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Influence of energy deficiency on the subcellular processes of Substantia Nigra Pars Compacta cell for understanding Parkinsonian neurodegeneration

Parkinson’s disease (PD) is the second most prominent neurodegenerative disease around the world. Although it is known that PD is caused by the loss of dopaminergic cells in substantia nigra pars compacta (SNc), the decisive cause of this inexorable cell loss is not clearly elucidated. We hypothesize that “Energy deficiency at a sub-cellular/cellular/systems level can be a common underlying cause for SNc cell loss in PD.” Here, we propose a comprehensive computational model of SNc cell, which helps us to understand the pathophysiology of neurodegeneration at the subcellular level in PD. The aim of the study is to see how deficits in the supply of energy substrates (glucose and oxygen) lead to a deficit in adenosine triphosphate (ATP). The study also aims to show that deficits in ATP are the common factor underlying the molecular-level pathological changes, including alpha-synuclein aggregation, reactive oxygen species formation, calcium elevation, and dopamine dysfunction. The model suggests that hypoglycemia plays a more crucial role in leading to ATP deficits than hypoxia. We believe that the proposed model provides an integrated modeling framework to understand the neurodegenerative processes underlying PD.

basal ATP states were observed) in which SNc neuron operates under different energy conditions. The four dynamic regimes are determined by how the basal ATP level behaves under different glucose and oxygen values. The region A was attributed to glucose and oxygen values for which no change in basal ATP level was observed. The region B was attributed to glucose and oxygen values for which there was an initial drop and subsequent return to basal ATP level. The region C was attributed to glucose and oxygen values for which there was an initial drop and a subsequent stabilization at a lower basal ATP level. The region D was attributed to glucose and oxygen values for which basal ATP level fluctuates (between high and low basal ATP levels). The region E was attributed to glucose and oxygen values for which cell undergoes degeneration (Suppl. Fig. 10). Dendrite:

Supplementary
and the postsynaptic current ( ) is given by, where, ̅ is the maximal conductance, is the reversal potential, is the postsynaptic membrane potential, [ ] is the neurotransmitter, and is the fraction of the receptors in the open state.

NMDA Receptors
The slower NMDA type of glutamate receptors can be represented with a two-state model similar to AMPA/kainate receptors, with a voltage-dependent term representing magnesium block. Using the scheme in Eqs. 1 and 2, the postsynaptic current is given by where, ̅ is the maximal conductance, is the reversal potential, ( ) is the magnesium block, is the postsynaptic membrane potential, and is the fraction of the receptors in the open state.
where, [ 2+ ] is the external magnesium concentration, and is the postsynaptic membrane potential.

GABA A Receptors
GABAA receptors can also be represented by the scheme in Eqs. 1 and 2, with the postsynaptic current given by where, ̅ is the maximal conductance, is the reversal potential, is the postsynaptic membrane potential, and is the fraction of the receptors in the open state.

GABA B Receptors
The stimulus dependency of GABAB responses, unfortunately, cannot be handled correctly by a two-state model. The simplest model of GABAB-mediated currents has two variables: and the postsynaptic current ( ) is given by, where, ̅ is the maximal conductance, (= ) is the reversal potential, is the postsynaptic membrane potential, is the fraction of the receptors in the open state, is the fraction of activated G-proteins, is the dissociation constant of the binding of on the K + channels, 1 and 2 are voltage-independent forward and backward rate constants for , 3 and 4 are voltage-independent forward and backward rate constants for , and [ ] is the neurotransmitter.

Overall Synaptic Current
The overall synaptic input current flux ( ) to SNc neuron is given by, where, is the excitatory AMPA synaptic current, is the excitatory NMDA synaptic current, is the inhibitory GABAA synaptic current, is the inhibitory GABAB synaptic current, is the Faraday's constant, and is the cytosolic volume. Voltage-independent forward rate constant for of GABAB