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AP Biology Chapter 7

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  • Figure 7.1 How do cell membrane proteins help regulate chemical traffic?
  • For the Cell Biology Video Structure of the Cell Membrane, go to Animation and Video Files.
  • Figure 7.2 Phospholipid bilayer (cross section)
  • Figure 7.3 The fluid mosaic model for membranes
  • Figure 7.4 Freeze-fracture
  • Figure 7.5 The fluidity of membranes
  • Figure 7.5a The fluidity of membranes
  • Figure 7.6 Do membrane proteins move?
  • Figure 7.5b The fluidity of membranes
  • Figure 7.5c The fluidity of membranes
  • Figure 7.7 The detailed structure of an animal cell’s plasma membrane, in a cutaway view
  • Figure 7.8 The structure of a transmembrane protein
  • Figure 7.9 Some functions of membrane proteins
  • Figure 7.9a–c Some functions of membrane proteins
  • Figure 7.9d–f Some functions of membrane proteins
  • Figure 7.10 Synthesis of membrane components and their orientation on the resulting membrane
  • Figure 7.11 The diffusion of solutes across a membrane
  • Figure 7.11a The diffusion of solutes across a membrane
  • Figure 7.11b The diffusion of solutes across a membrane
  • Figure 7.12 Osmosis
  • Figure 7.13 The water balance of living cells
  • Figure 7.14 The contractile vacuole of Paramecium : an evolutionary adaptation for osmoregulation
  • For the Cell Biology Video Water Movement through an Aquaporin, go to Animation and Video Files.
  • Figure 7.15 Two types of transport proteins that carry out facilitated diffusion
  • For the Cell Biology Video Na + /K + ATPase Cycle, go to Animation and Video Files.
  • Figure 7.16, 1 The sodium-potassium pump: a specific case of active transport
  • Figure 7.16, 2 The sodium-potassium pump: a specific case of active transport
  • Figure 7.16, 3 The sodium-potassium pump: a specific case of active transport
  • Figure 7.16, 4 The sodium-potassium pump: a specific case of active transport
  • Figure 7.16, 5 The sodium-potassium pump: a specific case of active transport
  • Figure 7.16, 6 The sodium-potassium pump: a specific case of active transport
  • Figure 7.16, 1–6 The sodium-potassium pump: a specific case of active transport
  • Figure 7.17 Review: passive and active transport
  • Figure 7.18 An electrogenic pump
  • Figure 7.19 Cotransport: active transport driven by a concentration gradient
  • For the Cell Biology Video Phagocytosis in Action, go to Animation and Video Files.
  • Figure 7.20 Endocytosis in animal cells
  • Figure 7.20 Endocytosis in animal cells—phagocytosis
  • Figure 7.20 Endocytosis in animal cells—pinocytosis
  • Figure 7.20 Endocytosis in animal cells—receptor-mediated endocytosis
  • Transcript

    • 1. Chapter 7 Membrane Structure and Function
    • 2. Overview: Life at the Edge
      • The plasma membrane is the boundary that separates the living cell from its surroundings
      • The plasma membrane exhibits selective permeability , allowing some substances to cross it more easily than others
      Copyright © 2008 Pearson Education, Inc., publishing as Pearson Benjamin Cummings
    • 3. Fig. 7-1
    • 4. Concept 7.1: Cellular membranes are fluid mosaics of lipids and proteins
      • Phospholipids are the most abundant lipid in the plasma membrane
      • Phospholipids are amphipathic molecules , containing hydrophobic and hydrophilic regions
      • The fluid mosaic model states that a membrane is a fluid structure with a “mosaic” of various proteins embedded in it
      Copyright © 2008 Pearson Education, Inc., publishing as Pearson Benjamin Cummings
    • 5. Membrane Models: Scientific Inquiry
      • Membranes have been chemically analyzed and found to be made of proteins and lipids
      • Scientists studying the plasma membrane reasoned that it must be a phospholipid bilayer
      Copyright © 2008 Pearson Education, Inc., publishing as Pearson Benjamin Cummings
    • 6. Fig. 7-2 Hydrophilic head WATER Hydrophobic tail WATER
    • 7.
      • In 1935, Hugh Davson and James Danielli proposed a sandwich model in which the phospholipid bilayer lies between two layers of globular proteins
      • Later studies found problems with this model, particularly the placement of membrane proteins, which have hydrophilic and hydrophobic regions
      • In 1972, J. Singer and G. Nicolson proposed that the membrane is a mosaic of proteins dispersed within the bilayer, with only the hydrophilic regions exposed to water
      Copyright © 2008 Pearson Education, Inc., publishing as Pearson Benjamin Cummings
    • 8. Fig. 7-3 Phospholipid bilayer Hydrophobic regions of protein Hydrophilic regions of protein
    • 9.
      • Freeze-fracture studies of the plasma membrane supported the fluid mosaic model
      • Freeze-fracture is a specialized preparation technique that splits a membrane along the middle of the phospholipid bilayer
      Copyright © 2008 Pearson Education, Inc., publishing as Pearson Benjamin Cummings
    • 10. Fig. 7-4 TECHNIQUE Extracellular layer Knife Proteins Inside of extracellular layer RESULTS Inside of cytoplasmic layer Cytoplasmic layer Plasma membrane
    • 11. The Fluidity of Membranes
      • Phospholipids in the plasma membrane can move within the bilayer
      • Most of the lipids, and some proteins, drift laterally
      • Rarely does a molecule flip-flop transversely across the membrane
      Copyright © 2008 Pearson Education, Inc., publishing as Pearson Benjamin Cummings
    • 12. Fig. 7-5 Lateral movement (~10 7 times per second) Flip-flop (~ once per month) (a) Movement of phospholipids (b) Membrane fluidity Fluid Viscous Unsaturated hydrocarbon tails with kinks Saturated hydro- carbon tails (c) Cholesterol within the animal cell membrane Cholesterol
    • 13. Fig. 7-5a (a) Movement of phospholipids Lateral movement (  10 7 times per second) Flip-flop (  once per month)
    • 14. Fig. 7-6 RESULTS Membrane proteins Mouse cell Human cell Hybrid cell Mixed proteins after 1 hour
    • 15.
      • As temperatures cool, membranes switch from a fluid state to a solid state
      • The temperature at which a membrane solidifies depends on the types of lipids
      • Membranes rich in unsaturated fatty acids are more fluid that those rich in saturated fatty acids
      • Membranes must be fluid to work properly; they are usually about as fluid as salad oil
      Copyright © 2008 Pearson Education, Inc., publishing as Pearson Benjamin Cummings
    • 16. Fig. 7-5b (b) Membrane fluidity Fluid Unsaturated hydrocarbon tails with kinks Viscous Saturated hydro- carbon tails
    • 17.
      • The steroid cholesterol has different effects on membrane fluidity at different temperatures
      • At warm temperatures (such as 37°C), cholesterol restrains movement of phospholipids
      • At cool temperatures, it maintains fluidity by preventing tight packing
      Copyright © 2008 Pearson Education, Inc., publishing as Pearson Benjamin Cummings
    • 18. Fig. 7-5c Cholesterol (c) Cholesterol within the animal cell membrane
    • 19. Membrane Proteins and Their Functions
      • A membrane is a collage of different proteins embedded in the fluid matrix of the lipid bilayer
      • Proteins determine most of the membrane’s specific functions
      Copyright © 2008 Pearson Education, Inc., publishing as Pearson Benjamin Cummings
    • 20. Fig. 7-7 Fibers of extracellular matrix (ECM) Glyco- protein Microfilaments of cytoskeleton Cholesterol Peripheral proteins Integral protein CYTOPLASMIC SIDE OF MEMBRANE Glycolipid EXTRACELLULAR SIDE OF MEMBRANE Carbohydrate
    • 21.
      • Peripheral proteins are bound to the surface of the membrane
      • Integral proteins penetrate the hydrophobic core
      • Integral proteins that span the membrane are called transmembrane proteins
      • The hydrophobic regions of an integral protein consist of one or more stretches of nonpolar amino acids, often coiled into alpha helices
      Copyright © 2008 Pearson Education, Inc., publishing as Pearson Benjamin Cummings
    • 22. Fig. 7-8 N-terminus C-terminus  Helix CYTOPLASMIC SIDE EXTRACELLULAR SIDE
    • 23.
      • Six major functions of membrane proteins:
        • Transport
        • Enzymatic activity
        • Signal transduction
        • Cell-cell recognition
        • Intercellular joining
        • Attachment to the cytoskeleton and extracellular matrix (ECM)
      Copyright © 2008 Pearson Education, Inc., publishing as Pearson Benjamin Cummings
    • 24. Fig. 7-9 (a) Transport ATP (b) Enzymatic activity Enzymes (c) Signal transduction Signal transduction Signaling molecule Receptor (d) Cell-cell recognition Glyco- protein (e) Intercellular joining (f) Attachment to the cytoskeleton and extracellular matrix (ECM)
    • 25. Fig. 7-9ac (a) Transport (b) Enzymatic activity (c) Signal transduction ATP Enzymes Signal transduction Signaling molecule Receptor
    • 26. Fig. 7-9df (d) Cell-cell recognition Glyco- protein (e) Intercellular joining (f) Attachment to the cytoskeleton and extracellular matrix (ECM)
    • 27. The Role of Membrane Carbohydrates in Cell-Cell Recognition
      • Cells recognize each other by binding to surface molecules, often carbohydrates, on the plasma membrane
      • Membrane carbohydrates may be covalently bonded to lipids (forming glycolipids ) or more commonly to proteins (forming glycoproteins )
      • Carbohydrates on the external side of the plasma membrane vary among species, individuals, and even cell types in an individual
      Copyright © 2008 Pearson Education, Inc., publishing as Pearson Benjamin Cummings
    • 28. Synthesis and Sidedness of Membranes
      • Membranes have distinct inside and outside faces
      • The asymmetrical distribution of proteins, lipids, and associated carbohydrates in the plasma membrane is determined when the membrane is built by the ER and Golgi apparatus
      Copyright © 2008 Pearson Education, Inc., publishing as Pearson Benjamin Cummings
    • 29. Fig. 7-10 ER 1 Transmembrane glycoproteins Secretory protein Glycolipid 2 Golgi apparatus Vesicle 3 4 Secreted protein Transmembrane glycoprotein Plasma membrane: Cytoplasmic face Extracellular face Membrane glycolipid
    • 30. Concept 7.2: Membrane structure results in selective permeability
      • A cell must exchange materials with its surroundings, a process controlled by the plasma membrane
      • Plasma membranes are selectively permeable, regulating the cell’s molecular traffic
      Copyright © 2008 Pearson Education, Inc., publishing as Pearson Benjamin Cummings
    • 31. The Permeability of the Lipid Bilayer
      • Hydrophobic (nonpolar) molecules, such as hydrocarbons, can dissolve in the lipid bilayer and pass through the membrane rapidly
      • Polar molecules, such as sugars, do not cross the membrane easily
      Copyright © 2008 Pearson Education, Inc., publishing as Pearson Benjamin Cummings
    • 32. Transport Proteins
      • Transport proteins allow passage of hydrophilic substances across the membrane
      • Some transport proteins, called channel proteins, have a hydrophilic channel that certain molecules or ions can use as a tunnel
      • Channel proteins called aquaporins facilitate the passage of water
      Copyright © 2008 Pearson Education, Inc., publishing as Pearson Benjamin Cummings
    • 33.
      • Other transport proteins, called carrier proteins , bind to molecules and change shape to shuttle them across the membrane
      • A transport protein is specific for the substance it moves
      Copyright © 2008 Pearson Education, Inc., publishing as Pearson Benjamin Cummings
    • 34. Concept 7.3: Passive transport is diffusion of a substance across a membrane with no energy investment
      • Diffusion is the tendency for molecules to spread out evenly into the available space
      • Although each molecule moves randomly, diffusion of a population of molecules may exhibit a net movement in one direction
      • At dynamic equilibrium, as many molecules cross one way as cross in the other direction
      Animation: Membrane Selectivity Animation: Diffusion Copyright © 2008 Pearson Education, Inc., publishing as Pearson Benjamin Cummings
    • 35. Fig. 7-11 Molecules of dye Membrane (cross section) WATER Net diffusion Net diffusion Equilibrium (a) Diffusion of one solute Net diffusion Net diffusion Net diffusion Net diffusion Equilibrium Equilibrium (b) Diffusion of two solutes
    • 36. Molecules of dye Fig. 7-11a Membrane (cross section) WATER Net diffusion Net diffusion (a) Diffusion of one solute Equilibrium
    • 37.
      • Substances diffuse down their concentration gradient , the difference in concentration of a substance from one area to another
      • No work must be done to move substances down the concentration gradient
      • The diffusion of a substance across a biological membrane is passive transport because it requires no energy from the cell to make it happen
      Copyright © 2008 Pearson Education, Inc., publishing as Pearson Benjamin Cummings
    • 38. (b) Diffusion of two solutes Fig. 7-11b Net diffusion Net diffusion Net diffusion Net diffusion Equilibrium Equilibrium
    • 39. Effects of Osmosis on Water Balance
      • Osmosis is the diffusion of water across a selectively permeable membrane
      • Water diffuses across a membrane from the region of lower solute concentration to the region of higher solute concentration
      Copyright © 2008 Pearson Education, Inc., publishing as Pearson Benjamin Cummings
    • 40. Lower concentration of solute (sugar) Fig. 7-12 H 2 O Higher concentration of sugar Selectively permeable membrane Same concentration of sugar Osmosis
    • 41. Water Balance of Cells Without Walls
      • Tonicity is the ability of a solution to cause a cell to gain or lose water
      • Isotonic solution: Solute concentration is the same as that inside the cell; no net water movement across the plasma membrane
      • Hypertonic solution: Solute concentration is greater than that inside the cell; cell loses water
      • Hypotonic solution: Solute concentration is less than that inside the cell; cell gains water
      Copyright © 2008 Pearson Education, Inc., publishing as Pearson Benjamin Cummings
    • 42. Fig. 7-13 Hypotonic solution (a ) Animal cell (b ) Plant cell H 2 O Lysed H 2 O Turgid (normal) H 2 O H 2 O H 2 O H 2 O Normal Isotonic solution Flaccid H 2 O H 2 O Shriveled Plasmolyzed Hypertonic solution
    • 43.
      • Hypertonic or hypotonic environments create osmotic problems for organisms
      • Osmoregulation , the control of water balance, is a necessary adaptation for life in such environments
      • The protist Paramecium, which is hypertonic to its pond water environment, has a contractile vacuole that acts as a pump
      Video: Chlamydomonas Video: Paramecium Vacuole Copyright © 2008 Pearson Education, Inc., publishing as Pearson Benjamin Cummings
    • 44. Fig. 7-14 Filling vacuole 50 µm (a) A contractile vacuole fills with fluid that enters from a system of canals radiating throughout the cytoplasm. Contracting vacuole (b) When full, the vacuole and canals contract, expelling fluid from the cell.
    • 45. Water Balance of Cells with Walls
      • Cell walls help maintain water balance
      • A plant cell in a hypotonic solution swells until the wall opposes uptake; the cell is now turgid (firm)
      • If a plant cell and its surroundings are isotonic, there is no net movement of water into the cell; the cell becomes flaccid (limp), and the plant may wilt
      Copyright © 2008 Pearson Education, Inc., publishing as Pearson Benjamin Cummings
    • 46.
      • In a hypertonic environment, plant cells lose water; eventually, the membrane pulls away from the wall, a usually lethal effect called plasmolysis
      Video: Plasmolysis Video: Turgid Elodea Animation: Osmosis Copyright © 2008 Pearson Education, Inc., publishing as Pearson Benjamin Cummings
    • 47. Facilitated Diffusion: Passive Transport Aided by Proteins
      • In facilitated diffusion , transport proteins speed the passive movement of molecules across the plasma membrane
      • Channel proteins provide corridors that allow a specific molecule or ion to cross the membrane
      • Channel proteins include
        • Aquaporins, for facilitated diffusion of water
        • Ion channels that open or close in response to a stimulus ( gated channels )
      Copyright © 2008 Pearson Education, Inc., publishing as Pearson Benjamin Cummings
    • 48. Fig. 7-15 EXTRACELLULAR FLUID Channel protein (a) A channel protein Solute CYTOPLASM Solute Carrier protein (b) A carrier protein
    • 49.
      • Carrier proteins undergo a subtle change in shape that translocates the solute-binding site across the membrane
      Copyright © 2008 Pearson Education, Inc., publishing as Pearson Benjamin Cummings
    • 50.
      • Some diseases are caused by malfunctions in specific transport systems, for example the kidney disease cystinuria
      Copyright © 2008 Pearson Education, Inc., publishing as Pearson Benjamin Cummings
    • 51. Concept 7.4: Active transport uses energy to move solutes against their gradients
      • Facilitated diffusion is still passive because the solute moves down its concentration gradient
      • Some transport proteins, however, can move solutes against their concentration gradients
      Copyright © 2008 Pearson Education, Inc., publishing as Pearson Benjamin Cummings
    • 52. The Need for Energy in Active Transport
      • Active transport moves substances against their concentration gradient
      • Active transport requires energy, usually in the form of ATP
      • Active transport is performed by specific proteins embedded in the membranes
      Animation: Active Transport Copyright © 2008 Pearson Education, Inc., publishing as Pearson Benjamin Cummings
    • 53.
      • Active transport allows cells to maintain concentration gradients that differ from their surroundings
      • The sodium-potassium pump is one type of active transport system
      Copyright © 2008 Pearson Education, Inc., publishing as Pearson Benjamin Cummings
    • 54. Fig. 7-16-1 EXTRACELLULAR FLUID [Na + ] high [K + ] low Na + Na + Na + [Na + ] low [K + ] high CYTOPLASM Cytoplasmic Na + binds to the sodium-potassium pump . 1
    • 55. Na + binding stimulates phosphorylation by ATP. Fig. 7-16-2 Na + Na + Na + ATP P ADP 2
    • 56. Fig. 7-16-3 Phosphorylation causes the protein to change its shape. Na + is expelled to the outside. Na + P Na + Na + 3
    • 57. Fig. 7-16-4 K + binds on the extracellular side and triggers release of the phosphate group. P P K + K + 4
    • 58. Fig. 7-16-5 Loss of the phosphate restores the protein’s original shape. K + K + 5
    • 59. Fig. 7-16-6 K + is released, and the cycle repeats. K + K + 6
    • 60. 2 EXTRACELLULAR FLUID [Na + ] high [K + ] low [Na + ] low [K + ] high Na + Na + Na + Na + Na + Na + CYTOPLASM ATP ADP P Na + Na + Na + P 3 K + K + 6 K + K + 5 4 K + K + P P 1 Fig. 7-16-7
    • 61. Fig. 7-17 Passive transport Diffusion Facilitated diffusion Active transport ATP
    • 62. How Ion Pumps Maintain Membrane Potential
      • Membrane potential is the voltage difference across a membrane
      • Voltage is created by differences in the distribution of positive and negative ions
      Copyright © 2008 Pearson Education, Inc., publishing as Pearson Benjamin Cummings
    • 63.
      • Two combined forces, collectively called the electrochemical gradient , drive the diffusion of ions across a membrane:
        • A chemical force (the ion’s concentration gradient)
        • An electrical force (the effect of the membrane potential on the ion’s movement)
      Copyright © 2008 Pearson Education, Inc., publishing as Pearson Benjamin Cummings
    • 64.
      • An electrogenic pump is a transport protein that generates voltage across a membrane
      • The sodium-potassium pump is the major electrogenic pump of animal cells
      • The main electrogenic pump of plants, fungi, and bacteria is a proton pump
      Copyright © 2008 Pearson Education, Inc., publishing as Pearson Benjamin Cummings
    • 65. Fig. 7-18 EXTRACELLULAR FLUID H + H + H + H + Proton pump + + + H + H + + + H + – – – – ATP CYTOPLASM –
    • 66. Cotransport: Coupled Transport by a Membrane Protein
      • Cotransport occurs when active transport of a solute indirectly drives transport of another solute
      • Plants commonly use the gradient of hydrogen ions generated by proton pumps to drive active transport of nutrients into the cell
      Copyright © 2008 Pearson Education, Inc., publishing as Pearson Benjamin Cummings
    • 67. Fig. 7-19 Proton pump – – – – – – + + + + + + ATP H + H + H + H + H + H + H + H + Diffusion of H + Sucrose-H + cotransporter Sucrose Sucrose
    • 68. Concept 7.5: Bulk transport across the plasma membrane occurs by exocytosis and endocytosis
      • Small molecules and water enter or leave the cell through the lipid bilayer or by transport proteins
      • Large molecules, such as polysaccharides and proteins, cross the membrane in bulk via vesicles
      • Bulk transport requires energy
      Copyright © 2008 Pearson Education, Inc., publishing as Pearson Benjamin Cummings
    • 69. Exocytosis
      • In exocytosis , transport vesicles migrate to the membrane, fuse with it, and release their contents
      • Many secretory cells use exocytosis to export their products
      Animation: Exocytosis Copyright © 2008 Pearson Education, Inc., publishing as Pearson Benjamin Cummings
    • 70. Endocytosis
      • In endocytosis , the cell takes in macromolecules by forming vesicles from the plasma membrane
      • Endocytosis is a reversal of exocytosis, involving different proteins
      • There are three types of endocytosis:
        • Phagocytosis (“cellular eating”)
        • Pinocytosis (“cellular drinking”)
        • Receptor-mediated endocytosis
      Animation: Exocytosis and Endocytosis Introduction Copyright © 2008 Pearson Education, Inc., publishing as Pearson Benjamin Cummings
    • 71.
      • In phagocytosis a cell engulfs a particle in a vacuole
      • The vacuole fuses with a lysosome to digest the particle
      Animation: Phagocytosis Copyright © 2008 Pearson Education, Inc., publishing as Pearson Benjamin Cummings
    • 72. Fig. 7-20 PHAGOCYTOSIS EXTRACELLULAR FLUID CYTOPLASM Pseudopodium “ Food”or other particle Food vacuole PINOCYTOSIS 1 µm Pseudopodium of amoeba Bacterium Food vacuole An amoeba engulfing a bacterium via phagocytosis (TEM) Plasma membrane Vesicle 0.5 µm Pinocytosis vesicles forming (arrows) in a cell lining a small blood vessel (TEM) RECEPTOR-MEDIATED ENDOCYTOSIS Receptor Coat protein Coated vesicle Coated pit Ligand Coat protein Plasma membrane A coated pit and a coated vesicle formed during receptor- mediated endocytosis (TEMs) 0.25 µm
    • 73. Fig. 7-20a PHAGOCYTOSIS CYTOPLASM EXTRACELLULAR FLUID Pseudopodium “ Food” or other particle Food vacuole Food vacuole Bacterium An amoeba engulfing a bacterium via phagocytosis (TEM) Pseudopodium of amoeba 1 µm
    • 74.
      • In pinocytosis , molecules are taken up when extracellular fluid is “gulped” into tiny vesicles
      Animation: Pinocytosis Copyright © 2008 Pearson Education, Inc., publishing as Pearson Benjamin Cummings
    • 75. Fig. 7-20b PINOCYTOSIS Plasma membrane Vesicle 0.5 µm Pinocytosis vesicles forming (arrows) in a cell lining a small blood vessel (TEM)
    • 76.
      • In receptor-mediated endocytosis , binding of ligands to receptors triggers vesicle formation
      • A ligand is any molecule that binds specifically to a receptor site of another molecule
      Animation: Receptor-Mediated Endocytosis Copyright © 2008 Pearson Education, Inc., publishing as Pearson Benjamin Cummings
    • 77. Fig. 7-20c RECEPTOR-MEDIATED ENDOCYTOSIS Receptor Coat protein Coated pit Ligand Coat protein Plasma membrane 0.25 µm Coated vesicle A coated pit and a coated vesicle formed during receptor- mediated endocytosis (TEMs)
    • 78. Fig. 7-UN1 Passive transport: Facilitated diffusion Channel protein Carrier protein
    • 79. Fig. 7-UN2 Active transport: ATP
    • 80. Fig. 7-UN3 Environment: 0.01 M sucrose 0.01 M glucose 0.01 M fructose “ Cell” 0.03 M sucrose 0.02 M glucose
    • 81. Fig. 7-UN4
    • 82. You should now be able to:
      • Define the following terms: amphipathic molecules, aquaporins, diffusion
      • Explain how membrane fluidity is influenced by temperature and membrane composition
      • Distinguish between the following pairs or sets of terms: peripheral and integral membrane proteins; channel and carrier proteins; osmosis, facilitated diffusion, and active transport; hypertonic, hypotonic, and isotonic solutions
      Copyright © 2008 Pearson Education, Inc., publishing as Pearson Benjamin Cummings
    • 83.
      • Explain how transport proteins facilitate diffusion
      • Explain how an electrogenic pump creates voltage across a membrane, and name two electrogenic pumps
      • Explain how large molecules are transported across a cell membrane
      Copyright © 2008 Pearson Education, Inc., publishing as Pearson Benjamin Cummings