Spike-timing theory of working memory

Abstract

Working memory (WM) is the part of the brain's memory system that provides temporary storage and manipulation of information necessary for cognition. Although WM has limited capacity at any given time, it has vast memory content in the sense that it acts on the brain's nearly infinite repertoire of lifetime long-term memories. Using simulations, we show that large memory content and WM functionality emerge spontaneously if we take the spike-timing nature of neuronal processing into account. Here, memories are represented by extensively overlapping groups of neurons that exhibit stereotypical time-locked spatiotemporal spike-timing patterns, called polychronous patterns; and synapses forming such polychronous neuronal groups (PNGs) are subject to associative synaptic plasticity in the form of both long-term and short-term spike-timing dependent plasticity. While long-term potentiation is essential in PNG formation, we show how short-term plasticity can temporarily strengthen the synapses of selected PNGs and lead to an increase in the spontaneous reactivation rate of these PNGs. This increased reactivation rate, consistent with in vivo recordings during WM tasks, results in high interspike interval variability and irregular, yet systematically changing, elevated firing rate profiles within the neurons of the selected PNGs. Additionally, our theory explains the relationship between such slowly changing firing rates and precisely timed spikes, and it reveals a novel relationship between WM and the perception of time on the order of seconds.

Figure 1. Illustration of polychronous neuronal groups and associative short-term plasticity.

(A) Synaptic connections between neurons n1, n2, …, n7 have different axonal conduction delays arranged such that the network forms two functional subnetworks, red and black, corresponding to two distinct PNGs, consisting of the same neurons. Firing of neurons n1 and n2 can trigger the whole red or black PNG: (B) If neuron n1 fires followed by neuron n2 10 ms later, then the spiking activity will start propagating along the red subnetwork, resulting in the precisely timed, i.e., polychronous, firing sequence of neurons n3,n4,n5,n6,n7, and in the short-term potentiation of the red synapses. (C) If neurons n2 and n1 fire in reverse order with the appropriate timings, activity will propagate along the black subnetwork making the same set of neurons fire but in a different order: n7,n5,n3,n6,n4, which temporarily strengthens the black synapses. Readout: post-synaptic neurons that receive weak connections from neurons n3, n4, and n5 with long delays and from neurons n6 and n7 with shorter delays (or, alternatively, briefly excited by the activity of the former and slowly inhibited by the latter) will fire selectively when the red polychronous pattern is activated, and hence could serve as an appropriate readout of the red subnetwork. A similar readout mechanism is illustrated in .

Figure 2. Associative short-term plasticity implemented in a form of short-term-STDP or via simulated NMDA receptors resulting in NMDA spikes.

(A) The synaptic change is triggered by the classical STDP protocol at time “stimulation” (marked by arrows) but the change decays to 0 (baseline) within a few seconds. Left panel shows that firing of only pre- or post-synaptic neurons does not trigger any synaptic change. The middle panel illustrates that firing in the order pre-before-post induces short-term augmentation, as opposed to the post-before-pre (Right panel) resulting in short-term depression. (B–C) Short-term amplification of synaptic responses via simulated NMDA receptors resulting in NMDA spikes. (B) Schematic diagram showing a multi-compartmental neuron (post) receiving a synapse from a pre-synaptic neuron (pre). (C) A train of presynaptic spikes is followed by a postsynaptic response delayed by 10 ms and caused by other synaptic inputs. Each pre-synaptic spike activates postsynaptic NMDA receptors and deactivates with time constant of 250 ms. (D) Persistent pre-then-post train of action potentials flips the dendritic compartment into up-state. While in the up-state, each pre-synaptic spike results in a large-amplitude dendritic excitatory postsynaptic potential (black trace V (dendritic)), often called NMDA spike, that can propagate to the soma and enhance the efficacy of the synaptic transmission in eliciting somatic spike. The red trace shows the control simulation when the post-synaptic spikes are absent: No significant increase in synaptic efficacy is observed in this case. Similarly, post-before-pre patterns do not result in significant enhancement of synaptic transmission unless the timing is such that there is a residual depolarization when pre-synaptic spike arrives, or there is a residual glutamate in synaptic cleft from the previous pre-spike when post neuron fired. The voltage traces in sub-panel (D) are simulations of a passive dendritic compartment with voltage-dependent NMDA conductance.

Figure 3. Properties of the emerging polychronous neuronal groups.

(A) The number of emerging distinct PNGs equals 7825 for the network/simulation used (described in Methods). On average, a PNG consists of 41 neurons, (B) and their average duration is 88 milliseconds. (C) Each PNG shares at least 10 neurons, on average, with 1050 other groups. 5% of neurons of any particular group are shared with any other group in the network (not shown). (D) Distribution of frequencies of activation of PNGs in the simulated and surrogate (inverted time) spike trains. Surrogate data emphasize the statistical significance of these events. Modified with permission from . (E, F) Each neuron participates in different groups.

Figure 4. Spike timing nature of working memory - Maintenance of a polychronous neuronal group in working memory.

(A) Bottom: Spike raster of a single trial: Blue dots, firing of all excitatory neurons in the network (inhibitory neurons not shown); Red dots, spikes of the neurons belonging to the selected target PNG (tPNG) during reactivations of the tPNG. tPNG activated in WM at seconds (see Methods). (A) Top: Average multiunit firing rate and short-term synaptic change for tPNG (red) and for the rest of the excitatory neurons (blue). The green curve illustrates how the short-term change would decay back to baseline in the absence of neural activity after stimulation. (B) Magnified spike rasters of two partial reactivations of the tPNG neurons at two different times: Red dots, spikes of tPNG neurons; Circles, expected firings (see Methods) of all neurons in the tPNG. Only neurons belonging to the tPNG are shown. (C) CV, inter-spike interval variability histogram for tPNG neurons: Red, tPNG in WM (notice high CV values); Blue, spontaneous network activity, no PNG in WM (spike raster not shown). (D) Cross-correlograms of two neurons from the tPNG: Red, tPNG in WM; Blue, spontaneous network activity. (E) Average firing rate histogram of three representative tPNG neurons (red) while the tPNG in WM, and of a control neuron (blue) from the rest of the network. (F) Histogram of the duration of PNGs put separately in WM: time of the last reactivation (after the offset of stimulation) of each PNG versus number of PNGs with a given maximum reactivation span.

Figure 5. Multiple overlapping polychronous neuronal groups in working memory.

(A) Spike raster and firing rate plots as in Figure 4. The first, red target PNG (tPNG) is activated at time 0 seconds; the second, black tPNG at time 5 seconds. The two PNGs co-exist in WM even though they share more than 25% or their neurons, which fire with different polychronous patterns. (B) Capacity tested by multiple items in WM. (C) Magnified plot of the spike rasters (red/black dots) of partial activation of the two tPNGs — red (left) and the black (right). Notation as in Figure 4B. (D) Red, left: cross-correlograms of two neurons that are part of the red but not the black PNG, when only the red PNG is in WM ( sec). Black, middle: cross-correlograms of neurons that are part of the black but not the red PNG, when only the black PNG is in WM (spike raster not shown). Right: cross-correlograms of two neurons, one from each target PNG, when both PNGs are in WM ( sec).

Figure 6. Novel cue in working memory - Formation of new polychronous neuronal groups.

(A–C) Over 90 second long spike raster: Blue dots, spikes of excitatory neurons; Cyan dots, spikes of inhibitory neurons. Red colored dots denote the spikes of 60 randomly selected excitatory neurons that received external stimulation with a polychronous pattern 10 times per second every 15 seconds (arrows). The pattern used for stimulation represents the external sensory input generated by a novel cue. This pattern does not correspond to the firing pattern of any of the existing PNGs. (A) 0.3 Hz non-specific noisy minis. (B) 0.1 Hz minis when . (C) Short-term STDP blocked when . (A,B,C) Identical conditions when . (D, E) The [74 … 83] second segment of the spike raster data of A and B are magnified in D and E, respectively. (A,D) In the presence of sufficient non-specific drive and short-term STDP, after repeated presentations a new PNG — representing the novel cue — emerges and gets frequently activated (about 4 Hz). (D) Neurons that became part of the new PNG initiated by the spiking of red neurons are marked black. The new group consists of 24 (out of 60) red and 118 black excitatory neurons. Notice that 36 of the stimulated red neurons did not become part of the newly formed PNG probably due to the lack of appropriate synaptic connections. (B,E,C) Hardly any replay in B and E, and no replay at all in C. Hampered PNG formation as WM mechanism was prevented.