DropletMVP
Poisson single-cell loading
Probability that a droplet contains 0, exactly 1, or 2+ cells during encapsulation.
Inputs
Result
Enter λ and calculate to see the occupancy distribution.
Interpretation
Single-cell platforms run at low λ so that among occupied droplets, very few contain two or more cells. The cost is that most droplets end up empty.
Formula
P(k) = λᵏ · e^(−λ) / k!
λ is the mean number of cells per droplet.
Variables
| Symbol | Variable | Unit |
|---|---|---|
| P(k) | Probability of k cells in a droplet | — |
| λ | Mean cells per droplet | — |
| k | Number of cells | — |
Assumptions & validity
This tool assumes:
- Cells are independent and randomly (uniformly) distributed — Poisson statistics.
- λ is the mean cells per droplet (= concentration × droplet volume).
- No cell–cell interactions, settling, or clumping.
- Achieving mostly single-cell occupancy requires low λ, so most droplets are empty.
Worked example
At λ = 0.1 cells per droplet:
P(0) = e⁻⁰·¹ ≈ 90.5% · P(1) = 0.1·e⁻⁰·¹ ≈ 9.0% · P(2+) ≈ 0.5%
Doublets are ~0.5% — but ~90% of droplets are wasted as empties.