Source code for dynamo.simulation.Gillespie

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Wed Jan 30 11:21:25 2019

@author: xqiu
"""

from .gillespie_utils import *
from .bif_os_inclusive_sim import sim_diff, sim_osc, simulate, osc_diff_dup
import pandas as pd
import scipy.sparse
import anndata


# deterministic as well as noise
[docs]def Gillespie( a=None, b=None, la=None, aa=None, ai=None, si=None, be=None, ga=None, C0=np.zeros((5, 1)), t_span=[0, 50], n_traj=1, t_eval=None, dt=1, method="basic", verbose=False, ): """A simulator of RNA dynamics that includes RNA bursting, transcription, metabolic labeling, splicing, transcription, RNA/protein degradation Parameters ---------- a: `float` or None rate of active promoter switches to inactive one b: `float` or None rate of inactive promoter switches to active one la: `float` or None lambda_: 4sU labelling rate aa: `float` or None transcription rate with active promoter ai: `float` or None transcription rate with inactive promoter si: `float` or None sigma, degradation rate be: `float` or None beta, splicing rate ga: `float` or None gamma: the fraction of labeled u turns to unlabeled s C0: `numpy.ndarray` (default: np.zeros((5, 1))) A numpy array with dimension of 5 x n_gene. Here 5 corresponds to the five species (s - promoter state, ul, uu, sl, su) for each gene. t_span: list of between and end time of simulation n_traj: number of simulation trajectory to use t_eval: `float` or None the time points at which data is simulated dt: `float` (default: `1`) delta t used in simulation method: `str` (default: basic) method to simulate the expression dynamics verbose: `bool` (default: False) whether to report running information Returns ------- adata: :class:`~anndata.AnnData` an Annodata object containing the simulated data. """ gene_num, species_num = C0.shape[0:2] adata_no_splicing, P = None, None if method == "basic": if t_eval is None: steps = (t_span[1] - t_span[0]) // dt # // int; %% remainder t_eval = np.linspace(t_span[0], t_span[1], steps) trajs_C = simulate_multigene( a=None, b=None, la=None, aa=None, ai=None, si=None, be=None, ga=None, C0=np.zeros((5, 1)), t_span=[0, 50], n_traj=1, t_eval=None, report=verbose, ) # unfinished, no need to interpolate now. uu, ul, su, sl = [np.transpose(trajs_C[:, :, i + 1, :].reshape((gene_num, -1))) for i in range(4)] u = uu + ul s = su + sl E = u + s layers = { "uu": scipy.sparse.csc_matrix(uu.astype(int)), "ul": scipy.sparse.csc_matrix(ul.astype(int)), "su": scipy.sparse.csc_matrix(su.astype(int)), "sl": scipy.sparse.csc_matrix(sl.astype(int)), "spliced": scipy.sparse.csc_matrix((s).astype(int)), "unspliced": scipy.sparse.csc_matrix((u).astype(int)), } # ambiguous is required for velocyto # provide more annotation for cells next: cell_ids = [ "traj_%d_step_%d" % (i, j) for i in range(n_traj) for j in range(steps) ] # first n_traj and then steps obs = pd.DataFrame( { "Cell_name": cell_ids, "Trajectory": [i for i in range(n_traj) for j in range(steps)], "Step": [j for i in range(n_traj) for j in range(steps)], } ) obs.set_index("Cell_name", inplace=True) elif method == "simulate_2bifurgenes": gene_num = 2 _, trajs_C = simulate_2bifurgenes( a1=20, b1=20, a2=20, b2=20, K=20, n=3, be1=1, ga1=1, be2=1, ga2=1, C0=np.zeros(4), t_span=t_span, n_traj=n_traj, report=verbose, ) # unfinished, no need to interpolate now. u = trajs_C[0][[0, 2], :].T s = trajs_C[0][[1, 3], :].T E = u + s layers = { "spliced": scipy.sparse.csc_matrix((s).astype(int)), "unspliced": scipy.sparse.csc_matrix((u).astype(int)), "ambiguous": scipy.sparse.csc_matrix((E).astype(int)), } # ambiguous is required for velocyto steps = u.shape[0] # provide more annotation for cells next: cell_ids = [ "traj_%d_step_%d" % (i, j) for i in range(n_traj) for j in range(steps) ] # first n_traj and then steps obs = pd.DataFrame( { "Cell_name": cell_ids, "Trajectory": [i for i in range(n_traj) for j in range(steps)], "Step": [j for i in range(n_traj) for j in range(steps)], } ) obs.set_index("Cell_name", inplace=True) elif method == "differentiation": gene_num = 2 # Data Synthesis using Gillespie r = 15 tau = 0.7 b = 0.5 * r / tau c = 0.3 * r K = 35 * r n = 5 beta = 0.5 / tau gamma = 0.2 / tau eta = 0.5 / tau delta = 0.05 / tau a_ut = 1.0 * r / tau a_t = 0.5 * r / tau params_untreat_unlab = { "a1": a_ut, "b1": b, "c1": c, "a2": a_ut, "b2": b, "c2": c, "a1_l": 0, "b1_l": 0, "c1_l": 0, "a2_l": 0, "b2_l": 0, "c2_l": 0, "K": K, "n": n, "be1": beta, "ga1": gamma, "et1": eta, "de1": delta, "be2": beta, "ga2": gamma, "et2": eta, "de2": delta, } params_treat_unlab = { "a1": a_t, "b1": b, "c1": c, "a2": a_t, "b2": b, "c2": c, "a1_l": 0, "b1_l": 0, "c1_l": 0, "a2_l": 0, "b2_l": 0, "c2_l": 0, "K": K, "n": n, "be1": beta, "ga1": gamma, "et1": eta, "de1": delta, "be2": beta, "ga2": gamma, "et2": eta, "de2": delta, } params_treat_lab = { "a1": 0, "b1": 0, "c1": 0, "a2": 0, "b2": 0, "c2": 0, "a1_l": a_t, "b1_l": b, "c1_l": c, "a2_l": a_t, "b2_l": b, "c2_l": c, "K": K, "n": n, "be1": beta, "ga1": gamma, "et1": eta, "de1": delta, "be2": beta, "ga2": gamma, "et2": eta, "de2": delta, } model_untreat_unlab = sim_diff(*list(params_untreat_unlab.values())) model_treat_unlab = sim_diff(*list(params_treat_unlab.values())) model_treat_lab = sim_diff(*list(params_treat_lab.values())) # synthesize steady state before treatment n_cell = 50 c0 = np.array([40, 100, 40, 100, 0, 0, 0, 0, 1000, 1000]) # same as the os model after this line of code n_species = len(c0) trajs_T, trajs_C = simulate( model_untreat_unlab, C0=[c0] * n_cell, t_span=[0, 200], n_traj=n_cell, report=True, ) ( kin_5, kin_40, kin_200, kin_300, one_shot, deg_begin, deg_end, ) = osc_diff_dup(n_species, trajs_C, model_treat_lab, model_treat_unlab, n_cell) uu = np.vstack( ( kin_5[0], kin_40[0], kin_200[0], kin_300[0], one_shot[0], deg_begin[0], deg_end[0], ) ) su = np.vstack( ( kin_5[1], kin_40[1], kin_200[1], kin_300[1], one_shot[1], deg_begin[1], deg_end[1], ) ) ul = np.vstack( ( kin_5[2], kin_40[2], kin_200[2], kin_300[2], one_shot[2], deg_begin[2], deg_end[2], ) ) sl = np.vstack( ( kin_5[3], kin_40[3], kin_200[3], kin_300[3], one_shot[3], deg_begin[3], deg_end[3], ) ) E, New = uu + ul + su + sl, ul + sl P = np.vstack( ( kin_5[4], kin_40[4], kin_200[4], kin_300[4], one_shot[4], deg_begin[4], deg_end[4], ) ) # append to .obsm attribute layers = { "uu": scipy.sparse.csc_matrix((uu).astype(int)), "ul": scipy.sparse.csc_matrix((ul).astype(int)), "su": scipy.sparse.csc_matrix((su).astype(int)), "sl": scipy.sparse.csc_matrix((sl).astype(int)), } # ambiguous is required for velocyto layers_no_splicing = { "new": scipy.sparse.csc_matrix((New).astype(int)), "total": scipy.sparse.csc_matrix((E).astype(int)), } # ambiguous is required for velocyto kin_len, one_shot_len, begin_len, end_len = ( kin_5[0].shape[0], one_shot[0].shape[0], deg_begin[0].shape[0], deg_end[0].shape[0], ) kin_Tl, kin_T_CP, deg_label_t = ( [0, 0.1, 0.2, 0.4, 0.8], [0, 5, 10, 40, 100, 200, 300, 400], [0, 1, 2, 4, 8], ) # label time for kinetics experiment is 1 (actually it is one-shot experiment) kin_cell_ids, kin_Trajectory, kin_Step = ( ["kin_traj_%d_time_%f" % (i, j) for j in kin_Tl for i in range(n_cell)], [i for j in kin_Tl for i in range(n_cell)], [j for j in kin_Tl for i in range(n_cell)], ) one_shot_cell_ids, one_shot_Trajectory, one_shot_Step = ( ["one_shot_traj_%d_time_%d" % (i, j) for j in kin_T_CP for i in range(n_cell)], [i for j in kin_T_CP for i in range(n_cell)], [j for j in kin_T_CP for i in range(n_cell)], ) # first n_traj and then steps begin_cell_ids, begin_Trajectory, begin_Step = ( ["begin_deg_traj_%d_time_%d" % (i, j) for j in deg_label_t for i in range(n_cell)], [i for j in deg_label_t for i in range(n_cell)], [j for j in deg_label_t for i in range(n_cell)], ) # first n_traj and then steps end_cell_ids, end_Trajectory, end_Step = ( ["end_deg_traj_%d_time_%d" % (i, j) for j in deg_label_t for i in range(n_cell)], [i for j in deg_label_t for i in range(n_cell)], [j for j in deg_label_t for i in range(n_cell)], ) # first n_traj and then steps cell_ids, Trajectory, Step = ( kin_cell_ids * 4, kin_Trajectory * 4, kin_Step * 4, ) cell_ids.extend(one_shot_cell_ids) Trajectory.extend(one_shot_Trajectory) Step.extend(one_shot_Step) cell_ids.extend(begin_cell_ids) Trajectory.extend(begin_Trajectory) Step.extend(begin_Step) cell_ids.extend(end_cell_ids) Trajectory.extend(end_Trajectory) Step.extend(end_Step) obs = pd.DataFrame( { "cell_name": cell_ids, "trajectory": Trajectory, "time": Step, "experiment_type": pd.Series( [ "kin_t_5", "kin_t_40", "kin_t_200", "kin_t_300", "one_shot", "deg_beign", "deg_end", ] ) .repeat( [ kin_len, kin_len, kin_len, kin_len, one_shot_len, begin_len, end_len, ] ) .values, } ) obs.set_index("cell_name", inplace=True) elif method == "oscillation": gene_num = 2 # Data Synthesis using Gillespie r = 20 tau = 3 beta = 0.5 / tau gamma = 0.2 / tau eta = 0.5 / tau delta = 0.05 / tau zeta = eta * beta / (delta * gamma) a1 = 1.5 * r / tau b1 = 1 * r / tau a2 = 0.5 * r / tau b2 = 2.5 * r / tau K = 2.5 * r n = 10 params_unlab = { "a1": a1, "b1": b1, "a2": a2, "b2": b2, "a1_l": 0, "b1_l": 0, "a2_l": 0, "b2_l": 0, "K": K, "n": n, "be1": beta, "ga1": gamma, "et1": eta, "de1": delta, "be2": beta, "ga2": gamma, "et2": eta, "de2": delta, } params_lab = { "a1": 0, "b1": 0, "a2": 0, "b2": 0, "a1_l": a1, "b1_l": b1, "a2_l": a2, "b2_l": b2, "K": K, "n": n, "be1": beta, "ga1": gamma, "et1": eta, "de1": delta, "be2": beta, "ga2": gamma, "et2": eta, "de2": delta, } model_unlab = sim_osc(*list(params_unlab.values())) model_lab = sim_osc(*list(params_lab.values())) # synthesize steady state before treatment n_cell = 50 c0 = np.array( [ 70, 70 * beta / gamma, 70, 70 * beta / gamma, 0, 0, 0, 0, 70 * zeta, 70 * zeta, ] ) n_species = len(c0) trajs_T, trajs_C = simulate( model_unlab, C0=[c0] * n_cell, t_span=[0, 100], n_traj=n_cell, report=True, ) ( kin_5, kin_40, kin_200, kin_300, one_shot, deg_begin, deg_end, ) = osc_diff_dup(n_species, trajs_C, model_lab, model_unlab, n_cell) uu = np.vstack( ( kin_5[0], kin_40[0], kin_200[0], kin_300[0], one_shot[0], deg_begin[0], deg_end[0], ) ) su = np.vstack( ( kin_5[1], kin_40[1], kin_200[1], kin_300[1], one_shot[1], deg_begin[1], deg_end[1], ) ) ul = np.vstack( ( kin_5[2], kin_40[2], kin_200[2], kin_300[2], one_shot[2], deg_begin[2], deg_end[2], ) ) sl = np.vstack( ( kin_5[3], kin_40[3], kin_200[3], kin_300[3], one_shot[3], deg_begin[3], deg_end[3], ) ) E, New = uu + ul + su + sl, ul + sl P = np.vstack( ( kin_5[4], kin_40[4], kin_200[4], kin_300[4], one_shot[4], deg_begin[4], deg_end[4], ) ) # append to .obsm attribute layers = { "uu": scipy.sparse.csc_matrix((uu).astype(int)), "ul": scipy.sparse.csc_matrix((ul).astype(int)), "su": scipy.sparse.csc_matrix((su).astype(int)), "sl": scipy.sparse.csc_matrix((sl).astype(int)), } # ambiguous is required for velocyto layers_no_splicing = { "new": scipy.sparse.csc_matrix((New).astype(int)), "total": scipy.sparse.csc_matrix((E).astype(int)), } # ambiguous is required for velocyto kin_len, one_shot_len, begin_len, end_len = ( kin_5[0].shape[0], one_shot[0].shape[0], deg_begin[0].shape[0], deg_end[0].shape[0], ) kin_Tl, kin_T_CP, deg_label_t = ( [0, 0.1, 0.2, 0.4, 0.8], [0, 5, 10, 40, 100, 200, 300, 400], [0, 1, 2, 4, 8], ) # label time for kinetics experiment is 1 (actually it is one-shot experiment) kin_cell_ids, kin_Trajectory, kin_Step = ( ["kin_traj_%d_time_%f" % (i, j) for j in kin_Tl for i in range(n_cell)], [i for j in kin_Tl for i in range(n_cell)], [j for j in kin_Tl for i in range(n_cell)], ) one_shot_cell_ids, one_shot_Trajectory, one_shot_Step = ( ["one_shot_traj_%d_time_%d" % (i, j) for j in kin_T_CP for i in range(n_cell)], [i for j in kin_T_CP for i in range(n_cell)], [j for j in kin_T_CP for i in range(n_cell)], ) # first n_traj and then steps begin_cell_ids, begin_Trajectory, begin_Step = ( ["begin_deg_traj_%d_time_%d" % (i, j) for j in deg_label_t for i in range(n_cell)], [i for j in deg_label_t for i in range(n_cell)], [j for j in deg_label_t for i in range(n_cell)], ) # first n_traj and then steps end_cell_ids, end_Trajectory, end_Step = ( ["end_deg_traj_%d_time_%d" % (i, j) for j in deg_label_t for i in range(n_cell)], [i for j in deg_label_t for i in range(n_cell)], [j for j in deg_label_t for i in range(n_cell)], ) # first n_traj and then steps cell_ids, Trajectory, Step = ( kin_cell_ids * 4, kin_Trajectory * 4, kin_Step * 4, ) cell_ids.extend(one_shot_cell_ids) Trajectory.extend(one_shot_Trajectory) Step.extend(one_shot_Step) cell_ids.extend(begin_cell_ids) Trajectory.extend(begin_Trajectory) Step.extend(begin_Step) cell_ids.extend(end_cell_ids) Trajectory.extend(end_Trajectory) Step.extend(end_Step) obs = pd.DataFrame( { "cell_name": cell_ids, "trajectory": Trajectory, "time": Step, "experiment_type": pd.Series( [ "kin_t_5", "kin_t_40", "kin_t_200", "kin_t_300", "one_shot", "deg_beign", "deg_end", ] ) .repeat( [ kin_len, kin_len, kin_len, kin_len, one_shot_len, begin_len, end_len, ] ) .values, } ) obs.set_index("cell_name", inplace=True) else: raise Exception("method not implemented!") # anadata: observation x variable (cells x genes) if verbose: print("we have %s cell and %s genes." % (E.shape[0], E.shape[1])) var = pd.DataFrame( { "gene_short_name": ["gene_%d" % (i) for i in range(gene_num)], "true_beta": [beta, beta], "true_gamma": [gamma, gamma], "true_eta": [eta, eta], "true_delta": [delta, delta], } ) # use the real name in simulation? var.set_index("gene_short_name", inplace=True) adata = anndata.AnnData( scipy.sparse.csc_matrix(E.astype(int)).copy(), obs.copy(), var.copy(), layers=layers.copy(), ) adata_no_splicing = anndata.AnnData( scipy.sparse.csc_matrix(E.astype(int)).copy(), obs.copy(), var.copy(), layers=layers_no_splicing.copy(), ) if P is not None: adata.obsm["protein"] = P adata_no_splicing.obsm["protein"] = P # remove cells that has no expression adata = adata[np.array(adata.X.sum(1)).flatten() > 0, :] adata_no_splicing = adata_no_splicing[np.array(adata_no_splicing.X.sum(1)).flatten() > 0, :] return adata, adata_no_splicing