Table 2. Summary of general assumptions made during model design.

Assumption	Comments
The blood-brain barrier (BBB) has just one layer.	The BBB is mainly composed of endothelial cells, which are connected to each other through tight junctions. The only way to cross the BBB is through specific transporters located in the luminal and abluminal membranes (double layer) of the brain capillary endothelia [86,87]. For simplicity, a single layer and one generic type of transporter were considered.
The BBB is the only way for molecules to reach the brain cells.	Since the surface of BBB is more than 1,000 times that of the choroid plexus [88], the BBB area is taken as the exclusive means for a given molecule to access the brain [89].
The L-type amino acid transporter (LAT) is the only one in along the BBB.	Large neutral amino acids (LNAAs), such as tyrosine (TYR), phenylalanine (PHE) and tryptophan (TRP) compete for the same type of transporter, called the L-type amino acid transporter (LAT) [90]. Although different subfamilies of LAT transporters are known, LAT-1 is here assumed to be the sole bidirectional, sodium-independent, high-affinity obligatory exchanger that works for facilitated diffusion.
Only TYR, PHE and TRP cross LAT-1.	In reality, LAT-1 is used not only for passage of TYR, PHE and TRP, but also for transporting brain- chained amino acids (BCAA) [91]. This fact appears to be of secondary importance, and the inhibitory competition of these BCAA in the uptake of TYR, PHE and TRP was not taken into account.
The transport of LNAA occurs directly from the blood serum to the neuronal cytosolic space.	In actuality, LNAAs reach the brain neurons by entering an astrocyte or moving through the extracellular space to a neuron. In the model, these steps are simplified to a single transport step across the BBB through LAT-1, directly to the neuron, as was proposed in the literature [48,49].
Only TYR and PHE affect the dopaminergic pathway, while TRP acts only in the serotonergic pathway.	Uptake of TYR, PHE and TRP can lead into both dopaminergic and serotonergic neurons through intersection points in the two pathways [92–94]. For simplicity, we assume that only TYR and PHE enter dopaminergic neurons, while TRP only enters serotonergic neurons.
The intracellular volume of a nerve terminal is Vi = 1.13x10-10 μl	Volume estimates are necessary for scaling the results. Direct information is unavailable and the estimates are quite coarse, but appear to be sufficient, as the relative sizes to each other are more important. If such a terminal is taken as a single synaptosome and approximated by a sphere with radius Ri = 300 nm, the corresponding intracellular volume is Vi = 1.13x10-10 μl (notice that this is not the cytosolic volume, but the cell volume as a whole).
The intracellular vesicular volume in a nerve terminal is Vv = 6.7x10-12 μl	Each terminal contains approximately 200–500 vesicles of approximately 40 nm in diameter [95–97]. Taking every vesicle as a sphere with radius Rv = 20 nm and multiplying its volume by 200 results in a total vesicular volume Vv = 6.7x10-12 μl.
The cytosolic volume in a nerve terminal is Vc = 1.06x10-10 μl	Taking Vi and Vv as above described, the cytosolic volume is, consequently, Vc = Vi−Vv = 1.06x10-10 μl.
The extracellular volume surrounding one nerve terminal is Ve = 1.78x10-11 μl	The extracellular space surrounding the nerve terminal is assumed to be a 15 nm-thick layer [98]. With the above settings, the extracellular space in the immediate vicinity of a terminal, if expressed as a sphere, has the volume Ve = 1.78x10-11 μl. Considering that there are two terminals, the total shared extracellular volume is 2Ve.
Conversion factor from grams of tissue to volume of water: fc = 0.7 ml/g	Units of metabolite concentrations and enzyme kinetic parameters must be consistent to calculate the kinetic orders for power-law approximation. Fluxes and affinities are usually given in molar concentration per unit of time (mol/l/h) and molar concentration (mol/l), respectively, or in fractions of these units. We used a conversion factor fc = 0.7 ml/g to switch between mol/g and mol/l [99,100], when necessary.
Every component in the model is assumed to be homogeneously spread throughout the same compartment.	The consideration of spatial heterogeneity would increase the complexity of the model manyfold.
The CORT concentration is assumed to vary proportionally and homogeneously regardless of the compartment.	Since CORT if a lipophilic molecule with low weight, it can cross the BBB by diffusion and quickly disperse toward the concentration equilibrium [101]. It has been shown that changes in CORT levels are easily detected in saliva and urine and that these measurements correlate well with free serum CORT concentrations [102,103]. Thus, absolute values and changes for CORT concentrations taken from saliva, urine or serum are assumed to represent alterations inside the brain cells [104].
Kynurenine metabolites are assumed to vary proportionally and homogeneously regardless of the compartment.	Information regarding KYN-associated metabolite concentrations in dopaminergic and serotonergic neurons is scarce. However, it is fair to assume that these levels are in the nanomolar (nm) range within tissues and in the extracellular space. The concentrations of the KYN metabolites of interest are considered uniformly distributed over brain cells and compartments.
Transcriptional and post- translational regulation mechanisms are not considered, so that protein expression is assumed to be directly proportional to gene expression.	Experiments with homozygote and heterozygote mutants in animals do not necessarily result in a 100% and a 50% reduction in protein expression or activity, respectively. However, for simplicity, transcriptional and post- translational mechanisms are ignored, and it is assumed that there is a linear correlation between gene and protein expression [105,106].
Proteins are represented as a fraction of the total amount of protein content in the control situation.	All variables of a mathematical model that in a simulation do not change over time can be explicitly represented as independent variables and defined as constants. Here, this is the case for the proteins involved in enzymatic reactions.
Enzyme concentrations vary to the same degree regardless of the compartment in which they are active.	Although the enzyme concentrations may vary according to the compartment where they are located, it is assumed that their levels change proportionally everywhere, according to the protocol of the experiment, in which proteins are independent variables with values set before each simulation.
Chronic stress is positively correlated to inflammation.	A large body of research has demonstrated an association between social stressors and inflammation. These studies provide evidence of the correlation among stress, depression and the immune system at the levels of proteins, signaling processes and the genome [107].
Chronic stress is positively correlated to cortisolemia.	Chronic stress leads to a reduction in the negative feedback affecting the HPA axis, thereby elevating the levels of CORT over time. In addition, immune cells become less sensitive to the anti-inflammatory effects of CORT, which leads to the so-called “glucocorticoid insensitivity” [108].
Aspects of comorbidities accompanying depression were not taken into account.	MDD usually manifests with other disorders, such as anxiety and post-traumatic stress disorder [109], whereas our model is based on findings concerning depressed patients and animal models of depression.
Neuronal firing was not taken into account.	Although neuronal firing activity plays a key role in neurotransmission and, consequently, in the levels of metabolites, our model focuses only on the biochemical reactions that regulate the monoamine systems.