SCIENCE · INVESTIGATE AND EXPLAIN

Distinguish a maintained compartment gradient from equilibrium

A compartment can maintain a stable composition while material continuously enters and leaves. This steady state differs from equilibrium: an energy-coupled pump can oppose a leak so that net accumulation is zero even though each one-way flux is nonzero. A constant pH reading therefore does not prove that transport has stopped.

Learning outcome: Hold pump4 and compare additional leak1 and3. Verify that outward leak equals the supplied inward pump in both states, while pH differences differ. Explain why balanced fluxes do not imply thermodynamic equilibrium.

Starting recap

Connect calibrated dimensions, cell organization, material balance and membrane energetics. State the model boundary before interpreting a changed condition.

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Try

Pump4 and total leak coefficient2 giveΔpH=2, compartmentpH5 and a100-fold hydrogen-ion ratio relative to cytosolpH7. Increasing total leak coefficient to4 at the same pump givesΔpH1, compartmentpH6 and a10-fold ratio. Both states can have nonzero opposing fluxes.

Open the experiment

Predict

Can increasing leak change the steady gradient even if the pump continues at the same rate?

Your prediction and reason

Experiment

Hold pump4 and compare additional leak1 and3. Verify that outward leak equals the supplied inward pump in both states, while pH differences differ. Explain why balanced fluxes do not imply thermodynamic equilibrium.

Balance a compartment pump against a leak

Worked teaching model · synthetic values · Phenomenological steady-state acidification: pump=b; outward leak=(1+a)ΔpH, so ΔpH=b/(1+a), cytosolpH7. Constant effective buffering and pump flux are stipulated, not a mechanistic proton-current law. No membrane voltage, ATP budget or time course is inferred.

Additional leak coefficient: 1 relative units Fixed inward pump flux: 4 relative units

Reset keeps your prediction, captures and practice history.

A steady gradient can require continuous opposing fluxes; a steady state is not equilibrium.

Pump and leak magnitudes balance while a nonzero gradient remains. Increasing leak lowers the gradient at fixed pump. The linear leak-versus-ΔpH relation is phenomenological; it is not a physical proton conductance law or a derived ATP stoichiometry.

Calculated quantities under stated assumptions
Quantity	Value	Unit
Steady-state pH difference	2	pH units
Compartment pH	5	pH
Compartment/cytosol hydrogen-ion ratio	100	ratio
Outward leak at steady state	4	relative flux units
Supplied inward pump	4	relative flux units

Retain prior predictions, settings and quantities in the notebook. These are original supplied/calculated comparisons, not physical specimen observations or laboratory participation.

A steady gradient can require continuous opposing fluxes; a steady state is not equilibrium.

Observation to attach to a capture

Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.

Understand

1. Orient: Distinguish a maintained compartment gradient from equilibrium

2. Explain the mechanism and boundary

The supplied phenomenological model sets inward pump flux toP and outward leak toLΔpH, whereL=1 plus the chosen additional leak. At steady stateP=LΔpH, soΔpH=P/L. CytosolicpH is fixed at7 and compartmentpH is7−ΔpH. This is a deliberately simplified relationship between pH difference and effective leak, not a molecular proton-current law.

Because pH is logarithmic, a two-unit pH difference corresponds to a100-fold hydrogen-ion concentration ratio. That concentration ratio is not itself a flux or a total proton inventory; buffering can store substantial proton equivalents in bound forms. Distinguish a measured free-ion state from the amount of energy and material required to maintain it.

In cells, membrane identity, trafficking and transporter placement help sustain different compartment conditions. The ER lumen, Golgi and vesicle interiors preserve topological relationships during membrane traffic, while mitochondria and chloroplasts are not simply interchangeable endomembrane compartments. The present leak model does not encode those identities, membrane voltage, ATP stoichiometry or time-dependent buffering.

3. Work a quantitative example

4. Predict and investigate

Predict first: Can increasing leak change the steady gradient even if the pump continues at the same rate?

Retain your initial prediction, control settings and all relevant displayed evidence in the lesson notebook. The schematic and calculated records are original synthetic teaching material, not measurements of a physical specimen.

5. Transfer and explain

Apply the mechanism to a changed case

In the same phenomenological model, pump3 and total leak coefficient1.5 maintain a compartment against cytosolicpH7. FindΔpH, compartmentpH and hydrogen-ion ratio.

Retain your calculation, units and assumptions in the lesson notebook before opening this public practice response.

Compare a worked response

ΔpH=3/1.5=2, compartmentpH5 and hydrogen-ion ratio10²=100. Opposing fluxes both equal3relative units; the state is maintained, not equilibrium. The result assumes the stipulated linear effective leak relation.

6. Reflect and retain evidence

Explain the link from cellular structure or membrane process to the modeled observation. State a competing explanation, an omitted variable and one independent comparison that could challenge your conclusion. Do not turn a simulated observation into a claim of laboratory participation or independently demonstrated practical skill.

Scientific sources and continuation

Supporting scientific reference, checked30October2026. Original prose, controls, datasets and diagrams; no source figure or exercise is reproduced. Return to General Biology I for the course-specific mixed responses, retained project evidence and remaining module status.

Apply

Public practice checks a specific claim. It does not establish independent mastery.

In the same phenomenological model, pump3 and total leak coefficient1.5 maintain a compartment against cytosolicpH7. FindΔpH, compartmentpH and hydrogen-ion ratio.

Your explanation and limitations

Continue

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