A Computational Model of Major Depression: the Role of Glutamate Dysfunction on Cingulo-Frontal Network Dynamics

Abstract

Major depression disease (MDD) is associated with the dysfunction of multinode brain networks. However, converging evidence implicates the reciprocal interaction between midline limbic regions (typified by the ventral anterior cingulate cortex, vACC) and the dorso-lateral prefrontal cortex (dlPFC), reflecting interactions between emotions and cognition. Furthermore, growing evidence suggests a role for abnormal glutamate metabolism in the vACC, while serotonergic treatments (selective serotonin reuptake inhibitor, SSRI) effective for many patients implicate the serotonin system. Currently, no mechanistic framework describes how network dynamics, glutamate, and serotonin interact to explain MDD symptoms and treatments. Here, we built a biophysical computational model of 2 areas (vACC and dlPFC) that can switch between emotional and cognitive processing. MDD networks were simulated by slowing glutamate decay in vACC and demonstrated sustained vACC activation. This hyperactivity was not suppressed by concurrent dlPFC activation and interfered with expected dlPFC responses to cognitive signals, mimicking cognitive dysfunction seen in MDD. Simulation of clinical treatments (SSRI or deep brain stimulation) counteracted this aberrant vACC activity. Theta and beta/gamma oscillations correlated with network function, representing markers of switch-like operation in the network. The model shows how glutamate dysregulation can cause aberrant brain dynamics, respond to treatments, and be reflected in EEG rhythms as biomarkers of MDD.

Keywords: bistability; deep brain stimulation; serotonin; subgenual; theta.

Figure 1.

Schematic of network architecture and mechanisms. (A) The conceptual network model included 2 subsets of networks: (1) The emotional network including vACC and (2) the cognitive network including dlPFC. The vACC and dlPFC are the hubs of each network, reciprocally connected via disynaptic inhibition. Each subnetwork included recurrently coupled excitatory pyramidal cells (E cells) and inhibitory interneurons (I cells). Emotional inputs from the limbic system target vACC and cognitive inputs from posterior parietal cortex (PPC) impinge on dlPFC. (B) Schematic drawing illustrating the slower glutamate reuptake in vACC described in MDD, which we simulated as a slow-down of glutamate decay in the synapses. (C) Schematic drawing illustrating the action of SSRIs through 5-hydroxytryptamine (5-HT_1A) receptors: An increase in an outward K⁺ current causes a small hyperpolarization of vACC excitatory cells, which is what we simulate computationally.

Figure 2.

“Healthy” operation in the network is the ability to switch from emotional to cognitive processing. (A) We simulated a task composed of (1) 10-s resting epoch, (2) 15-s SP epoch (vACC received 3 brief stimulus every 5 s), (3) 15-s WM epoch (dlPFC received 3 brief stimulus every 5 s), and (4) 20-s resting epoch. Stimulation pulses were 250 ms long Poisson trains at 200 sp/s impinging on AMPARs with conductance 2.4 nS. (B) Sample activity in 4 neurons of each network in one simulation. In black, vACC neurons and in gray, dlPFC neurons. (C) Histograms of average population activity in each network during one task simulation. Upper panels correspond to dlPFC activity (gray) and lower panels to vACC activity (black). (D) Local field potentials (LFP) normalized power spectrum for the activated state. In both subnetworks (vACC and dlPFC), spectra are characterized by the coexistence of theta (2–8 Hz) and beta/gamma (12–50 Hz) synchronization. Jackknife error bars around the mean mark the 95% CI.

Figure 3.

Glutamate decay slow-down reproduces the progressive nature of MDD. (A) Mild MDD network (2.5% slow-down in glutamate decay in the vACC). Activity histograms for a single simulation show aberrant activity in the vACC during the resting epoch. Although dlPFC only responded partially to the first inputs, it was still able to turn off activity in the vACC during the WM epoch. (B) Moderate MDD network (5% slow-down in glutamate decay in the vACC). vACC showed aberrant activity in resting epochs and dlPFC showed diminished responsivity to cognitive inputs, now being unable to turn off vACC. (C) Severe MDD network (7.5% slow-down in glutamate decay in the vACC). Aberrant vACC activity was not modulated by any kind of inputs. (D) LFP normalized power spectrum in the vACC. Synchronization in the theta frequency range was progressively reduced, whereas beta/gamma rhythms were enhanced as glutamate decay was gradually slowed down (healthy, 2.5% and 7.5% slow-down in glutamate decay). Jackknife error bars around the mean mark the 95% CI.

Figure 4.

Serotonin treatment response on MDD network models decreases with the progression of the disease. (A) Nonresponse: A moderate MDD model (5% slow-down in glutamate decay) treated with a low dose of SSRI (V_L = −70.05 mV), vACC showed aberrant activity in resting epochs, and dlPFC showed diminished responsivity to cognitive inputs. (B) Emotional inhibition: A moderate MDD model (5% slow-down in glutamate decay) treated with a high dose of SSRI (V_L = −70.5 mV); SSRI treatment could turn off aberrant activity in vACC in the resting epoch, but also inhibited the response of vACC to emotional stimuli during the SP epoch. (C) Optimal response on mild MDD model: Mild MDD (2.5% glutamate decay slow-down) treated with an optimized dose of SSRI (V_L = −70.18 mV). (D) Optimal response on severe MDD model: Severe MDD (7.5% glutamate decay slow-down) treated with an optimized dose of SSRI (V_L = −70.6 mV). (E) Bifurcation diagram for healthy and severe MDD models: Mean firing rate of excitatory neurons over stable active (upper branches) and inactive (lower branches) network states. The red (yellow) dots represent stable states for the healthy (severe MDD) model. The plot shows the existence of a bistable range, in which network function is bistable between the 2 network states. The blue dotted line represents the baseline network's operating regime, which is in the bistable range in the healthy model. For the severe MDD model, the baseline network's operating regime is on the right side of the bistable range, where only the high-rate state (activated state) is stable. The violet dotted line represents the hyperpolarization generated by the SSRI treatment in the optimal response. Note that the reduction in the bistable range in the severe MDD network generates a reduction in the stability of both activated and inactivated states. (F) LFP normalized power spectrum in the vACC of a severe MDD network treated with SSRI. Severe MDD model (7.5% glutamate decay slow-down) treated with progressively increasing doses of SSRI (V_L = −70, −70.4, and −70.6 mV). Synchronization in the theta frequency range was progressively enhanced, whereas beta/gamma rhythm amplitude decreased as the dose of SSRI increased. Jackknife error bars around the mean mark the 95% CI.

Figure 5.

DBS restores the switch between emotional and cognitive processes. (A) MDD network resistant to SSRI treatment: In a severe MDD model (10% slow-down in glutamate decay) treated with an insufficient dose of SSRI (V_L = −70.5 mV), vACC showed aberrant activity in resting epochs and dlPFC showed diminished responses to cognitive inputs. (B) DBS in treatment-resistant model: Treatment-resistant model (10% glutamate decay slow-down and V_L = −70.5 mV) treated with DBS at 130 Hz, simulated as impulses onto AMPARs on vACC interneurons. (C) LFP normalized power spectrum in the vACC of a severe MDD network treated with SSRI and DBS. Severe MDD model (10% glutamate decay slow-down) untreated (V_L = −70), treated with an insufficient dose of SSRI (V_L = −70.5), and treated with SSRI (V_L = −70.5) and DBS. Synchronization in the theta frequency range was progressively enhanced, whereas beta/gamma rhythm amplitude decreased with the dose of SSRI and DBS. Jackknife error bars around the mean mark the 95% CI.

Figure 6.

Graphical interpretation of vACC dynamics in healthy and MDD conditions. (A) The graphical representation of solutions of the rate model upon varying baseline excitability $\mathrm{\Delta }{I_{\mathrm{e}}}^{\mathrm{v}}$ presented a bistable dynamics (f_D = 1). Each subnetwork presented 2 stable attractors: The low rate (lower branch) and the high rate (upper branch) attractors, which coexisted for a range of $\mathrm{\Delta }{I_{\mathrm{e}}}^{\mathrm{v}}$ (bistable range). The blue dotted line represents the baseline network's operating regime. Inset: Schematic of an “energy landscape” representation that illustrates graphically the network's dynamics in A for a given value of $\mathrm{\Delta }{I_{\mathrm{e}}}^{\mathrm{v}}$ (baseline excitability). Population activity (ball) seeks minimum-energy states, but fluctuations can push activity uphill to change attractor. (B) Attractor solutions for the MDD rate model after enhancing recurrent excitation in vACC (f_D = 1.05 for mild MDD, f_D = 1.15 for moderate MDD, and f_D = 1.25 for severe MDD). The bistable range became narrower and got displaced to more negative currents progressively. MDD networks operated outside the bistable range for vACC, where only the activated state of the upper branch is stable. (C) Schematic “energy landscape” visualization of B. The energy slope increases with recurrent excitation (f_D) and the population activity (ball) seeks minimum-energy states, which in MDD networks are only activated states. (D) Nonresponse and emotional inhibition following SSRI treatment in the moderate MDD model (f_D = 1.15): A low-dose SSRI keeps the vACC network out of the bistable range, where only the activated state is stable (nonresponse), and a high-dose SSRI moved the vACC network beyond the bistable range, where only the inactivated state is stable (emotional inhibition). (E) Optimal response to SSRI treatment. The severe MDD network model (f_D = 1.25) treated with an optimal dose of SSRI ($\mathrm{\Delta }{I_{\mathrm{e}}}^{\mathrm{v}}$ = −0.035) operated in the bistable range, but the bistable range was narrower, and thus states were more unstable than in the healthy network (gray). (F) DBS treatment through interneurons: Severe MDD model (f_D = 1.25) treated with DBS increases the inhibitory current (${I_{\mathrm{i}}}^{\mathrm{v}}$ = 0.026) and operates in the bistable range (cyan dotted line).

Figure 7.

Mechanisms of oscillations. Theta and beta oscillations coexist in the bistable range, but differ in their mechanism. (A) Bistable range for the moderate MDD model (firing rate network, f_D = 1.1). We selected 3 network conditions ($\mathrm{\Delta }{I_{\mathrm{e}}}^{\mathrm{v}}$ = 0.005, 0.02, and 0.08, respectively) in the upper branch, progressively approaching the edge of the bistable range, to illustrate transient dynamics in B. (B) Damped oscillatory dynamics in the theta frequency range were generated by perturbing the steady state (initial condition, ${r_{\mathrm{e}}}^{\mathrm{v}}$ = 4 sp/s) of the 3 conditions indicated in A. Damped oscillations had larger amplitude for networks operating near the bistable range limit of the upper branch A. (C) Spiking simulations can present additional high-frequency oscillations. Normalized power spectra of spiking network activity upon progressive depolarization of the vACC excitatory population (depolarizing currents −0.015, 0, and 0.04 nA in ever lighter shades of gray, respectively) in the severe MDD model (spiking network, 7.5% glutamate decay slow-down) revealed changes in the amplitude and frequency of beta/gamma oscillations. (D) The mechanism of high-frequency oscillations in spiking simulations (C) kept a fixed relationship between neuronal firing rate and oscillation frequency, indicating that beta oscillations emerged in the spiking simulations through an oscillator coupling mechanism. Scatter plot shows the frequency of the power spectrum peak in the beta/gamma range versus the network's mean firing rate for a range of vACC depolarizing currents −0.015 to 0.06 nA (grayscale bar).

Figure 8.

Schematic summary: disease and oscillations. Theta and beta oscillations mark the distance to the bistable range. (A) Bistable range diagrams for mild and severe MDD models (firing rate network, f_D = 1.05 and 1.25, respectively). In the upper branch, the black oscillation represents schematically the amplitude of theta oscillations generated by the oscillatory instability, and the gray oscillation represents schematically the amplitude of beta-gamma generated by synchronization. As the severity of the MDD model increases, the network's state (black dotted line) lies further away from the bistable range edge and the amplitude of the theta oscillation is reduced and beta-gamma is increased. (B) Following a treatment (by reducing network excitability to gray dotted line), the system moves leftward approaching the stability limit of the upper branch. As the system approaches the bistable range, the amplitude of theta oscillations (black) increases and the frequency and amplitude of beta/gamma oscillations (gray) decrease. A network with more amplitude of theta oscillations is closer to the limits of the bistable range and is more likely to be brought into the optimized operating regime by small network hyperpolarization (i.e., SSRI or DBS treatment).