Computational modeling of AMPK and mTOR crosstalk in glutamatergic synapse calcium signaling

Abstract

Neuronal energy consumption is vital for information processing and memory formation in synapses. The brain consists of just 2% of the human body's mass, but consumes almost 20% of the body's energy budget. Most of this energy is attributed to active transport in ion signaling, with calcium being the canonical second messenger of synaptic transmission. Here, we develop a computational model of synaptic signaling resulting in the activation of two protein kinases critical in metabolic regulation and cell fate, AMP-Activated protein kinase (AMPK) and mammalian target of rapamycin (mTOR) and investigate the effect of glutamate stimulus frequency on their dynamics. Our model predicts that frequencies of glutamate stimulus over 10 Hz perturb AMPK and mTOR oscillations at higher magnitudes by up to 36% and change the area under curve (AUC) by 5%. This dynamic difference in AMPK and mTOR activation trajectories potentially differentiates high frequency stimulus bursts from basal neuronal signaling leading to a downstream change in synaptic plasticity. Further, we also investigate the crosstalk between insulin receptor and calcium signaling on AMPK and mTOR activation and predict that the pathways demonstrate multistability dependent on strength of insulin signaling and metabolic consumption rate. Our predictions have implications for improving our understanding of neuronal metabolism, synaptic pruning, and synaptic plasticity.

Fig. 1. Synaptic signaling consumes energy to transduce neuronal signals and support neuronal function.

During high-frequency synaptic signaling, represented with glutamate stimulus in (a), proportionally larger quantities of ATP are allocated to restoring resting potential of ions, like those shown for calcium illustrated in (b). At high frequencies, this may challenge the energy production capacity of neurons, which utilize glycolysis and oxidative phosphorylation to convert glucose to pyruvate and then produce ATP in dendritic mitochondria. The decreasing cellular energy state (higher AMP/ATP ratio) promotes the phosphorylation of AMPK, a kinase which promotes the production of cellular ATP, but also has an intricate feedback loop with mTORC1 and mTORC2 downstream of the insulin signaling cascade, shown in (c), which have implications in protein translation and synaptic plasticity. In this work, we develop and analyze a computational model to study the interactions of these pathways, illustrated in (d), in response to a synaptic stimulus across several timescales. Created with BioRender.com.

Fig. 2. Sensitivity analysis reveal key parameters regulating system behavior.

The model describing AMPK and mTOR phosphorylation due to glutamate-stimulated calcium influx contains 163 parameters and 60 equations in a well-mixed model. a Comparisons between model predictions of phosphorylation ratios relative to initial state after 10 Hz synaptic activation and experimental results from Marinangeli et al. 2018 primary neuron cells stimulated via Biciculin/4AP protocol. b Probability density functions of steady-state concentrations of pAMPK, pAKT, pmTORC1, and pmTORC2 resulting from a global sensitivity analysis of 10,000 parameter values for each 163 parameters in a 20% range. c Heatmap of PRCC values describing the correlation between parameter value and system output for AMPK, AKT, mTORC1, and mTORC2 phosphorylation for a subset of parameters belonging to the insulin signaling system. d Heatmap of PRCC values describing the correlation between parameter value and system output for AMPK, AKT, mTORC1, and mTORC2 phosphorylation for a subset of parameters belonging to the neuronal metabolism system. e Heatmap of PRCC values describing the correlation between parameter value and system output for AMPK, AKT, mTORC1, and mTORC2 phosphorylation for a subset of parameters belonging to the calcium signaling system. Color scale represents PRCC values.

Fig. 3. Effect of a simple 1 Hz glutamate on AMPK/mTORC dynamics.

At t = 0s, a 1 Hz pulse train over 50 s is applied to the system. Before stimulus, the system was allowed to reach a steady state. During each pulse, 100 μM of glutamate is applied, which decays with a rate constant of 200 ms. After the pulse train, the system was allowed to return to an apparent steady state with no additional glutamate input. Concentration trajectories for a cytosolic calcium concentration, b cytosolic AMP/ATP ratio, c cytosolic phosphorylated AMPK concentration, d phosphorylated mTORC1 concentration, e phosphorylated mTORC2 concentration, f phosphorylated ULK1 concentration are shown.

Fig. 4. mTOR oscillations are stimulus frequency dependent.

The system was stimulated with four different glutamate frequencies: a 0.1 Hz (blue), 1 Hz (orange), b 10 Hz (yellow), c 50 Hz (purple). After stimulus, simulations return to an apparent steady state with no additional glutamate input. Trajectories are shown for d cytosolic calcium concentration, e cytosolic AMP/ATP ratio, f phosphorylated AMPK concentration, g phosphorylated mTORC1 concentration, h phosphorylated mTORC2 concentration, i phosphorylated ULK1 concentration. Quantitative metrics for AMPK, mTORC1, and mTORC2 in response to pulse trains of glutamate stimulus are also shown: j Area under the curve (AUC) relative to the system without stimulus applied over the same integration window (100 s), k time to reach steady state, and l amplitude change quantified as percent change from steady-state value.

Fig. 5. Cellular metabolic rate influences steady-state behavior of AMPK and mTOR independent of calcium.

We apply a 10 Hz glutamate stimulus for 5 s, however, at t = 0 s, we also change the value of baseline energy consumption throughout the cell and plot concentration trajectories for a AMP/ATP, b active, phosphorylated AMPK, c active, phosphorylated mTORC1, d active, phosphorylated mTORC2, e active, phosphorylated pULK1. Additionally, in (f), we compare the changes in steady state for pAMPK, mTORC1, and mTORC2 with respect to changes in hydrolysis rate. In (g), we then compare how this change impacts AUC, normalized to the AUC of simulation with the base value of the parameter. In (h), we plot the time to reach steady state and in (i), the relative magnitude of the first peak of AMPK, mTORC1, and mTORC2 to its new steady-state value as a result of energy consumption from glutamatergic stimulus.

Fig. 6. Oscillatory regimes for mTOR activation are dependent on both metabolic activity and IRS.

The system displays oscillatory behavior dependent on both k_hyd and V_IR rates. We show the dependence of a mTORC1 and b mTORC2 stability on k_hyd by selecting two values of V_IR, 5.7368 [mM/s] (yellow) and 0.01 [mM/s] (purple). For each case, we simulate until an apparent steady state for a range of k_hyd and plot the curves of minima and maxima at steady state. In the oscillatory region, the minima and maxima diverge and show an oscillatory regime, denoted by yellow dashed line. Next, we hold k_hyd constant and vary V_IR to obtain the stability profiles for c mTORC1 and d mTORC2 dependent on V_IR For two values of k_hyd, 1 × 10⁻⁴ [mM/s] and 0.149 [mM/s] we simulate until an apparent steady state for a range of V_IR, then plot the curves of local minima and maxima at steady state for mTORC1 and mTORC2. For regions of monostability, outside of dashed lines, the curves of minima and maxima converge to the steady state. In oscillatory regimes, within the dashed lines, the local minima and maxima due to oscillations form an envelope. The size and shape of the envelope is dependent on both k_hyd and V_IR. Then, to characterize this relation in a 2D parameter space, we plot corresponding 3D surface plots for e mTORC1 and f mTORC2. We also plot the oscillation magnitudes for g mTORC1 and h mTORC2, showing the parameter space that results in sustained oscillations.

Fig. 7. Insulin and cellular metabolism govern phosphorylation rates of AMPK, mTORC1, and mTORC2.

a AMPK phosphorylation concentration trajectories for a range of values for insulin receptor activity, V_IR, and ATP consumption rates, k_hyd. b mTORC1 phosphorylation concentration trajectories for a range of values for insulin receptor activity, V_IR, and ATP consumption rates, k_hyd. c mTORC2 phosphorylation concentration trajectories for a range of values for insulin receptor activity, V_IR, and ATP consumption rates, k_hyd. d AMPK AUC normalized to the maximum AUC value of AMPK. e mTORC1 AUC normalized to the maximum AUC value of mTORC1. f mTORC2 AUC normalized to the maximum AUC value of mTORC1. Color for heatmaps are AUC relative to maximal AUC per graph.

Fig. 8. Insulin signaling and glutamate frequency influence dynamic behavior of AMPK and mTOR phosphorylation.

a AMPK phosphorylation concentration trajectories for a range of values for insulin receptor activity and glutamate stimulus frequency. b mTORC1 phosphorylation concentration trajectories for a range of values for insulin receptor activity and glutamate stimulus frequency. c mTORC2 phosphorylation concentration trajectories for a range of values for insulin receptor activity and glutamate stimulus frequency. d AUC for AMPK normalized to the maximum AUC value of AMPK. e AUC for mTORC2 normalized to the maximum AUC value of mTORC1. f AUC for mTORC2 normalized to the maximum AUC value of mTORC2. Color for heatmaps are AUC relative to maximal AUC per graph.

Fig. 9. Glutamate frequency and metabolic stress lead to increases in AMPK and mTOR deviations.

a AMPK phosphorylation trajectories for a range of values for glutamate frequency and ATP consumption rates, k_hyd. b mTORC1 phosphorylation trajectories for a range of values for glutamate stimulus frequency and ATP consumption rates, k_hyd. c mTORC2 phosphorylation trajectories for a range of values for glutamate stimulus frequency and ATP consumption rates, k_hyd. d AUC for AMPK normalized to maximal AUC value. e AUC for mTORC1 normalized to maximal AUC value. f AUC for mTORC2 normalized to maximal AUC value. Color for heatmaps are AUC relative to maximal AUC per graph.

Fig. 10. Cellular response to glutamate stimulus in neurons is regulated by insulin sensitivity and metabolics.

A schematic for the various factors that lead into the decision between long-term potentiation and long-term depression.