L01 Evolution 2011 - COPYRIGHT Mammalian Physiology BIOAP...

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1/13 COPYRIGHT Prof. Beyenbach Mammalian Physiology BIOAP 4580 , 2011 THE EVOLUTION OF MULTICELLULAR SYSTEMS (from single cell to invertebrate) 1) Fundamental mathematical equations in physiology a) Automotive and heteromotive transport. Automotive transport derives from molecular motion in fields of thermal energy. Diffusion and osmosis are examples of automotive transport. Heteromotive transport (convection) is the transport of the whole medium, convective transport, such as the volume flow of rivers and blood. Convective movement of air is known as ventilation. Volume flow ( ) is driven by a pressure difference and dependent on a proportionality constant. The proportionality constant for a flowing medium is the conductance (g), i.e. the hydraulic (h) conductance (eq. 1). Hydraulic conductance (g h ) is the inverse of hydraulic resistance (R h ), analogous to the flow of electrical current. If the conductance is constant (linear) the relationship is considered „ohmic‟, derived from “Ohm”, the measure of electrical resistance. (eq. 1) Volume flow through a tube, such as a blood vessel, is described by the Poiseuille equation (eq. 2) where the hydraulic conductance (g h ) describes the properties of the pathway and the flowing medium: 1) the diameter (d) and the length (L) of the tube, and 2) of the flowing medium. Thus, conductance depends on the geometry of the system and the nature of moving fluid. b) Bulk flow is mass transport carried by volume flow, (eq. 3) where is mass transport, is volume flow, and [x] is the concentration of solute x in
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2/13 solution. Examples are the flow of Na + and red blood cells in the blood stream, and particles carried by rivers, wind, ocean currents, or humans carried in mass transit systems (mostly North-South along the East and West Coasts of the US). c) Diffusion is the transport driven by a concentration difference (eq. 4) where is the rate of diffusion (flux = J), P is the permeability (akin to conductance) of the barrier separating two concentrations of solute x, and where ∆ [x] = [x] 1 - [x] 2 , the difference between the two concentrations. The permeability is further defined as (eq. 5) where D x is the diffusion coefficient of the diffusing solute x, A is the area available for diffusion, and L is the diffusion distance (thickness of the barrier). Permeability, like conductance, depends on the geometry of the system and the properties of the moving item. Examples abound: the diffusion of glucose from the lumen of capillaries to the cells , the diffusion of wastes (CO 2 or urea) from cells to the capillary lumen, as well as all diffusion across the cell membrane. Equation 4 describes pure diffusion, driven by the concentration difference alone, as in the case of the diffusion of molecules with no electrical charge: the so-called non- electrolytes such as glucose. The movement of electrolytes (Na + , K + , Cl - , Mg +2 , Ca +2 ) is, in addition, driven by voltage and is thus „electro-diffusion‟. The two forces,
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L01 Evolution 2011 - COPYRIGHT Mammalian Physiology BIOAP...

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