Source code for arbdmodel.kh_polymer_model

# -*- coding: utf-8 -*-
## Test with `python -m arbdmodel.kh_polymer_model`

import numpy as np

## Local imports
from .logger import logger, get_resource_path
from . import ParticleType, PointParticle
from .polymer import PolymerBeads, PolymerModel
from .interactions import AbstractPotential, HarmonicBond

"""Define particle types"""
_types = dict(
    A = ParticleType("ALA",
                     mass = 71.08,
                     charge = 0,
                     sigma = 5.04,
                 ),
    R = ParticleType("ARG",
                     mass = 156.2,
                     charge = 1,
                     sigma = 6.56,
                 ),
    N = ParticleType("ASN",
                     mass = 114.1,
                     charge = 0,
                     sigma = 5.68,
                 ),
    D = ParticleType("ASP",
                     mass = 115.1,
                     charge = -1,
                     sigma = 5.58,
                 ),
    C = ParticleType("CYS",
                     mass = 103.1,
                     charge = 0,
                     sigma = 5.48,
                 ),
    Q = ParticleType("GLN",
                     mass = 128.1,
                     charge = 0,
                     sigma = 6.02,
                 ),
    E = ParticleType("GLU",
                     mass = 129.1,
                     charge = -1,
                     sigma = 5.92,
                 ),
    G = ParticleType("GLY",
                     mass = 57.05,
                     charge = 0,
                     sigma = 4.5,
                 ),
    H = ParticleType("HIS",
                     mass = 137.1,
                     charge = 0.5,
                     sigma = 6.08,
                 ),
    I = ParticleType("ILE",
                     mass = 113.2,
                     charge = 0,
                     sigma = 6.18,
                 ),
    L = ParticleType("LEU",
                     mass = 113.2,
                     charge = 0,
                     sigma = 6.18,
                 ),
    K = ParticleType("LYS",
                     mass = 128.2,
                     charge = 1,
                     sigma = 6.36,
                 ),
    M = ParticleType("MET",
                     mass = 131.2,
                     charge = 0,
                     sigma = 6.18,
                 ),
    F = ParticleType("PHE",
                     mass = 147.2,
                     charge = 0,
                     sigma = 6.36,
                 ),
    P = ParticleType("PRO",
                     mass = 97.12,
                     charge = 0,
                     sigma = 5.56,
                 ),
    S = ParticleType("SER",
                     mass = 87.08,
                     charge = 0,
                     sigma = 5.18,
                 ),
    T = ParticleType("THR",
                     mass = 101.1,
                     charge = 0,
                     sigma = 5.62,
                 ),
    W = ParticleType("TRP",
                     mass = 186.2,
                     charge = 0,
                     sigma = 6.78,
                 ),
    Y = ParticleType("TYR",
                     mass = 163.2,
                     charge = 0,
                     sigma = 6.46,
                 ),
    V = ParticleType("VAL",
                     mass = 99.07,
                     charge = 0,
                     sigma = 5.86,
                 )
)

for k,t in list(_types.items()):
    t.resname = t.name
    t.is_idp = False
    
    ## Add types for IDPs
    _types[k+'IDP'] = ParticleType(t.name+'IDP', mass=t.mass, charge=t.charge, sigma=t.sigma, is_idp=True, resname=t.resname)


data= np.loadtxt(get_resource_path("kh_pairwise_epsilon.csv"), dtype=str)
epsilon_mj = dict()
for n1,n2,v in data:
    v = float(v)
    epsilon_mj[(n1,n2)] = v
    epsilon_mj[(n2,n1)] = v
    epsilon_mj[(n1+'IDP',n2)]=v
    epsilon_mj[(n2,n1+'IDP')]=v
    epsilon_mj[(n2+'IDP',n1)]=v
    epsilon_mj[(n1,n2+'IDP')]=v
    epsilon_mj[(n2+'IDP',n1+'IDP')]=v
    epsilon_mj[(n1+'IDP',n2+'IDP')]=v


    
[docs] class KhNonbonded(AbstractPotential): """ A class implementing the Kim-Hummer nonbonded potential energy model for protein interactions. This model combines electrostatic interactions with a modified Lennard-Jones potential that accounts for hydrophobic effects using the KH (Kim-Hummer) scaling approach. The potential is particularly useful for modeling interactions between intrinsically disordered proteins (IDPs) and folded proteins. Parameters ---------- debye_length : float, optional The Debye screening length in Angstroms, default is 10Å resolution : float, optional The spatial resolution for potential calculations, default is 0.1Å range_ : tuple, optional The range of distances (min, max) over which to compute the potential, default is (0, None) where None means no upper limit Attributes ---------- debye_length : float The Debye screening length in Angstroms max_force : float Maximum allowed force from this potential, set to 50 Methods ------- potential(r, types) Calculates the nonbonded potential energy between two atom types at distance r. Combines electrostatic interactions with a modified Lennard-Jones potential. References ---------- Kim, Y. C., & Hummer, G. (2008). Coarse-grained models for simulations of multiprotein complexes: application to ubiquitin binding. Journal of molecular biology, 375(5), 1416-1433. """ def __init__(self, debye_length=10, resolution=0.1, range_=(0,None)): AbstractPotential.__init__(self, resolution=resolution, range_=range_) self.debye_length = debye_length self.max_force = 50
[docs] def potential(self, r, types): """ Electrostatics """ typeA, typeB = types ld = self.debye_length q1 = typeA.charge q2 = typeB.charge D = 80 # dielectric of water ## units "e**2 / (4 * pi * epsilon0 AA)" kcal_mol A = 332.06371 u_elec = (A*q1*q2/D)*np.exp(-r/ld) / r """ KH scale model """ A_is_idp = B_is_idp = False try: A_is_idp = typeA.is_idp except: pass try: B_is_idp = typeB.is_idp except: pass _idp_scale = (int(A_is_idp)*int(B_is_idp)) alpha = 0.159 + _idp_scale * (0.228 - 0.159) epsilon0 = -1.36 + _idp_scale * (1.36 - 1.0) e_mj = epsilon_mj[(typeA.resname,typeB.resname)] epsilon = alpha * np.abs( e_mj - epsilon0 ) lambda_ = -1 if epsilon0 > e_mj else 1 sigma = 0.5 * (typeA.sigma + typeB.sigma) r6 = (sigma/r)**6 r12 = r6**2 u_lj = 4 * epsilon * (r12-r6) u_hps = lambda_ * np.array(u_lj) s = r<=sigma*2**(1/6) u_hps[s] = u_lj[s] + (1-lambda_) * epsilon u = u_elec + u_hps return u
[docs] class KhBeads(PolymerBeads): def __init__(self, polymer, sequence=None, spring_constant = 2.3900574, rest_length = 3.8, **kwargs): if sequence is None: raise NotImplementedError # ... set random sequence self.spring_constant = spring_constant PolymerBeads.__init__(self, polymer, sequence, rest_length=rest_length, **kwargs) assert(self.monomers_per_bead_group == 1) if len(sequence) != polymer.num_monomers: raise ValueError("Length of sequence does not match length of polymer") try: polymer.idp_array self.idp_array = polymer.idp_array except: logger.warning("KhBeads processing a polymer without 'idp_array' attribute set (boolean numpy array with one True/False value per amino acid with True corresponding to IDP... Assuming all amino acids are IDP.") self.idp_array = np.ones(polymer.num_monomers, dtype=bool) if len(self.idp_array) != polymer.num_monomers: raise ValueError(f'polymer {polymer} idp_array has incorrect size != {polymer.num_monomers}') def _generate_ith_bead_group(self, i, r, o): s = self.sequence[i] if self.idp_array[i]: s = s + 'IDP' return PointParticle(_types[s], r, name = s, resid = i+1) def _join_adjacent_bead_groups(self, ids): ## Two consecutive groups if len(ids) == 2: b1,b2 = [self.children[i] for i in ids] """ units "10 kJ/N_A" kcal_mol """ bond = HarmonicBond(k = self.spring_constant, r0 = self.rest_length, range_ = (0,100), resolution = 0.01, max_force = 10) self.add_bond( i=b1, j=b2, bond = bond, exclude=True ) elif len(ids) == 3: ... else: pass
[docs] class KhModel(PolymerModel): def __init__(self, polymers, sequences = None, rest_length = 3.8, spring_constant = 2.3900574, debye_length = 10, damping_coefficient = 10, idp_array = None, DEBUG=False, **kwargs): """ [debye_length]: angstroms [damping_coefficient]: ns """ logger.info("""You are using an implementation of the Kim-Hummer model as described for proteins with IDPs by the Mittal lab: Dignon GL, Zheng W, Kim YC, Best RB, Mittal J (2018) Sequence determinants of protein phase behavior from a coarse-grained model. PLOS Computational Biology 14(1) e1005941. https://doi.org/10.1371/journal.pcbi.1005941 based upon: Young C. Kim, Gerhard Hummer (2008) Coarse-grained Models for Simulations of Multiprotein Complexes: Application to Ubiquitin Binding. Journal of Molecular Biology 375(5) 1416-1433. https://doi.org/10.1016/j.jmb.2007.11.063. Please cite all appropriate articles!""") if 'timestep' not in kwargs: kwargs['timestep'] = 10e-6 if 'cutoff' not in kwargs: kwargs['cutoff'] = max(4*debye_length,20) if 'decomp_period' not in kwargs: kwargs['decomp_period'] = 1000 self.rest_length = rest_length self.spring_constant = spring_constant """ Assign sequences """ if sequences is None: raise NotImplementedError("KhModel must be provided a sequences argument") PolymerModel.__init__(self, polymers, sequences, monomers_per_bead_group=1, **kwargs) """ Update type diffusion coefficients """ self.types = all_types = [t for key,t in _types.items()] self.set_damping_coefficient( damping_coefficient ) """ Set up nonbonded interactions """ nonbonded = KhNonbonded(debye_length) for t in all_types: self._add_nonbonded_interaction(nonbonded, t) def _add_nonbonded_interaction(self, interaction, type_): i = self.types.index(type_) if type_ in self.types else 0 for j in range(i,len(self.types)): t = self.types[j] self.add_nonbonded_interaction( interaction, typeA=type_, typeB=t ) def _generate_polymer_beads(self, polymer, sequence, polymer_index = None): return KhBeads(polymer, sequence, rest_length = self.rest_length, spring_constant = self.spring_constant, monomers_per_bead_group = self.monomers_per_bead_group, polymer_index = polymer_index )
[docs] def set_damping_coefficient(self, damping_coefficient): for t in self.types: t.damping_coefficient = damping_coefficient
# t.diffusivity = 831447.2 * temperature / (t.mass * damping_coefficient) if __name__ == "__main__": from matplotlib import pyplot as plt nt = len(_types) # print("TYPES") # for n,t in _types.items(): # print("{}\t{}\t{}\t{}\t{}".format(t.name, t.mass, t.charge, t.sigma, t.lambda_)) type_string = 'WYFMLIVAPGCQNTSEDKHR' d = np.zeros([nt,nt]) for i in range(nt): n1 = type_string[i] t1 = _types[n1] for j in range(nt): n2 = type_string[j] t2 = _types[n2] d[nt-i-1,j] = epsilon_mj[(t1.name,t2.name)] plt.imshow(d.T) plt.show()