A Model for the Effect of Glia on the Communication Amongst Neurons
21.02.2019
Classic Hodgkin-Huxley model of neuron cells is based on currents passing through potassium, and sodium channels, whilst those from other channels are added up to "leak current". In model represented by equation 1, depolarization in cellular membrane is related to INa (sodium current), IK (potassium current), IL (leak current), and Iu (exciting current) [1].
v' = Iu - INa - IK - IL (equation 1)
Of course, this model fails to capture the role of nitric oxide in neural communication, leading up to long-term potentiation. Nitric oxide (NO) is a retrograde neurotransmitter, which exerts its biological activity on pre-synaptic cell upon being released from the post-synaptic cell [2]. As nitric oxide affects calcium channels, the Hodgkin-Huxley model demands to be expanded by interpolating high-threshold calcium current (ICa), low-threshold, T-type calcium current (IT), and calcium-dependent-and-voltage-independent hyperpolarization potassium current (IAHP) to afford equation 2. Indeed, this contemporary model was reported by Terman et al.,in 2002 [3]; however, the currents do not relate to NO.
v' = Iu - INa - IK - IL - IAHP - ICa - IT (equation 2)
​
To address this problem, we revisited equation 2 and improved upon it. Our results indicate that increasing the concentration of NO alters the dynamical behavior of membrane potential, in conjunction with calcium uptake into presynapsis, as shown in the following figures.
Complete set of equations, and paramaters we devised to append the biological activity of NO are given in the following document.
References
1) Hodgkin, Alan L., and Andrew F. Huxley. "A quantitative description of membrane current and its application to conduction and excitation in nerve." The Journal of physiology117.4 (1952): 500-544. [Link]
2) a) Arancio, O., et al. "Nitric oxide acts as a retrograde messenger during long-term potentiation in cultured hippocampal neurons." Journal of Physiology-Paris 90.5-6 (1996): 321-322. [Link]
b) Terman, David, et al. "Activity patterns in a model for the subthalamopallidal network of the basal ganglia." Journal of Neuroscience 22.7 (2002): 2963-2976. [Link]