Physiologically, hypokalaemia's dominant effect is the hyperpolarisation of cells. Remember that there is an electrochemical gradient across our cells: the complicated arrangement of the various ions on either side of our cells ends up making the interior of the cells negative, relative to their outsides. Sometimes this is referred to as the resting membrane potential, and this fact is exploited by excitable cells like neurones and muscle cells - the right signal causes rapid changes in the membrane potential, setting off a chain reaction that culminates in something useful (like the muscle contracting).
With less positively charged potassium ions on the outside of the cell (the definition of hypokalaemia), potassium ions from within the cell leave to replace them, causing the inside of the cell to become even more negatively charged than before. The result is that the cells become 'hyperpolarised' - less likely to fire off action potentials.
From this fact, most of the symptoms can be deduced:
- Cardiac arrhythmias can be induced by hypokalaemia. Also, certain ECG changes are typical: increased PR interval (slowed atrio-venticular conduction) and flattened or inverted T-waves (delayed repolarisation) are seen.
- Skeletal muscle weakness may exist, and occasionally be profound (anybody unlucky enough to see a hypokalaemic kwashiorkor child will attest to this). It usually involves the peripheral muscles, sparing the facial and respiratory muscles. At the final end of the continuum, rhabdomyolysis (destruction of skeletal muscle) may ensue.
- Smooth muscle weakness usually manifests clinically as constipation and paralytic ileus.
- Glucose intolerance is also sometimes found, and it is due to the fact that hypokalaemia impairs insulin release: the pancreas' beta cells also need to depolarise before the agree to give up their insulin.
- Polyuria and dehydration is the main symptom complex not directly caused by hyperpolarisation of cells. Potassium is the 'rate limiting' element to the thick ascending loop of Henle's Na+/K+/2Cl- pump (the others are usually present in abundance). A lack of potassium means that the pump can't absorb all the sodium it needs to, and since sodium carries water with it, you get both polyuria and dehydration.
- Metabolic alkalosis requires some expaining too, since it also isn't directly due to hyperpolarisation. At the distal parts of the kidney's nephrons, it is helpful to think of sodium being reabsorbed in exchange for either potassium or hydrogen. The situation is a little more complicated than this, but that doesn't matter. The point is that if potassium is low, more hydrogen must be booted out the cells to get enough sodium in. The result of this is, of course, a metabolic alkalosis (which is fortunately usually quite mild).
EDIT: I forgot the last point off the original version of this post!