Largest ever DNA computer
The overwhelming majority of the computing done today is with transistors in silicon chips, though there are a few other tacks which are being tried. One is using DNA, it can famously encode information, and it is a chemical, so in reactions it can do operations on this data.
In the long run they have been proposed as a way of solving some problems which are very slow to do with a normal computer because although a DNA computer does calculations slowly, DNA molecules are quite small, so it could do a lot of them at the same time, but we haven't quite reached this point yet.
Erik Winfree and Lulu Qian have built a system of DNA molecules that interact with one another, in lots of different reactions. DNA is a double helix, two spiral molecules, relatively weakly bonded to one another. Two DNA molecules can only connect to one another though when they have corresponding codes, and if only half of the code corresponds to one another only half of the molecules will connect, leaving the other half able to make another reaction.
By encoding inputs as the presence or absense of a molecule, a pair of these reactions can give outputs of another molecule, and behave like any conventional logic gates. Computers are made of logic gates so with enough reactions you can build a computer.
So far they have built a system of 130 DNA molecules which can do a calculation... they can find the closest integer to the sqare root of a number up to 16, and the reaction takes about 10 hours.
This, in itself, isn't very useful, but they have built all the infrastructure to be able to make more complicated systems, and read out the results.
The 10 hour calculation time means that it isn't going to be competing with silicon any time soon, but there are places where being able to do simple logic chemically could be useful, for example in a diagnostic test you might want to look for the presence of 3 different pieces of DNA only producing a result if you see them all, or you could only release a reactant only when the first 2 stages of a reaction had completed.
They are also suggesting that life is a complex system of interacting chemical reactions, so we may be able to learn something about it by studying these simple DNA computers.