Lec 21 -26 learning objectives: Unicellular organisms: Passive diffusion only, no specialization for gas exchange and circulation Various multicellular animals and plant lineages: Independent origins of gas exchange organs and/or circulatory systems Physical constraint (Fick’s Law) operating on convergent gas exchange organs – selection manipulates FL parameters to favor gas exchange Physical constraint (Hagen -Poiseuille Equation) operating on convergent circulatory systems – selection manipulates HPE parameters to favor circulation Lec 21: Fick’s Law: Flux (J) For diffusion = amount / area / time 𝐹𝑙𝑢𝑥 (𝑎𝑚𝑜𝑢𝑛𝑡
𝑎𝑟𝑒𝑎 × 𝑡𝑖𝑚𝑒)=𝑑𝑖𝑓𝑓𝑢𝑠𝑖𝑜𝑛 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 ×𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 (𝑎𝑚𝑜𝑢𝑛𝑡
𝑣𝑜𝑙𝑢𝑚𝑒)
𝑑𝑖𝑓𝑓𝑢𝑠𝑖𝑜𝑛 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 (𝑙𝑒𝑛𝑔𝑡ℎ) In other words: |𝐽|=𝐷 ∆𝐶
∆𝑥 - In gas exchange, Gas Flux (J) = amount / area / time - 𝐹𝑙𝑢𝑥 (𝑎𝑚𝑜𝑢𝑛𝑡
𝑎𝑟𝑒𝑎 ×𝑡𝑖𝑚𝑒)=𝑑𝑖𝑓𝑓𝑐𝑜𝑒𝑓𝑓×𝑝𝑎𝑟𝑡𝑖𝑎𝑙 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 (𝑎𝑚𝑜𝑢𝑛𝑡
𝑣𝑜𝑙𝑢𝑚𝑒)
𝑑𝑖𝑓𝑓𝑢𝑠𝑖𝑜𝑛 𝑑𝑖𝑠tan𝑐𝑒 (𝑙𝑒𝑛𝑔𝑡ℎ) Considering all molecules diffusing into cell/organism: Flow rate (dS/dt) For diffusion = total amount / time 𝐹𝑙𝑜𝑤 𝑟𝑎𝑡𝑒 (𝑎𝑚𝑜𝑢𝑛𝑡
𝑡𝑖𝑚𝑒)
= 𝑑𝑖𝑓𝑓𝑢𝑠𝑖𝑜𝑛 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 ×𝑎𝑟𝑒𝑎×𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 (𝑎𝑚𝑜𝑢𝑛𝑡
𝑣𝑜𝑙𝑢𝑚𝑒)
𝑑𝑖𝑓𝑓𝑢𝑠𝑖𝑜𝑛 𝑑𝑖𝑠tan𝑐𝑒 (𝑙𝑒𝑛𝑔𝑡ℎ) In other words: 𝑑𝑆
𝑑𝑡= 𝐷𝐴 ∆𝐶
∆𝑥 - In gas exchange, gas flow rate (dV/dt) = total amount / time - 𝐹𝑙𝑜𝑤 𝑟𝑎𝑡𝑒 (𝑎𝑚𝑜𝑢𝑛𝑡
𝑡𝑖𝑚𝑒)=𝑑𝑖𝑓𝑓𝑐𝑜𝑒𝑓𝑓×𝑎𝑟𝑒𝑎×𝑝𝑎𝑟𝑡𝑖𝑎𝑙 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 (𝑎𝑚𝑜𝑢𝑛𝑡
𝑣𝑜𝑙𝑢𝑚𝑒)
𝑑𝑖𝑓𝑓𝑢𝑠𝑖𝑜𝑛 𝑑𝑖𝑠tan𝑐𝑒 (𝑙𝑒𝑛𝑔𝑡ℎ) - 𝑑𝑉
𝑑𝑡≈𝐷𝐴 ∆𝑃𝑔
∆𝑥 - 𝐴= Large area, high flow - ∆𝑃𝑝 = Large differences in partial pressure, high flow - ∆𝑥 = Thin boundary, high flow Useful properties: Natural selection: Favors adaptations to maximize flow Gas exchange organs constraints/functional compromises: - Large area, but thin, so often fragile - Vulnerable to mechanical damage and high pressure in circulatory fluids
𝑎𝑟𝑒𝑎 × 𝑡𝑖𝑚𝑒)=𝑑𝑖𝑓𝑓𝑢𝑠𝑖𝑜𝑛 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 ×𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 (𝑎𝑚𝑜𝑢𝑛𝑡
𝑣𝑜𝑙𝑢𝑚𝑒)
𝑑𝑖𝑓𝑓𝑢𝑠𝑖𝑜𝑛 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 (𝑙𝑒𝑛𝑔𝑡ℎ) In other words: |𝐽|=𝐷 ∆𝐶
∆𝑥 - In gas exchange, Gas Flux (J) = amount / area / time - 𝐹𝑙𝑢𝑥 (𝑎𝑚𝑜𝑢𝑛𝑡
𝑎𝑟𝑒𝑎 ×𝑡𝑖𝑚𝑒)=𝑑𝑖𝑓𝑓𝑐𝑜𝑒𝑓𝑓×𝑝𝑎𝑟𝑡𝑖𝑎𝑙 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 (𝑎𝑚𝑜𝑢𝑛𝑡
𝑣𝑜𝑙𝑢𝑚𝑒)
𝑑𝑖𝑓𝑓𝑢𝑠𝑖𝑜𝑛 𝑑𝑖𝑠tan𝑐𝑒 (𝑙𝑒𝑛𝑔𝑡ℎ) Considering all molecules diffusing into cell/organism: Flow rate (dS/dt) For diffusion = total amount / time 𝐹𝑙𝑜𝑤 𝑟𝑎𝑡𝑒 (𝑎𝑚𝑜𝑢𝑛𝑡
𝑡𝑖𝑚𝑒)
= 𝑑𝑖𝑓𝑓𝑢𝑠𝑖𝑜𝑛 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 ×𝑎𝑟𝑒𝑎×𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 (𝑎𝑚𝑜𝑢𝑛𝑡
𝑣𝑜𝑙𝑢𝑚𝑒)
𝑑𝑖𝑓𝑓𝑢𝑠𝑖𝑜𝑛 𝑑𝑖𝑠tan𝑐𝑒 (𝑙𝑒𝑛𝑔𝑡ℎ) In other words: 𝑑𝑆
𝑑𝑡= 𝐷𝐴 ∆𝐶
∆𝑥 - In gas exchange, gas flow rate (dV/dt) = total amount / time - 𝐹𝑙𝑜𝑤 𝑟𝑎𝑡𝑒 (𝑎𝑚𝑜𝑢𝑛𝑡
𝑡𝑖𝑚𝑒)=𝑑𝑖𝑓𝑓𝑐𝑜𝑒𝑓𝑓×𝑎𝑟𝑒𝑎×𝑝𝑎𝑟𝑡𝑖𝑎𝑙 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 (𝑎𝑚𝑜𝑢𝑛𝑡
𝑣𝑜𝑙𝑢𝑚𝑒)
𝑑𝑖𝑓𝑓𝑢𝑠𝑖𝑜𝑛 𝑑𝑖𝑠tan𝑐𝑒 (𝑙𝑒𝑛𝑔𝑡ℎ) - 𝑑𝑉
𝑑𝑡≈𝐷𝐴 ∆𝑃𝑔
∆𝑥 - 𝐴= Large area, high flow - ∆𝑃𝑝 = Large differences in partial pressure, high flow - ∆𝑥 = Thin boundary, high flow Useful properties: Natural selection: Favors adaptations to maximize flow Gas exchange organs constraints/functional compromises: - Large area, but thin, so often fragile - Vulnerable to mechanical damage and high pressure in circulatory fluids
