def test_transcription_model(self):
#use simple production and degradation of mRNA and protein for testing
# mRNA production rate is k1, degradation rate is g1
# protein production rate is k2, degradation rate is g2
stoichiometry_matrix = sympy.Matrix([[1, -1, 0, 0],
[0, 0, 1, -1]])
propensities = to_sympy_matrix(['k1',
'g1*x',
'k2*x',
'g2*y'])
species = to_sympy_matrix(['x', 'y'])
correct_rhs = to_sympy_matrix(
["k1 - g1 * x",
"k2 * x - g2 * y",
"k1 + g1 * x - 2 * g1 * V_0_0",
"k2 * V_0_0 - (g1 + g2) * V_0_1",
"k2 * x + g2 * y + k2 * V_0_1 + k2 * V_0_1 - 2 * g2 * V_1_1"])
correct_lhs = to_sympy_matrix(['x','y','V_0_0', 'V_0_1', 'V_1_1'])
constants = ["k1","k2","g1","g2"]
model = Model(species, constants, propensities, stoichiometry_matrix)
lna = LinearNoiseApproximation(model)
problem = lna.run()
answer_rhs = problem.right_hand_side
answer_lhs = problem.left_hand_side
assert_sympy_expressions_equal(correct_rhs, answer_rhs)
self.assertEqual(correct_lhs, answer_lhs)
def test_creation_from_matrix_returns_itself(self):
"""
Given a `sympy.Matrix`, `to_sympy_matrix` should return the said matrix.
"""
m = sympy.Matrix([[1, 2, 3], [4, 5, 6]])
assert_sympy_expressions_equal(m, to_sympy_matrix(m))
def test_creation_from_matrix_returns_itself(self):
"""
Given a `sympy.Matrix`, `to_sympy_matrix` should return the said matrix.
"""
m = sympy.Matrix([[1, 2, 3], [4, 5, 6]])
assert_sympy_expressions_equal(m, to_sympy_matrix(m))
def test_creation_from_list_of_integers_returns_matrix(self):
"""
Given a list of integers, to_sympy_matrix should be able to convert it to a matrix of these integers
:return:
"""
m = sympy.Matrix([[1, 2, 3], [4, 5, 6]])
m_as_list = [[1, 2, 3], [4, 5, 6]]
assert_sympy_expressions_equal(m, to_sympy_matrix(m_as_list))
def test_creation_from_list_of_integers_returns_matrix(self):
"""
Given a list of integers, to_sympy_matrix should be able to convert it to a matrix of these integers
:return:
"""
m = sympy.Matrix([[1, 2, 3], [4, 5, 6]])
m_as_list = [[1, 2, 3], [4, 5, 6]]
assert_sympy_expressions_equal(m, to_sympy_matrix(m_as_list))
def test_creation_of_column_matrix_from_list_of_strings(self):
"""
Given a list of strings, to_sympy_matrix should be able to convert them into a column matrix of expresions
"""
m = sympy.Matrix([sympy.sympify('x+y+3'), sympy.sympify('x+3'), sympy.sympify('y-x'),
sympy.sympify('x+y+166')])
m_as_string = ['x+y+3', 'x+3', 'y-x', 'x+y+166']
matrix = to_sympy_matrix(m_as_string)
assert_sympy_expressions_equal(m, matrix)
def test_creation_from_list_of_strings_returns_matrix(self):
"""
Given a list of strings, to_sympy_matrix should be able to convert them into a matrix of expressions.
"""
m = sympy.Matrix([[sympy.sympify('x+y+3'), sympy.sympify('x+3')],
[sympy.sympify('y-x'), sympy.sympify('x+y+166')]])
m_as_string = [['x+y+3', 'x+3'], ['y-x', 'x+y+166']]
matrix = to_sympy_matrix(m_as_string)
assert_sympy_expressions_equal(m, matrix)
def test_creation_from_list_of_strings_returns_matrix(self):
"""
Given a list of strings, to_sympy_matrix should be able to convert them into a matrix of expressions.
"""
m = sympy.Matrix([[sympy.sympify('x+y+3'),
sympy.sympify('x+3')],
[sympy.sympify('y-x'),
sympy.sympify('x+y+166')]])
m_as_string = [['x+y+3', 'x+3'], ['y-x', 'x+y+166']]
matrix = to_sympy_matrix(m_as_string)
assert_sympy_expressions_equal(m, matrix)
def test_initialisation_of_stoichiometry_matrix_as_numpy_array(self):
"""
The model constructor should accept stoichiometry_matrix as a numpy matrix
e.g. np.array(['y_0+y_1', 'y_1+y_2'])
and return them as sympy Matrix
e.g. sympy.Matrix([[-1, 1, 0], [0, 0, 1]])
"""
answer = sympy.Matrix([[-1, 1, 0], [0, 0, 1]])
# Column
m = Model(self.SAMPLE_VARIABLES, self.SAMPLE_CONSTANTS,
self.SAMPLE_PROPENSITIES,
sympy.Matrix([[-1, 1, 0], [0, 0, 1]]))
assert_sympy_expressions_equal(m.stoichiometry_matrix, answer)
def test_creation_of_column_matrix_from_list_of_strings(self):
"""
Given a list of strings, to_sympy_matrix should be able to convert them into a column matrix of expresions
"""
m = sympy.Matrix([
sympy.sympify('x+y+3'),
sympy.sympify('x+3'),
sympy.sympify('y-x'),
sympy.sympify('x+y+166')
])
m_as_string = ['x+y+3', 'x+3', 'y-x', 'x+y+166']
matrix = to_sympy_matrix(m_as_string)
assert_sympy_expressions_equal(m, matrix)
def test_initialisation_of_stoichiometry_matrix_as_numpy_array(self):
"""
The model constructor should accept stoichiometry_matrix as a numpy matrix
e.g. np.array(['y_0+y_1', 'y_1+y_2'])
and return them as sympy Matrix
e.g. sympy.Matrix([[-1, 1, 0], [0, 0, 1]])
"""
answer = sympy.Matrix([[-1, 1, 0], [0, 0, 1]])
# Column
m = Model(self.SAMPLE_VARIABLES,
self.SAMPLE_CONSTANTS,
self.SAMPLE_PROPENSITIES,
sympy.Matrix([[-1, 1, 0], [0, 0, 1]]))
assert_sympy_expressions_equal(m.stoichiometry_matrix, answer)
def test_for_p53(self):
"""
Given the preopensities,
Given the soichiometry matrix,
Given the counter (list of Moments),
Given the species list,
Given k_vector and
Given ek_counter (list of moment)
The answer should match exactly the expected result
:return:
"""
stoichio = sympy.Matrix([
[1, -1, -1, 0, 0, 0],
[0, 0, 0, 1, -1, 0],
[0, 0, 0, 0, 1, -1]
])
propensities = to_sympy_matrix([
[" c_0"],
[" c_1*y_0"],
["c_2*y_0*y_2/(c_6 + y_0)"],
[" c_3*y_0"],
[" c_4*y_1"],
[" c_5*y_2"]])
counter = [
Moment([0, 0, 0], 1),
Moment([0, 0, 2], sympy.Symbol("yx1")),
Moment([0, 1, 1], sympy.Symbol("yx2")),
Moment([0, 2, 0], sympy.Symbol("yx3")),
Moment([1, 0, 1], sympy.Symbol("yx4")),
Moment([1, 1, 0], sympy.Symbol("yx5")),
Moment([2, 0, 0], sympy.Symbol("yx6"))
]
species = sympy.Matrix(["y_0", "y_1", "y_2"])
dbdt_calc = DBetaOverDtCalculator(propensities, counter,stoichio, species)
k_vec = [1, 0, 0]
ek_counter = [Moment([1, 0, 0], sympy.Symbol("y_0"))]
answer = dbdt_calc.get(k_vec,ek_counter).T
result = to_sympy_matrix(["c_0 - c_1*y_0 - c_2*y_0*y_2/(c_6 + y_0)"," 0"," 0"," 0"," c_2*y_0/(c_6 + y_0)**2 - c_2/(c_6 + y_0)"," 0"," -c_2*y_0*y_2/(c_6 + y_0)**3 + c_2*y_2/(c_6 + y_0)**2"])
assert_sympy_expressions_equal(answer, result)
def test_centralmoments_using_MM_model(self):
"""
Given the MM model hard codded bellow,the result of central moment should match exactly the expected one
:return:
"""
counter_nvecs = [[0, 0], [0, 2], [1, 1], [2, 0]]
mcounter_nvecs = [[0, 0], [0, 1], [1, 0], [0, 2], [1, 1], [2, 0]]
counter = [Moment(c,sympy.Symbol("YU{0}".format(i))) for i,c in enumerate(counter_nvecs)]
mcounter = [Moment(c,sympy.Symbol("y_{0}".format(i))) for i,c in enumerate(mcounter_nvecs)]
m = to_sympy_matrix([
['-c_0*y_0*(y_0 + y_1 - 181) + c_1*(-y_0 - y_1 + 301)',
0,
'-c_0',
'-c_0'],
[
'c_2*(-y_0 - y_1 + 301)',
0,
0,
0]
])
species = sympy.Matrix(map(sympy.var, ['y_0', 'y_1']))
propensities = to_sympy_matrix(['c_0*y_0*(y_0 + y_1 - 181)',
'c_1*(-y_0 - y_1 + 301)',
'c_2*(-y_0 - y_1 + 301)'])
stoichiometry_matrix = sympy.Matrix([[-1, 1, 0],
[0, 0, 1]])
expected = to_sympy_matrix([
["c_2*(-y_0 - y_1 + 301)"," -2*c_2"," -2*c_2"," 0"],
["-c_0*y_0*y_1*(y_0 + y_1 - 181) + c_1*y_1*(-y_0 - y_1 + 301) + c_2*y_0*(-y_0 - y_1 + 301) - c_2*y_2*(-y_0 - y_1 + 301) - y_1*(-c_0*y_0*(y_0 + y_1 - 181) + c_1*(-y_0 - y_1 + 301))"," -c_0*y_0 - c_1"," -c_0*y_0 - c_0*(y_0 + y_1 - 181) - c_1 - c_2"," -c_2"],
["-2*c_0*y_0**2*(y_0 + y_1 - 181) + c_0*y_0*(y_0 + y_1 - 181) + 2*c_1*y_0*(-y_0 - y_1 + 301) + c_1*(-y_0 - y_1 + 301) - 2*y_2*(-c_0*y_0*(y_0 + y_1 - 181) + c_1*(-y_0 - y_1 + 301))"," 0"," -4*c_0*y_0 + 2*c_0*y_2 + c_0 - 2*c_1"," -4*c_0*y_0 + 2*c_0*y_2 - 2*c_0*(y_0 + y_1 - 181) + c_0 - 2*c_1"]
])
answer = eq_central_moments(counter, mcounter, m, species, propensities, stoichiometry_matrix, 2)
assert_sympy_expressions_equal(answer, expected)
def test_derive_expr_from_counter_entry(self):
"""
Given the tuples of integers a, b and c
Then, the "composite derivatives" should be exactly "a_result", "b_result" and "c_result", respectively
:return:
"""
expr = sp.simplify("c_0*y_0*(y_0 + y_1 - 181)/(y_2+c_1*y_1)")
vars = sp.simplify(["y_0", "y_1", "y_2"])
count_entr_a = (0, 1, 3)
count_entr_b = (1, 1, 0)
count_entr_c = (0, 0, 0)
a_result = derive_expr_from_counter_entry(expr, vars, count_entr_a)
b_result = derive_expr_from_counter_entry(expr, vars, count_entr_b)
c_result = derive_expr_from_counter_entry(expr, vars, count_entr_c)
a_expected = sp.diff(sp.diff(expr, "y_2", 3), "y_1")
b_expected = sp.diff(sp.diff(expr, "y_0"), "y_1")
c_expected = expr
assert_sympy_expressions_equal(a_expected, a_result)
assert_sympy_expressions_equal(b_expected, b_result)
assert_sympy_expressions_equal(c_expected, c_result)
def test_centralmoments_using_p53model(self):
"""
Given the p53 model hard codded bellow,the result of central moment should match exactly the expected one
:return:
"""
counter_nvecs = [[0, 0, 0], [0, 0, 2], [0, 1, 1], [0, 2, 0], [1, 0, 1], [1, 1, 0], [2, 0, 0]]
mcounter_nvecs = [[0, 0, 0], [0, 0, 1], [0, 1, 0], [1, 0, 0], [0, 0, 2], [0, 1, 1], [0, 2, 0],
[1, 0, 1], [1, 1, 0], [2, 0, 0]]
counter = [Moment(c,sympy.Symbol("YU{0}".format(i))) for i,c in enumerate(counter_nvecs)]
mcounter = [Moment(c,sympy.Symbol("y_{0}".format(i))) for i,c in enumerate(mcounter_nvecs)]
m = to_sympy_matrix([
['c_0 - c_1*y_0 - c_2*y_0*y_2/(c_6 + y_0)',
0,
0,
0,
'c_2*y_0/(c_6 + y_0)**2 - c_2/(c_6 + y_0)',
0,
'-c_2*y_0*y_2/(c_6 + y_0)**3 + c_2*y_2/(c_6 + y_0)**2'],
[
'c_3*y_0 - c_4*y_1',
0,
0,
0,
0,
0,
0],
[
'c_4*y_1 - c_5*y_2',
0,
0,
0,
0,
0,
0
]])
species = to_sympy_matrix(['y_0', 'y_1', 'y_2'])
propensities = to_sympy_matrix(['c_0',
'c_1 * y_0',
'c_2*y_0*y_2/(c_6 + y_0)',
'c_3*y_0',
'c_4*y_1',
'c_5*y_2'])
stoichiometry_matrix = to_sympy_matrix([[1, -1, -1, 0, 0, 0],
[0, 0, 0, 1, -1, 0],
[0, 0, 0, 0, 1, -1]])
answer = eq_central_moments(counter, mcounter, m, species, propensities, stoichiometry_matrix, 2)
expected = to_sympy_matrix([
[" 2*c_4*y_1*y_2 + c_4*y_1 - 2*c_5*y_2**2 + c_5*y_2 - 2*y_1*(c_4*y_1 - c_5*y_2)"," -2*c_5"," 2*c_4"," 0"," 0"," 0"," 0"],
["c_3*y_0*y_2 + c_4*y_1**2 - c_4*y_1*y_2 - c_4*y_1 - c_5*y_1*y_2 - y_1*(c_3*y_0 - c_4*y_1) - y_2*(c_4*y_1 - c_5*y_2)"," 0"," -c_4 - c_5"," c_4"," c_3"," 0"," 0"],
["2*c_3*y_0*y_1 + c_3*y_0 - 2*c_4*y_1**2 + c_4*y_1 - 2*y_2*(c_3*y_0 - c_4*y_1)"," 0"," 0"," -2*c_4"," 0"," 2*c_3","0"],
["c_0*y_2 - c_1*y_0*y_2 - c_2*y_0*y_2**2/(c_6 + y_0) + c_4*y_0*y_1 - c_5*y_0*y_2 - y_1*(c_0 - c_1*y_0 - c_2*y_0*y_2/(c_6 + y_0)) - y_3*(c_4*y_1 - c_5*y_2)"," -c_2*y_0/(c_6 + y_0)"," 0"," 0"," -c_1 + 2*c_2*y_0*y_2/(c_6 + y_0)**2 - 2*c_2*y_2/(c_6 + y_0) - c_5 - y_1*(c_2*y_0/(c_6 + y_0)**2 - c_2/(c_6 + y_0))","c_4"," -c_2*y_0*y_2**2/(c_6 + y_0)**3 + c_2*y_2**2/(c_6 + y_0)**2 - y_1*(-c_2*y_0*y_2/(c_6 + y_0)**3 + c_2*y_2/(c_6 + y_0)**2)"],
["c_0*y_1 - c_1*y_0*y_1 - c_2*y_0*y_1*y_2/(c_6 + y_0) + c_3*y_0**2 - c_4*y_0*y_1 - y_2*(c_0 - c_1*y_0 - c_2*y_0*y_2/(c_6 + y_0)) - y_3*(c_3*y_0 - c_4*y_1)"," 0"," -c_2*y_0/(c_6 + y_0)"," 0"," c_2*y_0*y_1/(c_6 + y_0)**2 - c_2*y_1/(c_6 + y_0) - y_2*(c_2*y_0/(c_6 + y_0)**2 - c_2/(c_6 + y_0))"," -c_1 + c_2*y_0*y_2/(c_6 + y_0)**2 - c_2*y_2/(c_6 + y_0) - c_4"," -c_2*y_0*y_1*y_2/(c_6 + y_0)**3 + c_2*y_1*y_2/(c_6 + y_0)**2 + c_3 - y_2*(-c_2*y_0*y_2/(c_6 + y_0)**3 + c_2*y_2/(c_6 + y_0)**2)"],
["2*c_0*y_0 + c_0 - 2*c_1*y_0**2 + c_1*y_0 - 2*c_2*y_0**2*y_2/(c_6 + y_0) + c_2*y_0*y_2/(c_6 + y_0) - 2*y_3*(c_0 - c_1*y_0 - c_2*y_0*y_2/(c_6 + y_0))"," 0"," 0"," 0"," 2*c_2*y_0**2/(c_6 + y_0)**2 - 4*c_2*y_0/(c_6 + y_0) - c_2*y_0/(c_6 + y_0)**2 + c_2/(c_6 + y_0) - 2*y_3*(c_2*y_0/(c_6 + y_0)**2 - c_2/(c_6 + y_0))"," 0"," -2*c_1 - 2*c_2*y_0**2*y_2/(c_6 + y_0)**3 + 4*c_2*y_0*y_2/(c_6 + y_0)**2 + c_2*y_0*y_2/(c_6 + y_0)**3 - 2*c_2*y_2/(c_6 + y_0) - c_2*y_2/(c_6 + y_0)**2 - 2*y_3*(-c_2*y_0*y_2/(c_6 + y_0)**3 + c_2*y_2/(c_6 + y_0)**2)"]
])
assert_sympy_expressions_equal(answer, expected)