If the extracellular potassium concentration surrounding a myocyte increases, then the potassium gradient accross the cell membrane decreases, and therefore the resting membrane potential will become more positive. Similarly, if extracellular potassium decreases, the resting membrane potential will be more negative.
With this in mind, how does the heart rate change when extracellular potassium concentration increases/decreases?
Pathological potassium concentration promotes arrhythmia.
Increased extracellular potassium inactivates $Na^+$ channels and opens $K^+$ channels, causing the cells to become refractory [1]:
Increased extracellular potassium levels result in depolarization of the membrane potentials of cells due to the increase in the equilibrium potential of potassium. This depolarization opens some voltage-gated sodium channels, but also increases the inactivation at the same time. Since depolarization due to concentration change is slow, it never generates an action potential by itself instead, it results in accommodation. Above a certain level of potassium the depolarization inactivates sodium channels, opens potassium channels, thus the cells become refractory. This leads to the impairment of neuromuscular, cardiac, and gastrointestinal organ systems. Of most concern is the impairment of cardiac conduction which can result in ventricular fibrillation or asystole.
Decreased extracellular potassium leads to hyperpolarization [2]:
Lower potassium levels in the extracellular space will cause hyperpolarization of the resting membrane potential. As a result, a greater than normal stimulus is required for depolarization of the membrane in order to initiate an action potential.
In the heart, hypokalemia causes hyperpolarization in the myocytes' resting membrane potential. The more negative membrane potentials in the atrium may cause arrhythmias because of more complete recovery from sodium-channel inactivation, making the triggering of an action potential less likely. In addition, the reduced extracellular potassium (paradoxically) inhibits the activity of the $I_{Kr}$ potassium current and delays ventricular repolarization. This delayed repolarization may promote reentrant arrhythmias.
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