NPB 110B Notes 1 PDF

Lecture 2: Review 09/26/2024 Sources: Quantitative Physiology for Engineers (Feher) Medical Physiology (Boron and Boulpaep) Human Physiology (Widmaier, Raff and Strang) Human Physiology (Silverthorn) Topics Cell Organelles Cellular Membrane...

Lecture 2: Review 09/26/2024 Sources: Quantitative Physiology for Engineers (Feher) Medical Physiology (Boron and Boulpaep) Human Physiology (Widmaier, Raff and Strang) Human Physiology (Silverthorn) Topics Cell Organelles Cellular Membrane Diffusion Osmosis Tonicity Cells: Building Blocks of Biological Organisms Trillions of cells in the human body Cellular Organelles Lysosomes: digestive enzymes that break down various biomolecules Golgi Complex: processing and packaging proteins into vesicles Mitochondrion: energy (ATP) production Endoplasmic Reticulum (ER): protein and lipid synthesis and Ca+ storage Ribosomes: protein synthesis/creation from amino acids Nucleus: storage of genetic information Cytoskeleton: internal scaffolding/ skeleton of the cell used for transport Cytosol: fluid inside the cell Extracellular Fluid: fluid that surrounds the cells Functions of the Cellular Membrane All cells are surrounded by a cellular membrane that serves several important functions: Separates two aqueous compartments (cytoplasm inside the cell and the extracellular fluid outside the cell) Selectively permeable – some molecules able to pass through into or out of the cell, but others are unable to cross create charge difference Impermeable to charged molecules – separation of ions Potential difference across the membrane – act as capacitors - storage of charge Encapsulates the organs of the cell neurons want to have low capacitors (get the charge out) The Cellular Membrane is Composed of Phospholipids Phospholipids are amphipathic – molecules that have polar and nonpolar regions Phospholipids cluster in water with the polar/hydrophilic end at the surface and nonpolar region (tail) towards the interior Proteins are Embedded in the Cellular Membrane Proteins are large and usually charged molecules. Both make them difficult to diffuse through the cell membrane. Trans-membrane proteins serve as channels for charged ions and receptors for cellular communication. Proteins that leave the cell act as signals to other cells and provide materials for forming the extracellular matrix. Selective Permeability of the Cellular Membrane Size and charge affect the rate of diffusion across a membrane  Selective Permeability of the Cellular Membrane Transport across the membrane occurs through different mechanisms: 1. Diffusion/Facilitated Diffusion ex) glucose 2. Carrier-mediated Transport 3. Ion channels  Osmosis The movement of solvent (e.g. water) across a semipermeable membrane in response to a solute concentration gradient Usually there is an imbalance of total ion (solute) concentrations between the two sides of the membrane. Water is usually permeable through the membrane and will move from a region of lower to higher solute concentration, in order to equalize the solute concentrations on the two sides. As water moves from one side to another, there will be a change in the volume.  Tonicity - Describes a solution and how that solution affects cell volume Isotonic solution: osmotic balance, solute concentration is the same as the intercellular solution. No net movement of water Hypotonic solution: osmotic imbalance, solute concentration is lower than the intercellular solution. Water moves into the cell Hypertonic solution: osmotic imbalance, solute concentration is higher than the intercellular solution. Water moves out of the cell http://withfriendship.com/user/mithunss/tonicity.php Osmotic Pressure Osmotic pressure arises from unequal solute concentrations across a semipermeable membrane. This pressure is proportional to solute concentration and describes by van’t Hoff’s Law: 𝜋 Osmotic pressure 𝑅 Universal gas constant 𝜋 = 𝑅𝑇 𝐶 𝑇 Absolute temperature (Kelvins) 𝐶 Concentration of the solute The osmotic pressure difference ( ∆𝜋 ) depends on the net imbalance of solute concentrations across the membrane (∆𝐶). ∆𝜋 = 𝑅𝑇 ∆𝐶 The larger the concentration difference between two solutions, the larger the osmotic pressure difference driving water transport. Osmotic Pressure Another way to think about this is to add a reflection coefficient, 𝜎, that represents the relative permeability of the solute to water ∆𝜋 = 𝜎𝑅𝑇 ∆𝐶 higher Psolute -> smaller osmotic pressure 𝑃 Permeability of solute 𝑃 𝑃 Permeability of water 𝜎 =1− 𝑃 When 𝑃 ≅ 0 , 𝜎 ≅ 1 , which means the membrane reflects all solute molecules and does not allow them to pass, resulting in full osmotic pressure. Osmotic Pressure Recall that a mole is a weight measurement of a substance (Avogadro’s number of molecules, 6.02 x 1023). Each mole of an particle that contributes to osmosis is referred to as an osmole. 1 mole of glucose → osmoles? 1 osmole (glucose stays intact in solution) 1 mole of NaCl → osmoles? 2 osmoles (in solution NaCl dissociates into 1 mole of Na+ and 1 mole of Cl- ions, both of which are osmotically active) both contribute to the osmotic pressure Summary Cells are the building blocks of biological organisms. Cells are composed of organelles that serve distinct functions (energy production, transport, internal/external signaling). Cells are surrounded by a phospholipid membrane that separates the interior of the cell from its exterior. Cell membranes are permeable to water and its net movement into or out of the cell is called osmosis Tonicity describes water movement direction based on the concentration of solutes in the cell and the surrounding fluid. Osmotic pressure arises from unequal solute concentrations and is proportional to solute concentration.  Lecture 3: Ion Channels 09/30/2024 Sources: Quantitative Physiology for Engineers (Feher) Medical Physiology (Boron and Boulpaep) Human Physiology (Widmaier, Raff and Strang) Human Physiology (Silverthorn) Topics Charged Ions Active Transport of Ions Nicotinic Acetylcholine Receptor Determining the Structure of Receptors Sodium Potassium ATPase Chloride Exchangers Sodium Calcium Exchanger Passive Distribution of Ions Important Ions in Physiology differences in concentration gradients for ions differences in charge -> different equilibrium potentials because of the movement of ions (current) Name Symbol Charge Inside[C] Outside[C] Sodium Na+ 1 5-15 145 Potassium K+ 1 140 5 Chlorine Cl- -1 4 110 Calcium Ca2+ +2 1-2 x 10-4 2.5-5 [C] are in mM Cation are ions with a net positive charge. Anions are ions with a net negative charge. The charge on the ion is represented by the superscript sign following the symbol. For example, sodium (𝑁𝑎 ) has a charge of 1 and Calcium (𝐶𝑎 ) has a charge of 2. The Cellular Membrane is Selective Barrier to Ions Composed of phospholipids Membrane selectively allows passage of oxygen, nutrients, ions and waste to and from cell Contain trans-membrane proteins that serve a variety of functions: Receptors for signals Enzymes (facilitate chemical reactions) Transporters and Channels for molecules Lipophilic molecules can easily diffuse through membrane. Charged ions diffuse through channels or actively transported. Porter and Bonneville , Fine Structure of Cells and Tissues, 4th ed, 1973 Movement of Ions Through Channels three categories 7 depend on the gradient of the ion Channels can be selectively open at all times (leaky channels) Some channels are gated – open or close in response to specific triggers Ligand-gated: activated by the binding of a ligand like a neurotransmitter (Ach, GABA, glycine, etc.) Voltage-gated: activated by changes in membrane potential (e.g., Voltage gated 𝑁𝑎 and 𝐾 channels for action potentials. Voltage gated 𝐶𝑎 channels for neurotransmitter release). http://courses.washington.edu/psych333/ Two Categories of Ion Transport Ions in biological systems are not uniformly distributed (remember, for most cells the concentration of K+ inside is >> than outside the cell). Differences in concentration gradients across the cell membrane are achieved and maintained by active transport and passive distribution of ions and other charged molecules. Active transport and the ability to control passive permeabilities of ions underlie a wide range of physiological processes (the electrical excitability of neurons, absorption and secretory functions of the kidneys). Wide Range of Membrane Ion Channels and Transporters Active Transport of Ions Energy dependent movement of substances across the cellular membrane against their concentration gradient (from low to high). This creates concentration differences of various ions. Two types of active transport include: Primary (Direct) Energy to push ions against their concentration gradient comes directly from the breakdown of Adenosine-5'-triphosphate (ATP) Secondary (Indirect) Energy for transport of one ion comes from the potential energy stored in the concentration gradient of another ion. For example, using the energy of 𝑵𝒂 moving down its electrochemical gradient to transport other ions across the membrane.  don’t need to memorize the details nAChR: nicotinic acetylcholine receptor Historically, the best studied ion channel Found on postsynaptic membrane of neurons, muscle fibers and in the electric organ of the electric fish (Torpedo rays). Electric organ and muscle have four different subunits, 𝛼 , 𝛽 , 𝛾 and 𝛿. The nAChR from neurons has only 𝛼 and 𝛽 subunits. In a functional nAChR there are five subunits, 2 𝛼, and 3 non-𝛼 which form a cylinder around a central pore. ACh binds to the 𝜶 subunits. The cDNA for each subunit has been cloned, and the amino acid sequences have been determined. The four subunits are highly homologous and have very similar structures.  nAChR: nicotinic acetylcholine receptor Called nicotinic because nicotine is an agonist (a substance that mimics the effects of the endogenous neurotransmitter). Is an ionotropic neurotransmitter receptor— the receptor is itself an ion channel. When the neurotransmitter (Ach) binds to the receptor and activates it, the pore in the channel opens allowing cations to flow through. Another kind of AChR, the muscarinic AChR is a metabotropic receptor. The receptor is not a channel. When Ach binds it activates a second messenger cascade within the neuron that eventually results in the opening or closing of ion channels. don’t need to memorize all the details Determining the structure of nAChR Hydrophobic Hydrophilic Signal sequence Transmembrane regions Hydrophobicity plots of the amino acid sequence identifies membrane spanning regions of the molecule (each nAChR subunit has 4 membrane spanning regions. The amino terminus of the molecule is extracellular. It is preceded by a signal sequence, indicating that it is secreted from the cell. Two amino acids at the amino(N)-terminus of the molecule are associated with Ach binding to the subunit. Determining the structure of nAChR Site-directed mutagenesis: In order to determine which amino acids line the pore of the nAChR molecule, site-directed mutagenesis can alter particular amino acids in the molecule. The mutated molecule can then be expressed in Xenopus eggs to determine the effects of the mutation on channel function. Mutations in those amino acids would be expected to alter the receptors conductance or ion specificity. High-resolution imaging: Electron microscope imaging can resolve the channel topology to better than nm range, revealing many details of the structure.  Sodium potassium ATPase The sodium potassium ATPase (or sodium potassium exchange pump) transports 𝑵𝒂 out of the cell and 𝑲 back into the cell. out in - - No-Ki-A 3 2 I For every molecule of ATP hydrolyzed, three 𝑵𝒂 ions are transported out and two 𝑲 ions are transported in. Because of the unequal number of ions being transported into and out of the cell, the sodium potassium ATPase causes a small change in membrane potential. hyperpolarization (taking more positive charge out)  Chloride exchangers Intracellular chloride levels are kept low by two different chloride exchanger molecules. The 𝑵𝒂 driven 𝑪𝒍 bicarbonate secondary transport (neutral) exchanger moves 𝑪𝒍 out of the cell and 𝑯𝑪𝑶𝟑 into the cell. Exchange is driven by the movement of 𝑵𝒂 down its electrochemical gradient. The chloride bicarbonate exchanger helps to regulate 𝑝𝐻 as well as 𝐶𝑙 concentration in the cell. The 𝑲 , 𝑪𝒍 co-transporter moves 𝐶𝑙 out of the cell by using the energy of 𝐾 leaving the cell down its electrochemical gradient. 𝑪𝒂𝟐 regulation 𝐶𝑎 acts as a signaling molecule within a neuron. Transient increases in 𝐶𝑎 concentration are needed to release neurotransmitter at a presynaptic terminal, and as a second messenger in a number of processes. In order for 𝐶𝑎 signaling to work, intracellular 𝐶𝑎 levels must be kept low. Calcium ATPases in the cell membrane and in the membranes of intracellular organelles pump 𝐶𝑎 out of the cytoplasm.  Sodium calcium exchanger Sodium calcium exchanger moves one 𝑪𝒂𝟐 out of the cell against its electrochemical gradient for every three 𝑵𝒂 molecules that it moves into the cell down their electrochemical gradient. Uses the energy stored in the 𝑁𝑎 gradient, energy that must be replenished by the sodium potassium ATPase. The exchange is not electrically neutral: each forward cycle transfers one positive charge into the cell. sodium potassium ATPase creates the gradient -> the gradient moves other ions inside or outside of the cell  Sodium calcium exchanger Sodium calcium exchanger moves one 𝑪𝒂𝟐 out of the cell against its electrochemical gradient for every three 𝑵𝒂 molecules that it moves into the cell down their electrochemical gradient. The exchanger can run backwards (making 𝑁𝑎 leave the cell and 𝐶𝑎 enter the cell) under certain physiological conditions or by altering one or more of the ionic gradients involved in the exchanger. The direction of transport is determined by whether the energy provided by the entry of three 𝑁𝑎 is greater than or less than the energy required to extrude one 𝐶𝑎.  Passive Distribution of Ions Permeability dependent movement of substances across the cellular membrane. Types of passive transport include: Diffusion: movement based on concentration (high to low) Facilitated Diffusion: diffusion by gated channels Filtration: separation of solids from fluids Osmosis: movement of water based on concentration Ion concentration gradients can be maintained by selective permeability of the plasma membrane to various ions. Most cells at rest are permeable to 𝐾 but much less permeable to 𝑁𝑎 and 𝐶𝑎. Passive Distribution of Ions Permeability Determines how rapidly a solute can be transported through a membrane. It is represented in units of cm/sec (a velocity). Solute Permeability (cm/sec) Water 10-4-10-3 Urea 10-6 Glucose, Amino Acids 10-7 Cl- 10-11 Na+, K+ 10-13 When you multiply permeability by the solute concentration you determine the flux: the amount of solute that crosses a particular surface area in a unit of time. Summary Concentration gradients across the cell membrane are maintained by active transport and passive distribution. There are numerous ion channels and transporters. Active transport can be primary (directly use energy) or indirect (use potential energy from concentration gradients). Hydrophobicity plots, site-directed mutagenesis, and high resolution imaging are used to study ion channel structure. Important to remember the function of key ion channel examples: Nicotinic acetylcholine receptor (nAChR), sodium potassium ATPase, sodium calcium exchanger, chloride exchangers. Size and charge influence permeability—how rapidly a solute can be transported through a membrane  Lecture 4: Equilibrium potential I 10/01/2024 Sources: Quantitative Physiology for Engineers (Feher) Medical Physiology (Boron and Boulpaep) Human Physiology (Widmaier, Raff and Strang) Human Physiology (Silverthorn) Topics Ion Movement Ion Currents Membrane Potential Fick’s Law of Diffusion Ohm’s Law for Drift Nernst-Planck Equation Equilibrium Potential  Ion Channel Properties Ions Conducted: 𝑁𝑎 , 𝐾 , 𝐶𝑎 , 𝐶𝑙 Selectivity for ion type is determined by channel pore Ion permeation is passive (once channel is open). Not directly ATP-dependent ATP isn’t directly moving the ions Channels are not static. Ambient thermal energy opens and closes channel randomly High rate of ion flow: – Channels: ~108/sec – Enzymes: < 107/sec  Ion Channel Properties Ion Flow can saturate. Channels can be blocked by drugs and toxins (TTX, TEA, xylocaine, etc.) TTX (tetrodotoxin) which comes from the puffer fish, selectively blocks the voltage-gated 𝑁𝑎 channel. (Fugu, puffer fish) TEA (tetraethylammonium) selectively blocks the voltage-gated 𝐾 channel.  Ion Channel Properties Can allow ions to flow more easily in one direction than the other. When they do this they are called Rectifying Channel Rate of Ion Flow (the current, 𝐼) is Influenced by: – Channel conductance (𝐺), which depends on 1. Channel permeability, 𝑃, (intrinsic properties of the channel) Permeability Determines how rapidly a solute can be transported through a membrane. It is represented in units of cm/sec (a velocity). Solute Permeability (cm/sec) Water 10-4-10-3 Urea 10-6 Glucose, Amino Acids 10-7 Cl- 10-11 Na+, K+ 10-13 When you multiply permeability by the solute concentration you determine the flux: the amount of solute that crosses a particular surface area in a unit of time.  Ion Channel Properties Can allow ions to flow more easily in one direction than the other. When they do this they are called Rectifying Channel Rate of Ion Flow (the current, 𝐼) is Influenced by: – Channel conductance (𝐺), which depends on 1. Channel permeability, 𝑃, (intrinsic properties of the channel) 2. Amount of ion around the ion pore (related to the concentration gradient of the ion) 3. Voltage across membrane (𝑉 ) Movement of Ions Diffusion: Electricity: Concentration Gradient Electrical Gradient/Potential Voltage, Current, Resistance and Conductance (I) 𝑽 (Voltage): the “pressure” that moves electrons or ions through a circuit. Units: Volts 𝑰 (Current): is number of electrons or ions moving per unit time. Units: Amperes (𝐴) (1 coulomb/sec) 1 coulomb (𝐶) = 6.25 x 1018 charges 1 Faraday (𝐹) = 1 mole of charges = 96,500 coulomb (𝐶) These currents can be Negative (inward) currents and Positive (outward) currents depending on the charge of the ion and the direction of the flow (inside or outside the cell).  Ionic Currents: Sign Conventions depolarizing the cell (more positive) Negative Currents  Inward Currents A positively charged ion into the cell. Exit of a negatively charged ion from the cell. Eg: 𝑁𝑎 entering the cell = a negative current. hyperpolarizing the cell (more negative) Positive Currents  Outward Currents A negatively charged ion into the cell. Exit of a positively charged ion from the cell. Eg: 𝐾 leaving the cell = a positive current. https://wrhhs.org/chapter-2-membrane-excitability/  Ion Movement Movement of ions (current) through the membrane is influenced by both the concentration gradients inside and outside the cell and the membrane potential (electrical attraction and repulsion). An ion will move down its concentration gradient until it is opposed by the electrical gradient. These driving forces are described by Fick’s and Ohm’s Law Fick’s Law of Diffusion Diffusion takes place down the concentration gradient (high to low) Diffusion is directly proportional to the magnitude of the gradient, with proportionality constant 𝐷. 𝜕𝐶 𝐽 = −𝐷 𝜕𝑥 𝐽 Diffusion flux (moles/(cm2 s)) 𝐷 Diffusion coefficient (cm2/s) 𝜕𝐶 Concentration gradient (moles/cm3/cm) 𝜕𝑥 The negative sign indicates that 𝐽 flows from high to low concentration. Fick’s Law of Diffusion Rate of diffusion depends on five factors: Concentration gradient Permeability of the membrane Surface area of membrane Molecular weight of the solute light >> heavy Distance (thickness) of membrane thin >> thick Ohm’s Law for Drift Ions experience a force from the interaction of their electric charge and the electric field in the biological environment. The flow of ions in an electric field is described by: 𝜕𝑉 𝐽 Drift flux (moles/s cm2) 𝐽 = −𝜇𝑧 𝐶 𝜕𝑥 𝜇 Mobility (cm2/V s) ion’s ability to carry charge 𝑧 Ion charge 𝐶 Ion concentration (moles/cm3) 𝜕𝑉 Electric potential gradient (V/cm) 𝜕𝑥 The negative sign indicates that positively charged ions flow down the electric potential gradient directly proportional to the magnitude of the gradient, with proportionality constant µz[C]. Nernst-Planck Equation Ion flux across the membrane is influenced by both the electric field and concentration gradients. This is due to: (1) Different concentrations of ions inside and outside the cell (caused by active transport and passive distribution). Ions T will diffuse from high to low concentrations. plays a major role (2) The nonzero electric field within the membrane due to the separation of ions. A negative charge will move to an area with excess positive charge (and vice versa). Ion flux is thus the combination of diffusion and drift flux: 𝐽=𝐽 +𝐽 = −𝜇𝑧 𝐶 −𝐷 J = 0 -> nothing flows (no potential) Nernst Equation The current flow through the membrane is driven by electro- chemical potentials (concentration gradient and electric field) The membrane potential at which the net cross-membrane current is zero is described by the Nernst Equation: 𝑅 Gas constant no net flow 𝑇 Absolute Temperature 𝑅𝑇 𝐶 𝐸 = 𝑙𝑛 𝑧 Ion charge 𝑧𝐹 𝐶 𝐹 Faraday’s constant 𝐶 Ion concentration This relationship can be simplified ( treated as a constant): In -> log10 At T=20oC L At T=37oC 58 𝑚𝑉 𝐶 62 𝑚𝑉 𝐶 𝐸 = 𝑙𝑜𝑔 𝐸 = 𝑙𝑜𝑔 𝑧 𝐶 𝑧 𝐶  Equilibrium Potential When the net cross-membrane current is zero (membrane is at rest) the two forces that drive the current (the chemical gradient and electrical field) are equal and opposite in magnitude. The corresponding voltage is the Equilibrium Potential of the ion. Example for 𝐾 𝐾 = 4.5 𝑚𝑀 𝐾 = 155 𝑚𝑀 T=37oC 62 𝑚𝑉 𝐶 62 𝑚𝑉 4.5 𝐸= 𝑙𝑜𝑔 𝐸 = 𝑙𝑜𝑔 = −95 𝑚𝑣 𝑧 𝐶 1 155 The 𝐾 equilibrium potential (𝐸 ) is the electrical potential that counters the diffusion of 𝐾  Equilibrium Potential 58 𝑚𝑉 𝐶 𝐸 = 𝑙𝑜𝑔 𝑧 𝐶 Depends on a number of factors: 1. The charge on the ion (important for determining the electrical driving force) 𝑧 2. The concentrations of the ion inside and outside of the cell (important for determining the chemical driving force). 3. The temperature, which affects ion diffusion. 𝑇 Equilibrium Potential 58 𝑚𝑉 𝐶 𝐸 = 𝑙𝑜𝑔 𝑧 𝐶 58 𝑚𝑉 𝐸 = 𝑙𝑜𝑔 𝐶 − 𝑙𝑜𝑔 𝐶 𝑧 58 𝑚𝑉 58 𝑚𝑉 𝐸 = 𝑙𝑜𝑔 𝐶 − 𝑙𝑜𝑔 𝐶 𝑧 𝑧 Dependent Independent constant variable variable 𝑦 =𝑚 𝑥+𝑏 Note that the slope of the line is It is the equation of a line. 58 𝑚𝑉 for a 10-fold concentration difference Equilibrium Potential if the ion has a negative charge, can flip to concentration ratio (in/out) 58 𝑚𝑉 58 𝑚𝑉 𝐸 = 𝑙𝑜𝑔 𝐾 − 𝑙𝑜𝑔 𝐾 𝑧 𝑧 changes the concentration inside the cell -> the concentration outside the cell is also changed -> so the equilibrium potential is 0 𝐾 = 140 𝑚𝑀 ∆𝐾 = 100 to 10 ∆𝐸 = −8.48 − −66.48 = 58 𝑚𝑉 𝐾 = 180 𝑚𝑀 3 slope doesn’t change but equilibrium potential changes 𝐾 = 100 𝑚𝑀 10 mM 100 mM Summary Ion flux (or current) through the membrane is driven by electro-chemical potentials. Ionic currents can be negative (inward) and positive (outward) depending on the charge of the ion and the flow direction. An ion’s equilibrium potential across the cell membrane can be expressed in terms of the ratio of ion concentrations inside and outside the cell as defined by the Nernst Equation. The equilibrium potential is the voltage of the membrane at which the flux of the ion (current) will reverse direction. The Nernst equation can be considered a linear line equation with a slope of for every 10-fold concentration difference  Lecture 5: Equilibrium potential II 10/02/2024 Sources: Quantitative Physiology for Engineers (Feher) Medical Physiology (Boron and Boulpaep) Human Physiology (Widmaier, Raff and Strang) Human Physiology (Silverthorn) Topics IV Curves Patch Clamp Recording Rectifier Channels IV Curve: Current – Voltage Relationship. 𝐺= Conductance Notice that current changes with voltage, but conductance (the slope of the curve) is constant. This IV curve corresponds to a linear, non-rectifying, ohmic (all slope is constant synonyms) channel. IV Curve: Current – Voltage Relationship. 1 ohms law 𝑉=𝐼 𝑅=𝐼 𝐺 ∆𝐼 = 𝐺 ∆𝑉 Reversal Potential (𝐼 = 0) 𝐺= Conductance Reversal Potential: membrane potential at which the sign of the current changes. where it crosses the x-axis (one side goes to the positive and the other side goes to the negative) If the channel is permeable to a single ion, the reversal potential of that channel will be equal to the equilibrium potential of that ion. only if there is one ion going through Driving Force ∆𝐼 = 𝐺 ∆𝑉 𝐺= Conductance If we select one of the points to be the reversal potential, 𝑉 , then 𝐼 −𝐼 =𝐺 𝑉 −𝑉 If 𝑉 is the reversal potential then 𝐼 = 0. So the equation becomes: 𝐼 =𝐺 𝑉 −𝑉  Driving Force ∆𝐼 = 𝐺 ∆𝑉 𝐼 =𝐺 𝑉 −𝑉 𝐺= Conductance the further the distance between membrane potential and reversal potential, the greater the driving force is (greater I) Driving Force Since the second point could be any point, we can just call them 𝐼 and 𝑉 : 𝐼 = 𝐺 𝑉 − 𝑉 The difference between 𝑉 and 𝑉 is called the driving force: the motivation for the ions to move. If the driving force is zero, then 𝑉 = 𝑉 and the ions have no motivation to move. Driving Force ∆𝐼 = 𝐺 ∆𝑉 𝐼 =𝐺 𝑉 −𝑉 𝐺= Conductance Driving Force The current, 𝐼, will be zero only when: the Driving Force is zero (at Reversal Potential, 𝑉 ) the Conductance, 𝐺, is zero (the channel is closed) If the channel is only permeable to one ion this can also be written as ∆𝐼 = 𝐺 𝑉 − 𝐸 How do we know what an ion channel conducts? We can record from a channel, measuring the flow of ions (as a current). Currents through individual channels in a cell membrane can be measured using a technique called patch clamp recording. This technique records currents across a small patch of membrane attached to a glass pipette electrode. How do we know what an ion channel conducts? A narrow glass micropipette containing a salt solution may be pushed up against a cell, and then pulled back, capturing a fragment of membrane across the pipette tip. A voltage is imposed between an electrode inside the patch pipette and a reference electrode in contact with the surrounding salt solution. Current is carried by ions flowing through the membrane. a direct measurement of the ion going through How do we know what an ion channel conducts? open close If a membrane patch contains a single channel with 2 conformational states, the current will fluctuate between 2 levels as the channel opens and closes. The magnitude of the current through an open channel measures how rapidly ions are moving through that channel. This will depend on channel properties but also on the driving forces affecting the ion. Patch Clamp Recording When no potential is applied to the patch, no 𝐼 because there is no net flux of ions Application of 20 𝑚𝑉 to the electrode results in an outward current of 2 𝑝𝐴. Application of −20 𝑚𝑉 to the electrode results in an inward current of 2 𝑝𝐴.  Patch Clamp Recording Assume a hypothetical patch clamp experiment with 3 𝑚𝑀 𝐾 outside the cell and 90 𝑚𝑀 𝐾 inside the cell. As the voltage changes from −100 𝑚𝑉 to 25 𝑚𝑉 there is a change in the current flow through the channel.  Patch Clamp Recording K+ has a equilibrium potential of -75 mV (when the current is 0) With no potential applied the flux of 𝐾 along the concentration gradient produces an outward current. When 20 𝑚𝑉 is applied, the outward current increases driving force is greater When −50 𝑚𝑉 is applied, the outward current decreases driving force decreases When −100 𝑚𝑉 is applied, the current is now inward  IV curve of a rectifying channel This is an example of a rectifying ion channel. In this case the conductance and current through the channel changes with voltage. As the voltage decreases from 25 𝑚𝑉 to −100 𝑚𝑉 less current flows through the channel and the current direction reverses (from positive to negative). Types of Rectifying Channels Outwardly Rectifying Inwardly Rectifying A channel that is “outwardly- A channel that is "inwardly- rectifying" is one that passes rectifying" is one that passes current (positive charge) more current (positive charge) easily in the outward direction more easily in the inward (out of the cell) direction (into the cell)  Comparing IV curves Note that for non- rectifying channels, the slope is constant and can be calculated using the equation of a line. For rectifying channels, the slope is calculated at a specific voltage. To do this, one takes the tangent of the curve at that voltage and then estimates the slope of that tangent. This slope represents the conductance of the channel at that 𝑉. Chord vs. Slope Conductance In order to obtain the conductance of a channel, one must: 1. Record currents at several voltages. 2. Plot the points on an IV plot and try to fit them with a curve. 3. Take a tangent (again an estimation) at the voltage of interest for calculating conductance, 𝐺. 4. Determine the slope of the tangent. The procedure described above calculates what we call the slope conductance. A separate kind of conductance one can measure is called chord conductance and involves measuring the slope of the curve between two points as if it were a straight line (the reversal potential is one of the points). Chord and Slope Conductance at 𝑉 = −25 𝑚𝑉 The chord conductance (solid red line) at −25 𝑚𝑉 is 12 𝑝𝑆: 𝐼 0.6 𝑝𝐴 0.6 𝑝𝐴 𝐺= = = = 12 𝑝𝑆 𝑉−𝑉 −25 𝑚𝑉 − −75 𝑚𝑉 50 𝑚𝑉 The slope conductance (dashed red line) at −25 𝑚𝑉 is 3 𝑝𝑆. The conductance characteristics of a rectifying channel can only be precisely specified by the complete current voltage relationship. Summary The current voltage relationship (IV curve) for an ion channels is the change in current as a function of voltage. Patch clamping is a method that involves sealing the tip of a small glass pipette to the membrane of a cell to measure small currents. In this way the current voltage relationship for a channel can be determined for different voltages. In a non-rectifying ion channel the current through the channel changes in a linear manner with voltage. In a rectifying ion channel the conductance and current through the channel change with voltage (nonlinear relationship). Conductance of the channel can be estimated from the IV curve in at least two ways (slope and chord conductance).  Lecture 6: Resting membrane potential I 10/03/2024 Sources: Quantitative Physiology for Engineers (Feher) Medical Physiology (Boron and Boulpaep) Human Physiology (Widmaier, Raff and Strang) Human Physiology (Silverthorn) Topics Membrane Potential Ion Channels Flow of Ions due to Membrane Potential  Membrane Potential Is the voltage difference between the inside and outside of a cell (𝑉 −𝑉 ) and represented by 𝑉. Expressed/units in millivolts (𝑚𝑉) -85mV The result of charge separation by active and passive transport. All neurons have a resting membrane potential. resting membrane potential T There is a steady state electrical potential across the cell membrane that can range from −30 𝑚𝑉 to −100 𝑚𝑉 depending on the cell type.  Membrane Potential Changes to the membrane potential can be depolarizing (making the inside of the cell less negative) or hyperpolarizing (making the inside of the cell more -85mV negative). Movement of ions is controlled by the opening and closing of ion channels. Ions are charged particles that cannot pass through the hydrophobic lipid bilayer of the cell membrane.  Remember Ion channels… 1. Are transmembrane proteins with a central pore that is open to both the cell cytoplasm and the extracellular fluid. 2. Are gated and selective, only certain ions pass through. 3. Can change their conformation from open to closed or closed to open almost instantaneously. 4. Fluctuate around a mean open time specific to the channel. 5. When activated or deactivated by a stimulus (e.g., neurotransmitter binding, physical stimulation) the mean open time will increase or decrease. 6. Can be inactivated (if a voltage-sensitive channels) or desensitized (if sensitive to chemical signals) meaning that they cannot be opened. channel can be opened but is inactivated (has an extra gate) 7. Can be open but blocked, the channel pore is open but no ions can flow due to a molecule physically blocking the pore.  Resting membrane potential example A neuron at rest has a steady electrical potential across its membrane, with the inside of the cell being negative with respect to the outside. For a cell to remain in a steady state, a Extracellular Intracellular number of conditions need to be met: 1. Both the intracellular and extracellular Na+ 117 mM 30 mM solutions must be electrically neutral: K+ 3 mM 90 mM Outside the cell, the positive charges ( 𝐾 and 𝑁𝑎 ) are balanced by Cl- 120 mM 4 mM negative charges, 𝐶𝑙. A- 0 mM 116 mM Inside the cell, little 𝐶𝑙 to balance the positive charges, but high concentration of large organic anions (along with a small amount of 𝐶𝑙 ) balances the 𝑁𝑎 and 𝐾.  Resting membrane potential example A neuron at rest has a steady electrical potential across its membrane, with the inside of the cell being negative with respect to the outside. For a cell to remain in a steady state, a Extracellular Intracellular number of conditions need to be met: 2. The total concentrations of ions must Na+ 117 mM 30 mM be equal inside and outside to K+ 3 mM 90 mM maintain osmotic balance. More ions inside the cell will cause swelling. Cl- 120 mM 4 mM 3. There must be no net movement of A- 0 mM 116 mM any particular ion into/out of the cell. If there are no open channels the resting membrane potential (𝑉 ) is 0, because there is no charge separation across the membrane.  Resting membrane potential example In a real neuron at rest, many 𝑲 channels are open in the membrane. How will opening 𝐾 channels affect the 𝑉 ? Here, we are going to start with resting Extracellular Intracellular membrane potential, 𝑉 , at 0: 1. When we first open the 𝐾 channels, Na + 117 mM 30 mM will there be an electrical force on 𝐾 ? K + 3 mM 90 mM no (other channels aren’t opened -> no potential across the membrane) 2. Will there be a chemical force on Cl- 120 mM 4 mM 𝐾 ions? A- 0 mM 116 mM yes (the concentrations of K+ on each side of the membrane are different) 3. Which direction will 𝐾 ions move? outside (there is an outward current)  Resting membrane potential example In a real neuron at rest, many 𝑲 channels are open in the membrane. How will opening 𝐾 channels affect the 𝑉 ? Here, we are going to start with resting Extracellular Intracellular membrane potential, 𝑉 , at 0: 4. Will 𝐾 ions continue to move out of Na + 117 mM 30 mM the cell until there is an equal K + 3 mM 90 mM concentration of 𝐾 inside and outside? no (potential across the board membrane will be created after K+ ions move outside of the membrane, the electrical Cl- 120 mM 4 mM force will eventually be big enough to stop the flow of ions) A- 0 mM 116 mM  Resting membrane potential example In a real neuron at rest, many 𝑲 channels are open in the membrane. How will opening 𝐾 channels affect the 𝑉 ? Here, we are going to start with resting Extracellular Intracellular membrane potential, 𝑉 , at 0: 5. When will 𝐾 ions stop moving? Na+ 117 mM 30 mM when electrical force is equal to the concentration force Ex + = 16mV10910 = 8 mv K+ 3 mM 90 mM Cl- 120 mM 4 mM A- 0 mM 116 mM 6. If the cell membrane is permeable only to 𝐾 ions, what will be the resting membrane potential of the cell? the resting membrane potential of K+ (-85mV)  no need to memorize the details but pay attention to part 5 Changes in 𝑉 only require a few ions to move 1. The cell membrane is a capacitor, storing charge separated by the thickness of the membrane. The capacitance of a typical membrane is about 1𝜇𝐹/𝑐𝑚. 2. The charge, 𝑄, stored on a capacitor is the capacitance, 𝐶, times the voltage (𝑄 = 𝐶𝑉). For a resting 𝑉 of −85 𝑚𝑉, the charge stored is 10 85 10 = 8.5 3. This amount of charge is approximately equal to 5 10 (0.85 𝑝𝑚𝑜𝑙) ions per 𝑐𝑚. 4. If the neuron has a radius of 25𝜇 (and therefore a surface area of about 8 10 𝑐𝑚 ), this works out to 𝟒 𝟏𝟎𝟕 𝑲 ions having to leave the cell to produce a resting membrane potential of − 85𝑚𝑉. 5. This is only about 1/100,000 of the ions in the cell (0.001%), so 𝐾 movement has no measurable effect on the 𝐾 concentration. Resting 𝑉 is due to many different ions We can measure the 𝑉 of a cell using an electrode, and see whether changing the intra- and extra-cellular 𝐾 concentrations produces the changes in 𝑉 predicted by the Nernst equation. 1. When the intracellular and extracellular 𝐾 concen- trations are controlled by replacing the axoplasm with a solution of known 𝐾 concentration, the measured resting 𝑉 is always somewhat less negative than that predicted by the Nernst equation. Resting 𝑉 is due to many different ions We can measure the 𝑉 of a cell using an electrode, and see whether changing the intra- and extra-cellular 𝐾 concentrations produces the changes in 𝑉 predicted by the Nernst equation. 2. If the extracellular 𝐾 concentration is varied systematically, the Nernst equation should predict that changing the concentration by a factor of 10 should change the 𝑉 by 58 𝑚𝑉 at room temperature. 58 𝑚𝑉 𝐶 𝐸 = 𝑙𝑜𝑔 𝑧 𝐶 Resting 𝑉 is due to many different ions We can measure the 𝑉 of a cell using an electrode, and see whether changing the intra- and extra-cellular 𝐾 concentrations produces the changes in 𝑉 predicted by the Nernst equation. 3. This would result in a straight line of slope 58 𝑚𝑉 if one plots membrane potential against external 𝐾 concentration. 4. In fact, again, the membrane potential in this experiment is consistently more positive than the Nernst equation prediction.  Resting 𝑉 is due to many different ions What can explain the difference between the Nernst potential predictions and the actual membrane potential? What happens when we open 𝑁𝑎 channels when the 𝐾 channels are open. Extracellular Intracellular Remember, with only 𝐾 channels open, the membrane potential is at −85 𝑚𝑉: Na+ 117 mM 30 mM 1. When we first open the 𝑁𝑎 channels, K+ 3 mM 90 mM will there be an electrical force on 𝑁𝑎 ions? Cl- 120 mM 4 mM yes (Felectrical = zV = 85 mV into the cell) A- 0 mM 116 mM 2. Will there be a concentration force on 𝑁𝑎 ions? yes (Na+ ions go into the cell) Enc += Ibaul10gio' = 34 mu  Resting 𝑉 is due to many different ions What can explain the difference between the Nernst potential predictions and the actual membrane potential? What happens when we open 𝑁𝑎 channels when the 𝐾 channels are open. Extracellular Intracellular Remember, with only 𝐾 channels open, the membrane potential is at −85 𝑚𝑉: Na + 117 mM 30 mM 3. Which direction will sodium ions move? K + 3 mM 90 mM into the cell (negative current) 4. What will happen to the membrane Cl- 120 mM 4 mM A- 0 mM 116 mM potential? membrane potential is depolarizing 5. Now what will be the driving force on 𝐾 ions? K+ is no longer in equilibrium -> K+ ions start to leave the cell  Resting 𝑉 is due to many different ions What can explain the difference between the Nernst potential predictions and the actual membrane potential? What happens when we open 𝑁𝑎 channels when the 𝐾 channels are open. Extracellular Intracellular Remember, with only 𝐾 channels open, the membrane potential is at −85 𝑚𝑉: Na+ 117 mM 30 mM 6. When will the cell reach a constant K+ 3 mM 90 mM membrane potential? the influx of Na+ is exactly balanced by the efflux of K+ Cl- 120 mM 4 mM A- 0 mM 116 mM 7. The resting membrane potential of the neuron now will be somewhere between what two potentials? K+ and Na+ resting membrane potentials  Resting 𝑉 is due to many different ions In order to calculate where between those two numbers the resting 𝑉 will be, we need to know the conductances of the cell membrane for 𝑁𝑎 and 𝐾. Extracellular Intracellular If the conductance to 𝑁𝑎 is zero, what will the 𝑉 be? Na+ 117 mM 30 mM -85 mV K+ 3 mM 90 mM If the conductance to 𝐾 is zero, what will the 𝑉 be? Cl- 120 mM 4 mM 34 mV A- 0 mM 116 mM If the conductance to 𝑁𝑎 equals the conductance to 𝐾 , what will the 𝑉 be? 0 mV Van = quV10910 !8 = O mu  Resting 𝑉 is due to many different ions The membrane potential of a real neuron tends to be somewhere around −𝟕𝟎 𝒎𝑽, close to the 𝐸. This is because the cell at rest is much Extracellular Intracellular more permeable to 𝑲 than to 𝑁𝑎 (typically the 𝑁𝑎 conductance is 1 Na+ 117 mM 30 mM to 10% of the 𝐾 conductance). K+ 3 mM 90 mM 𝐶𝑙 channels are open in cells at rest. Intracellular 𝐶𝑙 concentrations are not Cl- 120 mM 4 mM well regulated, so 𝐶𝑙 ions move freely A- 0 mM 116 mM into/out of the cell until the 𝐶𝑙 concentrations are such that the 𝐸 is equal to the resting 𝑉. In some cells, however, 𝐶𝑙 is regulated by trans- porters, so it can also influence the 𝑉. Summary The membrane potential is result of charge separation of different ions (e.g., 𝑁𝑎 and 𝐾 ). The membrane potential is also the result of active and passive transport of these ions. Changes to the membrane potential can be depolarizing (making the inside of the cell less negative) or hyperpolarizing (making the inside of the cell more negative). Changes in membrane potential only require the movement of a few ions. In order to determine the resting membrane potential we need to know the conductance (or permeability) of the respective ions involved.  Lecture 7: Resting membrane potential II 10/07/2024 Sources: Quantitative Physiology for Engineers (Feher) Medical Physiology (Boron and Boulpaep) Human Physiology (Widmaier, Raff and Strang) Human Physiology (Silverthorn) Topics Goldman-Hodgkin-Kat (GHK) Equation Equivalent Circuit Representation Sodium calcium exchanger revisited Sodium Potassium ATPase revisited Goldman-Hodgkin-Kat (GHK) Equation In reality many charged molecules contribute to the overall electrical properties of the cell membrane. For a given concentration gradient, the greater the membrane permeability to an ion, the greater the contribution that ion will make to the membrane potential. The GHK equation is an expansion of the Nernst Equation that gives the resting membrane potential in terms of ion permeabilities and concentrations inside and outside the cell. 𝑃 𝐾 +𝑃 𝑁𝑎 +𝑃 𝐶𝑙 𝑉 = 58𝑚𝑉 𝑙𝑜𝑔 𝑃 𝐾 +𝑃 𝑁𝑎 +𝑃 𝐶𝑙 in the ln version can be treated as a constant, 58 mV at 20oC and 62 mV at 37oC Note that Cl- concentrations are reversed because Cl- is an anion and its movement has the opposite effect on membrane potential. Goldman-Hodgkin-Kat (GHK) Equation Takes into account the relative permeabilities of the main three ions contributing to the resting potential and also their concentrations to obtain a more accurate estimate. This model to describe ionic flow across the membrane makes several assumptions: Ion movement within the membrane obeys the Nernst Equation Ions move across the membrane independently (without interacting with each other) The electric field across the membrane is constant Thus this model falls short in describing membrane current when these assumptions are not valid. Equivalent Circuit Representation of a Membrane Biological membranes exhibit properties similar to electrical circuits: voltages (across the membrane and the equilibrium potentials), ion (current) flow and resistance, 𝑅, to this flow Conductance is the reciprocal of resistance: 𝐺 = Each ion carries a current that can be written as the product of the conductance to that ion and the difference between the membrane potential and the equilibrium potential. 𝑉 𝐼= =𝐺 𝑉=𝐺 𝑉 −𝐸 𝑅 Assuming independence, total current through the membrane is the sum of inward and outward currents. 𝐼 = 𝐼 + 𝐼 + 𝐼 + 𝐼 + ⋯+ 𝐼 Equivalent Circuit Representation of a Membrane Total current through the membrane is the sum of inward and outward currents 𝐼 =𝐼 +𝐼 +𝐼 +𝐼 +𝐼 Each ion current, 𝐼 , is the product of the conductance, 𝐺 , and the 𝐼 =𝐺 𝑉 −𝐸 difference between 𝑉 and 𝐸. 𝑑𝑉 𝐼 =𝐶 +𝐺 𝑉 −𝐸 +𝐺 𝑉 −𝐸 𝑑𝑡 +𝐺 𝑉 −𝐸 +𝐺 𝑉 −𝐸  Equivalent Circuit Representation of a Membrane At steady state: 𝐼 =0 𝐺 𝐸 +𝐺 𝐸 +𝐺 𝐸 +𝐺 𝐸 𝑉 = 𝑑𝑉 𝐺 +𝐺 +𝐺 +𝐺 =0 𝑑𝑡 This gives the resting membrane potential in terms of ionic L conductances and equilibrium potentials. can’t be a negative value Equivalent Circuit Representation of a Membrane The equilibrium potential resembles the electromotive force: the difference from the membrane potential will determine in which direction (into the cell or out) the ion will flow. The equilibrium potential is the reversal potential—voltage at which the direction of current reverses  Sodium calcium exchanger Sodium calcium exchanger moves one 𝑪𝒂𝟐 out of the cell against its electrochemical gradient for every three 𝑵𝒂 molecules that it moves into the cell down their electrochemical gradient. The exchanger can run backwards (making 𝑁𝑎 leave the cell and 𝐶𝑎 enter the cell) under certain physiological conditions or by altering one or more of the ionic gradients involved in the exchanger. The direction of transport is determined by whether the energy provided by the entry of three 𝑁𝑎 is greater than or less than the energy required to extrude one 𝐶𝑎.  Sodium calcium exchanger The energy released by 𝑁𝑎 moving into the cell depends on the driving force on 𝑁𝑎 ions: 𝐸 − 𝑉. The energy needed to move 𝐶𝑎 out of the cell depends on the driving force on the 𝐶𝑎 ion: 𝐸 − 𝑉 If 3 𝐸 − 𝑉 > 2 𝐸 − 𝑉 𝑁𝑎 ions move into the cell, while 𝐶𝑎 ions move out of the cells. If 3 𝐸 − 𝑉 < 2 𝐸 − 𝑉 , 𝑁𝑎 ions move out of the cell, while 𝐶𝑎 ions move into the cells.  Sodium calcium exchanger The energy released by 𝑁𝑎 moving into the cell depends on the driving force on 𝑁𝑎 ions: 𝐸 − 𝑉. The energy needed to move 𝐶𝑎 out of the cell depends on the driving force on the 𝐶𝑎 ion: 𝐸 − 𝑉 At some 𝑉 , the energy for moving three 𝑁𝑎 ions and the energy for moving one 𝐶𝑎 ion will be equal. If we call this the reversal potential (𝑉 ), then 3 𝐸 − 𝑉 = 2 𝐸 − 𝑉 or 𝑉 = 3 𝐸 − 2 𝐸 At membrane potentials, 𝑉 , more negative than the reversal potential, 𝑉 , 𝑁𝑎 moves in and 𝐶𝑎 moves out. At membrane potentials more positive, 𝐶𝑎 moves in and 𝑁𝑎 moves out.  Sodium potassium ATPase move ions against their concentration gradient The sodium potassium ATPase (or sodium potassium exchange pump) transports 𝑵𝒂 out of the cell and 𝑲 back into the cell. For every molecule of ATP hydrolyzed, three 𝑵𝒂 ions are transported out and two 𝑲 ions are transported in. Because of the unequal number of ions being transported into and out of the cell, the sodium potassium ATPase causes a small change in membrane potential.  Sodium potassium ATPase The sodium potassium ATPase (or sodium potassium exchange pump) transports 𝑵𝒂 out of the cell and 𝑲 back into the cell. With an active pump and assuming that all other permeating ions are in steady state, the GHK equation for 𝑉 becomes: 𝑟 𝑃 𝐾 +𝑃 𝑁𝑎 𝑉 = 58 𝑚𝑉 𝑙𝑜𝑔 𝑟 𝑃 𝐾 +𝑃 𝑁𝑎 The permeability of 𝐾 is modified (𝑟 𝑃 𝐾 ) to account for the action of the pump. The value of 𝑟 = 1.5 reflects this activity. Summary When the constant field assumption holds, membrane voltage can be described by ionic permeabilities and concentrations inside and outside the cell (the GHK equation). When the cell membrane is represented by an electrical circuit, membrane voltage can be described by ionic conductances and equilibrium potentials. The sodium calcium exchanger can run backwards depending on the membrane potential. This sodium potassium pump is electrogenic (provides a very small contribution to the cell’s resting membrane potential). This influence can be represented in the GHK equation.  Lecture 8: Action potential I 10/08/2024 Sources: Quantitative Physiology for Engineers (Feher) Medical Physiology (Boron and Boulpaep) Human Physiology (Widmaier, Raff and Strang) Human Physiology (Silverthorn) Topics Structure of the Neuron Voltage gated 𝑁𝑎 and 𝐾 Channels Ionic Basis of Action Potential Stages of the Action Potential Structure of the Neuron Cell Body/Soma: contains the nucleus and machinery for protein synthesis. Receives inputs from other neurons. Dendrites: highly branched outgrowths of the cell body. Also, receives inputs from other neurons. Axon/Nerve Fiber: process that extends from the cell body and carries output signal to target cells. Length varies (micron to over a meter). Axon Hillock: trigger zone where most electrical signals are generated. Myelin Sheath: concentric layers of cell membrane that enhance the speed of signal transmission. Nodes of Ranvier: space between adjacent sections of myelin. Exposed to extracellular fluid.  Diversity in Structure Neurons come in many different shapes and sizes depending on where they are in the nervous system and what their function is. Neurons can be classified by function into sensory neurons, motor neurons or interneurons. In general, however, they all have the same overall structure. Some properties of neurons 1. Neurons produce electrical potentials across their cell membranes. 2. Neurons can transmit electrical pulses quickly. 3. Neurons have freceptors which convert chemical messages to electrical. signals L 4. Neurons are differentiated cells; they are developmentally mature, and do not divide (non- mitotic) 5. Neurons are specialized for integration and transmission of information. 6. Neurons form circuits; neuronal circuits constitute the structural basis for brain function. Biological Electrical Signals Two basic types of electrical signals: Action Potentials A brief (ms scale) all-or-none depolarization of the membrane In a given neuron, does not vary in magnitude (identical) Conducted without decrement The principle way neurons communicate Allows rapid signaling over long distances efficient way to trace, Graded Potentials not an efficient way to transmit information Change in membrane potential whose magnitude is proportional to the stimulus intensity (vary in size) Decays with distance along the axon short distances to communicate Membrane Potential Changes doesn’t necessarily mean the membrane potential is posiive Depolarization Reduction in membrane potential Inside of cell becomes less negative Inside goes closer to zero and may move above zero to become positive could trigger action potential Membrane Potential Changes Hyperpolarization Increase in membrane potential Inside of cell becomes more negative Reduces the probability of generating action potentials  𝑁𝑎 and 𝐾 Channels Electrical signals are carried by separated 𝑁𝑎 , 𝐾 , 𝐶𝑙 , and 𝐶𝑎 ions. During an action potential 𝑁𝑎 and 𝐾 channels detect and reversibly change shape in response to changes in membrane potential (current flows during a narrow time window) 𝑁𝑎 Channel Inward current (𝑁𝑎 enters the cell) Membrane depolarization results in the channel opening Voltage-regulated and time-dependent gates Fast response 𝐾 Channel Outward current (𝐾 leaves the cell) Both opening and closing depends on membrane potential Slow response  Molecular mechanism of 𝑁𝑎 channel inactivation Voltage gated channel inactivation is caused by a special feature of the molecular structure of the channel, called the ball and chain. 1. When closed, the balls float freely. 2. When open, the balls are attracted to the open pore of the channel, and one will enter and block the pore. time dependent A number of experiments support this model. For example: When the balls are enzymatically removed (or by site directed mutagenesis), no inactivation of the channel occurs. If, after removing the balls, a synthetic peptide (i.e., the same amino acid sequence) is added, inactivation is restored.  Conductance of 𝑁𝑎 and 𝐾 Channels When an axonal membrane is depolarized more, more voltage gated 𝑁𝑎 and 𝐾 channels open. The conductance changes with membrane potential for the two channel types are very similar.  Conductance of 𝑁𝑎 and 𝐾 Channels The change in conductance with time is very different from the change with membrane potential for the two channel types: Voltage gated 𝑁𝑎 channels open immediately following depolarization, but then inactivate after less than a millisecond. Voltage gated 𝐾 channels, on the other hand, open after a delay, and do not inactivate.  Membrane Potential Changes Voltage-gated 𝑁𝑎 channel Voltage-gated 𝐾 channel has three states has two states 1) Deactivated: closed but capable of opening. 1) Deactivated: closed but capable of opening. 2) Activated: open 3) Inactivated: closed and not capable of opening. Inactivation is removed 2) Activated: open by repolarize-tion to ~ − 70 𝑚𝑉. See also: Smartsite/Resources/Animations/voltage_gated_ct.swf  Stages of the Action Potential 1. Resting membrane potential is near 𝐸 , 𝑃 > 𝑃 due to leaky 𝐾 channels. 𝐾 and 𝑁𝑎 voltage-gates are closed although 𝑁𝑎 time-dependent gate is open  Stages of the Action Potential 2. Membrane is brought to threshold voltage by depolarizing stimulus causing the 𝑁𝑎 voltage- dependent gate to open 3. 𝑁𝑎 flows through open time- dependent and voltage- dependent gates. Flow of 𝑁𝑎 into the cell rapidly depolarizes the membrane, causing more 𝑁𝑎 channels to open. 4. Closure of time-dependent 𝑁𝑎 gate and delayed opening of voltage-gated 𝐾 channels halts membrane depolarization.  Stages of the Action Potential 5. Open voltage-gated 𝐾 channels repolarize the membrane back to a negative membrane potential. 6. Slowly closing voltage-gated 𝐾 channels hyperpolarize membrane towards 𝐸 ; 𝑁𝑎 channels return to closed resting state (voltage-gate is closed, time- dependent gate is open). ready to start the next AP if needed 7. Closure of voltage-gated 𝐾 channels returns the membrane potential to its resting value.  Stages of the Action Potential The rising phase of the action potential is caused by the rapid opening of many 𝑁𝑎 channels, causing a large inward 𝑁𝑎 current, pushing the membrane potential towards the 𝑁𝑎 equilibrium potential. The peak of the action potential occurs near the peak of the 𝑁𝑎 current. At this time, some voltage gated 𝐾 channels are already open (as well as the non-voltage gated 𝐾 channels responsible for the resting membrane potential), so the peak approaches but does not reach the 𝑁𝑎 equilibrium potential.  Stages of the Action Potential The falling phase of the action potential is due to the rapid decrease of the 𝑁𝑎 current caused by 𝑁𝑎 channel inactivation, combined with the delayed increase in 𝐾 current. The undershoot is caused by the large outward 𝐾 current through the voltage gated 𝐾 channels, such that the conductance to 𝐾 is larger at this time than when the cell is at rest, forcing the membrane potential closer to the 𝐾 equilibrium potential. The Squid Giant Axon Invertebrate axons can be one million times larger in volume than our axons, which made them feasible to study in the 1930s. Action potentials were recorded in a squid giant axon bathed in normal sea water (similar to the squid extracellular fluid) and then in solutions containing lower concentrations of 𝑁𝑎. The Squid Giant Axon What will lowering external 𝑁𝑎 concentrations do to the driving force on sodium ions? the driving force becomes smaller If 𝑁𝑎 is in fact the ion responsible for the rising phase of the action potential, how will this affect the action potential? the peak of the action potential becomes smaller The Squid Giant Axon Sirs Alan Hodgkin and Andrew Huxley discovered the ionic basis Sir Alan Lloyd Hodgkin of the action potential, and won the Nobel Prize in 1963. Sir Andrew Fielding Huxley Activation of 𝑁𝑎 and 𝐾 voltage gated channels and the action potential Positive feedback: 𝑁𝑎 entry causes depolarization, which opens more voltage gated 𝑁𝑎 channels, which causes more depolarization. Negative feedback: voltage gated 𝐾 channels bring the action potential to an end and induce their own closing. Summary Neuronal structure and action potentials can vary depending on location and function. Action potentials (also called spikes) are all-or-none depolarization of the neuron membrane that involve fast acting 𝑁𝑎 channels and slower 𝐾 channels. Conductance of the 𝑁𝑎 and 𝐾 voltage gated channels is similar as a function of membrane potential, but different as a function of time. Voltage gated 𝑁𝑎 channels have three stages (ball and chain structure); voltage gated 𝐾 channels only have two stages. The generation of an action potential involves both positive and negative feedback mechanisms.  Lecture 9: Action potential II 10/09/2024 Sources: Quantitative Physiology for Engineers (Feher) Medical Physiology (Boron and Boulpaep) Human Physiology (Widmaier, Raff and Strang) Human Physiology (Silverthorn) Topics Absolute Refractory Period Relative Refractory Period Graded Potential Myelinated vs. Unmyelinated Axons Action potentials can vary across cell types Refractory Period During an action potential a second stimulus will not produce an action potential—the Refractory Period Limits the rate action potentials are generated and key in determining the direction of propagation- ensure only one direction. otherwise the signal will be complicated  Absolute Refractory Period It begins with the activation of voltage-gated 𝑁𝑎 channels. 𝑁𝑎 channels either open or inactive from first action potential. Ends when their inactivation is removed. Neuron incapable of generating another action potential no matter how strong the stimulus Ensures each action potential is separate and distinct  Relative Refractory Period A brief period after the absolute refractory period when repolarization is occurring It begins when 𝑁𝑎 channel inactivation is removed and ends when the voltage-gated 𝐾 channels deactivate. Threshold for action potential significantly elevated, a strong stimulus can reopen the 𝑁𝑎 gates and allow another action potential Refractory Period During the falling phase: Inactivation of the 𝑁𝑎 channel is maximal—few if any channels are available to increase 𝑁𝑎 conductance. 𝐾 conductance is very large During the relative refractory period a very large increase in the 𝑁𝑎 conductance is required to override the 𝐾 conductance and initiate a regenerative depolarization Action potentials can vary across cell types Duration of action potentials can range from as little as 200 microseconds to many milliseconds. Rate can vary from a few action potentials/second to frequencies near 1000/second. Differences are related to variations in the channel types underlying depolarization and repolarization. How would rapid repolarization influence the action potential frequency? increase the rate of action potential  Graded Potential Change in membrane potential (magnitude proportional to stimulus intensity) that decays (due to current leakage and internal resistance) along the cell. Occur in dendrites and cell body, occasionally near axon terminals. Can be a hyperpolarizing (inhibitory) or depolarizing (excitatory) stimulus.  Graded Potential Used for short-distance communication and to initiate action potentials (depolarization). They result from a brief injection of current, typically the result of synaptic transmission and the opening of ligand-gated ion channels. These are not the same as leak channels. They can also result from an experimenter injecting current using an electrode. Graded Potential Can vary in size and decrease over distance Graded Potential Can vary in size and decrease over distance Graded Potential vs. Action Potential ~ f Action potentials code stimulus intensity through changes in frequency. - Graded potentials code - ~ A stimulus intensity through W W changes in amplitude. 13 Graded Potential Leading to an Action Potential If a graded potential is strong, it will cause the cell to fire an action potential(s). Graded Potential vs. Action Potential Graded Potential Action Potential Type of Signal Input Signal Regenerating Conduction Signal Takes Place Dendrites, Cell Body Axon Trigger Zone Ion Channels Involved Mechanical, Chemical, Voltage-gated Channels Voltage-gated Ions Involved Na+, Cl-, Ca2+ Na+ and K+ Type of Signal Depolarizing or Hyperpolarizing Depolarizing Strength of Signal Stimulus Dependent, Can be All-or-None, Cannot be Summed Summed Initiator of Signal Entry of Ions Through Channel Above-Threshold Stimulus Unique Characteristics Summation, Stimulus Strength Threshold, Refractory Period Magnitude Graded (different amplitudes) Fixed amplitude Other Names PSPs (postsynaptic potentials), Spike or impulse EPPs (end-plate potentials), receptor potentials  Action Potential Propagation The action potential flows along the nerve axon Some current is passively lost through Myelin Sheath membrane. Two strategies to improve conduction properties: Axon 1) Increasing the diameter of the axon- decreasing the internal resistance 2) Myelination-increases electrical insulation around the axon Concentric wrappings of the membrane of glial cells Act as high resistance, low capacitance electrical insulators Allows rapid nerve impulse conduction - faster propagation than nonmyelinated fibers of the same axon diameter (10- 120 m/sec compared to 1 m/sec) Myelination brain doesn’t have myelination because the neurons are packed together (can’t have more graded potentials) cost: takes up some space A multilayered sheath of plasma membrane that wraps around axons and acts as an insulator. Thus, even though the axial path is high resistance due to the small axon diameter, current flows down the length of axon, not through the membrane. Signal Propagation Depending on the type of axon we will see two forms of action potential propagation: Direct conduction for unmyelinated axons signal travels down the axon Saltatory conduction for myelinated axons signals jumps from node to node (faster) Action Potential Propagation in Myelinated Axons The myelin sheath is interrupted at regular intervals, forming short uncovered regions called Nodes of Ranvier. Current appears to “jump” from node to node through Saltatory Conduction Myelin prevents current flow through the membrane Voltage gated 𝐾 and 𝑁𝑎 channels are located at the nodes Signal spreads from node to node (saltatory=jump) http://classes.midlandstech.edu/carterp/Courses/bio210/chap11/lecture1.html Action Potential Propagation Myelinated vs. Unmyelinated In unmyelinated axons, channels must open sequentially all the way down the axon membrane to maintain the amplitude of the action potential. Results in slow propagation Summary Due to the temporal dynamics of the ions channels there is a period following an action potential (the absolute and relative refractory periods) during which the probability of a subsequent action potential is greatly diminished. Differences in duration and rate of action potentials is due to variations in the voltage-dependent channel types. Myelination from glial cells, and increasing the diameter of axons both improve conduction of current along the nerve. Unlike action potentials, graded potentials are changes in membrane potential proportional to stimulus intensity. Saltatory conduction is the impulse propagation in myelinated axons between nodes of Ranvier. Lecture 10: Propagation of Electrical Signals 10/10/2024 Sources: Quantitative Physiology for Engineers (Feher) Medical Physiology (Boron and Boulpaep) Human Physiology (Widmaier, Raff and Strang) Human Physiology (Silverthorn) Topics Cable Parameters Cylinder Geometry Membrane Resistance Intracellular Resistance Length Constant Time Constant Benefits of Myelination 𝑟 𝜆= 𝜏=𝑟 𝑐 𝑟 A high membrane resistance, low membrane capacitance axon is ideal to propagate the signal. This would increase the length constant (decrease the loss of signal with distance) and decrease the time constant (increase the speed of impulse propagation). don’t lose current Current can not easily flow through the myelin sheath and the sheath does not easily store charge. Signal Propagation Active signal propagation propagation of action potential along axon involves opening of voltage-sensitive ion channels, resulting in changes in membrane conductance resulting ion currents actively regenerating signal Passive signal propagation does not involve any additional channels opening membrane conductance/permeability does not change electrical signal passively “flows” through cell Cable Parameters Parameter Units Definition/Relationship 𝑟 𝛺 𝑐𝑚 Membrane resistance (per unit length of axon) 𝑟 𝛺/𝑐𝑚 Intracellular resistance (per unit length of axon) 𝑐 𝜇𝐹/𝑐𝑚 Membrane capacitance (per unit length of axon) 𝑅 =𝑟 2 𝜋 𝑎 𝛺 𝑐𝑚 Specific membrane resistance (per unit area of membrane) 𝑅 =𝑟 𝜋 𝑎 𝛺 𝑐𝑚 Specific internal resistance (per unit cross-sectional area of axoplasm) 𝐶 =𝑐 / 2 𝜋 𝑎 𝜇𝐹/𝑐𝑚 Specific membrane capacitance (per unit area of membrane) Passive Properties of an Axon Current flow will be carried by the ions in the cell. The signal becomes smaller over distance because: The cytoplasm is a bad conductor (has a high axial resistance) The cell membrane together with the myelination layers are good, but not perfect insulators (there are channels that are open and allow for some of the current to “escape”) Passive Properties of an Axon The electrotonic potential, 𝑉, also decays exponentially with distance. 𝑉 is the maximum change in the membrane potential that is at the site of current injection. The decay of the membrane potential is represented by: 𝑉=𝑉 𝑒  Equivalent Circuit Model To understand the decay the axon is represented as a hollow cylindrical “cable” filled with axoplasm (i.e., an electrolyte solution). The electrical properties are represented in terms of axon length: 𝑟 , membrane resistance 𝑟 , intracellular resistance 𝑐 , membrane capacitance 𝑟 , external medium resistance (~0) Review of Surface Area of a Cylinder Surface Area= 𝜋 𝑑 𝐿 = 2 𝜋 𝑎 𝐿 Review of Cross-sectional Area of a Cylinder Cross-sectional Area= 𝜋 𝑎 𝐿  Voltage Decay 𝑟 The distance where the initial 𝜆= voltage, 𝑉 , response decays to 𝑟 1/e (or 37%) of its value. Length Constant The length constant is an index of how far depolarization can spread down a dendrite or axon. Just as water will flow farther down a wide hose with few leaks, current will flow farther down a wide axon/dendrite (low 𝑟 ) with few open membrane channels (high 𝑟 ).  Membrane Resistance, 𝑟 𝑟 𝜆= 𝑟 Length Constant The membrane resistance (𝒓𝑴 ) (𝜴 𝒄𝒎) Depends on the number of open (and conducting) channels in the membrane. The more channels, the lower the resistance. It corresponds to 1 𝑐𝑚 length To make it independent of geometry, we need to take into account the amount of membrane (i.e., surface area) for 𝐿 = 1𝑐𝑚 2 x pi x a x 1 cm 𝑅 𝑅 is the specific membrane resistance 𝑟 = 2 𝜋 𝑎 surface area  Intracellular Resistance, 𝑟 𝑟 𝜆= 𝑟 Length Constant The resistance to ion flow down the axon or dendrite (𝒓𝒊 , intracellular resistance) (𝜴/𝒄𝒎) Also called axial or internal longitudinal resistance Depends on the diameter of the fiber. The larger the diameter, the lower the 𝑟. To make it independent of geometry, we take into account the amount of cytoplasm (i.e., cross sectional area) for 𝐿 = 1𝑐𝑚 pi x a^2 x 1 cm 𝑅 𝑅 is the specific resistance of the cytoplasm 𝑟 = 𝜋 𝑎  The Length Constant, 𝜆 𝑟 The distance where the initial 𝜆= voltage, 𝑉 , response decays to 𝑟 1/e (or 37%) of its value. Length Constant 𝑉=𝑉 𝑒 When 𝑥 = 𝜆 𝑉=𝑉 𝑒 =𝑉 𝑒 𝑉 = 𝑒  The Length Constant, 𝜆 𝑟 The distance where the initial 𝜆= voltage, 𝑉 , response decays to 𝑟 1/e (or 37%) of its value. can’t travel far Length Constant The leakier axons have shorter lengths constants. 𝑟 𝑅 𝜋 𝑎 The more channels, the 𝜆= = 𝑟 2 𝜋 𝑎 𝑅 lower the 𝑟 Myelination increases the 𝑅 𝑎 𝑟 (this varies from cell to 𝜆= cell regardless of geometry) 2 𝑅 The Diameter of the axon: The larger the diameter, the lower the 𝑟  The Length Constant, 𝜆 neuron wants to have a large length constant 𝑟 The length constant is directly 𝜆= proportional to the square root of 𝑟 the axon radius, 𝑎. Length Constant The greater the specific membrane resistance, 𝑅 , the 𝑟 𝑅 𝜋 𝑎 greater the length constant and 𝜆= = 𝑟 2 𝜋 𝑎 𝑅 the less the loss of signal The greater the specific resistance 𝑅 𝑎 of the cytoplasm, 𝑅 , the smaller 𝜆= the length constant and the 2 𝑅 greater the loss of signal Membrane Capacitance, 𝑐 Because of its composition, the cell membrane keeps charge separated (allowing cells to be at ~ − 70𝑚𝑉) Acts as a capacitor. The closer the plates are together, the more charge they can store we don’t want capacitor to hold charge, we want the charge to pass along 𝐶 = capacitance 𝑄 𝐶= 𝑄 = charge 𝑉 𝑉 = voltage Equivalent Circuit Representation of a Membrane At steady state: 𝐼 =0 𝐺 𝐸 +𝐺 𝐸 +𝐺 𝐸 +𝐺 𝐸 𝑉 = 𝑑𝑉 𝐺 +𝐺 +𝐺 +𝐺 =0 𝑑𝑡 This gives the resting membrane potential in terms of ionic conductances and equilibrium potentials.  Membrane Time Constant, 𝜏 Membrane acts as a capacitor Channels act as Resistance 𝐼 =𝐼 +𝐼 Current likes to flow through the path with less resistance Current will first flow through the capacitor. As the capacitor gets charged, current will start to flow through the resistor Membrane Time Constant, 𝜏 Voltage changes instantaneously with the current input Voltage changes linearly in time with the current input capacitor still holds the charge Voltage changes exponentially in time with the current input some buildup of current but slowly goes away, then capacitor releases its stored charge  Membrane Time Constant, 𝜏 slow buildup of charge because capacitor is slowly taking some charge Capacitive Component Ionic Component Membrane Depolarization how long does it take to get to 63% of voltage - that we want (want it to be a small value) 𝜏=𝑟 𝑐 Membrane Time Constant, 𝜏 The membrane time constant, 𝜏, is defined as the time when the voltage response (𝑉) rises to 1 − or 63% of its 𝑉. It characterizes how fast current flow changes the membrane potential. It is the product of the membrane resistance, 𝑟 , and membrane capacitance, 𝑐. 𝜏=𝑟 𝑐 The shorter the time constant, the faster the speed of impulse propagation. we want it to be as small as possible Benefits of Myelination 𝑟 𝜆= 𝜏=𝑟 𝑐 𝑟 A high membrane resistance, low membrane capacitance axon is ideal to propagate the signal. This would increase the length constant (decrease the loss of signal with distance) and decrease the time constant (increase the speed of impulse propagation). Current can not easily flow through the myelin sheath and the sheath does not easily store charge. Summary The length constant, 𝜆, affects how far signals will be transmitted. we want it to be large The time constant, 𝜏, affects how fast signals can be transmitted, since the capacitance has to be charged. we want it to be small Leakier cells (with more open channels/density of channels) will have lower 𝑟 , which means smaller length constants which makes them bad conductors. Myelination increase membrane resistance and decreases membrane capacitance to maximize the conduction of action potentials.  Lecture 11: Transmitter Release 10/14/2024 Sources: Quantitative Physiology for Engineers (Feher) Medical Physiology (Boron and Boulpaep) Human Physiology (Widmaier, Raff and Strang) Human Physiology (Silverthorn) Topics Synapse Dendrites Depolarization Dependence 𝐶𝑎 Dependence Quantal Release Postsynaptic Potentials  Communication Between Neurons Synapse: where two neurons communicate. They are junctions between two neurons, or between a neuron and a muscle or gland that enables one cell to electrically and/or biochemically influence another cell. Each neuron forms ~1000 synaptic connections and receives anywhere between 5000-10000 inputs. Changes in synapses are believed to underlie learning Most synapses are between the axon of one AT: Axon Terminal neuron and the dendrite of another. These synapses are called axo-dendritic synapses. SP: Spine Although axo-dendritic synapses are the DS: Dendritic Shaft most common, axo-axonal, axo-somatic and dendrodendritc synapses also occur.  Communication Between Neurons Synapse: where two neurons communicate. They are junctions between two neurons, or between a neuron and a muscle or gland that enables one cell to electrically and/or biochemically influence another cell. Each neuron forms ~1000 synaptic connections and receives anywhere between 5000-10000 inputs. Changes in synapses are believed to underlie learning Most synapses are between the axon of one neuron and the dendrite of another. These synapses are called axo-dendritic synapses. Each red dot is a Although axo-dendritic synapses are the synapse onto most common, axo-axonal, axo-somatic and the neuron dendrodendritc synapses also occur. benefits of having different synapse locations: computational advantages (such as flexibility of where signals diverge or can be modified along the neuron if there are multiple sites of inputs) Synapses can take place at many locations  Cerebellar Purkinje Cell Dendrites provide an efficient way to pack in lots of inputs The cell body and the dendrites are the two main areas of the neuron to receive inputs. Cortical There is a characteristic shape Pyramidal Cell for each dendritic morphology which can be used for classification of neurons. Retinal Bipolar Cell Retinal Amacrine Cell Retinal Ganglion Cell  Dendritic spines Localized in Dendrites An important specialization of the dendrite is the presence of dendritic spines—small protrusions on dendritic shafts. Neurons that contain spines are sometimes called: “Spiny neurons” Spines are the site where excitatory synapses onto the dendrites take place. (inhibitory synapses tend to take place onto the “shaft” of dendrites) Spine remodelling is thought to be important for learning and memory Purpura DP, Science (1974) 186: 1126-8  Dendritic spines Spines are dynamic structures that can regulate synaptic transmission. Spines undergo pathological changes and have a reduced density in a Normal 6 month number of developmental, neurological old infant and psychiatric disorders such as chronic alcoholism, schizophrenia, and autism. 10-month old with Purpura DP, Science (1974) 186: 1126-8 mental disabilities Depolarization is Required for Transmitter Release how much the presynaptic cell is depolarized The amount of neurotransmitter released by a presynaptic terminal depends on the amount of depolarization The stellate ganglion of the squid was used to study the relationship between the membrane potential of the presynaptic terminals and the amount of transmitter release. The presynaptic depolarization and the postsynaptic response were simultaneously recorded. Depolarization is Required for Transmitter Release TTX blocks voltage-gated sodium channel The amount of neurotransmitter released by a presynaptic terminal depends on the amount of depolarization When tetrodotoxin (TTX) was added, the presynaptic action potential (red trace) gradually decreased. The amplitude of the postsynpatic action potential (blue trace) also decreased. TTX diminishes the action potential of the presynaptic cell blocks all the sodium channels -> no action potential but injects current to the cell so there is depolarization (still have postsynaptic response) Depolarization is Required for Transmitter Release When the presynaptic action potential is completely eliminated (TTX) depolarizations of known amplitude can be created by applying a brief current pulse to the presynaptic terminal. The amount of neurotransmitter released can then be indirectly measured by measuring the postsynaptic potential amplitude. Plotting the amplitude of the postsynaptic response as a function of artificial presynaptic depolarization (red circles) mimics the results from decreasing the presynaptic amplitude (blue circles).  𝐶𝑎 is Required for Transmitter Release Entry of 𝐶𝑎 into the nerve terminal is through voltage-gated 𝐶𝑎 channels. The 𝐶𝑎 dependence was examined by blocking the 𝐾 (TEA) and 𝑁𝑎 (TTX) action potential conductances (leaving only 𝐶𝑎 ). no action potential can be generated -> depolarize the cell with current (can control how much depolarization we see in presynaptic cell)  𝐶𝑎 is Required for Transmitter Release driving force of Ca2+ is high Depolarizing the presynaptic terminal to −18 𝑚𝑉 produced an inward 𝐶𝑎 current in the terminal and a large synaptic potential in the postsynaptic cell a large response in postsynaptic cell  𝐶𝑎 is Required for Transmitter Release no Ca2+ current because the driving force is around 0 mV Depolarizing the presynaptic terminal to 60 𝑚𝑉 (~ 𝐶𝑎 equilibrium potential) suppressed the 𝐶𝑎 and the synaptic potential in