pygbe.util package

Submodules

pygbe.util.an_solution module

It contains the functions to compute the cases that presents an analytical solutions. All functions output the analytical solution in kcal/mol

pygbe.util.an_solution.an_P(q, xq, E_1, E_2, R, kappa, a, N)

It computes the solvation energy according to Kirkwood-1934.

Parameters:

• q (array, charges.) –
• xq (array, positions of the charges.) –
• E_1 (float, dielectric constant inside the sphere.) –
• E_2 (float, dielectric constant outside the sphere.) –
• R (float, radius of the sphere.) –
• kappa (float, reciprocal of Debye length.) –
• a (float, radius of the Stern Layer.) –
• N (int, number of terms desired in the polinomial expansion.) –

Returns:

E_P

Return type:

float, solvation energy.

pygbe.util.an_solution.an_spherical(q, xq, E_1, E_2, E_0, R, N)

It computes the analytical solution of the potential of a sphere with Nq charges inside. Took from Kirkwood (1934).

Parameters:

• q (array, charges.) –
• xq (array, positions of the charges.) –
• E_1 (float, dielectric constant inside the sphere.) –
• E_2 (float, dielectric constant outside the sphere.) –
• E_0 (float, dielectric constant of vacuum.) –
• R (float, radius of the sphere.) –
• N (int, number of terms desired in the spherical harmonic expansion.) –

Returns:

PHI

Return type:

array, reaction potential.

pygbe.util.an_solution.constant_charge_single_energy(sigma0, r1, kappa, epsilon)

It computes the total energy of a single sphere at constant charge, inmmersed in water.

Parameters:

• sigma0 (float, constant charge on the surface of the sphere.) –
• r1 (float, radius of sphere.) –
• kappa (float, reciprocal of Debye length.) –
• epsilon (float, water dielectric constant.) –

Returns:

E

Return type:

float, total energy.

pygbe.util.an_solution.constant_charge_single_point(sigma0, a, r, kappa, epsilon)

It computes the potential in a point ‘r’ due to a spherical surface with constant charge sigma0 immersed in water. Solution to the Poisson-Boltzmann problem. .

Parameters:

• sigma0 (float, constant charge on the surface of the sphere.) –
• a (float, radius of the sphere.) –
• r (float, distance from the center of the sphere to the evaluation) – point.
• kappa (float, reciprocal of Debye length.) –
• epsilon (float, water dielectric constant.) –

Returns:

phi

Return type:

float, potential.

pygbe.util.an_solution.constant_charge_single_potential(sigma0, radius, kappa, epsilon)

It computes the surface potential on a sphere at constant charged, immersed in water.

Parameters:

• sigma0 (float, constant charge on the surface of the sphere.) –
• radius (float, radius of the sphere.) –
• kappa (float, reciprocal of Debye length.) –
• epsilon (float, water dielectric constant.) –

Returns:

phi

Return type:

float, potential.

pygbe.util.an_solution.constant_charge_twosphere_dissimilar(sigma01, sigma02, r1, r2, R, kappa, epsilon)

It computes the interaction energy between two dissimilar spheres at constant charge, immersed in water.

Parameters:

• sigma01 (float, constant charge on the surface of the sphere 1.) –
• sigma02 (float, constant charge on the surface of the sphere 2.) –
• r1 (float, radius of sphere 1.) –
• r2 (float, radius of sphere 2.) –
• R (float, distance center to center.) –
• kappa (float, reciprocal of Debye length.) –
• epsilon (float, water dielectric constant.) –

Returns:

E_inter

Return type:

float, interaction energy.

pygbe.util.an_solution.constant_charge_twosphere_identical(sigma, a, R, kappa, epsilon)

It computes the interaction energy for two spheres at constants surface charge, according to Carnie&Chan-1993.

Parameters:

• sigma (float, constant charge on the surface of the spheres.) –
• a (float, radius of spheres.) –
• R (float, distance center to center.) –
• kappa (float, reciprocal of Debye length.) –
• epsilon (float, water dielectric constant.) –

Returns:

E_inter

Return type:

float, interaction energy.

pygbe.util.an_solution.constant_potential_single_charge(phi0, radius, kappa, epsilon)

It computes the surface charge of a sphere at constant potential, immersed in water.

Parameters:

• phi0 (float, constant potential on the surface of the sphere.) –
• radius (float, radius of the sphere.) –
• kappa (float, reciprocal of Debye length.) –
• epsilon (float, water dielectric constant .) –

Returns:

sigma

Return type:

float, surface charge.

pygbe.util.an_solution.constant_potential_single_energy(phi0, r1, kappa, epsilon)

It computes the total energy of a single sphere at constant potential, inmmersed in water.

Parameters:

• phi0 (float, constant potential on the surface of the sphere.) –
• r1 (float, radius of sphere.) –
• kappa (float, reciprocal of Debye length.) –
• epsilon (float, water dielectric constant.) –

Returns:

E

Return type:

float, total energy.

pygbe.util.an_solution.constant_potential_single_point(phi0, a, r, kappa)

It computes the potential in a point ‘r’ due to a spherical surface with constant potential phi0, immersed in water. Solution to the Poisson-Boltzmann problem.

Parameters:

• phi0 (float, constant potential on the surface of the sphere.) –
• a (float, radius of the sphere.) –
• r (float, distance from the center of the sphere to the evaluation) – point.
• kappa (float, reciprocal of Debye length.) –

Returns:

phi

Return type:

float, potential.

pygbe.util.an_solution.constant_potential_twosphere(phi01, phi02, r1, r2, R, kappa, epsilon)

It computes the solvation energy of two spheres at constant potential, immersed in water.

Parameters:

• phi01 (float, constant potential on the surface of the sphere 1.) –
• phi02 (float, constant potential on the surface of the sphere 2.) –
• r1 (float, radius of sphere 1.) –
• r2 (float, radius of sphere 2.) –
• R (float, distance center to center.) –
• kappa (float, reciprocal of Debye length.) –
• epsilon (float, water dielectric constant.) –

Returns:

E_solv

Return type:

float, solvation energy.

pygbe.util.an_solution.constant_potential_twosphere_2(phi01, phi02, r1, r2, R, kappa, epsilon)

It computes the solvation energy of two spheres at constant potential, immersed in water.

Parameters:

• phi01 (float, constant potential on the surface of the sphere 1.) –
• phi02 (float, constant potential on the surface of the sphere 2.) –
• r1 (float, radius of sphere 1.) –
• r2 (float, radius of sphere 2.) –
• R (float, distance center to center.) –
• kappa (float, reciprocal of Debye length.) –
• epsilon (float, water dielectric constant.) –

Returns:

E_solv

Return type:

float, solvation energy.

pygbe.util.an_solution.constant_potential_twosphere_dissimilar(phi01, phi02, r1, r2, R, kappa, epsilon)

It computes the interaction energy for dissimilar spheres at constant potential, immersed in water.

Parameters:

• phi01 (float, constant potential on the surface of the sphere 1.) –
• phi02 (float, constant potential on the surface of the sphere 2.) –
• r1 (float, radius of sphere 1.) –
• r2 (float, radius of sphere 2.) –
• R (float, distance center to center.) –
• kappa (float, reciprocal of Debye length.) –
• epsilon (float, water dielectric constant.) –

Returns:

E_inter

Return type:

float, interaction energy.

pygbe.util.an_solution.constant_potential_twosphere_identical(phi01, phi02, r1, r2, R, kappa, epsilon)

It computes the interaction energy for two spheres at constants surface potential, according to Carnie&Chan-1993.

Parameters:

• phi01 (float, constant potential on the surface of the sphere 1.) –
• phi02 (float, constant potential on the surface of the sphere 2.) –
• r1 (float, radius of sphere 1.) –
• r2 (float, radius of sphere 2.) –
• R (float, distance center to center.) –
• kappa (float, reciprocal of Debye length.) –
• epsilon (float, water dielectric constant.) –
• Note – Even though it admits phi01 and phi02, they should be identical; and the same is applicable to r1 and r2.

Returns:

E_inter

Return type:

float, interaction energy.

pygbe.util.an_solution.get_K(x, n)

It computes the polinomials K needed for Kirkwood-1934 solutions. K_n(x) in Equation 4 in Kirkwood 1934.

Parameters:

• x (float, evaluation point of K.) –
• n (int, number of terms desired in the expansion.) –

Returns:

K

Return type:

float, polinomials K.

pygbe.util.an_solution.molecule_constant_charge(q, sigma02, r1, r2, R, kappa, E_1, E_2)

It computes the interaction energy between a molecule (sphere with point-charge in the center) and a sphere at constant charge, immersed in water.

Parameters:

• q (float, number of qe to be asigned to the charge.) –
• sigma02 (float, constant charge on the surface of the sphere 2.) –
• r1 (float, radius of sphere 1, i.e the molecule.) –
• r2 (float, radius of sphere 2.) –
• R (float, distance center to center.) –
• kappa (float, reciprocal of Debye length.) –
• E_1 (float, dielectric constant inside the sphere/molecule.) –
• E_2 (float, dielectric constant outside the sphere/molecule.) –

Returns:

E_inter

Return type:

float, interaction energy.

pygbe.util.an_solution.molecule_constant_potential(q, phi02, r1, r2, R, kappa, E_1, E_2)

It computes the interaction energy between a molecule (sphere with point-charge in the center) and a sphere at constant potential, immersed in water.

Parameters:

• q (float, number of qe to be asigned to the charge.) –
• phi02 (float, constant potential on the surface of the sphere 2.) –
• r1 (float, radius of sphere 1, i.e the molecule.) –
• r2 (float, radius of sphere 2.) –
• R (float, distance center to center.) –
• kappa (float, reciprocal of Debye length.) –
• E_1 (float, dielectric constant inside the sphere/molecule.) –
• E_2 (float, dielectric constant outside the sphere/molecule.) –

Returns:

E_inter

Return type:

float, interaction energy.

pygbe.util.an_solution.two_sphere(a, R, kappa, E_1, E_2, q)

It computes the analytical solution of a spherical surface and a spherical molecule with a center charge, both of radius R. Follows Cooper&Barba 2016

Parameters:

• a (float, center to center distance.) –
• R (float, radius of surface and molecule.) –
• kappa (float, reciprocal of Debye length.) –
• E_1 (float, dielectric constant inside the sphere.) –
• E_2 (float, dielectric constant outside the sphere.) –
• q (float, number of qe to be asigned to the charge.) –

Returns:

• Einter (float, interaction energy.)
• E1sphere (float, solvation energy of one sphere.)
• E2sphere (float, solvation energy of two spheres together.)
• Note
• Einter should match (E2sphere - 2xE1sphere)

pygbe.util.read_data module

It contains the functions to read the all the data from the meshes files, its parameters and charges files.

pygbe.util.read_data.readCheck(aux, REAL)

It checks if it is not reading more than one term. We use this function to check we are not missing ‘-‘ signs in the .pqr files, when we read the lines.

Parameters:

• aux (str, string to be checked.) –
• REAL (data type.) –

Returns:

X

Return type:

array, array with the correct ‘-‘ signs assigned.

pygbe.util.read_data.readElectricField(param, filename)

It reads the information about the incident electric field.

Parameters:

• param (class, parameters related to the surface.) –
• filename (name of the file that contains the infromation of the incident) – electric field. (filname.config)

Returns:

• electricField (float, electric field intensity, it is in the ‘z’) – direction, ‘-‘ indicates ‘-z’.
• wavelength (float, wavelength of the incident electric field.)

pygbe.util.read_data.readParameters(param, filename)

It populates the attributes from the Parameters class with the information read from the .param file.

Parameters:

• param (class, parameters related to the surface.) –
• filename (name of the file that contains the parameters information.) – (filename.param)

Returns:

dataType – other fucntions.

Return type:

we return the dataType of each attributes because we need it for

pygbe.util.read_data.read_fields(filename)

Read the physical parameters from the configuration file for each region in the surface

Parameters:filename (name of the file that contains the physical parameters of each) – region. (filename.config) Returns:

• Dictionary containing
• LorY (list, it contains integers, Laplace (1) or Yukawa (2),) – corresponding to each region.
• pot (list, it contains integers indicating to calculate (1) or not (2)) – the energy in this region.
• E (list, it contains floats with the dielectric constant of each) – region.
• kappa (list, it contains floats with the reciprocal of Debye length value) – of each region.
• charges (list, it contains integers indicating if there are (1) or not (0)) – charges in this region.
• coulomb (list, it contains integers indicating to calculate (1) or not (2)) – the coulomb energy in this region.
• qfile (list, location of the ‘.pqr’ file with the location of the charges.)
• Nparent (list, it contains integers indicating the number of ‘parent’) – surfaces (surface containing this region)
• parent (list, it contains the file of the parent surface mesh, according) – to their position in the FILE list, starting from 0 (eg. if the mesh file for the parent is the third one specified in the FILE section, parent=2)
• Nchild (list, it contains integers indicating number of child surfaces) – (surfaces completely contained in this region).
• child (list, it contains position of the mesh files for the children) – surface in the FILE section.

pygbe.util.read_data.read_surface(filename)

It reads the type of surface of each region on the surface from the configuration file.

Parameters:filename (name of the file that contains the surface type of each region.) – (filename.config). Returns:

• files (list, it contains the files corresponding to each region in the) – surface.
• surf_type (list, it contains the type of surface of each region.)
• phi0_file (list, it contains the constant potential/surface charge for the) – cases where it applies. (dirichlet or neumann surfaces)

pygbe.util.read_data.read_triangle(filename, surf_type)

It reads the triangles from the mesh file and it stores them on an array.

Parameters:

• filename (name of the file that contains the surface information.) – (filename.faces)
• surf_type (str, type of surface.) –

Returns:

triangle

Return type:

array, triangles indices.

pygbe.util.read_data.read_vertex(filename, REAL)

It reads the vertex of the triangles from the mesh file and it stores them on an array.

Parameters:

• filename (name of the file that contains the surface information.) – (filename.vert)
• REAL (data type.) –

Returns:

vertex

Return type:

array, vertices of the triangles.

pygbe.util.read_data.readcrd(filename, REAL)

It reads the crd file, file that contains the charges information.

Parameters:

• filename (name of the file that contains the surface information.) –
• REAL (data type.) –

Returns:

• pos ((Nqx3) array, positions of the charges.)
• q ((Nqx1) array, value of the charges.)
• Nq (int, number of charges.)

pygbe.util.read_data.readpqr(filename, REAL)

Read charge information from pqr file

Parameters:

• filename (name of the file that contains the surface information.) – (filename.pqr)
• REAL (data type.) –

Returns:

• pos ((Nqx3) array, positions of the charges.)
• q ((Nqx1) array, value of the charges.)

pygbe.util.semi_analytical module

It contains the functions needed to compute the near singular integrals in python. For big problems these functions were written in C++ and we call them through the pycuda interface. At the end you have a commented test to compare both types.

pygbe.util.semi_analytical.GQ_1D(K)

Gauss quadrature in 1D.

Parameters:K (int, desired number of gauss points.) – Returns:

• x (float, location of the gauss point.)
• w (float, weights of the gauss point.)

pygbe.util.semi_analytical.SA_arr(y, x, kappa, same, xk, wk)

It computes the integral line for all the sides of a triangle and for all the collocation points.

Parameters:

• y (array, vertices coordinates of the triangles.) –
• x (array, collocation points.) –
• kappa (float, reciprocal of Debye length.) –
• same (int, 1 if the collocation point is in the panel of integration,) – 0 otherwise.
• xk (float, position of the gauss point.) –
• wk (float, weight of the gauss point.) –

Returns:

• phi_Y (float, potential due to a Yukawa kernel.)
• dphi_Y (float, normal derivative of potential due to a Yukawa kernel.)
• phi_L (float, potential due to a Laplace kernel.)
• dphi_L (float, normal derivative of potential due to a Laplace kernel.)

pygbe.util.semi_analytical.intSide(v1, v2, p, kappa, xk, wk)

It solves the integral line over one side of the triangle .

Parameters:

• v1 (float, low extreme integral value.) –
• v2 (float, high extreme integral value.) –
• p (float, distance (height) between the plane of the triangle and the) – collocation point.
• kappa (float, reciprocal of Debye length.) –
• xk (float, position of the gauss point.) –
• wk (float, weight of the gauss point.) –

Returns:

• phi_Y (float, potential due to a Yukawa kernel.)
• dphi_Y (float, normal derivative of potential due to a Yukawa kernel.)
• phi_L (float, potential due to a Laplace kernel.)
• dphi_L (float, normal derivative of potential due to a Laplace kernel.)

pygbe.util.semi_analytical.lineInt(z, x, v1, v2, kappa, xk, wk)

Line integral to solve the non-analytical part (integral in the angle) in the semi_analytical integrals needed to calculate the potentials.

Parameters:

• z (float, distance (height) between the plane of the triangle and the) – collocation point.
• x (float, position of the collocation point.) –
• v1 (float, low extreme integral value.) –
• v2 (float, high extreme integral value.) –
• kappa (float, reciprocal of Debye length.) –
• xk (float, position of the gauss point.) –
• wk (float, weight of the gauss point.) –

Returns:

• phi_Y (float, potential due to a Yukawa kernel.)
• dphi_Y (float, normal derivative of potential due to a Yukawa kernel.)
• phi_L (float, potential due to a Laplace kernel.)
• dphi_L (float, normal derivative of potential due to a Laplace kernel.)

pygbe.util.semi_analyticalwrap module

Module contents