Figure 1.
Diagram of synaptic states in the model.
The three states on the left have weak weights, whereas the three states on the right are strong. Arrows indicate the transitions, whilst the symbols next to the arrows denote transition rates. The dotted arrows indicate transitions that are only active after a plasticity-inducing stimulation. In addition, all transition rates except those labeled change when a stimulation protocol is given (see text for details). In the absence of recent stimuli, values of the transition rates are
,
,
,
,
. In that case the synapse fluctuates between states 3 and 4. Note that the drawing of weak states with a single AMPA receptor and strong states with two AMPA receptors is intended to be merely a figurative rather than precise illustration; similarly with the “anchors”.
Figure 2.
The effects of tetanisation on the state transitions.
(A,B) Each diagram represents the state diagram for the model, and the super-imposed arrows indicate the transition rates that are significant in the given scenario, at the given time. To indicate how STC is incorporated into the model, we show a tetanised synapse and an unstimulated synapse. (A) Weak HFS only affects the synapse to which it is applied, and transition into the e-LTP state occurs over a period of a few minutes. (B) Strong HFS initially has the same effect as a weak tetanus. However, protein synthesis and diffusion are triggered by this stimulus: at 20 minutes after stimulus onset, both synapses are affected by rapid transition rates from their e-LTP to states, and also from their e-LTD to
states. Thus if weak HFS or LFS were given to the unstimulated synapse in this scenario, then the STC process would occur. (In the latter case one has “cross-capture”.) (C) The time course of the transition rate
from the strong basal state to the e-LTP state following weak HFS at time
. (D) The time course of the transition rate
from the e-LTP state to the
state following strong HFS starting at time
.
Figure 3.
Long-term potentiation and depression in the model.
(A) Weak HFS to population 1 at time results in e-LTP of that population. The increase in weight to about 150% lasts about 90 minutes. Population 2 is a “control pathway”, that has only test stimulation (to measure its strength) but no tetanic stimulus applied to it. Apart from the fluctuations its weight is stable. (B) Strong HFS to Pop. 1 at
results in
of that population. The control population is not affected. (C) Weak HFS to Pop. 1 at
results in e-LTD of that population. (D) Strong LFS to Pop. 1 at
results in
.
Figure 4.
Each diagram represents the state diagram for the model, and the the area of the circle around each state indicates the proportion of synapses occupying that state. (A) A single population of synapses is given weak HFS at . The stimulus results in a transient movement of synapses into the e-LTP state, followed by decay back to the initial state. (B) Multiple populations exhibiting synaptic tagging, capture and cross-capture. One population is given strong HFS at
. Synapses initially move into the e-LTP state, in which a tag is present, before moving into the
state via the eventual capture of PRPs. A second population is given weak HFS at
. Most of these synapses move swiftly into the
state once the stimulus is given; PRPs are already available as a result of the stimulus to Pop. 1, so capture occurs as soon as tag formation is complete. A third population is given weak LFS at
. Most of these synapses move swiftly into the
state once the stimulus is given; an LTD tag is set, and this can immediately “cross-capture”
proteins that have been synthesized and diffused as a result of the stimulus to Pop. 1.
Figure 5.
Synaptic tagging and capture in the model.
(A) Strong HFS to Pop. 1 at and weak HFS to Pop. 2 at
results in
of both populations. (B) Rescue of e-LTP decay: weak HFS to Pop. 2 at
followed by strong HFS to Pop. 1 at
. (C) Cross-capture: strong HFS to Pop. 1 at
followed by weak LFS to Pop. 2 at
.
Figure 6.
(A) Weak HFS at followed by weak LFS at
to same population leads to de-potentiation. (B) Weak HFS at
followed by weak LFS at
. In this case e-LTP is not reversed by the LFS; it has become immune to depotentiation. (C) Pop. 1 is given weak HFS at
followed by weak LFS at
, and pop. 2 is given strong HFS at
. Pop. 1 remains stable at baseline after the stimuli, while pop. 2 exhibits
. (D) Pop. 1 is given weak HFS at
followed by weak de-potentiation LFS at
, and pop. 2 is given strong HFS at
. In this instance both populations exhibit
.
Figure 7.
Theoretical mean and fluctuations in the synaptic strength.
(A) The time course of the expected value of the fEPSP for a population of 1000 synapses, given either weak HFS (blue, upper curve) or weak LFS (red, lower curve), administered at time . (B) The corresponding standard deviation of the fEPSP as a function of time. The fluctuation increases for e-LTP and decreases for e-LTD. (C,D) Analogous plots for a population given strong HFS or strong LFS; in this case the fluctuations decrease for both protocols.