Consequences of parameter differences in a model of short-term persistent spiking buffers provided by pyramidal cells in entorhinal cortex

Abstract

In previous simulations of hippocampus-dependent and prefrontal cortex-dependent tasks, we demonstrated the use of one-shot short-term buffering with time compression that may be achieved through persistent spiking activity during theta rhythm. A biophysically plausible implementation of such a first-in first-out buffer of short sequences of spike patterns includes noise and differences between the parameter values of individual model pyramidal cells. We show that a specific set of parameters determines model buffer capacity and buffer function, and individual differences can have consequences similar to those of noise. The set of parameters includes the frequency of network theta rhythm and the strength of recurrent inhibition (affecting capacity), as well as the time constants of the characteristic after-depolarizing response and the phase of afferent input during theta rhythm (affecting buffer function). Given a sufficient number of pyramidal cells in layer II of entorhinal cortex, and in each self-selected category of pyramidal cells with similar model parameters, buffer function within a category is reliable with category-specific properties. Properties include buffering of spikes in the order of inputs or in the reversed order. Multiple property sets may enable parallel buffers with different capacities, which may underlie differences of place field sizes and may interact with grid cell firing in a separate population of layer II stellate cells in the entorhinal cortex.

Figure 1

Short-term buffering based on persistent spiking. (a) Model responses of the cholinergically modulated after-depolarization (ADP) of a pyramidal neuron in layer II of the entorhinal cortex. Injecting current over 400 ms at low levels of acetylcholine (ACh) causes transitory spikes. At high levels of acetylcholine, repetitive spiking of the pyramidal neuron persists at a rate determined by the time course of ADP. When we include the effect of modulated membrane potential at theta rhythm, persistent spiking occurs regularly at the same phase of the theta cycle. (b) Short sequences of patterns of simultaneous spikes are sustained by the buffer. Spiking representations of items A to F, consisting of five or six spikes each (a total of 32 spiking neurons), enter the buffer at successive onset times. Buffered spike patterns are reactivated in their order of acquisition during each theta cycle. The spiking representation of A is terminated as E appears, and B is terminated as F appears, demonstrating first-in-first-out queuing with a capacity for sequences of four spiking patterns.

Figure 2

The membrane response of one neuron in each of the item representations A to F, during spike buffering in order and during item replacement. The simulation included a population of 29 persistent firing pyramidal neurons, of which subsets of two to eight spiking neurons represented individual items. (a) Four items are buffered before replacement occurs. The membrane response of each neuron exhibits spikes at order-specific phases of rhythmic buffer cycles, as well as subsequent hyperpolarization and the onset of an after-depolarizing response. (b) The expanded time scale of a small section of the simulation output shows buffer reactivation and item replacement. Recurrent “gamma” inhibition causes hyperpolarizing dips of pyramidal membrane potentials throughout the network at regular intervals that follow each spiking pattern. The spikes of consecutive reactivated spike patterns are separated by an interval small enough, so that spike-timing dependent potentiation (STDP) can be elicited in associative networks that receive the output of the buffer. “Replacement inhibition” elicited by a neural mechanism for first-in-first-out item replacement appears at the onset of buffered spike reactivation when input appears in a full buffer.

Figure 3

The membrane potentials of one neuron in each of six item representations (A to F), sustained in a reversed order buffer. During the simulation, each item was represented by a subset of five (A,C,E,F) or six (B,D) spiking neurons from a population of 32 model pyramidal cells. The buffer model uses no explicit item replacement mechanism, but demonstrates five item capacity in this simulation.

Figure 4

Simulations with noise in the model of six buffered items (A to F), each represented by spike patterns that initially elicit between two and eight spikes (total of 29 spiking neurons). Sustained spiking at low levels of noise is shown in Figure 1b. (a) At strong noise levels, an initial selection of spikes that reactivate in the same gamma interval is sustained for each item representation (13 of the 29 neurons). (b) When noise levels are elevated further, those representations exhibit separation into adjacent gamma intervals and a gradual drop-out of spikes (examples indicated by “separation” and “drop-out” arrows). Despite the separation of spikes in each pattern, the order of spikes sustained for consecutive items was not violated in these simulations, so that the order of item representations in a buffered sequence was maintained.

Figure 5

Correct reversed buffer spiking for 15 items (A to O) represented by 4 spiking neurons per item, with a buffer capacity of five items (e.g. K,L,M,N,O). The simulated buffer model did not utilize transmission modulation to regulate afferent and recurrent activity.

Figure 6

The membrane potential of one neuron in each of five reversed order buffered items (A to E), simulated with model pyramidal neurons that exhibit after-depolarization responses that span more than two theta cycles. The full simulation involved first-in first-out reversed order buffering of fifteen items, each of which was represented by four spiking neurons.

Figure 7

Simulated spike responses of five reversed order buffered item representations (A to E, with four spiking neurons each) in which pyramidal neurons were modeled with differences in the individual after-depolarization response rise time constant. Sustained spikes of neurons three and four drop-out (“dropout” arrows). The sustained spikes of neuron eight, though initially elicited as part of the representation of the third item, become associated with the representation of the second item (“shift” arrow).

Figure 8

Simulated forward order buffering in models with modified theta and gamma intervals. (a) Reduced theta frequency in a simulation with seven consecutive items (A to G) represented by patterns of three to five spikes each (a total of 26 spiking neurons). The increased duration of the theta cycles was able to accomodate the sustained reactivation of all seven spike patterns. (b) Stronger network-wide recurrent “gamma” inhibition in a simulation with six items represented by patterns of five or six spikes each. Buffer capacity was reduced to three items.

Figure 9

Membrane potential of pyramidal neurons in a simulated buffer with network-wide weak inhibition by “gamma” interneurons, with two items represented by two spiking neurons each. After about seven cycles of reactivation of the second buffered item representation, the two consecutive spike patterns merge into a single pattern of synchronous spikes. The membrane potential responses shown here were the result of a simulation with a buffer containing 32 persistent firing pyramidal cells, of which subsets of five or six spiking neurons represented six different items.

Figure 10

Spike responses during simulated reverse ordered buffering with differences between the strength of recurrent inhibition experienced by individual buffer neurons. (a) Three item representations (A to C) consisting of four spikes each, when some model neurons experience stronger “gamma” inhibition. Spiking of neuron three is delayed during buffer cycles between t = 1100 ms and t = 1500 ms (“delayed” arrow), but is then realigned. The difference of recurrent inhibition experienced by neuron four causes drop-out of its spiking after t = 1400 ms (“drop-out” arrow). (Note the difference in time scale compared to other figures.) (b) Eight item representations (A to H) consisting of four spikes each, when some model neurons experience weaker “gamma” inhibition. After t = 3000 ms, the spiking neurons three and four become aligned and therefore associated with spike patterns sustaining items different that the two they had previously been aligned with (“shift” arrows).

Figure 11

The relationship between effective hippocampal place fields and buffer capacity. Black curved lines indicate positions during a spatial task, at which the onset of spiking of a place cell (numbered 1 to 6) registers as input to ECII. Buffering that spike until three more input items are received results in the effective place field indicated by the cross-hatched area. If the spike is lost only after five more input items are received, then the effective place field is indicated by the cross-hatched plus right-diagonal area.

Figure 12

Simulated responses of the membrane potential of specialized populations of pyramidal neurons and interneurons that may interact to elicit first-in first-out item replacement in a persistent firing short-term buffer. The P_ADP unit shown represents the combined activity of all intrinsic spiking pyramidal neurons in our model of layer II of entorhinal cortex. The Pf unit represents pyramidal neurons that activate once during each theta cycle in which the buffer is filled to capacity, while the Pi unit represents pyramidal neurons that activate once during each theta cycle in which afferent input elicits activity in the buffer. Dotted circles indicate the buffer activity during three spurious “full buffer” spikes. The Ir unit represents interneurons that receive input from Pf and Pi neurons. Ir spikes exert replacement inhibition at P_ADP buffer pyramidal neurons. The response trace of Ir interneurons shows two occasions that elicit replacement inhibition spikes, namely when the fifth and sixth afferent input stimuli appear.