Bliss

Description

The Bliss model requires that the drug effect measured is a probability or fraction between 0 and 1. It works by multiplying the probabilities obtained by each drug alone, and expecting

\[E_{bliss}(d_1, d_2) = E_1(d_1) \cdot E_2(d_2)\]

Bliss synergy is quantified at each tested dose as the difference

\[synergy(d_1, d_2) := E_{bliss}(d_1, d_2) - E(d_1, d_2)\]

The values of Bliss synergy are interpreted as

Value	Interpretation
\[> 0\]	Synergistic
\[< 0\]	Antagonistic
\[= 0\]	Additive

Assumptions

• All dose response data is within the range [0, 1]

  • Properly, the data should measure a probability, such as a probablility of a cell remaining alive after treatment

• The response should be oriented so that each single drug \(i\) has \(E_i(0) = 1\)

Defaults

• Single-drug models:

  • Default: synergy.single.log_linear.LogLinear

  • Required: synergy.single.DoseResponse1D or subclass

2D

Load and plot example dataset

2D synergy models work with 1D arrays of drug 1 dose, drug 2 dose, and effect.

from synergy import datasets
from synergy.utils.plots import plot_heatmap, plot_surface_plotly, set_plotly_interactive

set_plotly_interactive()  # This should only be run in an interactive notebook setting - for other scripts skip this

d1, d2, E = datasets.load_2d_example()

Plot raw dose response data as a heatmap using synergy.utils.plots.plot_heatmap()

# plot_heatmap(d1, d2, E, title="Response Data", cmap="YlGnBu")

Plot raw dose response data as a 3D surface with synergy.utils.plots.plot_surface_plotly()

# scatter_points can be used to add a 3d scatter plot over the surface
# plotly's Scatter3D does not appear to work in Jupyter notebooks, but will work if you save the plot to file, e.g., with fname="plot.html"
# scatter_points can be a dict, or a pandas.DataFrame, as long as scatter_points["drug1.conc"], etc return the appropriate arrays.
scatter_points = {
    "drug1.conc": d1,
    "drug2.conc": d2,
    "effect": E
}
plot_surface_plotly(
    d1, d2, E, title="Response Data", cmap="YlGnBu", scatter_points=scatter_points,
    zlabel="Effect"
)  #  fname="plot.html")

Calculate synergy using the Bliss model

from synergy.combination.bliss import Bliss

model = Bliss()
synergy = model.fit(d1, d2, E)
plot_heatmap(d1, d2, synergy, cmap="PRGn", title="Bliss Synergy", center_on_zero=True)
# plot_surface_plotly(d1, d2, synergy, cmap="PRGn", title="Bliss Synergy", center_on_zero=True)

N-drug Combinations

The Bliss model generalizes to \(N\)-drugs by defining \(E_{bliss}\) as

\[E_{bliss}(\vec{d}) = \prod_{i=1}^{N}E_{i}(d_{i})\]

Synergy is defined and interpreted identically as in the 2D case.

from synergy.higher.bliss import Bliss
from synergy.utils.plots import plotly_isosurfaces
from synergy import datasets

d, E = datasets.load_3d_example()
model = Bliss()
synergy = model.fit(d, E)

plotly_isosurfaces(d, E, title="3D Response Data", cmap="YlGnBu")  # or add fname= to save to file
plotly_isosurfaces(d, synergy, title="3D Bliss Synergy", cmap="PRGn", center_on_zero=True)

References

Bliss, Chester I. “The toxicity of poisons applied jointly 1.” Annals of applied biology 26.3 (1939): 585-615.