BB15: Mathematical modelling of protein transport and signalling at synapses

Project completed October 14, 2011

Background

The human brain is massively interconnected. It contains billions of neurons, each with connections to thousands of other neurons. These connections, called synapses, are a channel through which neurons communicate. The strength of these connections can vary, and according to current understanding, this synaptic plasticity is the mechanism used to store memories.

In many cases, synaptic plasticity is governed by the number of receptors in the post-synaptic density (see Figure 1). The more receptors there are, the stronger the connection between the neurons. Individual receptors have a limited lifetime in a synapse as they are recycled in to and out of a synapse several times an hour. While individual receptors may be involved in short-term memory storage, they do not last long enough to store long-term memories. It has recently been suggested that clusters of receptors can result in long-term changes in synaptic strength and may be responsible for long-term memory.

Researchers at the Oxford Centre for Collaborative Applied Mathematics (OCCAM) have further developed this idea by proposing a realistic mechanism of receptor cluster generation and stability using ideas from the physical theory of vapour–liquid phase transformations.

Techniques and Challenges 

Receptors may bind to proteins on the post-synaptic density and be immobile, or be mobile within the membrane. Immobile receptors are sites at which the mobile receptors can nucleate, or collect. This is analogous to vapour-liquid phase transformations where a supercritical liquid droplet is formed from supersaturated vapour.

This model of cluster formation allows a synapse to exhibit bistability, meaning that there are two distinct stable states with different cluster sizes. Transitions between these two states correspond to writing or erasing information in the brain. Whether nucleation of receptors occurs depends on the density of the receptors.

When the density of receptors increases (for example after stimulation of the synapse) a cluster of receptors will begin to form. The cluster will grow until it reaches an equilibrium size, depending upon the influx of receptors and the area of the synapse.

Similarly, the cluster can disappear if the receptor concentration becomes too low, for example, after an inhibitory signal to the synapse. The evaporating cluster will also reach a (smaller) equilibrium size.

Results

Analysis of the model shows that the energy required for a receptor cluster to form depends on the cluster size as well as the influx and outflux of receptors and the synapse size. Importantly, if receptor density is increased, the energy required to form a cluster drops dramatically and makes it more likely for a cluster to form. This suggests that an increase in density for even a relatively short time period may be enough to initiate cluster formation.

The results of energy analysis were verified by Monte Carlo simulations of cluster formation and evaporation. It was found that the long-term stability of synaptic strength is achieved with the formation of large (about 200) receptor clusters, while smaller clusters may account for the shorter term strengthening.

While in neuroscience there is still some disagreement as to whether changes at individual synapses occur in an analogue or digital manner, several research results have suggested that changes in synapses occur in digital ‘all-or-none switch-like events’, which is consistent with this result on bistability.

The Future

A major simplification of the model was to consider only a single receptor cluster. In further simulations by the researchers, it was found that nucleation of more than one cluster at different nucleation sites did not change the main result of the model, as only one stable cluster is formed and the others vanish.

This result also suggests that non-clustered immobile receptors do not contribute to the vapour–cluster dynamics and need only to be treated as additional nucleation sites. However, a more detailed study is required to investigate the impact of multiple nucleation sites on fluctuations in the number of receptors in the clusters.

Related Publications

[11/26] Burlakov V.M., Emptage N., Goriely A., Bressloff P.C.: Synaptic bistability due to nucleation and evaporation of receptor clusters, Physical Review Letters

Triller A., Choquet D.: Trends Neurosci. 28, 133, 2005

Sekimoto K., Triller A.: Phys. Rev. E 79, 031905, 2009

Shouval H.Z.: Proc. Nat. Acad. Sci. USA 85, 14440, 2005