def create_default_init_cell_node_coords(self, bounding_box,
init_cell_radius, num_nodes):
cell_centre = calc_bounding_box_centre(bounding_box)
cell_node_thetas = np.pi * np.linspace(
0, 2, endpoint=False, num=num_nodes)
cell_node_coords = np.transpose(
np.array([
cell_centre[0] + init_cell_radius * np.cos(cell_node_thetas),
cell_centre[1] + init_cell_radius * np.sin(cell_node_thetas)
]))
edge_vectors = geometry.calculate_edge_vectors(num_nodes,
cell_node_coords)
edge_lengths = geometry.calculate_2D_vector_mags(
num_nodes, edge_vectors)
length_edge_resting = np.average(edge_lengths)
area_resting = geometry.calculate_polygon_area(num_nodes,
cell_node_coords)
if area_resting < 0:
raise StandardError("Resting area was calculated to be negative.")
return cell_node_coords, length_edge_resting, area_resting
def create_default_init_cell_verts(
bbox, cell_r
):
cell_centre = calc_bb_centre(bbox)
cell_node_thetas = np.pi * \
np.linspace(0, 2, endpoint=False, num=16)
cell_verts = np.transpose(
np.array(
[
cell_r * np.cos(cell_node_thetas),
cell_r * np.sin(cell_node_thetas),
]
)
)
# rotation_theta = np.random.rand()*2*np.pi
# cell_verts = np.array([
# geometry.rotate_2D_vector_CCW_by_theta(rotation_theta, x) for x in
# cell_verts], dtype=np.float64)
cell_verts = np.array(
[[x + cell_centre[0], y + cell_centre[1]] for x, y in
cell_verts],
dtype=np.float64,
)
edge_vectors = geometry.calculate_edge_vectors(cell_verts)
edge_lengths = geometry.calculate_vec_mags(edge_vectors)
rest_edge_len = np.average(edge_lengths)
rest_area = geometry.calculate_polygon_area(cell_verts)
if rest_area < 0:
raise Exception("Resting area was calculated to be negative.")
return cell_verts, rest_edge_len, rest_area
def set_next_state(
self,
next_state_array,
close_point_smoothness_factors,
x_cils,
x_coas,
):
self.tpoint += self.dt
self.insert_state_array_into_system_history(next_state_array)
verts = self.curr_state[:, [parameters.x_ix, parameters.y_ix]]
edge_displacement_vectors_plus = geometry.calculate_edge_vectors(verts)
edge_lengths = geometry.calculate_vec_mags(
edge_displacement_vectors_plus)
self.curr_state[:, parameters.edge_lengths_ix] = edge_lengths
self.curr_state[:, parameters.old_x_coa_ix] = x_coas
self.curr_state[:, parameters.old_x_cil_ix] = x_cils
# ==================================
if self.tpoint == self.next_randomization_event_tpoint:
self.next_randomization_event_tpoint += 1200
# randomization event has occurred, so renew Rac kgtp rate
# multipliers
self.rac_rands = \
self.renew_rac_rands(
self.tpoint)
# store the Rac randomization factors for this timestep
self.curr_state[:, parameters.rac_rands_ix] = self.rac_rands
# ==================================
rac_acts = self.curr_state[:, parameters.rac_act_ix]
rho_acts = self.curr_state[:, parameters.rho_act_ix]
self.curr_state[:, parameters.old_x_cil_ix] = x_cils
self.curr_state[:, parameters.old_x_coa_ix] = x_coas
rac_cyto = (1 - np.sum(rac_acts) -
np.sum(self.curr_state[:, parameters.rac_inact_ix]))
rho_cyto = (1 - np.sum(rho_acts) -
np.sum(self.curr_state[:, parameters.rho_inact_ix]))
insertion_array = np.zeros(16)
insertion_array[0] = 1
self.curr_state[:,
parameters.rac_cyto_ix] = (rac_cyto * insertion_array)
self.curr_state[:,
parameters.rho_cyto_ix] = (rho_cyto * insertion_array)
sum_forces, edge_forces_plus, edge_forces_minus, uevs, rgtp_forces, \
cyto_forces, \
edge_strains, local_strains, unit_inside_pointing_vecs = \
mechanics.calculate_forces(
verts,
rac_acts,
rho_acts,
self.rest_edge_len,
self.stiffness_edge,
self.halfmax_vertex_rgtp,
self.const_protrusive,
self.const_retractive,
self.rest_area,
self.stiffness_cyto,
)
self.curr_state[:, parameters.local_strains_ix] = local_strains
edgeplus_lengths = geometry.calculate_edgeplus_lengths(verts)
avg_edge_lengths = geometry.calculate_average_edge_length_around_nodes(
edgeplus_lengths)
conc_rac_acts = chemistry.calc_concs(rac_acts, avg_edge_lengths)
conc_rho_acts = chemistry.calc_concs(rho_acts, avg_edge_lengths)
self.curr_state[:, parameters.rac_rands_ix] = self.rac_rands
kgtp_racs = chemistry.calculate_kgtp_rac(
conc_rac_acts,
self.halfmax_vertex_rgtp_conc,
self.kgtp_rac,
self.kgtp_rac_auto,
x_coas,
self.rac_rands,
x_cils,
close_point_smoothness_factors,
)
kdgtps_rac = chemistry.calculate_kdgtp_rac(
conc_rho_acts,
self.halfmax_vertex_rgtp_conc,
self.kdgtp_rac,
self.kdgtp_rho_on_rac,
x_cils,
self.halfmax_tension_inhib,
self.tension_inhib,
np.array([ls if ls > 0 else 0.0 for ls in local_strains]),
)
kdgtps_rho = chemistry.calculate_kdgtp_rho(
conc_rac_acts,
self.halfmax_vertex_rgtp_conc,
self.kdgtp_rho,
self.kdgtp_rac_on_rho,
)
kgtp_rhos = chemistry.calculate_kgtp_rho(
conc_rho_acts,
x_cils,
self.halfmax_vertex_rgtp_conc,
self.kgtp_rho,
self.kgtp_rho_auto,
)
self.curr_state[:, parameters.kgtp_rac_ix] = kgtp_racs
self.curr_state[:, parameters.kgtp_rho_ix] = kgtp_rhos
self.curr_state[:, parameters.kdgtp_rac_ix] = kdgtps_rac
self.curr_state[:, parameters.kdgtp_rho_ix] = kdgtps_rho
# update mechanics parameters
self.curr_state[:, [
parameters.sum_forces_x_ix, parameters.sum_forces_y_ix
]] = sum_forces
self.curr_state[:, [parameters.edge_forces_plus_x_ix,
parameters.edge_forces_plus_y_ix]] = \
edge_forces_plus
self.curr_state[:, [parameters.edge_forces_minus_x_ix,
parameters.edge_forces_minus_y_ix]] = \
edge_forces_minus
self.curr_state[:, [
parameters.rgtp_forces_x_ix, parameters.rgtp_forces_y_ix
]] = rgtp_forces
self.curr_state[:, [
parameters.cyto_forces_x_ix, parameters.cyto_forces_y_ix
]] = cyto_forces
self.curr_state[:, [parameters.uiv_x_ix, parameters.
uiv_y_ix]] = unit_inside_pointing_vecs
self.curr_verts = verts
def make_chem_mech_space_parameter_defn_dict(C_total=3e6, H_total=1.5e6, num_nodes=15, num_cells=1, init_cell_radius=12.5e-6, cell_group_bounding_box=np.array([0, 50, 0, 50])*1e-6, stiffness_edge=2e-10, stiffness_cytoplasmic=100, kgtp_rac_multiplier=40, kgtp_rac_autoact_multiplier=1000, kdgtp_rac_multiplier=17, kdgtp_rho_mediated_rac_inhib_multiplier=30, kgtp_rho_multiplier=200, kgtp_rho_autoact_multiplier=350, kdgtp_rho_multiplier=250, kdgtp_rac_mediated_rho_inhib_multiplier=67, kdgdi_rac_estimate_multiplier=1, kdgdi_rho_estimate_multiplier=1, kgdi_rac_estimate_multiplier=1, kgdi_rho_estimate_multiplier=1, threshold_tension_mediated_rac_inhib=0.2*0.75, exponent_tension_mediated_rac_inhib=3, biased_rgtpase_distrib_defn=['unbiased random', 0, 0], threshold_rac_autoact_multiplier=0.5, threshold_rho_autoact_multiplier=0.5, threshold_rho_mediated_rac_inhib_multiplier=0.5, threshold_rac_mediated_rho_inhib_multiplier=0.5, space_at_node_factor_rac=1, space_at_node_factor_rho=1, migr_bdry_contact_factor_mag=2, init_rgtpase_cytosol_gdi_bound_frac = 0.8, init_rgtpase_membrane_inactive_frac = 0.1, init_rgtpase_membrane_active_frac = 0.1, intercellular_contact_factor_magnitudes=np.array([2]), halfmax_coa_sensing_dist_multiplier=3, max_protrusive_node_velocity=0.25e-6, sigma_rac=2e-4, sigma_rho_multiplier=0.2, force_rac_exp=3, force_rho_exp=3, force_rac_threshold_multiplier=0.5, force_rho_threshold_multiplier=0.5, closeness_dist_squared_criteria=(0.5e-6)**2, exponent_rac_autoact=3, exponent_rho_autoact=3, exponent_rho_mediated_rac_inhib=3, exponent_rac_mediated_rho_inhib=3, randomization_scheme=0, randomization_time_mean=20, randomization_time_variance_factor=0.25, randomization_width_baseline=2, randomization_width_halfmax_threshold=0.3, randomization_width_hf_exponent=3, randomization_centre=0.15, randomization_width=10, randomization_depth=1.0, randomization_function_type=0, randomization=False, skip_dynamics=False, randomization_rgtpase_distrib_strength=0.1, tension_mediated_rac_inhibition_half_strain=0.025, tension_mediated_rac_hill_exponent=3, tension_fn_type=0, coa_sensitivity_percent_drop_over_cell_diameter=0.25, coa_belt_offset_multiplier=1.0):
kgtp_rac_factor = 1.5e-4 # per second
kdgtp_rac_factor = 1.8e-4 # per second
kgtp_rho_factor = 1.5e-4 # per second
kdgtp_rho_factor = 3.5e-4 # per second
kdgdi_rac_estimate = 0.1*kdgdi_rac_estimate_multiplier # per second
kgdi_rac_estimate = 0.1*kgdi_rac_estimate_multiplier # per second
kdgdi_rho_estimate = 0.1*kdgdi_rho_estimate_multiplier # per second
kgdi_rho_estimate = 0.1*kgdi_rho_estimate_multiplier # per second
assert(init_rgtpase_cytosol_gdi_bound_frac + init_rgtpase_membrane_inactive_frac + init_rgtpase_membrane_active_frac == 1)
#--------------
kgtp_rac_baseline = kgtp_rac_factor*(kgtp_rac_multiplier + 1) # per second
kdgtp_rac_baseline = kdgtp_rac_factor*(kdgtp_rac_multiplier + 1) # per second
#--------------
kgtp_rho_baseline = kgtp_rho_factor*(kgtp_rho_multiplier + 1) # per second
kdgtp_rho_baseline = kdgtp_rho_factor*(kdgtp_rho_multiplier + 1) # per second
#--------------
kgtp_rac_autoact_baseline = kgtp_rac_autoact_multiplier*kgtp_rac_factor # per second
kgtp_rho_autoact_baseline = kgtp_rho_autoact_multiplier*kgtp_rho_factor # per second
#--------------
kdgtp_rho_mediated_rac_inhib_baseline = kdgtp_rac_factor*kdgtp_rho_mediated_rac_inhib_multiplier # per second
kdgtp_rac_mediated_rho_inhib_baseline = kdgtp_rho_factor*kdgtp_rac_mediated_rho_inhib_multiplier # per second
#--------------
kgdi_rac = kgdi_rac_estimate # per second
kdgdi_rac = kdgdi_rac_estimate # per second
#--------------
kgdi_rho = kgdi_rho_estimate # per second
kdgdi_rho = kdgdi_rho_estimate # per second
#--------------
threshold_rac_autoact = threshold_rac_autoact_multiplier*C_total
threshold_rho_autoact = threshold_rho_autoact_multiplier*H_total
#--------------
threshold_rho_mediated_rac_inhib = threshold_rho_mediated_rac_inhib_multiplier*H_total
threshold_rac_mediated_rho_inhib = threshold_rac_mediated_rho_inhib_multiplier*C_total
#--------------
force_rac_threshold = force_rac_threshold_multiplier*C_total
force_rho_threshold = force_rho_threshold_multiplier*H_total
#--------------
diffusion_const = 0.15*1e-12
diffusion_const_active = diffusion_const # micrometers squared per second
diffusion_const_inactive = diffusion_const # micrometers squared per second
#--------------
cell_node_thetas = np.pi*np.linspace(0, 2, endpoint=False, num=num_nodes)
cell_node_coords = np.transpose(np.array([init_cell_radius*np.cos(cell_node_thetas), init_cell_radius*np.sin(cell_node_thetas)]))
edge_vectors = geometry.calculate_edge_vectors(num_nodes, cell_node_coords)
edge_lengths = geometry.calculate_2D_vector_mags(num_nodes, edge_vectors)
length_edge_resting = np.average(edge_lengths)
eta = (sigma_rac*length_edge_resting)/max_protrusive_node_velocity
#--------------
factor_migr_bdry_contact = 10
#--------------
stiffness_cytoplasmic = 0.00001 # Newtons
#--------------
halfmax_coa_sensing_dist = halfmax_coa_sensing_dist_multiplier*25e-6
coa_belt_offset = coa_belt_offset_multiplier*2*init_cell_radius
ignore_list = ['intercellular_contact_factor_magnitudes', 'space_physical_bdry_polygon', 'space_migratory_bdry_polygon', 'cell_dependent_coa_signal_strengths']
relevant_labels = [label for label in standard_chem_mech_space_parameter_labels if label not in ignore_list]
parameter_definition_dict = dict(zip(relevant_labels, [eval(label) for label in relevant_labels]))
return parameter_definition_dict
def refine_raw_params(raw_params):
params = copy.deepcopy(raw_params)
params["coa_vertex_mag"] = raw_params["coa_mag"] / 16
params["coa_halfmax_dist"] = raw_params["coa_halfmax_dist"] / params["l"]
params["coa_distrib_exp"] = calc_coa_distrib_exp(
params["coa_halfmax_dist"])
params["init_cyto_rgtp"] = 1 - raw_params["init_inact_rgtp"] - \
raw_params["init_act_rgtp"]
# --------------
params["kgtp_rac"] = (params["kgtp"] * raw_params["kgtp_rac"] * params["t"]
) # per second
params["kdgtp_rac"] = (params["kgtp"] * raw_params["kdgtp_rac"] *
params["t"]) # per second
# --------------
params["kgtp_rho"] = (params["kgtp"] *
raw_params["kgtp_rho"]) * params["t"]
params["kdgtp_rho"] = (params["kgtp"] *
raw_params["kdgtp_rho"]) * params["t"]
# --------------
params["kgtp_rac_auto"] = \
raw_params["kgtp_rac_autoact"] * params["kgtp"] * params["t"]
params["kgtp_rho_auto"] = \
raw_params["kgtp_rho_autoact"] * params["kgtp"] * params["t"]
# --------------
params["kdgtp_rho_on_rac"] = (params["kgtp"] *
raw_params["kdgtp_rho_on_rac"] * params["t"]
) # per second
params["kdgtp_rac_on_rho"] = (params["kgtp"] *
raw_params["kdgtp_rac_on_rho"] * params["t"]
) # per second
# --------------
params["k_mem_off"] = (params["k_mem_off"] * raw_params["kgdi"] *
params["t"]) # per second
params["k_mem_on_vertex"] = (params["k_mem_on"] * raw_params["kdgdi"] *
params["t"] / 16) # per second
del params["k_mem_on"]
# --------------
params["diffusion_rgtp"] = \
raw_params["diffusion_rgtp"] * (params["t"] / (params["l"] ** 2))
# --------------
params["halfmax_vertex_rgtp"] = \
raw_params["halfmax_vertex_rgtp"] / 16
# --------------
params["cell_r"] = raw_params["cell_r"] / params["l"]
vert_thetas = np.pi * np.linspace(0, 2, endpoint=False, num=16)
cell_verts = np.transpose(
np.array([
params["cell_r"] * np.cos(vert_thetas),
params["cell_r"] * np.sin(vert_thetas),
]))
edge_vectors = geometry.calculate_edge_vectors(cell_verts)
edge_lengths = geometry.calculate_vec_mags(edge_vectors)
params["rest_edge_len"] = np.average(edge_lengths)
params["rest_area"] = geometry.calculate_polygon_area(cell_verts)
params["halfmax_vertex_rgtp_conc"] = params["halfmax_vertex_rgtp"] / \
params["rest_edge_len"]
params["vertex_eta"] = (params["vertex_eta"] * params["eta"] / 16) / \
(params["f"] / (params["l"] / params["t"]))
params["stiffness_edge"] = \
raw_params["stiffness_edge"] * \
params["l3d"] * \
params["l"] / params["f"]
params["const_protrusive"] = \
raw_params["lm_ss"] * raw_params["lm_h"] * \
(params["rest_edge_len"] * params["l"]) * \
params["halfmax_rgtp_max_f_frac"] / params["f"]
params["const_retractive"] = (raw_params["force_rho"] *
params["const_protrusive"])
params["stiffness_cyto"] = raw_params["stiffness_cyto"] / params["f"] / 16
# --------------
params["zero_at"] = raw_params["close_zero_at"] / params["l"]
params["one_at"] = raw_params["close_one_at"] / params["l"]
# --------------
params["rand_avg_t"] = raw_params["rand_avg_t"] * 60.0 / params["t"]
params["rand_std_t"] = raw_params["rand_std_t"] * 60.0 / params["t"]
params["rand_mag"] = raw_params["rand_mag"]
params["snap_period"] = raw_params["snap_period"] / params["t"]
return params