Abstract
Gradual accumulation of evidence is thought to be fundamental for decision-making, and its neural correlates have been found in several brain regions1,2,3,4,5,6,7,8. Here we develop a generalizable method to measure tuning curves that specify the relationship between neural responses and mentally accumulated evidence, and apply it to distinguish the encoding of decision variables in posterior parietal cortex and prefrontal cortex (frontal orienting fields, FOF). We recorded the firing rates of neurons in posterior parietal cortex and FOF from rats performing a perceptual decision-making task. Classical analyses uncovered correlates of accumulating evidence, similar to previous observations in primates and also similar across the two regions. However, tuning curve assays revealed that while the posterior parietal cortex encodes a graded value of the accumulating evidence, the FOF has a more categorical encoding that indicates, throughout the trial, the decision provisionally favoured by the evidence accumulated so far. Contrary to current views3,5,7,8,9, this suggests that premotor activity in the frontal cortex does not have a role in the accumulation process, but instead has a more categorical function, such as transforming accumulated evidence into a discrete choice. To probe causally the role of FOF activity, we optogenetically silenced it during different time points of the trial. Consistent with a role in committing to a categorical choice at the end of the evidence accumulation process, but not consistent with a role during the accumulation itself, a behavioural effect was observed only when FOF silencing occurred at the end of the perceptual stimulus. Our results place important constraints on the circuit logic of brain regions involved in decision-making.
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Acknowledgements
We thank K. Deisseroth for support with optogenetics. We thank A. Akrami, T. Buschman, J. Gold, B. Pesaran, B. Scott, D. Tank and M. Yartsev for comments on the manuscript. We thank A. Begelfer, K. Osorio and J. Teran for animal and laboratory support. T.D.H. was supported by National Institutes of Health (NIH) Award Number F32MH098572. C.A.D. was supported by a Howard Hughes Medical Institute predoctoral fellowship. C.D.K. was supported in part by the NIH Award Number T32MH065214.
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T.D.H., B.W.B., C.A.D. and J.C.E. collected electrophysiological data. T.D.H. analysed electrophysiological data. J.C.E. played an advisory role on electrophysiological experiments. C.D.K. carried out the optogenetic experiments, with assistance from B.W.B. C.D.K. analysed the optogenetics data, with input and assistance from T.D.H. and J.C.E. T.D.H., C.D.K. and C.D.B. wrote the paper. C.D.B. was involved in all aspects of experimental design and data analysis.
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Extended data figures and tables
Extended Data Figure 1 Rat behaviour and example neurons.
a, Mean psychometric function across all rats. Accuracy was highest for the largest click differences (the left and right endpoints of the curve) and lower for smaller click differences (the middle of the curve). b, Mean chronometric function across all rats. Trials were sorted by binned stimulus strength (difficulty), with mean click ratios ranging from 39:1 clicks s−1 for the easiest trials to 25:15 clicks s−1 for the hardest trials. In general, accuracy improved with longer stimulus durations. c, Mean psychophysical reverse correlation across all rats. This was calculated based on trials with minimum duration of at least 0.6 s. For each time point in each trial, we first computed the excess click rate difference (right − left clicks s−1) relative to the value expected given the random processes used to generate the trial. These excess click rates were averaged separately for trials ending with a right choice (red) and for trials ending with a left choice (green). The separation between the two traces indicates how strongly clicks from the corresponding time point influence the final decision. d, Peri-event time histograms (PETHs) aligned to stimulus onset were calculated for three example PPC neurons. Trials were sorted into four stimulus strength bins for each neuron. Green traces correspond to the preferred-direction stimuli and red traces correspond to anti-preferred-direction stimuli. Darker colours correspond to stronger stimuli (less difficult) and brighter colours correspond to weaker stimuli (more difficult). e, PETHs for three example FOF neurons using the same conventions. In both regions, individual neurons exhibit ramping activity that depends on stimulus strength.
Extended Data Figure 2 Behavioural model (ref. 10).
a, At each time point, the accumulator a (black trace) represents an estimate of the ‘right’ versus ‘left’ evidence accrued so far. At stimulus end, the model decides ‘right’ if a > Þ (the decision borderline) and ‘left’ otherwise, in which Þ is a free parameter. Light grey traces indicate alternative runs with different instantiations of model noise. These example trajectories are for illustrative purposes; the model estimates the full probability distribution of a at each time point. Right ↑ (left ↓) clicks change the value of a by positive (negative) impulses of magnitude C. 
is a diffusion constant, parameterizing noise in a. 
parameterizes noise associated with each click. λ parameterizes consistent drift in the decision variable a. In the ‘leaky’ case (λ < 0, illustrated), drift is towards a = 0, and later clicks impact the decision more than earlier clicks. In the ‘unstable’ case (λ > 0), drift is away from a = 0, and earlier clicks effect the decision more than later clicks. The time constant of the accumulation process is τ = 1/λ. B is the height of sticky decision bounds. If a reaches either bound, it leads to decision commitment before the end of the stimulus and later clicks have no effect on the choice. ϕ, τϕ parameterize sensory adaptation by defining the dynamics of C. Immediately after a click, the magnitude C is multiplied by ϕ. C then recovers towards an unadapted value of 1 with time constant τϕ. Facilitation thus corresponds to ϕ > 1, while depression corresponds to ϕ < 1. These properties are implemented by the following equations: if |a| ≥ B then da/dt = 0; else
are delta functions at the times of the auditory clicks. η are independent and identically distributed (i.i.d.) Gaussian variables drawn from N(1,σs). dW is a white-noise Wiener process. Adaptation dynamics are given by:
In addition, a lapse rate parameterizes the fraction of trials on which a random response is made. b, The behavioural model provides an estimate of the evolution of the distribution of a for each trial, with colour representing probability density for both panels. The forward version of the model (left panel) estimates the distribution of a at each time point based entirely on the click times and model parameters. Leftward (green) clicks push the distribution more negative and rightward (red) clicks push it more positive. The final value obtained by a at the end of the trial dictates the choice. In this example, the distribution of the final value of a is more heavily weighted towards negative values because there were more leftward than rightward clicks for this trial. A better estimate of the distribution of a can be obtained by also taking into account the subject’s choice made at the end of the trial (right panel). The final choice constrains the distribution of a at the final time point to have all its mass to one side of the decision boundary (in this example trial, despite the many leftward clicks, the subject chose right, and thus at the final time point, all the probability mass is at a > 0). This constraint is then propagated backwards in time, to obtain the distribution of accumulator values at each time point that is consistent both with the stimulus clicks and the subject’s final choice. The final result is an estimate of the distribution of a at each time point that takes into account the click times, the model parameters, and the subject’s choice. c, Illustration of non-sticky versus sticky decision bounds. Top: response of an accumulator to a sequence of downward (green arrows) and upward (red arrows) impulses when the bound parameter B is 2.5 and the bounds are not sticky. The fourth downward arrow (green) has no effect, because the bounds have been reached, and a cannot go beyond them. But subsequent upward arrows (red) do have an effect, because they do not push against the bounds. Bottom: response of an accumulator with the same parameters, receiving the same sequence of impulses, but when the bounds are sticky. Impulses subsequent to reaching the bound have no effect. We fit our rats’ behaviour data to this non-sticky bound model. We found that, similar to the version with the sticky bounds, the accumulation time constants were long (|τ| = 1/|λ| = 1.0 ± 0.2 s, mean ± s.e.m. across rats), and the bounds were high (17.1 ± 2.2, mean ± s.e.m. across rats). Such high bounds once again indicate that the bounds have minimal impact (consistent with this, the difference between the sticky and non-sticky bound models turned out to be negligible).
Extended Data Figure 3 Robustness of distinction between PPC and FOF to parameter variation.
a, The distinction between PPC and FOF encoding is robust to variation of the model’s time constant of integration. The slope of the tuning curves, drawn from the same analysis as Fig. 3c in the main text, except that here the analysis was carried out at a variety of integration time constants. b, Same analysis performed for a variety of heights for the sticky decision-commitment bounds. In both cases, the corresponding best-fit parameter was scaled by the factor shown on the horizontal axis, and the slope of tuning curve for FOF (in red) versus PPC (in black) was plotted as a function of that scale factor. Error bars show 95% confidence intervals. The slope of the FOF tuning curve is significantly sharper than the slope of the PPC tuning curve across the entire range of parameter values tested (P < 0.05). c, Tuning curve comparison between PPC and FOF with subset of PPC neurons selected such that the two regions have matched side selectivity. This resulted in n = 50 neurons for PPC and the original n = 128 neurons for FOF. The tuning curve is significantly steeper for FOF (P < 0.05). d, The same analysis as Fig. 3c in the main text, except that here we varied the latency applied between click time and neural representation (see Methods). While we would expect that an improper choice of latency would degrade the quality of the estimate of the accumulator value, the slope at the zero-crossing was still significantly larger for FOF compared to PPC for all comparisons (P < 0.05).
Extended Data Figure 4 Tuning curves based on model fit to aggregate rat behaviour.
The same analysis as Fig. 3 in the main text, except that rather than fitting the behavioural model on a rat-by-rat basis, it was fit to the aggregate behaviour of all rats. Thus, all rats share identical model parameter values for this figure. Although we would expect that to degrade the quality of the estimate of the accumulator value, the slope at the zero-crossing was still significantly larger for FOF than for PPC (PPC slope = 0.079 ± 0.004, FOF slope = 0.135 ± 0.026, mean ± 95% confidence interval).
Extended Data Figure 5 Individual neuron analyses.
a, The mapping between firing rate and accumulator value is shifted towards steeper slopes for the distribution of FOF neurons compared to the distribution of PPC neurons. Bars show the histogram of individual neuron slopes obtained from a sigmoidal fit of the relationship between firing rate and accumulator value, averaging across time from 0.15 to 0.5 s. Black bars correspond to PPC and red bars correspond to FOF. The arrows indicate the medians of the two distributions. While there is considerable overlap between the two populations, there is a significant shift towards greater steepness for the distribution of FOF neurons compared to PPC neurons (P < 0.001, rank sum test). A larger slope corresponds to a steeper change from low to high firing rates at the transition between negative and positive accumulator values. Thus, a steeper slope is associated with a more categorical as opposed to graded encoding of the accumulating evidence. b, To compare neural variability, we measured the fano factor for each neuron as a function of the accumulated evidence and compared across regions. There was not a significant difference in neural variability for the representations in the two areas (P = 0.23).
Extended Data Figure 6 Expected response profiles and click-triggered averages based on graded and categorical encodings.
a, Using stimuli corresponding to what was presented to the rats, individual trial responses r(t) were calculated based on the graded encoding r(t) = r = k1a(t) + k2, in which a(t) is the decision variable obtained from the behavioural model. Then, responses were averaged across trials sorting based on mean stimulus strength with the same exact method as described for Fig. 1. b, Same as a for a categorical encoding r(t) = k1sign(a(t))+k2. The ratio of the positive-to-negative encoding changes over time for each condition, leading to a ramping response profile. This highlights the point that ramping response profiles alone are not a sufficient demonstration of a gradual accumulation process. c, The black line shows the model prediction for the click-triggered average based on a graded encoding of accumulated evidence (r = k1a + k2) with a 0.2 s mean encoding lag to match the response lag of PPC. The grey line shows the data from Fig. 1. d, Same as c for a categorical encoding of accumulated evidence (r = k1sign(a) + k2) with a 0.1 s mean encoding lag to match the response lag of FOF. For both schemes, the encoding lag was taken from a Gaussian distribution with a 0.02 s standard deviation to account for variability in lag across neurons.
Extended Data Figure 7 Chemically sharpened fibre optics allow extensive inhibition during acute and chronic recordings from cortical regions expressing eNpHR3.0.
a, Image of a chemically sharpened 50 μm core, 125 μm cladding fibre. b, Light spot produced by a blunt and sharpened fibre 2 cm above the floor of a cylindrical container 10.5 cm in diameter. c, Laser power output from a blunt and sharpened fibre as a function of angle relative to the fibre optic tip. 25 mW input power. Power meter was 2.86 mm from the fibre tip. d, Single trace of an acute recording of spontaneous activity in anesthetized primary somatosensory cortex (S1, 1.5 mm posterior, 2.8 mm lateral from Bregma) expressing eNpHR3.0. Laser illumination period, 500 ms, marked by the green bar. e, Location of acute recording units (single and multi) in anaesthetized S1 relative to fibre tip and cortical surface. The level of inhibition was measured from ten repeated 500 ms laser illumination periods, delivered every 5 s. Percentage reduction displayed next to partially inhibited units. Unit in d indicated with an asterisk. f, Example multiunit activity from the FOF of a rat performing a memory guided orienting task. The 2-s laser illumination period initiated at cue onset, resulted in 97% inhibition of spiking activity for both trials where the rat made left or made right responses. g, Multiunit spiking activity (from f) aligned to laser onset (top) and laser offset (bottom). Spiking activity is strongly inhibited ∼16 ms after laser onset and recovers ∼60 ms after laser offset.
Extended Data Figure 8 Model-based analysis of halorhodopsin-mediated inactivation of the FOF (following J.C.E. et al., manuscript in preparation).
a–f, Full-trial inactivation (see Fig. 4a). a, Control trials with no inactivation taken from sessions with full-trial, 2 s, halorhodopsin inactivation. ‘Contra’ and ‘ipsi’ sides are relative to the side of the FOF that was inactivated on non-control trials. The curve shows the psychometric function predicted by the best-fit behavioural model based on the same stimuli that produced the behaviour. b, Comparison of the negative log likelihood for each candidate source of bias (see Methods). Smaller values correspond to a better fit. The post-categorization bias was significantly better than all other alternatives (P < 0.05, bootstrap). c–f, Data points show the proportion of contralateral choices for full-trial, 2 s inactivation of FOF. The curves show choice behaviour predicted by each alternative implementation of choice bias. b, Post-categorization bias. c, Accumulator shift. d, Unbalanced input gain. e, Unbalanced input noise. g–j, Peri-choice inactivation (Fig. 4b–d of main text). g, Control trials with no inactivation taken from sessions with either 500 ms or 250 ms peri-choice inactivation. The curve shows the psychometric function predicted by the best-fit behavioural model based on the same stimuli that produced the behaviour. h, Comparison of the negative log likelihood for both sources of bias. Smaller values correspond to a better fit. The post-categorization bias was significantly better than the accumulator bias (P < 0.05, bootstrap). i, j, Data points show the proportion of contralateral choices for peri-choice inactivation of FOF. The curves show choice behaviour predicted by the two versions of bias that predict an effect only at the end of the stimulus period. i, Post-categorization bias. j, Accumulator shift.
Extended Data Figure 9 FOF inactivation induced response bias does not correlate with click count or click train duration.
This figure shows further analysis of the data from Fig. 4 of the main text. a, b, During both the full-trial and 500 ms peri-choice inactivation sessions 50% of the trials had the click train duration fixed at 1 s (half inactivation half control trials). The remaining 50% were non-inactivation control trials with stimulus durations that varied randomly (not included in this analysis). All trial types were randomly interleaved. The Poisson nature of the click stimuli means that the number of clicks varied from trial to trial even for trials with the same duration and net click difference. a, We first asked whether the magnitude of the ipsilateral bias was correlated with the number of clicks for these fixed duration trials, and found that it was not (P = 0.80 and P = 0.88, for full trial and 500 ms peri-choice inactivations, respectively). b, In a separate analysis we asked whether given a fixed click difference, do more clicks lead to an excess bias. We first separated trials into groups with equivalent click differences (ipsi count − contra count). The actual click count of each trial was then subtracted by its group mean and normalized by its group standard deviation. This gives the z-score of the excess clicks on each trial given the click difference of that trial. We repeated this z-score normalization for the response bias on each trial (1 for respond ipsi, 0 for respond contra, bias = response on an inactivation trial − mean response on equivalent non-inactivation control trials). This gives a plot of the excess bias as a function of excess clicks. We found no significant correlation (P = 0.43 and P = 0.32 for full trial and 500 ms peri-choice inactivations, respectively). c, In the 250-ms inactivation experiment, click train durations varied both for control and inactivation trials. Here we asked whether the induced bias was correlated with the variable click train duration, and again found that it was not (P = 0.66).
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Hanks, T., Kopec, C., Brunton, B. et al. Distinct relationships of parietal and prefrontal cortices to evidence accumulation. Nature 520, 220–223 (2015). https://doi.org/10.1038/nature14066
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DOI: https://doi.org/10.1038/nature14066
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