lecture 3 - Diffusion: Entropy in Action Text pages 108 -...

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Unformatted text preview: Diffusion: Entropy in Action Text pages 108 - 123 Diffusion Module in Math Bench Brownian motion - random movement of molecules due to heat energy Velocity is proportional to temperature Computer simulation of Brownian motion of a single molecule Adapted from math.mit. edu/~kang/bm/bm_ harmonic_measure.htm Diffusion - random molecular movement resulting in their net redistribution from higher concentration to lower concentration. Initial State Final State Diffusion rate is directly proportional to the concentration gradient Thus, the force in diffusion is the concentration gradient!!! Diffusion Negative G, so it is spontaneous Notice increase in S (entropy!) Organisms rely on diffusion to move, obtain, and remove essential molecules. Examples? Diffusion is a rate! Often referred to as FLUX Molecules moving from one point to another per unit time e.g., mmoles/sec Abbreviated as J or dS/dT Fick's First Law of Diffusion force ("F) flux (J) = k length ("x) ! "F J = -k "x "C J = -D "x e.g., a membrane J = flux ("diffusion rate") D = diffusion coefficient C = concentration gradient x = distance (Negative sign means down the gradient, but biologists often drop the sign.) Diffusion across a membrane of area A and thickness x J or dS/dT = - DA C/x D = Diffusion coefficient A = area for diffusion C = concentration gradient of solute S Fick's Law of Diffusion: in Solution dS/dt = D T C/x Rate of Diffusion = dS/dt D = diffusion constant T = oK C = concentration gradient x = distance Fick's Law of Diffusion: Gases dS/dt = D T P/x Rate of Diffusion = dS/dt D = diffusion constant T = oK P = difference in pressure x = thickness of membrane D: Diffusion Coefficient Determined by physical characteristics of solution and solute Inversely proportional to solute's molecular weight Units are cm2/sec D: typical values Na+ = 1.33 x 10-5 cm2 /sec K+ = 1.96 x 10-5 cm2 /sec H+ = 9.31 x 10-5 cm2 /sec Hemoglobin (68 D) = 6.9 x 10-7 cm2 /sec Source: www.csupomona.edu/~seskandari/physiology Does diffusion work for large molecules? #C J = "D #x Molecule H2 O2 Sucrose Cytochrome C Hemoglobin Myosin Tobacco mosaic virus Molecular weight Diffusion coefficient (D) (Da) in water (cm2/sec) 2 4.5 x 10-5 1.6 x 10-5 5.2 x 10-6 3.2 x 10-6 6.9 x 10-7 1.1 x 10-7 4.4 x 10-8 32 342 12,700 68,000 570,000 40,000,000 ! Fick's Law of Diffusion across a membrane dS/dt = D T A C/x Rate of Diffusion = dS/dt D = diffusion constant T = oK A = area for diffusion C = difference in concentration x = thickness of membrane S S S S S 0 S S S S S S S Problem: Diffusion Distances X2 t = ---------2D t = elapsed time since diffusion began X is mean distance traveled by solute in time t D = diffusion coefficient of solute in free solution Problem: Diffusion Distances If a solute molecule diffuses 0.001 mm in 1 sec, how long would it take to diffuse 0.1 mm? Movement of small diffusible molecules For example, glucose molecular weight: 180 Da diffusion coefficient: 7.0 x 10-6 cm2/sec x t= 2D Typical Structure Cell membrane 2 Distance (x) 10 nm 1 m 10 m 300 m 1 mm 2 cm 10 cm Time (t) 100 ns 1 ms 100 ms 1.5 min 16.6 min 4.6 days 82.7 days ! Bacteria Eukaryotic cell Sea urchin embryo Volvox Human heart wall Squid giant axon Surface Area to Volume Ratios SA = 4r2 V = 4r3/3 Surface Area to Volume Ratios SA = 6 L2 V = L3 http://www.mhhe.com/biosci/esp/2001_gbio/folder_structure/ce/m2/s1/ Problem: Surface / Volume As cell radius increases, the surface increases by radius2 However the volume increases by radius3 Thus the surface area available to support the increased volume is not adequate http://www.tiem.utk.edu/~mbeals/area_volume.html http://www.tiem.utk.edu/~mbeals/area_volume.html Problem: Surface / Volume QUESTION: In Nature, what types of cells are the smallest and have the most surface area/volume? What are their characteristics that require them to be small? Review of membrane concepts Fluid Mosaic Model Liquid membrane Phospholipid compostion & Fluidity Fluidity & biological activity Membrane proteins - structure & functions (Pages 107 - 118 will help you review these concepts!) Diffusion across cell membranes 1) Differential permeability 2) Osmosis 3) Diffusion and electrical signaling Oil/Water Partition Coefficient Add Solute X Oil Shake well and determine how solute partitions between oil and water layers Water Oil/Water Partition Coefficient Oil O/W PC = [S]oil [S]water Water Simple Diffusion H2O Rate of Diffusion nmoles/ min/ 106 cells Log solubility in lipid Oil/Water Partition Coefficient Differential permeability - the relative abilities of different molecules to diffuse across membranes Fig. 6.9 Concepts: Diffusion of solutes and gases occurs in all organisms Diffusion distances and surface to volume ratios: place restrictions on cell size require many cells to assume shapes maximizing surface to volume ratios Concepts: The need to transport different polar or large solutes across membranes requires the evolution of different transport mechanisms. (We'll cover this later in Nutrient Assimilation) Concepts: Require unicellular and multicellular organisms to develop structures to deal with these issues Circulation of fluid (cytoplasm, blood, water, etc.) Respiratory structures Nutrient absorption ...
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