Event timing affects associative learning.

<p>Fruit flies are trained such that a control odour is presented alone, whereas a trained odour is paired with pulses of electric shock as reinforcement. Across groups, the inter-stimulus interval (ISI) between the onsets of the trained odour and shock is varied. Here, ISI is defined such that for negative ISI values, the trained odour precedes shock; positive ISI values mean that the trained odour follows shock. For each ISI, two fly subgroups are trained with switched roles for two odours (not shown). During the test, each subgroup is given the choice between the two odours; the difference between their preferences is taken as the learning index. Positive learning indices indicate conditioned approach to the trained odour, negative values reflect conditioned avoidance. Very long training ISIs support no significant conditioned behaviour. If the odour shortly precedes or overlaps with shock during training (ISI = −45 s, −15 s or 0 s), it is strongly avoided in the test (punishment learning). If the odour closely follows the shock-offset during training (ISI = 20 s or 40 s), flies approach it in the test (relief learning). *: <i>P</i><0.05/8 while comparing to zero in a sign test. Sample sizes are N = 8, 24, 34, 47, 24, 35, 12 and 12. Data from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032885#pone.0032885-Yarali2" target="_blank">[15]</a>, with permission from Informa healthcare.</p

Influence of the transmitter duration.

<p>With a fixed Ca⁺⁺ input, three different transmitter inputs are tested (top). They are all initiated at 210 s, rise to a peak of 7·10⁴ molecules/µm² within 40 ms after the onset, but decay with different time constants as indicated above the panels. We plot the resulting adenylate cyclase dynamics (middle) and the ISI-dependent associative effects (bottom). In terms of the percent sizes of associative effects, changing the transmitter decay time constant from 0.1 to 1 (the first two cases) hardly makes a difference. A slower decaying transmitter input (the last case) broadens the dynamics of adenylate cyclase activation/deactivation, resulting in much higher cAMP production in the control condition; thus, the percent associative effects remain small. As for the ISI-dependence of the associative effects, short transmitter inputs (the first two cases) give good fits to the situation in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032885#pone-0032885-g001" target="_blank">Fig. 1</a>; when a slower decaying transmitter input is used (the last case), the positive associative effect only occurs for large positive ISIs, due to the broadened adenylate cyclase activation/deactivation dynamics.</p

Influence of Ca⁺⁺ duration and intensity.

<p>Complementing the analysis shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032885#pone-0032885-g007" target="_blank">Fig. 7</a> we now vary the Ca⁺⁺ input while keeping the transmitter input fixed. In all three examples shown in (A), the Ca⁺⁺ input rises to a peak of 6·10⁻⁴ moles/L within 40 ms after the Ca⁺⁺ onset, but decays with different time constants, chosen as 0.1 s, 1 s and 10 s (A, top). In this scenario, the associative effects increase with increasing Ca⁺⁺ duration (A, bottom). In addition, a large decay constant causes a long tail of the Ca⁺⁺ input that enables negative associative effects for longer ISIs (A, the last case). In (B) we provide an exemplary Ca⁺⁺ input (B, top) which gives good fit to the behavioural results in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032885#pone-0032885-g001" target="_blank">Fig. 1</a> in terms of the ISI-dependency of the associative effects but not in terms of their sizes relative to each other (B, bottom). In this case, the Ca⁺⁺ concentration rises to a peak of 6·10⁻⁴ moles/L within 13 s after the onset, comparing well with the 15s- long odour presentation in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032885#pone-0032885-g001" target="_blank">Fig. 1</a>. Note that the best negative associative effect occurs with ISI = −13 s, similar to the behavioural situation in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032885#pone-0032885-g001" target="_blank">Fig. 1</a>. Finally, in (C), we study the effects of the intensity of the Ca⁺⁺ input. We fix the transmitter input and use the Ca⁺⁺ input depicted in (B), but scaled up and down by one order of magnitude. The intensity of Ca⁺⁺ strongly influences the sizes of both the negative and the positive associative effects; the balance between the two is however somewhat compromised with increasing Ca⁺⁺ intensity.</p

Components and initial concentrations for the first model.

<p>All values were chosen according to <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032885#pone.0032885-Rospars1" target="_blank">[46]</a> and were estimates from moth olfactory transduction (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032885#pone.0032885-Rospars1" target="_blank">[46]</a> for further references).</p

Relative timing of the transmitter and Ca⁺⁺ affects the adenylate cyclase.

<p>We stimulate the model with transmitter and Ca⁺⁺ (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032885#pone-0032885-g003" target="_blank">Fig. 3B</a> for the details). In the ‘control condition’ (left), Ca⁺⁺ precedes the transmitter by an onset-to-onset interval of 210 s. In ‘associative training’ (right), the two inputs follow each other with an inter-stimulus interval (ISI), which is varied across experiments. Negative ISIs indicate training with first Ca⁺⁺ and then the transmitter; positive ISIs mean the opposite sequence of inputs. For either condition, we take the area under the respective Gα*/AC* concentration curve as a measure of cAMP production. For each ISI, we calculate an ‘associative effect’, by subtracting the amount of cAMP produced during the respective associative training from that in the control condition. We then express the associative effect as percent of the area under the Gα*/AC* concentration curve in the control condition. These percent associative effects are plotted against the ISIs. For very large ISIs, we find no associative effect. If the Ca⁺⁺ is closely paired with the transmitter, we find negative associative effects; the strongest negative associative effect (−15.5%) is obtained when using ISI ∼−3 s. If on the other hand Ca⁺⁺ follows the offset of the transmitter during training, we find positive associative effects; the largest positive associative effect (6.3%) is obtained for ISI ∼26 s. Thus, depending on the relative timing of Ca⁺⁺ and transmitter during training, opposing associative effects come about, closely matching the behavioural situation in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032885#pone-0032885-g001" target="_blank">Fig. 1</a>.</p

Rate constants of the reactions for the first model.

<p>Apart from k₅ and k_-5, all values were chosen according to <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032885#pone.0032885-Rospars1" target="_blank">[46]</a>. Thus, k₁, k_-1, k₂, k_-2 were estimates from moth olfactory transduction or vertebrate phototransduction (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032885#pone.0032885-Rospars1" target="_blank">[46]</a> for further references). For the parameters k₅ and k_-5 (see also Eqs. 13 and 14), the listed base-line values were chosen to mimic the experimentally measured dynamics of adenylate cyclase activation/deactivation in response to transmitter <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032885#pone.0032885-Abrams3" target="_blank">[42]</a>, for a detailed sensitivity-analysis, see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032885#pone-0032885-g005" target="_blank">Fig. 5A</a>. k₅ and k_-5 were sensitive to Ca⁺⁺ (Eqs. 13 and 14).</p

Regulation of the adenylate cyclase by the transmitter and Ca⁺⁺.

<p>A. Adapting the model of Rospars et al. <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032885#pone.0032885-Rospars1" target="_blank">[46]</a>, the transmitter reversibly binds to its respective G protein coupled receptor (GPCR) to form a complex, resulting in reversible receptor activation (GPCR*). GPRC* catalyzes the dissociation of the trimeric G protein (Gαβγ) into an activated α-subunit (Gα*) and the β- and γ-subunits (Gβγ). Gα* spontaneously deactivates (Gα) and reassembles with Gβγ, or it reversibly interacts with the adenylate cyclase (AC) to form an enzymatically active complex (Gα*/AC*), which serves as the output. Following data from <i>Aplysia </i><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032885#pone.0032885-Yovell1" target="_blank">[41]</a>–<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032885#pone.0032885-Onyike1" target="_blank">[43]</a>, Ca⁺⁺ in turn transiently increases the rate constants for both the formation and the dissociation of the Gα*/AC* complex (represented by the thickened arrows). The k_subscript denote the rate constants of the respective reactions. B. When this model is stimulated with a transmitter input alone the Gα*/AC* concentration rises to a peak of ∼0.42 molecules/µm² in ∼20 s after stimulus onset, and decays back to zero within the next ∼100 s (left). If a Ca⁺⁺ input immediately precedes the transmitter, the build-up of the Gα*/AC* concentration is transiently accelerated (middle). If on the other hand the Ca⁺⁺ input follows the transmitter, the decay of the Gα*/AC* concentration is transiently accelerated (right). For graphical reasons, normalized concentrations are calculated by dividing with the peak Gα*/AC* concentration given transmitter input alone. The transmitter concentration reaches a peak of ∼6.7·10⁴ molecules/µm² in ∼7 s and decays back to zero within ∼18 s; the Ca⁺⁺ concentration starts rising ∼4.5 s after the onset, reaches a peak value of 5.6·10⁻⁴ moles/L at ∼6 s and decays back to zero within ∼8.5 s after the onset. Also these inputs are plotted as normalized concentrations.</p

Adenylate cyclase as a molecular coincidence detector.

<p>In a variety of associative learning systems, a potential coincidence between the trained stimulus and the reinforcement is detected at the pre-synapse by a particular kind of adenylate cyclase. The stimulus acts on the respective neurons, raising the intracellular Ca⁺⁺ concentration. The reinforcement induces the release of a transmitter that binds to its respective G protein coupled receptors (GPCR) on the very same neurons and activates the G protein (G*). If stimulus and reinforcement are appropriately timed, the two types of input act synergistically on the adenylate cyclase (AC*), triggering cAMP signalling, and thus lead to the strengthening of the output from these neurons to the respective conditioned behaviour pathway.</p

Rate constants of the reactions for the alternative model.

<p>All parameter values were as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032885#pone.0032885-Adams1" target="_blank">[45]</a> and thus measured or estimates from neutrophil actin polymerization (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032885#pone.0032885-Adams1" target="_blank">[45]</a> for further references). k₅ and k_-5, which are not included in the table, changed upon stimulation with Ca⁺⁺ (Eqs. 13 and 14); their base-line values were varied in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032885#pone-0032885-g010" target="_blank">Fig. 10</a>.</p

Components and initial concentrations for the alternative model.

<p>Apart from the initial concentrations of AC and G*/AC*, values were as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032885#pone.0032885-Adams1" target="_blank">[45]</a> and thus estimates from neutrophil actin polymerization (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032885#pone.0032885-Adams1" target="_blank">[45]</a> for further references).</p