Estimate when oxygen, nutrients, or pH first reach a configured limit in the evaluated droplet.
Rate evidence pendingSelect a cell line to view the evidence basis and recommended planning margin.DetailsSelect a cell line to view the evidence basis and recommended planning margin.
SettingsConfigure the evaluated droplet
Biology and droplet target
Define the productive droplet being evaluated and the nutrient environment inside it.
Use custom rates when OCR/GCR measurements are available for the exact passage and condition.
Medium composition sets glucose, glutamine, bicarbonate, lactate baseline, and buffer capacity.
Log-mapped from 70 pL to 7 nL for fine control at picoliter-to-nanoliter scale.
This is the droplet whose first-limit time is reported. Bulk demand uses occupancy classes, so empty droplets remain empty.
Proxy and literature defaults remain available for planning only.
Emulsion population and gas reservoirs
Oxygen is shared through droplets, continuous oil, residual oil, and gas phase. Empty droplets add aqueous oxygen capacity but no cellular demand.
Mean cells per droplet across the emulsion. Determines total bulk cellular oxygen demand and empty-droplet fraction.
Aqueous droplets plus continuous carrier oil generated by emulsification. The aqueous fraction below applies to this generated emulsion volume.
Additional carrier oil outside the generated droplet emulsion: overlayer, loop volume, tubing, or reservoir. Total liquid fill = generated emulsion + excess reservoir oil.
Capacity ratio controls the oil oxygen reservoir relative to aqueous medium at the same pO₂. Embedded oil CO₂ capacity is disabled because no CO₂-specific record meets the provenance requirements.
Unvalidated planning assumption — user supplied. Leave blank or 0 to disable oil-phase CO₂ storage.
Presets set gas-to-oil, reservoir-to-emulsion, and oil-to-droplet exchange half-times.
Sets the cross-section or wall area used for gas exchange and auto-calculates closed-headspace volume from liquid fill.
For tubes this is liquid cross-section diameter; for PTFE tubing it is the tubing inner diameter.
Used only for the 600 µm PTFE tubing format. Tubing capacity is πr²L.
Auto mode makes absolute volume matter through surface-area-to-volume, reservoir depth, and finite headspace. Ideal mode preserves the scale-invariant concentration model for comparison.
Independent of the selected boundary gas. 100% means equilibrium with humidified air at the selected temperature.
Water-equivalent oil oxygen relative to humidified air equilibrium. Lower this for degassed oil, higher for preoxygenated oil.
Independent starting state for excess or loop oil. Closed-headspace runs often depend strongly on this value.
This selector changes interpretation and warnings only. The default pH layer uses carbonate/alkalinity chemistry with linear non-bicarbonate buffering, not a full explicit-medium charge-balance solver.
Use reference mode when entered half-times should be geometry-scaled. Use effective measured mode to apply your entered gas, oil, and droplet half-times directly with no automatic geometry rescaling.
Exchange kinetics
Use presets for planning, or set measured exchange half-times after sensor calibration.
In effective measured mode this exact value is used with no vessel geometry rescaling.
In effective measured mode this exact value is used with no vessel geometry rescaling.
Reference mode treats this as a 1 nL reference half-time. Effective measured mode uses it directly for the current droplet size.
Unvalidated planning assumption — user supplied. Required only when oil CO₂ capacity is enabled.
Unvalidated planning assumption — user supplied. No O₂ half-time is reused.
Unvalidated planning assumption — user supplied. No universal O₂-to-CO₂ factor is applied.
Unvalidated planning assumption — user supplied. Used only when oil-phase CO₂ is disabled and a gas CO₂ boundary is active.
Surface exposure of emulsion oil to headspace, in addition to residual oil exchange.
Static packed emulsions can be oxygen-limited in the center; mixing or thin layers move this toward 1.
Scales oil-to-target-droplet exchange only.
Auto mode compares oil-mediated exchange against local occupied-droplet depletion and switches to grouped transport when depletion competes with equilibration.
Atmosphere, temperature, and viability limits
Define gas composition, finite or replenished headspace, and endpoint thresholds.
Q₁₀ correction is applied to OCR, GCR, lactate production, and glutamine consumption.
Sets the replenished gas boundary at exposed surfaces. Initial liquid and closed-headspace states are entered separately below.
Balance gas is calculated as 100 − O₂ − CO₂; mixtures above 100% are blocked.
Closed mode tracks finite headspace O₂ and CO₂ moles from the initial headspace values below.
Set container geometry in Emulsion & Gas. This read-only summary keeps gas and vessel assumptions synchronized.
In standard vessels this is auto-calculated from vessel capacity minus emulsion and reservoir oil. Select custom geometry to enter it manually. Zero represents a filled closed vessel with no gas compartment.
Independent closed-headspace starting O₂. Use this to represent oxygenated liquid sealed under nitrogen or other nonequilibrium transfers.
Independent closed-headspace starting CO₂. This matters only when finite-headspace carbon balance is enabled.
Closed vessels always use finite headspace CO₂ mass balance; external-reservoir options apply only to replenished gas boundaries.
Carbonate mode solves DIC, bicarbonate, carbonate, water, and linear non-bicarbonate buffer alkalinity. Legacy mode keeps the older Henderson-Hasselbalch approximation for backward comparison.
Choose whether the viability endpoint is tied to the boundary gas, air saturation, or an absolute measured threshold.
Meaning depends on the threshold mode above.
Metabolic modifiers and growth
Adjust rates, supplements, inhibitors, proliferation, and output precision.
Cell number grows after the lag phase using logistic growth when enabled.
Stress-limited mode suppresses growth as local O₂, glucose, glutamine, or pH deteriorate. Legacy mode keeps the older purely logistic comparison behavior.
Upper density for proliferation; prevents impossible exponential growth inside nanoliter droplets.
Michaelis-Menten oxygen sensitivity for respiratory uptake near low O₂.
Below this O₂, glycolysis and lactate production rise gradually.
Use the measured-rate mode unless you explicitly intend to extrapolate a rate measured at another temperature.
Temperature at which the entered/default rates were measured.
Applied once to OCR, GCR, LPR, and glutamine consumption when Q₁₀ mode is selected.
Target-droplet glucose endpoint threshold.
Target-droplet glutamine endpoint threshold.
Experiment additives
Selections are recorded for context only. No universal additive, serum, or Warburg multiplier is applied without condition-matched measurements. Q₁₀ correction is applied only when explicitly selected above.
Gas-exchange diagnostics
Inspect compartment capacities, exchange balance, and limiting assumptions.
Run a calculation to update flux balance.
Rate scenarios
Deterministic low-demand, nominal, and high-demand runs from stored metabolic-rate bounds.
Scenario
First configured threshold crossing
Limiter
Final O₂
Final pH
Run a calculation to populate deterministic rate scenarios.
Sensitivity sweep
First configured threshold-crossing change across droplet volume and λ, with the current reservoir settings.
Volume
λ
Target cells
First configured threshold crossing
Limiter
Run a sweep to populate this table.
Calibration
Fit measured O₂ time series to transport half-times for the current physical setup.
Select the state matched to the uploaded or pasted measurements.
Two-parameter fits report likelihood-weighted local correlation and identifiability warnings.
Paste CSV or whitespace-separated pairs. First column is time in hours, second is observed O₂ in µM.
Paste a measured O₂ series and run calibration to fit transport half-times for the current setup.
Time
Observed O₂
Predicted O₂
Residual
Run calibration to populate residuals.
Detailed time series and export data
Raw time-series values are available for inspection and export after a current calculation.
Time
Target O₂
Bulk O₂
Emulsion oil O₂
Reservoir oil O₂
CO₂
Glc
Gln
pH
Cells
Status
Run a calculation to populate this table.
Embedded data and references
Review the built-in values and replace them with measured inputs when available.
Use as a forecaster, not a substitute for measurement. Metabolic rates vary by passage, density, serum lot, stimulation state, oxygen history, and instrument normalization. For critical experiments, replace defaults with measured OCR/GCR/LPR values and calibrate oxygen exchange using a sensor.
Category
Entity
References / notes
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How to use this forecaster
Describe the experiment. Choose the cell line and medium, then enter the productive-droplet volume and cells in that droplet.
Describe the physical setup. Set emulsion volume, aqueous fraction, oil reservoir, vessel, and whether gas is replenished or sealed.
Calculate and read the first limit. The main result is the first configured viability endpoint; the four endpoint values explain why it occurred.
Plan with deterministic cases. Compare high-demand, nominal, and low-demand cases. They are scenario cases, not a confidence interval.
Act on cautions. Only current setup cautions appear with the result. Open Model Scope and Diagnostics for assumptions, transport details, and raw time series.
Model structure. Oxygen is integrated as coupled compartments: evaluated droplet, bulk droplet population, emulsion oil, residual oil, and gas phase. Glucose and glutamine are evaluated inside the productive droplet. pH can use a carbonate/alkalinity solver with DIC, bicarbonate, carbonate, water, and linear non-bicarbonate buffer alkalinity, or the legacy Henderson-Hasselbalch approximation for backward comparison.
Equations and calculation model
Concentration units. Oxygen is represented in aqueous-equivalent μM. For a droplet volume in nL, 1 μM corresponds to 1 fmol/nL. Glucose, glutamine, lactate, bicarbonate, and CO₂ are tracked in mM; 1 fmol/nL equals 0.001 mM.
Droplet geometry and population
The droplet volume slider is logarithmic.
V_nL = 0.07 × 10^(2t), 0 ≤ t ≤ 1 V_μm³ = V_nL × 10⁶ r = (3V / 4π)^(1/3) A = 4πr²
The emulsion population is calculated from total emulsion volume and aqueous fraction. Bulk growth uses Poisson occupancy classes so empty droplets stay empty.
Carrier oil is represented as an oxygen reservoir in water-equivalent concentration units. This preserves Henry-law concentration gradients while allowing fluorinated oil to hold much more oxygen than water.
Geometry-corrected mode scales half-times by vessel area, emulsion depth, residual oil depth, storage mode, and exposed surface. Ideal mode is retained only as a comparison.
Metabolic rate inputs
Default and user-entered rates are used directly as condition-matched values in fmol/cell/min. The model applies no universal temperature, serum, additive, Warburg, or inhibitor multiplier. Temperature still affects gas solubility and carbonate chemistry.
Below the Pasteur threshold, glycolysis and lactate production increase smoothly up to the selected maximum multiplier.
Substrate and pH integration
Carbonate / alkalinity pH mode. The default pH layer treats aqueous tracked carbon as dissolved inorganic carbon (DIC) and solves carbonate speciation from total alkalinity, water dissociation, and linear non-bicarbonate buffer capacity.
Consumption and production are integrated with adaptive sub-steps to avoid unstable fast-exchange updates. For bicarbonate-buffered media, the initial dissolved CO₂ is inferred from starting pH and bicarbonate. The pH boundary mode then chooses whether the boundary is held at starting pH, driven by selected-gas CO₂, or governed by finite closed-headspace CO₂ mass balance.
When proliferation is enabled, target-cell number follows logistic growth with the configured carrying capacity.
K = carrying_capacity_cells_per_nL × V_droplet,nL n(t) = K n₀ exp(rt) / (K + n₀(exp(rt) − 1)) r = ln(2) / doubling_time
First configured threshold crossing. The displayed time is the first crossing of target-droplet oxygen threshold, glucose minimum, glutamine minimum, pH floor, or pH ceiling. It is not a survival or function endpoint unless prospectively linked to one. If no crossing occurs within the configured horizon, the result is displayed as ≥ horizon.