Cell Model
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As mentioned in lecture, circuits are used not just to model...circuits, but also many things in life. For example, almost all living cells maintain an internal voltage with respect to their surroundings and can therefore be modeled with Thévenin equivalent circuits:
Morpheus sort of talks about this in The Matrix, but the units he uses are underspecified and ambiguous and would therefore be marked down on an exam.
Because a cell is full of conductive salt water and because it sits in conductive salt water, a cellular circuit has two electrical nodes: an intracellular (inside the cell) node and an extracellular (outside the cell) node. These two nodes are separated by the insulating cell membrane. Cells generate their voltage by using two different proteins that sit across their membrane: Ion Pumps, which transport ions such as Potassium (K+), Sodium (Na+), Calcium (Ca+2), etc... either into or out of the cell (using energy in the form of ATP), and ion channels, which allow ions to flow through them passively.
An ion pump forces charged particles to move, generating a current, so it can be modeled as a current source. An ion channel passively lets charged molecules flow through it, and can be modeled as a resistor:
Healthy Cell
Below is a cell/cell membrane that has three different ion channels and three different ion pumps in it. Determine the Thévenin equivalent circuit of this cell. Make the negative terminal of your equivalent circuit be the extracellular salt solution.
Fill in VCell in millivolts and RCell in Megaohms.
Poisoned Cell :(
Cells use the voltage they develop across their membrane to do many things. Often the voltage range required for proper operation is only a few millivolts, however. Your neurons, for example, modulate this voltage to send signals, but if you push the cell voltage outside of its normal range the neurons can stop firing their signals...which can stop an organism's heart or modulate thoughts. Other cells use the membrane voltage to drive pumps that collect resources or expel waste. If the membrane voltage changes drastically the cell could starve or poison itself on its own waste.Of course nature will take advantage of such a vulnerability and many toxins and poisons work by messing up the Thévenin equivalent circuit of the cell in some way. Tetrodotoxin (TTX), produced by the fugu fish, blocks the Sodium (Na+) and Potassium (K+) pumps as shown below (causing their currents to become 0).
Fill in the new, TTX-poisoned VCell in millivolts and RCell in Megaohms. Hint: Does TTX affect the ion channels?
Punctured Cell :( :(
The cell above recovers from the fugu assault. But nature is harsh. Soon afterwards the cell is punctured by something that leaves a large hole in the membrane:
This hole adds a new additional resistance across the membrane of 10Ω. Fill in the new, approximate stabbed-cell VCell in millivolts and RCell in Megaohms. Your answer must be accurate to within 10% of the exact answer.