2. Ion channels that permit ions to pass between the interior of the cell and the extra-cellular medium are an important part of a living cell. There are multiple mechanisms that happen in an ion channel, but the simplest is that ions flow through the cell preferentially in one direction as a result of diffusion arising from a difference of ion concentrations on the inside and outside of the cell. Cout Cin As a first model of an ion channel, let's see how it would behave if the flux through the open channel were simply due to diffusion arising from a concentration difference. We'll model the open channel as a cylinder as shown in the figure at the left. Δε Δε where D is the diffusion Fick's law for flow due to a concentration gradient is J =-D constant and J has dimensions corresponding to number per unit area per unit time. 2.1 A typical ion channel radius is about 1 nm (nanometer), and the thickness of the cell membrane is about 7 nm. The concentration of Na+ ions inside a mammalian heart cell is about 0.6 ions/nm³, and in the fluid surrounding the cell is about 6.0 ions/nm³. The diffusion constant for ions is about 10° nm²/s (nanometers/second). If the channel were just an open cylinder, how many ions per second would flow through the channel and in which direction? 2.2 What is responsible for the flow of the ions through the channel in this model? A. The ions are attracted to the channel and since there are more on one side than the other there is a net flow from the more dense concentration side to the less. B. The ions move randomly as a result of collisions with the fluid molecules and since there are more on one side than the other there is a net flow from the more dense concentration side to the less. C. There are more ions in the high concentration region. Their collisions with each other drive the ions in all direction and since there are more on one side than the other there is a net flow from the more dense concentration side to the less. D. The ions sense when the channel is open and explicitly move towards it. 2.3 Can this "diffusion constant, D" be the same constant as in the other Fick's law equation, = 2D At? Show whether they have the same dimensionality or not. (x²) =
2. Ion channels that permit ions to pass between the interior of the cell and the extra-cellular medium are an important part of a living cell. There are multiple mechanisms that happen in an ion channel, but the simplest is that ions flow through the cell preferentially in one direction as a result of diffusion arising from a difference of ion concentrations on the inside and outside of the cell. Cout Cin As a first model of an ion channel, let's see how it would behave if the flux through the open channel were simply due to diffusion arising from a concentration difference. We'll model the open channel as a cylinder as shown in the figure at the left. Δε Δε where D is the diffusion Fick's law for flow due to a concentration gradient is J =-D constant and J has dimensions corresponding to number per unit area per unit time. 2.1 A typical ion channel radius is about 1 nm (nanometer), and the thickness of the cell membrane is about 7 nm. The concentration of Na+ ions inside a mammalian heart cell is about 0.6 ions/nm³, and in the fluid surrounding the cell is about 6.0 ions/nm³. The diffusion constant for ions is about 10° nm²/s (nanometers/second). If the channel were just an open cylinder, how many ions per second would flow through the channel and in which direction? 2.2 What is responsible for the flow of the ions through the channel in this model? A. The ions are attracted to the channel and since there are more on one side than the other there is a net flow from the more dense concentration side to the less. B. The ions move randomly as a result of collisions with the fluid molecules and since there are more on one side than the other there is a net flow from the more dense concentration side to the less. C. There are more ions in the high concentration region. Their collisions with each other drive the ions in all direction and since there are more on one side than the other there is a net flow from the more dense concentration side to the less. D. The ions sense when the channel is open and explicitly move towards it. 2.3 Can this "diffusion constant, D" be the same constant as in the other Fick's law equation, = 2D At? Show whether they have the same dimensionality or not. (x²) =
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Transcribed Image Text:2. Ion channels that permit ions to pass between the interior of the cell and the extra-cellular medium are
an important part of a living cell. There are multiple mechanisms that happen in an ion channel, but the
simplest is that ions flow through the cell preferentially in one direction as a result of diffusion arising
from a difference of ion concentrations on the inside and outside of the cell.
Cout
Cin
As a first model of an ion channel, let's see how it would behave if the flux through the open
channel were simply due to diffusion arising from a concentration difference. We'll model
the open channel as a cylinder as shown in the figure at the left.
Δε
Δε
where D is the diffusion
Fick's law for flow due to a concentration gradient is J =-D
constant and J has dimensions corresponding to number per unit area per unit time.
2.1 A typical ion channel radius is about 1 nm (nanometer), and the thickness of the cell membrane is
about 7 nm. The concentration of Na+ ions inside a mammalian heart cell is about 0.6 ions/nm³, and in the
fluid surrounding the cell is about 6.0 ions/nm³. The diffusion constant for ions is about 10° nm²/s
(nanometers/second). If the channel were just an open cylinder, how many ions per second would flow
through the channel and in which direction?
2.2 What is responsible for the flow of the ions through the channel in this model?
A. The ions are attracted to the channel and since there are more on one side than the other there is a
net flow from the more dense concentration side to the less.
B. The ions move randomly as a result of collisions with the fluid molecules and since there are
more on one side than the other there is a net flow from the more dense concentration side to the
less.
C. There are more ions in the high concentration region. Their collisions with each other drive the
ions in all direction and since there are more on one side than the other there is a net flow from
the more dense concentration side to the less.
D. The ions sense when the channel is open and explicitly move towards it.
2.3 Can this "diffusion constant, D" be the same constant as in the other Fick's law equation,
= 2D At? Show whether they have the same dimensionality or not.
(x²) =
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