Computer
Simulations of Synaptic Signaling
We
are studying the biochemical signaling cascades that are triggered
by calcium influx into the postsynaptic spine, and that regulate
adaptive changes in the synaptic machinery. Our tools to study the
function of the highly interconnected biochemical pathways include
both biochemical experiments and computer simulations. Our goal
is to create simulations that will generate testable predictions
about the flow of protein phosphorylation events in spines and dendrites,
under conditions of calcium influx that cause changes in synaptic
strength.
Data for "Realistic" Simulations
Most
of the major molecules forming the signaling machinery at the postsynaptic
membrane of dendritic spines have now been characterized by our
lab and others [1, 2]. To build realistic simulations it is necessary
to determine the relative stoichiometry of the molecules whose functions
will be simulated.
We
are using quantitative western blots of proteins in the postsynaptic
density fraction and in synaptosome to estimate the relative numbers
of the molecules of interest, for example we are determining the
ratios of subunits of the NMDA receptor to PSD95 and to subunits
of CaM kinase II. We can then calculate average numbers of each
molecule present in the major anatomical classes of spines of pyramidal
neurons in area CA1 of the hippocampus [3], based on information
about glutamate receptor currents and about spine geometry found
in the literature. The biochemical measurements and calculations
serve two purposes. They give us a more precise view of the likely
predominance of certain pathways, based on the relative number of
interplaying signaling molecules, and they provide starting parameters
for computer simulations of the signaling cascades at the postsynaptic
site of glutamatergic synapses, following influx of calcium.
Computer
Simulations
In
order to numerically simulate the entry of Ca ions into the spine,
its diffusion, and the biochemical reactions triggered by the Ca
influx, we use MCell: (http://www.mcell.cnl.salk.edu)
,a software package for stochastic simulation of biochemical processes
in vivo. MCell was originally developed to model the events
at the neuromuscular junction: acetylcholine release, diffusion,
binding to acetylcholine receptors and the nicotinic acetylcholine
channel kinetics [3,4]. However, in collaboration with the MCell
group at the Salk Institute, we are extending it so that it can
be used for modeling of other biochemical processes.
Contrary
to the traditional numerical approach, in which a system of partial
differential reactiondiffusion equations is solved numerically,
MCell uses the MonteCarlo approach to simulate diffusion of individual
molecules (ions) and their reactions in an arbitrarily shaped space.
It requires the number and positions of all molecules, diffusion
constants, binding and unbinding constants for all reactions and
a description of the geometry where the process that is simulated
takes place.
Diffusion is performed in MCell as a random walk. During one time
step each diffusing molecule moves in a randomly chosen direction
and travels a distance that is randomly chosen from the theoretical
diffusion distribution for the given diffusion coefficient of the
molecule and the time step. Therefore, contrary to the majority
of random walk algorithms, MCell does not use a lattice for diffusion.
Reactions are also treated as stochastic events. The probability
that two individual molecules bind is calculated from the binding
rate. Only the molecules that come close enough during diffusion,
as determined by the ray tracing algorithm, can possibly bind. Dissociation
probability is determined from the dissociation rate. Virtually
any geometry within which diffusion and reaction take place can
be specified, which gives MCell a significant advantage in simulation
of in vivo processes over the traditional approaches based on partial
differential equations.
We are presently deriving models for the kinetics of activation
of CaM kinase II, and devising in vitro experiments with purified
CaM kinase II to test the models at levels of calcium and calmodulin
that the enzyme is likely to encounter near the postsynaptic membrane.
In this way, we will determine the appropriate reaction rates and
probabilities to incorporate into a model of the spine synapse.
Eventually, we will devise experiments to test predictions of our
models for activation of CaM kinase II, and its modulation, in living
neurons.
References:
[1]
Kennedy M.B. (2000) SignalProcessing Machines at the Postsynaptic
Density. Science 290: 750754
[2]
Sheng, M. (2001) Molecular organization of the postsynaptic specialization.
Proceedings of the National Academy of Sciences 98: 70587061
[3]
Harris K.M., Jensen., and Tsao B. (1992) Threedimensional structure
of dendritic spines and synapses in rat hippocampus (CA1) at postnatal
day 15 and adult ages: implications for the maturation of synaptic
physiology and longterm potentiation. Journal of Neuroscience
12: 26852705
[4]
Bartol TM Jr., Land BR, Salpeter EE, Salpeter MM (1991) Monte
Carlo simulation of miniature endplate current generation in the
vertebrate neuromuscular junction. Biophysics Journal
59: 12901307
[5]
Stiles, J.R., Bartol, T.M., Salpeter, M.M, Salpeter, E.E., and Sejnowski,
T.J., (2000) Synaptic variability: new insights from reconstructions
and Monte Carlo simulations with MCell. In Synapses,
W.M. Cowan, C.F. Stevens, and T.C. Suddhof, eds. (Baltimore, Johns
Hopkins Univ. Press), 681731.
