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A cell memberane is selectively permeable: some ions can flow through it, and others cannot. When ions diffuse across the membrane, the difference in concentration creates an electric potential difference and an electric field. The difference in concentration of potassium ions inside and outside of the cell is the main contribution to the "resting potential" of a neuron. The Nernst potential is the potential difference across a cell membrane due to the diffusion of ions through it: kgT In AV = Ze Co kg = 1.38 x 10-23 J/K is Boltzmann's constant, T is the temperature in degrees kelvin (K), e is the proton charge, Z is the ionic charge, e is the molar concentration inside the membrane, and c, is the molar concentration outside the membrane. For a singly ionized molecule – like sodium (Na*) or potassium (K+) ions – we have Z = 1. (a) Suppose that the extracellular fluid of a cell – the fluid outside the cell memberane – has a potassium ion con- centration of 0.0045 mol/L and the intracellular fluid – the fluid inside the cell membrane – has a potassium ion concentration of 0.138 mol/L. How much work is required to transport a sodium ion across the membrane, from the outside of the cell to the inside, if the temperature is 37°C? (Ignore the effects of any other ions.) Every neuron has trillions of molecular machines called sodium-potassium pumps embedded in their membranes that use ATP as fuel to do this work. (b) A typical cell membrane has a thickness of about 4 nm. Estimate the electric field (magnitude and direction) inside of the cell membrane. Include a picture that indicates the inside of the cell, the outside, the concentration of ions, and the direction of the electric field.

A cell memberane is selectively permeable: some ions can flow through it, and others cannot. When ions diffuse across the membrane, the difference in concentration creates an electric potential difference and an electric field. The difference in concentration of potassium ions inside and outside of the cell is the main contribution to the "resting potential" of a neuron. The Nernst potential is the potential difference across a cell membrane due to the diffusion of ions through it: kgT In AV = Ze Co kg = 1.38 x 10-23 J/K is Boltzmann's constant, T is the temperature in degrees kelvin (K), e is the proton charge, Z is the ionic charge, e is the molar concentration inside the membrane, and c, is the molar concentration outside the membrane. For a singly ionized molecule – like sodium (Na*) or potassium (K+) ions – we have Z = 1. (a) Suppose that the extracellular fluid of a cell – the fluid outside the cell memberane – has a potassium ion con- centration of 0.0045 mol/L and the intracellular fluid – the fluid inside the cell membrane – has a potassium ion concentration of 0.138 mol/L. How much work is required to transport a sodium ion across the membrane, from the outside of the cell to the inside, if the temperature is 37°C? (Ignore the effects of any other ions.) Every neuron has trillions of molecular machines called sodium-potassium pumps embedded in their membranes that use ATP as fuel to do this work. (b) A typical cell membrane has a thickness of about 4 nm. Estimate the electric field (magnitude and direction) inside of the cell membrane. Include a picture that indicates the inside of the cell, the outside, the concentration of ions, and the direction of the electric field.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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3 Nernst Potential A cell memberane is selectively permeable: some ions can flow through it, and others cannot. When ions diffuse acros the membrane, the difference in concentration creates an electric potential difference and an electric field. The difference in concentration of potassium ions inside and outside of the cell is the main contribution to the "resting potential" of a сross neuron. The Nernst potential is the potential difference across a cell membrane due to the diffusion of ions through it: kgT In AV = Ze Co kg = 1.38 x 10-23 J/K is Boltzmann's constant, T is the temperature in degrees kelvin (K), e is the proton charge, Z is the ionic charge, c, is the molar concentration inside the membrane, and c, is the molar concentration outside the membrane. For a singly ionized molecule – like sodium (Na*) or potassium (K+) ions – we have Z = 1. (a) Suppose that the extracellular fluid of a cell – the fluid outside the cell memberane – has a potassium ion con- centration of 0.0045 mol/L and the intracellular fluid – the fluid inside the cell membrane – has a potassium ion concentration of 0.138 mol/L. How much work is required to transport a sodium ion across the membrane, from the outside of the cell to the inside, if the temperature is 37C? (Ignore the effects of any other ions.) Every neuron has trillions of molecular machines called sodium-potassium pumps embedded in their membranes that use ATP as fuel to do this work. (b) A typical cell membrane has a thickness of about 4 nm. Estimate the electric field (magnitude and direction) inside of the cell membrane. Include a picture that indicates the inside of the cell, the outside, the concentration of ions, and the direction of the electric field.
Transcribed Image Text:3 Nernst Potential A cell memberane is selectively permeable: some ions can flow through it, and others cannot. When ions diffuse acros the membrane, the difference in concentration creates an electric potential difference and an electric field. The difference in concentration of potassium ions inside and outside of the cell is the main contribution to the "resting potential" of a сross neuron. The Nernst potential is the potential difference across a cell membrane due to the diffusion of ions through it: kgT In AV = Ze Co kg = 1.38 x 10-23 J/K is Boltzmann's constant, T is the temperature in degrees kelvin (K), e is the proton charge, Z is the ionic charge, c, is the molar concentration inside the membrane, and c, is the molar concentration outside the membrane. For a singly ionized molecule – like sodium (Na*) or potassium (K+) ions – we have Z = 1. (a) Suppose that the extracellular fluid of a cell – the fluid outside the cell memberane – has a potassium ion con- centration of 0.0045 mol/L and the intracellular fluid – the fluid inside the cell membrane – has a potassium ion concentration of 0.138 mol/L. How much work is required to transport a sodium ion across the membrane, from the outside of the cell to the inside, if the temperature is 37C? (Ignore the effects of any other ions.) Every neuron has trillions of molecular machines called sodium-potassium pumps embedded in their membranes that use ATP as fuel to do this work. (b) A typical cell membrane has a thickness of about 4 nm. Estimate the electric field (magnitude and direction) inside of the cell membrane. Include a picture that indicates the inside of the cell, the outside, the concentration of ions, and the direction of the electric field.
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