# Excitable cells!  --- # Topics - Rationale - Resting membrane potential - Action potentials --- # Rationale Multicellular organisms need intercellular signalling Animals (cf. plants) need fast signalling Simple diffusion over long distances is slow --- # Diffusion time Diffusion is *really* slow over longer distances $$ t ≈ \frac{x^2}{2D} $$ <small>where $t$ is time, $x$ is mean distance travelled, and $D$ is the diffusion coefficient of the substance</small> e.g. for K⁺ - 4 nm (cell membrane width) takes 4 nanoseconds - 1 cm takes 7 hours --- # Resting membrane potential > The electrical potential difference across the membrane of a quiescent cell that is maintained when not conducting impulses across it. --- # Cell membrane  --- # Cell membrane Phospholipid bilayer Insulator with conducting material on either side Resting potential -70 mV inside to out: 1. Selective membrane permeability to ions due to channels - K⁺-selective ion channels *always* open, so 100 x more permeable to K⁺ than Na⁺ 2. Different ionic concentrations on either side of membrane ^ Former (selective permeability) is most important factor as it can change --- ## Establishing the RMP: the electrochemical gradient 1. K⁺-selective ion channels - Passive diffusion of K⁺ down its concentration gradient (150mM -> 5mM) out of the cell 1. Na⁺/K⁺–ATPase - 3 Na⁺ out, 2 K⁺ in - Net movement of positive charge out of the cell - Only directly contributes -4mV to the resting potential - However it establishes the chemical gradient of K⁺ and Na⁺ Na⁺ itself contributes little to the resting potential as the membrane is impermeable to it. ^ 20% of an animals cell energy expenditure --- # Nernst equation Calculates the potential difference that an ion would produce over a **permeable** membrane $$ E = \frac{RT}{zF} \ln \frac{[ion]\_{out}}{[ion]\_{in}} $$ Simplifies at 18ºC for **monovalent** ions to: $$ E = 58 \log \frac{[ion]\_{out}}{[ion]\_{in}} $$ <small>$E$ is the equilibrium potential for a specific ion, $R$ the gas constant (8.314 J.K^-1.mol^-1), $T$ the temperature (K), $F$ Faraday's constant (96,500 C.mol^-1), and $z$ the ionic valency (e.g. +1 for Na⁺)</small> --- | Ion | Intracellular (mM) | Extracellular (mM) | Nernst potential (mV) | | --- | --- | --- | --- | | K⁺ | 150 | 5 | -90 | | Cl^- | 10 | 125 | -70 | | Na⁺ | 15 | 150 | +60 | As the membrane potential lies at –70mV, it's clear that another factor other than simple chemical gradient is involved in determining the potential difference – and that is the permeability of the membrane. --- # Action potentials  --- # Action potentials Rapid membrane depolarisation – a transient reversal of membrane polarity "All or none" response Generated by voltage–gated Na⁺ channels (blocked by tetrodotoxin 🐡 and local anaesthetics) Threshold stimulus: ~15 mV Duration: 2–3 ms --- # Mechanism of action potentials 1. Stimulus depolarises membrane to theshold potential of –55 mV 2. Voltage–gated Na⁺ channels open 3. Na⁺ membrane permeability suddenly increases 4. This generates a *larger* potential difference than the stimulus (–70 to +50 mV ≈ 120mV) 5. Voltage–gated Na⁺ channels rapidly inactivate 6. Delayed action voltage–gated K⁺ channels open 7. Membrane potential becomes negative again as Na⁺ permeability falls and K⁺ permeability increases ---  --- # Features of action potentials Propogation is 2-stage: 1. **Passive spread** of depolarisation to the adjacent area of membrane via local currents 2. **Regeneration** through the action potential as the resultant potential difference is amplified back to full size --- # Features of action potentials Both **positive** and **negative** feedback loops are involved: - "All or none" effect is due to the positive feedback loop between membrane depolarisation and Na⁺ permeability - Delayed action voltage–gated K⁺ channels produce negative feedback, returning membrane to its resting potential Only a small number of ions flow during channel opening – the change in membrane permeability is the most significant effect on potential difference, not the number of ions flowing --- # Refractory period - Absolute refractory period: - Na⁺ channels are still open and cell is completely inexcitable - Relative refractory period: - 10–15 ms when a further action potential can only be triggered by greater than normal stimuli The refractory period ensures that the action potential can only spread in one direction. --- # Voltage–gated Na⁺ channel  --- # Voltage–gated Na⁺ channel 4 domains of 6 α–helices, with three states: 1. Closed (resting) 2. Open (action potential) 3. Inactivated (refractory) Depolarisation causes charged S4 domain to move outwards, opening pore Opens for 0.7ms before inactivation Tetrodotoxin block the mouth from the outside LAs (ester & amide) block the channel after diffusing through the membrane --- # Saltatory conduction Active conduction (action potential) has a slower velocity of propogation than passive conduction due to the latency between threshold potential and full size depolarisation Cell membranes behave as capacitors as they are thin and hold charge well Myelin increases the resistance and reduces the capacitance of the membrane, so action potentials can only occur at nodes of Ranvier Between the nodes, local currents cause depolarisation of the next node (passive = faster) Myelin conserves energy due to the reduced ion flux requiring less energy to restore resting ionic concentrations --- # Saltatory conduction  --- # Ventricular action potential Longer in duration than in nerves (250ms vs 3ms) Distinct plateau phase of maintained depolarisation allows sustained contraction of myocardium and is absolutely refractory to further stimulation, preventing tetany Lower resting membrane potential at –85 to –90 mV ---  --- # Ventricular action potential - **Phase 0:** Rapid depolarisation by the fast $i\_{Na}$ from Na⁺ channels transiently opening - **Phase 1:** Partial repolarisation – a rapid decrease in Na⁺ permeability - **Phase 2:** Plateau – slow Ca²⁺ channels open allowing inward flow of Ca²⁺, maintaining depolarisation and contraction <small>- Catecholamines increase activation of L-type Ca²⁺ channels, whilst Ca²⁺ channel antagonists (e.g. verapamil) reduce it</small> - **Phase 3:** Repolarisation – Na⁺, K⁺, and Ca²⁺ permeabilities return to normal - **Phase 4:** Resting – membrane potential governed mainly by potassium --- # Sinoatrial node No resting state: intrinsic pacemaker potential generates autorhythmicity Maximum polarisation of –55 mV during diastole No Phase 1 or 2 as no plateau phase ---  --- # Sinoatrial node - **Phase 4:** Spontaneous diastolic depolarisation shifts membrane to action potential threshold by $i\_f$ (slow influx of Ca²⁺) - **Phase 0:** Depolarisation by opening long-lasting voltage-gated Ca²⁺ channels and inward movement of Ca²⁺ ($i\_{CaL}$). - *No Na⁺ current involved at the SAN* - Low peak depolarisation of 20mV - **Phase 3:** Repolarisation: - Reduction in depolarising currents ($i\_f$ & $i\_{CaL}$ inactivated at positive potentials) - Increase in repolarising currents ($i\_K$ activated by positive potentials) causing late increase in K⁺ permeability <small>$i\_f$ (funny current) is a high background leak of Ca²⁺ through Na⁺ channels.</small> --- # Autonomic effects on SAN Parasympathetics increase K⁺ permeability in the SAN, hyperpolarising it and inhibiting spontaneous depolarisation. Sympathetics increase Ca²⁺ achieving the opposite effect. --- # Thank you [https://kenners.org/talks/excitable-cells](https://kenners.org/talks/excitable-cells)