Computational model of the distributed representation of operant reward memory: combinatoric engagement of intrinsic and synaptic plasticity mechanisms

Abstract

Operant reward learning of feeding behavior in Aplysia increases the frequency and regularity of biting, as well as biases buccal motor patterns (BMPs) toward ingestion-like BMPs (iBMPs). The engram underlying this memory comprises cells that are part of a central pattern generating (CPG) circuit and includes increases in the intrinsic excitability of identified cells B30, B51, B63, and B65, and increases in B63-B30 and B63-B65 electrical synaptic coupling. To examine the ways in which sites of plasticity (individually and in combination) contribute to memory expression, a model of the CPG was developed. The model included conductance-based descriptions of cells CBI-2, B4, B8, B20, B30, B31, B34, B40, B51, B52, B63, B64, and B65, and their synaptic connections. The model generated patterned activity that resembled physiological BMPs, and implementation of the engram reproduced increases in frequency, regularity, and bias. Combined enhancement of B30, B63, and B65 excitabilities increased BMP frequency and regularity, but not bias toward iBMPs. Individually, B30 increased regularity and bias, B51 increased bias, B63 increased frequency, and B65 decreased all three BMP features. Combined synaptic plasticity contributed primarily to regularity, but also to frequency and bias. B63-B30 coupling contributed to regularity and bias, and B63-B65 coupling contributed to all BMP features. Each site of plasticity altered multiple BMP features simultaneously. Moreover, plasticity loci exhibited mutual dependence and synergism. These results indicate that the memory for operant reward learning emerged from the combinatoric engagement of multiple sites of plasticity.

Figure 1.

The connectome. The connectome of the model represents the topology of monosynaptic connections among cells. Cells highlighted in orange are generally active during the protraction phase of a BMP, whereas cells highlighted in blue are generally active during the retraction phase of a BMP (e.g., Kabotyanski et al. 1998; Jing and Weiss 2001; Jing et al. 2003, 2004; Cropper et al. 2004; Nargeot and Simmers 2012). Activity in closure motor neuron B8 (highlighted in green) shifts between the protraction phase for rBMPs and the retraction phase for iBMPs (see Fig. 3). Note, the network included one hypothetical excitatory connection from B63 to B64 (not shown) because our previous modeling studies indicate that some additional excitatory drive onto B64 is necessary to elicit the retraction phase (Cataldo et al. 2006; see Materials and Methods for details).

Figure 2.

Simulation of BMPs. Activity was elicited by injecting a sustained 1.9 nA depolarizing current into command-like neuron CBI-2. The color code of the voltage traces matches that in Figure 1. The variability among the simulated BMPs resulted from the noise that was included in all simulations. Here, both the somatic and axonal compartments of B31, B51, and B64 (e.g., B31s and B31a, respectively) are illustrated. (A) Control simulation. (B) Simulated activity after incorporating neuronal correlates of operant conditioning. See Figure 4 and text for details related to the implementation of these correlates.

Figure 3.

Methods for analyzing BMPs. Four measures of network activity were used. First, the overall number of BMPs was counted. Three simulated BMPs are illustrated here. Second, BMPs were classified as being iBMPs or other pattern types, such as the depicted rBMPs (see Materials and Methods). Third, the mean, SD, and CV of the inter-burst intervals (IBIs) were calculated. The beginning of a burst was defined as the first spike in B31a, which matches methods used to identify bursts in empirical studies (e.g., Nargeot et al. 1997). Finally, activity maps were generated by counting the number of spikes in each cell during 20 nonoverlapping 1 sec time bins that ranged ±10 sec from the terminus of activity in B31a.

Figure 4.

Implementing neural correlates of operant conditioning. Empirical studies indicate that the memory engram of operant reward learning is encoded as decreases in the input conductance of B30, B63, and B65 (A); increases in the electrical coupling between B63 and B30, and between B63 and B65 (B); increases in the excitability of B30, B63, and B65 (C); and a decrease in the input conductance and an increase in the excitability of B51 (D). In each panel, the black trace represents the control simulations, whereas the red trace represents the simulated neuronal correlate of the memory engram following operant conditioning. (A) The input conductances of B63 (A1), B30 (A2), and B65 (A3) were measured by injecting a −0.5 nA, 2-sec duration current pulse (indicated by bar below trace) into each individual cell. (B) Coupling coefficients were measured by injecting a −1 nA, 2-sec duration current pulse into B63 (left trace) and measuring the voltage deflections in B30 and B65 (traces to right; note change in scale among panels). (C) The excitabilities of B63 (C1), B30 (C2), and B65 (C3) were measured by injecting a 2-sec duration depolarizing current pulse into each cell. The magnitudes of currents were adjusted to be subthreshold in the control simulation (0.4 nA in B63, 0.73 nA in B30, and 0.74 nA in B65). Identical pulses were injected after incorporating neuronal correlates of the memory engram. (D) The input conductance (D1) and excitability (D2) of B51 were measured by injecting 1-sec duration current pulses; either a −0.5 nA pulse to measure input conductance, or a 0.25 nA pulse to measure excitability. In all examples, the cells are embedded within the connectome (see Fig. 1).

Figure 5.

The simulated neuronal correlates of memory altered the functional properties of the network. (A) Memory-induced changes in the total number of BMPs and numbers of iBMPs versus other patterns. The number and types of BMPs were assessed during 20 simulations of 6 min of activity. In the control simulations, overall patterns occurred at a rate of 1.71 ± 0.08 BMPs/min (mean ± standard error), and iBMPs at a rate of 0.43 ± 0.04 BMPs/min. In contrast, the rates during the operant memory simulations were 3.78 ± 0.13 BMPs/min for overall patterns and 1.93 ± 0.07 BMPs/min for iBMPs. Each error bar denotes the standard error of the plot below it. (B) Memory-induced increase in the regularity of rhythmic activity. The inter-burst intervals (IBIs) were measured in control simulations and simulations following the incorporation of neuronal correlates of memory, and the CV was calculated in each case for 15 simulations that had at least 10 BMPs. Changes in CV indicate changes in the regularity with which BMPs occur. Decreases in CV represent greater regularity, whereas increases in CV represent less regularity. Histograms and fitted Gaussian curves show the distribution of all 135 IBIs in each condition (B1), and bar plots show corresponding CVs (B2). (C) Memory-induced reconfiguration of the activity map. Activity maps were generated by averaging the activity in 100 BMPs from control simulations (C1) and from simulations with the total ensemble of operant changes (C2). No distinction was made regarding the classifications of the individual BMPs. Note that, because patterns can occur in close proximity, activity maps may capture spiking from adjacent patterns (e.g., activity in protraction neurons toward the end of retraction). To highlight changes in activity that occurred after learning, the operant memory activity map was subtracted from the control map (C3). This subtraction, which is referred to as a “dynamic memory map,” revealed the changes in average spiking for each cell in the network, regardless of whether they were direct targets of modulation.

Figure 6.

Relationships among passive properties and modeled conductances. Due to the presence of electrical coupling among B30, B63, and B65, changes in one modeled conductance may affect the input conductance and coupling ratio of multiple cells. These effects were accounted for by solving the equations for the input conductances and coupling ratios among B30, B63, and B65 over a range of parameters in a three-neuron circuit (Eqs. 2–6). (A) Diagram of the three-neuron circuit and its component conductances, including leakage conductances (g_leak) and coupling conductances (g_es). An additional conductance (g_others) accounted for voltage-dependent conductances and coupling to neurons omitted from the three-neuron circuit (see Materials and Methods for details). (B) Effects of changes in modeled conductances on the B63–B30 coupling ratio. Although heatmaps display each variable as a function of relative changes in its two most impactful parameters, analytical solutions included all parameters (Eq. 2–6). All changes are relative to control, with “0” indicating no change and “1” a 100% change. Black circle and triangle mark respective positions of the control and operant parameters in parameter space. Black lines denote parameter values that yield no change in the plotted variable. (C) B63–B65 coupling ratio. (D) B30 input conductance. (E) B63 input conductance. (F) B65 input conductance.

Figure 7.

Relative contributions of modified input conductance and electrical coupling to changes in network activity. (A) Decreasing only the input conductances of B30, B63, and B65 led to a large increase in motor pattern rate and reduced bias toward iBMPs. Conversely, increasing only the coupling ratio among these cells led to a smaller increase in rate, and to an increased bias toward iBMPs (n = 20 for each group). (B) Both changes in input conductance (G_in) and coupling ratio (CR) led to an increase in regularity (reduction in CV; n = 15 for each group). (C) Control-subtracted activity maps for changes in input conductances (C1) or coupling ratios (C2). Both sets of changes led to distinct activity reconfiguration, neither of which fully recapitulated the reconfiguration induced by operant memory (see Fig. 5D). (D) Motor pattern rate over a range of changes to input conductances and coupling ratios among B30, B63, and B65. Both variables contributed to BMP rate, although input conductance had a larger effect. Dashed black lines denote the effects of changing one variable while keeping the other constant at control values. White line denotes the diminished effect of varying coupling ratios when input conductances are reduced by 25%. Changes in coupling ratios and input conductances are relative to control, with “0” indicating no change and “1” a 100% change. A total of 95 unique sets of parameters were simulated. (E) Contribution of changes in input conductances or coupling ratios to motor pattern regularity. Both variables affected regularity. The various peaks and valleys indicate that unique combinations of changes may have unique effects on regularity. White line denotes the diminished effect of varying input conductances when coupling ratios were increased by 75%. Surface plots on panels D and E display median values for simulations ran over a subset of the parameter space. Note that CVs were only calculated for a further reduced subset of the parameter space (60 out of 95 unique parameter sets) in which simulations generated at least 10 BMPs over 6 min.

Figure 8.

The relative contributions of individual sites of plasticity in isolation. (A) Contribution of each site of plasticity to pattern rate and bias (n = 20 for each group). Notably, changes in the input conductance of B51 contributed a strong bias toward iBMPs at the cost of a small reduction in overall rate, whereas changes in the input conductance of B63 contributed a large increase in pattern rate at the cost of a decrease in bias toward iBMPs. (B) Contribution of each site to BMP regularity (n = 15 for each group). The input conductance of B30 and each of the two coupling ratios all contributed to a decrease in CV. Simulations used to calculate the CV (but not BMP rate) for B51 and B65 input conductances were extended from 6 to 10 min so as to obtain 10 BMPs for CV calculation in each simulation.