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Targeted photostimulation uncovers circuit motifs supporting short-term memory

Nature Neuroscience volume 24, pages 259–265 (2021)Cite this article

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Abstract

Short-term memory is associated with persistent neural activity that is maintained by positive feedback between neurons. To explore the neural circuit motifs that produce memory-related persistent activity, we measured coupling between functionally characterized motor cortex neurons in mice performing a memory-guided response task. Targeted two-photon photostimulation of small (<10) groups of neurons produced sparse calcium responses in coupled neurons over approximately 100 μm. Neurons with similar task-related selectivity were preferentially coupled. Photostimulation of different groups of neurons modulated activity in different subpopulations of coupled neurons. Responses of stimulated and coupled neurons persisted for seconds, far outlasting the duration of the photostimuli. Photostimuli produced behavioral biases that were predictable based on the selectivity of the perturbed neuronal population, even though photostimulation preceded the behavioral response by seconds. Our results suggest that memory-related neural circuits contain intercalated, recurrently connected modules, which can independently maintain selective persistent activity.

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Fig. 1: Targeted photostimulation during performance of the delayed-response task.
Fig. 2: Network response to targeted photostimulation.
Fig. 3: Functional connectivity depends on response type.
Fig. 4: Photostimulation causes predictable changes in behavior.
Fig. 5: Modular network architecture can explain sparse and persistent photostimulation responses.
Fig. 6: Behavioral biases in a modular network.

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Data availability

Two-photon imaging and photostimulation data are available at Figshare (https://doi.org/10.25378/janelia.13546157).

Code availability

Code for network models is available at the Github repository (https://github.com/kpdaie/Daie_targeted_photostim_2020).

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Acknowledgements

We thank R. Darshan, B. Mohar, A. Finkelstein, H. Inagaki, S. Romani, A. Singh, M. Pachitariu and S. Peron for comments on the manuscript; T. Pluntke and R. Mohar for animal training; X. Zhang, K. Ritola and H. Inagaki for making the ST ChrimsonR constructs; E. Fardone for histology; and P. Rickgauer, I. Fiete, B. Kang and T. Wang for discussions. This work was funded by the Howard Hughes Medical Institute. K.D. is a Helen Hay Whitney Foundation postdoctoral fellow and was supported by the Simons Collaboration on the Global Brain.

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Authors and Affiliations

  1. Janelia Research Campus, Howard Hughes Medical Institute, Ashburn, VA, USA

    Kayvon Daie, Karel Svoboda & Shaul Druckmann

  2. Stanford University, Stanford, CA, USA

    Shaul Druckmann

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  1. Kayvon Daie
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Contributions

K.D., K.S. and S.D. conceived and designed the experiments. K.D. performed the experiments and modeling. K.D., K.S. and S.D. analyzed the data and wrote the paper.

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Correspondence to Karel Svoboda or Shaul Druckmann.

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Extended data

Extended Data Fig. 1 Coexpression of GCaMP6s and ST-chrimsonR and microscope for simultaneous imaging and targeted photostimulation.

After experiments brains were harvested and sectioned (100 µm coronal sections). Images show co-expression of GCaMP6s (green) and ST-chrimsonR-FusionRed (red) from a section that was under the cranial window (n = 1 mouse). b, Schematic of the microscope. Photostimulation laser, 1040 nm (Fidelity HP, Coherent); Imaging laser, 920 nm (Chameleon Ultra II, Coherent); GG, pair of 3 mm galvanometer mirrors (Cambridge, 6215H); ETL, electric tunable lens, (EL-10–30-C, Optotune); SL 2, scan lens photostimulation path, 33 mm focal length, a stack of 3 × 100 mm focal length lenses (AC-254-100b, Thorlabs); SL 1, scan lens imaging path, 30 mm focal length (55-S30-16T, Special Optics); DM, 1000 nm short-pass dichroic mirror (Edmund optics); TL, Tube lens 160 mm focal length (Special Optics); Obj., 16x objective, 0.8 NA, 3 mm working distance (CFI75 LWD, Nikon); PMT, photomultiplier tubes (H10770(P)B-40, Hamamatsu). c, Optical point-spread functions. Measurements were made by imaging 500 nm fluorescent beads (YG, Polysciences). Reported values correspond to the full-width at half maximum.

Extended Data Fig. 2 Trial-type selectivity.

a, Left, map of selectivity for individual neurons in one behavioral session. Selectivity was calculated as the difference in activity on correct right and left trials at the end of the delay epoch. Selective neurons were distributed across the field of view. Right, neurons displayed heterogeneous dynamics. Dashed lines, the sample, delay and response epochs. b, Selectivity of the neural population based on fluorescence measurements. For each behavioral session all neurons were categorized based on their selectivity at each time point: \(V_i^{sel.} = {\mathrm{Sign}}\left( {\langle f_{i,j}^{R,non}(t)\rangle _{_{j = correct\,trials\,train,\,t = epoch}} - \langle f_{i,j}^{L,non}(t)\rangle _{_{j = correct\,trials\,train,\,t = epoch}}} \right)\) where trial averaging was performed over a randomly-chosen training subset of 20% of correct trials denoted as ‘correct trials train’. tepoch refers to the 2 s window centered on the end of the delay. The remaining 80% of trials (correct trials test, test subset) were used to compute the population selectivity (PS(t)) as: \(PS(t) = 1/\sqrt {(N)} \sum _{i = 1...N}\)\(\left( {\langle f_{i,j}^{R,non.}(t)\rangle _{j = correct\,trials\,test} - \langle f_{i,j}^{L,non.}(t)\rangle _{j = correct\,trials\,test}} \right)V_i^{sel.}\) where N is the number of neurons in the FOV. Dashed lines, sample, delay and response epochs; (Errorshade s.e.m. across sessions; n = 84 sessions). c, Number of selective neurons. A one-tailed T-test was used to compare the epoch-averaged activity on left and right trials for each neuron: \(\bar f_{i,j}^{R,non.} = \langle f_{i,j}^{R,non.}(t)\rangle _{t = epoch}\) & \(\bar f_{i,j}^{L,non.} = \langle f_{i,j}^{L,non.}(t)\rangle _{t = epoch}\) Selective neurons are defined as neurons with p < 0.05. The epoch labeled ‘Late Delay/Early responses’ corresponds to the last 0.5 s of the delay and the first 0.5 s of the response, this is the window for which selectivity was calculated throughout the paper. (n = 8 mice, data presented as mean number of neurons with p < 0.05; errorbars, s.e.m.).

Extended Data Fig. 3 Electrophysiology during targeted photostimulation.

a, Position of photostimulation beam (reconstructed from galvo position encoders). Photostimulation was performed in a spiral pattern (red) that lasted for 3 ms. Laser power was then turned off for 1 ms while the beam was redirected to the next neuron in the sequence (cyan). After the last (8th) neuron was photostimulated the beam was directed back to the first neuron. b, Full photostimulation scan trajectory. The sequence across neurons was repeated 10 times per trial and is shown as a trace for the x-position (top) and y-position (bottom). Colors denote laser power state (cyan: off, red: on). (c-f), Loose-seal, cell-attached recordings during photostimulation in anesthetized mice. Single neurons (n = 7) were photostimulated using the pattern shown in Extended Data Fig. 3a with laser power of either 50, 100 or 150 mW. c. Response of a targeted neuron to photostimulation. Each trace is the response to one train of ten photostimuli (3 ms spirals, 28-ms inter-spiral interval) Magenta bars, photostimuli (150 mW). d, Spikes evoked by single photostimuli as a function of laser power. The weakest photostimuli (50 mW) failed to drive spikes in most neurons. All photostimulation experiments done during behavior used either 100 or 150 mW, which evoked on the order of one spike per photostimulus. e, Spike latency as a function of laser power. The spike latency for 150 mW was 5 ± 2 ms (b-c, mean ± s.e.m.). Colored lines, data from individual neurons. f, Simultaneous GCaMP6s fluorescence and extracellular voltage of one neuron, showing that photostimulation (150 mW) produced increases in spiking that were associated with large increases in fluorescence. Top: spike raster. Each row corresponds to a trial. Spikes marked as vertical lines. Bottom: Trial-averaged fluorescence response. Fluorescence transient decayed with a 1 s time constant, consistent with previous observations21, and much faster than decay observed when photostimulating groups of neurons during the delay epoch.

Extended Data Fig. 4 Spatial resolution of photostimulation.

a, Lateral resolution in awake, non-behaving mice. Normalized fluorescence response vs. lateral displacement of the photostimulus with: Δ activity (normalized) = (fpost,xy−fpre,xy)/(fpost,0−fpre,0). fpre,xy, average fluorescence before photostimulation (150 ms); fpost,xy, fluorescence averaged immediately after the photostimulation (1 s) with a lateral displacement of xy micrometers from the imaged cell. Changes in activity were limited to a radius of less than 30 micrometers (FWHM, 8 μm). b, Axial resolution. Δnorm.(z) vs. axial displacement of photostimulus (FWHM, 80 μm). (a-b, n = 9 neurons from one mouse, 10 trials for each photostimulus location) c, Additional resolution measurements in behaving mice. Left, groups of 8 neurons (red) and 8 non-neuronal spots (cyan) were targeted for photostimulation. Right, photostimulation of the non-neuronal spots produced only weak activation within 20 microns of the photostimulus. We therefore treat neurons located 30 microns or more from a target neuron throughout as ‘coupled’. Neurons within 20 μm of a target with altered activity were ‘directly photostimulated’. (n = 4 photostim. groups from 2 sessions in 1 mouse; a-c, data presented as mean ± s.e.m.). d, Characterization of off-target effects of photostimulation in three dimensions. We imaged 4 planes (n = 3 mice) or 5 planes (n = 1) (350 × 310 μm per plane) separated by 40 μm along the axial dimension. Individual non-neuronal spots were photostimulated in the most superficial plane. e, Total number of neurons excited (neurons with p < 0.05, one-tailed T-test compared to non-photostim. trials) following photostimulation of individual non-neuronal spots. Neurons located more than 50 μm along the lateral dimension from the targets were excluded from this analysis to restrict detection of excitation to directly photostimulated neurons. Photostimulation of non-neuronal spots with 150 mW excited 3 neurons on average (range 0—9.6, 95% CI, magenta circles, p < 0.05, one-tailed T-test). 50 mW photostimuli excited 1 neuron on average (range 0–5, 95% CI, black circles). Given the relatively low density of selective neurons (~20% of the population), these off-target spikes will be mostly in non-selective neurons. (Bar heights, mean number of neurons.) f, The amplitude of excitation within 20 μm of the photostimulation beam decays along the axial dimension with σaxial = 30 μm for 50 mW σaxial = 48 μm for 150 mW photostimulation (dashed lines) in agreement with ours and previous45,46 measurements. (Error shade, s.e.m. across targeted spots; b-c, n = 27 spots, 150 mW; n = 38 sites, 50 mW). g, The number of coupled neurons in a 350 × 310 μm field-of-view observed during behavior increases with increasing power from 5 (range, 1–9, 75% CI) at 50 mW up to 18 (range, 8–34) for 150 mW. The number of coupled neurons detected during 50 mW photostimulation was not distinguishable (p = 0.5, T-test) from the estimated false positive rate of 4 neurons. High power photostimulation therefore improves our ability to probe circuit connectivity. (Bar heights, mean number of neurons.) h-k, Spatial spread of photostimulation with 50 mW (i), 100 mW (j) and 150 mW (k) along the axial dimension measured using volumetric imaging during behavior. At 0, 40, 80 and 120 μm below the photostimulation plane excitation decreases with increasing lateral distance from the photostimulus. Excitation is strong in regions directly beneath the photostimulus even when using 50 mW suggesting that much of this out of plane excitation is related to synaptic coupling in a column47. Error bars, s.e.m. l-m, Selectivity of the targeted neurons vs. selectivity of all directly photostimulated neurons from volumetric imaging experiments. The strong correlation (Pearson correlation, 0.95, 50 mW (c); 0.83 150 mW (d)) indicates that the selectivity of each photostimulation group is dominated by the targeted neurons. n, Estimating off-target effects of photostimulation. The photostimulation PSF was modeled as \(Ne^{ - xy^2/\sigma _{lat.}^2 - z^2/\sigma _{ax.}^2}\), where N is the number of spikes produced by the photostimulus (Extended Data Fig. 3) and the widths σ are calculated based on the FWHM values reported in Extended Data Fig. 4. The number of directly photostimulated neurons and total spikes per photostimulus was estimated using this PSF and the estimated density of cortical pyramidal neurons48 (105/mm3). Strong photostimuli (150 mW) were estimated to produce an additional 0.94 spikes per spike in the target neuron, distributed across 2–3 non-targeted neurons. Weaker photostimuli (50 mW) have better spatial resolution46, resulting in a modest reduction in the estimated number of off-target spikes, but also a reduction in the number of target spikes.

Extended Data Fig. 5 Dynamics of activity-dependent fluorescence.

a, GCaMP6s fluorescence decay after short bursts of spiking activity from visual cortex neurons simultaneously recorded with cell-attached electrophysiology in anaesthetized mice21,44. The decay time constant (τ) was defined as the time at which the activity decays to 1/e of its peak value. τ’s were 1.2 s, 1 s, 1 s and 0.9 s following bursts of 1, 2, 3 or 4 action potentials respectively. Average fluorescence response kernel was extracted according to the following equation: \(\kappa _{GCaMP6s} = Ae^{ - t/\tau _{{\mathrm{decay}}}}(1 - e^{ - t/\tau _{{\mathrm{rise}}}})\); A = 0.31 τdecay = 0.87 s and τrise = 0.06 s. b, Deconvolved fluorescence. Smoothed (MATLAB; csaps, P = 0.96) Δ activity (pg) (Fig. 2b) were deconvolved with κGCaMP6s to estimate the spiking dynamics. 95% of photostimulation groups produce changes in estimated spike rate that remain elevated 2 seconds or longer following photostimulation. c, ALM contains neurons in which selectivity peaks at the end of the delay epoch and rapidly decays to zero following the response cue45. This rapid decay of firing rate can be used to estimate GCaMP6s τ’s during behavior46. Extracellular electrophysiological recordings of example neurons with late-delay right (top) and left (bottom) selectivity45. d, Two-photon imaging of activity in neurons with moderate to strong late delay epoch selectivity (Defined as neurons with p < 0.2; two-tailed T-test) and with weak response epoch selectivity (Two-tailed T-test, p > 0.2; mean, 13.5 neurons per session, range, 6–22). Top, average response of R neurons. Bottom, average response of L neurons. e, Average population selectivity (Extended Data Fig. 2b) of delay selective neurons from d. From the electrophysiological recordings, we assume that spike rate selectivity of these neurons drops to zero. Population selectivity calculated from fluorescence decayed with τ = 0.98 s following the end of the delay, consistent with the measured decay times of GCaMP6s in panel a. This is expected to be an upper bound on the GCaMP6s fluorescence τ because selectivity in some of these neurons may not instantaneously drop to zero and produce erroneously long estimates of τ. f, Comparison of persistence during behavioral task vs. non-task periods. The same groups of neurons were photostimulated during behavior and immediately after the animal completed the behavioral session (3 mice, n = 4 sessions, 10 photostimulation groups). Average Δ activity decayed more slowly during the task than in the non-task period. (d-f, Errorshade, s.e.m across photostimulation groups). g, Decay time constants for each directly photostimulated neuron (84 neurons) during the task (τtask) and during the non-task period (τnon-task). τtask (mean, 3.1 s, range, 1.8 s — 4.3 s, 75% CI) were longer than τnon-task (mean, 1.7 s, range, 1.2–2.4, 75% CI; p < 10−5, two-tailed T-test; errorbars, s.e.m.).

Extended Data Fig. 6 Functional connectivity.

a-b, Relation between coupling strength and selectivity of photostimulation is qualitatively similar whether considering selectivity of targeted neurons or directly activated neurons. a, Coupling strength (ΔR and ΔL) vs. average selectivity of directly photostimulated neurons (plot is the same as Fig. 3b). Data were binned in quintiles along x-axis (Error bars, s.e.m.). b, Coupling strength vs. average selectivity of targeted neurons. Data were binned in quintiles along x-axis (Error bars, s.e.m., n = 215 photostimulation groups, 8 mice). c-d, Coupling strength during behavioral task and non-task period (n = 3 mice, n = 4 sessions, n = 10 photostimulation groups). c, Δ activity of directly photostimulated neurons during the non-task period immediately following the conclusion of the behavioral session vs. Δ activity during the task. Response amplitudes were correlated, but the amplitude of excitation is generally much lower (p < 10−5, two-tailed T-test) during the non-task period (mean, 0.33, 0.03–0.66, 75% CI) vs. during the task (mean, 0.51, 0.10–0.93, 75% CI). d, Δ activity of coupled neurons is also much smaller during the non-task period than during the task (p < 10−5, two-tailed T-test).

Extended Data Fig. 7 Effect of photostimulation on behavior.

a, Behavioral performance during a single session. Performance dropped from 73/105 correct (69%) on non-photostimulation lick left trials to 14/38 (37%) on photostimulation group 1 trials. b, A bootstrap distribution of performance on non-photostimulation trials was generated by randomly sampling 38 of the 105 non-photostimulation trials 10,000 times (b, bottom left). For each of the 10,000 random samplings, we counted the number of correct trials to determine the p-value for each photostimulation group. Bootstrap distributions were used to determine the 95% confidence intervals in Fig. 4a. Changes in performance on left and right trials were uncorrelated for each photostimulation group (p = 0.27). This is consistent with the fact that left trials and right trials have very different dynamics, producing different interactions with the same photostimulation c, Cumulative distribution of p-values (Two-sided bootstrap (panel b)). from individual sessions (bars from a) for photostimulation (black) and non-photostimulation (white) trials. Gray bar, 95% confidence interval of bootstrap; white line, mean cumulative distribution. Inset: Distribution of photostimulation groups with p < 0.05 for photostimulation (black) and non-photostimulation trials (gray). d, Δ correct vs. change in activity along a ‘coding direction’ (CD) which maximally separates trial-averaged activity14. CD was calculated using a subset of trials. Single-trial activity from non-photostimulation (top) and photostimulation trials (bottom) was projected along the CD. The relationship between CD activity and behavior was similar for photostimulation and non-photostimulation trials because photostimulation triggered only sparse changes in population activity. e, Schematic, photostimulated change in neural population in activity space. To take into account changes caused by photostimulation compared to trial-to-trial changes we computed the photostimulation vector (Methods). f, Left, photostimulation vector, contributions of individual neurons. Right, selectivity of individual neurons (Si, Methods). g, Activated population selectivity is the dot product of selectivity (Si) and the photostimulation vector. h, % change in behavioral choice vs. selectivity of directly photostimulated neurons. Data are from an additional 3 mice (separate from the main figures). Large groups (25 neurons) were photostimulated for the full delay epoch (1 s) (Error bars, s.e.m.; n = 27 photostimulation groups, 3 mice). i, Absolute value of % change in behavioral choice vs. selectivity of directly photostimulated neurons (Pearson correlation, 0.1; p = 0.035). Dots, average for a single photostimulation group for 1 trial type (right or left trials). Filled circles, mean in equal-spaced bins. Right, magnification of binned data to illustrate trend (Same data as Fig. 4c,d; error bars, s.e.m; n = 215 photostimulation groups, 8 mice).

Extended Data Fig. 8 Models.

a-b, Non-modular models fail to recapitulate experimental findings. a, Δ activity of a line attractor model to targeted photostimulation of 8 neurons. Photostimulated activity spreads throughout the network. Magenta bars, timing and location of photostimulation. b, Δ activity of a discrete attractor model to targeted photostimulation of 8 neurons. This model responds transiently to targeted photostimulation because of the non-linear synaptic connections. See Methods for description of models. c-d, Δ activity in models including thalamus and ALM also require modular connectivity. ALM and thalamus are strongly coupled and both contain delay epoch selectivity33. c, Response of model with modular thalamocortical connections to targeted photostimulation of 8 neurons. d. Response of model with modular cortico-cortical connections to targeted photostimulation of 8 neurons. Top, model schematic. Bottom, Δ activity. Model recapitulates the sparse persistent responses to photostimulation. Magenta bars, timing and location of photostimulation. e-g, Metrics of modularity from analyzing eigenvalues of subsampled connectivity matrices are consistent with modular structure in networks inferred from the data. The non-modular network in Fig. 4h has a single persistent mode (eigenvalue equal to 1), whereas the modular network has 10 such modes. We develop an analysis aimed at determining which of these two models more closely resembles the connectivity inferred from the data in Fig. 5i,j. e, Eigenvalues of subsampled networks. If we were to draw a box around one of the modules in Fig. 5g, we would find that the maximum eigenvalue of this subnetwork is 1, whereas an equivalent box in the non-modular model in Fig. 5h would have a maximum eigenvalue of 0.48. To extend this ‘local eigenvalue’ analysis to the inferred networks in Fig. 5i,j we wouldn’t know which neurons to draw this box around, so to make the analysis more general, we instead draw many boxes at random locations along the diagonal and calculate the maximum eigenvalue of subnetwork within the box. f, Modular networks have higher maximum eigenvalue in subsampled networks. Bars indicate the mean of the maximal eigenvalue across 215 subsampled networks for non-modular networks (left) and modular networks (right). On average, the modular network has larger local eigenvalues (mean, 0.94, range, 0.84–1.0, 75% CI) than the non-modular network (mean, 0.62, range, 0.61–63, 75% CI; error bars, s.e.m.). g, Maximal eigenvalue in subsampled networks from inferred connectivity implies modular structure. For the inferred connectivity matrix (Fig. 5i,j), we identify all neurons within 70 µm of a photostimulation target whose activity was significantly perturbed by photostimulation (\(p_i^{pg}\)<0.05, methods), and calculate the maximum eigenvalue of this subnetwork. Bars indicate the mean of the maximal eigenvalue across 215 subsampled networks for inferred connectivity from non-photostimulated data alone (left) and data with both non-photostimulated trials and photostimulated trials (right). We find that the largest local eigenvalue in networks trained to match photostimulation and non-photostimulation trials was similar to the modular network in Fig. 4g (mean, 0.98, range 0.75–1.27, 75% CI, n = 215 networks). Networks trained to match the activity during non-photostimulation trials only h, had a maximum eigenvalue that were similar to the non-modular network (mean, 0.41, range, 0.19–0.62, 75% CI). h, Connection weights in networks inferred from non-photostimulated data. Connection weights from presynaptic R (top panel), & L (bottom panel) neurons onto post-synaptic R (blue) and L (red) neurons as a function of distance between neurons. (n = 215 photostimulation groups, 8 mice; Error bars, s.e.m.) i-j, Probing spatial scale of modularity with single-target photostimuli. i, We photostimulated either 1) a group of eight neurons (8 target) or 2) individual neurons from the group (1 target; n = 4 mice). Traces along diagonal, responses of the targeted neurons (magenta). Neurons within the group were not coupled (off diagonal black traces). j, Δ activity vs. lateral distance to nearest target. Excitatory coupling was the same for both 1 target (black) and 8 target (magenta) photostimulation suggesting an absence of cooperativity between neurons in photostimulation groups. 8 target photostimulation produces enhanced inhibition compared with 1 target photostimuli suggesting competitive inhibition between neurons in the photostimulation groups. (Error bars, s.e.m.).

Extended Data Fig. 9 Network models of responses to both global inhibition and local excitation.

Modular network behavior for different strength and sign of inter-modular connections. The modular network shown in Fig. 5g has inter-modular connections with mean −0.5/M and a range from −1/M to 0. Here we vary the mean and amplitude of these inter-modular connections so that inter-module connections have both an excitatory and inhibitory component: \(w_{inter} = \alpha _{ex}w_{ex} + \alpha _{inh}w_{inh}\). The scaling factors α determine the respective maximum eigenvalues and were varied from α=0 to α=1. a, Heatmap shows difference of activity of all neurons between simulations in which a single module is stimulated and simulations in which no modules were stimulated. Each sub-panel corresponds to a specific values of αex and αinh. b, Change in behavioral output as a function of selectivity of target neurons for each pair of αex and αinh.

Extended Data Fig. 10 Modular networks.

Two models that match both the current data and previous findings on robustness to global photoinhibition15. a-e, Robustness through intermodular connections. a, Schematic of coarse graining. Magenta traces show the response of the network to broad photoinhibition illustrating the network’s robustness to these particular perturbations. Trained networks recovered from photoinhibition and produced graded persistent activity. (Errorshade, s.e.m across repetitions (n = 10)). c, Δ activity of each module during photoinhibition. d-e, Persistent sparse responses to local excitation. d, Average Δ activity of 3 simultaneously photostimulated modules. We note that the persistent response is a consequence of the assumed long intrinsic modular time constants. e, Sparse network response (Fig. 2a, Fig. 5f). Δ activity of all modules following photostimulation of modules 1–3. f-j, Hybrid discrete/continuous attractor model14. f, Schematic of the two simulated units. g, Shape of the non-linear synaptic function. h, Large amplitude inhibition of both neurons produces a rapid recovery. Activity of each of the two simulated neurons is shown for control (dashed line) and perturbation trials (non-dashed). Magenta line shows the duration of inhibition. Perturbation was delivered along the [1,1] direction and thus recovery is fast. Shading indicates s.e.m across 100 simulated trials. i, Local excitation produces long transient. Trace, response of one of the units to a brief photostimulation. Magenta line, timing and location of photostimulation. Shading, s.e.m across 100 simulated trials. j, Modular hybrid network. Left, schematic of network with ten weakly interacting 100 neuron modules with the synaptic non-linearity shown in g. Right, targeted photostimulation of 8 neurons (magenta lines) produces sparse and persistent activity as in experimental results.

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Daie, K., Svoboda, K. & Druckmann, S. Targeted photostimulation uncovers circuit motifs supporting short-term memory. Nat Neurosci 24, 259–265 (2021). https://doi.org/10.1038/s41593-020-00776-3

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