BB10: Understanding collective behaviour of systems of interacting particles

Project completed August 3, 2012

Background

Although most protein synthesis occurs in the cell body, in neurons some mRNAs are transported along microtubules into branched projections, called dendrites, to support local protein synthesis. Increasing evidence indicates that local protein synthesis in dendrites plays a critical role in mediating the enduring changes in synaptic structure and function that underlie long-term memory. Moreover, various types of dysfunction in this transport appear to be a major contributing factor to neurodegenerative diseases associated with memory loss, including Alzheimer’s disease.

Researchers at the Oxford Centre for Collaborative Applied Mathematics (OCCAM) have developed a model for mRNA transport that includes interactions with the complex biological geometry in order to study the role of local protein synthesis in long-term memory.

Techniques and Challenges

Within dendrites, mRNA is assembled into granules, which then undergo rapid bi-directional transport by multiple molecular motors, such as kinesin and dynein. Brief periods of slow movement or pauses often interrupt rapid transport, consistent with localisation at synaptic sites. The stochastic model developed of the motor-driven transport of mRNA granules along dendrites combines intermittent bi-directional transport with signalling and uptake from targeted synaptic sites. Coupling the transport model with synaptic signalling cascades provides a framework for studying the role of local protein synthesis in long-term plasticity. However, it is a challenge to analyse a model that accurately describes the random intermittent behaviour of a motor-driven mRNA granule and the interaction with the complex geometry of a neuron.

The random dynamics of the mRNA granule is described by the differential Kolmogorov equation—a high-dimensional, linear, partial differential equation. Interactions with the cellular domain are included by applying inhomogeneous terms and appropriate boundary conditions. Several techniques are available to help analyse the model, such as singular perturbation theory and Green’s function methods.

Results

The first step in the project was to develop a stochastic model for transport and delivery of a single mRNA granule. It was found that mRNA granules might use a simple search strategy, intermittently switching between a fast transport phase and an immobile search phase, to locate a synaptic target. An intermittent search strategy is good for finding a small, hidden target in a large domain. Locating a synapse in a large branched domain, like a typical dendrite, is difficult because the searching mRNA granule can choose an incorrect branch. This effect is mitigated if the fast transport phase includes both forward (away from the cell body) and backward motion, enabling the mRNA to return to the correct branch. While this result provides an explanation for bi-directional transport in dendrites, it was also found that the probability of finding the synaptic target is an exponentially decreasing function of the number of branch nodes between the cell body and the synapse. Another possibility is that synapses produce a local signal. In particular, it was found that tau and MAP2 (microtubule-associated proteins that play a key role in Alzheimer’s disease) can act like a traffic signal, regulating the flow of cargo transported within dendrites or axons by affecting the interaction between molecular motors and microtubules.

In the final stage of the project, a stochastic model of multiple mRNA granules was developed and analysed in order to confirm that the population behaviour is qualitatively described by the single mRNA search process.

The Future

Coupling a stochastic model of biomolecular transport with the complex geometry of a living cell is a challenging, but ubiquitous problem. Along with mRNA transport in dendrites as studied here, other examples include a transcription factor searching DNA within the nucleus for a specific gene, diffusion of receptors in the cell membrane of a dendrite, and diffusion in the crowded cytoplasm.

This project resulted in numerous contributions to this emerging field, and the researchers are in the process of finishing a comprehensive review of the subject, to appear in Reviews of Modern Physics.

Related Publications

[12/45] Bressloff P.C., Newby J.M.: Stochastic models of intracellular transport

[11/73] Bressloff P.C., Newby J.M.: Filling of a Poisson trap by a population of random intermittent searchers

[11/13] Bressloff P.C., Newby J.M.: Quasi-steady state analysis of two-dimensional random intermittent search processes, Physical Review E

[10/39] Newby J.M., Bressloff P.C.: Local synaptic signaling enhances the stochastic transport of motor-driven cargo in neurons, Physical Biology

[10/04] Newby J.M., Bressloff P.C.: Random intermittent search and the tug-of-war model of motor-driven transport, Journal of Statistical Mechanics

[09/28] Newby J.M., Bressloff P.C.: Quasi-steady state reduction of molecular motor-based models of directed intermittent search, Bulletin of Mathematical Biology

Hirokawa N.: mRNA transport in dendrites: RNA granules, motors, and tracks, Journal of Neuroscience, 26:7139–7142, 2006

Bramham C. R., Wells D. G.: Dendritic mRNA: transport, translation and function, Nature Review Neuroscience, 8:776–789, 2007