Distinct effects of prefrontal and parietal cortex inactivations on an accumulation of evidence task in the rat — TEI-tagged view

ErlichpersName, BruntonpersName, DuanpersName, HankspersName, BrodypersName, CarandinipersName (2015date). “Distinct effects of prefrontal and parietal cortex inactivations on an accumulation of evidence task in the rat.” eLifetitle·j.

Object of study — the CAUSAL ROLES of two regions that have NEURAL CORRELATESterm OF GRADUALLY ACCUMULATING EVIDENCE and HAVE BEEN PROPOSED AS CENTRAL TO DECISION-MAKING

Research question — NUMEROUS BRAIN REGIONS HAVE BEEN SHOWN TO HAVE NEURAL CORRELATESterm OF GRADUALLY ACCUMULATING EVIDENCE FOR DECISION-MAKING, BUT THE CAUSAL ROLES OF THESE REGIONS IN DECISIONSterm DRIVEN BY ACCUMULATIONterm OF EVIDENCE HAVE YET TO BE DETERMINED

Contribution — a strong causal role for one region and A MINIMAL ROLE FOR PPCterm IN DECISIONSterm GUIDED BY ACCUMULATING AUDITORY EVIDENCE, EVEN WHILE FINDING A STRONG ROLE FOR PPCterm IN INTERNALLY-GUIDED DECISIONSterm

Full text — tagged

Distinct effects of prefrontal and parietal cortex inactivationsterm on an accumulationterm of evidence task in the rat eLife 4 :e05457.

https://doi.org/10.7554/eLife.05457 Copy to clipboard Download BibTeX Download .RIS Abstract eLife digest Introduction Results Discussion Materials and methods References Article and author information Metrics Numerous brain regions have been shown to have neural correlatesterm of gradually accumulating evidence for decision-making, but the causal roles of these regions in decisionsterm driven by accumulationterm of evidence have yet to be determined. Here, in rats performing an auditory evidence accumulationterm task, we inactivated the frontal orienting fields (FOFterm) and posterior parietal cortex (PPCterm), two rat cortical regions that have neural correlatesterm of accumulating evidence and that have been proposed as central to decision-making. We used a detailed model of the decisionterm process to analyze the effect of inactivationsterm. Inactivationterm of the FOFterm induced substantial performanceterm impairments that were quantitatively best described as an impairment in the output pathway of an evidence accumulator with a long integration time constantterm (>240 ms). In contrast, we found a minimal role for PPCterm in decisionsterm guided by accumulating auditory evidence, even while finding a strong role for PPCterm in internally-guided decisionsterm.

https://doi.org/10.7554/eLife.05457.001 Imagine that you have to buy a computer before the start of the school year. You have a few options, such as a laptop or a desktop, each with its own advantages and disadvantages. A laptop is relatively light and portable, whereas a desktop has more memory and is cheaper. You will gradually accumulate evidence for and against each option, but before school starts, you have to make a decisionterm.

This gradual accumulationterm of evidence is an important element in many forms of decisionterm making. It is known that the activity of many regions within the brain seem to represent accumulationterm of evidence, but relatively little is known about the causal role played by each region in the decision-making process. Now, by performing a series of experiments on rats, ErlichpersName et al. have clarified the precise roles of two of these regions: the frontal orienting fields in prefrontal cortex and the posterior parietal cortex. In the experiments the rats listened to a series of clicks from two speakers, one to the left and one to the right, and then had to decide if more clicks came from the left or the right speaker.

The rats normally used all of the accumulated evidence (up to 1 second) for their decisionterm. When the posterior parietal cortex was silenced (using a drug called muscimol), the rats continued to use all of the evidence available to them. However, when the frontal orienting fields were silenced (again using muscimol), decisionsterm were driven only by evidence accumulated over the most recent past (just a few hundred milliseconds). So in the computer example, without the help of the frontal orienting fields, you would choose the laptop if the most recent piece of evidence was for the laptop, even if older evidence argued strongly for the desktop.

These results show that the frontal orienting fields are necessary for making decisionsterm based on accumulated evidence, but further experiments suggested that the accumulationterm process itself seems to happen elsewhere in the brain. Another set of related experiments showed that the posterior parietal cortex is involved in a different type of decisionterm making, namely ‘free choice’ decisionsterm in which the rat decides between two options when there is no correct answer, such as picking a cookie from a pile of identical cookies.

https://doi.org/10.7554/eLife.05457.002 Gradual accumulationterm of evidence for or against different choices has been implicated in many types of decision-making, including value-based decisionsterm ( Basten et al., 2010 ; Milosavljevic et al., 2010 ; Cavanagh et al., 2011 ; Hunt et al., 2012 ; Solway and Botvinick, 2012 ), social decisionsterm ( Krajbich and Rangel, 2011 ), economic decisionsterm ( Gluth et al., 2012 ), gambling decisionsterm ( Busemeyer and Townsend, 1993 ), memory-based decisionsterm ( Ratcliff, 1978 ), numerical comparison decisionsterm ( Sigman and Dehaene, 2005 ), visual search decisionsterm ( Purcell et al., 2010 ; Heitz and Schall, 2012 ), and perceptual ( Gold and Shadlen, 2007 ; Ratcliff et al., 2007 ; Mante et al., 2013 ) decisionsterm. It is therefore considered a core decision-making process. Although neural correlatesterm of evidence accumulationterm have been reported in several interconnected primateterm brain regions—such as PPCterm ( Shadlen and Newsome, 2001 ; Roitman and Shadlen, 2002 ; Hunt et al., 2012 ), prefrontal cortex ( Hunt et al., 2012 ) including frontal eye fields (FEF; Kim and Shadlen, 1999 ; Purcell et al., 2010 ; Ding and Gold, 2012 ; Heitz and Schall, 2012 ; Mante et al., 2013 ), striatum ( Ding and Gold, 2010 ), and superior colliculus ( Horwitz and Newsome, 1999 ; Ratcliff et al., 2007 )—the specific roles of these different brain regions in decisionsterm driven by accumulationterm of evidence have not yet been distinguished.

We recently developed a rat model of gradual accumulationterm of evidence for decision-making, using a task that allows detailed quantitative modeling of the accumulationterm and decisionterm processes (‘Poisson Clicks’ task; BruntonpersName et al., 2013 ). In separate work from our laboratory using the Poisson Clicks task, electrophysiological recordings in rat PPCterm and Frontal Orienting Fields (FOFterm; ErlichpersName et al., 2011 ) revealed classic neural correlatesterm of evidence accumulationterm ( Figure 1 of HankspersName et al., 2015 ). Specifically, we found neurons in these rat regions that ramp up their activity during the stimulus, and the slope of that ramp is correlated with the strength of the momentary evidence just as one would expect from neurons whose firing rates represent the accumulationterm of evidence over time, and just as previously reported in monkey regions that have been suggested as analogous to the rat PPCterm and FOFterm (primateterm PPCterm: Shadlen and Newsome, 1996 , 2001 ; Roitman and Shadlen, 2002 ; and monkey FEF: Ding and Gold, 2012 ; Mante et al., 2013 ; for PPCterm analogy, see Whitlock et al., 2008 ; Reep and Corwin, 2009 ; Wilber et al., 2014 ; for FOFterm/FEF analogy see ErlichpersName et al., 2011 ).

Figure 1 Download asset Open asset Poisson clicks accumulationterm task trials and interleaved side LED trialsterm·var.

Each accumulationterm task trial begins with the onset of the center LED, which signals to the rat to enter the center port. The subject holds his nose in the center port for 2 s, until the center LED offset, which is the go cue. The majority of trials (90%) are accumulationterm trials. On accumulationterm trials, clicks play from the right and left speakers (right + left click rate = 40 clicks/s), terminating with the go cue. After the go cue reward is available at the side port associated with the greater number of clicks. The stimulus durationterm·var on each trial is set by the experimenter to be in the range 0.1–1 s. On Side LED trialsterm·var, no sound is played during the fixation period and one of the side ports is illuminated once the rat withdraws from the center port to indicate that reward is available there. Accumulationterm and side LED trialsterm·var are randomly interleaved, as are left and right trials.

https://doi.org/10.7554/eLife.05457.003 In addition to having neural correlatesterm of accumulating evidence ( HankspersName et al., 2015 ), several properties of the rat FOFterm suggest it as a candidate for a causal role in decisionsterm driven by accumulationterm of evidence. Accumulationterm of evidence involves both maintaining a memory of evidence accrued so far and addition of new evidence to the memory, and is therefore linked to short-term memory processes. The rat FOFterm has delay activity that correlatesterm with short-term memory, and plays a causal role in short-term memory for future orienting responses ( ErlichpersName et al., 2011 ). Furthermore, the rat FOFterm is well-situated to play an important role in perceptual decision-making, since it receives inputs from multiple sensory cortices ( Condé et al., 1995 ), and it projects to the superior colliculus (SC; Stuesse and Newman, 1990 ), a subcortical region that, in both rodents and primatesterm, is involved in controlling orienting motions ( Isa and Sasaki, 2002 ; Felsen and Mainen, 2008 ) and is thought to be involved in decisionsterm reported through such orienting motions. Moreover, the rat FOFterm is reciprocally connected with the rat PPCterm ( Reep et al., 1987 , 1994 ), which is currently considered a critical, central node in rodent perceptual decision-making ( CarandinipersName and Churchland, 2013 ). The rodent PPCterm itself also has neural correlatesterm of accumulating evidence ( HankspersName et al., 2015 ), and it shares with the FOFterm some of the key properties that suggest a causal role in decisionsterm driven by accumulationterm of evidence. The rodent PPCterm has delay activity that correlatesterm with performanceterm on short-term memory tasks ( Nakamura, 1999 ; Harvey et al., 2012 ), and, as shown through inactivationsterm, plays a causal role in short-term memory for orienting acts ( Harvey et al., 2012 ) and like FOFterm receives input from many sensory cortices as well as top-down input from prefrontal cortex, including FOFterm ( Wilber et al., 2014 ). For these reasons, the FOFterm and the PPCterm are the most prominent candidate regions in rodent association cortex for being important nodes in orienting decisionsterm guided by accumulationterm of evidence. We focus on these two areas here.

We implanted bilateralterm cannula in both FOFterm and PPCterm of rats trained to perform the Poisson Clicks task, and inactivated these regions with the GABA-A agonist muscimol while the rats performed the task. Consistent with expectations drawn from neural correlatesterm in the rat FOFterm, inactivationterm of the FOFterm impaired performanceterm in the task. We used quantitative modeling to characterize which aspect of the accumulationterm and decisionterm process was impacted by inactivationterm of the FOFterm. The results of these analyses revealed a specific location for the FOFterm in the causal circuit underlying the Poisson Clicks behavior: the behavioral impairment caused by FOFterm infusions could be parsimoniously and quantitatively explained as an impairment in the premotor output pathway of an evidence accumulator with a long accumulation time constantterm·var (240 ms or more). It is possible that the decisionterm itself (i.e., the categorization of the graded accumulator value into a discrete choice, which is a process subsequent to graded evidence accumulationterm) could occur in the FOFterm.

In contrast, we found that PPCterm inactivationsterm had a relatively minor effect on the Poisson Clicks task. This was true even while the same PPCterm inactivationsterm had strong effects on interleaved ‘free-choice’ trials, in which no sensory evidence was provided and rats were rewarded regardless of their choice of response. Our data thus suggest that the PPCterm plays a minimal causal role in decisionsterm guided by accumulationterm of auditory evidence, while playing an important role in internally-guided decisionsterm.

Together, our findings from inactivationsterm of the PPCterm and the FOFterm provide important constraints on the neural circuitry underlying decisionsterm guided by accumulationterm of auditory evidence in the rat.

We trained male Long-Evans rats (n = 14 rats) on the Poisson Clicks accumulationterm task ( Figure 1 , BruntonpersName et al., 2013 ). On each trial of this task, illumination of the center LED indicated that the rat should place its nose in the center port and remain there while click trains with Poisson-generated inter-click-intervals were played from the left and right speakers. The rats learned to report which side had played the greater total number of clicks by nose-poking into the corresponding side port ( Figure 2A ). We refer to these trials as ‘accumulationterm trials’.

Figure 2 with 2 supplements see all Download asset Open asset Behavioral evidence of accumulationterm.

( A ) Behavior as a function of total right minus total left clicks. For very easy trials (large click differences) performanceterm is ≈90% correct. The circles (with very small error bars) are the mean ±95% binomial confidence intervalsterm·stat across accumulator trials from all rats 1 day before an infusion session (n = 47,580 trials across 14 rats). The thick line is the psychometric curve generated by the accumulator model fit to these trials. ( B ) The time-constant of accumulationterm as fit by the model for each rat in the experiment. The median (810 ms) is marked by a thin gray line. ( C ) Chronometric plot generated using the same data as in panel ( A ). The rats' performanceterm increases with longer duration stimuli, consistent with an accumulationterm strategy. The circles and error bars are the mean ±95% binomial confidence intervalsterm·stat across trials on the easiest (blue), middle (purple) and hardest (magenta) thirds of trials defined by the absolute value of the ratios of left vs right click rates. The thick lines are the model generated chronometric curves. ( D ) Reverse correlation analyses showing that clicks throughout the stimulus were used in the rats' decisionterm process, supporting the long accumulation time constantsterm·var in ( B ). The thick dark red and green lines are the means ± std. err. across trials for where the rats went right and left. Thin light red and green lines are the model generated reverse correlation.

https://doi.org/10.7554/eLife.05457.004 In order to control for motor effects of inactivationsterm, the accumulationterm trials were randomly interleaved, in most sessions, with trials that we refer to as ‘side LED’ trials. On side LED trialsterm·var no sounds were played during fixation. Immediately after the end of fixation, one of the two side ports was illuminated, indicating availability of reward at the lit port ( Figure 1 ). The right and left side LED trialsterm·var, together, comprised ≈10% of the total trials.

To demonstrate that subjects accumulated the sensory evidence provided by the auditory clicks, we fit an accumulator model using the individual click times and the rats' choices on each trial ( Figure 2—figure supplement 1 ; see also BruntonpersName et al., 2013 ). Different parameter value regimes of this model can implement many different strategies, such as responding based on the first few clicks, or last few clicks, or to a burst of clicks, and many others. Consistent with previous results, maximum likelihood fitsterm·stat resulted in best-fit parameters associated with a gradual evidence accumulationterm strategy. Most importantly for this study, this strategy was characterized by a long accumulator time-constant, just under 1 s ( Figure 2B , Table 1 ), which is the duration of the longest stimuli used here. As expected for a gradual accumulationterm strategy in which clicks from the entire stimulus are weighted equally, performanceterm improved for longer stimuli with the same underlying click rates ( Figure 2C ; Ratcliff and Rouder, 1998 ; Usher and McClelland, 2001 ; BruntonpersName et al., 2013 ), and a psychophysical reverse correlation analysis ( Kiani et al., 2008 ; Raposo et al., 2012 ; BruntonpersName et al., 2013 ) indicates that rats used clicks from all times of the stimuli to make their decisionterm ( Figure 2D ).

Table 1 Best-fit parameters https://doi.org/10.7554/eLife.05457.006 Ratname λ σ a 2 σ s 2 σ i n i t 2 B ϕ τ ϕ Þ lapse B115 1.409 0.113 102.130 0.523 14.849 0.175 0.064 0.157 0.094 T055 1.226 0.001 11.248 0.043 16.014 0.253 0.351 0.118 0.078 T057 0.810 0.031 74.478 0.027 15.060 0.156 0.093 0.020 0.075 T058 1.087 0.000 17.612 0.000 15.875 0.025 0.276 −0.122 0.051 T061 0.620 0.000 96.545 0.502 16.038 0.380 0.041 0.236 0.066 T062 −0.098 0.000 49.361 0.619 15.761 0.139 0.047 0.518 0.083 A065 2.047 0.000 37.685 0.207 15.729 0.147 0.092 −0.465 0.031 A066 0.349 0.000 15.565 0.000 12.705 0.072 0.462 0.041 0.170 A077 −2.739 0.197 128.586 22.801 9.253 0.184 0.031 0.886 0.001 A078 −2.070 0.000 104.688 0.000 18.086 0.283 0.026 0.062 0.063 A060 −1.542 0.000 54.786 0.000 15.416 0.010 0.115 0.180 0.245 A062 2.258 0.296 156.860 0.486 16.839 0.527 0.076 0.466 0.119 A083 −0.790 47.441 31.788 1.384 16.282 0.015 0.059 0.033 0.107 A084 1.371 0.064 70.267 1.690 15.011 0.016 0.086 0.467 0.110 Meta-Rat 1.227 0.001 57.614 0.043 16.042 0.221 0.109 0.065 0.102 BiFOF −4.144 * 62.423 237.642 1.754 22.013 0.082 0.039 0.737 * 0.010 BiPPC 1.331 0.531 42.175 0.000 14.860 0.512 0.175 −0.249 0.321 This table shows the values of the parameters which maximize the likelihood of the full 9-parameter accumulator model for each rat, as well as for the ‘meta-rat’ (made from taking all of the control days that were 1 day before an infusion, n = 47,580 trials), the fit to the bilateralterm FOFterm data (n = 1809), and the fit to the bilateralterm PPCterm data (n = 1569).

indicate parameters that were significantly different from the control ‘Meta-Rat’.

We report the results of five different types of inactivationsterm: unilateralterm FOFterm, bilateralterm FOFterm, unilateralterm PPCterm, bilateralterm PPCterm, and combined bilateralterm FOFterm + unilateralterm PPCterm inactivationsterm, for a total of 26,521 trials from 161 infusions into the FOFterm and PPCterm of 14 rats ( Figure 3A and Figure 3—figure supplement 1 ). We initially performed muscimol inactivationsterm of the FOFterm and PPCterm in 6 rats performing the Poisson Clicks Task (group 1). In order to verify the results and perform follow-up and control experiments, we performed inactivationsterm in two further groups (group 2, n = 4; group 3, n = 4). The specific order and outcome of the infusions in each rat is shown in Figure 3—figure supplement 2 .

Figure 3 with 3 supplements see all Download asset Open asset FOFterm Infusions.

( A ) Top-down view of rat cortex with the locations of the FOFterm and the PPCterm, into which cannulae were implanted. ( B ) Bilateralterm infusion of muscimol into the FOFterm results in a substantial impairment on accumulationterm trials but has no effect on side LED trialsterm·var. In black are data from control sessions 1 day before an infusion (n = 8 sessions, 4 rats). In blue are data from bilateralterm FOFterm infusions (n = 8 sessions, 4 rats, 75 ng per side). The circles with error bars indicate the mean ± s.e. across sessions. Accumulationterm trials are binned by #R − #L clicks, spaced so there are equal number of trials in each bin. The lines are a 4-parameter sigmoid fit to the data. ( C ) Unilateralterm infusion of muscimol into the FOFterm results in a profound ipsilateral biasterm·var on accumulationterm trials but has no effect on side LED trialsterm·var. In black are data from control sessions 1 day before an infusion (n = 34 sessions, 12 rats). In red are data from right FOFterm infusions (n = 17 sessions, 12 rats, 150 or 300 ng). In green are data from left FOFterm infusions (n = 17 sessions, 12 rats, 150 or 300 ng).

https://doi.org/10.7554/eLife.05457.007 We placed cannulae in the center of the location currently identified as FOFterm (+2.0 mm AP, ±1.3 mm ML from Bregma, Figure 3—figure supplement 1A ). These are the same coordinates used by ErlichpersName et al. (2011) , and are also the coordinates at which neural correlatesterm of accumulationterm of evidence were observed in the Poisson Clicks task ( HankspersName et al., 2015 ). For the first bilateralterm FOFterm inactivationterm session we infused 300 ng of muscimol per side, for a total of 600 ng. After these infusions rats did not perform the task. We subsequently used a smaller dose of 75 ng per side (Note: this is half the dose used in the bilateralterm PPCterm experiment described below). This resulted in a significant 10.3% decrement on performanceterm on accumulationterm trials (p = 0.018, GLMMterm test; Figure 3B ). The effect was individually significant in 3/4 rats ( Figure 3—figure supplement 3A ). Side LED trialsterm·var were unimpaired (p > 0.5; Figure 3B ), indicating that the impairment on accumulationterm trials was not simply a motor effect.

Unilateralterm infusions of muscimol into the FOFterm resulted in a profound biasterm towards ipsilateral responses in the Poisson Clicks task ( Figure 3C ). Averaged across all unilateralterm FOFterm infusion sessions, the ipsilateral biasterm·var (defined as ipsilateral % correct − contralateral % correct), was 52 ± 7% (mean ± s.e.) for accumulationterm trials ( t -testterm·stat across 12 rats t 11 = 7.27, p < 10 −4 ; two rats in group 3 failed to perform sufficient numbers of trials during FOFterm inactivationsterm to be included in this analysis). Unilateralterm FOFterm infusions reduced performanceterm to chance on even the easiest contralateral accumulationterm trials ( Figure 3C ; green data points for #R − #L ≫ 0, and red data points for #R − #L ≪ 0). The ipsilateral biasterm·var induced by FOFterm inactivationterm was highly reproducible: 87% (26/30) of individual infusion sessions resulted in a positive ipsilateral biasterm·var (sign-testterm·stat, p < 0.001), and in every single rat there were more rightward responses after rightward infusions than leftward infusions ( Figure 3—figure supplement 3B ).

Importantly, as in the bilateralterm inactivationsterm, there was no significant effect on side LED trialsterm·var ( t -testterm·stat t 5 = 1.55, p > 0.15; Figure 3C , side LED Trialsterm·var), nor did unilateralterm FOFterm inactivationsterm have an effect on the response time on side LED trialsterm·var (repeated-measures ANOVAterm·stat, F(1,3) = 0.65, p > 0.4). This indicates that the effect of FOFterm inactivationterm was not simply an overall motor effect. Furthermore, the inactivationsterm produced no observable effects outside of the behavioral task. Infused animals appeared normal in their home cages both immediately after the infusion and after the behavioral session. Our localized inactivationsterm thus contrast with previous literature, in which large permanent unilateralterm lesions of the rat prefrontal cortex (including but extending well beyond the FOFterm), produced persistent, ipsiversive circling in the lesioned animals ( Crowne and Pathria, 1982 ).

Which aspects of the evidence accumulationterm and decisionterm process were impaired by the FOFterm inactivationsterm? To address this question, we took advantage of the accumulator model of BruntonpersName et al. (2013) , which uses the knowledge the precise time of each click in each individual trial, as well as the rat's decisionterm on each trial, to estimate 9 parameters that characterize the accumulationterm and decisionterm processes ( Figure 2—figure supplement 1 ). Each parameter quantifies a specific aspect of the decisionterm process. For example, τ , the time constant of the accumulatorterm·def (also described by the parameter λ = 1/ τ ), characterizes the time period over which the subject accumulates evidence. A negative value of λ indicates a leaky accumulatorterm·def, a positive value of λ indicates an unstable accumulatorterm·def, and perfect accumulationterm would have τ = ∞ (i.e., λ = 0). Another example parameter is the lapse rateterm·def, which quantifies the fraction of trials in which the subject behaves as if it had ignored the clicks that were played and had instead made its decisionterm randomly. Deviations from the perfect values ( λ = 0, lapse = 0) in either of these parameters can give rise to psychometric curves with shallow slopes, and both types of imperfections can produce curves qualitatively similar to the experimental curve obtained after bilateralterm FOFterm inactivationterm ( Figure 4A ). But the similarity between the psychometric curves for the two imperfections is partly due to the fact that these psychometric curves ignore the specific timing of individual clicks. In contrast, because the two imperfections would have very different signatures in terms of how clicks at different times affect the rats' decisionsterm, and click timing is fully taken into account in the behavioral model, the model can clearly distinguish the two imperfections. Using the control data, the best-fitting parameter values for the behavioral model had τ ≈ 0.8 s–indicating that subjects accumulated information over almost the entire stimulus durationterm·var but were on average slightly unstable–and a lapse rateterm·def of ≈0.1 (black cross, Figure 4B ). For data from bilateralterm inactivationterm sessions, the maximum likelihood parameter values (center of blue likelihood peak, Figure 4B ) changed significantly. The inactivationterm data now had a dramatically different and much shorter accumulation time constantterm·var of the opposite sign to the control data, τ ≈ −0.24 s (leaky accumulationterm over only a quarter of a second). In contrast, the best-fitting lapse rateterm·def remained essentially unchanged from control. As described above, attempting to fit the inactivationterm data by keeping the time constantterm unchanged and increasing the lapse rateterm·def could qualitatively match the psychometric curve (magenta line, Figure 4A ), but it produced an extremely poor fit relative to the full behavioral model (magenta cross in low likelihood region, Figure 4B ). Thus, after bilateralterm FOFterm inactivationterm, the subjects behaved as if their lapse rateterm·def was unchanged, and their accumulator had become much leakier ( Table 1 ).

Figure 4 Download asset Open asset Bilateralterm FOFterm inactivationterm is best fit as a reduction in the time-constant of accumulationterm.

( A ) When analyzed in terms of the psychometric function, changes to either lapse rateterm·def alone or accumulation time constantterm·var alone can match the bilateralterm FOFterm inactivationterm data. The black line shows the psychometric curve from control data, collected 1 day before bilateralterm FOFterm sessions (n = 1526 trials). Blue dots with error bars show the experimental data from bilateralterm FOFterm inactivationterm sessions (n = 1809 trials). The magenta line is the psychometric curve obtained by fitting only the lapse rateterm·def parameter to the inactivationterm data, while keeping all other parameters at their control values (corresponds to magenta cross in panel B ). The blue line shows the psychometric curve from the accumulator model fit to the inactivationterm data (corresponds to peak of blue likelihood surface in panel B ), which has a change w.r.t. control in accumulation time constantterm·var τ (=1/ λ ), but no change in lapse rateterm·def. ( B ) Fitting the detailed click-by-click, trial-by-trial accumulator model ( BruntonpersName et al., 2013 ) to the inactivationterm data clearly distinguishes between lapse and λ . The panel shows the normalized likelihood surface, indicating quality of the model fit to the inactivationterm data as a function of the lapse and the λ (=1/ τ ) parameters. The black cross shows parameter values for the control data. The best fit to the inactivationterm data is at the peak of the blue likelihood surface ( λ = −4.15, lapse = 0.048), significantly different from control for λ , but not different from control for lapse. This best-fit lambda corresponds to λ = −0.241 s, a substantially leaky integrator. ( C ) Performanceterm as a function of stimulus durationterm·var for bilateralterm FOFterm sessions (blue, mean ± std. err.) and the control sessions 1 day before (black, mean ± std. err.). The lines are the chronometric curves generated by the accumulator model (for inactivationterm data, parameter values at peak of blue likelihood surface in panel B ). ( D ) Reverse correlation showing the relative contribution of clicks from different times to the rats' decisionsterm for data from bilateralterm FOFterm inactivationterm sessions. Compare to Figure 2D . The thick dark shading shows the mean ± std. err. across trials based on the rats' choices. The thin bright lines are the reverse correlation traces generated by the accumulator model (parameter values at peak of blue likelihood surface in panel B ).

https://doi.org/10.7554/eLife.05457.011 Figure 4—source data 1 MATLAB file containing resampled bilateralterm FOFterm model fits.

This MATLAB file contains three variables. BF: a 300 × 9 matrix. Each row is the set of parameters which maximized the likelihood of the accumulator model fit to a resampling of the bilateralterm FOFterm data. Each column is a parameter. LL: a 300 × 1 vector with the negative log likelihood of the corresponding row of BF. parameter_names: a 9 × 1 cell with the names of the columns of BF.

https://doi.org/10.7554/eLife.05457.012 Download elife-05457-fig4-data1-v1.mat To further validate these results we resampled the trials (with replacement) and refit the model on the resampled trials 300 times. Based on this analysis, only two parameters shifted significantly from the control data: λ (95% C.I. = [−7.91 −1.31]; control value was 1.22) and Þ (95% C.I. = [0.10 1.50]; control value was 0.065). The change in λ is both significant and substantial, and accounts for most of the change in performanceterm. The change in decisionterm boundary, Þ (pronounced ‘sho’) is significant but very small, corresponding a horizontal shift in the psychometric curve of only one click. It is largely due to the difficulty of performing a perfectly balanced bilateralterm infusion. In particular, one rat, A077, was strongly biased during the bilateralterm FOFterm inactivationsterm ( Figure 3—figure supplement 3A ). On average, the noise and lapse parameters also increased but due to large covariance between these parameters, it is not possible to say which of them was significantly shifted ( Figure 4—source data 1 ).

To further examine the relative contributions of the λ and Þ changes we fit two 1-parameter models. First, we fit the bilateralterm FOFterm data with a 1-parameter Þ model where only the decisionterm boundary could change and the other 8 parameters were fixed at their best control data values. The log likelihood of the best Þ model was −1221.6, substantially worse than the model in which all 9 parameters were allowed to vary (−1102.5). Using Bayesian or Akaike Information Criteria (BIC or AIC; Burnham and Anderson, 2004 ), we find that the extra parameters are indeed justified ( Table 2 ). Second, we fit the bilateralterm FOFterm data to a 1-parameter λ model where only the accumulationterm time-constant could change. For this model, the best-fit value of λ was −12.4 and the log likelihood of the model was −1121.1 compared to −1102.5 for the best 9-parameter model, a difference of only 18.5. According to BIC, the 1-parameter model is the more likely model, supporting the idea that the major effect of bilateralterm FOFterm inactivationterm was a change in the time constantterm of accumulationterm ( Table 2 ).

Table 2 Bilateralterm FOFterm model comparison https://doi.org/10.7554/eLife.05457.013 Model # of param. Log likelihood BIC AIC full model 9 −1102.5 2272.5 2223 † Þ model 1 −1221.6 2450.7 2445.2 λ model 1 −1121.1 2249.7 * 2244.2 This table shows the three models fit to the bilateralterm FOFterm data (n = 1809 trials).

indicates the model with the lowest (the most likely) Bayesian information criterion (BIC)term·def.

indicates the model with the lowest (most informative) Akaike information criterion (AIC).

In this case, the AIC and BIC select different models, suggesting a better model may be somewhere in between. That is, a model that includes the accumulator time-constant and perhaps a few additional parameters from the full model.

To probe the conclusions derived from the trial-by-trial model fit, we used model-free analyses of the data ( BruntonpersName et al., 2013 ). Leaky accumulationterm with a time constantterm τ ≈ −0.24 s would result in short trials (with a stimulus durationterm·var less than a quarter of a second) being essentially unimpaired, while long duration trials would be more strongly impaired. This was indeed observed in the data, with a tight correspondence between the quantitative model and experimental data (chronometric curves, shown in Figure 4C ). A further property of a leaky accumulatorterm·def is that the more recent the clicks are, with respect to the end of the stimulus, the bigger their impact on the subject's decisionterm. This was also observed in the data, again with a tight correspondence between quantitative model and experimental data (reverse correlation analysis, shown in Figure 4D ).

These results indicate that the FOFterm is either (a) itself directly involved in the process of accumulating evidence, and the inactivationsterm made the accumulator leaky; or (b) the FOFterm is a requisite component in the output pathway of an accumulator with a long time constantterm, that is, the FOFterm is part of the chain of regions that transform evidence accumulated with a time-constant longer than 0.24 s into an orienting decisionterm.

We also used an accumulator model to analyze the strong ipsilateral biasterm·var induced by unilateralterm FOFterm inactivationsterm. The original model of BruntonpersName et al. ( Figure 2—figure supplement 1 ) contains only one parameter, the decisionterm boundary Þ, that can generate a left/right biasterm. We therefore extended the model with three additional parameters, each of which represented a possible imperfection that could generate a side biasterm. Simultaneously fitting all 12 parameters substantially increased the computational difficulty of the fitting process. In particular, efficiently fitting the original model was made possible by analytical computation of the gradient ( BruntonpersName et al., 2013 ). Determining the gradient for 12 parameter model was outside the scope of this manuscript. We consequently took the strategy of first fitting the original 9-parameter model to the control data from 1 day before infusion sessions, and then, starting from those best-fitting parameter values, asking which of the bias-inducing single-parameter changes would best fit the data from the unilateralterm FOFterm inactivationsterm (other parameters were held fixed at the control data best-fit values). In other words, we asked, ‘if we changed only one parameter, which one would it be to best fit the data?’ Finding the maximum likelihood value was made practical by the fact that each of the four fits performed was a single-parameter fit.

The four single-parameter changes we considered corresponded to hypotheses regarding possible functions of the FOFterm, and are conceptually illustrated in Figure 5 . (a) First, we considered the possibility that the FOFterm is part of the output pathway of the accumulator, perhaps part of computing or representing the animal's discrete choice after having categorized the accumulator value (into ‘Go Right’ vs ‘Go Left’ categories) ( HankspersName et al., 2015 ), potentially in the service of preparing a motor action ( ErlichpersName et al., 2011 ). Unilaterally perturbing the FOFterm might then biasterm this post-categorization representation. To implement this idea in the model, we added a parameter that biased outcomes after the R/L decisionterm was made on each trial. Independently of the stimulus that led to the decisionterm, we let a randomly-chosen fraction, κ R , of right decisionsterm and a randomly-chosen fraction κ L of left decisionsterm be reversed (i.e., R → L and L → R; see Figure 5A ). These reversals scale the vertical endpoints of the psychometric curve towards the Went Right = 50% level. The scaling is biased when κ R ≠ κ L . (b) Next, we considered the possibility that since the FOFterm has been suggested as analogous to primateterm FEF, perturbing it might affect attentional processes, perhaps causing a lateralized sensory neglect that would biasterm the perceptual impact of auditory clicks from the two different sides. In other words, during unilateralterm inactivationterm, right and left clicks could have different magnitudes of their impact on the accumulating evidence ( C R and C L , instead of the single common C of Equation 1 in Figure 2—figure supplement 1 ). We described this as a ‘unbalanced input gainterm·def’ (see Figure 5B ). (c) We next considered the possibility that the FOFterm plays a role in the accumulationterm process itself, and quantified biasesterm in accumulationterm through an ‘accumulationterm shift’ that shifts the value of the accumulator, a , at the end of the stimulus (see Figure 5C , equivalent to Þ in Figure 2—figure supplement 1 ). Changes in this parameter will cause horizontal shifts in the psychometric curve. (d) In the fourth and final model, we considered a second possible form of lateralized sensory neglect, in the form of ‘unbalanced input noise’ (see Figure 5D ). In this version of the model, right and left clicks could have different signal-to-noise ratios by having different values of the sensory noise parameter ( σ s , R 2 and σ s , L 2 , instead of the single common σ s 2 of Figure 2—figure supplement 1 ). For each of models (a), (b), and (d), the original fit to the control data was constrained to be balanced. To fit the biasterm generated by unilateralterm FOFterm inactivationterm, that constraint was relaxed. For each model, we kept the corresponding ipsilateral parameter fixed, and let the contralateral parameter be free to best fit the data. The difference between the best-fitting contralateral parameter minus the ipsilateral parameter was then defined as the biasterm for that model.

Figure 5 Download asset Open asset Conceptual illustration of four model parameters, used to quantify different sources of a lateralized biasterm.

( A ) Post-categorization biasterm·def: after categorizing the accumulator value into ‘Go Left’ or ‘Go Right’ decisionsterm, a fraction, κ L , of Left decisionsterm are reversed into Right decisionsterm, and a fraction, κ R , are reversed from Right to Left. ( B ) Biased input gain, which can be thought of as a form of sensory neglect: Left and Right clicks have different impact magnitudes on the value of the accumulator. In this illustration left clicks have a much stronger impact, and decisionsterm will consequently be biased to the left. ( C ) Accumulationterm shift: before categorizing the accumulator into ‘Go Left’ vs ‘Go Right’ decisionsterm (by comparing the accumulator's value to 0), a constant is added to the value of the accumulator. ( D ) Biased sensory noise, which by differentially affecting signal-to-noise rations from the two sides, can be thought of as a form of sensory neglect distinct from biased input gain: Left and Right clicks have different magnitudes of noise in their impact. In this illustration, left clicks are more variable than right clicks, which biasesterm decisionsterm to the right.

https://doi.org/10.7554/eLife.05457.014 Of these four models, the one that best fit the experimental data was (a), the post-categorization biasterm·def model in which the FOFterm is part of the output pathway of the accumulator ( Figure 6A , Figure 6—figure supplement 1B ). The value of κ contralateral to the inactivationterm ( κ C ) that best fit the data was 0.52, suggesting that on over 50% of trials rats reversed their contra-choices to ipsi-choices. The next best model (which was worse by ≈50 log-units than the post-decision model, Figure 6A ) was (b), the biased input gain model. This model failed to accurately fit the data on difficult trials (in which |#Contra − #Ipsi Clicks| is small, Figure 6—figure supplement 1C ). The best-fit model for (c), the accumulator shift model, was clearly a poor fit even when analyzed through psychometric curves, fitting particularly poorly for trials with a preponderance of contralateral clicks ( Figure 6—figure supplement 1D ). The worst fitting model was (d), the unbalanced input noise model ( Figure 6—figure supplement 1E ).

Figure 6 with 2 supplements see all Download asset Open asset Unilateralterm FOFterm inactivationterm is best fit as a post-categorization biasterm·def.

( A ) A comparison of the likelihoods (i.e., best model fits) for the four different biasterm mechanisms illustrated in Figure 5 . The post-categorization biasterm·def model is better than the next best model (biased input gain) by 50 log-units. ( B ) The 2-dimensional normalized likelihood surface for the two best single-parameter models: post-categorization biasterm·def and input gain biasterm. For visualization, we plot the contra-ipsi biasterm for the two parameters. That is, the difference between the contralateral and ipsilateral values for each parameter. The y-axis is κ C − κ I . The x-axis is C C − C I . By definition, in the control model (black marker) these biasesterm are 0. The peak of the magenta likelihood surface for the inactivationterm data is significantly different from control for post-categorization biasterm·def (from 0 to 0.4588) but not significantly different from control for input gain biasterm. ( C ) Psychometric curves for control and inactivationterm data. The black line is the model fit to the control data (see Figure 2A for the data points). The magenta circles with error bars are experimental data from unilateralterm FOFterm inactivationterm sessions, and indicate fraction of Contra choice trials (mean ± binomial 95% conf. int.) across trial groups, with different groups having different #Contra − #Ipsi clicks. The magenta line is the psychometric curve generated by the post-categorization biasterm·def model. ( D ) Performanceterm as a function of stimulus durationterm·var for data from control sessions 1 day before (black), and for data from unilateralterm FOFterm sessions (magenta, mean ± std. err.). The lines are the chronometric curves generated by the corresponding model ( E ) Reverse correlation analyses showing the relative contributions of clicks throughout the stimulus in the rats' decisionterm process. The thick dark red and green lines are the means ± std. err. across trials for contralateral and ipsilateral trials. Thin light red and green lines are the reverse correlation traces generated by the post-categorization biasterm·def model. ( F ) Psychometric curves for single-sided trials in control (black), right FOFterm infusion (red) and left FOFterm infusion (green) sessions, demonstrate that even for very easy trials FOFterm infusions produce a vertical scaling, consistent with post-categorization biasterm·def.

https://doi.org/10.7554/eLife.05457.015 We verified that the post-categorization model was best by using a leave-one-session-out cross validationterm·stat. For each of the 30 unilateralterm FOFterm infusion sessions, we fit the 4 models to the 29 other sessions and then evaluated the likelihood of the fit on the left-out session. Using this approach we found a significant main effect of model on likelihood/trial (repeated-measures ANOVAterm·stat F(3,87) = 10.76, p < 10 −5 ) and Bonferroni-Holm corrected post-hoc t -teststerm·stat reveal that all models were significantly different from each other (p < 0.005) except the noise and accumulator shift models (p > 0.4).

To ask whether a combination of changes to two parameters could provide a significantly better description of the data than our single-parameter fits, we estimated the 2-dimensional likelihood surface for the two best models. This surface ( Figure 6B ) clearly demonstrated that fitting the data requires a large shift away from the balanced control value in the post-categorization biasterm·def, but not in input gain. Thus, the dominant effect of unilateralterm FOFterm inactivationterm could be parsimoniously explained by a post-categorization biasterm·def, consistent with the known role of the FOFterm in movement planning ( ErlichpersName et al., 2011 ). As described above, a feature of the post-categorization model is that the psychometric curve after unilateralterm inactivationsterm should be a vertical scaling of the control psychometric curve. This scaling was found in the data, with a tight correspondence between the curve generated by the quantitative model and the experimental psychometric curve ( Figure 6C ). A similar tight correspondence between model and data were also found for the chronometric curves ( Figure 6D ) and the reverse correlation ( Figure 6E ).

Although computationally challenging, we have also explored whether higher dimensional models might reveal a different set of results. Using the Metropolis–Hastings algorithmterm·stat, we estimated the best-fit posterior distribution for an 8-parameter model. This model contains the four biasterm parameters, as well as λ , σ a 2 , σ S , I 2 , and κ I . For computational tractability, the remaining 4 parameters (initial noise, bounds, and the two click adaptation parameters) were fixed at the values of the best-fit control model. With 40,000 samples of this 8 dimensional distribution ( Figure 6—figure supplement 2 ), we estimate that four parameters changed significantly from their control values. First, accumulator noise increased from 5 × 10 −4 to 0.746 (95% C.I. = [0.125 12.123], p = 10 −4 ), which is still a small value and would have a negligible impact on behavioral performanceterm. Second, accumulator shift changed from 0.065 to 0.323 ([0.136 0.890], p = 0.013), which would also have a minimal effect on overall reward rate. Third, κ I , the changes from ipsi to contra choices decreased from 0.102 to 0.029 ([0.002 0.071], p = 10 −4 ). Finally, supporting our earlier analysis, κ C , increased from 0 to 0.498 ([0.176 0.536], p < 10 −3 ) which results in a very substantial behavioral impact, since this sets the asymptotic performanceterm on the easiest contralateral trials to ≈50%. As in the 2D model ( Figure 6B ) the gain of contralateral clicks increased (although not significantly). The likelihood of the best 8-parameter model was only marginally higher than the best 1-parameter post-categorization model ( Table 3 ), consistent with the small shifts in the other parameters (log likelihood of the 8-D model: −1957.52; log likelihood of the 1-D model: −1963.08). Using AIC and BIC we find that the increase in likelihood is too small to justify the increase in number of parameters.

Table 3 Unilateralterm FOFterm model comparison https://doi.org/10.7554/eLife.05457.018 Model # of parameters Log likelihood BIC AIC Post-categorization biasterm·def 1 −1963.1 3934.4 * 3928.2 † Unbalanced input gainterm·def 1 −2013.1 4034.4 4028.2 Accumulator shift 1 −2217.4 4443.0 4436.8 Unbalanced input noise 1 −2272.7 4553.7 4547.4 8-parameter model 8 −1957.5 3981.1 3949.9 This table shows the three models fit to the unilateralterm FOFterm data (n = 3836 trials).

indicates the model with the lowest Bayesian information criteria (BIC), that is, the most likely model.

indicates the model with the lowest Akaike information criteria (AIC), that is, the most informative model.

The 1-parameter post-categorization model has the lowest AIC and BIC, supporting the view that the major effect of unilateralterm FOFterm inactivationterm is not related to the accumulationterm process per se.

One of the characteristics of a post-categorization biasterm·def model is that since the biasing process occurs after the accumulated evidence has been categorized into ‘Go Right’ or ‘Go Left’, the biasterm is independent of whether trials are easy (large value of |# R − # L clicks |) or difficult (small value of |# R − # L clicks |). To further probe this hypothesis, we randomly intermixed regular accumulationterm trials with a new set of unusually easy ‘single-sided’ trials ( Figure 6F ). In these trials the speaker from only one side produced clicks at 100 clicks/s (noticeably higher than the 40 Hz rate on accumulationterm trials), lasting until the ‘Go’ signal indicating the end of center port fixation. Consistent with the post-categorization biasterm·def hypothesis, the unilateralterm FOFterm inactivationsterm produced a vertically-scaled ipsilateral biasterm·var in these single-sided trials that was similar to that seen during the accumulationterm trials ( Figure 6F , compare to Figure 6C data): that is, the biasterm was independent of how easy or how difficult the trials were.

Given that unilateralterm PPCterm lesions in rats lead to contralateral neglect ( Crowne et al., 1986 ; Reep et al., 2004 ), that PPCterm has been posited as central to rodent perceptual decision-making ( Harvey et al., 2012 ; CarandinipersName and Churchland, 2013 ), and that neural correlatesterm of the gradually accumulating evidence are found in PPCterm in our task ( HankspersName et al., 2015 ), we predicted that unilateralterm PPCterm inactivationsterm would cause a strong contralateral impairment (or, in other words, in the context of our binary forced-choice task, an ipsilateral biasterm·var, similar to that seen with the FOFterm inactivationsterm). Surprisingly, our unilateralterm PPCterm inactivationsterm resulted in a small effect that was ≈10× smaller than the effect in the FOFterm. The average ipsilateral biasterm·var was 4.2 ± 2.4% (mean ± s.e.) ( Figure 7A ; t -testterm·stat t 13 = 1.76, p > 0.1). Moreover, this small biasterm was largely due to data from the first infusion session in group 1 rats ( Figure 2—figure supplement 2A ) which led to a small but significant shift in rightward responding in right vs left infusions in the group 1 rats (p = 0.024, GLMMterm test). No consistent effects of unilateralterm PPCterm infusions were found in 10 subsequent infusion sessions with group 1 (a total of 11 group 1 unilateralterm PPCterm infusion sessions, Figure 3—figure supplement 2 ), even when the muscimol doseterm·var was substantially increased, to 600 ng ( Figure 7B ).

Figure 7 with 1 supplement see all Download asset Open asset PPCterm Infusions.

( A ) As in Figure 3B , but for unilateralterm infusions of muscimol into the PPCterm, which result in a minimal impairment. In black are data from control sessions 1 day before an infusion (n = 65 sessions, 14 rats). In red are data from right PPCterm infusions (n = 31 sessions, 14 rats, 150 or 300 ng). In green are data from left PPCterm infusions (n = 34 sessions, 14 rats, 150 or 300 ng). ( B ) As in ( A ), but using very high doses of muscimol. Only very small effects are seen. In black are data from control sessions 1 day before an infusion (n = 11 sessions, 9 rats). In red are data from right PPCterm infusions (n = 3 sessions, 3 rats, 600 or 2500 ng muscimol). In green are data from left PPCterm infusions (n = 8 sessions, 8 rats, 600 or 2500 ng). ( C ) Bilateralterm infusion of muscimol into the PPCterm does not produce a markedly bigger impairment. In black are data from control sessions 1 day before an infusion (n = 8 sessions, 4 rats). In blue are data from bilateralterm PPCterm infusions (n = 8 sessions, 4 rats, 150 ng per side). ( D ) Schematic view of the brain, duplicated from Figure 3A to remind readers of the location of FOFterm and PPCterm on the cortical surface.

https://doi.org/10.7554/eLife.05457.019 To test whether PPCterm inactivationterm could produce a quickly adapting effect (i.e., perhaps an effect from muscimol inactivationterm is observable only in the first session), we repeated our unilateralterm PPCterm inactivationsterm using a second group of rats. However, no significant effect was found in any of the PPCterm infusion sessions in group 2 rats even on the first day of infusion (GLMMterm test, p = 0.92; Figure 2—figure supplement 2B ). Notably, even extremely high doses (up to 2500 ng) of muscimol in PPCterm, were ineffective at biasing the rats on accumulationterm trials ( Figure 7B ). Thus, our data from group 2 suggest that the biasterm on the first day in group 1 occurred by chance.

Our PPCterm coordinates for group 1 and 2 (At 3.8 mm posterior and ≈3 mm lateral to Bregma) were based on the Paxinos and Watson rat atlas, the neural correlatesterm of accumulationterm found at this location ( HankspersName et al., 2015 ) and several published studies of rat PPCterm ( Paxinos and Watson, 2004 ; Nitz, 2006 ; Whitlock et al., 2012 ). Nevertheless, some authors have suggested that PPCterm is slightly more posterior: 4–6 mm posterior to Bregma ( Kolb and Walkey, 1987 ; Wilber et al., 2014 ). We therefore repeated the PPCterm experiments with a third group of rats, this time implanting cannulae at 4.5 mm posterior to Bregma ( Figure 3—figure supplement 1C ). Once again, as in group 2, there was no ipsilateral biasterm·var due to muscimol (at 300 ng) in the PPCterm (GLMMterm test, p = 0.47), nor was there a detectable effect on the first inactivationterm session.

Performanceterm of side LED trialsterm·var at regular muscimol dosesterm·var (150 or 300 ng) was not significantly affected by PPCterm infusions ( Figure 7A ; t -testterm·stat t 7 = 1.0, p > 0.35), and the response times on these trials were also unaffected (repeated-measures ANOVAterm·stat, F(1,6) = 2.48, p > 0.15). At very large doses, a significant effect on side LED trialsterm·var led to a small correlation between dose and biasterm for side LED trialsterm·var ( r = 0.43, p = 0.032; Figure 8 yellow circles). Given the very large muscimol dosesterm·var used, and the fact that visual cortical areas lie immediately posterior to PPCterm ( Paxinos and Watson, 2004 ), this weak correlation on side LED trialsterm·var may be a result of spread of muscimol to the adjacent visual cortex.

Figure 8 Download asset Open asset Summary of dose-bias relationship for all unilateralterm infusions.

Infusions into the FOFterm are in magenta and into the PPCterm are in yellow. Circles indicate biasterm on LED trials, squares indicate biasterm on accumulationterm trials. The magenta line is the linear fit between signed dose of FOFterm infusion (+for right infusions, −for left infusions) and performanceterm biasterm (right − left % correct) on accumulationterm trials (r = 0.85, p < 10 −9 ). The yellow line is the linear fit between signed dose of PPCterm infusion and performanceterm biasterm on accumulationterm trials (r = 0.19, p > 0.05). The plotted x-location of the side LED trialsterm·var are slightly offset for visualization.

https://doi.org/10.7554/eLife.05457.021 To summarize, unilateralterm inactivationterm of PPCterm did not reliably biasterm accumulationterm trials in three separately tested groups of rats. Based on the large doses used we suspected that the lack of effect was not due to a failure to inactivate PPCterm. There was no correlation between dose and biasterm magnitude in our PPCterm infusions on accumulationterm trials ( Figure 8 , yellow squares; p > 0.09), strongly contrasting with the significant correlation between dose of muscimol infused into the FOFterm and biasterm on accumulationterm trials (accumulationterm trials r = 0.85, p < 10 −9 ; Figure 8 , magenta squares). The correlation in the FOFterm data was specific to accumulationterm trials (p > 0.5 for side LED trialsterm·var; Figure 8 , magenta circles).

It is possible that during unilateralterm inactivationsterm, the silenced PPCterm may be compensated for by the PPCterm of the opposite hemisphere. In this case, bilateralterm inactivationsterm of the PPCterm should produce a behavioral impairment markedly larger than any small impairment found after unilateralterm inactivationsterm. To probe this hypothesis, we initially used a high dose (300 ng per side) for bilateralterm PPCterm infusions in group 1 rats, but only 2 of 6 rats completed trials, with inconsistent results. The maximum dose at which subjects still performed substantial numbers of trials was 150 ng per side, double the dose per side for the bilateralterm FOFterm inactivationsterm described above. During the bilateralterm PPCterm inactivationterm sessions there was a very small but significant 3.6% decrease in performanceterm on accumulationterm trials ( Figure 7B , p < 0.02 vs isoflurane, GLMMterm test). This effect was not individually significant in any rat (0/4). Critically, the effect size we found was not bigger–in fact, it was slightly smaller–than the average unilateralterm PPCterm effect, and thus does not provide support for the hypothesis of hemispheric compensation. Performanceterm on side LED trialsterm·var was not significantly different between bilateralterm PPCterm infusion and control sessions ( t -testterm·stat, p > 0.4; Figure 7B ). Fitting the accumulator model to the bilateralterm PPCterm data, we find that the only parameter to change was the lapse (but the confidence intervalsterm·stat overlapped with the control value), suggesting that the effects on performanceterm were unrelated to any specific aspect of the accumulationterm process.

Our results from PPCterm contrasted with previous studies that found a strong effect of PPCterm inactivationsterm in a mouse memory-guided navigation task ( Harvey et al., 2012 ) and a strong effect of permanent unilateralterm PPCterm lesions in inducing contralateral neglect in rats ( Crowne et al., 1986 ; Reep et al., 2004 ). This motivated us to seek a positive control task. The primateterm literature suggested an internally-guided decisionterm task whose trials could be readily intermixed with our evidence accumulationterm task. Wilke et al. (2012) interspersed regular memory-guided saccade trials (‘instructed’ trials), in which a single saccade target was presented on each trial, with internally-guided ‘free choice’ trials, in which both an ipsilateral and a contralateral target were presented, and the monkey was rewarded regardless of its response choice. By design, subjects were free to respond as they pleased in free choice trialsterm·def, and they typically displayed a biasterm towards one side or another in these trials. Wilke et al. found that muscimol inactivationterm of area LIP within PPCterm produced no effect on choices in the instructed memory-guided saccade trials, but produced a profound ipsilateral biasterm·var during intermixed free choice trialsterm·def. Inspired by Wilke et al.'s results, we modified the task for seven of our group 2 and group 3 cannulated rats (The six group 1 rats and one group 3 rat had been already sacrificed for histology). We randomly intermixed 25% free choice trialsterm·def with 65% accumulationterm trials and 10% Side LED trialsterm·var ( Figure 9A ). Free-choice trialsterm·def were indicated by a lack of auditory click stimuli, and by illumination of both side LEDs after the animals had withdrawn from the center port. We refer to sessions with interleaved accumulationterm, side LED, and free-choice trialsterm·def as ‘free-choice’ sessions. After a few free-choice sessionsterm·def with no infusions, rats performed the mix of trials reliably, and expressed a consistent biasterm on free choice trialsterm·def but no detectable biasterm on accumulationterm trials.

Figure 9 with 1 supplement see all Download asset Open asset Unilateralterm PPCterm inactivationsterm induce a strong ipsilateral biasterm·var during internally guided decisionsterm, and can induce a strong biasterm on accumulationterm trials if the FOFterm is bilaterally inactivated.

( A – D ) Effect of unilateralterm PPCterm or FOFterm inactivationsterm on free choice trialsterm·def intermixed with regular accumulationterm trials. ( A ) A schematic of the three interleaved trial types: Accumulationterm, Side LED and Free Choice trialsterm·def. Accumulationterm and side LED trialsterm·var proceeded as described in Figure 1 . On free choice trialsterm·def (25% of all trials), after withdrawal from the center port both side LEDs were illuminated and rats were rewarded for going to either port. ( B ) After a few sessions, rats quickly developed an intrinsic biasterm on free choice trialsterm·def even while showing no biasterm on instructed trials (Accumulationterm and side LED trialsterm·var). When muscimol was infused into the PPCterm free choices were significantly biased toward the side of the infusion. This panel shows an example from a single infusion day where the side of the infusions was chosen to be opposite to their intrinsic free-choice biasterm, together with data from the previous and subsequent control day. ( C ) Unilateralterm PPCterm infusions generated a significant 26 ± 9% (mean ± s.e. across rats, n = 7) ipsilateral biasterm·var on free choice trialsterm·def compared to control sessions (the day earlier). During infusion sessions there was a small 8 ± 4% (mean ± s.e., n = 7 rats) contralateral biasterm on accumulationterm trials, perhaps compensatory to the free choice ipsilateral biasterm·var. There was no effect on side LED trialsterm·var ( D ). Unilateralterm FOFterm infusions generated significant ipsilateral biasesterm·var on free choice and accumulationterm trials, but not on side LED trialsterm·var. One rat (A077) was extremely biased (90% Ipsilateral choices) on Side LED trialsterm·var during FOFterm inactivationterm, indicated as an outlier. *p < 0.01. (n = 25 session, 7 rats) ( E ) Combined bilateralterm infusion of muscimol into the FOFterm with unilateralterm infusion of muscimol into the PPCterm results in a substantial ipsilateral biasterm·var on accumulationterm trials. In black are data from control sessions 1 day before an infusion (n = 32 sessions, 4 rats). In red are data from bilateralterm FOFterm infusions with right PPCterm infusion (n = 8 sessions, 4 rats, 75 ng per side in the FOFterm, 300 ng in right PPCterm). In green are data from bilateralterm FOFterm infusions with left PPCterm infusion (n = 8 sessions, 4 rats, 75 ng per side in the FOFterm, 300 ng in left PPCterm). See Figure 9—figure supplement 1 for the individual rat results and GLMMterm fits.

https://doi.org/10.7554/eLife.05457.022 In remarkable parallel to Wilke et al.'s results in primatesterm, unilateralterm PPCterm inactivationsterm (300 ng of muscimol) during free-choice sessionsterm·def produced a very strong and reliable ipsilateral biasterm·var on free choice trialsterm·def ( Figure 9B,C ; t -testterm·stat t 26 = 3.70, p = 0.001). The strong ipsilateral biasterm·var in free choice trialsterm·def was observed even while, consistent with our previous PPCterm inactivationsterm, there was no ipsilateral biasterm·var on the intermixed accumulationterm trials ( t -testterm·stat t 26 = −0.99, p = 0.329) nor on the Side LED trialsterm·var ( t -testterm·stat t 8 = 1.42, p = 0.194; Figure 9C ). The free-choice biasterm was highly reproducible: 85% (23/27, sign-testterm·stat, p < 0.001) individual rat PPCterm inactivationterm sessions produced an increased fraction of ipsilateral free choices when compared to free choices on immediately preceding control days (see Figure 9B for an example of PPCterm infusions that were selected to ‘push’ the rats away from their innate preference seen on the day before and the day after the infusion). The effect on free choice trialsterm·def was thus similar in its robustness and reproducibility to the effect of unilateralterm FOFterm inactivationterm on accumulationterm trials. These free choice trial inactivationterm results provide a clear positive control for our PPCterm inactivationsterm. Moreover, they are consistent with the parietal neglect literature in both rats ( Crowne et al., 1986 ; Reep et al., 2004 ) and primatesterm ( Mesulam, 1999 ).

Inactivationterm of FOFterm, like the PPCterm, also induced an ipsilateral biasterm·var on free choice trialsterm·def ( t -testterm·stat, t 24 = 3.86, p = 0.001). Consistent with our previous experiments, FOFterm inactivationsterm in free-choice sessionsterm·def continued to produce an ipsilateral biasterm·var on accumulationterm trials ( t -testterm·stat t 24 = 4.85, p < 0.001) but not on side LED trialsterm·var ( t -testterm·stat t 18 = 1.65, p = 0.117; Figure 9D ).

Are there any conditions under which silencing the PPCterm could affect choices in auditory click accumulationterm trials? To probe whether inactivationterm of the FOFterm could reveal an effect of PPCterm inactivationterm, we bilaterally inactivated the FOFterm while simultaneously infusing 300 ng of muscimol unilaterally into the PPCterm. This combination of infusions produced a significant 15.1% biasterm ipsilateral to the side of the PPCterm infusion ( Figure 9E , p < 0.0012, GLMMterm test). These data constitute a second positive control for our unilateralterm PPCterm inactivationsterm. The data furthermore suggest that during auditory evidence accumulationterm the PPCterm may have a real but weak influence on choice that is normally overridden by a stronger signal from the FOFterm.

In two-alternative forced choice tasks driven by accumulationterm of sensory evidence, such as the random dots task used with primatesterm ( Newsome et al., 1989 ) or the Poisson Clicks task used here with rats ( BruntonpersName et al., 2013 ), subjects gradually accumulate evidence over time; make a decisionterm by categorizing the graded value of the accumulated evidence into a binary choice; use their decisionterm to prepare a movement; and finally execute their decision-reporting motor act (these different components could potentially overlap). In primatesterm, five recurrently interconnected brain regions have been associated with the overall process (superior colliculus, striatum, PPCterm, FEF, and dlPFC; Horwitz and Newsome, 1999 ; Kim and Shadlen, 1999 ; Shadlen and Newsome, 2001 ; Roitman and Shadlen, 2002 ; Ratcliff et al., 2007 ; Ding and Gold, 2010 , 2012 ; Heitz and Schall, 2012 ; Mante et al., 2013 ), but despite some theoretical suggestions ( Lo and Wang, 2006 ), the specific contributions of each brain region to the different aspects of the overall process, and the circuit logic of the network, remain unclear. Here we focused on the role of two rat cortical areas, posterior parietal cortex (PPCterm) and frontal orienting fields (FOFterm), that are considered critical for rodent decision-making ( ErlichpersName et al., 2011 ; Sul et al., 2011 ; Harvey et al., 2012 ; CarandinipersName and Churchland, 2013 ), and that display neural correlatesterm of gradually accumulating auditory evidence ( HankspersName et al., 2015 ). As in primatesterm, the specific roles of each of these rat areas within the overall evidence accumulationterm and decisionterm process remain undetermined.

Using a within-subject design, we implanted cannulae in both of these areas, and carried out pharmacological inactivationsterm, quantifying the impairments by fitting to the data detailed models of the decision-making process for the Poisson Clicks task. Different parameters of the models quantified different possible variations from control behavior. We also compared inactivationterm effects on the Poisson Clicks task (‘accumulationterm trials’) to three types of control trials: free-choice (in which the animal was free to choose either of two visual stimuli to obtain a reward); single-sided (in which decisionsterm were guided by a simple auditory stimulus that did not require gradual evidence accumulationterm, and rats had to withhold their response for several hundred milliseconds after receiving enough information to make their decisionterm); and side LED trialsterm·var (in which decisionsterm were guided by a simple visual stimulus that did not require gradual evidence accumulationterm, and rats were free to report their decisionterm as soon as they made it).

In other studies with the same behavioral task, we have used optogenetic inactivationterm ( HankspersName et al., 2015 ). Although optogenetics allows high temporal resolution inactivationterm, its radius of effect in our hands is only ≈750 μm (see Extended Data Figure 7 of HankspersName et al., 2015 ). In contrast, inactivating larger regions is much more readily achieved with muscimol, for which the radius of inactivationterm can be increased simply by increasing the infusion dose. In addition, muscimol directly inactivates all neurons within its radius of effect, not only infected neurons. Moreover, in some tasks, including the Poisson Clicks task, we find that the behavioral effect of optogenetic silencing begins to decay after a few weeks, while the effect of muscimol is stable. This stability in particular was essential for the current study, which used within-subject manipulations over hundreds of days. Optogenetic and pharmacological silencing therefore have complementary advantages and disadvantages. Here we focused on pharmacological inactivationterm.

Our results demonstrate that the FOFterm is an essential part of the circuit for decisionsterm driven by accumulating evidence ( Figure 3 ). Unilateralterm FOFterm inactivationsterm had a strong effect on both accumulationterm trials, signaled by auditory clicks, and on free choice trialsterm·def, signaled by a bilateralterm visual stimulus ( Figure 9 ), indicating that the effects are not specific to a single sensory modality. Critically, the model-based analyses suggested a specific location for the FOFterm within the functional process chain required by our accumulationterm of evidence task. The specific suggestion is that the FOFterm is not part of the accumulator but is instead part of the premotor output pathway that leads from the graded evidence accumulator to the decision-reporting motor act. This suggestion is derived from (a) the sharp reduction in the accumulation time constantterm·var induced by bilateralterm FOFterm inactivationsterm (from slightly unstable τ ≈ +0.8, to very leaky τ ≈ −0.24 s), which demonstrates that the FOFterm is either involved in the accumulationterm process itself, or is part of the output pathway of the accumulator ( Figure 4 ); (b) the effects induced by unilateralterm inactivationterm of the FOFterm, which are captured in quantitative detail, for both accumulationterm trials and single-side trials, as having induced a post-categorization biasterm·def that is subsequent to the accumulationterm process ( Figure 6 ); and (c) the lack of an effect of FOFterm inactivationsterm on side LED trialsterm·var, which rules out a simple motor role for the FOFterm ( Figure 3 ). A parsimonious explanation of this set of results is thus that the FOFterm is a requisite premotor component of the output pathway of an evidence accumulator with a long time constantterm (>0.24 s). This suggestion is different from, but consistent with, the FOFterm's known role in short-term memory, as well as the FOFterm's greater importance in memory-guided (i.e., long time constantterm) vs sensory-guided (short time constantterm) orienting decisionsterm ( ErlichpersName et al., 2011 ). In decisionsterm driven by gradual accumulationterm of evidence, the gradual accumulationterm process occurs prior to the binary decisionterm. An intriguing possibility suggested by our results that the decisionterm process itself–that is, the categorization of the gradually accumulated evidence into a binary choice–might be performed in the FOFterm, perhaps in conjunction with the superior colliculus ( Lo and Wang, 2006 ).

It is possible that unilateralterm FOFterm inactivationsterm would induce a hemispheric imbalance so strong that a real but nuanced role for the FOFterm in gradual accumulationterm might have been obscured by a strong post-categorization biasterm·def. We nevertheless currently favor the interpretation of the FOFterm's role as subsequent to, not part of, the graded accumulator. We favor this interpretation first, because of its parsimony; second, because parallel electrophysiological work from our laboratory found that the representation of the accumulated evidence in the FOFterm could be approximately described as the answer to the categorical question ‘if the GO signal came now, which side port should I choose?’; third, using AAV-CaMKII-eNpHR3.0 for optogenetic inactivationterm we found that transient unilateralterm silencing of the FOFterm was unable to cause an effect on behavior if it occurred during the evidence accumulationterm period, sufficiently prior to the GO signal ( HankspersName et al., 2015 ).

Those results, in combination with the pharmacological data, three control trial types, and model-based analyses reported here, all consistently support the interpretation of the FOFterm as a requisite component of the output pathway of an evidence accumulator with a long time constantterm (>0.24 s). This view is consistent with the fact that side LED trialsterm·var, which involve decisionsterm that do not require gradual evidence accumulationterm or storing a motor plan in short-term memory, are not impacted by FOFterm inactivationsterm. Such decisionsterm, including perhaps decisionsterm that require auditory evidence accumulationterm over only short times (<0.24 s), may depend on pathways that bypass the FOFterm, perhaps involving direct connections from auditory cortex to the striatum ( Znamenskiy and Zador, 2013 ).

With pharmacological infusions, one concern is spread of inactivationterm to other structures. We based the volume and concentration of our infusions on previous literature to achieve inactivationterm volumes of 1 mm radius for our small doses and 3 mm radius for our largest doses ( Martin, 1991 ; Krupa et al., 1999 ). This spread is within the anterior-posterior bounds of FOFterm, but could have spread medially to cingulate cortex (CG1) or laterally to M1 ( Paxinos and Watson, 2004 ). The white matter below FOFterm prevent spread ventrally into the basal ganglia. In a previous study, we directly tested the effects of M1 inactivationterm and found them to be weaker than FOFterm inactivationsterm and also they affected sensory-guided and single-sided trials equally ( ErlichpersName et al., 2011 ). As such, it is unlikely that the effects we are attributing to FOFterm are due to M1 inactivationterm. We targeted our inactivationsterm to 2 mm anterior and 1.25 mm lateral to Bregma. According to the Rat Atlas ( Paxinos and Watson, 2004 ) CG1 may be within the spread of the drug. However, according to a recent cell-based mapping technique the medial boundary of FOFterm has been underestimated ( Brecht et al., 2004 ), suggesting that most of spread of drug would be within FOFterm. Moreover, the CG1 is thought to play a role in cost-benefit decisionsterm ( Hillman and Bilkey, 2012 ; Holec et al., 2014 ), cognitive flexibility ( Ragozzino and Rozman, 2007 ), or emotional reactivity ( Bissière et al., 2008 ), not in movement planning. Therefore, the effects observed are more likely due to changes in FOFterm rather than an adjacent cortical region.

Given the view that the PPCterm plays a key causal role in rodent perceptual decisionsterm ( Harvey et al., 2012 ; CarandinipersName and Churchland, 2013 ) and that neural activity in PPCterm displays correlatesterm of accumulating auditory evidence ( HankspersName et al., 2015 ), we were surprised to find that unilateralterm inactivationterm of the PPCterm did not cause a side biasterm on accumulationterm, side LED, or single-sided trials. Compensation from the unperturbed hemisphere did not explain the lack of an effect, because bilateralterm inactivationterm of the PPCterm caused a minimal decrease in performanceterm (3.6%) that was not significantly different from unilateralterm inactivationsterm. Thus, the PPCterm seems to play a far more subtle role than the FOFterm in choice behavior during decisionsterm guided by auditory evidence accumulationterm.

Unilateralterm PPCterm inactivationsterm did cause a strong ipsilateral biasterm·var under two conditions: in internally-guided decisionsterm (free choice trialsterm·def, signaled by a visual stimulus, Figure 9A–C ), and when the FOFterm was simultaneously bilaterally inactivated in accumulationterm trials (auditory stimulus, Figure 9E ). These results suggest that in the intact brain, weak but real side choice signals from the PPCterm may be overridden by stronger signals from the FOFterm. They also suggest that the PPCterm's role may not be specific to a particular sensory modality.

The PPCterm is relatively extended in the medial-lateral direction (≈4 mm) but it is thin (≈0.75 mm) in the anterior-posterior direction ( Paxinos and Watson, 2004 ; but see Wilber et al., 2014 ). The anatomical characteristics of the PPCterm pose two possible confounds: insufficient inactivationterm of the PPCterm in the medial-lateral direction and potential spread to adjacent regions in the anterior-posterior direction. If we assume the spread of muscimol across the cortical is isotropic (white matter acts as a physical barrier, so we assume that the ventral spread is restricted), then an individual injection, due to the wide and thin shape of PPCterm, will either fail to inactivate all of PPCterm or spread to adjacent regions. Based on the literature ( Martin, 1991 ; Krupa et al., 1999 ) we expect our smallest infusion to have a ≈1 mm radius and our largest to have a >3 mm radius. This technical limitation would have posed a serious challenge for our results if we observed very different effects of our small and large infusions. However, despite using a wide range of doses, we observed no significant dose–response effect with unilateralterm PPCterm infusions ( Figure 8 ). A clear dose–response relationship (as we found in the FOFterm) would indicate that bigger infusions were silencing more and more PPCterm neurons required for behavior in the task. Instead, the fraction of inactivated PPCterm neurons had no impact on the magnitude of the behavioral effect, which is what we would expect if PPCterm neurons were not required for choice behavior in the task. Nonetheless, further experiments would be required to completely rule out the possibility that a small number of PPCterm neurons, in the most medial or lateral edge of the PPCterm, were spared and that these few neurons were sufficient to support intact behavioral performanceterm on the Clicks task.

Spread of muscimol into areas immediately anterior or posterior to the PPCterm was inevitable with our largest doses, and, in the two cases where positive effects were observed, this raises concerns about region specificity. Immediately anterior to the PPCterm is the somatosensory cortex (for the trunk). Particularly in light of the intact motor capacities, as indicated by the intact side LED trialsterm·var, the somatosensory cortex is not expected to have caused any of the observed effects. Immediately posterior to the PPCterm are a set of individually small visual areas, collectively referred to as secondary visual cortex (V2; Coogan and Burkhalter, 1993 ; Montero, 1993 ; Wang and Burkhalter, 2007 ). These visual areas are unlikely to be involved in auditory click accumulationterm trials, and are therefore not expected to have caused the effects we saw after simultaneous unilateralterm PPCterm and bilateralterm FOFterm inactivationsterm ( Figure 9E ). However, the biasterm we observed on free-choice trialsterm·def may have been partly due to an effect in one or more of these small secondary visual areas. Nevertheless, ipsilateral biasesterm·var in untrained orienting responses (potentially analogous to the free-choice task) due to PPCterm lesions have been observed in the rat even when those choices were to tactile or auditory stimuli ( Corwin et al., 1996 ; Burcham et al., 1997 , 1998 ). We also note that our free choice results closely parallel the results from primateterm PPCterm free choice experiments ( Wilke et al., 2012 ), which do not suffer from this spillover concern.

A minimal effect following PPCterm inactivationterm in our rat auditory click accumulationterm task is reminiscent of Guo et al.'s, finding of no effect after PPCterm inactivationterm in a mouse somatosensory-cued, memory-guided task ( Guo et al., 2014 ). But it contrasts with Harvey et al.'s finding of a severe performanceterm impairment after PPCterm inactivationterm in a mouse visually-cued, memory-guided navigation task ( Harvey et al., 2012 ). Following our own preliminary reports of PPCterm inactivationsterm in the Poisson Clicks task ( ErlichpersName et al., 2012 , 2014 ), Raposo et al. (2014) reported an impairment after rat PPCterm inactivationsterm in a visual, but not in an auditory, version of a closely related task. This contrasts with a preliminary report from Yates et al. that suggested no effect from primateterm PPCterm inactivationterm in a visual accumulationterm of evidence task ( Yates et al., 2014 ), as well as with multiple reports of no effect from primateterm PPCterm inactivationterm in visual memory-guided saccade tasks ( Chafee and Goldman-Rakic, 2000 ; Wardak et al., 2002 ; Liu et al., 2010 ; Wilke et al., 2012 ). The Raposo et al. results therefore suggest that rodent PPCterm may be unlike primateterm PPCterm in being required for accumulationterm of evidence for a specific modality, vision. Nevertheless, the precise location of the border between rodent PPCterm and visual cortex, as well as the amount of inter-animal variability in this location, remain active research questions ( Wilber et al., 2014 ; see, for example, Reep et al., 1994 ; Corwin and Reep, 1998 for definitions from the same authors, based on the same data, that alternately describe the border as located at −5.0 mm from Bregma or −4.4 mm from Bregma). The uncertainty in the location of the PPCterm/visual cortex border raises an alternative possibility, which is that the impairments in memory-guided visual tasks observed by Harvey et al. and Raposo et al. (and potentially the free-choice effects seen here) could have been due to inactivationterm spillover into one of the immediately adjacent small secondary visual areas, as described above, rather than inactivationterm of the PPCterm itself. This would make all the inactivationterm results ( Harvey et al., 2012 ; Guo et al., 2014 ; Raposo et al., 2014 ; Yates et al., 2014 ; and the results presented here.), including mouse, rat, and primateterm, fully consistent with each other. While such a reconciliation of results across multiple species may have some intellectual appeal, we emphasize that experiments that would either clearly support or rule out this possibility remain to be done.

To date, the accumulationterm of evidence literature is mostly composed of electrophysiological experiments with primatesterm. Based on a number of criteria, the rat PPCterm and FOFterm have been suggested as analogous to the primateterm PPCterm and FEF, respectively ( Kolb and Walkey, 1987 ; Reep and Corwin, 2009 ; ErlichpersName et al., 2011 ), and accumulationterm of evidence signals very similar to those in primatesterm have been found in these two rat areas ( HankspersName et al., 2015 ). It is therefore tempting to speculate that our results in rat might also hold in primateterm, and to consider potential interpretations that would be consistent across mammalian model systems.

There have been no published inactivationterm experiments in primateterm PPCterm or FEF during accumulationterm of evidence tasks. There have, however, been inactivationterm experiments in related tasks, which in general are in agreement with our findings: prefrontal perturbations strongly biasterm behavior while posterior parietal perturbations do not. In memory-guided saccade tasks, LIP inactivationsterm have no effect on the choice of saccading either towards or away from the correct hemifield ( Chafee and Goldman-Rakic, 2000 ; Wardak et al., 2002 ; Liu et al., 2010 ; Wilke et al., 2012 ), while FEF and prefrontal inactivationsterm reliably generate profound ipsilateral choice biasesterm ( Sommer and Tehovnik, 1997 ; Dias and Segraves, 1999 ; Chafee and Goldman-Rakic, 2000 ). Similarly, in a covert visual search task, LIP inactivationterm has no effect on error rates ( Wardak et al., 2002 ), while inactivationterm of the FEF generates significant increase in error rates for contralateral targets ( Wardak et al., 2006 ). Again similarly, in a memory-guided task with distractors, Suzuki and Gottlieb, (2013) found no errors after LIP inactivationsterm while finding significant contralateral errors after prefrontal cortex inactivationsterm.

We are aware of only a few studies where LIP inactivationterm produces choice biasesterm ( Wardak et al., 2002 ; Balan and Gottlieb, 2009 ; Wilke et al., 2012 ). One of these studies ( Wilke et al., 2012 ) inspired our intermixing free choice trialsterm·def with accumulationterm trials. Consistent with a good analogy between rat PPCterm and primateterm PPCterm, our results in rats closely paralleled Wilke et al.'s results in primatesterm, with our accumulationterm of evidence trials playing the role of their memory-guided saccade trials ( Figure 8 ). Also consistent with our rat data and with a good analogy between rat and primateterm PPCterm, a preliminary report has suggested that unilateralterm primateterm PPCterm inactivationsterm have no effect on accumulationterm of evidence trials, while causing an ipsilateral biasterm·var on free choice trialsterm·def ( Yates et al., 2014 ).

There has been one perturbation study in the primateterm FEF during an accumulationterm of evidence task ( Gold and Shadlen, 2000 ). This microstimulation study concluded that ‘developing oculomotor commands may reflect the formation of the monkey's direction judgement’ (i.e., its decisionterm). Our results in rat FOFterm are consistent with those of Gold and Shadlen, but go considerably further in specifically suggesting the FOFterm as a requisite premotor component of the output pathway of a long time constantterm (>0.24 s) evidence accumulator.

There has been one perturbation study in the primateterm PPCterm during an accumulationterm of evidence task ( HankspersName et al., 2006 ). This microstimulation study used a reaction time version of the Random Dots task, and found a pattern of results following LIP microstimulation that could be quantitatively explained in an accumulation-to-bound model if the microstimulation added a small constant offset to the value of the accumulator ( HankspersName et al., 2006 ). Unlike the task used by HankspersName et al., our task (and that of Yates et al., 2014 ) was not a reaction time task, which could explain the difference in results. An alternative possibility, noted in their discussion ( HankspersName et al., 2006 ), and which would reconcile our results with theirs, is that microstimulation may activate axon terminals or fibers of passage ( Histed et al., 2009 , 2013 ; but see Tehovnik and Slocum, 2013 ). The behavioral effects produced by microstimulation of LIP may thus have been due to activation of neurons with somata not in LIP, but in regions of the brain that project to LIP. Since muscimol does not affect axons or fibers of passage, this possibility would be consistent with our data.

If the PPCterm plays a causal role in internally-guided decisionsterm, but does not play a causal role in choice behavior during accumulationterm of evidence tasks, what role is then played by the firing rate correlatesterm of evidence accumulationterm signals observed in PPCterm, in both rats and primatesterm? Accumulationterm signals are also correlated with confidence ( Kiani and Shadlen, 2009 ; Komura et al., 2013 ). One possibility is that, instead of being used to drive choice behavior, the accumulationterm signals observed in the PPCterm are used for computing choice confidence ( Kiani and Shadlen, 2009 ). Confidence could be part of a process for optimizing behavior over many trials, or, in a reaction time version of the task, confidence could be part of determining when the subject chooses to commit to a decisionterm.

In the rat, our data now suggests a specific functional role for the FOFterm in decisionsterm driven by accumulationterm of evidence: the FOFterm appears to be a requisite component of the output pathway of an evidence accumulator with a long time constantterm (>0.24 s). Decisionsterm with shorter processing times may involve circuits that bypass the FOFterm. It is possible that categorizing the graded accumulator's value into a discrete choice–the final decisionterm itself–could occur in the FOFterm. In contrast, the PPCterm seems to play a surprisingly minimal, or subtle, role in choice behavior during decisionsterm guided by accumulationterm of evidence, even while it plays an important role in internally-guided decisionsterm. Neither region appears likely to play a major causal role in the gradual evidence accumulationterm process per se.

Animal use procedures were approved by the Princeton University Institutional Animal Care and Use Committee and carried out in accordance with National Institutes of Health standards. All subjects were male Long-Evans rats (Taconic, NY). Rats were placed on a restricted water schedule to motivate them to work for water reward. Rats were kept on a reversed 12 hr light–dark cycle and were trained in their dark cycle.

We trained 14 male Long-Evans rats on the Poisson Clicks accumulationterm task ( Figure 1 ). Training took place in a behavior box with three nose ports (left, center and right), and with two speakers, placed above the right and left nose ports. Each accumulationterm trial began with a visible light-emitting diode (LED) turning on in the center port. This cued the trained rat to place its nose in the center port, and keep it there until the LED was turned off. We refer to this period as the ‘nose in center’ or ‘fixation’ period. The duration of fixation was 2 s for all accumulationterm trials. During the fixation period a variable duration auditory stimulus (0.1–1 s, experimenter controlled) would play, consisting of two randomly timed trains of clicks, playing simultaneously, one from the left and one from the right speaker. At the end of the auditory stimulus, the LED in the center port would extinguish, which was the signal to the rat to make their response by poking into one of the side ports. The timing of the clicks from each speaker was generated by two independent Poisson processes. The total generative click rate (left + right rate) was held constant at 40 clicks/s, and trial difficulty was controlled by adjusting the relative left vs right rates, as well as the duration of the stimulus. Trials where rats exited the center port during the fixation period were considered violation trials, aborted, and a new trial was started. These trials are not included in any analyses.

To test whether the apparent vertical scaling of the psychometric curve after unilateralterm FOFterm inactivationsterm was due to a lack of asymptotically easy trials, we interleaved ‘single-sided’ trials with accumulationterm trials (and side LED trialsterm·var in some sessions). A single-sided trial was much like an accumulationterm trial, but all the clicks came from one speaker and were played at a Poisson rate of 100 Hz. Since the 100 Hz stimuli were easily distinguished from 40 Hz stimuli and these trials did not require accumulationterm (all clicks on one side), rats probably made their decisionterm quickly. However, they were still required to wait until the go cue. These trials comprised ≈8% of a trials in a session.

In order to control for motor effects of inactivationsterm, in group 2 and 3 rats, we included, randomly interleaved with other trial-types, ‘side LED’ trials. On side LED trialsterm·var no sounds were played during fixation, which lasted 1 s. Immediately after the end of fixation, one of the two side ports was illuminated, indicating availability of reward at the lit port ( Figure 1 ). The right and left side LED trialsterm·var, together, comprised ≈10% of the total trials.

In order to find a task that was sensitive to inactivationterm of the PPCterm, we randomly interleaved ‘free-choice’ trials with the other trial-types. Free-choice trialsterm·def were similar to side LED trialsterm·var except at the end of fixation both side LEDs were illuminated and rats were rewarded regardless of whether they poked in the right or left nose port. These sessions took place after all of the experiments presented in Figures 3–7, 8E .

Control non-infusion sessions (used to generate Figure 2—figure supplement 2 ) with poor performanceterm (<70% correct overall or fewer than eight correct trials on each side without fixation violations) were excluded from analyses. These sessions were rare and were usually caused by problems with the hardware (e.g., a clogged water-reward valve or a dirty IR-photodetector). We collected ≈145,000 control trials (range [57692 265332]) over ≈450 (range [291640]) sessions from each rat (n = 14) from sessions without intracranial infusions or pre-session anesthesia for a total of 2,057,074 control trials.

Surgical methods were identical to those described previously ( ErlichpersName et al., 2011 ). Briefly, rats were anesthetized with isoflurane and placed in a stereotax. The scalp was deflected and the skull was cleaned of tissue and blood. The stereotax was used to mark the locations of craniotomies for the FOFterm and PPCterm on the skull. Craniotomies and durotomies were performed and then the skull was coated with a thin coat of C&B Metabond (Parkell Inc., NY). Guide cannula (Plastics One, VA) were lowered to brain surface with dummy cannula extending 0.5 mm into the brain. The guide cannula were placed and secured to the skull one at a time with a small amount of Absolute Dentin (Parkell Inc., NY). After the three guide cannula were in place (One bilateralterm FOFterm cannula and one cannula for each PPCterm) dental acrylic (Duralay, Reliance Dental Mfg. Co, IL) was then used to cover the skull and further secure the cannula. Rats were given 5 days to recover on free water before resuming training.

Group 1 rats (n = 6) were implanted bilaterally in FOFterm (+2 AP, ±1.25 ML mm from Bregma) with 22 AWG guide cannula (C232G-2.5, Plastics One, VA) and the medial (3.8 mm posterior, 2.2 mm lateral to Bregma) and lateral (3.8 mm posterior, 3.4 mm lateral to Bregma) PPCterm with 26 AWG guide cannula (6 cannula per rat total). Group 2 rats (n = 4) were implanted in FOFterm and in PPCterm (3.8 mm posterior, ±2.8 mm lateral to Bregma; a total of 4 cannulae per animal) with bilateralterm 22 AWG guide cannula. Group 3 rats (n = 4) were implanted with bilateralterm 22 AWG guide cannula in FOFterm and in PPCterm (4.5 mm posterior, ±3.0 mm lateral to Bregma; 4 cannulae per animal).

The tip of the guide sat at brain surface and the dummy extended 0.5 mm into cortex. The injector for the 22 AWG guide cannula was a 28 AWG cannula that extended 1.5 mm below the bottom of the guide cannula. The injector for the 26 AWG guide cannula was a 33 AWG cannula that extended 1.5 mm below the bottom of the guide cannula.

In general, infusions were performed once a week with control training days taking place on all other days of the week in order to minimize adaptation to the effects of the muscimol and to have good stable performanceterm in the sessions immediately before infusion sessions. On an infusion day, the rat was placed into an induction chamber with 2% isoflurane, and then transferred to a nose cone with 2% isoflurane for the infusion procedure. Caps and dummy cannula were removed and cleaned. Injectors were placed into the relevant guide cannula and extended 1.5 mm past the end of the guide, into cortex. We used a hamilton syringe connected via tubing filled with mineral oil to the injector to infuse 0.3 µl of muscimol (of various concentrations–see ‘Results’ and Figure 3—figure supplement 2 ) into cortex. After injection, we left the injector in the brain for 4 min to allow diffusion before removal. After 4 min, cleaned dummies were placed into the guide cannula and capped and the rat was removed from isoflurane. After 30 min of recovery from isoflurane the rat was placed into a behavior box as usual. See Figure 3—figure supplement 2 for the complete list of all infusion doses, regions, and order for each rat. Previous experiments in rat cortex, performing autoradiographic estimates ( Martin, 1991 ), as well as simultaneous muscimol inactivationterm and recordings ( Krupa et al., 1999 ), suggest that at the doses of muscimol we used, the expected area of inactivationterm would have an approximately ≈1 mm radius for the smallest doses and >3 mm radius for the largest doses.

Since the only difference between left and right infusions (and FOFterm and PPCterm infusions) are the location of the infusion any differences in behavior can only be attributed to the infusion and not to handling. For bilateralterm infusions, we were interested in non-lateralized impairments compared to baseline performanceterm. To rule out the possibility that the handling of rats for the infusion procedure could affect performanceterm we did isoflurane-only sessionsterm·var where rats were handled as they would be for an infusion (taken to the infusion room, placed into an induction chamber with 2% isoflurane, dummies removed, cleaned and replaced, etc) but given no infusion. These isoflurane-only sessionsterm·var were used as a baseline to compare with the bilateralterm infusion sessions.

All analysis and statistics were computed either in Matlab (version 7 or better, The Mathworks, MA) or R (version 2.15.2, R Foundation for Statistical Computing, Vienna, Austria). Sessions where there were too few trials, or otherwise had problems during the infusions were excluded. We only included the first 250 trials of a session because the effect of muscimol can decrease after a few hours, although the results are robust to including all trials.

The accumulator model uses 9-parameters (described in Figure 2—figure supplement 1 ) to transform the stimulus on each trial (input to the model as the left and right click times) into a probability distribution about the choice of the rat. For example, if for a given set of parameter, the model predicts that trial 1 will result in 75% chance of the rat going right, and the rat in fact went right, that trial would be assigned a likelihood of 0.75. In the case that the rat went left, the trial would be assigned a likelihood of 0.25. We fit the model assuming that the trials are independent. Therefore, for a model with parameters θ for all decisionsterm D, the likelihood is given by: P ( D | θ ) = ∏ i P ( d i | t i , R , t i , L , θ ) , the product of the likelihoods of the decisionsterm on trial i , d i , given the times of the right clicks t i , R , times of the left clicks t i , L , and the set of 9 parameters, θ . A detailed description of the procedure for fitting the accumulator model can be found in the Modeling Methods section of the supplement of BruntonpersName et al. (2013) . For panels A, C, and D in Figure 2 we first concatenated 47,580 trials across sessions and rats from sessions 1 day before an infusion session. The values of the parameters that maximized P ( D | θ ) for these concatenated data are described as ‘Meta-Rat’ in Table 1 . Since the model is fit to the individual trials, we emphasize that the psychometric, chronometric and reverse correlations plot for a given model are not generated using a curve-fitting procedure for each panel. We also fit each rat individually and show the best-fit parameters for each rat in Table 1 .

Even at the very easiest trials, rat behavior in our task often asymptotes at ≈90% correct. To fit this, the model includes a ‘lapse’ parameter, which represents a fraction of trials in which subjects will ignore the stimulus and choose randomly. The presence of the lapse parameter also puts a lower bound on the likelihood of any individual trial, and thus no individual trial can dominate the results and the consequent fits of the model.

In Figures 3, 4E, 6, 8E , Figure 2—figure supplement 2A the psychometric curves were generated by concatenating trial data across sessions for each rat and fitting (using Matlab's nlinfit) a 4-parameter sigmoid as follows: y = y 0 + a 1 + e − ( x − x + 0 ) b .

For these fits, x is the click difference on each trial (#Right Clicks − #Left Clicks), y is ‘P(Went Right)’, and the four parameters to be fit are: x 0 , the inflection point of the sigmoid; b , the slope of the sigmoid; y 0 , the minimum ‘P(Went Right)’; and a + y 0 is the maximum ‘P(Went Right)’. These fits are for visualization only.

For chronometric analyses ( Figures 2C , 4C , 6D and Figure 2—figure supplement 2C ), we concatenated trials for each rat across sessions and binned trials into easy, medium and hard quantiles with equal number of trials based on the relative generative left-right click rate. For each of these three difficulty levels we binned trials by stimulus durationterm·var.

The detailed methods of generating the psychophysical reverse correlations ( Figures 2D, 4D, 5D and Figure 6—figure supplement 1 ) can be found in the BruntonpersName et al. (2013) . For this analysis separation of right (red lines) and left (green lines) trials at each time in the trial indicates that there was a difference in local click rate at that time for trials in which the rat responded to the right vs to the left. If rats only used the early clicks for their decisionterm (a primacy strategy), the lines would begin separated and come together. Likewise, if they only used the clicks at the end of the stimulus (a recency strategy) the lines would start together and separate towards the end of the trial. To generate the accumulator model's reverse correlation, each trial was assigned as the left and right trial, according to the model's prediction for that trial. For example, if the model predicted that a trial had a 67% chance of a rightward choice, this trial would contribute 0.67 to the right trials and 0.33 to the left trials psychophysical kernel.

The unilateralterm infusion experiments are designed specifically to test for lateralized effects. On left and right infusion days animals are handled in the exact same way: taken into the room where the infusions happen, placed under light isoflurane anesthesia, etc (described in detail in the Infusions section of the ‘Materials and methods’). The only difference is the side of the infusion. As such, this within-subject design is effective at testing biasesterm to respond toward or away from the side of the infusion. The simplest way to estimate biasterm resulting from unilateralterm inactivationsterm is to subtract the contralateral % correct from the ipsilateral % correct for each infusion session. To compute the overall biasterm we averaged the biasterm across sessions for each rat and then tested using a t -testterm·stat whether the biasterm across rats was significantly different from 0. However, this statistical test is conservative, since it collapses across all trials of differing difficulty levels and different sessions. As well, this overall biasterm measure was inappropriate for testing the effects within each group, since the n per group was low.

To avoid false negative results (type II errorterm·stat), as a more sensitive measure of inactivationterm effects we used a Generalized Linear Mixed-Model (GLMM)term·stat as implemented in the function ‘lmer’ in package ‘lme4’ ( Bates and Sarkar, 2007 ; Bates et al., 2007 ). For unilateralterm infusions we specified a mixed-effects model where the rats' choice on each trial was a logistic function of #Right − #Left Clicks (Δ Clicks), infusion side and their interaction as fixed effects. The rat and an interaction of rat, infusion side, and Δ Clicks were modeled as within-subject random effects. The statistic reported in the text for unilateralterm infusions was the p value for the infusion side fixed effect. The plots in Figure 3—figure supplement 3 (FOFterm) and Figure 7—figure supplement 1 (PPCterm) show that the model fits for each rat are quite good, and reflect how the random effects of the model allow for each rats' data to be fit, while also finding significant fixed effects. The logistic fit sometimes misses the end point performanceterm, which, for the FOFterm inactivationsterm, was generally worse than the GLMMterm fit.

For bilateralterm infusions we specified a similar model comparing bilateralterm infusions to isoflurane-only sessionsterm·var. For these models the relevant statistic was the significance of the interaction between infusion and Δ Clicks, that is, a change in the slope of the logistic. Details of the data and code used to generate and compare the models is described in Supplementary file 1 ‘Using the lme4 package to fit generalized-linear mixed models in R’.

To test whether there were effects of unilateralterm infusions on response times (RT) on side LED trialsterm·var, measured as time from go cue to side port response, we took the mean RT for each rat for left and right choices on left and right infusion days. We separated leftward and rightward responses because there can be large differences from rat to rat in the left vs right response times. We then did a repeated-measures ANOVAterm·stat (Rat X [Left vs Right] X [Ipsi vs Contra]) to test whether there was an effect of muscimol on RTs. Since ANOVA must be balanced, only 4 rats (out of a possible 8 group 2 and 3 rats) performed enough side LED trialsterm·var from FOFterm infusions for this analysis. For the PPCterm infusions 7 of 8 rats performed enough trials to be included.

For the analyses of biasesterm during free-choice sessionsterm·def we compared the biasterm (ipsilateral − contralateral % correct) on the infusion day with the control session 1 day before and performed t -teststerm·stat across sessions for each region (PPCterm or FOFterm) and trial-type (free-choice, accumulationterm or side LED). Some free-choice sessionsterm·def had no side LED trialsterm·var which is why there are fewer sessions in the t -teststerm·stat for that trial-type. Side LED trialsterm·var were also not analyzed for sessions if the biasterm in the side LED trialsterm·var during the preceding control day was greater than 20%.

To fit the 9-parameter accumulator model to the bilateralterm FOFterm infusion data we concatenated all 1809 trials across all rats. We validated the error in these fits by bootstrapping. Specifically, we generated 300 sets of 1809 trials data by randomly sampling with replacement from the original data set. We then fit the 9-parameter model to each of these 300 data sets, generating 300 sets of 9 best-fit parameters. We used this distribution of fits to generate confidence intervalsterm·stat for each of the parameters. In order for a parameter to be considered as significantly different from the control value, the control value from the meta-rat fit had to be outside of the 95% confidence intervalterm·stat of the bootstrapped marginal distribution for that parameter.

To better understand what aspect of the task was impaired by unilateralterm FOFterm inactivationterm we took advantage of the knowledge of the times of all the clicks and the rats' choices using our previous modeling work ( Figure 2—figure supplement 1 , BruntonpersName et al., 2013 ) to fit four constrained Accumulator Models to the unilateralterm FOFterm infusion data. For all of these analyses we relabeled the trials for left/right trials to ipsi/contra trials based on the side of the infusion. For the infusion meta-rat we combined all 3836 trials from unilateralterm FOFterm sessions. Second, to avoid computing the gradient for a 12-parameter model, we fit constrained Accumulator Models that had one parameter free and the other parameters fixed to the best-fit parameters from the control meta-rat Accumulator Model. The details of the free parameter of each model are described in the results section.

We used MALTAB's built-in Metropolis–Hastings sampler (mhsample.m in the Statistics Toolbox) to sample from the 8-parameter distribution (described in the ‘Results’). We generated 4 separate Markov chains of 10,000 samples each, starting from the best-fit control parameters with a burnin of 100. For the proposal distribution we used a uniform distribution with the range selected for each parameter (e.g., a smaller range for input gain than for input noise). We used a thin of 4, based on test runs with known gaussian distributions. Figure 6—figure supplement 2 shows the samples generated by this sampling process.

To compare models with different numbers of parameters we used two commonly used metrics, the Bayesian and Akaike information criterion (BIC and AIC)term·stat. The BIC is defined as, BIC = −2 × LL + k × ln ( n ). Where LL is the maximum log likelihood of a model with k free parameters on n data points. The AIC is similarly defined, AIC = −2 × LL + 2 × k . The main difference being that AIC is not a function of the size of the data set. Since the cost of additional parameters in AIC is only 2 k , the AIC favors more complicated models compared to BIC.

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https://doi.org/10.1038/nature12077 Google Scholar Author details Jeffrey C ErlichpersName NYU-ECNU Institute of Brain and Cognitive Science, NYU Shanghai, Shanghai, China Princeton Neuroscience Institute, Department of Molecular Biology, Princeton University, Princeton, United States Contribution JCE, Participated in all aspects of this project For correspondence jerlich@nyu.edu Competing interests The authors declare that no competing interests exist.

"This ORCID iD identifies the author of this article:" 0000-0001-9073-7986 Bingni W BruntonpersName Princeton Neuroscience Institute, Department of Molecular Biology, Princeton University, Princeton, United States Department of Biology, UW Institute of Neuroengineering, University of Washington, Seattle, United States Contribution BWB, Collaborated with TDH and JCE in adapting the model from BruntonpersName et al. (2013) for this project Competing interests The authors declare that no competing interests exist.

"This ORCID iD identifies the author of this article:" 0000-0002-4831-3466 Chunyu A DuanpersName Princeton Neuroscience Institute, Department of Molecular Biology, Princeton University, Princeton, United States Contribution CAD, Participated in data collection and provided comments on the manuscript Competing interests The authors declare that no competing interests exist.

"This ORCID iD identifies the author of this article:" 0000-0002-3095-8653 Timothy D HankspersName Princeton Neuroscience Institute, Department of Molecular Biology, Princeton University, Princeton, United States Contribution TDH, Collaborated with BWB and JCE in adapting the model from BruntonpersName et al. (2013) for this project, Acquisition of data, Analysis and interpretation of data, Drafting or revising the article Competing interests The authors declare that no competing interests exist.

Carlos D BrodypersName Princeton Neuroscience Institute, Department of Molecular Biology, Princeton University, Princeton, United States Howard Hughes Medical Institute, Princeton University, Princeton, United States Contribution CDB, Conception and design, Analysis and interpretation of data, Drafting or revising the article For correspondence brodypersName@princeton.edu Competing interests The authors declare that no competing interests exist.

Chunyu A DuanpersName Carlos D BrodypersName Timothy D HankspersName The funders had no role in study design, data collection and interpretation, or the decisionterm to submit the work for publication.

We thank A Begelfer, K Osorio and J Teran for animal and laboratory support. TDH was supported by National Institutes of Health (NIH) Award Number F32MH098572. CAD was supported by a Howard Hughes Medical Institute International Student Research Fellowship.

Animal experimentation: This study was performed in strict accordance with the recommendations in the Guide for the Care and Use of Laboratory Animals of the National Institutes of Health. All of the animals were handled according to approved institutional animal care and use committee (IACUC) protocol (#1853) of Princeton University. All surgery was performed under isoflurane anesthesia and analgesics were given for 5 days after surgery, as recommended by the institute veterinarian. Every effort was made to minimize suffering.

© 2015, ErlichpersName et al.

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