Figure 4.

Models relying on spike timing dependent plasticity (STDP) or biochemical processes can account for trace processes. (Ai) In the model by Izhikevich (2007), the coincident firing of a pre- and then a postsynaptic neuron (within 10 ms; marked by a rectangle) elicits a synaptic eligibility trace c(t) in the corresponding synapse. This eligibility trace decays exponentially to zero. Reinforcement d(t), here a dopamine (DA) release delayed by 1–3 s in combination with the residual eligibility trace, increases the synaptic strength s(t) [s(t) = c × d] of the particular synapse. (Aii) Repeated reinforcement of such a pre–post firing event increasingly strengthens the particular synapse. This in turn increases the probability of coincident firings of this synapse. Adapted from Izhikevich (2007), with permission. (B) Lingering Ca²⁺ and coincidence detection by an adenylyl cyclase (AC) might account for trace conditioning in the model by Yarali et al. (2012). (Bi) Ca²⁺ influx and Gα activation (induced by CS and US, respectively) synergistically act on the AC, leading to increased cAMP production and strengthening of the synaptic output. (Bii) In this model Ca²⁺ is supposed to transiently accelerate both the formation and dissociation rates (k_A and k_D) of the AC^*/Gα^* complex to the same extent. When the system is in equilibrium (k_A and k_D are the same), Ca²⁺ has no effect on the cAMP level. But when Ca²⁺ influx shortly precedes the transmitter induced activation of Gα^*, the formation (k_A) of AC^*/Gα^* is at this time point the dominant reaction. This leads to a rise in AC^*/Gα^* concentration and thus, enhanced cAMP production. When Ca²⁺ influx follows Gα^*, the dissociation of AC^*/Gα^* is promoted, leading to decreased cAMP production. (Biii) This model can account for trace conditioning by changing the Ca²⁺ decay time constants (different decay time constants chosen are 0.1, 1 and 10 s). The larger decay constants (e.g., 10 s) cause a long tail of Ca²⁺ transient (upper row). This allows for associations of stimuli over longer interstimulus intervals (ISIs; bottom row) and is critical for reproducing the behavioral measurements of trace conditioning. The longer the Ca²⁺ decay time is, the larger the negative “associative” effect is in the simulation. This reveals that lingering Ca²⁺ in KCs might contribute to bridge the temporal gap between CS and US. Note that in this model the US onset is set to 0 and the CS onset shifts to the left for increasing ISIs (CS–US intervals). The negative associative effects correspond to the learned odor avoidance in olfactory aversive delay and trace conditioning. The Ca²⁺ influx is always constant (rising to a Ca²⁺ concentration peak of 6 × 10^-4 mol/L within 40 ms). Adapted from Yarali et al. (2012).