Potassium is crucially important to help your heart beat rhythmically. If you have high blood pressure, heart failure or heart rhythm problems, getting enough potassium is especially important. Although potassium and cholesterol aren't directly related, eating a potassium-rich diet just might lower your cholesterol enough to avoid medication.
Researchers defined low potassium intake as less than 2.4 grams per day and high intake as more than four grams per day. A study of 5,600 men and women over 65 found those with the least potassium in their diet were 1.5 times more likely to have a stroke than those with the most.
One large banana will contain around 422 mg of potassium, which means it contributes about one-tenth of the recommended daily intake. As well as being rich in potassium, bananas contain more than a quarter of the daily requirement of vitamin B6. They are also rich in folic acid, making them an important food for women who are (trying to become) pregnant.
Bananas are also a rich source of tryptophane, an essential amino acid. It is a precursor of serotonin, which in turn is a precursor of melatonin. Serotonin regulates our mood and thus our sense of happiness and well-being. Low levels are linked to depression. Melanonin regulates your internal clock and helps you sleep. Low levels are linked to sleeplessness.
This all means that regularly eating a banana helps maintaining a healthy beating heart, while at the same time keeping you happy and giving you a good night’s sleep.
Maybe we should alter the age-old saying ‘an apple a day keeps the doctor away’ to ‘a banana a day keeps health problems at bay’.
 Green et al: Serum potassium level and dietary potassium intake as risk factors for stroke in Neurology - 2002
 Young: How to increase serotonin in the human brain without drugs in Journal of Psychiatry and Neuroscience – 2007. Pdf here.