I have been wondering, what are known dietary causes for constipation?
Is there a reason that combining Rice and Meat in a meal would cause constipation? Is there some gut reaction that is causing these symptoms?
The major dietary causes are not enough water and not enough fibre. (See the Risk Factors section of this Mayo Clinic article, which focuses on medical causes of constipation.) There's nothing complicated about mystery little factors in your food that combine to create a problem. If you eat only white rice and meat for a meal, with no vegetables, then you are eating a lot less fibre than someone who added vegetables to that meal or who ate beans instead of meat.
First thing to do if you're suffering constipation is to drink a lot more water. Second thing to do is add vegetables and legumes to your meals. There are things you can do beyond that, but they are not dietary and should probably be suggested by someone more familiar with your personal situation. More water and more fibre are generally a safe approach, so if you're sure your situation is caused by what you eat and drink, fix that.
A note that if you are ill or are taking any medication, it's a whole different story and you shouldn't do anything (not even eating extra fibre) without discussing it with your doctor.