Unveiling the Mystery of Membrane Potential in a Neuron

The membrane potential is critical for neural processes and communication. This paper presents the implementation of simple mathematical analysis using the two differential equations of the conventional Morris Lecar model to study the dynamics of membrane potential under the influence of various parameters. The concept in this work is basic and straightforward, however, it brings forward significant facets of membrane potential. Simulation results show that firstly, it is an underdamped system and provides valuable information in terms of the rise time, peak time, and settling time. Secondly, it is found that both the membrane voltage and its second derivative increase simultaneously with the stimulating current. Thirdly, it is observed that an increase in calcium conductance causes both the membrane voltage and its double derivative to rise, ultimately leading to the generation of a nerve impulse, particularly in the case of the double derivative of the membrane voltage. Fourthly, it is noteworthy that although the double derivative of the membrane potential decreases with an increase in potassium conductance, the dynamics of membrane potential increases with an increase in potassium conductance. Lastly, the analysis reveals that, even a slight deviation from the baseline temperature results in changes in the dynamics of both the membrane voltage and its double derivative, indicating that temperature also has a substantial effect on neuronal functions and communication mechanisms. This work, therefore, enhances the comprehension of the underlying neural mechanisms and aids in the development of effective therapeutic interventions.