Working Memory and Decision-Making in a Frontoparietal Circuit Model

Abstract

Working memory (WM) and decision-making (DM) are fundamental cognitive functions involving a distributed interacting network of brain areas, with the posterior parietal cortex (PPC) and prefrontal cortex (PFC) at the core. However, the shared and distinct roles of these areas and the nature of their coordination in cognitive function remain poorly understood. Biophysically based computational models of cortical circuits have provided insights into the mechanisms supporting these functions, yet they have primarily focused on the local microcircuit level, raising questions about the principles for distributed cognitive computation in multiregional networks. To examine these issues, we developed a distributed circuit model of two reciprocally interacting modules representing PPC and PFC circuits. The circuit architecture includes hierarchical differences in local recurrent structure and implements reciprocal long-range projections. This parsimonious model captures a range of behavioral and neuronal features of frontoparietal circuits across multiple WM and DM paradigms. In the context of WM, both areas exhibit persistent activity, but, in response to intervening distractors, PPC transiently encodes distractors while PFC filters distractors and supports WM robustness. With regard to DM, the PPC module generates graded representations of accumulated evidence supporting target selection, while the PFC module generates more categorical responses related to action or choice. These findings suggest computational principles for distributed, hierarchical processing in cortex during cognitive function and provide a framework for extension to multiregional models.SIGNIFICANCE STATEMENT Working memory and decision-making are fundamental "building blocks" of cognition, and deficits in these functions are associated with neuropsychiatric disorders such as schizophrenia. These cognitive functions engage distributed networks with prefrontal cortex (PFC) and posterior parietal cortex (PPC) at the core. It is not clear, however, what the contributions of PPC and PFC are in light of the computations that subserve working memory and decision-making. We constructed a biophysical model of a reciprocally connected frontoparietal circuit that revealed shared and distinct functions for the PFC and PPC across working memory and decision-making tasks. Our parsimonious model connects circuit-level properties to cognitive functions and suggests novel design principles beyond those of local circuits for cognitive processing in multiregional brain networks.

Keywords: NMDA receptor; attractor network; decision-making; parietal cortex; prefrontal cortex; working memory.

Figure 1.

Circuit schematic of the firing-rate model. A module is defined as a set of two excitatory populations where each population is selective to one of two spatial, directional, or object stimuli (left). Each excitatory population is recurrently connected and also receives inhibition from a common pool of interneurons. The effects of inhibition and recurrent excitation are to generate bistability for WM and winner-take-all dynamics and ramping activity through slow reverberation for DM. Population A (B) receives input either from spatially selective stimulus A′ (B′) or from another population A (B) in another module. The circuit dynamics can be simplified (right) by linearizing inhibition, so that effectively inhibition is represented by negative weights. Thus, the effect of the pool of interneurons is implicit in the inhibitory connections between the excitatory populations. In general, synaptic weights J can connect two selective populations of either the same (J_same > 0) or opposite (J_diff < 0) stimulus selectivity and can be either local or long range. The structure J_S = J_same − J_diff denotes the total recurrent strength, while the tone J_T = J_same + J_diff denotes the net input onto a population. Synapses labeled with triangles and circles denote net-excitatory and net-inhibitory connections, respectively.

Figure 2.

Tradeoffs between WM and DM function in a local attractor network model. A, Neural activity for a single WM trial. The colored bars mark presentation of input current to the population A (blue) and B (red), with strength I_app = 0.0295 nA. For a recurrent structure J_S = 0.35 nA, the circuit generates a stimulus-selective persistent memory state, but it is vulnerable to intervening distractors. B, At increased recurrent structure J_S, WM activity in the circuit is robust against distractors. C, Robustness of WM as a function of recurrent structure J_S and stimulus strength I_app. In the purple lower region, the stimulus is too weak for the target to induce a transition from the (stable) baseline state to the memory state. In the green middle region, the network can perform WM that is robust against intervening distractors. In the orange upper region, the stimulus current is strong enough for a distractor to disrupt target-related memory. D, WM robustness increases with increasing recurrent structure J_S. The robust stimulus range is defined as the range of stimulus strength I_app in which persistent activity is robust against distractors (i.e., by the height of the green region in C). E, Neural activity during DM for zero-contrast stimulus (i.e., equal strength input to both populations), for 100 trials in which the blue population first reached threshold. The colored bar marks stimulus presentation, with strength I_e = 0.0118 nA. The black trace marks the firing rate of the winning population for the trial with median reaction time. Note that the time range shown here is shorter than for the WM simulations in A and B. F, At increased recurrent structure J_S, integration is shorter, limiting evidence accumulation, and ramping to threshold occurs sooner. G, Integration time constant as a function of recurrent structure J_S and stimulus strength I_e for a zero-contrast signal. The integration time constant is defined as the absolute value of the inverse eigenvalue of the unstable mode of the saddle point in the system (Wong and Wang, 2006). The inverse of the integration time constant is plotted. The white region marks where the symmetric state is stable, and therefore the network is not in a winner-take-all regime. H, DM performance degrades with increasing recurrent structure. For a fixed stimulus strength (here with I_e = 0.0118 nA), the integration time constant decreases with J_S. Correspondingly, the discrimination threshold increases, indicating degraded performance. Note that the two single modules shown in A, B, E, and F have the same circuit parameters as the two modules of the distributed circuit in subsequent figures.

Figure 3.

A distributed cortical model reproduces spatially selective persistent activity through local and long-range connections. A, The circuit is composed of two reciprocally connected modules, PPC and PFC, and each module consists of two excitatory neural populations selective to a stimulus A and B, respectively. The circuit model is endowed with self-excitation and cross-inhibition. Neurons in the PPC receive the sensory stimulus and convey the information to the PFC via long-range net-excitatory and net-inhibitory projections, as in Figure 1. B–D, Local and long-range structures jointly contribute to persistent activity. B, PPC and PFC populations reach the same level of persistent activity in the steady state across the three scenarios depicted in C, demonstrating the joint contributions of long-range and local connectivity. Gold bar denotes stimulus presentation. C, Structure values reflecting local (within-module) and long-range (across-module) connectivity for three scenarios are shown: (1) PPC and PFC both independently support persistent activity (green, top); (2) neither PPC nor PFC is capable of persistent activity independently (purple, middle); and (3) only PFC independently supports persistent activity (bottom, red). Black horizontal line denotes the threshold for a local module to support persistent activity independently (i.e., multiple stimulus-selective attractor states). D, Steady-state firing rate for the activated population of the PPC module in the memory state, as a function of PPC local structure and PFC → PPC feedback. The PFC local and feedforward PPC → PFC structures are fixed. In the region in the upper right corner, the baseline state is unstable. In the region to the right of the white dashed line, the PPC is an independent attractor. The white asterisk marks the parameter values used for the WM and DM simulations in Figures 4, 5, 6, 7, and 8.

Figure 4.

Firing-rate dynamics in the PPC–PFC circuit during a WM task. A, Top, the blue trace shows the response of the target-selective neural population in the PPC in response to a target presented at t = 0 ms, with no distractors. Red, orange, light orange, and pink traces show the responses of the distractor-selective population to distractors presented at t = 100, 150, 200, and 300 ms, respectively. Bottom, The cyan trace shows activity of the target-selective population in the PFC that receives the stimulus indirectly through the long-range projections from the PPC, in the no-distractor condition. The other traces show the distractor-selective population in response to distractors, as for PPC. However, these responses are not visible due to the strong filtering by surround suppression within PFC. B, Temporal dynamics of the two suppressed populations in PPC and PFC around the time of stimulus presentation (asterisks in A). C, Autocorrelation of the spontaneous firing rate shows the difference in fluctuation timescales τ_fluct between the PPC (127 ms, blue) and the PFC (438 ms, cyan). Firing rate traces were smoothed with a Gaussian window of 20 ms width before calculating the autocorrelation, and dashed lines are exponential fits.

Figure 5.

Relationship between neural dynamics and behavioral performance during a WM task with distractors (colors correspond to the schematic in Fig. 3A). A, Example of a correct, not distracted, trial. The target-selective population in PPC encodes the target in WM following stimulus onset at t = 0 ms (top, blue), while the distractor-selective PPC population transiently but strongly encodes the distractor following its presentation at t = 1300 ms (top, red). After distractor offset, feedback from the PFC switches the PPC back to encoding the target, enabling a correct response at the end of the trial. The PFC (bottom) is activated by the response of the PPC to the target, which is maintained in WM by the target-selective population in the PFC as well. Distractor presentation causes a transient suppression of the delay activity in the neurons encoding the target (cyan), but the distractor is not represented strongly (magenta) as it is in the PPC. B, Example of an error, distracted, trial. If the target precedes the distractor by a short interval (100 ms in this example), there is an increased probability of the distractor representation overriding the target representation, so that the distractor is encoded in persistent activity in both PPC and PFC (top, red; and bottom, purple). C, Simulated behavioral performance as a function of TDOA. Distractibility decreases with longer TDOA (blue). Simulated lesion of PFC greatly increases distractibility (red). D, Effects of the removal of PFC → PPC feedback. Absence of PFC feedback onto the PPC forces the PPC to encode the last presented stimulus, leaving it vulnerable to distractors.

Figure 6.

PPC and PFC differentially encode accumulated evidence during perceptual DM. A, The theoretical accumulator (top), PPC (middle), and PFC (bottom) integrate sensory evidence as a function of time and trial difficulty. Thick traces show an average over 60 trials for each difficulty condition, while thin traces in the accumulator show single trials. Traces corresponding to PPC and PFC include both correct and error trials. B, The firing rate vs accumulator relationship is more categorical, with a steeper slope at zero accumulator value, in the PFC than in the PPC, which has a more graded coding. The slopes at zero crossing are 0.13 and 0.19 for PPC and PFC, respectively (see also Hanks et al. (2015)). C, The relationship between firing rate in PPC and PFC and accumulator value as a function of time is stable. The eight accumulator values (from purple to red) correspond to the horizontal axis in B.

Figure 7.

Dynamics of the distributed circuit model during a visuospatial DM task. A, Top, Target and distractor cells in the selection module receive stimulus inputs, integrate perceptual evidence, and discriminate the inputs (marked by target discrimination time). Bottom, Following target discrimination in the selection module, the corresponding population of action cells is activated and begins ramping (marked by onset time). When one of the action populations reaches a threshold of 40 Hz (black dashed lines), an overt response is triggered and a reaction time is registered. Green (orange) traces correspond to easy (hard) trials. Target and distractor cells are shown in thick and thin lines, respectively. Dashed lines mark the target discrimination time in selection cells defined as the time when the difference in firing rate of the two populations has reached 12 Hz. Dotted lines mark the onset time in action cells defined as the time when the firing rate of one of the populations has reached 7 Hz. B, Target discrimination times in the selection module (top) and onset times in the action module (bottom) correlate with reaction times, both across and within contrast conditions. Reaction times were split into quintiles for each contrast level. Only correct trials are shown. C, Psychometric and chronometric curves as a function of contrast for control and no PFC feedback (right).

Figure 8.

Pathway-specific excitation-inhibition balance disruption and speed–accuracy tradeoff. The degree of balance disruption is quantified by the percentage of the total inhibition required to balance excitation to a cell (100% corresponds to full balance). A, Speed–accuracy tradeoff. Reaction times decrease both as a function of contrast and the degree of balance disruption (top). The fraction of correct trials increases as a function of contrast but decreases as a function of the degree of balance disruption (bottom). B, Error trials with (left) and without (right) pathway-specific balance. For balanced trials (100% inhibition), errors are due to mis-selection from cells in the selection module and subsequent ramping of a population of cells in the action module (top). For imbalanced trials (i.e., with excitatory bias; 40% inhibition), errors can be due to early ramping in cells in the action module before any divergence has begun in the selection module (bottom). Dashed black lines mark the target discrimination time in the selection module, and dotted black lines mark the onset time in the action module.

Figure 9.

Amelioration of the tradeoff between DM and WM function in a distributed circuit with interareal differences in local recurrent structure. The local structures for Modules 1 and 2, J_S^1→1 = J₁ and J_S^2→2 = J₂, respectively, are varied systematically to obtain the performance measures of “discrimination threshold” for DM and “robust stimulus range” for WM. A–F, In A–C, the distributed circuit is endowed with both feedfoward and feedback connections, while in D–F the feedback connection from PFC is absent (i.e., J_S^2→1 = J_T^2→1 = 0). A, The discrimination threshold increases with increasing J₁, while largely insensitive to J₂. B, The robust stimulus range increases with increasing J₂ and with decreasing J₁. C, The discrimination threshold decreases and the relative stimulus range increases by varying the structure difference J₂–J₁ while keeping the total structure J₁ + J₂ = 0.76 nA fixed. Performance in both measures improves with J₂ > J₁ (i.e., an increase in local recurrent strength from Module 1 to Module 2). D, Without PFC feedback, the dependence of the discrimination threshold for DM on structure is similar to the control case. E, Without PFC feedback, the robust stimulus range for WM is largely independent of J₂ and the magnitude of the currents that render the system distractible is an order of magnitude below that of the control case. F, Both the discrimination threshold and relative stimulus range (Eq. 17) decrease in the case without PFC feedback as the structure difference J₂–J₁ is varied while keeping the total structure J₁ + J₂ = 0.76 nA fixed. Readout of the response from the PFC or PPC module is marked in dark or light green, respectively.