It's not the number of neurons that increase the computing power of a particular species' brain, and hence the potential complexity of its behavior. Rather it is the structure of the synapses - the microscopic spaces between neurons - how many proteins are present there, and how many different types of structures those proteins combine to construct, according to Dr. Seth Grant and his colleagues. Their recent article in Nature Neuroscience is summarized in Nicholas Wade's article in today's Science Times.
This study is particularly interesting for its comparison of synaptical structure across different species. I find the structure of the neuron a fascinating subject because our behavioral complexity - the difference between humans being able to speak and reflect on their own thoughts versus a slug's simpler cognitive capacities - is the difference between the number of proteins present in their nerve cells, and that influences, as this article puts it, our processing power. Here's why: Our billions of neurons are like strands of microscopic wire strung end-to-end throughout our nervous systems. They communicate with each other both chemically and electrically and if the message is strong enough, those communications result in a behavior - a hand moves, the heart beats, anger is registered on another's face and we run, etc.... Proteins are the building blocks for the various chemicals that neuron's pass between each other to facilitate or hinder the activity of the succeeding neuron. They also help package those chemicals for distribution, they create mechanical devices which propel those packages through pores in the synapse, others which pick up excess chemicals and return them to the cell. Still other proteins are embedded along the membrane of each neuron that allow passage of different charged particles in and out of the cell, which permits the 'firing' of nerve cells that you have probably heard people talk about. All electrical activity, whether it fires up your lamp at home or your neurons, is a result of differences in charge. (Think of how putting the positive ends of two magnets together creates a force that you can actually feel) Simpler species have only evolved systems that use one or two types of charged particles to flow - say, potassium and sodium. Whereas more complex species have additional types - they (we) allow potassium, sodium, calcium and chloride - those channels also have evolved subtypes each of which has a somewhat different mechanical structure and hence a different action. Each of those differences adds a new way one cell can 'fire' or talk to another nerve or muscle cell. Some cells give one big burst of electricity, others give groups of bursts in rhythmic patterns. Some cells produce messages which function only to change the message of another cell. It is the summed action of millions of these cells which ultimately determines whether a behavior happens or not. Does our hand raises and grasp our cup of coffee without looking while continuing to type a blog entry with one hand? Or does it knock it off the desk instead?
The advantage of a complex animal's computing power is like the difference between having an alphabet with three letters and one with 26. With three letters one has a modest number of combinations one can produce: ABC, ACB, AAB, BBA, etc... Those three letters do give us a decent number of combinations and you could think of each of those combinations as a 'message' output by the cell. But then think of our 26-letter alphabet and consider the number of words in our dictionary. An increase of 23 letters (a small number of building blocks) buys us millions of possibilities in terms of how we can combine them. A sea slug with only a few varieties of potassium channels only has a few possible ways its nerves can fire - hence the limited repertoire of behaviors one might expect from the slug. They can move their gill to get oxygen, they can wiggle their tail for movement and avoid danger, they desire nutrition and pursue it, but we don't expect them to suddenly learn to fox trot no matter how much training we might provide. The human brain is capable of a startling number of actions and subtle variations on those actions (it also has an impressive number of ways it can mess up as well). That is because of the inherent combinatorial possibilities afforded us by the way our 1000 neural proteins have evolved to combine. It ain't a perfect machine by a long shot, we have also evolved violence, neuroticism, and schizophrenia, but it is pretty remarkable system nonetheless. Our ability to cook, write poems, and reflect on our carbon footprint have evolved because we have more ways our cells can 'fire.'
Hopefully that added to your understanding of this article and didn't just confuse you. Feel free to ask questions if this subject interests you.