Aspartame is a simple peptide-like molecule, an amide formed from phenylalanine and aspartic acid, the resultant peptide present as its methyl ester, if MSG is giving you grief then it isn't altogether hugely surprising, although only small quantities of aspartame are actually used afaik. Glutamate is the main excitatory neurotransmitter (GABA, gamma-aminobutyric acid fulfilling the role of the primary inhibitory neurotransmitter in the brain) and along with the various metabotropic glutamate receptors (a metabotropic receptor exerts its effects on a neuron when activated via a cascade of intracellular second messengers, leading to upregulation, downregulation of whatever genes it ultimately controls, whilst the initial event from the other main type, ionotropic receptors is docking of the ligand [active compound doing the binding] with its receptor binding site, leading to a conformational change in the shape of the receptor protein, and generally doing something like causing a ligand-gated ion channel [some ion channels are gated to a specific voltage threshold, these are the voltage-gated ion channels, typical examples being most types of sodium and calcium channels whilst some are what is called a ligand-gated ion channel, which, unsurprisingly, opens in such a direct manner in response to binding of a neuroactive substance] to open,
This allows ions to exchange between the cells interior, the cytoplasm, and the extracellular environment, causing minute chemical currents to be generated by the exchange. In the case of the ionotropic glutamate receptors, named for the ligands which were first discovered to bind although not always endogenous, there are three types, NMDA, AMPA and kainate, these are the three ionotropic glutamate receptor types, NMDA actually stands for N-methyl-d-aspartate, an analog of the amino acid aspartic acid, NMDA receptors are a bit peculiar in that they are gated both by voltage and by the presence of drugs/neurotransmitters. It also requires the amino acid glycine to bind, in addition and within the same time frame as glutamate, the primary ligand for these receptors as a co-agonist before the channel will open and the neuron depolarize and transmit its action potential in response to presynaptic stimulation from neurons responding to events going on upstream (I.e preceding the firing of the glutamatergic neuron). In the case of NMDA receptors however, normally its channel, a voltage/ligand gated calcium channel has, at resting potential (when not stimulated by a neurotransmitter or exogenous drug) its central pore, the part that does the actual conduction of the ion flux when activated, blocked by a magnesium cation (a cation is a positively charged ion, an anion is an ion with a negative electrical charge)
When glutamate (and in the case of the NMDAr, aspartate, although the response to aspartate is weaker than that of glutamate in terms of the amplitude of the response) binds, along with glycine to its regulatory site, ensuring against 'accidental' activation of the channel, the channel boots out the Mg ion and a calcium current is generated after a specific voltage threshold induced by prior neurons signalling to the NMDAergic neuron. In excess, this isn't a good thing (here we are talking rather, about potent agonists rather than natural release as it should be) because the resultant calcium flux can in excess cause what is known as excitotoxicity, essentially overloading the cell due to a surfeit of the excitatory neurotransmitter, glutamate (or aspartate) and killing it.
Especially in the case of glutamate, this can cause seizures, and is implicated very heavily in epileptiform disorders of various kinds, as well as in schizophrenia, where there is thought to be a hypofunction of NMDA receptors.
Can go into this more if you want, but there is a fair amount of controversy over aspartame. In essence however, aspartate can mimic glutamate (and is an endogenous neurotransmitter in its own right, filling a similar general profile in comparison with glutamate) at the NMDA receptor.