On the molecular level, a model of the dendritic spine is being extended to include calcium binding to calmodulin and calmodulin binding and trapping by CaM-kinase II (Holmes, 2000). The goal is to develop a better understanding of synaptic modification and, eventually, to express the essence of these biochemical reactions in a synaptic modification rule. We are developing a stochastic reaction-diffusion model to study reactions in small spaces such as dendritic spines.
On the synaptic level, work is being done to develop more accurate descriptions of NMDA and AMPA conductances for use in neuron level models. Calcium influx through NMDA receptor channels has been shown to be important for the induction of LTP and LTD, and good quantitative models of the NMDA and AMPA conductances are needed to get accurate quantitative estimates of calcium influx. To do this, diffusion models of the synaptic cleft have been developed (Holmes, 1995) and the effects of ambient glutamate and the time course of glutamate release on AMPA and NMDA conductances are being explored. We have also compared deterministic and stochastic models of NMDA and AMPA channel opening with stochastic models done with the software program MCell (Li and Holmes 2000).
On the neuron level, work is being done to construct realistic models of CA1 pyramidal cells. We take morphological reconstructions from public data bases as the neuron structure and then we fit parameter values given experimental recordings from CA1 pyramidal cells done by our collaborator Larry Grover from Marshall University. Recently we have found that there are a number of problems with taking morphology from public databases (Holmes et al 2006). Even if morphological and electrophysiological data come from the same cell, it is necessary to calibrate models with data because of possible errors in reconstruction measurements or in estimates of spine numbers. We have used our models to quantify the changes in synaptic level parameters necessary to explain LTP (Holmes and Grover 2006). We find that the currently popular hypotheses for explaining LTP (increase in AMPA receptor number or unsilencing silent synapses) are not sufficient mechanisms to explain LTP. Other hypotheses, such as an increase in AMPA single channel conductance or an increase in the probability of vesicle release are sufficient mechanisms in the models, but whether these mechanisms occur in the adult is a matter of debate. We are also looking at methods to estimate voltage conductance parameters for use in models. More recent simulations are done with NEURON but we have used either my own simulator or GENESIS in the past.
As an advance is made on one level, its implications are incorporated in other levels. By working on the molecular, synapse, and neuron levels simultaneously, the goal is to be able to get a description of a neuron appropriate for a fourth level of modeling, the network level.