Please help me solved these problems!

In 1952, A. Hodgkin and A. Huxley published a series of papers which culminated with a model for the electrical activity of a neuron. This model made a profound impact on subsequent research in electrophys- iology including neuronal, cardiac, pancreatic, and other cell types that are electrically active. Their work earned them the 1963 Noble Prize in Physiology or Medicine. In this assignment, you will explore a simplication of their model that describes the onset of electrical excitation of a neuron. The model treats the cell membrane of the neuron and surrounding intracellular and extracellular space as an RC circuit. In the simplied model, the currents (which are carried by ions instead of electrons) pass through a pore /channel in the membrane that allows potassium (K) to pass through (a linear (Ohmic) resistor), a non-linear sodium (Na) channel, and a linear leakage current. The membrane itself acts as a capacitor. Ion concentration differences between intra and extracellular spaces act as batteries. The equation for the voltage across the membrane, V, also called the transmembrane potential, is C...% = .f(V) + I = gN.m(v>3 00? Does the solution have an inection point? If so, what is the value of V at the inection point? (c) *'krir When a neuron Whose transmembrane potential, V, is described by Eq. 1 is stimulated by another neuron, the value of I in the equation becomes positive. If the stimulation causes I to increase from 0 to 0.5 [r A / cm2, how do the solutions to the new equation (with this nonzero I), for each of the ICs given in part (a), behave as t goes to 00. When a stimulus is sufficiently large for the solution to approach Excited, we say that the stimulus succeeded in exciting the cell. (d) *'k'ki' For 1 > 1*, it is possible for a stimulus 1 to excite a cell. What is the (smallest) value of I * (approximately) that makes this statement true? Explain how you came to your conclusion. (e) *'krix' When the transmembrane potential reaches a level close to the excited state, the potas . . 2 . Slum conductance increases to around 30 mS/ cm and the sodium conductance decreases to below 10 IDS/C1112. For the simplied model considered here, these changes in conductance are imple- mented by changing the parameters G'Na and G K to the new values : Once these new conductances are in place in Eq. what does a solution starting at the excited state found in part (a) do as t > 00? How are the steady states different compared to the original situation in part (a)