In 1848, a railroad worker named Phineas Gage suffered an accident that was to secure him a place in neuroscience lore. While constructing a new railway line, a mistimed explosion propelled an iron bar into the base of his skull, where it passed behind his left eye before exiting through the top of his head. Gage survived the accident, but those who knew him reported significant changes in his personality and behaviour.

Gage’s ability to make decisions was particularly impaired by his injury. Decision-making involves weighing up the costs and benefits associated with alternative courses of action. It entails looking into the future to decide whether an anticipated reward will justify the effort or expense necessary to obtain it. This process is dependent on a region of the brain called the prefrontal cortex, the area that sustained the most damage in Phineas Gage.

While many studies have shown correlations between activity in particular parts of prefrontal cortex and the outcome of decisions, little is known about how this activity evolves over time as a decision is made. To explore this process, Hunt et al. trained macaque monkeys to choose between pairs of images that were associated with specific rewards (quantities of fruit juice) and costs (either amounts of work or fixed delays).

Electrode recordings revealed changes in prefrontal activity that varied over time as the monkeys deliberated over each pair of images, choosing for example between a large reward after a long delay versus a smaller reward immediately. This activity was consistent with a mathematical model of decision-making, which also explains data from brain imaging experiments in humans. This provides an important link between human data and electrode recordings in animals.

However, some of the patterns of activity observed in both macaques and humans appeared to reflect the speed at which decisions were made, rather than the outcome of the decisions themselves. By extracting information about decision speed on each decision from each region, it was shown that communication between regions of prefrontal cortex changes when choices are between two different amounts of work, as opposed to two different delays. Further experiments are needed to explore this phenomenon and to determine how other brain regions interact with the prefrontal cortex to support the decision-making process.

Correlates of decision variables are routinely found in prefrontal cortex (PFC) during value-guided decision making (Clithero and Rangel, 2014; Kennerley and Walton, 2011). They have been richly described using static, economic models of choice (Glimcher and Fehr, 2014). Neuroeconomic accounts explain firing rates of single neurons or human neuroimaging data in terms of experimental variables that motivate choice behaviour. These include the magnitude or likelihood of available reward, and the costs involved in obtaining those rewards. By forming neural representations of such quantities, it is argued that the brain can use these representations to guide selection of the most valuable alternative. Our present understanding of economic decision formation has been founded upon careful study of neural representations of value and how they differ across PFC subregions (Glimcher and Fehr, 2014; Rushworth et al., 2012; Rangel and Hare, 2010).

However, an alternative perspective on the origins of neural representations during decision making stems from choice models from mathematical psychology (Busemeyer and Townsend, 1993). Such models seek to explain decisions in terms of their temporal evolution or dynamics. Whilst originally accounting for temporally varying features of behaviour, such as reaction times and eye gaze (Busemeyer and Townsend, 1993; Ratcliff and Rouder, 1998; Krajbich et al., 2010), they have also successfully captured temporally varying features of neural activity, most notably in the lateral intraparietal cortex (LIP) during perceptual choice (Shadlen and Newsome, 2001; Gold and Shadlen, 2007). These psychological models can also be related to other dynamical models (Bogacz et al., 2006) such as nonlinear attractor network models firmly rooted in neurobiology (Wang, 2002). The common feature of both psychological and neurobiological accounts is that they focus on the temporal evolution of a decision signal across time, rather than the strength with which it represents decision variables at a particular fixed point in time.

Contrasting the two perspectives, it becomes apparent that even if neuronal activity underwent the exact same physiological process on different trials (such as a ramp-to-threshold), it might nevertheless appear to represent certain economic features of a decision. Put simply, as the decision unfolds, neural activity will be higher on trials that ramp quickly than on those that ramp slowly. It will therefore correlate with any variable that affects the decision speed, and this effect will appear most prominent at timepoints in the trial when the ramping process, or rate of change, is maximal. Even in more complex dynamical situations, it is easy to see how economic variables that predict the rate of change would appear to be represented in neural activity if analysed without knowledge of the underlying dynamics. This might particularly be true of the value of the chosen item (‘chosen value’), which strongly affects behavioural reaction times in economic choice tasks.

This should then influence how we interpret the meaning of such activity (Hunt, 2014; O’Doherty, 2014). The neuroeconomic perspective often labels chosen value representations as a ‘post-decision’ signal, arguing that chosen value signals do not reflect the decision competition itself but instead the outcome of the comparison process (Cai and Padoa-Schioppa, 2012; Blanchard and Hayden, 2014). One interpretation of such representations is that they are needed for subsequent computation of a reward prediction error (Rangel and Hare, 2010). Yet the dynamical perspective proposes that they may in fact originate as a consequence of time evolving decision processes. Rather than casting a chosen value representation as signaling ‘pre-decision’ or ‘post-decision’ variables to downstream brain areas, it argues that such correlates inevitably emerge as a decision is made. In its most extreme form, this hypothesis might contend that chosen value signals would be fully accounted for by variation in underlying decision rates.

To assess this proposal more carefully, it becomes critical to index how neural dynamics unfold on individual trials. In PFC, tackling this problem provides unique challenges. Several recent studies have recovered single-trial dynamical information in structures close to motor output, based upon neuronal spiking data (Thura and Cisek, 2014; Kaufman et al., 2015; Murakami et al., 2014; Bollimunta et al., 2012; Kiani et al., 2014; Carnevale et al., 2015). Yet the distance of PFC from either sensory input or motor output produces neural activity that is poorly aligned with simple features of the experimental task (Rigotti et al., 2013). Attempts to understand PFC activity should therefore extract its dynamical state based on neural information alone, rather than first sorting spike trains by motor output or experimental variables as is common in other approaches. It is also unclear whether neuronal firing rates are in fact the most reliable source of single-trial information. The esotericism of PFC neuronal responses is compounded by a high degree of stochasticity in neuronal spike trains, delivering statistical challenges to obtaining single-trial information (Churchland et al., 2007; Park et al., 2014). Current techniques sometimes overcome this problem by examining tens or hundreds of simultaneously recorded single neurons (Churchland et al., 2007). Whilst this can be fruitful, such data is rarely available in humans, where the contribution of PFC to value-guided choice is most critical.

In the present study, we therefore sought an alternative index of single-trial neural dynamics that overcame these limitations. We focussed on observations at the mesoscopic scale of the local field potential (LFP). One advantage of this approach is that it can be easily related to simultaneously recorded neuronal spike trains on a trial-by-trial basis in animals, but also underlies the magnetoencephalography (MEG) signal observable in humans (Buzsáki et al., 2012). As such, we could recover dynamical information from electrophysiology recordings in macaque monkeys and also from non-invasive magnetoencephalography (MEG) recordings in humans. This provides an important bridge between observations at microscopic (cellular) and macroscopic (whole-brain) scales. Importantly, our index provides information about the speed of a local internal neural decision process that goes beyond a simple behavioural measure of reaction time.

Using this index, we could draw several new conclusions about PFC activity during choice. We first demonstrate a temporal evolution from action value difference to chosen action signals that are selectively present in dorsolateral prefrontal cortex (DLPFC) neurons, but not anterior cingulate cortex (ACC) or orbitofrontal cortex (OFC). This contrasts against the ubiquitous encoding across all three subregions of ‘chosen value’. However, we then demonstrate that correlates of chosen value may arise as a consequence of dynamical processing, as opposed to being purely represented as a neuroeconomic post-decision variable. Next, by simultaneously indexing decision formation across multiple PFC subregions, we show that functional interactions can be reshaped in a task-dependent manner. We find that OFC and ACC dynamics selectively influence dorsolateral DLPFC activity on delay- and effort-based decisions respectively. Finally, our observations can be related to predictions from a dynamical neural network model of choice. This provides formal links to established dynamical mechanisms underlying perceptual decision-making.

We examined a study of cost-benefit decision making in which single neuron firing and local field potentials (LFPs) were recorded simultaneously from three PFC subregions fundamental to value-guided choice in four macaque monkeys: orbitofrontal cortex (OFC), anterior cingulate cortex (ACC) and dorsolateral prefrontal cortex (DLPFC). On each trial, subjects chose between two pictures that led to a certain reward magnitude (quantity of fruit juice) after paying a certain cost (Figure 1A). On half of trials this cost was physical effort needed to obtain reward, and on half of trials it was delay to reward. Subjects were overtrained on the cost and benefit paired with each picture. Their choices were well described by a linear trade-off between reward and cost combined with a softmax choice function (see Hosokawa et al., 2013 for detailed behavioural modelling). This allows a straightforward definition of ‘value’ used in the analyses below (see methods). Throughout the paper, we analyse neuronal firing and LFP during a 1s choice phase, when subjects fixated centrally whilst both pictures were on screen. After this 1s period, a go cue appeared, instructing subjects to saccade to their preferred picture to indicate their choice.

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Extracting single-trial information about choice dynamics from event-related LFP

One approach to bridging across data scales would be to extract single-trial information about choice-related dynamics from one scale, and use it to explain variance in the other. The evoked LFP appeared consistent across different recording electrodes and sessions (Figure 2—figure supplement 1), and possessed a high single-trial signal to noise ratio (Figure 2—figure supplement 2). We therefore pursued a data-driven index of single-trial dynamics from LFP data.

The approach we adopted was to apply principal components analysis (PCA) across trials (see Methods). For each subject, the input data for macaque PCA was decision-locked raw LFP data, stacked across all electrodes from all recording sessions to form a large matrix X. X has dimensions nSingleTrials by nTimebins (Figure 2A). PCA decomposes X into temporal principal components V, with dimensions nTimepoints by nComponents, and component weights U, with dimensions nSingleTrials by nComponents (Figure 2A). The principal components (PCs) in V provide a set of temporal basis functions (Figure 2B) that capture the principal modes of variation in the shape of the waveform across trials. The single-trial weights in U tell us how much of each PC is present in each single-trial response. They are returned separately for each electrode. Because data are stacked, however, the decomposition has the same meaning across different electrodes and recording sessions.

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The top two PCs were strikingly consistent across all four macaque subjects (Figure 2C). Importantly, they were readily interpretable in terms of their effects on LFP dynamics. PC1 (Figure 2B, left panel) resembled the basic shape of the event-related field potential (Figure 1D). Adding or subtracting PC1 therefore captures variation across trials in response amplitude (Figure 2D, left panel). More notable, however, was PC2, which was relatively flat at the beginning of the decision, but from 200 ms onwards resembled the temporal derivative of PC1 (Figure 2B, right panel). Adding or subtracting the temporal derivative of a waveform controls the latency at which it peaks (Figure 2D, right panel) (Friston et al., 1998; Mayhew et al., 2006). Knowledge about PC2 weights therefore provides a parsimonious description of single-trial ERP latencies, a key feature of the dynamical ERP response. Consistent with this idea, PC2 weights were also found to correlate with the phase of low frequency (theta frequency [4-–8 Hz]) oscillations during the decision period (Figure 2—figure supplement 3).

In light of this, we hypothesised that factors modulating reaction time in value-based choice studies (Busemeyer and Townsend, 1993) would affect the weight of PC2, controlling the latency of the LFP waveform. We found chosen value had a strong and consistent effect on PC2 across all regions studied. When chosen value was higher, PC2 was more positive, implying the waveform peaked earlier in time (Figure 2E; Figure 2—figure supplement 4). On ‘error trials’, where the subject chose the less valuable option, PC2 weights were more positive than on correct (Figure 2E). Under the assumption that higher value trials, and error trials, were associated with faster decision dynamics (Busemeyer and Townsend, 1993; Ratcliff and Rouder, 1998), PC2 weights therefore provide a neurally-derived index of the speed of the decision on each trial. Crucially, however, they are obtained separately for each individual electrode. They therefore provide a local measurement of neural dynamics, beyond a simple behavioural measure of reaction time. PC1 weights, capturing response amplitude rather than latency, were primarily influenced by value sum (same sign for both chosen and unchosen value, with the exception of ACC) (Figure 2—figure supplement 5).

Internal single-trial dynamics explain neural activity over and above external variables

We next considered whether our internal LFP-derived index might explain features of neural firing that we could not previously explain using external experimentally-derived variables. We explored this idea using multiple regression. We regressed experimental factors onto neural firing rates (see Supplementary file 1 for full list) to capture variance explained by these factors, as in Figure 1B. However, we also included as a coregressor the single-trial PC2 weight for that trial, estimated from the decomposition of the LFP. This allows us to examine the influence of PC2 weights on neuronal firing, having controlled for the contribution of all external decision variables. To avoid contamination between spikes and LFP, we used LFP data recorded simultaneously from a neighbouring electrode in the same cortical area. (Note that reaction time is not included as an additional measure of trial-by-trial decision dynamics in our task, as the imposed 1s choice delay prior to response led to a floor effect in subjects’ response times.)

Figure 3A and B shows two individual neurons from DLPFC that exemplify the action value-to-choice transformation depicted in Figure 1B/C. As can be seen, variance in their firing is explained by the action value difference early (~200-–400 ms), and the chosen action late (~600–800 ms) in the decision process. In both cases, the LFP-derived PC2 single trials weights explain additional variance as this value-to-choice transformation occurs (Figure 3A/B). Across the population, PC2 had a similar effect at this point in time (Figure 3C). 44.9% of neurons in DLPFC were found to have a significant modulation by LFP-derived PC2 weights during the choice epoch (23.4% positively modulated, 21.5% negatively modulated, p<0.01 in a 250 ms–750 ms window, corrected for multiple comparisons across time). This finding forms a link between choice dynamics at mesoscopic and microscopic scales, over and above that which can be obtained from examining time-varying value correlates (as in Figure 1). Additional analyses confirmed that this relationship could not be explained as a simple consequence of first-order correlations between LFP amplitude and firing rate (Whittingstall and Logothetis, 2009).

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Having formed this link between our measure of single-trial LFP dynamics and neural firing, we could then address several questions concerning the roles of these dynamics in value-guided decision making.

Influence of single-trial LFP components on single unit chosen value correlates

The representation of chosen value is found in many neural structures during choice, but its interpretation has remained unclear. It has been pointed out that this is a ‘post-decision’ variable, and several suggestions have been offered for why this might need to be encoded (Rangel and Hare, 2010). In our study, the timecourse of this signal (found across all three cortical areas, Figure 1—figure supplement 1) appears similar to the timecourse of influence of the LFP PC2 weights on neuronal firing (Figure 3C). We sought to explore the relationship between chosen value correlates identified in single unit firing and our single-trial indices of ERP amplitude (PC1) and latency (PC2).

To address this, we reanalysed the findings in Figure 1B, but asked whether including the top two LFP principal components in our regression model selectively reduced the variance explained by chosen value, but not by action value difference or chosen action (see Methods). As a control, we compared this model to one where two noise components (PC101 and PC102) from the LFP PCA were included as coregressors instead of PC1 and PC2. We found that including the LFP-derived PC1/PC2 as coregressors caused a significant reduction in chosen value coding, but not of action value difference or chosen action coding (Figure 4; Figure 4—figure supplement 1). Similar results could also be obtained via an alternative approach, in which instead of using noise components, principal components were shuffled across trials in a fashion that preserved their underlying correlation with chosen value, or by examining the contribution of PC1 or PC2 alone (Figure 4—figure supplement 2).

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We then asked whether chosen value coding was reduced more by local (within-region) neural dynamics, compared to global (whole-brain) dynamics. We found a smaller but significant reduction could also still be found even if these ‘local’ principal components (i.e. from the same brain region) were orthogonalised with respect to those of another, simultaneously recorded brain region, when compared to performing the same analysis in reverse (Figure 4—figure supplement 3). This implies that some of the neuronal variance attributed to chosen value correlates originates as a consequence of the speed and amplitude at which dynamics unfold locally within a particular cortical area, and demonstrates the utility of our single-trial index for capturing these local dynamics.

OFC and ACC dynamics have distinct influences on delay- and effort-based decisions respectively

ACC and OFC have established roles in effort- and delay-based decisions respectively (Rudebeck et al., 2006; Prevost et al., 2010; Croxson et al., 2009; Kurniawan et al., 2013; Kable and Glimcher, 2007; Parvizi et al., 2013). Because our LFP decomposition indexes decision dynamics locally, we hypothesised that the internal dynamics of ACC and OFC might preferentially influence activity in DLPFC on different trial types. Specifically, we predicted that firing rates in DLPFC would be preferentially affected by ACC internal dynamics on effort-based trials, but by OFC internal dynamics on delay-based trials. We could test this hypothesis by examining sessions in which DLPFC, ACC and OFC were all recorded simultaneously. We built a regression model in which LFP-derived PC2 weights from OFC and ACC competed for variance in explaining neural firing in DLPFC (see Methods). We estimated this separately on delay and effort trials. Both areas were found to influence DLPFC activity (Figure 5—figure supplement 1), but strikingly, ACC explained more variance in DLPFC firing on effort trials than delay trials (Figure 5A, magenta), whereas the converse was true for OFC (Figure 5A, black). This was not found to be true for analyses performed in the reverse direction (using DLPFC/ACC PC2 weights to explain OFC firing, or DLPFC/OFC PC2 weights to explain ACC firing).

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Notably, OFC and ACC PC2 weights modulated DLPFC neuron firing from around 200 ms after choice onset (Figure 5—figure supplement 1), consistent with the time at which DLPFC neurons first begin to encode choice values (Figure 1B). These effects on DLPFC firing were maintained for several hundred milliseconds. Critically however, just prior to when response coding in DLPFC was peaking (around 800 ms, see Figure 1B), the contribution of ACC and OFC PC2 to DLPFC neuron firing changed in a cost-specific way. OFC PC2 began to selectively explain spiking variance on delay trials, whilst ACC began to explain spiking variance on effort trials (Figure 5—figure supplement 1).

We also found that when we performed a median split on DLPFC neurons by the degree to which they encoded chosen value in the analysis shown in Figure 1B, neurons with high chosen value selectivity were also those preferentially influenced by other regions’ dynamics (Figure 5B). If DLPFC chosen value coding is interpreted as reflecting the speed at which a decision process unfolds, then these findings imply that the influence of one region’s internal dynamics on another region’s dynamics can be flexibly reshaped according to current task demands. This was not true, by contrast, when a median split was performed based upon the response selectivity of the DLPFC neuronal population.

Similar single-trial choice dynamics can be obtained from human MEG data

The LFP value correlates in Figure 1E showed similar temporal profiles to a previous study in which human subjects made binary value-guided choices whilst undergoing MEG (Hunt et al., 2012). We therefore asked whether the MEG signal from this study, in the PFC subregion where this temporal profile had been observed (ventromedial prefrontal cortex, MNI 6, 28, –8 mm), could also be subjected to a similar single-trial PCA decomposition as our LFP data. Each subject provides a single ‘virtual electrode’ from which observations are made, and so data were stacked to form the matrix X with dimensions nSingleTrials ([=nTrials*nSubjects]) by nTimebins (see Methods). This was then decomposed as for the macaque data. We found a similar relationship between PC1 and PC2 (Figure 6A) controlling waveform amplitude and latency (Figure 6B). Moreover, PC2 had a similar relationship to chosen value and error trials as in macaques (Figure 6C). Finally, in this experiment, we also had a direct behavioural readout of decision formation on every trial as subjects could respond at any time after decision onset. Subject reaction times were strongly negatively predictive of PC2, over and above any contribution of chosen value, unchosen value or errors (Figure 6C). Our observations here provide a link between the dynamics of choice at the mesoscopic scale in macaques and its macroscopic counterpart in humans.

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Several features of the data are explained by competition via mutual inhibition

The transition in value correlates observed at the macroscopic scale in human MEG can be explained with reference to a class of recurrent neural network models displaying competition via mutual inhibition (Hunt et al., 2012). Such models have success in explaining many features of neural data in perceptual choice (Shadlen and Newsome, 2001; Wang, 2002), focusing on how a decision might be implemented locally within a single cortical area of interest. We therefore asked whether these models might explain some of our observations at the microscopic (single-neuron) level, and whether a similar decomposition approach can be applied to mesoscopic (LFP) predictions from the network model as to our data.

We simulated a spiking attractor network model of choice, configured with the same connectivity structure and parameters as had been used in a previous study of perceptual decision-making (Wang, 2002) (Figure 7A; see also ‘Supplementary details of network modelling’). We analysed the model predictions as we had the data, regressing action value difference, chosen value and chosen action onto single-neuron firing rates. Strikingly, value correlates in the network model possessed the same temporal profile as in DLPFC neurons (compare Figure 1B with Figure 7B). One discrepancy was the more sustained chosen value signal in the network model than in the data (which may result from inputs to the model persisting even after an attractor basin has been reached). We then ran a similar dimensionality reduction on summed network activity, a proxy for the model’s LFP predictions, as we had done on both macaque LFP and human MEG data. By contrast with the LFP data, we obtained a single principal component that controlled both waveform amplitude and latency (see ‘Supplementary details of network modelling’, and Figure 7—figure supplement 1). This suggests that within the network model there is covariation between these two features of the simulated ERP waveform, whereas in the data they are orthogonal. However, this principal component correlated with value in a similar fashion to both macaque and human data (compare Figure 2E/6C with Figure 7C). We then regressed the principal component back onto single unit firing rates, as in Figure 3. We found a similar timecourse of influence of the model’s principal component on single unit firing to that found in the data (compare Figure 3C with Figure 7D, cyan). Moreover, we found that the internal dynamics of the model extracted from the PCA explained chosen value coding in a similar fashion to that observed in data (Figure 4), causing a marked reduction (compare Figure 7B with Figure 7D, green). Our observations in this study may therefore be explained mechanistically via a simple attractor network model of choice, which similarly captured LFP dynamics in our previous human MEG study (Hunt et al., 2012). Further details of network modelling are provided in Supplementary Information.

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Many previous studies (Kim et al., 2008; Daw et al., 2006; Padoa-Schioppa, 2013; Hampton et al., 2006; Padoa-Schioppa and Assad, 2006), including our own (Kennerley et al., 2011), note the representation of chosen value in multiple brain structures during choice. Why this quantity is encoded so widely has been a matter of debate (Rangel and Hare, 2010). It is important to remember that this encoding comes from the viewpoint of the experimenter, seeking to describe variability across trials at a particular timepoint in the trial or decision process. As we have shown here, and would be predicted from previous behavioural studies (Busemeyer and Townsend, 1993; Ratcliff and Rouder, 1998; Krajbich et al., 2010), decision processes are dynamic and decision formation inherently exhibits variability across trials. This means that what appears to the experimenter as encoding of a decision related-signal may be a consequence of another ongoing process. To paraphrase a recent observation (Cisek, 2006), “the role of a decision-making system is to produce decisions, not to describe them.”

Decision-making systems accumulate evidence in favour of different alternatives across time, and generate a categorical choice. This has been most carefully considered in integrate-to-bound models of perceptual choice and their neural correlates (Gold and Shadlen, 2007). Crucially, the time at which sensory evidence is maximally encoded in a neural integrator is not at the beginning of the decision (when no integration has occurred), nor at the end (when the bound has been reached on all trials), but in the middle of the decision process – when on some trials the bound has been reached, whereas on others little net evidence has been accumulated for each alternative. It can be very difficult in practice to infer when a decision begins or ends, and this poses difficulties when labelling a neural correlate as ‘pre-decision’ or ‘post-decision’. The dynamical perspective instead explains certain correlates as emerging as the decision is formed. These signals may still remain of functional significance for other computations (such as subsequent computation of the reward prediction error [Rangel and Hare, 2010]), but our perspective on how they are generated is changed.

Value-guided choices are, like perceptual decisions, a dynamical process (Busemeyer and Townsend, 1993; Krajbich et al., 2010; Summerfield and Tsetsos, 2012). This brings into focus the potentially important role played by decision dynamics in generating correlates of chosen value. In the present study, we found that in DLPFC correlates of chosen value occurred maximally during the transformation from an initial representation of evidence (action value difference) to an eventual representation of choice (chosen action) (Figure 1B). A similar temporal progression could also be found in the network model of competition via mutual inhibition (Figure 7B). Crucially, however, a portion of the variance captured by chosen value was then explained away by including the speed and amplitude of the local LFP response on that trial as a coregressor, estimated via PCA decomposition of the LFP (Figure 4).

It is important to note that there are some caveats to this interpretation. Firstly, only some, not all, of the variance was removed by including PCA components as coregressors. As such, it may be the case that there is coding of chosen value during the decision that is not explained by the amplitude and speed of the evoked response during decision formation. However, despite the reasonable signal-to-noise ratio observed in LFP data, single-trial PC weights will likely contain a degree of observation noise. Hence our estimates likely form a lower bound on how much of the chosen value signal might be explained away by LFP dynamics. To address this question further, future studies might seek to estimate the degree of observation noise in estimating dynamics, and the theoretical limit that this imposes on how much variance could be explained in neural firing. A further important caveat is that chosen value correlates may be explained by different mechanisms at different points in the trial. LFPs are often interpreted as measurements of local synaptic input, and this may imply that our principal components mediate chosen value representations at the level of single units. It is also clear from Figure 1—figure supplement 1 that correlates of chosen value are present in single unit firing until the end of the decision epoch. Future work may investigate the origin and functional significance of this persistent chosen value coding, perhaps for use at later task stages.

Our single-trial index also provides critical information about how dynamics simultaneously unfold at different speeds in different brain areas. This was evidenced most clearly by examining the interaction between OFC and ACC principal component weights, and DLPFC neuronal firing. Previous work has suggested a functional specialisation of OFC and ACC for delay- and effort-based decisions, respectively. In rats, lesions made to OFC lead to impulsive choices (of a small, immediate reward over a larger, delayed reward) whereas lesions made to ACC lead to less effortful choices (of a small, easily obtained reward over a larger reward demanding more work) (Rudebeck et al., 2006). In humans, functional imaging activations yield a similar double dissociation between effortful and delay-based decisions (Prevost et al., 2010; Croxson et al., 2009; Kurniawan et al., 2013; Kable and Glimcher, 2007), and further evidence can be drawn from the effects of electrical stimulation of ACC (Parvizi et al., 2013). Our results extend these findings by suggesting that the rate at which dynamics unfold in OFC preferentially influences a decision signal in DLPFC on delay-based trials relative to effort-based trials, whereas the converse is true for ACC’s influence on DLPFC (Figure 5). This supports the view that the effective influence of one brain region on another is modulated by the type of decision currently being made (Hunt et al., 2014; Tauste Campo et al., 2015). We note, however, that our analysis does not test the possibility is that a third (unobserved) variable could jointly affect both regions, doing so differentially on effort vs. delay trials.

Variation in ERP latency also corresponds to a shift in the phase of an oscillation (at low frequencies, present in the evoked response). Consistent with this, we found PC2 weights correlated with the phase of oscillations in the theta range (4-–8 Hz) as the decision was made (Figure 2—figure supplement 3). This suggests a possible way in which future studies may link our measure of LFP latency to spike-LFP coupling (Koralek et al., 2013; Canolty et al., 2010) or inter-regional LFP coherence (Nacher et al., 2013) during cognitive tasks.

The network model attempts to capture the dynamics of a single cortical region, but not interactions between regions. In our study, competitive dynamics similar to the model (saccadic action value difference transforming into chosen action) were clearly visible in DLPFC (Figure 1B/7B), but not in other regions (Figure 1—figure supplement 1). However, at the mesoscopic scale, dynamics of chosen value correlates were relatively indistinguishable across regions (Figure 2E, Figure 1—figure supplement 3). One explanation for these phenomena is that competition proceeds in a distributed fashion across multiple areas (Rushworth et al., 2012; Hunt et al., 2014; Cisek, 2012). Competition in DLPFC might occur selectively in saccadic action space, but this might be complemented by parallel competitions in other regions in other reference frames. Examples of such competitions might include those over particular decision attributes (e.g. OFC for delay, ACC for effort/physical action value), abstract goods (Padoa-Schioppa, 2013; Padoa-Schioppa and Assad, 2006), internal state variables (Bouret and Richmond, 2010), attentional allocation (Lim et al., 2011), goal or task-relevant prioritisation (Hunt et al., 2014; Hare et al., 2009) or other reference frames critical for the decision at hand (Hunt et al., 2013). Though lesion evidence clearly implicates areas like ACC, OFC and ventromedial PFC as critical and dissociable in value-based decision-making (Kennerley et al., 2006; Rudebeck et al., 2008; Camille et al., 2011; Noonan et al., 2010), our results indicate that identifying ‘chosen value’ signals is not sufficient to understand the functional dissociations of these areas in the decision-making process. Further studies are needed to fully understand the reference frame in which different decision areas contribute to decision-making (Hunt et al., 2013; 2014; Boorman et al., 2013), with a careful consideration of the relationship between underlying choice dynamics and neuronal correlates of value. Future recurrent network models of choice involving hierarchical competitions across multiple areas (Hunt et al., 2014; Chaudhuri et al., 2015) might also capture this distributed approach, and seek to explain our observations concerning the selective effort- and delay-based interactions across areas (Figure 5). A distributed account would predict that in other experimental paradigms, single neurons would show similar competitive dynamics to our DLPFC neurons but in complementary frames of reference (Rustichini and Padoa-Schioppa, 2015; Strait et al., 2014).

PCA is one of many possible approaches to obtaining a useful set of temporal basis functions to describe variation in ERP waveforms, and it may be improved upon by future investigations. We selected it for its simplicity, and its known properties of returning a temporal derivative when capturing evoked responses of variable durations (Friston et al., 1998; Mayhew et al., 2006; Woolrich et al., 2004). Directly computing the ERP waveform and its temporal derivative would also be a valid approach to derive temporal basis functions. However, this approach may face problems if different components of the evoked response do not covary with each other. For example, the large, fast evoked response observed across all regions within 200 ms of stimulus onset (Figure 1D) was comparatively small in the first two principal components (Figure 2B). This implies that cross-trial variation in this early sensory-evoked component occurred largely orthogonal to cross-trial variation in the later (putatively decision-related) component. This feature of the data is identified automatically using PCA.

The LFP decomposition returned by PCA shows a notable similarity to that observed in decompositions of trial-averaged waveforms from multi-electrode recordings in motor cortex during movement (Churchland et al., 2012). This provides links to dynamical systems perspectives on such activity. Unlike previous studies, however, our approach leverages mesoscopic dynamics containing high signal to noise ratio and reproducibility to extract single-trial information. This dispenses any requirement to first relate neural activity to experimental variables by averaging or regression (Churchland et al., 2012; Mante et al., 2013). We contend that this is particularly important in studying PFC and other areas distant from sensory input or motor output, whose relationship to experimental variables may often be considerably more complex than the experimenter envisaged (Rigotti et al., 2013).

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Author details

1. Laurence T Hunt

   1. Sobell Department of Motor Neuroscience, University College London, London, United Kingdom
   2. Wellcome Trust Centre for Neuroimaging, University College London, London, United Kingdom

   Contribution

   LTH, Conception and design, Acquisition of data, Analysis and interpretation of data, Drafting or revising the article

   For correspondence

   laurence.hunt@ucl.ac.uk

   Competing interests

   No competing interests declared.

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

2. Timothy EJ Behrens

   1. Wellcome Trust Centre for Neuroimaging, University College London, London, United Kingdom
   2. Oxford Centre for Functional MRI of the Brain, Nuffield Department of Clinical Neuroscience, Oxford University, John Radcliffe Hospital, Oxford, United Kingdom

   Contribution

   TEJB, Conception and design, Analysis and interpretation of data, Drafting or revising the article

   Competing interests

   TEJB: Senior editor, eLife.

3. Takayuki Hosokawa

   1. Helen Wills Neuroscience Institute, University of California, Berkeley, Berkeley, United States
   2. Department of Psychology, University of California, Berkeley, Berkeley, United States
   3. Laboratory of Systems Neuroscience, Graduate School of Life Sciences, Tohoku University, Sendai, Japan

   Contribution

   TH, Acquisition of data, Drafting or revising the article

   Competing interests

   No competing interests declared.

4. Jonathan D Wallis

   1. Helen Wills Neuroscience Institute, University of California, Berkeley, Berkeley, United States
   2. Department of Psychology, University of California, Berkeley, Berkeley, United States

   Contribution

   JDW, Conception and design, Drafting or revising the article

   Competing interests

   No competing interests declared.

5. Steven W Kennerley

   1. Sobell Department of Motor Neuroscience, University College London, London, United Kingdom
   2. Helen Wills Neuroscience Institute, University of California, Berkeley, Berkeley, United States
   3. Department of Psychology, University of California, Berkeley, Berkeley, United States

   Contribution

   SWK, Conception and design, Acquisition of data, Analysis and interpretation of data, Drafting or revising the article

   Competing interests

   No competing interests declared.

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