Researchers have come to a consensus that on a timescale of hours to a few days synapses change chemically through one of two processes: long-term potentiation (LTP), the strengthening of a synapse; or long-term depression (LDP), the weakening of a synapse. There is debate, however, over what determines how this strength changes. One of the keys to the process appears to be the number of AMPA receptor proteins, which bind glutamate, an excitatory neurotransmitter that is believed to be involved in learning and memory. Researchers have observed AMPA traveling from the inside of a neuron to the downstream end of a synapse, but they remain uncertain as to whether the migration into and out of the synapse is the major component in determining synaptic strength. "There's a lot of data out there that actually measures over time how the strength of a synapse varies during LTP/LTD," says Paul Bressloff, a theoretical neuroscientist, who used a system of differential equations to model AMPA receptors' movements. "They know these things happen, and they make hypotheses about how things could fit together, but they don't do any quantitative study to see if it could really work. And that's what we've basically done."
Bressloff, along with mathematical biologist Berton Earnshaw, conceived of the dendritic spine--the mushroom shape at the downstream end of the neuron--as a two-compartment box: On the far downstream end, essentially in the synapse, scaffolding proteins suspend AMPA receptors so they can bind glutamate signals coming from the upstream neuron. The other end leads back down the dendrite into the main body of the neuron. The pair devised 10 differential equations to track the rate at which AMPA moves around into and out of the synapse. One of their main assumptions within their model is that diffusion between compartments is fast and that things equilibrate quickly.
Bressloff and Earnshaw discovered that during the induction phase of LTP--when an experience or stimuli sets off learning--new AMPA receptors are "shoved" into the synapse to communicate with glutamate, Bressloff says. This event often correlates with a rise of calcium ions flowing into the cell. However, Bressloff explains, a calcium-ion concentration shift happens too quickly to create a memory--because of the fast equilibration, it will be resolved within a minute. "You need mechanisms at different timescales to make a memory stable," he notes. "What the scaffolding proteins do is convert that short memory into something that can last for hours."
Whereas the team's model proved that the presence of more scaffolding proteins available at the far downstream end of the neuron (and into the synapse) to AMPA receptors increased during LTP, they found the opposite condition for LDP. So, rather than the number of AMPA receptors themselves, the abundance of scaffolding proteins appears to determine synaptic strength, effectively allowing AMPA receptors to receive signals from glutamate. "You need these scaffolding proteins, number one," Bressloff remarks. Beyond that, he continues, "at the timescale of hours, scaffolding proteins can be moved in and out, so again things would lose the memory, so you need something else, like changing the actual structure of the dendritic spine." Like a number of other topics in neuroscience, whether the spine shifts shape or, possibly, new proteins are synthesized, how memories are formed for the long-haul is still up for debate.