Fig 1.
Model of the closed-loop mesocortical circuit.
(A) A three-dimensional minimal rendering of the human brain essentially featuring the anatomical localization of the two brain regions, DLPFC and VTA, whose reciprocal interaction constitutes the mesocortical circuit. (B) A simplified illustration of the synaptic contact made by a terminal of the dopaminergic afferent projections onto a pyramidal neuron or GABAergic interneuron in the cortex. The DA-releasability (RDA) and D1R-sensitivity (D1Rsens) are the presynaptic and postsynaptic factors, respectively, which crucially regulate the transmission at dopaminergic synapses. (C) In the neural mass model of the mesocortical circuit, the cortical neurons are broadly categorized into the populations of excitatory pyramidal neurons and inhibitory GABAergic interneurons. The excitatory population, on receiving cue input, self excites itself (with the synaptic efficacy WPP) and also excites the population of inhibitory neurons in the cortex (WPI) as well as DA neurons in midbrain (WPD). On excitation, the inhibitory population inhibits excitatory population (WIP) as well as itself (WII) whereas the DA neuron population releases DA in the cortex (RDA) through dopaminergic projections and causes accumulation of the cortical DA pool, [DA].
Table 1.
The definitions of the key dynamical variables and the free parameters of the closed-loop mesocortical model.
Table 2.
List of parameters present in the mathematical model and its stochastic framework along with their values.
The parameters with values in bold font are the free parameters varied in the present study.
Fig 2.
The delay-associated state of the mesocortical dynamics is characterized by the global equilibrium state of its various dynamical elements.
(A) Given a fixed value of D1R-sensitivity D1Rsens (here D1Rsens = 3, normal control), the bifurcation profiles of the dynamical elements are shown with DA releasability RDA as the bifurcation parameter. Critical RDA, and the corresponding critical cortical dopamine content [DA] and D1R stimulation level D1Ract, mark the beginning of bistable regime favoring the working memory maintenance during delay period. The higher stable states of the bifurcation profiles are together associated with the sustained-firing state of the cortical dynamics whereas the lower stable states together signify the basal spontaneous-activity state. The ranges of [DA] and D1Ract spanned by their higher stable states represent the spans or windows of cortical DA content and D1R stimulation, respectively, underlying the entire modulation profile of the cortical dynamics. The maximum limit to which [DA] or D1Ract may may increase with increase in RDA marks the saturation level. The cue-threshold in the aPN bifurcation profile signifies the minimum excitation of the pyramidal population by cue input, which causes switching to the sustained-firing state. (B) Alteration in D1Rsens further affects the bifurcation profiles. Most prominently, increase in D1Rsens causes leftward shift of the bifurcation region.
Fig 3.
Effects of variation in D1R-sensitivity on the critical DA releasability, on the critical as well as saturations levels of cortical DA content, and on the modulation-associated windows of DA content and D1R stimulation.
Increase in D1Rsens causes significant decrease in the critical RDA (A) and [DA] (B) marking an early beginning of the bifurcation regime. The variations in critical RDA and [DA] (C) exhibit a strong positive correlation. Moreover, the saturation level of [DA] (D) significantly decreases with increase in D1Rsens, causing the modulation-associated window of DA (E) to shift to lower values as well as shrinks in its span. However, the modulation-associated window of D1R stimulation (F) does not vary with change in D1Rsens.
Fig 4.
Effects of variation in D1R-sensitivity on the phase-lag between the dopaminergic modulation profiles of sustained pyramidal and interneuron activities.
(A) The phase-lag between the peak aPN and the peak aIN activities with respect to the associated [DA] levels is seen to considerably decrease with increase in D1Rsens signifying a steeper modulation of the neuronal activities with unit change in [DA]. (B) However, the phase-lag with respect to the associated D1Ract levels does not vary.
Fig 5.
Effects of variation in D1R-sensitivity on the range of optimal DA facilitating optimal WM maintenance.
(A) An illustration for the concept of optimal DA range or window associated with the region of optimal sustained aPN activity. It is assumed here that the sustained pyramidal activity above 80% of the peak activity in the modulation profile facilitates efficient WM maintenance. (B) The optimal DA window is seen to considerably shrink and shift to lower values as the D1Rsens is increased.
Fig 6.
The global potential landscape of the noisy mesocortical dynamics.
For the normal control parameters DA-releasability (RDA = 0.0058nM.ms−1) and D1R-sensitivity (D1Rsens = 3) of the mesocortical dynamics, the global potential landscape is shown over the aPN-D1Ract plane, along with its contour projection onto the plane. The system in sustained-firing state is depicted by a ball sitting in the corresponding basin of attraction whose depth provides the potential barrier (PB) restricting the noise-induced transition of the system to spontaneous-activity state. The contour projection illustrates the fluctuation size in the system state around its mean point, which governs the signal-to-noise ratio (SNR) of the cortical sustained activity facilitating WM maintenance.
Fig 7.
The conserved features of WM-robustness across variation in D1R-sensitivity.
(A) For the different D1Rsens, PB for the sampled levels of sustained pyramidal activities along the aPN-modulation profile always follows a concave profile. The sampled activities from the pre-peak side of the aPN-modulation profile are marked with color-filled squares and that from the post-peak side are shown in color-filled circles. The sampled activities, 90% (cyan), 80% (blue), 70% (magenta), 60%(red), are percentage activities with respect to the peak 100% (green) sustained activity. (B) The average PB of the post-peak set of sustained activities (including the peak activity) in the aPN-modulation profile is always higher than that of the pre-peak set for every D1Rsens. (C) Similarly, SNR for the sampled levels of sustained pyramidal activities always follows a concave profile under different condition of D1Rsens. (D) Moreover, the average SNR of the post-peak set of sustained activities is always higher than that of the pre-peak set for all values of D1Rsens.
Fig 8.
Effects of variation in D1R-sensitivity on the WM-robustness in terms of potential barrier (PB).
Increase in D1Rsens causes a consistent decrease in the PB of any individual level of sustained activity either sampled from the pre-peak (A) or from the post-peak (B) set of the modulation profile of cortical sustained aPN activity. The percentage activities are with respect to the peak (100%) sustained activity. (C) The percent decrease in the average PB of pre-peak and post-peak sets across increase in D1Rsens shows higher vulnerability of the pre-peak set to change in D1R-sensitivity.
Fig 9.
Effects of variation in D1R-sensitivity on the WM-robustness in terms of signal-to-noise ratio (SNR).
Similar to the PB, increase in D1Rsens causes a consistent decrease in the SNR of any individual level of sustained activity either sampled from the pre-peak (A) or from the post-peak (B) set of the modulation profile of cortical sustained aPN activity. The percentage activities are with respect to the peak (100%) sustained activity. (C) The percent decrease in the average SNR of the pre-peak and post-peak sets across increase in D1Rsens indicates higher vulnerability of the pre-peak set to change in D1R-sensitivity.