The human brain efficiently solves certain operations such as object recognition and categorization through a massively parallel network of dedicated processors. However, human cognition also relies on the ability to perform an arbitrarily large set of tasks by flexibly recombining different processors into a novel chain. This flexibility comes at the cost of a severe slowing down and a seriality of operations (100–500 ms per step). A limit on parallel processing is demonstrated in experimental setups such as the psychological refractory period (PRP) and the attentional blink (AB) in which the processing of an element either significantly delays (PRP) or impedes conscious access (AB) of a second, rapidly presented element. Here we present a spiking-neuron implementation of a cognitive architecture where a large number of local parallel processors assemble together to produce goal-driven behavior. The precise mapping of incoming sensory stimuli onto motor representations relies on a “router” network capable of flexibly interconnecting processors and rapidly changing its configuration from one task to another. Simulations show that, when presented with dual-task stimuli, the network exhibits parallel processing at peripheral sensory levels, a memory buffer capable of keeping the result of sensory processing on hold, and a slow serial performance at the router stage, resulting in a performance bottleneck. The network captures the detailed dynamics of human behavior during dual-task-performance, including both mean RTs and RT distributions, and establishes concrete predictions on neuronal dynamics during dual-task experiments in humans and non-human primates.

A ubiquitous aspect of brain function is its quasi-modular and massively parallel organization. The paradox is that this extraordinary parallel machine is incapable of performing a single large arithmetic calculation. How come it is so easy to recognize moving objects, but so difficult to multiply 357 times 289? And why, if we can simultaneously coordinate walking, group contours, segment surfaces, talk and listen to noisy speech, can we only make one decision at a time? Here we explored the emergence of serial processing in the primate brain. We developed a spiking-neuron implementation of a cognitive architecture in which the precise sensory-motor mapping relies on a network capable of flexibly interconnecting processors and rapidly changing its configuration from one task to another. Simulations show that, when presented with dual-task stimuli, the network exhibits parallel processing at peripheral sensory levels, a memory buffer capable of keeping the result of sensory processing on hold. However, control routing mechanisms result in serial performance at the router stage. Our results suggest that seriality in dual (or multiple) task performance results as a consequence of inhibition within the control networks needed for precise “routing” of information flow across a vast number of possible task configurations.

Until now, the modeling of dual tasks is only specified at a level of mathematical description and functional cognitive architecture [4] , [18] , [24] , [25] . At the neurophysiological level, understanding what kind of collective neural organization leads from massively parallel single-unit processing to a serial unfolding of two successive decisions has not been established. This situation is, to a large degree, due to the fact that there have been detailed monkey electrophysiology of single-task decision making [26] , [27] , but no comparable investigation of dual-tasks. Here we present an effort to bridge this gap between an abstract mathematical description and the underlying complex neurophysiology. We present a detailed model, based on realistic properties of spiking neurons which is capable of flexibly linking processors to form novel tasks. As a consequence of this flexibility, the network exhibits a functional serial bottleneck at the level of the “router” circuit needed to link processors. The model presents detailed predictions for future electrophysiological studies of dual-tasks and serial computations in the human and non-human primate brain.

The psychological refractory period (PRP) provides a classic and clear demonstration in experimental psychology of the coexistence of parallel processing and serial processing bottlenecks within a cognitive task. When performing two tasks in rapid succession on two successively presented targets T1 and T2, delays are observed in some but not all of the T2 processing stages. Analysis of these delays suggests that a “central decision stage” suffers from seriality while perceptual and response operations occur in parallel [4] , [6] , [7] , [16] , [17] . Despite the fact that the PRP has been one the most widely studied paradigms to investigate dual-task interference, no network implementation had been proposed which provides a plausible implementation of its underlying mechanisms. Boxological and schematical models of the PRP [4] , [18] , [19] have successfully determined a theoretical framework which provides a synthesis of two basic aspects of cognitive architecture: 1) its chronometric organization, 2) its components that can act in parallel and those that impose seriality. According to these models, each task involves three successive stages of processing: a perceptual, a central, and a motor component. The perceptual stage of sensory processing - which is performed in a modular (parallel) fashion - does not provide a major contribution to temporal variability. A subsequent stage of serial processing involves a stochastic integration process, traditionally used to model decision making in single tasks [20] – [23] and is a main source for the variability in response time. In contrast, the last motor processing stage has only a small contribution to response variability and can be performed in parallel without interfering with other processing stages from concurrent tasks. Despite their simplicity, these models have been very successful in explaining a broad range of behavioral data, including the complex response time distributions of dual-task experiments, which can be precisely predicted only after untangling the serial and parallel stages of each task [18] .

A ubiquitous aspect of brain function is its modular organization, with a large number of processors (neurons, columns, or entire areas) operating simultaneously and in parallel. Human cognition relies, to a large extent, on the ability to perform an arbitrarily large set of tasks by flexibly recombining different processors into a novel chain (e.g. respond with the right hand to the red square) [1] – [3] . Yet this flexibility does not happen without a cost. Chaining individual computations is done at a very slow pace (100–500 ms per step) and with a considerable temporary tying-up of the brain's resources, generating what is known as “dual-task interference” – the inability to perform several tasks at once [4] – [8] . Several cognitive theories support this view, arguing that while most mental operations are modular and parallel, certain specific processes which establish flexible links amongst existing processors impose a serial processing bottleneck [3] , [9] – [15] .

Results

Architecture of the Model In accordance with previous theoretical proposals [28], [29] here we propose that seriality in dual (or multiple) task performance results as a consequence of inhibition within the control networks needed for precise “routing” of information flow across a vast, virtually infinite, number of possible task configurations. To examine this hypothesis, we will explore dual-task performance in a recurrent network of spiking neurons capable of performing flexible routing of information according to specific task instructions. Contrary to previous computational work addressing flexible mapping [30]–[33], our objective is not to study flexible behavior per se but to understand the conditions under which a computational model capable of flexible sensory-motor mapping shows patterns of interference when two tasks have to be performed simultaneously or in close succession [17], [18], [34]. Following classic experimental procedures of the PRP [35], the interference experiments we address here involve different sensory modalities, to avoid sources of interference in early sensory processing (with the exception of the last section, where we investigate the effects of masking). The model that we simulate is described in detail in the Materials and Methods section and in Figure 1. It includes two sensory modalities organized in a hierarchy in which each successive layer receives inputs from neurons of the previous layer thus generating progressively complex receptive fields. Within each hierarchical level, for simplicity we explore in detail only two distinct neural populations for each sensory modality, which correspond to the neural coding of the two task-relevant dimensions (red and orange populations in Figure 1 representing, for example, a high and low pitch sound, respectively). Other task-irrelevant stimuli were encoded by a large pool of non task-selective excitatory neurons (pink populations in Figure 1), as done in many other spiking networks modeling decision-making [36]. PPT PowerPoint slide

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larger image TIFF original image Download: Figure 1. Network architecture. Schematic of the spiking neuron network model. Each population, represented with a circle, contains between 80 and 640 neurons. Circles with diagonal textures indicate inhibitory populations and all other circles indicate populations of pyramidal cells. Whenever two populations of neurons are connected this indicates full connectivity between them. The network includes two sensory modalities (sensory 1 and 2), organized in a hierarchy in which each successive layer receives inputs – mediated by rapid (time constant of 2ms) AMPA receptors - from various populations of the previous layer thus generating progressively more complex receptive fields. Each stimulus (for example, S1) is represented by the co-activation of four specific neural populations in the first layer of the sensory hierarchy. Just for illustration purposes, each stimulus is represented as a solid circle and the different features of this stimulus as parts of this circle, i.e. the 4 red neurons in the first layer represent a stimulus when they are active together. Sensory modules are also connected through non-specific feedback connections mediated by slow (time constant of 100ms) NMDA receptors. Both sensory modalities converge to the router, which is a common integrator. The integrator neurons feed back to the sensory neurons, generating recurrent activity which can maintain and amplify sensory information. Integrator neurons connect to response neurons and thus route information from sensory to motor neurons. Subsets of the neurons in the router link information from stimuli to responses in a flexible manner. Router neurons also receive input from task-setting neurons and thus act as detectors of the conjunction of the relevant task and the appropriate stimulus. The circuit involved in mapping S1 to R1 of Task 1 as well as the task-setting of Task 1 is emphasized in bold. Response execution is triggered by a set of bursting neurons that signal a threshold-cross of the input received from the routing neurons that integrate information. Response neurons feed back to the router and to inhibit the neurons immediately after the response. This inhibition prevents perseveration and is required to stabilize the network in a single response mode. In a typical PRP experiment, which we model here, subjects are instructed to respond to both tasks as fast as possible in a particular order. To enforce this response order in the network we organized the task-setting neurons in a hierarchy [52] in which the neurons coding for Task 1 and Task 2 are controlled by a switch composed of task-order units (see Materials and Methods section for a detailed description). https://doi.org/10.1371/journal.pcbi.1000765.g001 Each element in this sensory hierarchy is a canonical cortical circuit comprising excitatory pyramidal cells and local inhibitory cells, previously shown to be capable of performing elementary functions of working memory and decision making [36]–[38]. Only excitatory pyramidal cells project with long-range connections to neurons higher and lower in the sensory hierarchy, while inhibitory neurons only project locally. Feedforward and feedback connections in the model differ both in the properties of the receptors that mediate the transmission as well as in their specificity [39]–[42]. Feedforward connections are highly specific: Each neuron projects to a single homogeneous population in the next higher level. For simplicity, they are assumed to be all mediated by fast AMPA receptors, although in reality a small fraction of NMDA receptors would be expected. In the reciprocal direction, feedback connections are more broadly connected: each neuron sends non-specific feedback connections to all excitatory cells in the previous level [40], [41]. Again, for simplicity we assume that feedback transmission is mediated by slow NMDA receptors. Since the contribution of NMDA receptors to synaptic transmission varies with the level of postsynaptic depolarization, this ordering of glutamate receptors between the feedforward and feedback streams broadly assigns a driving role to the feedforward input and a modulatory one to the feedback, as in previous models [43]. Both sensory modalities project to a router which connects the sensory representations to a set of possible responses. Neurons in the router integrate sensory evidence and trigger a response when their activity reaches a threshold [44]. An explicit instruction - presented before the stimulus – sets the task for a given trial, i.e. specifies the specific mapping which indicates which response has to be executed when the stimulus is presented. The network that stores task instructions is referred throughout this work as the task-setting network. Excitatory populations in this network are activated by the presence of task-relevant stimuli in sensory areas and, through their patterns of projection to “router” neurons (see below), encode different stimulus-response mappings. As with the sensory modalities, we only simulate two task-setting populations which are sufficient for the experiments considered here. An important aspect of our model is a circuit which we refer as the “router”. As in previous models of flexible decision making that do not rely on synaptic plasticity to dynamically adjust their behavior [33], [45], [46], task-setting neurons affect the decision process by gating a specific subset of “router” neurons, which implement the possible mappings between stimuli and responses. Here we assume a reduced ensemble of stimuli and responses and simply model as many selective populations in the router as there are combinations of stimuli and responses [33], [47]. Simulating a completely flexible network capable of mapping arbitrarily large stimulus and response sets, would require a high degree of overlap in the cortical representation implemented by task-setting and routing neurons. We will come back to this possibility and its possible implications for serial processing in the discussion. As with all other neurons in the network, task-setting neurons are entailed with self excitation and lateral inhibition. Excitatory neurons in the task-setting network are connected to the router through NMDA connections. When an excitatory population of the task-setting network is in an “active” state it excites the subset of neurons in the router receiving inputs from task relevant sensory populations and connecting them to the appropriate motor populations. A neuron in the router which receives excitation from task-setting neurons is set in a mode of integration in which it can accumulate sensory information (Text S1,A). This architecture also serves as a selection mechanism, assuring that task-irrelevant stimuli that are represented in sensory cortex do not elicit any output (Figure 2). PPT PowerPoint slide

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larger image TIFF original image Download: Figure 2. Single-trial dynamics for task relevant and irrelevant stimuli. Firing rates of representative trials of task-relevant (A–D) and task-irrelevant (E–H) stimuli. Each panel shows the firing rates averaged across a population (thick line) overlapped with spike rasters (each row of dots represent the spiking activity of a neuron in the population). Average firing rates were calculated by convolving the spike raster from a single trial with a gaussian filter of σ = 12ms. (A) Stimulus presentation (indicated with a dashed vertical line) generates a wave of activity that propagates through the successive stages of the sensory hierarchy. The colored circles represent the features coded by the various populations, following the notation of figure 1. (B) Router neurons show ramping activity until a response threshold is reached. (C) Activity in task-setting neurons is triggered by excitatory input from sensory neurons and is sustained for the duration of the task. (D) The response is signaled by a burst of excitatory neurons in the response network. (E–H) Same as panels A–D, but with the connections from sensory to task-setting areas removed. In the absence of projection from task-setting neurons (G) the activity in the router (F) does not reach the threshold to trigger a response in motor areas (H), despite strong activation in sensory areas (E). https://doi.org/10.1371/journal.pcbi.1000765.g002 Response execution is triggered in response selection networks (motor 1 and 2 in Figure 1) by a set of bursting neurons that signal a threshold-crossing of the input received from the integrating neurons, modeled as in previous work by Wang and collaborators [44]. To ensure that the network did not enter in a response perseveration mode (Figure S1), we implemented an inhibition of return mechanism [48] typical of a control network. After response execution, response neurons feed back to inhibit the sensory, routing and task-setting neurons involved in the task (similar to the “termination” signals in Dehaene and Changeux, 1997 [49] and recently observed in single-cell recordings in awake behaving monkeys performing a sequential task [50]). This architecture ensured that the network did not respond spontaneously, to irrelevant stimuli or to mappings different than those set by the explicit task-instruction and that it did not show perseveration of responses to task-relevant stimuli. We emphasize that here we have not investigated how a large repertoire of tasks can be encoded with a finite number of neurons. Rather, we ensure that the network has stable performance for a small number of tasks and then explore the operation of this network during dual-task performance. Our simulations of dual task experiments showed that when both tasks were close together in time, response order could be reversed on a fraction of trials so that the first response was given to the stimulus that was presented second (Figure S2). This coincides with experimental observation in task-interference experiments when the response order is not fixed [51]. Here we wanted to explore a comparatively simpler situation, typically studied in psychophysical experiments, in which participants are explicitly told to respond to two tasks in a specific order, as fast as possible. This required the implementation of a task-setting network [52] that determined the order of the tasks. The task-setting network was bistable. It was composed of two excitatory populations that projected to the inhibitory population of the other task. Three hundred milliseconds before the presentation of the first stimulus, excitatory neurons in the order-setting network are activated by a brief (100 ms) external input. Due to the strong self-recurrent connections, the network maintains high levels of activity after removal of the external input and tonically inhibits T2 neurons in the task-setting network. When the response to T1 is emitted, inhibition from the router resets the order-network permitting the activation of T2 task setting-neurons (Text S1,B). In summary, we generated a network based on a large-scale implementation of simple canonical neuronal circuits endowed with self-recurrence and lateral inhibition. The network has a hierarchical sensory organization which ultimately feeds stochastic evidence to “router” neurons which (if activated by a specific task-setting context) both accumulate evidence towards a motor decision and route sensory input to the relevant motor neurons.

Time Course of Neural Activations during Single-Task Performance Each stimulus has four features. The four populations encoding low-level features of a stimulus receive a brief pulse of constant current during stimulus presentation (100 ms). This initial impulse generates a transient response in the earliest input neurons (Figure 2A–D), which increase their firing rate from the default level of around 2 Hz to around 40 Hz. This transient response initiates a wave of activation that propagates through the network [47], [53], [54]. Each layer works as an integrator of the previous layer and thus the neural response becomes increasingly expanded in time as one progress in the hierarchy. At the highest level, recurrent connections are strong enough to assure a very low decay rate of stimulus information, resulting in an effective form of working memory as observed in several areas of occipito-temporal and frontal cortex [55]–[57]. The last stage in the sensory hierarchy projects to the router using AMPA receptors. Neurons in the router also receive currents from task-setting neurons, but these projections use NMDA receptors. These NMDA currents control the recurrence in the router, and they determine the degree of integration of AMPA currents. As a result of this architecture, neurons in the router act as detectors of the conjunction of stimulus presence and task relevance as observed in [58]–[60]. A neuron which receives task-setting currents integrates the sensory input rapidly (Figure 2B), while a neuron that does not integrates the input only partially (Figure 2E–H). Thus, task-setting neurons accomplish their role by assuring that the wave in the sensory system initiated by an irrelevant stimulus does not trigger a response. The integration process continues until a threshold is crossed, which is signaled by a nonlinear response: a powerful burst of spikes in the motor network (Figure 2D). The activation of these response neurons, in turn, initiates a cascade of feed-back inhibition that resets activation in task-related neurons [50].

Time Course of Neural Activations during Dual-Task Performance The principal aim of this paper is to explore the operation of the model in a classic dual-task paradigm: the psychologically refractory period (PRP), widely studied in the psychophysical literature. We explored the response of the model with two different stimuli, presented simultaneously or at a short stimulus onset asynchrony (SOA). When the separation between stimuli (SOA) is much longer than the response time to the first task (RT1), the neural activations associated with the first and second task do not interfere with each other and the observed dynamics is similar to that observed during single-task performance (Figure 2A–D). The most interesting situation is for SOA values close to or shorter than RT1 (Figure 3A–D, SOA = 100ms) in which case the two waves of activation evoked by each stimulus partially interfere. In the model, this interference does not occur at the sensory level: even at short SOA, while a first target T1 is being processed, sensory neurons associated with the second target T2 still initiate a wave of activations which is very similar to that in the single-task condition. However, due to competition between task-setting neurons, the routing neurons of T2 are not gated and hence do not integrate sensory information while T1 is being processed. In this instance there is a very interesting dissociation: local-recurrence in the sensory hierarchy is sufficient to maintain T2 stimulus information, but this information is not piped to the motor response and awaits liberation of the router. This constitutes a key aspect of this network – during a temporary waiting period, T2 has to be maintained in a “local memory” which does not propagate throughout the network. After the response to the first task has been executed, the T1 pathway is reset and Task 2 setting neurons activate, gating the router neurons of T2 and allowing them to begin to integrate information about the second incoming stimulus. Thus, the shift in the locus of “task-related attention” (which information is amplified in sensory areas and routed to response networks) is the natural consequence of the progression of the task in the router and task-setting network. PPT PowerPoint slide

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larger image TIFF original image Download: Figure 3. Neural activations during dual-task performance. (A–D) Firing rates in the dual-task condition inside the interference regime (SOA = 100ms). Each panel is defined as in Figure 2, with black and grey lines corresponding to populations from the first and second tasks, respectively. The specific populations plotted are indicated with colored circles, following the notation of Figure 1 (the circles to the left correspond to the first task). (E) Firing rates are plotted for 1200 trials (100 at each SOA) for neurons responding to the first and second tasks (left and right columns in each panel, respectively). White lines indicate the onset of the stimuli of task 1 and 2, and grey lines mark the specific times at which the average activity at each SOA crossed 1/3 of its peak value. In early sensory areas, both the onset and offset of the response are time-locked to stimulus presentation at short SOA, thus indicating a completely parallel mode of activation. In contrast, task-setting, response and integrating neurons show a highly serial activation profile. The onset and the offset of these neurons for task 2 in the interference regime are locked to the end of the corresponding process of task 1. In the non-interference regime, however, the onset of these neurons is locked to stimulus presentation. Higher sensory modules showed a hybrid profile, indicating that the same neuron can be involved in a phasic parallel response and also exhibits sustained activity until the response. In the interference regime, the onset of these neurons is locked to the presentation of the stimulus, but the offset show a sequential locking to the ending of task 1. Firing rates were calculated by filtering the instantaneous population firing rate with an exponential causal kernel with a time constant of 20 ms. https://doi.org/10.1371/journal.pcbi.1000765.g003 Note that the second key aspect of our network is that routing neurons of T1 and T2 cannot be simultaneously activated. In our network this is controlled through a competition between task setting neurons, but a similar result would be obtained if this competition would be implemented by lateral inhibition between routing neurons. This would occur, for example, if the number of possible mappings largely exceeds the number of neurons in the router so that routing can only occur by a distributed assembly of active cells. We will come back to this possibility in the discussion. In the interference regime, the network includes groups of neurons with very different response properties (Figure 3E); the existence of these different types of neuronal firing patterns constitutes a key prediction of our simulations. Early sensory neurons show a response which is essentially unaffected by interference, reflecting fully parallel behavior. In contrast, the motor and task-setting neurons are strictly serial, only showing strong activation after task 1 has been completed. The behavior of the router neurons is intermediate; they are mostly serial, but can undergo moderate integration (insufficient to boost a response) before completion of T1. Interestingly, late sensory neurons act as a buffer. They have an onset which is locked to the stimulus and are active until the response, so that they hold a memory of T2 which is retrieved when the router becomes available. This population of neurons is therefore engaged in different components of the task; first, a transient response which results in stimulus encoding, and second, a later memory trace which is eventually broadcasted to the motor neurons involved in the second task. All the previous analysis relied on spiking activity. Recently, much effort has been devoted to understand the relevance of complementary measures of brain function such as synaptic currents, local field potentials, and induced oscillations. Our neuronal network has the potential to study these measures. We first explored whether input currents in the router could be more informative than spiking activity of T2 processing stages. We measured input currents to the router at different processing stages of T2: Spontaneous activity, S2 queuing (memory phase), and S2 routing. During queuing, currents in the router reflected a steady level of activity which was significantly larger than during spontaneous activity (Figure S3). Thus, during this regime, subthreshold activity in the router is tightly coupled to spiking activity of late sensory neurons. During the routing stage, synaptic current activity ramps, coupling to the progression of spiking activity in the router. An interesting observation was that this pattern was virtually identical for all receptor currents (NMDA, AMPA and GABA). Although the input from the task-setting network is carried by NMDA-receptors, the local amplification in the router circuit also engages AMPA currents and the NMDA specificity is lost very rapidly (Figure S3). The task-switching circuit was endowed with high efficiency inhibition to achieve rapid switching from one task-setting program to another. This endowed the task-setting circuit with high frequency oscillations as can be seen in the raster plots of Figure 2. Since the task-setting circuit drives the router, we asked how these oscillations propagate into the network and whether measures of oscillatory activity could be more informative than simply spiking activity to identify distinct processing stages from neuronal responses. We analyzed the spectrogram of sensory, routing and task setting T2 neurons throughout the trial (Figure S4). Responses were locked to RT1. Both router and task setting neurons showed clear event-related spectrograms, as seen for firing rates. The spectral content of the responses of both populations are quite distinct: task-setting circuit activity occurs in high-frequency bands (peaking around 70 Hz) while router neurons, which act as slow integrators, display low-frequency responses (∼20 Hz). Router neurons do not inherit high frequency oscillations of the driving task-setting neurons because these connections are mostly mediated through NMDA receptors which have a slow time constant. Rhythmic activity in the sensory neurons showed distinct oscillatory activity during buffering and routing (Figure S4, left panel). During routing, responses of sensory neurons showed high power in the 40–60 Hz range while during routing they were more broad band and showed an increase in lower-frequency activity. Firing rates of sensory neurons during buffering and routing were not different (Figure 2). Spike density coherence between sensory and router neurons also showed distinct profiles during distinct phases of task processing: phase coherence was not-significant during spontaneous activity, it showed significant coupling for low frequencies during routing and broad-band coherence during T2 queuing (Figure S5).

Effects of Noise and Oscillatory Inputs on Response Times The previous results showed that our model can explain the precise shape of response time distributions in dual-task performance. Here we investigate the underlying physiological markers which result in such distributions, i.e. the relation between neuronal and response time variability. All neurons in the model receive strong background Poisson inputs, which assures a spontaneous activity of 2–5 spikes/s. We hypothesized that in trials in which input noise in the sensory neurons coincides with stimulus presentation (presented for 100 ms) response times would be faster. We also hypothesized that in the case of low-frequency noise (∼5Hz), the coincidence effect of external-stimulus and internal noise fluctuations, should manifest in a phase-locking relation of stimulus presentation to internal rhythms, as observed in both psychophysical [63], [64] and neurophysiological [65] experiments. We first used a general linear regression model to investigate how noise fluctuations affected response times in the PRP. The explanatory (independent) variables were external noise fluctuations for each population group and temporal bin, and the response (dependent) variable was either RT1 (Figure 6A) or RT2 (Figure 6B). PPT PowerPoint slide

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larger image TIFF original image Download: Figure 6. Response time sensitivity to stochastic fluctuations and low-frequency oscillations. (A,B) Coefficients of the linear regression model used to relate fluctuations in background inputs to response time variability. Black traces correspond to stimulus-selective excitatory populations at different processing levels, as indicated in the figure's legend. Red traces correspond to inhibitory neurons within the same area. Shades depict 95% confidence intervals. A positive coefficient means that higher activity due to noise leads to faster responses. (A) Estimates for Task-1 sensory and router populations, with RT1 as the independent variable. The x-axis indicates the time relative to stimulus onset, and thus positive values correspond to noise fluctuations occurring after stimulus onset. (B) Estimates for Task-2 sensory and router populations, with RT2 as the independent variable. Here, neural activity across different trials was locked to response 1 before the regression analysis. (C) Mean response times (green trace) for single-task simulations as a function of the phase between stimulus onset and background noise. The x-axis depicts the phase of stimulus onset relative to the background fluctuation (brown trace, bottom), and the y-axis depicts the mean response time in milliseconds. Error bars indicate the standard error of the mean. 50 trials were simulated for each individual phase. Also shown in grey-scale are the response time histograms (bin size of 40 ms). https://doi.org/10.1371/journal.pcbi.1000765.g006 We simulated 900 trials of the PRP for an SOA of 50 ms. For each trial, the population average of - dynamic gating variable mediating background AMPA currents (see Materials and Methods section) - was measured every 1 ms, assigning a value of 0 if its value exceeded the median value over all trials, and a value of 1 otherwise, independently for each population and time step. Independent variables were obtained by averaging these values within windows of 100 ms. Similar populations - for example, all neurons in the first level of the sensory hierarchy selective to the same stimulus - were averaged together. A positive regression coefficient means that higher activity of a group of neurons leads to faster responses. The time-course of the coefficients of the regression (Figure 6) showed a very clear temporal organization. For Task-1 sensory neurons (Figure 6A), fluctuations in the first sensory level which were coincident with stimulus presentations were highly predictive of RT1. On the contrary, fluctuations beyond this window were essentially independent of response time. In successive stages of the hierarchy the window of correlation was delayed. As we showed previously, RT2 variability accumulates RT1 variability (due to changes in the onset of the routing of T2) and intrinsic variability of the T2 routing process. To understand the impact of noise on each of these processes, we measured the time-course of the noise input to Task-2 responding neurons locked to the response to Task 1 (Figure 6B). Significant noise contributions were observed before the integration onset (Figure 6B, upper panel), suggesting that although sensory integration is delayed during the PRP, fluctuations in the memory trace of S2 during T2 queuing or before have an influence on RT2. Thus, spontaneous Poisson-noise fluctuations were effective when they coincided in time with external stimulus currents. If noise currents were carried by low-frequency oscillations [66] this effect could result in phase locking of RTs to the rhythmic oscillatory activity. We tested explicitly this possibility by running single-task simulations where excitatory neurons in the first sensory level received a low-frequency (5 Hz), low-amplitude (0.06% of the external background noise), oscillatory input. This additional input resulted in a small synchronous fluctuation on top of the large external background input. The phase of the stimulus onset relative to the background rhythm was varied across trials in order to study its effects on average response times and their distributions (Figure 6C). The relative phase between stimulus onset and rhythmic background activity had a marked effect on response times, compatible with recent experimental findings [65] and theoretical proposals [66] linking low-frequency oscillations to attentional selection. Our model provides a simple physiological explanation of why phase-locking stimulus to low-frequency oscillations may result in shorter response times. When the phase is such that the peak of noise fluctuations coincides with stimulus presentation, the stimulus is enhanced and this reduces response time. On the contrary, when stimulus presentation coincides with the valley of noise oscillations, input to the router is less effective and response times are longer.