A major challenge in computational psychiatry is to relate changes that occur at the synaptic level to the cognitive computations that underlie neuropsychiatric symptoms (Wang and Krystal, 2014; Huys et al., 2016). For example, one line of research has implicated N-methyl-D-aspartate receptor (NMDA-R) hypofunction in the pathophysiology of schizophrenia (Nakazawa et al., 2012; Kehrer et al., 2008; Olney and Farber, 1995). Some of the strongest evidence in support of this hypothesis comes from the observation that subanaesthetic doses (~0.1–0.5 mg/kg) of the NMDA-R antagonist ketamine produce psychotomimetic effects in humans, especially cognitive aspects (Krystal et al., 1994; Umbricht et al., 2000; Malhotra et al., 1996; see Frohlich and Van Horn, 2014 for review). But how do we link our understanding of the pharmacological actions of ketamine to its effects on cognition? One strategy to bridge across these different scales is to consider behaviour at the intermediate level of the cortical microcircuit.

Circuit models present a promising avenue to address the challenges of neuropsychiatric research due to their biophysically detailed mechanisms. By perturbing the circuit model at the synaptic level, specific behavioural and neural predictions can be made. For example, NMDA-Rs have long been argued to play a central role in temporally extended cognitive processes such as working memory, supported by studies of the effects of NMDA-R antagonism in prefrontal cortical microcircuits (Wang et al., 2013). Using a cortical circuit model, a precise pattern of working memory deficits can be predicted by hypofunction of NMDA-Rs, eliciting changes in excitation-inhibition balance (E/I ratio) (Murray et al., 2014). This predicts changes in behaviour consistent with those observed in healthy volunteers administered with ketamine (Murray et al., 2014), and also in patients with schizophrenia (Starc et al., 2017). Yet it currently remains unclear whether this approach might generalise to explain the behavioural consequences of NMDA-R antagonism in other temporally extended cognitive processes.

A closely related cognitive process to working memory is evidence accumulation – the decision process whereby multiple samples of information are combined over time to form a categorical choice (Gold and Shadlen, 2007). Recent research has advanced our understanding of how such evidence accumulation decisions are made in the healthy brain. Of particular relevance to psychiatric research, it has been possible to disentangle systematic biases in decision-making and reveal the mechanisms through which they occur. For instance, when choosing between two series of bars with distinct heights, people have a preference to choose the option where evidence is more broadly distributed across samples (Tsetsos et al., 2016; Tsetsos et al., 2012). Although this ‘pro-variance bias’ may appear irrational, and would not be captured by many normative decision-making models, it becomes the optimal strategy when the accumulation process is contaminated by noise (Tsetsos et al., 2016). These behaviours have presently been well-characterised using algorithmic level descriptions of decision formation, yet in order to understand how these decision biases might be affected by NMDA-R hypofunction, a mechanistic explanation is needed.

As with working memory, an influential technique used to investigate evidence accumulation at the mechanistic level has been biophysically grounded computational modelling of cortical circuits (Wang, 2002; Wong and Wang, 2006; Murray et al., 2017). Through strong recurrent connections between similarly tuned pyramidal neurons, and NMDA-R mediated synaptic transmission, these circuits can facilitate the integration of evidence across long timescales. Crucially, these neural circuit models bridge synaptic and behavioural levels of understanding, by predicting both choices and their underlying neural activity. These predictions reproduce key experimental phenomena, mirroring the behavioural and neurophysiological data recorded from macaque monkeys performing evidence accumulation tasks (Wang, 2002; Wong et al., 2007). Whether neural circuit models can provide a mechanistic implementation of the pro-variance bias, and other systematic biases associated with evidence accumulation, is currently unknown. Moreover, while NMDA-R antagonists have been tested during various decision-making tasks (Shen et al., 2010; Evans et al., 2012), the role of the NMDA-R in shaping the temporal process of evidence accumulation has not been characterised experimentally.

Here, we used a psychophysical behavioural task in macaque monkeys, in combination with spiking cortical circuit modelling and pharmacological manipulations, to gain new insights into decision-making biases in both health and disease. We trained two subjects to perform a challenging decision-making task requiring the combination of multiple samples of information with distinct magnitudes. Replicating observations from humans, monkeys showed a pro-variance bias. The pro-variance bias was also present in the spiking circuit model, revealing an explanation of how it may arise through neural dynamics. We then investigated the effects of NMDA-R hypofunction in the circuit model, by perturbing NMDA-R function at distinct synaptic sites. Perturbations could either elevate or lower the E/I ratio which strengthen or weaken recurrent circuit dynamics, with each effect making dissociable predictions for evidence accumulation behaviour. These model predictions were tested experimentally by administering monkeys with a subanaesthetic dose of the NMDA-R antagonist ketamine (0.5 mg/kg, intramuscular injection). Ketamine produced decision-making deficits consistent with a lowering of the cortical E/I ratio.

To study evidence accumulation behaviour in non-human primates, we developed a novel two-alternative perceptual decision-making task (Figure 1A). Subjects were presented with two series of eight bars (evidence samples), one on either side of central fixation. Their task was to decide which evidence stream had the taller/shorter average bar height, and indicate their choice contingent on a contextual cue shown at the start of the trial. The individual evidence samples were drawn from Gaussian distributions, which could have different variances for different options (Figure 1B). This task design had several advantages over evidence accumulation paradigms previously employed with animal subjects. Subjects were given eight evidence samples with distinct magnitudes (Figure 1C) – encouraging a temporal integration decision-making strategy. Precise experimental control of the stimuli facilitated analytical approaches probing the influence of evidence variability and time course on choice, and allowed us to design specific trials that attempted to induce systematic biases in choice behaviour.

Figure 1

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Two monkeys (Macaca mulatta) completed 29,726 trials (Monkey A: 10,748; Monkey H: 18,978). Despite the challenging nature of the task, subjects were able to perform it with high accuracy (Figure 2A–B, Figure 2—figure supplement 1A–B). The precise control of the discrete stimuli allowed us to evaluate the impact of evidence presented at each time point on the final behavioural choice, via logistic regression (see Materials and methods). Stimuli presented at a time point with a larger regression coefficient have a strong impact on the choice, relative to time points with smaller coefficients. We found that the subjects utilised all eight stimuli throughout the trial to inform their decision, and demonstrated a primacy bias such that early stimuli have stronger temporal weights than later stimuli (Figure 2C–D, Figure 2—figure supplement 1C–D). A primacy bias has been reported in prior studies in monkeys, and is consistent with a decision-making strategy of bounded evidence integration (Kiani et al., 2008; Nienborg and Cumming, 2009; Wimmer et al., 2015). As it was clear both monkeys could accurately perform the task, all subsequent figures are presented with data collapsed across subjects for conciseness, but results separated by subjects are consistent (see supplementary figures).

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We next probed the influence of evidence variability on choice. We designed specific choice options with different levels of standard deviation across samples in an attempt to replicate the pro-variance bias previously reported for human subjects (see Materials and methods) (Tsetsos et al., 2016; Tsetsos et al., 2012). On each trial, one option was allocated a narrow distribution of bar heights, and the other a broad distribution. In different conditions, either the broad or narrow stimuli stream could be the correct choice (‘Broad Correct’ Trials or ‘Narrow Correct’ Trials), or there could be no clear correct answer (‘Ambiguous’ Trials) (Figure 3A, Figure 3—figure supplements 1 and 2). If subjects chose optimally, and only the mean bar height influenced their choice, their accuracy would be the same in ‘Broad Correct’ and ‘Narrow Correct’ trials and they would be indifferent to the variance of the distributions in ‘Ambiguous’ trials. We show that our monkeys deviate from such behaviours. The monkeys are more accurate on ‘Broad Correct’ trials than on ‘Narrow Correct’ trials (Figure 3B, Figure 3—figure supplements 1 and 2). Furthermore, in the ‘Ambiguous’ trials, the monkeys demonstrated a preference for the broadly distributed stream, which has greater variability across samples (Figure 3C, Figure 3—figure supplements 1 and 2). Such a pro-variance bias pattern of decision behaviour is similar to what was found in human subjects (Tsetsos et al., 2016; Tsetsos et al., 2012; Figure 3D–E).

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To further probe the pro-variance bias, we studied choices from a larger pool of ‘Regular’ trials in which the mean evidences and variabilities of the two streams were set independently on each trial (Figure 4A–B, Figure 4—figure supplements 1 and 2). ‘Regular' trials allowed us to explore the pro-variance bias across a greater range of choice difficulties (Figure 4C) and quantitatively characterise its effect using regression analysis. On ‘Regular’ trials, subjects also demonstrated a preference for options with broadly distributed evidence. Regression analysis confirmed that evidence variability was a significant predictor of choice (Figure 4D; see Materials and methods).

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In addition, we defined the pro-variance bias (PVB) index as the ratio of the regression coefficient for evidence standard deviation over the regression coefficient for mean evidence. Although evidence standard deviation was irrelevant in determining the correct option to choose in the task, and it is important to note that we were not suggesting it is explicitly computed by the monkey subjects, the sensitivity of choice behaviour to evidence standard deviation could also arise as a by-product of the neural computations to evaluate the task-relevant mean evidence (as shown later in the Results). PVB index thus served as a unitless, descriptive measure of the evidence accumulation process, quantifying the subjects’ sensitivity to evidence standard deviation relative to the evidence accumulation process. A PVB index value of 0 thereby indicates no pro-variance bias, whereas a PVB index value of 1 indicates the subject is as sensitive to evidence standard deviation as they are to mean evidence. The PVB index thus provides a quantitative measure of the pro-variance bias. A key motivation for defining PVB index is as a potentially useful measure for assessing changes in decision-making behaviour, such as via pharmacological perturbation (performed in later experiments in this paper). For example, if a perturbation simply weakened the overall sensitivity of choice to stimulus information, this would presumably down-scale the mean and standard deviation regression coefficients proportionally, yielding no change in the PVB index as a ratio. In contrast, if a perturbation to the decision-making process differentially impacts how evidence mean vs. standard deviation impact choice, then this would be reflected as a change in the PVB index. From the ‘Regular’ trials, the PVB index across both monkeys was 0.173 (Monkey A = 0.230; Monkey H = 0.138).

Recent work has suggested that when traditional evidence accumulation tasks are performed, it is hard to dissociate whether subjects are combining information across samples, or whether conventional analyses may be disguising a simpler heuristic (Waskom and Kiani, 2018; Stine et al., 2020). In particular, an alternative decision-making strategy which does not involve temporal accumulation of evidence is to detect the single most extreme sample. Because the extreme sample will occur at different times in each trial, if a subject employed this strategy, the choice regression weights across time points would be distributed as in Figure 2C–D. Therefore, it is possible for these findings to be mistakenly interpreted as reflecting evidence accumulation. We wanted to quantitatively confirm that subjects were using the strategy we envisioned when designing our task, namely evidence accumulation. Additionally, we wanted to further investigate the relative contributions of mean evidence and evidence variability on choices. A logistic regression approach probed the influence upon choice of mean evidence, evidence variability, first/last samples, and the most extreme samples within each stream (Figure 4—figure supplements 1E,H & and 2C,F,I,L, see Materials and methods). A cross-validation approach revealed choice was principally driven by the mean evidence, verifying that subjects performed the task using evidence accumulation (Supplementary file 1, see Materials and methods).

Although this analysis revealed choices were not primarily driven by an ‘extreme sample detection’ decision strategy, another concern was whether partially employing this strategy could explain the pro-variance effect we observed. To address this, we compared the influence of ‘evidence variability’ versus the influence of ‘extreme samples’ on subjects’ choices. Cross-validation revealed that choices were better described by a model incorporating evidence variability, rather than the extreme sample values (Supplementary file 2). We also demonstrated that including evidence variability as a co-regressor improved the performance of all combinations of nested models (Supplementary file 3). In summary, it can be concluded that although subjects integrated across samples, they were additionally influenced by sample variability.

Previous studies have revealed that a ‘frequent winner’ bias – whereby subjects prefer to choose options where there is a greater number of cases of stronger evidence between the simultaneously presented stimuli – coexists with the pro-variance bias (Tsetsos et al., 2016). Furthermore, both of these biases may arise from the same selective accumulation mechanism (Tsetsos et al., 2016). Therefore, we next analysed whether our subjects’ choices were also influenced by a ‘frequent winner’ bias (Figure 4—figure supplement 3; Materials and methods). After controlling for the influence of mean evidence on choices, we found that neither subject demonstrated a ‘frequent winner’ bias.

Existing algorithmic-level proposals for generating a pro-variance bias in human decision-making rely on the disregarding of sensory information before it enters the accumulation process, depending on its salience (Tsetsos et al., 2016). To investigate a possible alternative basis for the pro-variance bias, at the level of neural implementation, we sought to characterise decision-making behaviour in a biophysically-plausible spiking cortical circuit model (Figure 5A–B, Figure 5—figure supplement 1; Wang, 2002; Lam, 2017). In the circuit architecture, two groups of excitatory pyramidal neurons are assigned to the left and right options, such that high activity in one group signals the response to the respective option. Excitatory neurons within each group are recurrently connected to each other via AMPA and NMDA receptors, and this recurrent excitation supports ramping activity and evidence accumulation. Both groups of excitatory neurons are jointly connected to a group of inhibitory interneurons, resulting in feedback inhibition and winner-take-all competition (Wang, 2002; Wong and Wang, 2006). The two groups of excitatory neurons receive separate inputs - with each group receiving information about one of the two options (i.e. Group A receives I_A reflecting the left option; Group B receives I_B reflecting the right option). Specifically, we assume the bar heights from each stream are remapped, upstream of the simulated decision-making circuit, to evidence for the corresponding option depending on the cued context. Therefore, taller bars correspond to larger inputs in a ‘ChooseTall’ trial and smaller inputs in a ‘ChooseShort’ trial. Combined together, this synaptic architecture endows the circuit model with decision-making functions.

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The spiking circuit model was tested with the same trial types as the monkey experiment. Importantly, not only can the circuit model perform the evidence accumulation task, it also demonstrated a pro-variance bias comparable to the monkeys (Figure 5C–F). Regression analysis showed that the circuit model utilises a strategy similar to the monkeys to solve the decision-making task (Figure 5—figure supplement 1B). The temporal process of evidence integration in the circuit model disproportionately weighted early stimuli over late stimuli (Figure 5G), similar to the evidence integration patterns observed in both monkeys. However, the circuit model demonstrated an initial ramp-up in stimuli weights due to the time needed for it to reach an integrative state.

To understand the origin of the pro-variance bias in the spiking circuit, we mathematically reduced the circuit model to a mean-field model (Figure 6A), which demonstrated similar decision-making behaviour to the spiking circuit (Figure 6B-C, Figure 6—figure supplement 1). The mean-field model, with two variables representing the integrated evidence for the two choices, allowed phase-plane analysis to further investigate the pro-variance bias. A simplified case was considered where the broad and narrow streams have the same mean evidence, and the stimuli evidence varies over time in the broad stream but not the narrow stream (i.e. ${\mathrm{\sigma }}_{\mathrm{N}}$=0) (Figure 6E-H). This example provides an intuitive explanation for the pro-variance bias: a momentarily strong stimulus has an asymmetrically greater influence upon the decision-making process than a momentarily weak stimulus. Input streams with larger variability and thus a higher chance to display both strong inputs and weak inputs, can thus leverage such asymmetry more so than input streams with small variability, resulting in pro-variance bias. Such asymmetry arises from the expansive non-linearities of the firing rate profiles (Figure 6D, see Materials and methods).

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To explore whether this explanation may account for the pro-variance bias in the circuit model and monkey behaviour (Figures 4 and 5), we re-analysed the data separating trials into two halves: those with more or less total evidence (summed across both streams) (Figure 5—figure supplement 2). The circuit model demonstrated a smaller PVB index (larger mean evidence and smaller evidence standard deviation regression weights) for trials with more total evidence than for trials with less total evidence (Figure 5—figure supplement 2C). This was consistent with the prediction from the F-I non-linearity: trials with more total evidence, and thus larger total input, will more strongly drive the neurons to the near-linear regime of the firing rate profile, where the effect of the expansive non-linearity was weaker (Figure 6D). Similar analysis of the monkey behavioural data revealed a similar trend of smaller PVB index (larger mean evidence and smaller evidence standard deviation regression weights) for trials with more total evidence than less total evidence, though the effect was insignificant (Figure 5—figure supplement 2G). In addition, distinct temporal weighting on stimuli were observed in both the circuit model and experimental data, for trials with more versus less total evidence (Figure 5—figure supplement 2D,H).

An advantage of the circuit model over existing algorithmic level explanations of the pro-variance bias is it can be used to make testable behavioural predictions in response to different synaptic or cellular perturbations, including excitation-inhibition (E/I) imbalance. In turn, perturbation experiments can constrain and refine model components. Therefore, we studied the behavioural effects of distinct E/I perturbations, and upstream sensory deficit, on decision making and in particular, pro-variance bias (Figure 7, Figure 7—figure supplement 1). Three perturbations were introduced to the circuit model: lowered E/I balance (via NMDA-R hypofunction on excitatory pyramidal neurons), elevated E/I balance (via NMDA-R hypofunction on inhibitory interneurons), or sensory deficit (as weakened scaling of external inputs to stimuli evidence) (Figure 7A).

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While all circuit models were capable of performing the task (Figure 7B–E), the choice accuracy of each perturbed model was reduced when compared to the control model. This was quantified by the regression coefficient of mean evidence (Figure 7F). In addition, the regression coefficient for evidence standard deviation was reduced for each perturbed model in comparison to the control model, indicating a lesser influence of evidence variability on choice (Figure 7G). Finally, in a dissociation between the three model perturbations, the PVB index was increased by lowered E/I, decreased by elevated E/I, and roughly unaltered by sensory deficits (Figure 7H). Further regression analyses indicated no obvious shift in utilised strategies relative to the control model (Figure 7—figure supplement 1). Crucially, the effect of E/I and sensory perturbations on PVB index and regression coefficients were generally robust to the strength and pathway of perturbation (Figure 7—figure supplements 2 and 3).

Disease and pharmacology-related perturbations likely concurrently alter multiple sites, for instance NMDA-Rs of both excitatory and inhibitory neurons. We thus parametrically induced NMDA-R hypofunction on both excitatory and inhibitory neurons in the circuit model. The net effect on E/I ratio depended on the relative perturbation strength to the two populations (Lam, 2017). Stronger NMDA-R hypofunction on excitatory neurons lowered the E/I ratio, while stronger NMDA-R hypofunction on inhibitory neurons elevated the E/I ratio. Notably, proportional reduction to both pathways preserved E/I balance and did not lower the mean evidence regression coefficient (a proxy of performance) (Figure 7—figure supplement 2A). On the other hand, decision making performance was maximally susceptible to perturbations in the orthogonal direction, along the E/I axis (Lam, 2017). Furthermore, along this axis PVB index monotonically increased with lowered E/I ratio and decreased with elevated E/I ratio, demonstrating a robust prediction from our circuit model (Figure 7—figure supplement 2C). Sensory deficit perturbations did not significantly alter PVB index, until the limit where decision making performance was greatly impaired (Figure 7—figure supplement 4). Finally, the temporal weightings were distinctly altered by the elevated- and lowered- E/I perturbations (Figure 7I). The circuit model thus provided the basis of dissociable prediction by E/I-balance perturbing pharmacological agents.

Since the decision making choice accuracy depends on E/I ratio along an inverted-U shape – where the control, E/I balanced model is right next to the (slightly lowered E/I) peak (Lam, 2017)- both elevating and lowering E/I ratio drive the model away from the peak, resulting in lowered mean evidence regression weight. The evidence standard deviation regression weight similarly follows an inverted-U shape, but with the peak at a more strongly lowered E/I ratio (Figure 7—figure supplement 2). As such, elevating E/I ratio consistently lowers the evidence standard deviation regression weight, but lowering E/I ratio by a small amount initially increases the evidence standard deviation regression weight, and only decreases the evidence standard deviation regression weight after such peak in the inverted-U shape is passed at greater perturbation strengths. Notably, regardless of the magnitude with which E/I ratio is lowered, PVB index is consistently increased, providing a robust measure of pro-variance bias.

To explore these predictions experimentally, we collected behavioural data from both monkeys following the administration of a subanaesthetic dose (0.5 mg/kg, intramuscular injection) of the NMDA-R antagonist ketamine (see Materials and methods, Figure 8, Figure 8—figure supplement 1). After a baseline period of the subjects performing the task, either ketamine or saline was injected intramuscularly (Monkey A: 13 saline sessions, 15 ketamine sessions; Monkey H: 17 saline sessions, 18 ketamine sessions). Administering ketamine had behavioural effects for around 30 min in both subjects. The data collected during this period formed a behavioural database of 8521 completed trials (Monkey A Saline: 1710; Monkey A Ketamine: 2276; Monkey H Saline: 2669; Monkey H Ketamine: 1866). Following ketamine administration, subjects’ choice accuracy was markedly decreased (Figure 8A), without a significant shift in their strategies (Figure 8—figure supplement 1, Supplementary file 4).

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To understand the nature of this deficit, we studied the effect of drug administration on the pro-variance bias (Figure 8B–F). Although subjects were less accurate following ketamine injection, they retained a pro-variance bias (Figure 8C). Regression analysis confirmed ketamine caused choices to be substantially less driven by mean evidence (Figure 8D), but still strongly influenced by the standard deviation of evidence across samples (Figure 8E). The PVB index was significantly higher when ketamine was administered, than saline (permutation test p=8×10⁻⁶, Figure 8F). Of all the circuit model perturbations, this was only consistent with lowered E/I balance (Figure 7H).

In further analysis, we also controlled for the influence of ketamine on the subjects’ lapse rate – i.e. the propensity for the animals to respond randomly regardless of trial difficulty. We modelled this lapse rate using an additional term that bounded the logistic function at Y₀ and (1-Y₀), rather than 0 and 1 (Figure 8—figure supplement 2, see Materials and methods, Equation 9). In other words, lapse rate refers to the asymptote error rate at the limit of strong evidence. Consistent with the psychometric function (Figure 8C), we found that ketamine significantly increased the subjects’ lapse rate (Subject A: Lapse_(Saline)=1.49×10⁻¹¹, Lapse_(Ketamine)=0.118, permutation test, p<0.0001; Subject H: Lapse_(Saline)=0.012, Lapse_(Ketamine)=0.0684, permutation test, p=0.019). Crucially, however, the PVB effect was still present in the regression model that included the effect of lapses. This confirms that the change in lapse rate was not responsible for any of the behavioural effects of ketamine outlined above. We also investigated the time-course of ketamine’s influence on the PVB index (Figure 8—figure supplement 3). This confirmed that the rise in PVB was an accurate description of a common behavioural deficit throughout the duration of ketamine administration.

Additional observations further supported the lowered E/I hypothesis for the effect of ketamine on monkey choice behaviour. Quantitative model comparison, using cosine similarity, Euclidean distance, and Kullback–Leibler (KL) divergence, revealed the effect of ketamine injection on monkey choice behaviour was better explained by lowered E/I perturbations in the circuit model, than by sensory deficit or elevated E/I perturbations (Figure 8—figure supplements 4–6). Very strong sensory deficit may also increase PVB index, but with minimal decision making performance and a psychometric function very different from the monkey data (Figure 7—figure supplement 4, Figure 8—figure supplement 7). In addition, we investigated the effect of ketamine on the time course of evidence weighting (Figure 8G). It caused a general downward shift of the temporal weights; but had no strong effects on how each stimulus was weighted relative to the others in the stream. This shifting of the weights could reflect a sensory deficit, but given the results of the pro-variance analysis, collectively the behavioural effects of ketamine are most consistent with lowered E/I balance and weakened recurrent connections. Notably, the saline data demonstrate a U-shaped pattern different from the primacy pattern observed in non-drug experiments (Figure 2C,D) and spiking circuit models (Figure 7I). This may be due to task modifications for the ketamine/saline experiments compared with the non-drug experiments, but could also potentially arise from distinct regimes of decision making attractor dynamics (e.g. see Genís Prat-Ortega et al., 2020).

To quantify the effect of lapse rate on evidence sensitivity and regression weights in general, we examined the effect of a lapse mechanism downstream of spiking circuit models (Figure 8—figure supplements 8–9). Using the lapse rate fitted to the experimental data collected from the two monkeys, we assigned such portions of trials to have randomly selected choices for each circuit model, and repeated the analysis to obtain psychometric functions and various regression weights. Crucially, while the psychometric function as well as evidence mean and standard deviation regression weights were suppressed, the findings on PVB index were not qualitatively altered in the circuit models, further supporting the finding that the lapse rate does not account for changes in PVB under ketamine.

Previous studies have shown human participants exhibit choice biases when options differ in the standard deviation of the evidence samples, preferring choice options drawn from a more variable distribution (Tsetsos et al., 2016; Tsetsos et al., 2012). By utilising a behavioural task with precise experimenter control over the distributions of time-varying evidence, we show that macaque monkeys exhibit a similar pro-variance bias in their choices akin to human participants. This pro-variance bias was also present in a spiking circuit model, which demonstrated a neural mechanism for this behaviour. We then introduced perturbations at distinct synaptic sites of the circuit, which revealed dissociable predictions for the effects of NMDA-R antagonism. Ketamine produced decision-making deficits consistent with a lowering of the cortical excitation-inhibition balance.

Biophysically grounded neural circuit modelling is a powerful tool to link cellular level observations to behaviour. Previous studies have shown recurrent cortical circuit models reproduce normative decision-making and working memory behaviour, and replicate the corresponding neurophysiological activity (Wang et al., 2013; Murray et al., 2014; Wang, 2002; Wong and Wang, 2006; Murray et al., 2017; Wong et al., 2007; Wimmer et al., 2014). However, whether they are also capable of reproducing idiosyncratic cognitive biases has not previously been explored. Here we demonstrated pro-variance and primacy biases in a spiking circuit model. The primacy bias results from the formation of attractor states before all of the evidence has been presented. This neural implementation for bounded evidence accumulation corresponds with previous algorithmic explanations (Kiani et al., 2008).

The results from our spiking circuit modelling also provide a parsimonious candidate mechanism for the pro-variance bias within the evidence accumulation process. Specifically, strong evidence in favour of an option pushes the network towards an attractor state more so than symmetrically weak evidence pushes it away. Previous explanations for pro-variance bias proposed computations at the level of sensory processing upstream of evidence accumulation. In particular, a ‘selective integration’ model proposed that information for the momentarily weaker option is discarded before it enters the evidence accumulation process (Tsetsos et al., 2016). Conceptually, our model was analogous to previous models in that weak evidence is weighted less relative to strong evidence. However, there are key differences between the two models. In ‘selective integration’ and similar models concerning sensory processes, an asymmetric filter was applied to the stimuli before the stimuli were evaluated by the decision making process, in some upstream area that can be potentially modulated based on task demands. In contrast, in our circuit model pro-variance bias arose from the non-linearity activity profile (Figure 6D, See Materials and methods) of model neurons. In that sense, pro-variance bias was an intrinsic phenomenon of the evidence integration process in our circuit model.

Despite the conceptual analogy between our circuit model and the ‘selective integration’ model in which weak stimuli were asymmetrically weighted, our circuit model cannot be directly mapped to the latter. In the ‘selective integration’ model, the asymmetry is realized as a discounting of the momentarily weaker stimuli by a constant factor. In our circuit model, the asymmetry arose from the non-linearity of the transfer function. However, the transfer function was not static, but dynamically evolved with the state of the model (e.g. in the mean-field model, the transfer function depended on the two decision variables, See Materials and methods). Due to this complexity, the asymmetry of the circuit model cannot be reduced to one simple expression, and was instead closely entangled with the attractor dynamics of the system.

Crucially, our circuit model generated dissociable predictions for the effects of NMDA-R hypofunction on the pro-variance bias (PVB) index that were tested by follow-up ketamine experiments. While it remains an open question where and how in the brain the selective integration process takes place, our modelling results suggest that purely sensory deficits may not capture the alterations in choice behaviour observed under ketamine, in contrast to E/I perturbations in decision-making circuits (Figure 7H). Multiple complementary processes may simultaneously contribute to pro-variance bias during decision making, especially in complex behaviours over longer timescales. Future work will aim to contrast between these two models with neurophysiological data recorded while monkeys are performing this task.

On the other hand, there may also be limits in the extent to which our findings can be directly compared to those from previous studies in humans (Tsetsos et al., 2016; Tsetsos et al., 2012). For example, human studies have revealed that a ‘frequent winner’ bias coexists with the pro-variance bias and may arise from the same selective integration mechanism. Unlike previous studies, our subjects did not exhibit a ‘frequent winner’ bias. Furthermore, although both studies demonstrate a PVB, the temporal weighting of evidence in the previous human studies exhibit recency, unlike the primacy found in the present study. This may be in part due to differences in the underlying computational regimes that are used for evidence integration, or may be due to more trivial differences between the experimental paradigms – for example, different paradigms have identified primacy (Kiani et al., 2008), recency (Cheadle et al., 2014) or noiseless sensory evidence integration (Brunton et al., 2013). A stronger test will be to record neurophysiological data while monkeys are performing our task; this would help to distinguish between the ‘selective integration’ hypothesis and the cortical circuit mechanism proposed here.

The PVB index, as the ratio of standard deviation to mean evidence regression weights, serves as a conceptually useful measure to interpret changes in pro-variance bias due to ketamine perturbation in this study. Given the model does not feature any explicit processes that mediate pro-variance bias, PVB should be understood as an emergent phenomenon arising from the decision-making process. In this context, a sensory-deficit perturbation, which down-scales the incoming evidence strength without perturbing the decision-making process, should proportionally down-scale the evidence mean and standard deviation regression weights, thus maintaining the PVB index. In contrast, lowering and elevating E/I ratio distinctly alter the dynamics of the decision-making process and thus differentially perturb the PVB index. It is also important to study how changes in the PVB index are driven by changes in the mean vs. standard deviation regression coefficients, as considering PVB index alone can obscure these effects. For instance, based on the model, the increase in PVB index by lowering E/I is generally due to a stronger decrease in mean regression coefficient than standard deviation regression coefficient (Figure 7—figure supplement 2). However, small perturbations of lowering E/I may actually increase PVB index due to an increase in standard deviation regression coefficient and a decrease in mean regression coefficient. As a support of this model finding, while the two monkeys both demonstrate a significant decrease in mean regression weight by ketamine, one monkey seems to demonstrate a trend to decrease standard deviation regression weight and the other seems to demonstrate a trend to increase (Figure 8—figure supplement 2). The two monkeys, both interpreted as lowered E/I ratio using the model-based approach in this study, may therefore experience slightly different degrees of E/I reduction when administered with ketamine, as shown through concurrent changes in NMDA-R conductances in the circuit model (Figure 7—figure supplement 2).

In this study we did not undertake quantitative fitting of the circuit model parameters to match the empirical data. Rather we took a previously developed circuit model and only manually adjusted input strengths to be loosely in the regime of experimental behavior. There are technical and theoretical challenges in quantitatively fitting to psychophysical behavior with biophysically-based circuit models, including reduced mean-field models, which have impeded such applications in the field. Critical challenges include computational cost of simulation, a large number of parameters with unknown effective degeneracies on behavior, and treatment of noise in mean-field reductions. Future work, beyond the scope of the present study, is needed to bridge these gaps in relating circuit models to psychophysical behavior.

Instead of direct model fitting, here we studied biophysically-based spiking circuit models for two primary purposes: to examine whether a behavioral phenomenon, such as pro-variance bias, can emerge from a regime of circuit dynamics, and through what dynamical circuit mechanisms; and to characterize how the phenomenon and underlying dynamics is altered by modulation of neurobiologically grounded parameters, such as NMDA-R conductance. The circuit modelling in this study demonstrates a set of mechanisms which is sufficient to produce the phenomenon of interest. The bottom-up mechanistic approach in this study, which makes links to the physiological effects of pharmacology and makes testable predictions for neural recordings and perturbations, is complementary to top-down algorithmic modeling approaches.

Our pharmacological intervention experimentally verified the significance of NMDA-R function for decision-making. In the spiking circuit model, NMDA-Rs expressed on pyramidal cells are necessary for reverberatory excitation, without which evidence cannot be accumulated and stable working memory activity cannot be maintained. NMDA-Rs on interneurons are necessary for maintaining background inhibition and preventing the circuit from reaching an attractor state prematurely (Murray et al., 2014; Wang, 2002). By administering ketamine, an NMDA-R antagonist, specific short-term deficits in choice behaviour were induced, which were consistent with a lowering of the cortical excitation-inhibition balance in the circuit model. This suggests the NMDA-R antagonist we administered systemically was primarily acting to inhibit neurotransmission onto pyramidal cells and weaken the recurrent connection strength across neurons. It is important to note that in addition to the main role of ketamine as a NMDA-R antagonist, it might also target other receptor sites (Chen et al., 2009; Zanos et al., 2016; Moaddel et al., 2013). However, of all receptors, ketamine has by far the highest affinity for the NMDA-R receptor (Frohlich and Van Horn, 2014). The effects of synaptic perturbations could be interpreted in terms of their net effect on E/I balance, at least to the first order (Murray et al., 2014; Lam, 2017). For instance, in the circuit model, proportional NMDA hypofunction on both E and I neurons maintains E/I balance and minimally impairs circuit computation, while the effect of disproportionate NMDA hypofunction on E and I neurons is well captured by the direction of net change in E/I ratio (Figure 7—figure supplements 2 and 3). Given the highest affinity of ketamine to NMDA-Rs, the effect of NMDA-R-hypofunction should dominantly determine the direction of E/I imbalance, and should not be counter-balanced by the effect of other perturbations. Finally, other receptors and brain areas are likely altered by systemic ketamine administration, which is beyond the scope of the microcircuit model in this study.

The physiological effects of NMDA-R antagonism on in vivo cortical circuits remains an unresolved question. A number of studies have proposed a net cortical disinhibition through NMDA-R hypofunction on inhibitory interneurons (Nakazawa et al., 2012; Krystal et al., 2003; Lisman et al., 2008; Lewis et al., 2012). The disinhibition hypothesis is supported by studies finding NMDA-R antagonists mediate an increase in the firing of prefrontal cortical neurons, in rodents (Jackson et al., 2004; Homayoun and Moghaddam, 2007) and monkeys (Ma et al., 2018; Ma et al., 2015; Skoblenick and Everling, 2012; Skoblenick et al., 2016). On the other hand, the effects of NMDA-R antagonists on E/I balance may vary across neuronal sub-circuits within a brain area. For instance, in a working memory task, ketamine was found to increase spiking activity of response-selective cells, but decrease activity of the task-relevant delay-tuned cells in primate prefrontal cortex (Wang et al., 2013). Such specificity might explain why several studies reported less conclusive effects of NMDA-R antagonists on overall prefrontal firing rates in monkeys (Wang et al., 2013; Zick et al., 2018). In vitro work has also revealed the excitatory post-synaptic potentials (EPSPs) of prefrontal pyramidal neurons are much more reliant on NMDA-R conductance than parvalbumin interneurons (Rotaru et al., 2011). Other investigators combining neurophysiological recordings with modelling approaches have also concluded that the action of NMDA-R antagonists is primarily upon pyramidal cells (Wang et al., 2013; Moran et al., 2015). Our present findings, integrating pharmacological manipulation of behaviour with biophysically-based spiking circuit modelling, suggest that the ketamine-induced behavioural biases are more consistent with a lowering of excitation-inhibition balance and weakening of recurrent dynamics. Future work with electrophysiological recordings during the performance of our task, under pharmacological interventions, can potentially dissociate the effect of ketamine on E/I balance specifically in cortical neurons exhibiting decision-related signals. Notably, the decision making behaviours in our circuit model arise from attractor dynamics relying on unstructured interneurons to provide lateral feedback inhibition. Recent experiments found that, in mouse parietal cortex during a decision-making task, inhibitory parvalbumin (PV) interneurons - thought to provide feedback inhibition - may be equally selective as excitatory pyramidal neurons (Najafi et al., 2020). Depending on the pattern and connectivity of their feedback projections to pyramidal neurons, such a circuit structure supports different forms of evidence accumulation in cortical circuits (Lim and Goldman, 2013). It remains to be seen how the pro-variance bias effect and the current predictions extend to circuit models with selective inhibitory interneurons.

The minutes-long timescale of the NMDA-R mediated decision-making deficit we observed was also consistent with the psychotomimetic effects of subanaesthetic doses of ketamine in healthy humans (Krystal et al., 1994; Krystal et al., 2003). As NMDA-R hypofunction is hypothesised to play a role in the pathophysiology of schizophrenia (Kehrer et al., 2008; Olney and Farber, 1995; Krystal et al., 2003; Lisman et al., 2008), our findings have important clinical relevance. Previous studies have demonstrated impaired perceptual discrimination in patients with schizophrenia performing the random-dot motion (RDM) decision-making task (Chen et al., 2003; Chen et al., 2004; Chen et al., 2005). Although RDM tasks have been extensively used to study evidence accumulation (Gold and Shadlen, 2007), previously this performance deficit in schizophrenia was interpreted as reflecting a diminished representation of sensory evidence in visual cortex (Chen et al., 2003; Butler et al., 2008). Based on our task with precise temporal control of the stimuli, our findings suggest that NMDA-R antagonism alters the decision-making process in association cortical circuits. Dysfunction in these association circuits may therefore provide an important contribution to cognitive deficits - one that is potentially complementary to upstream sensory impairment. Crucially, our task uniquely allowed us to rigorously verify that the subjects used an accumulation strategy to guide their choices (cf. previous animal studies [Gold and Shadlen, 2007; Roitman and Shadlen, 2002; Hanks et al., 2015; Morcos and Harvey, 2016; Katz et al., 2016]), with these analyses suggesting the strategy our subjects employed was relatively consistent with findings in human participants. This consistency further ensures our findings may translate across species, in particular to clinical populations.

Another related line of schizophrenia research has shown a decision-making bias known as jumping to conclusions (JTC) (Ross et al., 2015; Huq et al., 1988). The JTC has predominately been demonstrated in the ‘beads task’, a paradigm where participants are shown two jars of beads, one mostly pink and the other mostly green (typically 85%). The jars are hidden, and the participants are presented a sequence of beads drawn from a single jar. Following each draw, they are asked if they are ready to commit to a decision about which jar the beads are being drawn from. Patients with schizophrenia typically make decisions based on fewer beads than controls. Importantly, this JTC bias has been proposed as a mechanism for delusion formation. Based on the JTC literature, one plausible hypothesis for behavioural alteration under NMDA-R antagonism in our task may be a strong increase in the primacy bias, whereby only the initially presented bar samples would be used to guide the subjects’ decisions. However, following ketamine administration, we did not observe a strong primacy – instead all samples received roughly the same weighting. There are important differences between our task and the beads task. In our task, the stimulus presentation is shorter (2 s, compared to slower sampling across bead draws), and is of fixed duration rather than terminated by the subject’s choice, and therefore may not involve the perceived sampling cost of the beads task (Ermakova et al., 2019).

Our precise experimental paradigm and complementary modelling approach allowed us to meticulously quantify how monkeys weight time-varying evidence and robustly dissociate sensory and decision-making deficits – unlike prior studies using the RDM and beads tasks. Our approach can be readily applied to experimental and clinical studies to yield insights into the nature of cognitive deficits and their potential underlying E/I alterations in pharmacological manipulations and pathophysiologies across neuropsychiatric disorders, such as schizophrenia (Wang and Krystal, 2014; Huys et al., 2016) and autism (Wang and Krystal, 2014; Yizhar et al., 2011; Lee et al., 2017; Marín, 2012). Finally, our study highlights how precise task design, combined with computational modelling, can yield translational insights across species, including through pharmacological perturbations, and across levels of analysis, from synapses to cognition.

Stimuli generation and data analysis for the experiment were performed in MATLAB. The spiking circuit model was implemented using the Python-based Brian2 neural simulator, with a simulations time step of 0.02ms. Further analyses for both experimental and model data were completed using custom-written Python and MATLAB codes. Data has been uploaded to Dryad under the doi:10.5061/dryad.pnvx0k6k3. Code is available on GitHub at https://github.com/normanlam1217/CavanaghLam2020CodeRepository (copy archived at https://github.com/elifesciences-publications/CavanaghLam2020CodeRepository).

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Author details

1. Sean Edward Cavanagh

   Department of Clinical and Movement Neurosciences, University College London, London, United Kingdom

   Contribution

   Conceptualization, Data curation, Software, Formal analysis, Investigation, Visualization, Methodology, Writing - original draft, Writing - review and editing

   Contributed equally with

   Norman H Lam

   For correspondence

   sean.cavanagh.12@ucl.ac.uk

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0001-9275-2725

2. Norman H Lam

   Department of Physics, Yale University, New Haven, United States

   Contribution

   Conceptualization, Data curation, Software, Formal analysis, Investigation, Visualization, Methodology, Writing - review and editing

   Contributed equally with

   Sean Edward Cavanagh

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0001-5817-6680

3. John D Murray

   Department of Psychiatry, Yale University School of Medicine, New Haven, United States

   Contribution

   Conceptualization, Resources, Supervision, Funding acquisition, Writing - review and editing

   Contributed equally with

   Laurence Tudor Hunt and Steven Wayne Kennerley

   For correspondence

   john.murray@yale.edu

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0003-4115-8181

4. Laurence Tudor Hunt

   1. Department of Clinical and Movement Neurosciences, University College London, London, United Kingdom
   2. Wellcome Trust Centre for Neuroimaging, University College London, London, United Kingdom
   3. Max Planck-UCL Centre for Computational Psychiatry and Aging, University College London, London, United Kingdom
   4. Wellcome Centre for Integrative Neuroimaging, Department of Psychiatry, University of Oxford, Oxford, United Kingdom

   Contribution

   Conceptualization, Resources, Supervision, Funding acquisition, Writing - review and editing

   Contributed equally with

   John D Murray and Steven Wayne Kennerley

   For correspondence

   laurence.hunt@psych.ox.ac.uk

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-8393-8533

5. Steven Wayne Kennerley

   Department of Clinical and Movement Neurosciences, University College London, London, United Kingdom

   Contribution

   Conceptualization, Resources, Supervision, Funding acquisition, Project administration, Writing - review and editing

   Contributed equally with

   John D Murray and Laurence Tudor Hunt

   For correspondence

   s.kennerley@ucl.ac.uk

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-5696-7507

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