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

bash
# 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.