and Yongye, Austin B. and Tschampel, Sarah M. and González-Outeiriño, Jorge and Daniels, Charlisa R and Foley, B. Lachele and Woods, Robert J.},
title = {GLYCAM06: A generalizable biomolecular force field. Carbohydrates},
journal = {Journal of Computational Chemistry},
volume = {29},
issue = {4},
pages = {622-655},
year = {2007},
type = {Journal Article}
}
@inbook{Kollman1997
author = {Kollman, P.A. and Dixon, R. and Cornell, W. and Fox, T. and Chipot, C. and Pohorille, A.},
title = {Computer Simulation of Biomolecular Systems},
......
wrappers/python/openmm/app/data/amber14/GLYCAM_06j-1.xml 0 → 100644
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wrappers/python/openmm/app/data/glycam-hydrogens.xml 0 → 100644
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wrappers/python/openmm/app/forcefield.py
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......@@ -492,9 +492,13 @@ class ForceField(object):
A template matcher is a callable object that can be invoked as::
template = f(forcefield, residue)
template = f(forcefield, residue, bondedToAtom, ignoreExternalBonds, ignoreExtraParticles)
where ``forcefield`` is the ForceField invoking it and ``residue`` is a openmm.app.Residue object.
where ``forcefield`` is the ForceField invoking it, ``residue`` is an openmm.app.Residue object,
``bondedToAtom[i]`` is the set of atoms bonded to atom index i, and ``ignoreExternalBonds`` and
``ignoreExtraParticles`` indicate whether external bonds and extra particules should be considered
in matching templates.
It should return a _TemplateData object that matches the residue. Alternatively it may return
None, in which case the standard logic will be used to find a template for the residue.
......@@ -981,11 +985,11 @@ class ForceField(object):
template = None
matches = None
for matcher in self._templateMatchers:
template = matcher(self, res)
template = matcher(self, res, bondedToAtom, ignoreExternalBonds, ignoreExtraParticles)
if template is not None:
match = compiled.matchResidueToTemplate(res, template, bondedToAtom, ignoreExternalBonds, ignoreExtraParticles)
if match is None:
raise ValueError('A custom template matcher returned a template for residue %s, but it does not match the residue.' % res.name)
raise ValueError('A custom template matcher returned a template for residue %d (%s), but it does not match the residue.' % (res.index, res.name))
return [template, match]
if templateSignatures is None:
templateSignatures = self._templateSignatures
......
wrappers/python/openmm/app/modeller.py
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......@@ -35,7 +35,7 @@ __author__ = "Peter Eastman"
__version__ = "1.0"
from openmm.app import Topology, PDBFile, ForceField
from openmm.app.forcefield import AllBonds, CutoffNonPeriodic, CutoffPeriodic, DrudeGenerator
from openmm.app.forcefield import AllBonds, CutoffNonPeriodic, CutoffPeriodic, DrudeGenerator, _getDataDirectories
from openmm.app.internal import compiled
from openmm.vec3 import Vec3
from openmm import System, Context, NonbondedForce, CustomNonbondedForce, HarmonicBondForce, HarmonicAngleForce, VerletIntegrator, LangevinIntegrator, LocalEnergyMinimizer
......@@ -653,8 +653,28 @@ class Modeller(object):
The built in hydrogens.xml file containing definitions for standard amino acids and nucleotides is loaded automatically.
This method can be used to load additional definitions for other residue types. They will then be used in subsequent
calls to addHydrogens().
Parameters
----------
file : string or file
An XML file containing hydrogen definitions. It may be either an
absolute file path, a path relative to the current working
directory, a path relative to this module's data subdirectory (for
built in sets of definitions), or an open file-like object with a read()
method from which the data can be loaded.
"""
tree = etree.parse(file)
tree = None
try:
# this handles either filenames or open file-like objects
tree = etree.parse(file)
except IOError:
for dataDir in _getDataDirectories():
f = os.path.join(dataDir, file)
if os.path.isfile(f):
tree = etree.parse(f)
break
if tree is None:
raise ValueError('Could not locate file')
infinity = float('Inf')
for residue in tree.getroot().findall('Residue'):
resName = residue.attrib['name']
......@@ -869,7 +889,8 @@ class Modeller(object):
parents = [atom for atom in residue.atoms() if atom.element != elem.hydrogen]
parentNames = [atom.name for atom in parents]
hydrogens = [h for h in spec.hydrogens if (variant is None and pH <= h.maxph) or (h.variants is None and pH <= h.maxph) or (h.variants is not None and variant in h.variants)]
hydrogens = [h for h in hydrogens if h.terminal is None or (isNTerminal and h.terminal == 'N') or (isCTerminal and h.terminal == 'C')]
hydrogens = [h for h in hydrogens if h.terminal is None or (isNTerminal and 'N' in h.terminal) or (isCTerminal and 'C' in h.terminal) or
((not isNTerminal) and (not isCTerminal) and '-' in h.terminal)]
hydrogens = [h for h in hydrogens if h.parent in parentNames]
# Loop over atoms in the residue, adding them to the new topology along with required hydrogens.
......
wrappers/python/tests/TestForceField.py
View file @ d83c2724
......@@ -466,7 +466,7 @@ class TestForceField(unittest.TestCase):
self.assertRaises(Exception, lambda: ff.createSystem(top))
# Register a template matcher that selects a particular one.
def matcher(ff, res):
def matcher(ff, res, bondedToAtom, ignoreExternalBonds, ignoreExtraParticles):
return ff._templates['HOH2']
ff.registerTemplateMatcher(matcher)
......@@ -1193,7 +1193,29 @@ self.scriptExecuted = True
"""
ff = ForceField(StringIO(xml))
self.assertTrue(ff.scriptExecuted)
def test_Glycam(self):
"""Test computing energy with GLYCAM."""
ff = ForceField('amber14/protein.ff14SB.xml', 'amber14/GLYCAM_06j-1.xml')
pdb = PDBFile('systems/glycopeptide.pdb')
system = ff.createSystem(pdb.topology)
for i, f in enumerate(system.getForces()):
f.setForceGroup(i)
integrator = VerletIntegrator(0.001)
context = Context(system, integrator, Platform.getPlatformByName('Reference'))
context.setPositions(pdb.positions)
energies = {}
for i, f in enumerate(system.getForces()):
energy = context.getState(getEnergy=True, groups={i}).getPotentialEnergy().value_in_unit(kilojoules_per_mole)
energies[f.getName()] = energy
# Compare to values computed with ParmEd.
self.assertAlmostEqual(32.14082401103625, energies['HarmonicBondForce'], 4)
self.assertAlmostEqual(48.92017455984504, energies['HarmonicAngleForce'], 3)
self.assertAlmostEqual(291.61241586209286, energies['PeriodicTorsionForce'], 4)
self.assertAlmostEqual(1547.011267801862, energies['NonbondedForce'], 4)
self.assertAlmostEqual(1919.6846822348361, sum(list(energies.values())), 3)
class AmoebaTestForceField(unittest.TestCase):
"""Test the ForceField.createSystem() method with the AMOEBA forcefield."""
......
wrappers/python/tests/TestModeller.py
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......@@ -952,6 +952,20 @@ class TestModeller(unittest.TestCase):
validate_equivalence(self, topology_LYN, topology_after)
def test_addHydrogensGlycam(self):
"""Test adding hydrogens for GLYCAM."""
pdb = PDBFile('systems/glycopeptide.pdb')
Modeller.loadHydrogenDefinitions('glycam-hydrogens.xml')
modeller = Modeller(pdb.topology, pdb.positions)
hydrogens = [a for a in modeller.topology.atoms() if a.element == element.hydrogen]
modeller.delete(hydrogens)
self.assertTrue(modeller.topology.getNumAtoms() < pdb.topology.getNumAtoms())
modeller.addHydrogens()
self.assertEqual(modeller.topology.getNumAtoms(), pdb.topology.getNumAtoms())
for res1, res2 in zip(pdb.topology.residues(), modeller.topology.residues()):
names1 = sorted([a.name for a in res1.atoms()])
names2 = sorted([a.name for a in res2.atoms()])
self.assertEqual(names1, names2)
def test_removeExtraHydrogens(self):
"""Test that addHydrogens() can remove hydrogens that shouldn't be there. """
......
wrappers/python/tests/systems/glycopeptide.pdb 0 → 100755
View file @ d83c2724
HETATM 1 N NLN A 1 -4.410 -2.879 8.958 1.00 0.00 N
HETATM 2 CA NLN A 1 -3.080 -3.453 8.940 1.00 0.00 C
HETATM 3 C NLN A 1 -2.993 -4.600 7.943 1.00 0.00 C
HETATM 4 O NLN A 1 -3.241 -5.752 8.293 1.00 0.00 O
HETATM 5 CB NLN A 1 -2.698 -3.999 10.312 1.00 0.00 C
HETATM 6 CG NLN A 1 -1.301 -4.603 10.292 1.00 0.00 C
HETATM 7 ND2 NLN A 1 -0.855 -5.115 11.441 1.00 0.00 N
HETATM 8 OD1 NLN A 1 -0.638 -4.606 9.257 1.00 0.00 O
HETATM 9 HA NLN A 1 -2.357 -2.689 8.655 1.00 0.00 H
HETATM 10 HB2 NLN A 1 -2.718 -3.191 11.043 1.00 0.00 H
HETATM 11 HB3 NLN A 1 -3.407 -4.772 10.606 1.00 0.00 H
HETATM 12 HD21 NLN A 1 -1.440 -5.086 12.264 1.00 0.00 H
HETATM 13 H1 NLN A 1 -4.979 -3.382 8.293 1.00 0.00 H
HETATM 14 H2 NLN A 1 -4.295 -1.929 8.634 1.00 0.00 H
HETATM 15 H3 NLN A 1 -4.764 -3.055 9.888 1.00 0.00 H
ATOM 16 N ALA A 2 -2.638 -4.282 6.695 1.00 0.00 N
ATOM 17 CA ALA A 2 -2.520 -5.283 5.654 1.00 0.00 C
ATOM 18 C ALA A 2 -2.103 -4.653 4.333 1.00 0.00 C
ATOM 19 O ALA A 2 -2.951 -4.252 3.539 1.00 0.00 O
ATOM 20 CB ALA A 2 -3.846 -6.002 5.430 1.00 0.00 C
ATOM 21 H ALA A 2 -2.444 -3.321 6.455 1.00 0.00 H
ATOM 22 HA ALA A 2 -1.769 -6.019 5.941 1.00 0.00 H
ATOM 23 HB1 ALA A 2 -4.606 -5.279 5.134 1.00 0.00 H
ATOM 24 HB2 ALA A 2 -3.727 -6.747 4.644 1.00 0.00 H
ATOM 25 HB3 ALA A 2 -4.153 -6.494 6.353 1.00 0.00 H
HETATM 26 N NLN A 3 -0.792 -4.566 4.099 1.00 0.00 N
HETATM 27 CA NLN A 3 -0.269 -3.986 2.879 1.00 0.00 C
HETATM 28 C NLN A 3 1.253 -4.011 2.869 1.00 0.00 C
HETATM 29 O NLN A 3 1.896 -3.068 3.325 1.00 0.00 O
HETATM 30 CB NLN A 3 -0.712 -2.535 2.726 1.00 0.00 C
HETATM 31 CG NLN A 3 -0.162 -1.926 1.444 1.00 0.00 C
HETATM 32 ND2 NLN A 3 -0.484 -0.653 1.201 1.00 0.00 N
HETATM 33 OD1 NLN A 3 0.541 -2.593 0.688 1.00 0.00 O
HETATM 34 H NLN A 3 -0.133 -4.909 4.783 1.00 0.00 H
HETATM 35 HA NLN A 3 -0.632 -4.553 2.022 1.00 0.00 H
HETATM 36 HB2 NLN A 3 -1.800 -2.488 2.695 1.00 0.00 H
HETATM 37 HB3 NLN A 3 -0.347 -1.952 3.572 1.00 0.00 H
HETATM 38 HD21 NLN A 3 -1.065 -0.149 1.855 1.00 0.00 H
ATOM 39 N ALA A 4 1.829 -5.096 2.345 1.00 0.00 N
ATOM 40 CA ALA A 4 3.270 -5.240 2.277 1.00 0.00 C
ATOM 41 C ALA A 4 3.658 -6.566 1.637 1.00 0.00 C
ATOM 42 O ALA A 4 3.815 -7.570 2.329 1.00 0.00 O
ATOM 43 CB ALA A 4 3.892 -5.195 3.669 1.00 0.00 C
ATOM 44 H ALA A 4 1.258 -5.846 1.982 1.00 0.00 H
ATOM 45 HA ALA A 4 3.689 -4.430 1.682 1.00 0.00 H
ATOM 46 HB1 ALA A 4 3.489 -6.006 4.275 1.00 0.00 H
ATOM 47 HB2 ALA A 4 4.973 -5.306 3.588 1.00 0.00 H
ATOM 48 HB3 ALA A 4 3.660 -4.240 4.140 1.00 0.00 H
HETATM 49 N NLN A 5 3.812 -6.567 0.311 1.00 0.00 N
HETATM 50 CA NLN A 5 4.180 -7.765 -0.416 1.00 0.00 C
HETATM 51 C NLN A 5 4.288 -7.488 -1.909 1.00 0.00 C
HETATM 52 O NLN A 5 4.072 -6.362 -2.352 1.00 0.00 O
HETATM 53 CB NLN A 5 3.144 -8.866 -0.219 1.00 0.00 C
HETATM 54 CG NLN A 5 3.531 -10.125 -0.983 1.00 0.00 C
HETATM 55 ND2 NLN A 5 2.696 -11.162 -0.887 1.00 0.00 N
HETATM 56 OD1 NLN A 5 4.564 -10.158 -1.648 1.00 0.00 O
HETATM 57 OXT NLN A 5 4.591 -8.387 -2.689 1.00 0.00 O
HETATM 58 H NLN A 5 3.671 -5.716 -0.214 1.00 0.00 H
HETATM 59 HA NLN A 5 5.144 -8.126 -0.058 1.00 0.00 H
HETATM 60 HB2 NLN A 5 3.069 -9.111 0.840 1.00 0.00 H
HETATM 61 HB3 NLN A 5 2.175 -8.523 -0.581 1.00 0.00 H
HETATM 62 HD21 NLN A 5 1.859 -11.083 -0.328 1.00 0.00 H
TER 63 NLN A 5
HETATM 64 C1 0GB B 1 0.467 -5.709 11.506 1.00 0.00 C
HETATM 65 C2 0GB B 1 1.537 -4.647 11.131 1.00 0.00 C
HETATM 66 O2 0GB B 1 1.427 -4.300 9.719 1.00 0.00 O
HETATM 67 C3 0GB B 1 2.956 -5.193 11.405 1.00 0.00 C
HETATM 68 O3 0GB B 1 3.925 -4.126 11.214 1.00 0.00 O
HETATM 69 C4 0GB B 1 3.100 -5.748 12.843 1.00 0.00 C
HETATM 70 O4 0GB B 1 4.398 -6.374 12.982 1.00 0.00 O
HETATM 71 C5 0GB B 1 2.040 -6.742 13.153 1.00 0.00 C
HETATM 72 O5 0GB B 1 0.682 -6.181 12.877 1.00 0.00 O
HETATM 73 C6 0GB B 1 2.102 -7.229 14.614 1.00 0.00 C
HETATM 74 O6 0GB B 1 1.068 -8.204 14.848 1.00 0.00 O
HETATM 75 H1 0GB B 1 0.525 -6.543 10.805 1.00 0.00 H
HETATM 76 H2 0GB B 1 1.375 -3.746 11.727 1.00 0.00 H
HETATM 77 H3 0GB B 1 3.174 -5.991 10.691 1.00 0.00 H
HETATM 78 H4 0GB B 1 3.028 -4.925 13.557 1.00 0.00 H
HETATM 79 H5 0GB B 1 2.198 -7.598 12.494 1.00 0.00 H
HETATM 80 H2O 0GB B 1 0.516 -4.026 9.549 1.00 0.00 H
HETATM 81 H3O 0GB B 1 3.765 -3.742 10.342 1.00 0.00 H
HETATM 82 H61 0GB B 1 3.069 -7.684 14.826 1.00 0.00 H
HETATM 83 H62 0GB B 1 1.959 -6.391 15.297 1.00 0.00 H
HETATM 84 H4O 0GB B 1 5.058 -5.747 12.656 1.00 0.00 H
HETATM 85 H6O 0GB B 1 0.227 -7.823 14.574 1.00 0.00 H
HETATM 86 C1 0GB B 2 0.000 0.000 0.000 1.00 0.00 C
HETATM 87 C2 0GB B 2 -0.515 -0.760 -1.254 1.00 0.00 C
HETATM 88 O2 0GB B 2 0.121 -2.069 -1.341 1.00 0.00 O
HETATM 89 C3 0GB B 2 -0.195 0.040 -2.536 1.00 0.00 C
HETATM 90 O3 0GB B 2 -0.838 -0.601 -3.673 1.00 0.00 O
HETATM 91 C4 0GB B 2 -0.686 1.505 -2.447 1.00 0.00 C
HETATM 92 O4 0GB B 2 -0.227 2.231 -3.612 1.00 0.00 O
HETATM 93 C5 0GB B 2 -0.182 2.176 -1.220 1.00 0.00 C
HETATM 94 O5 0GB B 2 -0.507 1.376 0.000 1.00 0.00 O
HETATM 95 C6 0GB B 2 -0.744 3.602 -1.058 1.00 0.00 C
HETATM 96 O6 0GB B 2 -0.204 4.207 0.132 1.00 0.00 O
HETATM 97 H1 0GB B 2 1.091 0.000 0.000 1.00 0.00 H
HETATM 98 H2 0GB B 2 -1.595 -0.899 -1.172 1.00 0.00 H
HETATM 99 H3 0GB B 2 0.884 0.034 -2.700 1.00 0.00 H
HETATM 100 H4 0GB B 2 -1.778 1.521 -2.431 1.00 0.00 H
HETATM 101 H5 0GB B 2 0.904 2.238 -1.310 1.00 0.00 H
HETATM 102 H2O 0GB B 2 -0.028 -2.531 -0.506 1.00 0.00 H
HETATM 103 H3O 0GB B 2 -0.580 -1.533 -3.662 1.00 0.00 H
HETATM 104 H61 0GB B 2 -0.480 4.218 -1.918 1.00 0.00 H
HETATM 105 H62 0GB B 2 -1.832 3.572 -0.978 1.00 0.00 H
HETATM 106 H4O 0GB B 2 -0.462 1.708 -4.391 1.00 0.00 H
HETATM 107 H6O 0GB B 2 -0.364 3.613 0.871 1.00 0.00 H
HETATM 108 C1 0GB B 3 2.993 -12.398 -1.585 1.00 0.00 C
HETATM 109 C2 0GB B 3 4.351 -12.967 -1.089 1.00 0.00 C
HETATM 110 O2 0GB B 3 5.443 -12.102 -1.521 1.00 0.00 O
HETATM 111 C3 0GB B 3 4.580 -14.386 -1.656 1.00 0.00 C
HETATM 112 O3 0GB B 3 5.765 -14.961 -1.041 1.00 0.00 O
HETATM 113 C4 0GB B 3 3.375 -15.320 -1.390 1.00 0.00 C
HETATM 114 O4 0GB B 3 3.592 -16.579 -2.071 1.00 0.00 O
HETATM 115 C5 0GB B 3 2.102 -14.719 -1.865 1.00 0.00 C
HETATM 116 O5 0GB B 3 1.913 -13.348 -1.299 1.00 0.00 O
HETATM 117 C6 0GB B 3 0.877 -15.586 -1.516 1.00 0.00 C
HETATM 118 O6 0GB B 3 -0.321 -14.965 -2.019 1.00 0.00 O
HETATM 119 H1 0GB B 3 3.052 -12.206 -2.657 1.00 0.00 H
HETATM 120 H2 0GB B 3 4.347 -13.008 0.002 1.00 0.00 H
HETATM 121 H3 0GB B 3 4.747 -14.316 -2.733 1.00 0.00 H
HETATM 122 H4 0GB B 3 3.294 -15.511 -0.318 1.00 0.00 H
HETATM 123 H5 0GB B 3 2.170 -14.634 -2.951 1.00 0.00 H
HETATM 124 H2O 0GB B 3 5.252 -11.205 -1.219 1.00 0.00 H
HETATM 125 H3O 0GB B 3 6.485 -14.325 -1.150 1.00 0.00 H
HETATM 126 H61 0GB B 3 0.971 -16.578 -1.957 1.00 0.00 H
HETATM 127 H62 0GB B 3 0.790 -15.698 -0.434 1.00 0.00 H
HETATM 128 H4O 0GB B 3 4.480 -16.885 -1.839 1.00 0.00 H
HETATM 129 H6O 0GB B 3 -0.349 -14.059 -1.695 1.00 0.00 H
TER 130 0GB B 3
CONECT 1 2 13 14 15
CONECT 2 1 3 5 9
CONECT 3 16 2 4
CONECT 4 3
CONECT 5 2 6 10 11
CONECT 6 5 7 8
CONECT 7 6 12 64
CONECT 8 6
CONECT 9 2
CONECT 10 5
CONECT 11 5
CONECT 12 7
CONECT 13 1
CONECT 14 1
CONECT 15 1
CONECT 16 3
CONECT 18 26
CONECT 26 18 27 34
CONECT 27 26 28 30 35
CONECT 28 39 27 29
CONECT 29 28
CONECT 30 27 31 36 37
CONECT 31 30 32 33
CONECT 32 31 38 86
CONECT 33 31
CONECT 34 26
CONECT 35 27
CONECT 36 30
CONECT 37 30
CONECT 38 32
CONECT 39 28
CONECT 41 49
CONECT 49 41 50 58
CONECT 50 49 51 53 59
CONECT 51 50 52 57
CONECT 52 51
CONECT 53 50 54 60 61
CONECT 54 53 55 56
CONECT 55 54 62 108
CONECT 56 54
CONECT 57 51
CONECT 58 49
CONECT 59 50
CONECT 60 53
CONECT 61 53
CONECT 62 55
CONECT 64 7 65 72 75
CONECT 65 64 66 76 67
CONECT 66 65 80
CONECT 67 65 68 77 69
CONECT 68 67 81
CONECT 69 67 70 78 71
CONECT 70 69 84
CONECT 71 69 73 79 72
CONECT 72 64 71
CONECT 73 71 74 82 83
CONECT 74 73 85
CONECT 75 64
CONECT 76 65
CONECT 77 67
CONECT 78 69
CONECT 79 71
CONECT 80 66
CONECT 81 68
CONECT 82 73
CONECT 83 73
CONECT 84 70
CONECT 85 74
CONECT 86 32 87 94 97
CONECT 87 86 88 98 89
CONECT 88 87 102
CONECT 89 87 90 99 91
CONECT 90 89 103
CONECT 91 89 92 100 93
CONECT 92 91 106
CONECT 93 91 95 101 94
CONECT 94 86 93
CONECT 95 93 96 104 105
CONECT 96 95 107
CONECT 97 86
CONECT 98 87
CONECT 99 89
CONECT 100 91
CONECT 101 93
CONECT 102 88
CONECT 103 90
CONECT 104 95
CONECT 105 95
CONECT 106 92
CONECT 107 96
CONECT 108 55 109 116 119
CONECT 109 108 110 120 111
CONECT 110 109 124
CONECT 111 109 112 121 113
CONECT 112 111 125
CONECT 113 111 114 122 115
CONECT 114 113 128
CONECT 115 113 117 123 116
CONECT 116 108 115
CONECT 117 115 118 126 127
CONECT 118 117 129
CONECT 119 108
CONECT 120 109
CONECT 121 111
CONECT 122 113
CONECT 123 115
CONECT 124 110
CONECT 125 112
CONECT 126 117
CONECT 127 117
CONECT 128 114
CONECT 129 118
END
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