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Neural substrate of dynamic Bayesian inference in the cerebral cortex

Abstract

Dynamic Bayesian inference allows a system to infer the environmental state under conditions of limited sensory observation. Using a goal-reaching task, we found that posterior parietal cortex (PPC) and adjacent posteromedial cortex (PM) implemented the two fundamental features of dynamic Bayesian inference: prediction of hidden states using an internal state transition model and updating the prediction with new sensory evidence. We optically imaged the activity of neurons in mouse PPC and PM layers 2, 3 and 5 in an acoustic virtual-reality system. As mice approached a reward site, anticipatory licking increased even when sound cues were intermittently presented; this was disturbed by PPC silencing. Probabilistic population decoding revealed that neurons in PPC and PM represented goal distances during sound omission (prediction), particularly in PPC layers 3 and 5, and prediction improved with the observation of cue sounds (updating). Our results illustrate how cerebral cortex realizes mental simulation using an action-dependent dynamic model.

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Figure 1: Auditory virtual navigation task.
Figure 2: Two-photon (2P) imaging of neuronal activity in PPC and PM during the task.
Figure 3: Action-dependent distance representation.
Figure 4: Probabilistic decoding.
Figure 5: Goal-distance neurons estimate distance with dynamic Bayesian inference.

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Acknowledgements

We thank the GENIE Program and the Janelia Research Campus for distributing GCaMP6f. We thank S.D. Aird for editing the manuscript and K. Mori for technical assistance. This work was supported by a Grant-in-Aid for Scientific Research on Innovative Areas: Prediction and Decision Making (23120007) (K.D.), KAKENHI 26730124 (A.F.) and 15H01452 (A.F.), and internal funding from the Okinawa Institute of Science and Technology Graduate University (K.D. and B.K.). We are grateful for generous support from the Okinawa Institute of Science and Technology Graduate University to the Neural Computation and Optical Neuroimaging Units.

Author information

Authors and Affiliations

Authors

Contributions

A.F. designed the study, built the setup, collected and analyzed data, and wrote the paper. B.K. designed the study, built the setup and wrote the paper. K.D. designed the study and wrote the paper.

Corresponding author

Correspondence to Kenji Doya.

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Competing interests

The authors declare no competing financial interests.

Integrated supplementary information

Supplementary Figure 1 Action-dependent licking behavior

During no-sound zones in intermittent 1 and intermittent 2 conditions, linear regression analysis compared the increase of licking between slow- and fast-locomotion trials. Trials in each session were equally divided into slow and fast trials. The regression analysis was defined as follows: Lick(t) = β0 + β1t, where β0-1 were regression coefficients. Lick(t) was the licking frequency at time t. Slope of licking (β1) was significantly steeper in fast trials than slow trials, suggesting that mice use action-dependent distance estimation (left, mean ± s.e.m.; right, central mark in box: median, edge of box: 25th and 75th percentiles, whiskers: most extreme data points not considered outliers (beyond 1.5× the inter-quartile range); * P < 0.01 in Wilcoxon signed-rank test, intermittent 1, P = 1.27 × 10-4, z = 3.83, intermittent 2, P = 9.81 × 10-8, z = 5.33) (number of sessions: intermittent 1, n = 94; intermittent 2, n = 94).

Supplementary Figure 2 Muscimol injection in PPC

(a) Injection locations in 3 mice detected with DiI (top). Section is 1.7 mm posterior from bregma11. Spread of muscimol estimated with fluorophore-conjugated muscimol (muscimol-BODIPYR TMR-X conjugate) (bottom). Muscimol-BODIPY was injected in 5 mice (1 left, 2 right, 2 both hemispheres). Injected locations are superimposed on the right hemisphere. Standard muscimol spreads 2 or 3 times farther than muscimol-BODIPY42,43, suggesting that muscimol in our study spread mainly in PPC. (b) Licking behavior in one session after PBS or muscimol injection (first licks red, others black). After muscimol injection, the lick-initiation point became variable. Also, in intermittent 1 condition, mouse tended to receive rewards after overrunning the no-sound zone. (c) Correlation between the start-to-lick distance and start-to-goal distance. Correlation coefficients were significantly lower in muscimol-injected sessions than PBS sessions in both the continuous and intermittent conditions (Mann-Whitney U-test, continuous, P = 4.78 × 10-4, z = 3.49; intermittent, P = 1.96 × 10-4, z = 3.72). (d) Average distance of licking for reward acquisition. Silencing of PPC increased overrun (start licking over 8.3 cm past the goal) (* P < 0.01 in Mann-Whitney U-test, continuous, P = 4.26 × 10-5, z = 4.09; intermittent 1, P = 1.79 × 10-15, z = 7.96; intermittent 2, P = 0.0221, z = 2.29) (Number of trials in PBS and muscimol sessions: continuous, n = 1,407, 1,188; intermittent 1, n = 293, 240; intermittent 2, n = 259, 230).

Supplementary Figure 3 Imaging locations

Imaging locations in each mouse. At each location, neuronal activity was imaged in layers 2, 3 and 5. Some recorded regions covered secondary visual cortex mediomedial area (V2MM) or mediomedial cortex (MM) of the visual area. We analyzed them as a part of the posteromedial cortex (PM).

Supplementary Figure 4 Sound-responsive neurons

(a) Example traces of activity in a single, sound-responsive neuron in response to sound presentation (color indicates sound azimuth, 20 averages). Inset shows sound-azimuth coding in which minimum and maximum activity after sound presentations was normalized to 0 and 1. (b) Sound-responsive neurons. Proportion of sound-responsive neurons with maximum activity in each azimuth (left). PPC or PM neurons preferred 0 and 2π/3 or 0 degrees, respectively. Proportion of sound-responsive neurons per field of view (middle, box plot as in Supplementary Fig. 1, * P < 0.05 in Mann-Whitney U-test, layers 2, 3, 5, P = 0.942, 0.0402, 0.817, z = 0.0731, 2.05, 0.232) (number of sessions in PPC and PM, n = [17, 16], [15, 15], [14, 17]). Latencies of sound responsive neurons (right, * P < 0.05 in Mann-Whitney U-test, P = 0.876, 0.135, 0.0170, z = 0.156, 1.50, 2.39) (number of sound responsive neurons in PPC and PM, n = [356, 373], [108, 334], [61, 63]).

Supplementary Figure 5 Example traces of task-irrelevant neurons

Activity traces of task-irrelevant neurons from the Fig. 2b data set.

Supplementary Figure 6 Neuronal activity represents goal distance but not sound intensity

(a) Regression analysis was used to investigate whether the activity of goal-distance neurons correlated with goal distance (Distance), the distance held constant during no-sound zones (Step), or the sound intensity (Sound). The regression analysis was defined as follows: y(t) = β0 + β1φ(variable(t)), where β0-1 were regression coefficients. y(t) was the unfiltered neural activity trace . variable(t) was either Distance, Step or Sound at frame t. φ is the Gaussian basis function in equation (3). (b) Root mean squared error (RMSE) was compared between the regression analysis of Distance and Step or Distance and Sound. RMSE of Distance was significantly smaller than of other variables both in goal-distance neurons and after-reaching neurons, indicating goal distance representation (box plot as in Supplementary Fig. 1, * P < 0.05 in Wilcoxon signed-rank test, P = 0.0428 to 0, z = 2.03 to 27.0) (number of goal-distance neurons in layers 2, 3, 5: PPC, n = 1,116, 1,054, 483, PM, n = 601, 479, 129) (number of after-reaching neurons: PPC, n = 744, 854, 367, PM, n = 193, 204, 54).

Supplementary Figure 7 After-reaching neurons in individual mice

Every trace shows the average activity of after-reaching neurons in one mouse (PPC n = 6, PM n = 6). Activity traces in continuous and intermittent conditions are shown in different panels (presentation as in Fig. 3c).

Supplementary Figure 8 Regression analysis of after-reaching neurons

(a) Linear regression analysis investigated whether the activity of each after-reaching neuron had a positive slope before the mouse reached the goal (equation (5) and Fig. 3c). Slopes of activity between 25.1 and 8.4 cm, and between 8.4 and 0 cm are shown. Neurons with significantly positive or negative slopes are shown with dark colors (P < 0.05 in two-sided student t-test). Slopes were significantly positive with and without sound in PPC in all conditions, but in PM in intermittent 1 condition they were not significantly positive without sound. (* P < 0.01 in Wilcoxon signed-rank test; PPC with sound, P = 0, z = 13.6 to 25.0; without sound, P = 1.19 × 10-6 to 0, z = 4.86 to 14.1; PM with sound, P = 2.53 × 10-6 to 0, z = 4.71 to 11.7; without sound, P = 0.497 to 9.97 × 10-10, z = 0.679 to 6.11) (number of after-reaching neurons in layers 2, 3, 5: PPC, n = 744, 854, 367; PM, n = 193, 204, 54). (b) Comparison of slopes with and without sound. Colored and white boxes show slopes with and without sound, respectively. Although slopes were significantly positive even without sound in a, they were less steep than those with sound (box plot as in Supplementary Fig. 1, ** P < 0.01 in Wilcoxon signed-rank test, PPC layer 2, P = 0, 0, z = 14.0, 9.89, layer 3, P = 0, 0, z = 18.9, 15.3, layer 5, P = 0, 0, z = 12.3, 9.72; PM layer 2, P = 9.51 × 10-7, 4.24 × 10-9, z = 4.90, 5.87, layer 3, P = 0.00559, 2.47 × 10-7, z = 2.77, 5.16, layer 5, P = 0.00202, 0.118, z = 3.09, 1.56). (c) Comparison of slopes between PPC and PM. In layers 2 and 3, PPC had steeper slopes than PM without sound (*P < 0.05, ** P < 0.01 in Mann-Whitney U-test; 25.1 – 8.4 cm, layer 2, P = 0.142, 0.185, z = 1.47, 1.32, layer 3, P = 2.60 × 10-14, 0.0142, z = 7.62, 2.45, layer 5, P = 0.357, 0.758, z = 0.922, 0.308; 8.4 – 0 cm, layer 2, P = 0.00320, 0.122, z = 2.95, 1.55, layer 3, P = 2.15 × 10-7, 2.79 × 10-6, z = 5.19, 4.69, layer 5, P = 0.209, 0.350, z = 1.26, 0.935).

Supplementary Figure 9 Stability of distance representation among conditions

(a) Neural activity traces. Before-reaching neurons were categorized into 4 groups, depending on the distance preferences in the continuous condition (top 4 columns) (PPC layer 2, n = 82, 53, 66, 171; layer 3, n = 14, 19, 22, 145; layer 5, n = 26, 8, 16, 66; PM layer 2, n = 60, 38, 87, 223; layer 3, n = 23, 16, 76, 160; layer 5, n = 17, 4, 18, 36). Activity of after-reaching neurons is shown in the bottom column (PPC layers 2, 3, 5, n = 744, 854, 367; PM, n = 193, 204, 54). Averaged trace of every neuron was normalized before calculating the mean population activity. (b) Stability of distance representations. Plots show the difference in distance preference between continuous and intermittent conditions and compare PPC and PM (box-plot as in Supplementary Fig. 1, * P < 0.05, ** P < 0.01 in Mann-Whitney U-test; intermittent1, P = 0.808 to 6.82 × 10-14, w = 50, z = 0.249 to 7.49; intermittent2, P = 0.955 to 0.00222, z = 0.0561 to 3.06).

Supplementary Figure 10 Probabilistic decoding in layers 3 and 5

Data presentation as in Figs. 4b–e, but for layers 3 and 5 (* P < 0.01 in Mann-Whitney U-test) (layer 3, Root mean squared error, continuous, P = 0.853 to 0, z = 0.185 to 17.1, intermittent 1, P = 0.956 to 3.33 × 10-16, z = 0.0546 to 8.17, intermittent 2, P = 0.810 to 1.15 × 10-9, z = 0.240 to 6.09; MAP, continuous, P = 0.694 to 1.57 × 10-12, z = 0.394 to 7.07, intermittent 1, P = 0.786 to 0.0308, z = 0.272 to 2.16, intermittent 2, P = 0.901 to 7.32 × 10-4, z = 0.124 to 3.38; s.d. of posterior, P = 3.33 × 10-16 to 0, z = 8.15 to 24.2) (layer 5, Root mean squared error, continuous, P = 4.10 × 10-9 to 0, z = 5.88 to 19.1, intermittent 1, P = 0.197 to 0, z = 1.29 to 11.4, intermittent 2, P = 0.0239 to 0, z = 2.26 to 9.09; MAP, continuous, P = 0.838 to 0, z = 0.204 to 10.5, intermittent 1, P = 0.270 to 1.15 × 10-6, z = 1.10 to 4.86, intermittent 2, P = 0.977 to 2.18 × 10-7, z = 0.0285 to 5.18; s.d. of posterior, P = 0, z = 10.2 to 26.2) (number of trials in PPC and PM: layer 3 continuous, n = 1,581, 1,571; intermittent 1, n = 331, 348; intermittent 2, n = 334, 331; layer 5 continuous, n = 1,445, 1,438; intermittent 1, n = 347, 331; intermittent 2, n = 308, 331).

Supplementary Figure 11 Sound presentation decreases decoding errors

(a) Root mean squared error (RMSE) of decoding. Data is the same as in Fig. 4c and Supplementary Fig. 10, but RMSE was binned each 0.42 cm (median ± robust standard error). (b) Difference of root mean squared error (ΔRMSE). ΔRMSE was defined as the difference of median RMSE between intermittent and continuous conditions. Linear regression analysis tested how ΔRMSE changed with and without sound. The regression analysis was defined as follows: y(distance) = β0 - β1distance, where β0-1 were regression coefficients. y(distance) was ΔRMSE at a distance bin. In some distance zones, slopes of ΔRMSE (β1) significantly decreased with sound or increased without sound (median ± robust standard error, * P < 0.05 in Wilcoxon signed-rank test, P = 0.0353 to 6.10 × 10-4, w = 19 to 102) (number of sessions in layers 2, 3, 5: PPC, n = 17, 15, 14; PM, n = 16, 15, 14). (c) Comparison of ΔRMSE during sound and no-sound zones. Box plot as in Supplementary Fig. 1 (* P < 0.01 in Mann-Whitney U-test: PPC layers 2, 3, 5, P = 2.31 × 10-5, 0.00295, 1.56 × 10-6, z = 4.23, 2.97, 4.80; PM, P = 0.00135, 6.27 × 10-4, 0.188, z = 3.20, 3.42, 1.32) (number of zones in layers 2, 3, 5: PPC, n = 68 (that is, 17 sessions times 4), 60, 56; PM, n = 64, 60, 56).

Supplementary Figure 12 Probabilistic decoding without moving average of neural activity

Data presentation as in Fig. 5, but without moving average of neural activity. In Fig. 5, a 3-frame moving average (97.1 ms) of neural activity was used (Online Methods). Decoding performances without smoothing the activity were similar to the one with 3-frame moving averaged activity, suggesting that distance predictions during no-sound zones were not an artifact of filtering. (a, c) * P < 0.05 in Wilcoxon signed-rank test (median ± robust standard error; a, P = 0.916 to 0, z = 0.106 to 34.4; c, P = 0.989 to 0, z = 0.0141 to 19.1) (number of trials in continuous, intermittent 1 and intermittent 2 conditions: PPC layer 2, n = 1,785, 398, 367; layer 3, n = 1,585, 331, 334; layer 5, n = 1,445, 347, 308; PM layer 2, n = 1,721, 362, 317; layer 3, n = 1,571, 348, 331; layer 5, n = 1,438, 331, 331). (b, d) * P < 0.05, ** P < 0.01 in Mann-Whitney U-test (box plot as in Supplementary Fig. 1; (b) PPC layer 2, P = 0, 0, z = 12.3, 10.7, layer 3, P = 3.33 × 10-16, 0, z = 8.18, 9.15, layer 5, P = 0, 0, z = 11.2, 9.30; PM layer 2, P = 6.21 × 10-8, 8.40 × 10-14, z = 5.41, 7.46, layer 3, P = 1.89 × 10-15, 6.66 × 10-16, z = 7.95, 8.07, layer 5, P = 0.192, 0.00599, z = 1.31, 2.75; (d) PPC layer 2, P = 4.46 × 10-9, 1.99 × 10-5, z = 5.87, 4.27, layer 3, P = 4.14 × 10-6, 0.0183, z = 4.60, 2.36, layer 5, P = 4.95 × 10-12, 1.10 × 10-7, z = 6.91, 5.31; PM layer 2, P = 0.214, 0.142, z = 1.24, 1.47, layer 3, P = 0.0199, 0.00137, z = 2.33, 3.20, layer 5, P = 0.979, 0.434, z = 0.0264, 0.782).

Supplementary Figure 13 Action-dependent distance estimation

Linear regression analysis investigated whether the estimated distance of decoder (maximum a posterior: MAP) depended on the locomotion speed of mice during no-sound zones. The regression analysis was defined as follows: y(t) = β0 + β1t, where β0-1 were regression coefficients. y(t) was MAP at frame t. Trials in each session were equally divided into fast-locomotion and slow-locomotion trials. Slopes of MAPs were steeper in fast trials than slow trials, suggesting action-dependent distance prediction of mice (box plot as in Supplementary Fig. 1, * P < 0.05, ** P < 0.01 in Mann-Whitney U-test, PPC layer 2, P = 3.97 × 10-4, 8.60 × 10-4, z = 3.54, 3.33, layer 3, P = 0.00284, 0.00229, z = 2.98, 3.05, layer 5, P = 0.0869, 0.377, z = 1.71, 0.883; PM layer 2, P = 3.23 × 10-4, 0.616, z = 3.60, 0.502, layer 3, P = 0.00335, 0.821, z = 2.93, 0.226, layer 5, P = 0.0332, 0.0704, z = 2.13, 1.81) (number of slow and fast trials in layers 2, 3, 5 in intermittent 1 condition: PPC, n = [194, 204], [163, 168], [171, 176]; PM, n = [174, 188], [167, 181], [160, 171]) (slow and fast trials in intermittent 2 condition: PPC, n = [177, 190], [162, 172], [148, 160], PM, n = [153, 164], [161, 170], [162, 169]).

Supplementary Figure 14 Dynamic Bayesian inference in cortical microcircuits

Overall neural representations, prediction and updating of decoding were similar between PPC and PM. These regions have similar anatomical connections of motor and sensory inputs. Distance estimation was better in PPC than PM. This might be related to the stronger motor inputs to PPC than PM. Aud: auditory cortex; M2: secondary motor cortex; RSP: retrosplenial cortex.

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Funamizu, A., Kuhn, B. & Doya, K. Neural substrate of dynamic Bayesian inference in the cerebral cortex. Nat Neurosci 19, 1682–1689 (2016). https://doi.org/10.1038/nn.4390

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