Physiology 1.05 Flow Down Gradients PDF

Physiology 1.05 Pre-learning and LECTURE Foundational Physiology - Flow Down Gradients BMS 100 Week 4 Overview Pre-learning: Modeling “flow down gradients” Parameters in the model Flow, gradients, resistances, conductances Types of flow, ty...

Physiology 1.05 Pre-learning and LECTURE Foundational Physiology - Flow Down Gradients BMS 100 Week 4 Overview Pre-learning: Modeling “flow down gradients” Parameters in the model Flow, gradients, resistances, conductances Types of flow, types of gradients: Fluid flow – Poiseuille’s law Diffusion – Fick’s law Basic “bioelectricity” – Ohm’s law Cases – get to know: Mary – diabetes Robert – heart failure Flow down gradients – overview Flow = movement of a substance from one point in a system (A) to another point in the system (B) ▪ Flow is measured by the amount of substance (volume, moles, charge) that moves over time (seconds, minutes) ▪ The driving force for the flow of a substance is the energy gradient between point A and point B ▪ The amount of flow is directly related to the size of the energy gradient between A and B ▪ The greater the gradient, the greater the flow Every system will have factors that resist this flow Flow down gradients – a model A B Why is this concept important? Life depends on the movement of substances from one point in the body to another Fluids and gases must constantly be moving from one point in the body to another ▪ Example – flow of gases and fluid through “large tubes” is determined by certain variables described by Pouiseille’s law ▪ Example – molecular flow of gases, water, and solutes can be driven by diffusion, by electrostatic interactions, or by pressure gradients described by Fick’s law, Ohm’s law, and others Pause and generate… List 5 specific processes in the body that you think depend on flow of a substance down a gradient (write them down) ▪ Example – blood moves from the heart to a large vessel ▪ ____________________________________________ ▪ ____________________________________________ ▪ ____________________________________________ ▪ ____________________________________________ ▪ ____________________________________________  Flow down gradients – movement of gases and liquids through a vessel Movement of a gas or liquid through a tube can be described with the following parameters in the model: ▪ Hydrostatic pressure causes gas or liquid to flow from point A to B ▪ Physical structures resist flow (resistance): the dimensions of the tube that the substance flows through ▪ Substance characteristics that impact flow: viscosity of the fluid ▪ The rate of flow is determined by Poiseuille’s law: 𝝅𝒓𝟒 F = (P1 – P2) · 𝟖𝝁𝒍 Poiseuille’s law - defined F = flow ▪ volume of liquid that passes through a tube per unit time (i.e. L/min) P = hydrostatic pressure ▪ the force that a substance 𝜋𝑟 4 exerts on the walls of its F = (P1 – P2) · container 8𝜇𝑙 r = radius of the tube that the fluid is moving through l = the length of the tube 𝝁 = the viscosity of the fluid ▪ Less viscous fluids are more “runny” (i.e. water) and more viscous fluids are more “syrupy” (i.e. …. syrup) Poiseuille’s law - defined F = flow 𝜋𝑟 4 ▪ volume of liquid that passes F = (P1 – P2) · through a tube per unit time 8𝜇𝑙 (i.e. L/min) P = hydrostatic pressure ▪ the force that a substance exerts on the walls of its Flow increases when container these increase r = radius of the tube that the fluid is moving through l = the length of the tube 𝝁 = the viscosity of the fluid ▪ Less viscous fluids are more Flow decreases when runny (i.e. water) and more these increase viscous fluids are more “syrupy” (i.e. …. syrup)  Poiseuille’s Law A B  Poiseuille’s Law A B Poiseuille’s law – take-home Therefore, flow of… ▪ Water through a garden hose ▪ Blood or lymph through its vessels ▪ Air through an airway … can be affected by the: ▪ difference in hydrostatic pressure between two points in the tube/vessel ▪ cross-sectional “size” of the tube/vessel (radius) ▪ distance between the two points in the tube/vessel (l) ▪ how viscous (“syrupy”) the flowing substance is Poiseuille’s law – take-home For the respiratory tract and the cardiovascular system, it is clinically relevant to think of flow of gas or blood to tissues (in terms of mL/min) The body controls flow through vessels by: ▪ Controlling the pressure in the large vessels ▪ Controlling the radius of the small vessels NOTE: the resistance is inversely related to the 4th power of the radius ▪ What happens to the resistance if the radius decreases by half? Poiseuille’s law – take-home Poiseuille’s law caveats: ▪ Accurate for rigid, simply-shaped tubes with non-turbulent fluid flow As tubes become more branched or irregularly-shaped, harder to quantify resistance If flow becomes turbulent, the resistance changes as well If a tube is flexible – like an artery – Poiseuille’s law also is not exact ▪ For all of the above variations, radius of the tube is still the most important determinant of resistance A simplified equation that includes a measured (not calculated) resistance can also describe flow: ∆𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒 Flow = 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 (a variant of Ohm’s law) Poiseuille’s law – take-home Poiseuille’s law caveats: ▪ As tubes become more branched or irregularly- shaped, harder to quantify resistance ▪ If flow becomes turbulent, the resistance changes as well ▪ If a tube is flexible – like an artery – Poiseuille’s law also is not exact ▪ Radius is most important determinant of resistance Flow down gradients - diffusion Diffusion in biology: ▪ Movement of a solute or a gas in a gas mixture from an area of high concentration to low concentration Usually this movement occurs across a barrier composed of a membrane(s) Simplified equation - Fick’s law - quantifies how the rate of diffusion is affected by various parameters: ▪ Flow = flux = amount of solute moving across a barrier per unit time ▪ Force driving flux → concentration gradient (C2 – C1) difference in concentration on either side of the membrane ▪ Resistances: Membrane surface area and membrane thickness Permeability of the membrane to the substance Flow down gradients - diffusion 𝑨(𝑪𝑨 −𝑪𝑩 ) Fick’s law: 𝑭 = 𝒌 ∙ 𝒕 Fick’s law - defined F = flow/flux ▪ number of molecules of a substance diffusing from point A to point B over time (𝐶𝐴 − 𝐶𝐵 ) = concentration gradient ▪ Difference in concentration on either side of the membrane 𝑨(𝑪𝑨 − 𝑪𝑩 ) A = surface area of the membrane 𝑭=𝒌 ∙ 𝒌 = a constant that increases 𝒕 when: ▪ The substance is a smaller molecule that dissolves better in the barrier ▪ The permeability of the barrier to the substance increases t = thickness of the membrane Fick’s law - defined F = flow/flux ▪ number of molecules of a 𝐴(𝐶𝐴 − 𝐶𝐵 ) substance diffusing from point A to point B over time 𝐹=𝑘 ∙ 𝑡 (𝐶𝐴 − 𝐶𝐵 ) = concentration gradient ▪ Difference in concentration on either side of the membrane A = surface area of the membrane 𝒌 = a constant that increases Flow increases when when: these increase ▪ The substance is a smaller molecule that dissolves better in the barrier ▪ The permeability of the barrier to the substance increases t = thickness of the membrane Flow decreases when this increases  Fick’s Law A B  Fick’s Law A B Fick’s law in the body A typical capillary Fick’s law in the body A typical capillary A B Fick’s law – take-home Therefore, flow/flux of… ▪ Solutes through capillaries ▪ Substances through cell membranes ▪ Oxygen and carbon dioxide from alveolus to blood … can be affected by the: ▪ Concentration difference ▪ Surface area available for the solute/gas to cross ▪ The permeability of the membrane ▪ Solubility and molecular size of the substance ▪ The distance between the two compartments Fick’s law – take-home Tissue/cellular structure has adapted to meet the constraints of Fick’s law: The thickness of the membrane/barrier to diffusion needs to be very small - flux is very slow over distances greater than 0.1 mm How have we adapted? Membranes have channels or transporters in order to increase permeability of the membrane The need for channels/transporters depends on the solubility of the substance in the membrane Fick’s law – take-home Tissue/cellular structure has adapted to meet the constraints of Fick’s law: Cells that are specialized for transporting large amounts of solute have: ▪ more transporters ▪ structural features that increase the surface area:volume ratio Our bodies manipulate concentration gradients all the time ▪ Metabolism ▪ Transporters that INCREASE gradients Fick’s law – take-home Fick’s law caveats: There are many “versions” of Fick’s law – the one discussed here is the easiest to apply to clinically-relevant situations ▪ it’s mathematically accurate for gases diffusing across fluid barriers, and “close enough” for other situations ▪ Saturation of protein transporters will reduce flux In most physiological situations diffusion happens so quickly that we don’t worry too much about the rate of flux ▪ Diffusion “failure” is a common theme in disease Flow down gradients – movement charged particles across a barrier Movement of a dissolved, charged particle – i.e. an ion – across a barrier – i.e. a membrane – depends on: ▪ The charge of the particle ▪ The difference in “concentration” of charges across the membrane – this gradient is known as voltage A type of potential energy → how much work it takes to move a charged particle through an electric field ▪ The permeability of the membrane to the charged particle The rate of flow of charges across a membrane is known as current (I) and is simply defined by Ohm’s law: 𝑉 𝐼= 𝑅 Ohm’s law - defined I = current ▪ the number of charges or charged particles that move across the membrane per unit time 𝑽 = voltage 𝑉 ▪ For our purposes, this is the 𝐼= energy generated by 𝑅 separating charges across the cell membrane R = resistance ▪ More channels for a charged particle → less resistance Ohm’s law - defined I = current ▪ the number of charges or 𝑉 charged particles that move 𝐼= across the membrane per unit 𝑅 time 𝑽 = voltage ▪ For our purposes, this is the Current increases energy generated by when this increases separating charges across the cell membrane R = resistance ▪ More channels for a charged Current decreases particle → less resistance when this increases  Ohm’s Law A B - + - + - - + + - + - + - - + - + + - + - - - + - + + - + - + - + - - + + + - +  Ohm’s Law A B - + - + - - + - - + - + + + - + + - - - + + - - + - - + - + - + + - + - + + - + Ohm’s law – take-home Opposites attract – like charges repel ▪ The particles move “down a gradient” of voltage according to their charge ▪ Electric field of the charged particle is responsible for establishing voltage ▪ Resistance is anything that impedes the movement of the particle 𝑉 𝐼= 𝑅 Ohm’s law – take-home In biology, Ohm’s law is most useful when thinking about + unequal distributions of + + - - - + charges very close on either + - side of a membrane + - + - ▪ Overall positive and + + - - - negative charges are - - + + balanced in all + - physiologic - + - + compartments + + - + ▪ The electric field declines - - + - very rapidly as charges - + are separated by distance + - Physiology Concepts II Flow Down Gradients - Cases BMS 100 Week 4 Case 1 Mary is a 64-year-old woman with a 17-year history of Type 2 diabetes mellitus controlled by metformin and diet. Today she presents with slowly progressive numbness and coldness in her feet. The right foot is worse than the left On investigation, you note: ▪ Mary’s right foot is cooler and more pale than her left foot ▪ Her posterior tibial pulse is weaker on her right than on her left, and the dorsalis pedis pulse on her right is not detectable ▪ The capillary refill time on the right great toe is 15 seconds, and on the left it is 3 seconds ▪ She cannot disintguish between sharp and dull stimuli over her right foot Case 1 Below are an arteriole and an elastic artery from a patient without vascular disease and one with type II diabetes Long-term DM | No vascular disease Small vessels (arterioles) Large vessels (elastic arteries) Case 1 – Questions to answer Clearly correlate Mary’s findings on history and physical exam to the known vascular changes that accompany diabetes mellitus ▪ Use the physico-chemical laws that were discussed in the pre-learning and the lecture How many of these laws are in play? How many are less important? ▪ Try to explain every clinical feature are there some clinical features that are less likely to be due to vascular changes? What would these be? Case 2 Robert is a 75-year-old gentleman with a long history of coronary artery disease and high blood pressure. He had been diagnosed with NYHA stage II heart failure 5 years ago. Today he presents because: ▪ his foot swelling has been getting worse – at the end of the day he has a great deal of difficulty putting on his shoes ▪ He has become more short of breath in the last few days On investigation you note: ▪ His blood pressure is 156/98 mm Hg – other vitals are within normal limits ▪ His feet are notably swollen, and this swelling continues part-way up the shin ▪ He is breathing quickly at rest – his respiratory rate is 25 breaths/min Heart failure – some basics Most patients with heart failure develop two general types of problems: Impaired “forward-flow” ▪ due to decreased cardiac output and worsening blood supply to important tissues like the brain, heart, kidneys ▪ The tissues with poor blood supply suffer impaired function “fluid backup” ▪ Blood is not moved from the veins at its usual rate, since the ventricles have a worsened cardiac output ▪ Blood “backs up” in the venous system Case 2 – Questions to answer What aspect(s) of Robert’s medical history best explain his foot swelling? How about his shortness of breath? How does these relate to the physicochemical laws discussed in the pre-learning and during the lecture? Physiology 1.05 Foundational Physiology - Flow Down Gradients BMS 100 Questions from prelearning? Poiseuille’s law Fick’s law Ohm’s law Combining forces There are many situations in physiology where more than one force acts on the same substance ▪ Filtration through a capillary → diffusion and hydrostatic pressure ▪ Distribution of ions across a membrane → diffusion and electrostatic forces Often these forces “pull” or “push” the same substance in opposite directions ▪ Which way will the substance move?  Starling forces The purpose of a capillary is to transport substances to and from tissues Water → ▪ Hydrostatic pressure ▪ Diffusion “Everything else” ▪ Diffusion ▪ Protein-mediated transport ▪ Endocytosis Starling forces - simplified [ "𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝐹𝑜𝑟𝑐𝑒𝑠" − "𝐷𝑖𝑓𝑓𝑢𝑠𝑖𝑜𝑛 𝐹𝑜𝑟𝑐𝑒𝑠" ] 𝐹𝑙𝑢𝑥 = "𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑜 𝐻2𝑂 𝑓𝑙𝑢𝑥" Starling forces - simplified 𝐅𝐥𝐮𝐱 = 𝐋𝐩 𝐏𝐜𝐚𝐩 − 𝐏𝐈𝐒𝐅 − 𝛔 𝛑𝐜𝐚𝐩 − 𝛑𝐈𝐒𝐅  Starling forces - simplified Variables: 𝐋𝐩 = the “leakiness” of the capillary wall to water ▪ The “inverse” of resistance 𝐏 = hydrostatic pressure 𝛑 = osmotic pressure “cap” = the fluid within the capillary “ISF” = the fluid within the interstitial space 𝛔 = how much protein leaks through the capillary wall 𝐅𝐥𝐮𝐱 = 𝐋𝐩 𝐏𝐜𝐚𝐩 − 𝐏𝐈𝐒𝐅 − 𝛔 𝛑𝐜𝐚𝐩 − 𝛑𝐈𝐒𝐅 Starling forces These forces are difficult to measure experimentally ▪ The value of the variables in different situations and in different locations is the subject of much debate Flux vs. Flow? ▪ Flux = flow along a defined membrane surface area Describes tissue swelling in a wide variety of situations ▪ Inflammation/infection ▪ Changes in pressure within the circulation Starling forces and the microcirculation  Nernst potential We know that: ▪ Charged particles can move across a membrane based on electrostatic forces Energy “powering” movement along the gradient? Resistance? ▪ Dissolved particles can move across a membrane based on their concentration gradient Energy “powering” movement along the gradient? Resistance? The Nernst equation tells us the balance… ▪ Does the particle move into or out of the cell, assuming it can cross the membrane?  Nernst potential The equation for the Nernst potential accounts for the following: ▪ Diffusional forces and electrical fields are very small at large distances Distribution of ions very close to either side of the membrane ▪ The charge of the particle ▪ The ratio of the particles’s concentration intracellular:extracellular It does not include the flow of ions (current) or the resistance of the membrane to flow… ▪ It gives the energy gradient Nernst potential (−60𝑚𝑉) 𝑃 𝑖 𝐸𝑃 = 𝑙𝑜𝑔10 𝑍𝑝 𝑃 𝑜 𝐸𝑃 = the membrane voltage at which a particle (P) moves into and out of the cell at the same rate ▪ → Equilibrium 𝑍𝑝 = the charge and valence of P (anions are negative) 𝑃 𝑖 = ratio of intracellular:extracellular concentrations of P 𝑃 𝑜 Describes the voltage across a membrane that is permeable to P given the ratio of [P] inside:outside Nernst potential (−60𝑚𝑉) 𝑃 𝑖 𝐸𝑃 = 𝑙𝑜𝑔10 𝑍𝑝 𝑃 𝑜 Nernst potential (−61𝑚𝑉) 𝑃 𝑖 𝐸𝑃 = 𝑙𝑜𝑔10 𝑍𝑝 𝑃 𝑜 10 Na+ 1 K+ 9 anion- Net charge +2 8 K+ 1 Na+ 11 anion- Net charge -2 Nernst potential Why is there an unequal distribution of sodium and potassium across the membrane? Why is there an unequal distribution of charge? 10 Na+ 1 K+ 9 anion- Net charge +2 8 K+ 1 Na+ 11 anion- Net charge -2  Nernst potential (−61𝑚𝑉) 𝑃 𝑖 𝐸𝑃 = 𝑙𝑜𝑔10 𝑍𝑝 𝑃 𝑜 12 Na+ 1 K+ 13 anion- Net charge 0 Na+ - 12 K+ 1 Na+ 13 anion- Net charge 0 Nernst potential Why is it helpful to understand Nernst potentials? Living cells always have a membrane potential ▪ Established by selective transporters and channels This charge and ion balance serves important functions: ▪ Cellular signaling ▪ Transport of substances ▪ Regulation of cell volume Medications and pathologies impact the membrane potential of many different types of cells Challenge A neuron relies on an inside-negative membrane potential for the purposes of signaling ▪ Action potentials ▪ Graded potentials The membrane potential is about -75 mV in many neurons ▪ However, the Nernst potential for potassium is close to -90 mV ▪ Why is the membrane potential of a neuron close to, but not the same, as the equilibrium (Nernst) potential for K+? Challenge Hints: ▪ Goldman Field equation predicts the membrane potential when it is permeable to more than one substance 𝑝𝐾 𝐾+ 𝑖 +𝑝𝑁𝑎+ 𝑁𝑎+ 𝑖 +𝑝𝐶𝑙 𝐶𝑙− V𝑚 = −61 × 𝑙𝑜𝑔10 𝑝𝐾 𝐾+ 𝑜+𝑝𝑁𝑎+ 𝑁𝑎+ 𝑜+𝑝𝐶𝑙 𝐶𝑙− 𝑜 𝑖 Basically the Nernst equation, but it relates the membrane potential to the relative permeability of the membrane to sodium, potassium, and chloride 𝑝𝐾 = membrane permeability to K+, 𝑝𝑁𝑎 = membrane permeability to Na+…