Checkerboard Assay

Pairwise reagent-synergy assays commonly use a "checkerboard" layout: the concentration of reagent A decreases linearly along each row of a microplate, and the concentration of reagent B decreases linearly along each column. Together the two gradients form a grid of unique A/B combinations — 64 of them on an 8x8 plate.

This layout is also a nice test of Pourfecto's scheduling: an eight-channel pipette can dispense reagent A across an entire row in one motion (pipette oriented horizontally) and reagent B across an entire column in one motion (pipette oriented vertically). The optimal schedule needs only 16 active dispense operations — one per row for A, one per column for B. A single-channel pipette, by contrast, would need 2 * 64 = 128 operations, since it can only reach one well at a time. A 96-channel pipette can't be used at all here, since it dispenses to every well simultaneously and can't vary volume independently by row or column.

This example builds the experiment in Pourfecto, lets it choose from a set of available pipetting configurations, and checks whether it converges on the 16-operation eight-channel solution.

using Pourfecto, CHESSCore, Unitful

Defining reagents and source labware

Reagents are created from names with string_to_component. This example needs two solid reagents (A and B) and water to dissolve them.

A = string_to_component("A", Solid)
B = string_to_component("B", Solid)
water = string_to_component("water", Liquid)

Each reagent's stock solution lives in its own deep reservoir.

A_reservoir = build_location(location_kinds[:DeepReservoir])
B_reservoir = build_location(location_kinds[:DeepReservoir])
target_plate = build_location(location_kinds[:WP96])

A_stock = 100u"g" * A + 100u"mL" * water
B_stock = 100u"g" * B + 100u"mL" * water

children(A_reservoir)[1].stock = A_stock
children(B_reservoir)[1].stock = B_stock

Filling the target plate

This fills the 8x8 block of the 96-well target plate so that the volume of A_stock decreases by 10 µL per row and the volume of B_stock decreases by 10 µL per column, starting from 80 µL of each.

drug_vol = 80
for row in 1:8
    for col in 1:8
        children(target_plate)[row, col].stock =
            (drug_vol - 10 * (row - 1))u"µL" * A_stock +
            (drug_vol - 10 * (col - 1))u"µL" * B_stock
    end
end

A heatmap of the target plate shows the checkerboard pattern just created — the combined A/B volume is highest in the top-left corner and decreases toward the bottom-right.

plot(target_plate; well_heatmap=true)

Planning and scheduling

Pourfecto is given four candidate configurations to choose from: a single-channel pipette, an eight-channel pipette (both orientations), and a plate-filling PlateMaster. The algorithm runs twice — once with the default "min_cost_flow" objective, and once asking Pourfecto to minimize the number of active flow operations directly.

configs = ["single_channel", "eight_channel_vertical", "eight_channel_horizontal", "plate_master"]

pc_default = pourfecto([A_reservoir, B_reservoir], [target_plate], configs)

pc_min_active = pourfecto(
    [A_reservoir, B_reservoir], [target_plate], configs;
    objective="min_active_flow",
)

Comparing the two schedules

Both objectives should transfer the same total volume of liquid — they're solving the same planning problem, just scheduling it differently.

total_flow_default = sum(flows(pc_default))
total_flow_min_active = sum(flows(pc_min_active))

An "active" flow is any scheduled operation that actually moves liquid (as opposed to a zero-volume slot in the flow matrix).

active_default = sum(flows(pc_default) .> 1e-4)
active_min_active = sum(flows(pc_min_active) .> 1e-4)

min_active_flow collapses the schedule toward the eight-channel strategy described above, using far fewer discrete operations to deliver the same total volume:

(total_flow_default=total_flow_default, total_flow_min_active=total_flow_min_active,
    active_default=active_default, active_min_active=active_min_active)

With this configuration set, the minimum-active-flow schedule reaches the theoretical optimum of 16 operations (one eight-channel dispense per row for A, one per column for B).

Checking the plan against the targets

planned_stocks reconstructs the stock composition Pourfecto actually planned to deliver to each target well. Comparing it against target_stocks confirms the plan reproduces the requested checkerboard pattern.

planned = planned_stocks(pc_min_active)
requested = target_stocks(pc_min_active)

all(isapprox.(planned, requested; rtol=1e-3))

Finally, plot_flows visualizes the scheduled transfers between source and target labware for the minimum-active-flow plan.

plot_flows(pc_min_active)

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