Background and state of the art
Synaptic plasticity is regarded as the molecular basis of learning and memory. It involves complex molecular machinery with various protein interactions but it is not yet clear how the components give rise to the different aspects of synaptic plasticity.
The figures give a sketch of the LTP- and LTD-states. The ability of the synapse to stay in different stable stationary states is referred to as multi- or bistability in the literature. The transition from one stationary state to another requires a positive-feedback aspect in the biochemical reactions. Until now, first steps have been done in modelling the synaptic plasticity process. Beside models with a small number of components concerning the positive-feedback mechanism of CaMKII phosphorylation, e.g. by Lisman, there are very few extended mathematical models of biochemical systems containing switches which lead to synaptic plasticity, e.g. by Castellani or Hayer. Moreover, many current experimental strategies consist in a search for putative memory tags, s. Kelleher Ill.
Within the past few years, an accumulation of observations including the trafficking of AMPA-receptor subunits and the identification of numerous interacting proteins involved in synaptic plasticity have created a new state of knowledge about the molecular mechanisms leading to long-term potentiation (LTP) or long-term depression (LTD) at synapses [1].
A repeated short-time excitation of an active synapse can fix it in the LTP- respectively in the LTD-state. It is well accepted that the AMPA-receptor sorting and trafficking play crucial roles in synaptic plasticity. The occurrence of the homomeric form of this receptor in the postsynaptic membrane governs the strength of synaptic transmission.
The Project
The project deals with the modelling and the simulation of the molecular mechanisms of LTP and LTD in the synaptic transmissions. The base of synaptic plasticity is regarded as a multistable molecular reaction, which stays in distinguished stable states like LTP, LTD and possible further states after having been induced by stress related signals [2].
Most biochemical reactions described in the literature are monostable. The proposed project aims in the explanation of fundamental mechanisms of multistable reactions both in synaptic plasticity and in more general context. An essential part of such reactions is a positive-feedback loop, which has been found in various biochemical and medical investigations. Using modules known form these investigations, bistable and multistable reactions are created which reproduce the behaviour of the particular application.
Starting from a small core system of ordinary differential equations containing multistability, synaptic plasticity is modelled by the enrichment of the core system by further regulatory paths. Occurring parameters are to be identified by a comparison with clinical and experimental data. The resulting nonlinear dynamical system is discussed concerning parameter sensitivity and robustness with respect to the kinetics.
It is known that AMPA-receptors are trafficking from the cytosol into and away from synapses. Thus, the confirmed and tested ordinary differential equations including the reaction kinetics are completed by active diffusion and other transport processes. In general, the resulting partial differential equations have a highly complex solution behaviour, which has to be carefully discussed and adapted to clinical experiences. The local resolution of the model enables us to explain the marking process of different synapses in one nerve cell.
Further to the synaptic plasticity, it is assumed that fundamental regulatory mechanisms act in several biochemical applications. With respect to the immense number of possible substances and regulatory paths in extended biochemical systems like the synaptic plasticity, mathematical models allow to check virtually a large number of hypotheses and to estimate a priori the gain of knowledge expected by time-expensive experimental investigations.
Key Literature
- Malinow, R. and Malenka, R.C.: AMPA receptor trafficking and synaptic plasticity, Ann. Rev. Neurosci. 25:103-126, 2002.
- Langemann, D., Pellerin, L. and Peters, A.: Modelling molecular mechanisms of synaptic plasticity - making sense of AMPA receptor trafficking (in preparation, 2007).