Ashgabat, Turkmenistan; Dushanbe, Tajikistan; Tashkent, Usbekistan;Uzbekistan; Bishkek, Kyrgyzstan, and (until 1997) Almaty, Kazakhstan are capital cities that are nestled up tight against borders, with tremendously large countries stretching away from them. Indeed, these capitals are quite close to each other, in relation to how large the countries are.
Here is a map. Below, I have drawn a line from the nearest border to each capital to the other side of the country. This can be hard to make out because the nearest-border is often so close and the other border is so far out.
Why is this? There is no rule that Central Asian capitals must be like this. Compare Tehran, Kabul, and Tblisi that are relatively more central.
Perhaps they are spread across the Silk Road, where you might expect cities to grow. But that does not explain why each one got control of a back-country in one direction, rather than all around.
Of course, each one has its own history, but I am less interested in why any one capital is like this than in whether there something in common to those four border-capitals.