PMC

Dependence of fade-out and merging of mnemonic activity bumps on set size. The fraction of mnemonic activity bumps that fade out (black) or merge with each other (gray) during a 9 s delay is plotted as a function of set size. When set size is below WM capacity (3 in A with wide connectivity, 6 in B with narrow connectivity), activity bumps seldom fade out or merge. For a set size above WM capacity, the probabilities for merging and fade-out increase sharply. With a sufficiently large set size, a plateau is reached where the sum of the fade-out and merging probabilities is ∼100%, hence an activity bump either fades out or merges with another bump.

Network model structure and simulation protocol. A, Model scheme. The network is composed of spiking excitatory pyramidal cells (Exc) and inhibitory interneurons (Inh). Pyramidal cells are uniformly placed on a ring, labeled by their preferred directions (shown by arrows). The connections between pyramidal cells are structured as a Gaussian function of the difference in the preferred directions (top), and the connections onto and from the interneurons are uniform. B, Simulation protocol. A cue array is presented to the network from 0.25 s to 0.5 s, followed by a delay period up to 9 s. C, D, Sample cue arrays of 6 uniformly and randomly distributed directions, respectively.

Performance fit using different models. The simulation uses the wide-connectivity network and random cue arrays. A, Typical response offset histograms for set size 3 and 6 (left and right, respectively) with 1 s delay, fitted by discrete-slot model (P_m and s.d., red line) and our model (S.D., green line). B, P_m and P_c decrease as a sigmoid function of set size (delay duration is 1 s). P_c at high threshold (blue line) decreases more smoothly than that at low threshold (black line), which resembles P_m. C, s.d. and S.D. increase as a sigmoid function of set size (delay duration is 1 s). s.d. reaches a plateau as set size is >4 (capacity). D, P_m and P_c decrease as a function of delay duration (set size is 4 at the capacity); P_c at low threshold is nearly constant against the time. E, s.d. and S.D. increase as a function of delay duration (set size is 4 at the capacity); s.d. is nearly constant against the time.

The effects of delay duration on performance. A, Same sample trials as in A, except shown for a 9 s delay. For a set size, 4, near WM capacity (lower left), bump fade-out or merging may occur late in the delay. B, Top, WM capacity depends on the delay duration and the E-E connections (left for wide; right for narrow connectivity). Bottom, SD increases as a function of set size for different delay durations, with wide (left) or narrow (right) connectivity. The network performance is essentially independent of the delay duration for small or large set size. However, for an intermediate set size, the performance of the network deteriorates with a prolonged delay period, as found in the human experiment (). C, The set size at which SD reaches a threshold level (10°) is linear with WM capacity for all the conditions considered, different delays, and narrow and wide connectivities.

Performance as a function of size set in a change-detection task. A, Experimental scheme of a change-detection task. In each trial, network views a cue array (with 2, 4, 6 or 8 colors) and a test array (with the same set size as the cue), separated by a 1 s delay, and identifies whether they are the same. In half of the trials, the test arrays are identical to the cue arrays, namely same trials, where the amplitude of change is 0°, while in the other half of the trials, one color in the cue array is changed to a color with an amplitude from 10° to 90° away from its value, namely diff trials. B, A downstream match-nonmatch neural circuit underlies the probability of responding to same. C, Hit rate decreases and false-alarm rate increases as a function of set size. D, Psychometric curves show the probability to respond to different as a function of the amplitude of change, |θ_in − θ_test|, for different set sizes. E, Performance curve from CDT mimics that from DRT, showing that the change-detection performance (the probability of correct response) would decrease when the set size increases.

WM capacity depends on E-E connections. A, Dependence of WM capacity on E-E connectivity. The WM capacity is color coded and shown on the plane of two parameters characterizing E-E connections: the strength J⁺ and spatial width σ. When J⁺ is too weak or σ is too small (navy), the persistent activity is absent. Outside of that region, WM capacity ranges from 2 to 7; it is larger with more narrowly structured local synaptic excitation (smaller σ), which needs to be compensated by larger connection strength J⁺ to ensure sufficient recurrent excitation for WM maintenance. For a fixed J⁺ = 4.02, WM capacity increases at first and then decreases with the increasing connection width, peaking at 7 (vertical white line). For a fixed σ = 5°, WM capacity increases with the increasing connection strength (horizontal white line). B, C, Performance of a narrow connectivity network (×a in A) with uniform and random cue arrays. Correct rate and SD show a step-like transition as set size increases for uniform cue arrays (black), while there is a smooth function for random cue arrays (red). All the fitting curves are sigmoid functions. D, The relative precision for random cue arrays exhibits power-law dependence on set size. The total width of activity bumps (E) and average firing rate of pyramidal cells (F) are normalized for both uniformly and randomly distributed arrays of directional cues.

Neural spiking activity, WM performance and normalization. The network has a wide E-E connectivity. A, Spatiotemporal neural activity pattern of pyramidal cells in response to an array of 2, 3, 4, or 6 directions. Pyramidal cells are labeled along the y-axis according to the preferred directions. The x-axis represents time. Firing rate is color coded. After being briefly presented during the cue period (marked as C on x-axis), each stimulus evokes a bell-shaped activity pattern of localized pyramidal cells (bump). In the lower right panel, some activity bumps fade out, some merge with each other, while all the elicited activity bumps in the other three panels persist in a 1 s delay period. Notably, the width of persistent activity bumps decreases with the set size. B–D, The performance of the network. B, The product of the set size and its correct rate of the reports exhibits a maximum. The corresponding set size defines WM capacity. WM capacity is smaller with longer delay duration. C, The correct rate is ∼100% for a set size below WM capacity, but declines sharply to ∼20% for a set size above it. D, SD is ∼2° for a set size below WM capacity, and sharply increases to ∼18° for a set size above it. E, F, A constant memory resource by network normalization. The total width of mnemonic activity bumps (E) and average firing rate of pyramidal cells (F) are almost invariant to set sizes, and roughly the same for 1 s and 9 s delays.

Behavioral manifestation of merging in the change-detection task and free-recall task. A, Merging happens even when two cues are sufficiently separated from each other: θ_in,1 = 130° and θ_in,2 = 230° (white arrows) in DRTs. Two stimuli evoke two activity bumps, which eventually merge into a single wide bump. Therefore, the reports bias to the center of θ_in,1 and θ_in,2. B, The distribution of the difference between the report and the original cue, θ_in,2 − θ_out,2 or θ_out,1 − θ_in,1 (θ_in,1 < θ_in,2), across 100 trials. A positive (respectively, negative) distance from the original cue implies convergence (respectively, divergence) of two activity bumps. The distribution skews significantly to the positive side, indicating that merging happens in a large amount of trials. Such a skewed distribution of reports can be tested in behavioral experiments. C, Experimental scheme of a change-detection task to test merging. In each trial, network views a cue array (3 colors) and a test array, separated by a 1 s delay, and identifies whether they are the same. Three types of cues, i.e., far (low-similarity), close (high-similarity), and far+close, and three types of tests, i.e., same, diff1 (divergent side), and diff2 (convergent side; changed colors in diff1 and diff2 are circled) are applied in the task; the task is a mixture of same (50%) and diff1 (50%) tests. D1, D2, A sample from far+close trials (2 greens + 1 blue) exhibits a merging process between 2 greens (a, b), the memory traces of which converge to an intermediate level (still greens); the memory trace of the blue (c) only drifts around its initial cue. D3, Distributions of the response offset in different trials. That with low similarity (black bars) centers at 0°; that with high similarity (red bars) shows a strong bias to the convergent side (>0°). E, Performance for each test. Low- and high-similarity trials show similar performance in the same test (upper left). High-similarity trials show a better performance in the diff1 test (upper right), indicating that similarity of the cue array improves the change-detection performance in the task (lower left), whereas it also shows that the similarity could deteriorate the performance in the diff2 test (lower right).

Dynamics of persistent, fade-out, and merging activity bumps in WM delay. The network has a narrow connectivity. A, Spatiotemporal activity in response to a brief stimulus of uniform cue arrays with 6 items (capacity). All activity bumps persist throughout the delay. White lines are memory traces. The spatial distribution of pyramidal cells' firing rate (last 1 s in the delay) shows a bell-shaped profile (activity bump). B, Same as in A except for a set size above WM capacity. Two bumps (67.5° and 337.5°) fade out, and two bumps (247.5° and 292.5°) merge into one wide bump. The other bumps persist throughout the delay. The activity profile shows a wide plateau for the merging bumps and comparatively sharp peaks for the persistent bumps. C, Firing activity of single neurons marked as a, b, and c in B. Left, Neurons near the peak of a persistent bump (22.5°) spike at a high rate in the cueing stage and show persistent activity at ∼50 Hz during the delay. Middle, Neurons in a fade-out bump (67.5°) abruptly drop their activities in the middle of the delay, implying a sudden death of the corresponding item. Right, Firing activity of neurons (from 247.5° to 292.5°) within and between two bumps that eventually merge into one. Neurons within bumps (e.g., red) behave in a manner similar to those in the left panel. Neurons at the edge of bumps (e.g., yellow) are not boosted by the cue stimulus, but their firing rates gradually ramp up to a stable level during the delay. Neurons in the middle of two bumps (e.g., dark green, ∼270°) spike at a low rate in the early phase and suddenly jump to persistent activity in the late delay. D, E, The feedback dynamics between neural firing and recurrent excitatory drive (data from B). D, Instantaneous average firing rate, R(t), of each bump as a function of time. M, P, and F denote merging, persistent, and fade-out bumps, respectively. R(t) values of fade-out bumps suddenly drop to 0 Hz at a random time in WM delay as an all-or-none process. R(t) values of persistent bumps stay at ∼25 Hz with small fluctuations. R(t) values of merging bumps gradually increase (black) or jump (yellow) to ∼45 Hz after merging. E, Instantaneous average excitatory synaptic conductance, G(t), of each activity bump as a function of time. G(t) values of fade-out bumps quickly decay to ∼28 nS preceding the sudden decreases of R(t); G(t) values of merging bumps increase above 35 nS (larger than the maximum value of G(t) of persistent bumps) preceding the merging process. F, The average firing rate R̄ plotted against the average excitatory synaptic conductance Ḡ for different activity bumps (from 100 simulations using the same network and cue arrays as those in B). Three activity groups can be clearly discerned: merging bumps (blue) have high R̄ and Ḡ, while fade-out bumps (black) have low R̄ and Ḡ.