Drug-Combination Synergy Analysis
Decide whether a two-drug combination does more than expected (synergy), exactly as expected (additivity), or less (antagonism) — and pick the right reference model for the data you have.
"Synergy" only means something relative to a null model of additivity, and the models define additivity differently — so the first decision is which model, driven by what data you measured.
Step 0 — Pick the model by the data you have
| You measured… |
Use model |
Tool |
Input |
| Single effects of A, B, and A+B at one dose pair |
Bliss |
DrugSynergy_calculate_bliss |
effect_a, effect_b, effect_combination (each a fraction 0–1) |
| Effects of A, B, A+B across several dose points |
HSA |
DrugSynergy_calculate_hsa |
effects_a, effects_b, effects_combo (arrays) |
| Single-agent dose-response curves + one combination point |
Loewe |
DrugSynergy_calculate_loewe |
doses_a_single/effects_a_single, doses_b_single/effects_b_single, dose_a_combo, dose_b_combo, effect_combo |
| Single-agent dose-response + combo point, want Chou-Talalay CI |
Combination Index |
DrugSynergy_calculate_ci |
same as Loewe + assumption |
| A full dose × dose viability matrix |
ZIP |
DrugSynergy_calculate_zip |
doses_a, doses_b, viability_matrix (% , 0–100) |
Effects must be on a consistent inhibition scale. Bliss/HSA/Loewe expect fractional inhibition 0–1 (0 = no effect, 1 = complete kill). If your data is % viability, convert: inhibition = 1 − viability/100. ZIP takes the viability matrix in % directly. Mixing scales is the most common error.
Step 1 — What each model's "additivity" means
| Model |
Null (additive) expectation |
Best when |
| Bliss independence |
drugs act independently: E_exp = E_a + E_b − E_a·E_b |
different mechanisms; quick single-point screen |
| HSA (highest single agent) |
combo should beat the better single agent: E_exp = max(E_a, E_b) |
conservative "does it beat monotherapy?" question |
| Loewe additivity |
a drug combined with itself = additive (dose equivalence) |
same/similar mechanism; needs dose-response |
| ZIP |
combines Bliss + Loewe; potency shift of one drug's curve by the other |
dose-matrix screens (the SynergyFinder default) |
| Chou-Talalay CI |
CI<1 synergy, =1 additive, >1 antagonism (median-effect) |
classic isobologram-style analysis with dose-response |
There is no single "correct" model — state which one you used. Bliss and Loewe genuinely disagree for some combinations (that's expected, not an error); reporting two models (e.g. Bliss + HSA, or Loewe + ZIP) is good practice.
Step 2 — Run it
# Bliss (single dose pair, fractional inhibition)
tu run DrugSynergy_calculate_bliss '{"operation":"calculate_bliss",
"effect_a":0.4,"effect_b":0.3,"effect_combination":0.7}'
# -> expected 0.58, bliss_synergy_score 0.12, "Strong synergy"
scripts/synergy_reference.py computes the Bliss, HSA, and Loewe-style expected combination effects side-by-side from one dose pair, so you can see at a glance whether the models agree before running the full tools.
Step 3 — Interpret the score
For Bliss/HSA/Loewe/ZIP, the synergy score is (observed − expected) (often ×100):
| Score (fractional, ×100 scale) |
Call |
| > +10 |
synergy |
| −10 to +10 |
additive (no meaningful interaction) |
| < −10 |
antagonism |
For Combination Index (Chou-Talalay): **CI < 1 = synergy**, CI = 1 additive, CI > 1 antagonism (note the opposite direction — lower is more synergistic).
- A positive Bliss/HSA score means the combination exceeds the additive expectation at that point.
- Synergy is often dose-dependent — a combination can be synergistic at one ratio and antagonistic at another; for a matrix, report the synergistic region, not one number.
Step 4 — Gotchas (state these)
- Scale mismatch (% viability vs fractional inhibition) — convert first (Step 0).
- Effects near 0 or 1 (ceiling). If both single agents already kill ~everything, the combo can't show synergy (no headroom) — Bliss/HSA saturate; interpret with care.
- ZIP/Loewe/CI need real dose-response with ≥3 non-zero, measurable-effect dose points per drug, or the Hill fit fails (the tools say so).
- Model disagreement is normal — don't shop for the model that gives "synergy"; pre-specify the model and report it.
- A synergy score is not efficacy — a strongly synergistic combination can still be weak overall; report the absolute combination effect too.
Honest limitations
- These are reference-model synergy scores, not statistical tests — for confidence, replicate and report variability across the dose matrix.
- Synergy in vitro does not guarantee clinical benefit (PK/PD, toxicity, scheduling all matter).
Related skills
tooluniverse-dose-response — fit the single-agent IC50/EC50 curves that Loewe/CI/ZIP need.tooluniverse-cell-line-profiling — look up pre-computed combination synergy (SYNERGxDB).tooluniverse-drug-repurposing / tooluniverse-network-pharmacology — rationale for combinations.
1---2name: tooluniverse-drug-synergy3description: Drug-combination synergy analysis — quantify whether two drugs together are synergistic, additive, or antagonistic using the standard reference models (Bliss independence, HSA / highest single agent, Loewe additivity, ZIP, and the Chou-Talalay Combination Index). Use when you have measured single-drug and combination effects (inhibition/viability) and need a synergy score. Explains which model to use, what data each one needs, and how to read the score. NOT for looking up pre-computed synergy in a database (use the SYNERGxDB tool / cell-line-profiling skill).4---5
6# Drug-Combination Synergy Analysis
7
8Decide whether a two-drug combination does **more than expected** (synergy), exactly as expected (additivity), or **less** (antagonism) — and pick the right reference model for the data you have.
9
10"Synergy" only means something relative to a **null model of additivity**, and the models define additivity differently — so the first decision is *which model*, driven by *what data you measured*.
11
12## Step 0 — Pick the model by the data you have
13
14| You measured… | Use model | Tool | Input |
15|---|---|---|---|
16| Single effects of A, B, and A+B at **one** dose pair | **Bliss** | `DrugSynergy_calculate_bliss` | `effect_a`, `effect_b`, `effect_combination` (each a fraction 0–1) |
17| Effects of A, B, A+B across **several** dose points | **HSA** | `DrugSynergy_calculate_hsa` | `effects_a`, `effects_b`, `effects_combo` (arrays) |
18| Single-agent **dose-response curves** + one combination point | **Loewe** | `DrugSynergy_calculate_loewe` | `doses_a_single`/`effects_a_single`, `doses_b_single`/`effects_b_single`, `dose_a_combo`, `dose_b_combo`, `effect_combo` |
19| Single-agent dose-response + combo point, want Chou-Talalay CI | **Combination Index** | `DrugSynergy_calculate_ci` | same as Loewe + `assumption` |
20| A full **dose × dose viability matrix** | **ZIP** | `DrugSynergy_calculate_zip` | `doses_a`, `doses_b`, `viability_matrix` (% , 0–100) |
21
22> **Effects must be on a consistent inhibition scale.** Bliss/HSA/Loewe expect *fractional inhibition* `0–1` (0 = no effect, 1 = complete kill). If your data is % viability, convert: `inhibition = 1 − viability/100`. ZIP takes the viability matrix in % directly. Mixing scales is the most common error.
23
24## Step 1 — What each model's "additivity" means
25
26| Model | Null (additive) expectation | Best when |
27|---|---|---|
28| **Bliss independence** | drugs act independently: `E_exp = E_a + E_b − E_a·E_b` | different mechanisms; quick single-point screen |
29| **HSA (highest single agent)** | combo should beat the *better* single agent: `E_exp = max(E_a, E_b)` | conservative "does it beat monotherapy?" question |
30| **Loewe additivity** | a drug combined with itself = additive (dose equivalence) | same/similar mechanism; needs dose-response |
31| **ZIP** | combines Bliss + Loewe; potency shift of one drug's curve by the other | dose-matrix screens (the SynergyFinder default) |
32| **Chou-Talalay CI** | CI<1 synergy, =1 additive, >1 antagonism (median-effect) | classic isobologram-style analysis with dose-response |
33
34There is no single "correct" model — **state which one you used.** Bliss and Loewe genuinely disagree for some combinations (that's expected, not an error); reporting two models (e.g. Bliss + HSA, or Loewe + ZIP) is good practice.
35
36## Step 2 — Run it
37
38```bash
39# Bliss (single dose pair, fractional inhibition)
40tu run DrugSynergy_calculate_bliss '{"operation":"calculate_bliss",
41 "effect_a":0.4,"effect_b":0.3,"effect_combination":0.7}'
42# -> expected 0.58, bliss_synergy_score 0.12, "Strong synergy"
43```
44
45`scripts/synergy_reference.py` computes the Bliss, HSA, and Loewe-style expected combination effects side-by-side from one dose pair, so you can see at a glance whether the models agree before running the full tools.
46
47## Step 3 — Interpret the score
48
49For Bliss/HSA/Loewe/ZIP, the synergy score is `(observed − expected)` (often ×100):
50
51| Score (fractional, ×100 scale) | Call |
52|---|---|
53| > +10 | synergy |
54| −10 to +10 | additive (no meaningful interaction) |
55| < −10 | antagonism |
56
57For **Combination Index (Chou-Talalay)**: **CI < 1 = synergy**, CI = 1 additive, CI > 1 antagonism (note the opposite direction — lower is more synergistic).
58
59- A positive Bliss/HSA score means the combination exceeds the additive expectation at that point.
60- Synergy is often **dose-dependent** — a combination can be synergistic at one ratio and antagonistic at another; for a matrix, report the synergistic *region*, not one number.
61
62## Step 4 — Gotchas (state these)
63
64- **Scale mismatch** (% viability vs fractional inhibition) — convert first (Step 0).
65- **Effects near 0 or 1 (ceiling).** If both single agents already kill ~everything, the combo can't show synergy (no headroom) — Bliss/HSA saturate; interpret with care.
66- **ZIP/Loewe/CI need real dose-response** with ≥3 non-zero, measurable-effect dose points per drug, or the Hill fit fails (the tools say so).
67- **Model disagreement is normal** — don't shop for the model that gives "synergy"; pre-specify the model and report it.
68- **A synergy score is not efficacy** — a strongly synergistic combination can still be weak overall; report the absolute combination effect too.
69
70## Honest limitations
71
72- These are *reference-model* synergy scores, not statistical tests — for confidence, replicate and report variability across the dose matrix.
73- Synergy in vitro does not guarantee clinical benefit (PK/PD, toxicity, scheduling all matter).
74
75## Related skills
76- `tooluniverse-dose-response` — fit the single-agent IC50/EC50 curves that Loewe/CI/ZIP need.
77- `tooluniverse-cell-line-profiling` — look up *pre-computed* combination synergy (SYNERGxDB).
78- `tooluniverse-drug-repurposing` / `tooluniverse-network-pharmacology` — rationale for combinations.
mims-harvard