Ion current through a membrane is like a queue at a turnstile. Sometimes the turnstile is free — ions pass through quickly. Sometimes it gets stuck — the flow drops. A weak magnetic field, it turns out, doesn't push ions from behind; it simply changes the number of open turnstiles.
The authors built an equilibrium model where a transport channel can exist in several states — some conduct current, others don't. The magnetic field redistributes the probabilities of these states. If the field increases the fraction of conducting states, the current through the ion channel increases. If it decreases, the current drops. Thus, both enhancement and suppression fit into a single picture.
The theory predicts a characteristic dependence on the field and sensitivity to the type of state. This provides a tool for quantitative testing: you can measure how the current changes when a weak magnet is switched on and compare it with the calculation. This is important for understanding how living cells respond to magnetic fields — from the geomagnetic background to medical procedures.
Weak magnetic fields are comparable to the field of an ordinary fridge magnet, about 1 millitesla, and they can indeed influence ion transport in cells.