leg-joint
epithelium model¶%load_ext autoreload
%autoreload 2
%matplotlib inline
%run nb_init.py
The autoreload extension is already loaded. To reload it, use: %reload_ext autoreload
eptm = lj.Epithelium(lj.data.small_xml(),
save_dir='saved_graphs',
identifier='division',
copy=True)
eptm.isotropic_relax()
2015-01-26 11:14:59,162 -leg_joint.epithelium -INFO -Instanciating epithelium division 2015-01-26 11:14:59,214 -leg_joint.epithelium -INFO -Initial cells 2015-01-26 11:14:59,214 -leg_joint.epithelium -INFO -Initial junctions 2015-01-26 11:14:59,554 -leg_joint.epithelium -INFO -Update geometry
Let's take a slice of the epithelium to pick a cell and look at the division
eptm.set_local_mask(None)
lj.local_slice(eptm, theta_c=0, theta_amp=np.pi/9, zed_c=0, zed_amp=6.)
fig, axes=plt.subplots(1, 2, figsize=(12, 8), sharey=True)
lj.plot_2pannels(eptm,
cell_kwargs={'c_text':True},
edge_kwargs={'c':'g', 'lw':1, 'alpha':0.4},
axes=axes)
eptm.set_local_mask(None)
cell n°3 looks fine, let's call it mother_cell
, and look at it more closely.
mother_cell = eptm.graph.vertex(3)
## Clear local mask and set it to be centered on
## the mother cell
eptm.set_local_mask(None)
eptm.set_local_mask(mother_cell, wider=True)
## Create a figure
fig, axes=plt.subplots(1, 2, figsize=(10, 4))#, sharey=True)
axes = lj.plot_2pannels(eptm, axes=axes)
## Show the forces exerted on the vertices of our cell
axes = lj.plot_2pannels_gradients(eptm, axes=axes, scale=10., approx=1)
axes = lj.plot_2pannels_gradients(eptm, axes=axes, scale=10., approx=0)
plt.tight_layout()
plt.draw()
area0 = eptm.cells.areas[mother_cell]
growth_rate = 1.5
eptm.cells.prefered_vol[mother_cell] *= growth_rate
eptm.update_gradient()
fig, axes=plt.subplots(1, 2, figsize=(10, 4))
axes = lj.plot_2pannels(eptm, axes=axes)
axes = lj.plot_2pannels_gradients(eptm, axes=axes, scale=20., approx=0)
axes = lj.plot_2pannels_gradients(eptm, axes=axes, scale=20., approx=1)
plt.tight_layout()
jv0, jv1 = eptm.cells.junctions[mother_cell][2]
def grad_norm(jv):
return (eptm.grad_ix[jv]**2 + eptm.grad_zed[jv]**2 + eptm.grad_wy[jv]**2)**0.5
grad_norm(jv0), grad_norm(jv1)
(5080.824747678576, 5080.824747678571)
for jv0, jv1 in eptm.cells.junctions[mother_cell]:
print(jv0, jv1, grad_norm(jv0), grad_norm(jv1))
63 64 4845.101480534979 5080.824747678576 63 67 4845.101480534979 5080.824748899601 64 70 5080.824747678576 5080.824747678571 67 68 5080.824748899601 5080.824748779011 68 69 5080.824748779011 4845.101479826948 69 70 4845.101479826948 5080.824747678571
pos0, pos1 = lj.find_energy_min(eptm, method='fmin_ncg')
print('Current relative area: %.3f'
% (eptm.cells.areas[mother_cell] / area0))
Current relative area: 1.568
pos0, pos1 = lj.find_energy_min(eptm, method='fmin_ncg')
Optimization terminated successfully. Current function value: 9.986988 Iterations: 1 Function evaluations: 2 Gradient evaluations: 4 Hessian evaluations: 0
%pdb
Automatic pdb calling has been turned ON
@before_after
def show_division(eptm, mother_cell):
septum = lj.cell_division(eptm, mother_cell, verbose=True)
return septum
eptm.graph.set_edge_filter(None)
eptm.graph.set_vertex_filter(None)
septum = show_division(eptm, mother_cell)
if septum is not None:
jv0, jv1, mother_cell, daughter_cell = septum
2015-01-26 11:33:16,373 -leg_joint.epithelium -INFO -Cell 152 is born 2015-01-26 11:33:17,106 -leg_joint.epithelium -INFO -Division completed
import scipy.optimize as opt
opt.fmin_ncg?
eptm.isotropic_relax()
pos0, pos1 = show_optimisation(eptm)
eptm.isotropic_relax()
Optimization terminated successfully. Current function value: 11.149816 Iterations: 1 Function evaluations: 2 Gradient evaluations: 4 Hessian evaluations: 0
Please refer the original definition in Farhadifar et al. Curr Biol. 2007, Suppplementary figure S1)
In ASCII art
(letters represent junctions and number represent cells):
e 2 d
\ / e d e 2 d
b \/ \ /
1 | 3 ----> ab ----> 1 a-b 3
a /\ / \
/ \ f c f 4 c
f 4 c
The arguments can be either:
eptm.set_local_mask(None)
cell1, cell3 = eptm.graph.vertex(912), eptm.graph.vertex(4745)
eptm.set_local_mask(cell1)
eptm.set_local_mask(cell3)
%pdb
Automatic pdb calling has been turned OFF
@before_after
def show_type1(eptm, cells):
cell1, cell3 = cells
modified_cells, modified_jverts = lj.type1_transition(eptm, (cell1, cell3))
show_type1(eptm, (cell1, cell3))
po0, pos1 = show_optimisation(eptm, tol=1e-5, approx_grad=0)
Optimization terminated successfully. Current function value: 7.159777 Iterations: 1 Function evaluations: 2 Gradient evaluations: 4 Hessian evaluations: 0