Conceived and designed the experiments: SD MS. Performed the experiments: AZ. Analyzed the data: AZ MS. Contributed reagents/materials/analysis tools: DFS PRR SD. Wrote the paper: AZ PRR SD MS.
The authors have declared that no competing interests exist.
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.
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)
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
Until now, the modeling of dual tasks is only specified at a level of mathematical description and functional cognitive architecture
In accordance with previous theoretical proposals
Following classic experimental procedures of the PRP
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
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
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
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
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
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 (
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 = 12
Response execution is triggered in response selection networks (motor 1 and 2 in
To ensure that the network did not enter in a response perseveration mode (
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 (
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.
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 (
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
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 (
The most interesting situation is for SOA values close to or shorter than RT1 (
(A–D) Firing rates in the dual-task condition inside the interference regime (SOA = 100ms). Each panel is defined as in
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 (
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 (
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
Rhythmic activity in the sensory neurons showed distinct oscillatory activity during buffering and routing (
An appealing aspect of the PRP paradigm (
(A) Sketch of the PRP paradigm. Stimulus S1 is mapped to R1, and stimulus S2 to response R2. RT1 is defined as the time between S1 onset and the response R1. RT2 is defined as the time between the onset of S2 and the response R2. The SOA - defined as the time between onsets of S1 and S2 - is systematically varied, typically between 0 and 1000 ms. (B) Scheme of the mathematical formalism traditionally used to explain the delay in RT2 during the PRP. The vertical axis labels RT. The column on the left indicates the first task, and each colored box within the column represents a different stage of processing: Perceptual component (red), Central component (grey), and Motor component (blue). The series of columns on the right indicate the processing time for task 2 at different SOA, labeled on the x-axis. For each column, the three different boxes represent the three different stages of task 2: Perceptual component (green), Central component (grey), and Motor component (brown). As SOA progresses, the Perceptual component starts later. All components can be performed in parallel except for the Central component, which establishes a bottleneck. (C) Effect of SOA manipulations in response times for the proposed neural architecture. Average response times to the second task show a dependency on SOA similar to observations from PRP experiments: RT2 decreased with SOA within the interference range with a slope of −1, and is constant in the non-interference regime. RT1 is unaffected by SOA manipulations. In most PRP studies, response times are measured from the onset of the corresponding stimulus (T1 or T2). Other studies have used a different convention in which response times to both tasks are reported from trial onset (i.e., onset of T1). Here we show the PRP effect under both conventions, by defining the variable R2 = RT2 + SOA. The PRP effect is observed as an invariance of R2 with SOA for short SOA values, and a linear increase of R2 with SOA for large SOA values. Data points show averages across 300 trials. Error bars depict the standard error of the mean. (D–G) Effect of task complexity and SOA in response times. Each panel (containing two plots) defines the manipulation type (perceptual or central) and the affected task. Human data (taken from
Specifically, the main experimental characteristics of the PRP phenomenon are
RT2 shows a linear decrease with slope of −1 for short SOA and a slope of 0 for large SOA
RT1 is typically unaffected by SOA
Pre-bottleneck manipulations (experimental factors that affect sensory processing) additively affect both RT1 and RT2 inside the interference range when the first task is being manipulated. When the second task is manipulated, under-additive effects are seen at short SOA, due to the absorption of pre-bottleneck components while T2 is being queued by T1 processing
Bottleneck manipulations (experimental factors that affect the difficulty of the S-R mapping) additively affect the task that is being manipulated
RT distributions are long-tailed (Wald-type distributions)
RT2 tightly covaries with RT1, but only for short SOA (i.e. in the interference regime)
RT2 variance increases as SOA decreases, since it accumulates the variability of both RT1 and RT2 in the interference regime
We first explored the main effects of the PRP (without specific task manipulations) by simulating an experiment in which two stimuli were presented at an SOA which varied between 0 and 800 ms, sampled at [0, 50, 100, 150, 200, 250, 300, 400, 500, 600, 700, 800] ms (
(A and B) The model produces distributions of response times with a long tail. (B) As observed experimentally, for short SOA values (SOA = 0 ms in the figure), RT2 is more variable, since it concatenates the variances of both tasks. (C to E) Scatter plot of RT2 vs. RT1 for SOAs of 0ms (C), 150ms (D) and 500ms (E) (300 trials for each SOA). For short SOA values, the RTs are tightly correlated, a correlation that is caused by interference and sequentiality. (F) Cumulative RT distribution for varying SOA values. For increasing SOA values both the mean and the variance decrease. Simulated SOA values are indicated in the legend with arrows.
Second, we observed the classic RT2 profile with varying SOA values: An initial decrease with a slope of −1 (
Based on typical experimental procedures, we then explored the effect of different manipulations on the first and second task on mean response times, and their interaction with SOA (
First we investigated the effect of changing the complexity of sensory processing. In a number comparison task, changing the notation (for instance replacing the digit 3 by the word
We then explored another important manipulation which affects the complexity of the sensory-motor mapping, i.e. the amount of sensory evidence in favor of the correct decision. In experiments in which a decision is taken on an analog variable (movement, intensity, numerosity, size etc…) the two competing stimuli can be made arbitrarily close, rendering the decision progressively more difficult. This results in increased errors and RTs, and attractor dynamic networks have been very successful in modeling these phenomena
The response times histogram for SOA = 0 ms is displayed in
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
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 (
(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).
We simulated 900 trials of the PRP for an SOA of 50 ms. For each trial, the population average of
The time-course of the coefficients of the regression (
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 (
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
Behavioral experiments which have combined the basic features of different manifestations of central processing such as the PRP (two rapid responses) or the attentional blink (extinction of a second rapidly presented stimulus) have suggested that both forms of processing limitations may arise in part from a common bottleneck
To evaluate whether our model could, without modification, also account for AB experiments, we studied the effect of a mask applied after T2. The mask was modeled as a brief stimulation of non-specific excitatory cells in the first layer of the sensory hierarchy, thus modeling the activation of a neural representation competing with the target T2
We simulated 100 trials at each SOA value, varying the SOA between 50 and 500 ms at 50 ms intervals. In contrast to the previous PRP simulations, when the SOA between T1 and T2 was short we observed a small (but significant) number of errors and, most importantly, a large number of trials in which the network failed to respond to T2 (
When T2 is masked the model displays characteristic aspects of AB experiments. (A) Probability of responding correctly to T2 given T1 correct, for varying SOA (error bars depict the standard error of the mean). (B–D) Single-trial population firing rates of relevant populations for trials with
For short SOA values, the network exhibits a highly stochastic behavior: the same configuration of stimuli and SOA may lead to
The interpretation of our results is that the mask results in an accelerated exponential fading of the representation of T2 stimulus in short-term memory
A series of experimental observations have shown that the AB is attenuated (i.e. the probability of seeing T2 increases) with increased T1 strength. For example, the blink is attenuated when a blank is placed after T1, i.e. masking is delayed
We examined this hypothesis performing two different simulations. First, we increased the strength of T1 by 10% relative to the previous PRP and AB simulations. This resulted in an attenuated AB for the second task (76±4% correct vs. 49±5% correct without the manipulation; p-value <0.0005; 100 trials at a fixed SOA of 50 ms). Despite perfect performance for T1 in these simulations, RT1 was smaller when T1 was stronger (with strong T1: RT1 = 318±5 ms; without the manipulation: RT1 = 396±9 ms; p-value<0.0005). Thus increasing T1 strength decreases RT1 and increases the probability of retrieving the second stimulus.
The second manipulation, conversely, involved masking the first target T1, simulating the most typical AB paradigm in which both T1 and T2 are masked. As for the first manipulation, 100 trials were simulated at a fixed SOA of 50 ms and we now added a mask identical to the one previously used for T2. In this condition, performance in the first task was still accurate (92±3% correct) while T2 visibility was decreased significantly (26±4% correct). This effect can be understood by the increased latency of the inhibitory signal following routing of T1, which increased RT1 from 396±9 ms in the unmasked condition to 869±50 ms when T1 was masked.
In summary, our simulations show that T1 manipulations that facilitate the first task and therefore reduce its duration have the effect of reducing the attentional blink for T2, as experimentally observed
The present model constitutes, to our knowledge, the first spiking-neuron model of a global architecture capable of simulating the entire sensory-motor chain of processing in a dual-task setting. We could explain the detailed dynamics of behavior (including both mean RTs and RT distributions) during dual-task-performance, by simulating a large-scale network of realistic neurons, comprising about 20.000 spiking neurons and 46.000.000 synaptic connections. For consistency with the majority of previous PRP experiments, we simulated an experimental design in which stimuli involve distinct sensory modalities and the responses distinct effectors. Under these circumstances, interference occurs exclusively at the routing stage, commonly referred to in psychology as the response selection stage
Based solely on the known dynamics of neurotransmitter receptors, the model reproduces, in a quantitative manner, a large number of behavioral observations of dual-task interference (see
A sequential delay in RT2. This delay decreases with a slope of −1 as SOA increases reflecting a sequential bottleneck.
The absence of any effect of the second task on response times to the first task (mean and distribution).
Strong correlations between RT1 and RT2 which progressively diminish as SOA increases.
Distinct interference patterns associated with different task manipulations: changes which affect the sensory delay processing of Task 2 are absorbed during the slack time separating task 1 and task 2, while changes which affect the accumulation time (i.e. central processing in the router) propagate additively.
Switch from the PRP (delayed response to T2) to the blink (an absence of the response to T2) by adding a mask after the T2 stimulus.
An increase in blink probability when T1 visibility is reduced.
These results are in full accordance with the central interference model
Several brain-imaging experiments implicated a number of cortical systems in the PRP phenomenon. The cerebral basis of processing bottlenecks has been investigated with Event Related Potential studies (ERPs), which have shown that the PRP results in reduced and/or delayed components
The spatial resolution of EEG is very imprecise and thus a better characterization of the locus of central processing bottlenecks in the brain comes from fMRI studies, which have pinpointed a broad parietofrontal network that exhibits various manifestations of central capacity limits
Our network postulates a hierarchical organization of this system: neurons controlling the whole-task structure (order network) gate neurons controlling the individual tasks (task-setting network), which, in turn, gate the routing from the sensory representations to the motor intention stage. Such a hierarchical organization has been demonstrated in humans in the prefrontal cortex as the Broca region and its homologue in the right hemisphere implement executive processes that control start and end states as well as the nesting of task segments that combine in hierarchically organized action plans
Understanding the emergence of serial behavior in the human brain is an important and central theoretical question in cognitive psychology as modularity and parallel processing are hallmarks of brain computations. Different authors have proposed cognitive architectures that can explain how components of the mind work to produce coherent cognition
Here we have tentatively proposed that seriality in dual (or multiple) task performance results from the necessity to establish a task set through the activation of a “router” network. This router network is shared by all sensory-motor mappings and its activity can, potentially, code for a virtually infinite number of possible tasks. A task-setting program acts as a gate, permitting routing neurons to propagate information if they receive the appropriate sensory input. This system acts as a control mechanism that avoids erroneous, conflicting or unwanted stimulus-response associations. We showed that a concrete implementation of such a control system results in serial behavior of the routing process when probed in dual-task situations.
In our network, seriality and its behavioral manifestations, the PRP and the Attentional Blink, emerged from competition between task-setting neurons which, through a lateral inhibition process, prevented the simultaneous activation of two task settings. This form of control is necessary to ensure correct task performance in conflicting mappings - as classically demonstrated in the Stroop paradigm in which the same stimulus may lead to distinct responses according to task requirements
Another possible origin of seriality relates to the coding properties of the router (for a simple illustration see
Previous modeling efforts have established cognitive architectures which can account for human complex problem solving
The router circuit in our model builds on previous computational models which have studied the role of contextual signals on transient sensory-motor mappings
In the present model, the router binds sensory and motor representations. Similar conceptions of flexible routing circuits have been applied to other instances of information binding such as, linking the attributes of an object in pattern recognition
Our network provides an implementation of simple boxological models of dual-task execution in the PRP
A critical aspect of our network is that while the router is occupied by T1, the T2 stimulus was maintained in the recurrent activity of high-level sensory units, thus forming a memory which remains local because it cannot activate the router. This coexistence of parallel mechanisms – a cascade of sensory processes which encode the stimulus - and of serial bottlenecks – queuing by the routing process - constitutes a hallmark of PRP observations. Our network implemented this local memory as a local attractor showing progressive integration and exhibiting a metastable form of memory that could be maintained for a few hundred milliseconds. According to this proposed mechanism, the memory trace remains stored in a local network and is relatively fragile as it can readily be overridden by a mask. The critical observation is that the mask can only override processing of T2 if it the router is occupied by T1.
To our knowledge, our model is the first one to propose a concrete neural implementation of the mechanisms leading to the PRP. In contrast, several computational models have been recently proposed for the attentional blink
We emphasize that our model does not intend to give a detailed account of all the findings from attentional blink experiments, but instead to show how the same mechanisms that lead to delayed responses in the PRP can lead to missed targets in the AB. Recent reviews of the extensive AB literature argue for a multifactor origin in this processing deficit
One aspect of the attentional blink phenomena which our model fails to replicate is the relative increase in performance observed at very short SOA (∼100 ms), an effect known as lag-1 sparing
In fact, we see the extension of the present model along the lines just discussed: the different types of neurons used in our implementation (briefly reviewed in the next section) have been found in the awake behaving monkey and may serve as a basis from which to construct complex cognitive programs, as those implemented in systems like ACT-R
Most, if not all, types of neurons used in our implementation have been observed in studies that measured single-neuron activity in awake behaving monkeys during single-task performance. Here we will briefly mention the main types of neurons in the various areas of our model and compare them to neurophysiological data, a comparison that will have to remain somewhat superficial as we cannot attempt to discuss the precise relationships between the variety of tasks employed in the neurophysiological studies and the PRP task implemented here. Firstly, the properties of the sensory areas of our model are consistent with what is known about representations in areas of sensory cortex. Neuronal activity in low level sensory cortex is largely (but not entirely) determined by the incoming sensory information
Our network can also explain timing and latencies of the sequence of events identified in single-task physiological experiments in monkeys
Our observations also raise a note of caution on the interpretation of processing latencies from physiological data. A concrete example is conveyed in our model by the measurement of activity in the routing neurons. Spiking activity shows a clear sequential scheme: routing neurons of T2 start integrating only once routing of T1 has completed (
Our data showed that fluctuation in response time could be accounted by the dynamics of noise fluctuations in relation to the timing of stimulus routing (
The correlates of the bottleneck have yet to be studied at the single cell level and our simulations therefore generated a number of new predictions that could be tested in future neurophysiological experiments. First the model establishes the existence of routing and task-setting neurons with well distinct dynamics and connectivity with different neuronal populations. At the anatomical level, routing neurons should receive inputs from all sensory modalities and from task setting neurons. At the functional level, they should be characterized by their firing in response to specific conjunctions of stimuli and responses, a preference which may change dynamically according to task context, on a time scale of about 100 ms or more (for supporting evidence, see
The model contains 21,000 neurons and 46,634,400 synapses. Neurons were either excitatory or inhibitory. All neurons were modeled as conductance-based leaky integrate and fire units. The membrane potential of each cell below the threshold for spike generation is described by:
All neurons receive large amounts of background synaptic activity which determines the level of spontaneous activity. External inputs and background activity are mediated exclusively by AMPA receptors.
Recurrent excitation is mediated by AMPA and NMDA receptors, and inhibition is mediated by GABA receptors. The total synaptic currents are given by:
For NMDA receptors:
Neurons are grouped into homogeneous populations. A total of 84 unique populations were included in the simulations. In sensory and routing areas these homogeneous populations were grouped into larger groups, forming local
Sensory areas are modeled through a hierarchy of modules, to account for convergence and increased receptive fields at higher levels of processing
Within local modules, connections are structured according to a “Hebbian” learning rule: coupling strength between pairs of neurons is considered to be high for neurons inside a selective population, and low when connecting neurons from competing populations. Specifically, for synapses connecting neurons within the same selective population, a potentiated weight
Feedforward and feedback connections have different degrees of specificity. Feedforward connections are highly specific: neurons from one excitatory population project exclusively to one excitatory population in the immediate higher level. These connections are mediated exclusively through AMPA receptors (
The router is made of two networks identical to the local modules in the sensory areas, but setting the value of
Motor commands are simulated as in
The task-setting network is composed of two identical modules. Each of these is composed of two populations, one excitatory (400 neurons) and one inhibitory (100 neurons). Excitatory neurons connect to themselves (
The order in which tasks are performed is controlled by an additional network (Order-setting network) which inhibits the portion of the task-setting network responsible for the amplification of the second task, until the response to the first task is emitted. The mechanism by which this occurs is as follows. The order network is a bistable network composed of one excitatory and one inhibitory population of 400 and 100 neurons respectively (self-recurrent excitatory connections:
Inhibitory mechanisms were included in the network to avoid response perseveration. Direct connections were included between bursting motor neurons and local inhibitory neurons in: router (
As in previous works
The proposed network simulates a generic PRP experiment. Observers (and the network) must perform two tasks as fast as possible, in a pre-specified order. Each task involves a simple two-alternative decision. In the network, the set of possible task-related stimuli in each modality is restricted to two, as is often the case in real PRP experiments.
All neurons receive background Poisson input to maintain a spontaneous activity of a few Hertz. The presentation of a task-relevant stimulus increased the external input of the four selective populations in the first level sensory network, from the background level of 2,400 Hz (as may result from 800 afferent neurons spiking at a spontaneous rate of 3Hz) to 2,717 Hz, for 100 ms (thus
In
In the attentional blink (AB) simulations, a mask is presented after the task-relevant stimulus. This was modeled as in previous studies
Each simulated trial lasted 3400 ms. The first stimulus was presented at 700 ms, and the second stimulus was presented according to the SOA. The code was written in
Response perseveration without ‘corollary discharge’ from motor neurons. Smoothed firing rates of selected populations - during one trial of single-task performance - when the ‘corollary discharge’ from motor neurons to inhibitory neurons participating in memory maintenance - last level sensory neurons - is removed. Response times are indicated with red vertical arrows. (A) Stimulus selective neurons from the first sensory level show a phasic response to stimulus presentation. (B) Last level sensory areas maintain high levels of activity until a response is emitted; in the absence of inhibition from motor neurons, these neurons keep feeding routing (C) and task-setting (D) neurons, resulting in response perseveration.
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Stochasticity in task choice. In the main simulations the order in which tasks have to be performed is constrained to mimic the condition of most PRP experiments. A recent experiment
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Input currents to the router circuit during different processing stages of T2. Input currents to the router during three different processing phases of T2: before stimulus presentation (“Spontaneous”, left panel), during the phase in which T1 is being routed and S2 is buffered in memory (“Queued”, center panel), and during routing of T2 (“Routing”, right panel). The mean recurrent inputs (y-axis) flowing through AMPA (blue trace), NMDA (green trace), and GABA (red trace) receptors were obtained by simulating 50 PRP trials at SOA = 0 ms, recording these currents every 2 milliseconds. The time windows considered for each phase were (x-axis): Rest: [−150,0] ms relative to stimulus presentation; Queued: window of 150 ms centered (in each trial) around the time that the T1 task-setting neurons were active; Routing: [−150,0] ms relative to the response time to the second task. Shades depict the standard error of the mean. To assure that each of these windows overlapped with the corresponding processing stages independently of fluctuations in response time, we filtered the trials, considering only the subset of trials (37 of 50) for which the following conditions were met: T1 task-setting neurons were active for more than 150 ms and less than 350 ms, and RT2 <1000 ms.
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Spectral analysis of sensory, router, and task-setting neurons involved in T2 processing. We analyzed the spectrogram of sensory (left panel), routing (center panel) and task setting (right panel) T2 neurons throughout the trial. Colored circles at the top identify the populations analyzed in the notation of
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Spike-density coherence between sensory and router neurons during different processing stages. We measured the spike density coherence between sensory and router neurons, during three different phases of task processing: before stimulus presentation (left column), during active routing of T1 (center column), and during active routing of T2 (right column). Each phase lasts 100 ms. The top row corresponds to populations selective to T1 and bottom row to T2. Each population is the scheme is colored following the nomenclature of
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Combinatorial router. A) In the model, each neuron in the router coded exclusively for particular combinations of stimulus and response. This would lead to scaling issues when the number of possible mappings increases. Here we sketch a different coding schema for the router, one that works on the basis of combinatorial codes. A small portion of the network is simulated, containing only parts of the router and motor networks. See the main text and the model of Lo & Wang (Lo & Wang, 2006) for details of the circuit, specially the disynaptic inhibitory circuit by which the router both excites the different motor neurons and inhibit the tonic inhibition of those same motor units, implementing a threshold detection mechanism for the activity in the router. Two populations of excitatory neurons need to code for three different stimuli, each one mapped to a different response. Thus, the simultaneous activation of both router populations lead to a third response different from the one generated by each population alone, by tuning the synaptic efficacies such that the response in the center of panel A (light brown) receives a larger excitatory input than the other responses only when both router inputs are active. (BCD) Population firing rate of both router populations - during a simulation of the model - for the three possible stimuli. X-axis indicates the time relative to stimulus onset, and y-axis depicts the population firing rate calculated with an exponential causal kernel of 20 ms. The time of the motor burst is indicated by a colored vertical line, with color codes as in panel A. The simultaneous presentations of both Stim1 and Stim3 does not lead to the superimposed execution of the two responses obtained when each stimulus is presented alone (panels B and D), but to a third and different response (panel C). Thus, the implementation of inhibitory control mechanisms to arrange the sequential routing of tasks presented at short SOA is required in a combinatorial code to achieve precise stimulus-response mappings - and may lead to through the same mechanisms discussed in the main text to dual-task interference as observed in the PRP and the AB. Lo, C. C., & Wang, X. J. (2006). Cortico-basal ganglia circuit mechanism for a decision threshold in reaction time tasks. Nature Neuroscience, 9, 956–963.
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Supporting Notes.
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Results of the ANOVAs of the interference simulations. Each column corresponds to a different ANOVA. Each line represents a different effect: task manipulation, SOA, and their interaction. The top row indicates the identity of the variable under analysis and the second row indicates the type of manipulation (i.e., Notation 1 corresponds to a perceptual manipulation of the first task). Red indicates a significant effect.
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We thank Stefano Fusi, Kong-Fatt Wong, Xiao-Jing Wang and Gustavo Deco for sharing an early version of the computer code used in this study. We also thank Charles Schroeder and Howard Bowman for helpful comments on the manuscript.