What a great question. I think these are all related, because they are all tied to power and money. Let's start with science. What projects are most likely to receive funding? Probably those that will produce a lot of money or power. Let's face it, who will give a ton of money for something that will not produce money? Who has that much money to give? Well, the government. So, we see that science is heavily tied to politics. This is one of the points that the anthropologist Stanley Tambiah makes. Finally, commerce comes into play, because any lucrative scientific discovery must be sellable for further profits. In the end, money and power ties these all together.
The main importance is that all three of these things interact and their interaction impacts our lives in a very major way. Governments and people need to understand the relations so they can try to manage them for the best. As an example of this, look at the idea of global warming.
Science tells us that global warming is going to be a major problem. However, the immediate needs of commerce are threatened by this idea because serious action to combat global warming would require things to be done that would alter the current structure of commerce. Because of this, politicians are pressured to try to control the science or the commerce or both.
So in this case, the relationship is that science threatens commerce which puts pressure on politicians to mediate the dispute. If we don't understand this relationship, we cannot fully understand the problem or its potential solutions.
There is a strong interrelationship between the three disciplines. This connection can be expressed in many ways. One such connection is that politics helps to give the structure of the advancement in the other two realms. Social orders have grown and matured with developments in both business and scientific growth. Given the ways both have tendencies to change society, politics helps to give structure which can best maximize this growth for all of its citizens. On a more intellectual level, all three disciplines can be considered to be governed by specific laws and principles. Understanding and applying these ideas are of critical importance to those who seek to better comprehend the implications of each branch.